**Modification of Surface Energy and Wetting of Textile Fibers**

Franco Ferrero and Monica Periolatto

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60812

#### **Abstract**

The modification of the surface energy of textile fibers to improve functional prop‐ erties such as the wettability was reviewed. This modification can be achieved by physical or chemical methods or by the combination of both. Applications of plas‐ ma treatment to improve the wettability of natural and synthetic fibers were consid‐ ered and some methods of wettability measurement were mentioned. Subsequently the methods aimed to confer water and oil repellency were discussed and the treat‐ ment by UV curing of fluorochemicals was explained in detail. Finally the sol-gel techniques useful to modify the surface properties of textiles were introduced and the results of water and oil repellency achievable by sol-gel were presented.

**Keywords:** Surface energy, Wetting, Textile fibers, Plasma, Contact angle, Water re‐ pellency, Oil repellency, Fluorochemicals, UV-curing, Sol-gel

#### **1. Introduction**

The modification of the surface energy of textile fibers is pursued with the aim of improving their own hydrophilicity, wettability, and dyeability or of conferring functional properties such as hydro and oil repellency, soil release, adhesion improvement, and antistatic perform‐ ances. If the modification is confined to a thin surface layer of the fibers, the bulk properties of a textile material, such as mechanical strength, flexibility, breathability, and softness, should not be compromised.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The wettability of a surface depends on the surface tension of the liquid that goes into contact with the same. Water has a very high surface tension (72.8 mN/m), so it tends to wet only surfaces bearing highly polar groups; otherwise, it forms spherical drops with contact angles higher than 90°. Instead, apolar liquids of lower surface tension get drops flatter than those of water. Hydrophobic or oleophobic surfaces are difficult to wet by water or apolar liquids, respective‐ ly, and are called low-energy surfaces. Wetting, in reality, is much more complex than as described by classical laws. This primarily comes from the non-ideality of solid substrates that are both rough and chemically heterogeneous [1]. Such a situation commonly occurs in the case of textile materials and can be evidenced by the hysteresis of the contact angle [2].

The surface modification of textile fibers can be achieved by physical or chemical methods or by the combination of both. Plasma treatments and exposure to radiations are mainly represen‐ tative of physical methods, although their effects are often accomplished in the presence of reactive gases or after impregnation with suitable chemicals. However, chemical treatments can generally be carried out with oxidants or other finishing agents, followed by thermal treatment. Among the latter methods, sol–gel techniques are the more promising for surface modification.

Among the textile fibers, there are many differences regarding wettability and surface struc‐ ture. Natural fibers have cellular structures that are more complex than those of man-made fibers obtained by chemical spinning. Wool and fine animal fibers are mainly composed of keratin, but show the structure of composite material formed by an assembly of cuticle cells in the form of scales and cortical cells surrounded by a keratin cell membrane and held together by an intercellular cement. The cell membrane consists of a chemically resistant protein layer and a lipidic layer that constitutes a hydrophobic barrier to the transfer of water and dye molecules from an aqueous solution [3]. Therefore, a wettability improvement of these fibers can be obtained by the removal of the hydrophobic lipidic layer and by the introduction of polar groups on the surface, both performed by chemical and/or physical means. A chemical treatment is usually made by chlorination, which modifies the scale edges of wool and increases the critical surface tension of the fibers. In such a manner, the chlorinated fibers are made more wettable and dyeable and can be coated with polymers, conferring the shrink-resist effect. However, many research works are carried out to find alternative processes that avoid chlorination in order to remove the problem of the formation of absorbable organohalogen compounds in wastewaters [4]. To this aim, plasma treatments have extensively been studied, but even other cheaper eco-friendly processes have been experimented, in particular for dyeability improve‐ ment, such as treatment with enzymes or ultraviolet (UV) irradiation. A list of selected references is reported in Table 1.

Cotton and cellulose fibers are more homogeneous than wool and are richer in hydroxyl groups ththat confer higher hydrophilicity; hence, their surface modifications are mainly directed to confer hydro and oil repellency. This topic will be treated in paragraphs 3 and 4. Moreover, the exhaust dyeing of cotton with anionic dyes, i.e., direct and reactive, request a high concentration of electrolytes in dyebath to reduce negative charges on the fiber surface and to promote the exhaustion of dyes. This requirement creates environmental issues due to the removal of high concentrations of salts and dyes from wastewaters. To overcome such


**Table 1.** Processes of wool surface modifications.

The wettability of a surface depends on the surface tension of the liquid that goes into contact with the same. Water has a very high surface tension (72.8 mN/m), so it tends to wet only surfaces bearing highly polar groups; otherwise, it forms spherical drops with contact angles higher than 90°. Instead, apolar liquids of lower surface tension get drops flatter than those of water. Hydrophobic or oleophobic surfaces are difficult to wet by water or apolar liquids, respective‐ ly, and are called low-energy surfaces. Wetting, in reality, is much more complex than as described by classical laws. This primarily comes from the non-ideality of solid substrates that are both rough and chemically heterogeneous [1]. Such a situation commonly occurs in the case

The surface modification of textile fibers can be achieved by physical or chemical methods or by the combination of both. Plasma treatments and exposure to radiations are mainly represen‐ tative of physical methods, although their effects are often accomplished in the presence of reactive gases or after impregnation with suitable chemicals. However, chemical treatments can generally be carried out with oxidants or other finishing agents, followed by thermal treatment. Among the latter methods, sol–gel techniques are the more promising for surface

Among the textile fibers, there are many differences regarding wettability and surface struc‐ ture. Natural fibers have cellular structures that are more complex than those of man-made fibers obtained by chemical spinning. Wool and fine animal fibers are mainly composed of keratin, but show the structure of composite material formed by an assembly of cuticle cells in the form of scales and cortical cells surrounded by a keratin cell membrane and held together by an intercellular cement. The cell membrane consists of a chemically resistant protein layer and a lipidic layer that constitutes a hydrophobic barrier to the transfer of water and dye molecules from an aqueous solution [3]. Therefore, a wettability improvement of these fibers can be obtained by the removal of the hydrophobic lipidic layer and by the introduction of polar groups on the surface, both performed by chemical and/or physical means. A chemical treatment is usually made by chlorination, which modifies the scale edges of wool and increases the critical surface tension of the fibers. In such a manner, the chlorinated fibers are made more wettable and dyeable and can be coated with polymers, conferring the shrink-resist effect. However, many research works are carried out to find alternative processes that avoid chlorination in order to remove the problem of the formation of absorbable organohalogen compounds in wastewaters [4]. To this aim, plasma treatments have extensively been studied, but even other cheaper eco-friendly processes have been experimented, in particular for dyeability improve‐ ment, such as treatment with enzymes or ultraviolet (UV) irradiation. A list of selected references

Cotton and cellulose fibers are more homogeneous than wool and are richer in hydroxyl groups ththat confer higher hydrophilicity; hence, their surface modifications are mainly directed to confer hydro and oil repellency. This topic will be treated in paragraphs 3 and 4. Moreover, the exhaust dyeing of cotton with anionic dyes, i.e., direct and reactive, request a high concentration of electrolytes in dyebath to reduce negative charges on the fiber surface and to promote the exhaustion of dyes. This requirement creates environmental issues due to the removal of high concentrations of salts and dyes from wastewaters. To overcome such

of textile materials and can be evidenced by the hysteresis of the contact angle [2].

modification.

140 Wetting and Wettability

is reported in Table 1.

problems, many treatments with plasma, chemicals, and polymers were experimented to impart a cationic character to the cotton fiber surface [27]. Chitosan, 2-amino-2-deoxy-(1 → 4) β-D-glucopyranan, derived from the deacetylation of the chitin component of the shells of crustaceans, is undoubtedly one of the more promising multifunctional polymers for surface modification of textiles [28]. It is a biopolymer with unique properties such as biodegradability, nontoxicity, and antimicrobial activity; hence, it was mainly applied to textiles as an antimi‐ crobial finishing agent. Moreover, cotton treated with chitosan shows improved absorption of anionic dyes due to electrostatic attraction arising from the cationized amino groups of chitosan in an acidic medium. However, chitosan should stably be bonded to the fiber surface to ensure the fastness of treatment to washing. To this aim, crosslinking agents such as dialdehydes are used, although these are toxic chemicals. On the contrary, an eco-friendly grafting of chitosan onto cotton can be carried out by radical UV curing in the presence of a low concentration of a photoinitiator [29, 30].

A list of selected references on the surface modification of cotton and cellulose fibers is reported in Table 2, whereas a recent review was published by Kalia et al. [31].


**Table 2.** Processes of surface modifications of cotton and cellulose fibers.

Synthetic fibers such as polyamide and polyester have a compact structure with a low content of polar groups, whereas polypropylene is lacking of them; these are substantially hydropho‐ bic and can be subjected to surface etching by plasma and oxidation to increase porosity and wettability, but the latter purpose is often pursued by grafting of polar monomers or applica‐ tion of hydrophilic coating.

In a similar manner, hydrophobicity and oleophobicity can be increased with a suitable coating obtained by plasma. A selection of articles published in the last 15 years is reported in Table 3.


APP: Atmospheric pressure plasma; LPP: low-pressure plasma; PA: polyamide; PET: polyethylene terephtalate; PP: polypropylene.

**Table 3.** Selected articles on the surface modification of synthetic fibers by plasma treatment.

#### **2. Wettability by plasma treatments**

chitosan in an acidic medium. However, chitosan should stably be bonded to the fiber surface to ensure the fastness of treatment to washing. To this aim, crosslinking agents such as dialdehydes are used, although these are toxic chemicals. On the contrary, an eco-friendly grafting of chitosan onto cotton can be carried out by radical UV curing in the presence of a

A list of selected references on the surface modification of cotton and cellulose fibers is reported

in Table 2, whereas a recent review was published by Kalia et al. [31].

**Process type Topic Reference** LPP, APP Penetration into textile structures Poll 2001 [32]

LPP Dyeability of fabrics Ozdogan 2002 [33]

LPP Repellent coating Allan 2002 [34]

APP Hydrophobic coating Kim 2006 [37]

LPP Dyeability of Tencel Mak 2006 [40]

APP Dyeability of fabrics by acid dyes Karahan 2008 [38]

LPP Hydrophilicity improvement Pandiyaraj 2008 [39]

Chitosan Crosslinking for antimicrobial cotton El-tahlawy 2005 [41]

Chitosan Crosslinking on UV-irradiated fibers Alonso 2009 [42] Chitosan UV curing for antimicrobial textiles Ferrero 2012 [29]

Chitosan UV curing for antimicrobial textiles Periolatto 2012 [30]

Chitosan UV curing for antimicrobial cotton Ferrero 2013 [43]

Synthetic fibers such as polyamide and polyester have a compact structure with a low content of polar groups, whereas polypropylene is lacking of them; these are substantially hydropho‐ bic and can be subjected to surface etching by plasma and oxidation to increase porosity and wettability, but the latter purpose is often pursued by grafting of polar monomers or applica‐

In a similar manner, hydrophobicity and oleophobicity can be increased with a suitable coating obtained by plasma. A selection of articles published in the last 15 years is reported in Table 3.

APP: atmospheric pressure plasma; LPP: low-pressure plasma.

tion of hydrophilic coating.

**Table 2.** Processes of surface modifications of cotton and cellulose fibers.

LPP Fluorination McCord 2003 [35]

APP Bleaching and dyeing Prabaharan 2005 [36]

low concentration of a photoinitiator [29, 30].

142 Wetting and Wettability

Plasma is commonly defined as an ionized gas in a neutral state with an equal density of positive and negative charges. It is often referred to as the "fourth state of matter," which can be reached in a wide range of temperatures and pressures. From a chemical point of view, plasma mostly consists of a mix of activated gaseous particles comprising free electrons, radicals, ions, UV radiations, and various highly excited neutral and charged species. It is considered to be a very interesting medium for material processing technologies, with particular regard to surface engineering. In fact, a large variety of treatments aimed at surface modification of different substrates can be carried out, including etching, cleaning, activation, and coating, as detailed below:

**•** *Etching*: the removal of the bulk substrate material, occurs when the interaction between the solid surface and plasma generates gaseous byproducts, including atoms or molecules, carried away from the surface substrate, removing minimal fractions of bulk material.


Plasmas can be classified by taking into account the employed generation technology (power supply and pressure range) into two major categories: thermal plasmas (very high tempera‐ ture, not suitable for heat-sensitive materials) and non-thermal plasmas (close to room temperature and suitable for treating textiles). Non-thermal plasmas are also known as lowtemperature plasmas and can be subdivided into many different technologies considering the electrical power supply, the operating pressure (low or atmospheric), and the geometrical arrangements.

The laws of plasma physics would make it easier to generate large-volume plasmas at reduced pressure rather than at atmospheric pressure. Moreover, in a closed system under low pressure, it is easier to control the characteristics and composition of the gas atmosphere from which the plasma is generated and, hence, the process chemistry rather than in a system at atmospheric pressure open to ambient air. Nevertheless, a closed system is not easily adaptable to a continuous process of fabric treatment. Therefore, although most of the plasma applica‐ tions on polymeric materials, including textiles, have been studied using low-pressure plasma (LPP), the atmospheric pressure plasma (APP) technique has demonstrated to be the most interesting tool for large-scale applications on textiles.

Plasma treatments are able to modify the fiber surface, leaving the bulk properties unaffected, and this characteristic is very important for the modification of textile fibers that should not lose their mechanical and chemical properties after treatment. Moreover, the finishing of textile fabrics by plasma technologies can advantageously replace some wet chemical applications as environmental friendly processes, since they do not require water and a high amount of chemicals. By controlling the plasma variables, such as the nature of gas, discharge power, pressure, and exposure time, a great variety of surface properties can be improved, mainly cleaning, wettability, hydrophobic and oleophobic properties, soil release, adhesion of coatings, dyeability, printability, and flame resistance.

An exhaustive book on the applications of plasma technologies to textiles was published by Shishoo [62], whereas the surface modifications by plasma treatments were reviewed by Radu et al. [63] and Morent et al. [64]. Reviews on atmospheric plasma treatments were published by Kale et al. [65] and, more recently, by Wolf [66]. In particular, the plasma pre-treatments to improve dyeability were considered by Deshmukh and Bhat [67], whereas Hossain and Hegemann studied the deposition of thin coatings on synthetic fibers to confer a substrate independent dyeability [68].

The modification induced by plasma treatment on a polymeric surface as a film is easily measured by contact angle determination with the sessile drop method. In the case of textile materials, instead, the measure is strongly affected by the heterogeneous surface structure; therefore, the porosity of the fabrics can often determine a suction effect on the water drop, preventing the contact angle determination. Another technique consists of weight variation measurement by a Wilhelmy balance during capillary wicking. The variety of techniques commonly used to measure contact angles has recently been highlighted by Yuan et al. [69].

Moreover, the hydrophilicity of plasma-treated fabrics can be tested according to the BS 4554:1970 method, known as the drop test, in which a drop of 100.0 µL of deionized water is placed on the surface of the specimen. The time required for the droplet to completely penetrate the fabric was measured by means of a stopwatch.

Poll et al. [32] measured the hydrophilization effect induced by plasma through the suction test. A capillary is filled with a colored test liquid and positioned onto the surface of the fabric layer to be checked. The liquid is absorbed by the fabric to form a colored circle. The diameter of the circle formed after an exposure time of 20 s is a measure of the hydrophilization effect.

Another wettability test can be performed on a fabric strip that is kept vertical, with the lower end immersed in water–dye liquor. A spontaneous wicking occurs due to capillary forces. The absorption height *h* is recorded as a function of time, and the absorption rate is calculated (capillary rise method, as shown in Figure 1; reprinted with the kind permission of the author in [70]).

**Figure 1.** Capillary rise method.

**•** *Cleaning*: the removal of contamination in the form of etching, but with very high selectivity. Only the unwanted surface contaminant is volatilized and removed, whereas the substrate

**•** *Activation*: the enhancement of the substrate energy, which generates chemically reactive

**•** *Coating*: the deposition of a functional thin film, occurs if the plasma–solid surface interac‐ tion creates a solid-phase material. This process is sometimes called plasma enhanced

Plasmas can be classified by taking into account the employed generation technology (power supply and pressure range) into two major categories: thermal plasmas (very high tempera‐ ture, not suitable for heat-sensitive materials) and non-thermal plasmas (close to room temperature and suitable for treating textiles). Non-thermal plasmas are also known as lowtemperature plasmas and can be subdivided into many different technologies considering the electrical power supply, the operating pressure (low or atmospheric), and the geometrical

The laws of plasma physics would make it easier to generate large-volume plasmas at reduced pressure rather than at atmospheric pressure. Moreover, in a closed system under low pressure, it is easier to control the characteristics and composition of the gas atmosphere from which the plasma is generated and, hence, the process chemistry rather than in a system at atmospheric pressure open to ambient air. Nevertheless, a closed system is not easily adaptable to a continuous process of fabric treatment. Therefore, although most of the plasma applica‐ tions on polymeric materials, including textiles, have been studied using low-pressure plasma (LPP), the atmospheric pressure plasma (APP) technique has demonstrated to be the most

Plasma treatments are able to modify the fiber surface, leaving the bulk properties unaffected, and this characteristic is very important for the modification of textile fibers that should not lose their mechanical and chemical properties after treatment. Moreover, the finishing of textile fabrics by plasma technologies can advantageously replace some wet chemical applications as environmental friendly processes, since they do not require water and a high amount of chemicals. By controlling the plasma variables, such as the nature of gas, discharge power, pressure, and exposure time, a great variety of surface properties can be improved, mainly cleaning, wettability, hydrophobic and oleophobic properties, soil release, adhesion of

An exhaustive book on the applications of plasma technologies to textiles was published by Shishoo [62], whereas the surface modifications by plasma treatments were reviewed by Radu et al. [63] and Morent et al. [64]. Reviews on atmospheric plasma treatments were published by Kale et al. [65] and, more recently, by Wolf [66]. In particular, the plasma pre-treatments to improve dyeability were considered by Deshmukh and Bhat [67], whereas Hossain and Hegemann studied the deposition of thin coatings on synthetic fibers to confer a substrate

remains unaffected by the process.

arrangements.

144 Wetting and Wettability

sites on a previously nonreactive surface.

chemical vapor deposition or plasma polymerization.

interesting tool for large-scale applications on textiles.

coatings, dyeability, printability, and flame resistance.

independent dyeability [68].

Ferrero [58] applied this method to the wettability measurements on plasma-treated synthetic fabrics (polyester and acrylic). The processing of capillary rise data proposed in this work allowed the assessment of wettability improvement by plasma treatment carried out in different gases (nitrogen, air, and oxygen). Wettability is strongly enhanced by plasma treatment, and after some time, the height reaches an equilibrium value *heq*, as shown, for example, in Figure 2, where the wicking curves of untreated and plasma-treated PETs are compared. It is evident that wettability is strongly improved by a mild nitrogen plasma treatment (25 W, 30 s, 65-Pa pressure in a Plasmod apparatus).

**Figure 2.** Comparison between the wicking curves of untreated and plasma-treated PET fabrics.

The maximum equilibrium height *h*eq can be related to the equilibrium static contact angle *θeq*, generally smaller than the dynamic one, by equation (1):

$$h\_{eq} = \frac{2\gamma\cos\theta\_{eq}}{\rho g R\_s} \tag{1}$$

where *γ* and *ρ* are the surface tension and density of the liquid, respectively, *RS* is the mean static radius of pores, and *g* is the gravity acceleration. In the early stages of the process, the hydrostatic pressure in equation (1) can be neglected; hence, *h* can be related to *θ*, advancing contact angle of the liquid on the solid, by Washburn's equation (2):

$$h^2 = \frac{r\chi\cos\theta}{2\eta}t\tag{2}$$

where *r* in fiber networks means an equivalent radius of the capillary porous structure, and *η* is the viscosity of the liquid.

Hence, *h2* values plotted against time show a straight line according to equation (3):

$$h^2 = D \cdot t \tag{3}$$

where the slope *D* is a capillary diffusion coefficient related to the size of the capillaries *r* and to the physicochemical characteristics of the liquid. Therefore, a surface treatment of a fabric that modifies *r* and the contact angle, such as plasma treatment, causes variation of this diffusion coefficient. It was observed that *D* is affected by the nature of the gas plasma, power, exposure time, and aging. On polyester fabric, nitrogen plasma induces higher wettability than air and oxygen, probably mainly due to surface etching, whereas the wettability of acrylic fabric slightly increases in air plasma with respect to nitrogen.

### **3. Water and oil repellency by UV curing**

different gases (nitrogen, air, and oxygen). Wettability is strongly enhanced by plasma treatment, and after some time, the height reaches an equilibrium value *heq*, as shown, for example, in Figure 2, where the wicking curves of untreated and plasma-treated PETs are compared. It is evident that wettability is strongly improved by a mild nitrogen plasma

treatment (25 W, 30 s, 65-Pa pressure in a Plasmod apparatus).

**Figure 2.** Comparison between the wicking curves of untreated and plasma-treated PET fabrics.

*eq*

*h*

contact angle of the liquid on the solid, by Washburn's equation (2):

fabric slightly increases in air plasma with respect to nitrogen.

generally smaller than the dynamic one, by equation (1):

is the viscosity of the liquid.

Hence, *h2*

146 Wetting and Wettability

The maximum equilibrium height *h*eq can be related to the equilibrium static contact angle *θeq*,

2 cos *eq*

*gR* g q

r

<sup>2</sup> cos 2 *<sup>r</sup> h t* g q

h

where *r* in fiber networks means an equivalent radius of the capillary porous structure, and *η*

values plotted against time show a straight line according to equation (3):

where the slope *D* is a capillary diffusion coefficient related to the size of the capillaries *r* and to the physicochemical characteristics of the liquid. Therefore, a surface treatment of a fabric that modifies *r* and the contact angle, such as plasma treatment, causes variation of this diffusion coefficient. It was observed that *D* is affected by the nature of the gas plasma, power, exposure time, and aging. On polyester fabric, nitrogen plasma induces higher wettability than air and oxygen, probably mainly due to surface etching, whereas the wettability of acrylic

*S*

where *γ* and *ρ* are the surface tension and density of the liquid, respectively, *RS* is the mean static radius of pores, and *g* is the gravity acceleration. In the early stages of the process, the hydrostatic pressure in equation (1) can be neglected; hence, *h* can be related to *θ*, advancing

<sup>=</sup> (1)

<sup>=</sup> (2)

<sup>2</sup> *h Dt* = × (3)

Cotton has always been the principal fiber for clothing fabrics due to its attractive character‐ istics such as softness, comfort, warmness, biodegradability, and low cost. However, the high concentration of hydroxyl groups on the cotton surface makes the fabric water absorbent and easily stained by liquids. Therefore, additional finishes are required to impart hydrophobicity and self-cleaning properties to cotton fabrics. The same finishes are applied to other fabrics, although based on less hydrophilic fibers such as wool, silk, polyamides, and polyester.

In general, water repellency of a fabric can be defined as the fabric's ability to withstand wetting or penetration by water under test conditions. It is important to distinguish between the terms "water repellent" and "waterproof". A fabric is made water repellent by the surface modifi‐ cation or deposition of hydrophobic material on the fibers. Water repellent fabrics have open pores and are permeable to air and water vapor. They are resistant to wetting by rain drops, water spreading, and wicking. Waterproofing involves filling the pores in the fabric with a material that is impermeable to water and, usually, to air as well. Water-repellent, but not waterproof, fabrics allow passage of water once the hydrostatic pressure is sufficiently high. Waterproof and water-repellent finishes are required, in particular, for cotton fabrics.

Polysiloxanes are widely used for textile finishing to impart desirable properties such as softness, crease resistance, and water repellency. However, the specific properties conferred by siloxanes depend on the nature of organic functional groups that are incorporated in the polymer structure [71]. Moreover, water and oil repellency is required for protective clothes and is currently achieved by thermal polymerization of fluorinated monomers, which enable a strong increase of water and oil contact angles on the treated fabrics [72]. However, the application of a polymeric coating to a cotton fabric in the form of a thin film ensures good homogeneity of the conferred properties, but the fabric could lose comfort characteristics, such as handling and breathability. Therefore, an alternative method that allows the uniform adsorption of monomers onto each fiber and the formation of polymer chains inside the fibers should be preferred, since the interpenetration of components and uniform distribution of monomers, even at a low concentration, contribute to obtaining textile materials with modified surface properties without a high add-on of polymer. This result can be achieved by a radiation curing method.

Radiation processes have several commercial applications for the coating of metals, plastics, and glass in printing, wood finishing, film and plastic crosslinking, and in adhesives and electrical insulations. The advantages of this technology are well known: energy savings (lowtemperature process), low environmental impact (no solvent emissions), simple, cheap, small equipment, and high treatment speed. Despite these advantages, there have been few appli‐ cations of radiation curing in the textile industry, such as nonwoven fabric bonding, fabric coating, pigment printing, silk grafting, and surface modification of cotton and synthetic fibers [73, 74]. In fact, in textile finishing processes, the conventional thermal curing technique is still used, regardless of energy consumption and cost. Among the textile finishing processes by radiation curing, pigment printing of fabrics has received much attention [75], whereas coatings for shrink-resistant wool, flame-retardant fabrics, and durable press finishes have also been investigated. Recently, studies on the effects of radiations on textile dyeing have been reviewed by Bhatti et al. [76], whereas the application of ultraviolet irradiation to wool dyeing processes has been experimented [24–26].

Water-repellent fabrics have been obtained by γ-radiation grafting of poly(vinyl methyl siloxane) or methyl hydrogen silicone on hydrophilic substrates. In industrial applications, UV light from a mercury vapor lamp is preferred for thin coatings because of its high efficiency of energy absorption and low equipment cost. In UV curing, radical or cationic species are generated by the interaction of UV light with a suitable photoinitiator, which quickly induces the curing reaction of reactive monomers and oligomers at low temperature, with lower environmental impact and lower process cost than the thermal process. If a monomer and photoinitiator mixture is adsorbed onto the fibers and subsequently UV cured, the polymeric chains can form inside the textile structure, which can be also involved in the formation of graft bonds, making the treatment solid and water resistant.

Ferrero et al. [77] proposed the water-repellent finishing of cotton fabrics by radical UV curing of silicone and urethane-acrylates with different formulations. The results of contact angle, wettability, and moisture adsorption showed that water repellency is already significant at a low resin add-on, whereas the treated fabric maintains its own breathability. SEM analysis confirmed that UV curing yields a coating layer onto each single fiber than a film on the fabric surface.

Polyester and nylon fabrics were made superhydrophobic by the UV curing of a polydime‐ thylsiloxane-containing polyurethane oligomer that was synthesized on purpose. The UVcurable system helps the super hydro-repellent polydimethylsiloxane moiety to anchor onto textile surface, improving the washing stability of the treatment [78].

Moreover, photografting as a surface modification method to provide permanent wettability and wicking performance to deep-groove polypropylene fibers was proposed by Zhu and Hirt [79]. In this case, polyacrylamide and polyacrylic acid were grafted on the fibers by UV irradiation; then, the advancing water contact angle on single fibers decreased from 100° to 55°, and spontaneous wicking of water was observed after surface modification.

On the other hand, a number of research papers have been published on the production and application of different types of fluorochemicals for textile finishing. Fluorochemicals are organic compounds consisting of perfluorinated carbon chains with more fluorine than hydrogens attached to carbon, having thermal and chemical stability. These chains, evenly distributed on the fiber with proper orientation, present an essentially fluorinated surface, which imparts water and oil repellency. In fact, the critical surface tension for fluorocarbon surfaces is in the range of 6 mN/m (-CF3) to 28 mN/m, whereas for bleached cotton, it is 44 mN/ m. One of the most successful ways of obtaining this condition is the incorporation of the fluorinated groups into polymer molecules in which perfluoro groups constitute the side chains [80]. The fluorochemicals used nowadays are based on C6 carbon chains, which have substituted the C8 fluorocarbons that release perfluorooctanesulfonate and perfluorooctanoic acid, higly hazardous and toxic substances. Selected articles regarding the surface modification of fibers achieved by fluorination are listed in Table 4.


**Table 4.** Selected articles on the surface modification of textile fibers by fluorination.

been investigated. Recently, studies on the effects of radiations on textile dyeing have been reviewed by Bhatti et al. [76], whereas the application of ultraviolet irradiation to wool dyeing

Water-repellent fabrics have been obtained by γ-radiation grafting of poly(vinyl methyl siloxane) or methyl hydrogen silicone on hydrophilic substrates. In industrial applications, UV light from a mercury vapor lamp is preferred for thin coatings because of its high efficiency of energy absorption and low equipment cost. In UV curing, radical or cationic species are generated by the interaction of UV light with a suitable photoinitiator, which quickly induces the curing reaction of reactive monomers and oligomers at low temperature, with lower environmental impact and lower process cost than the thermal process. If a monomer and photoinitiator mixture is adsorbed onto the fibers and subsequently UV cured, the polymeric chains can form inside the textile structure, which can be also involved in the formation of

Ferrero et al. [77] proposed the water-repellent finishing of cotton fabrics by radical UV curing of silicone and urethane-acrylates with different formulations. The results of contact angle, wettability, and moisture adsorption showed that water repellency is already significant at a low resin add-on, whereas the treated fabric maintains its own breathability. SEM analysis confirmed that UV curing yields a coating layer onto each single fiber than a film on the fabric

Polyester and nylon fabrics were made superhydrophobic by the UV curing of a polydime‐ thylsiloxane-containing polyurethane oligomer that was synthesized on purpose. The UVcurable system helps the super hydro-repellent polydimethylsiloxane moiety to anchor onto

Moreover, photografting as a surface modification method to provide permanent wettability and wicking performance to deep-groove polypropylene fibers was proposed by Zhu and Hirt [79]. In this case, polyacrylamide and polyacrylic acid were grafted on the fibers by UV irradiation; then, the advancing water contact angle on single fibers decreased from 100° to

On the other hand, a number of research papers have been published on the production and application of different types of fluorochemicals for textile finishing. Fluorochemicals are organic compounds consisting of perfluorinated carbon chains with more fluorine than hydrogens attached to carbon, having thermal and chemical stability. These chains, evenly distributed on the fiber with proper orientation, present an essentially fluorinated surface, which imparts water and oil repellency. In fact, the critical surface tension for fluorocarbon surfaces is in the range of 6 mN/m (-CF3) to 28 mN/m, whereas for bleached cotton, it is 44 mN/ m. One of the most successful ways of obtaining this condition is the incorporation of the fluorinated groups into polymer molecules in which perfluoro groups constitute the side chains [80]. The fluorochemicals used nowadays are based on C6 carbon chains, which have substituted the C8 fluorocarbons that release perfluorooctanesulfonate and perfluorooctanoic acid, higly hazardous and toxic substances. Selected articles regarding the surface modification

55°, and spontaneous wicking of water was observed after surface modification.

processes has been experimented [24–26].

surface.

148 Wetting and Wettability

graft bonds, making the treatment solid and water resistant.

textile surface, improving the washing stability of the treatment [78].

of fibers achieved by fluorination are listed in Table 4.

Fluorochemical finishings are commercially available as water emulsions and are applied to fabrics by the pad–dry–cure method, i.e., bath impregnation followed by squeezing, drying in air at 80–100 °C, and final curing at 150–175 °C in hot flue for some minutes. Fluorochemicals give water-repellent and soil-release finishes in conjunction with other water repellents, called extenders, which are able to yield fiber coatings with good resistance to washing. Castelvetro et al. [81] studied the performance of fluoropolymer latexes applied by padding to wool, cotton, and polyester fabrics. They evaluated the performances of the fabrics by means of technological standard test methods whose results correlated well with static and dynamic contact angle measurements.

Alternative fluorination methods have been proposed. Maity et al. [90] experimented the direct fluorination of cotton using elemental fluorine and admicellar polymerization, with a surfac‐ tant and fluoromonomer system. Selli et al. [91] used a SF6 plasma to confer water and oil repellency to cotton and PET, whereas plasma sputtering was used by Wi et al. to obtain a water-repellent PTFE coating on cotton fibers [92].

On the other hand, Ferrero et al. [88] extended the study of the UV-curing method to the use of perfluoro-alkyl-polyacrylate resins that are able to impart water as well as oil repellency to cotton fabrics, and the results obtained by UV curing were compared with those obtained by conventional thermal polymerization. This study was focused on the use of commercial finishes for thermal application, Repellan EPF and NFC, by Pulcra Chemicals, and Oleophobol CP-C, by Huntsman, supplied in water emulsions (about 17% solid content, dispersible in cold water in all ratios). Darocur 1173 (2-hydroxy-2-methyl-1-phenylpropan-1-one supplied by Ciba Specialty Chemicals) as a radical photoinitiator was added in an amount of 2% weight on the resin, enough to obtain a film by UV curing with each formulation considered. Water was added as a diluent to the mixtures, continuously stirred until complete homogeneity, in order to enable uniform spread of the liquids on cotton. The formulations were applied by dipping onto strips of fabric that were subsequently dried in an oven. The amount of resin put on the fabrics was adjusted according to the desired final weight add-on and the emulsion concentration. Weight percentages of 3% and 5% on the weight fiber were usually applied in order to obtain the desired properties without loss of fabric handling.

The surface-coated fabrics were exposed to UV radiation using a medium-pressure mercury lamp with a light irradiance on the fabric of about 20 mW/cm2 , in a small box equipped with a quartz window under nitrogen atmosphere, since oxygen interferes with the formation of radicals. The required radiation dose was obtained by adjusting the distance of the textile from the lamp and the exposure time, which was assessed between 40 and 60 s. Instead, thermal curing was carried out in 2–3 min at 140 °C or 150 °C according to the indications of the producer.

Resin emulsion is adsorbed by the fibers, so the polymerized product does not form films onto the fabric surface, but penetrate inside. To test if UV curing was effective even inside the fabric compared with the thermal treatment, the polymerization yield was evaluated by the deter‐ mination of the unpolymerized resin extracted by chloroform at room temperature from the cured fabrics. Repellan EPF shows the highest yields after UV curing and is about similar to those reached with the thermal treatment (93–96%), whereas Repellan NFC shows lower, although acceptable, yields in UV curing (80–81%) than in the thermal one (98%). With these finishes, the yields remained unaffected by exposure time and resin add-on. Oleophobol CP-C gives lower yields either in thermal or UV curing, with a marked dependence on add-on and exposure time; hence, 60 s is needed to obtain a good yield for a 3% add-on (91%).

The surface properties of coated and uncoated textiles were tested with optical measurements of static and dynamic contact angles of water and oil drops on the textile. The measuring liquids were HPLC grade water (72.8 mN/m at 25 °C) and olive oil (32.0 mN/m). The contact angle values should be higher, as the hydrophobic or oil repellency behavior of the textile is greater. On cotton samples finished with both curing methods, water and oil repellency fastness to domestic washing was evaluated after five washings according to UNI-EN ISO 105-C01.

In Figure 3, the results of dynamic contact angle measurements of water on cotton finished by Repellans before and after washing are compared. In this evaluation, the analysis of advancing and receding contact angles and the resulting difference, i.e. the hysteresis, can give informa‐ tion on the influence of surface roughness and chemical heterogeneity on fabric wettability [81]. A Δθ>0 is typical of most real surfaces, as confirmed by all the results obtained. With both resins, the advancing contact angles were slightly reduced after five washing cycles, and this proved the good wash fastness of water repellency, regardless of the curing type and polymer add-on. The hysteresis values generally decreased, indicating a lower surface heterogeneity, probably due to the washing effect. Oleophobol gave slightly lower contact angles but was practically unaffected by repeated washings.

water in all ratios). Darocur 1173 (2-hydroxy-2-methyl-1-phenylpropan-1-one supplied by Ciba Specialty Chemicals) as a radical photoinitiator was added in an amount of 2% weight on the resin, enough to obtain a film by UV curing with each formulation considered. Water was added as a diluent to the mixtures, continuously stirred until complete homogeneity, in order to enable uniform spread of the liquids on cotton. The formulations were applied by dipping onto strips of fabric that were subsequently dried in an oven. The amount of resin put on the fabrics was adjusted according to the desired final weight add-on and the emulsion concentration. Weight percentages of 3% and 5% on the weight fiber were usually applied in

The surface-coated fabrics were exposed to UV radiation using a medium-pressure mercury

a quartz window under nitrogen atmosphere, since oxygen interferes with the formation of radicals. The required radiation dose was obtained by adjusting the distance of the textile from the lamp and the exposure time, which was assessed between 40 and 60 s. Instead, thermal curing was carried out in 2–3 min at 140 °C or 150 °C according to the indications of the

Resin emulsion is adsorbed by the fibers, so the polymerized product does not form films onto the fabric surface, but penetrate inside. To test if UV curing was effective even inside the fabric compared with the thermal treatment, the polymerization yield was evaluated by the deter‐ mination of the unpolymerized resin extracted by chloroform at room temperature from the cured fabrics. Repellan EPF shows the highest yields after UV curing and is about similar to those reached with the thermal treatment (93–96%), whereas Repellan NFC shows lower, although acceptable, yields in UV curing (80–81%) than in the thermal one (98%). With these finishes, the yields remained unaffected by exposure time and resin add-on. Oleophobol CP-C gives lower yields either in thermal or UV curing, with a marked dependence on add-on and exposure time; hence, 60 s is needed to obtain a good yield for a 3% add-on (91%).

The surface properties of coated and uncoated textiles were tested with optical measurements of static and dynamic contact angles of water and oil drops on the textile. The measuring liquids were HPLC grade water (72.8 mN/m at 25 °C) and olive oil (32.0 mN/m). The contact angle values should be higher, as the hydrophobic or oil repellency behavior of the textile is greater. On cotton samples finished with both curing methods, water and oil repellency fastness to domestic washing was evaluated after five washings according to UNI-EN ISO 105-C01.

In Figure 3, the results of dynamic contact angle measurements of water on cotton finished by Repellans before and after washing are compared. In this evaluation, the analysis of advancing and receding contact angles and the resulting difference, i.e. the hysteresis, can give informa‐ tion on the influence of surface roughness and chemical heterogeneity on fabric wettability [81]. A Δθ>0 is typical of most real surfaces, as confirmed by all the results obtained. With both resins, the advancing contact angles were slightly reduced after five washing cycles, and this proved the good wash fastness of water repellency, regardless of the curing type and polymer add-on. The hysteresis values generally decreased, indicating a lower surface heterogeneity, probably due to the washing effect. Oleophobol gave slightly lower contact angles but was

, in a small box equipped with

order to obtain the desired properties without loss of fabric handling.

lamp with a light irradiance on the fabric of about 20 mW/cm2

practically unaffected by repeated washings.

producer.

150 Wetting and Wettability

**Figure 3.** Dynamic contact angles of water before and after washing on cotton fabrics finished with Repellan EPF and NFC (adv: advancing; rec: receding) [with kind permission from Springer Science+Business Media: Ferrero F., Periolat‐ to M., Udrescu C. Water- and oil-repellent coatings of perfluoro-polyacrylate resins on cotton fibers: UV curing in com‐ parison with thermal polymerization. Fibers and Polymers 2012; 13 (2), 191–198, p. 195, Fig. 1].

Static contact angles of oil before and after washing are compared in Figure 4, and the results confirmed the satisfactory wash fastness of oil repellency, in particular with Repellan NFC, without differences between the thermal and UV curing methods.

**Figure 4.** Static contact angles of oil before and after washing on cotton fabrics finished with Repellan EPF and NFC. [with kind permission from Springer Science+Business Media: Ferrero F., Periolatto M., Udrescu C. Water and oil-re‐ pellent coatings of perfluoro-polyacrylate resins on cotton fibers: UV curing in comparison with thermal polymeriza‐ tion. Fibers and Polymers 2012; 13(2), 191–198, p. 195, Fig. 2].

The contact angle value on untreated cotton, both with water and oil, was 0° due to the immediate absorption of the drops. It is evident of the high water and oil repellency conferred by the treatment. Measurements on 10 different points of the same sample surface are in good agreement (average values estimated with a confidence interval of ±2° at a 95% confidence level), showing a good uniformity of the coating. The results of thermal and UV curing are very close and poorly affected by weight gain and UV curing time, suggesting that a low polymer add-on is enough to modify the fiber surface.

With each finishing type, water contact angles are higher than with oil, in agreement with the results reported in the literature with other finishes on cotton [84, 94], although the values are lower than 150°, which is considered the lower limit for super hydrophobic surfaces showing the so-called Lotus effect. However, the UV-cured resins yielded oil contact angles mostly higher than 120°, denoting super oil-repellent surfaces.

X-ray photoelectron spectroscopy (XPS) analysis gives the chemical composition of the fabric surface and provides useful information on the fiber coating. Table 5 shows the relative peak intensities of C1s, O1s, F1s, and Cl2p in XPS measurements of untreated and finished cotton fabrics. For the untreated cotton, only two peaks corresponding to C and O are observed. F1s intensity was found to be about the same for samples that were thermally or UV cured, whereas Repellan NFC showed the lowest values.


**Table 5.** Relative intensities in the XPS spectra of untreated and resin-treated cotton fabrics (3% polymer add-on and 60-s UV curing time).

Information on how fluorine binds to the polymer surface can be obtained from the highresolution C1s signals. According to Selli et al. [91], the C1s spectrum was resolved into six components corresponding to the groups reported in Table 6 with the relative peak areas. For each resin, small differences arise from the comparison between thermal and UV curing, whereas higher differences can be observed between coatings of the different fluorocarbons. With Oleophobol CP-C, the coatings yielded the lowest percentage of the –CF2- groups and, conversely, the highest for the –CO- groups, although these differences did not affect water and oil repellency. However, in any case, a much lower concentration of the –CF3 groups was found. Such considerations suggest that the lower content of fluorine groups yielded by Repellan NFC coating is enough to confer the requested surface properties to cotton.

In conclusion, UV curing of cotton with commercial perfluoro-alkyl-polyacrylates applied in water emulsion yielded water- and oil-repellent cotton fabrics like the thermal process. The polymerization yields as well as the contact angles with water and oil were of the same order of those obtained with thermal curing, even at low-resin add-ons. Moreover, the UV-cured resins yielded mostly super oil-repellent surfaces, whereas water and oil repellency was adequately maintained after washing.


**Table 6.** High-resolution C1s spectra for resin-treated cotton fabrics (3% polymer add-on and 60-s UV curing time).

XPS analyses showed small differences between thermal and UV-cured coatings with each resin, whereas lower percentages of fluorine groups were observed in the case of Repellan NFC coatings without worsening of water and oil repellency, suggesting that such properties can be obtained with a low polymer add-on (3%) and with the lowest fluorine content.

Therefore, UV curing can be indicated as a valid alternative and environment-friendly method to confer water-resistant hydro and oil repellency to cotton fabrics. A comparison with plasma polymerization on cotton of the same perfluoro-alkyl-polyacrylates [93] confirmed that UV curing yields similar results, but with a simpler apparatus that can easily be introduced in the production lines of continuous fabric finishing.

#### **4. Water and oil repellency by sol–gel techniques**

very close and poorly affected by weight gain and UV curing time, suggesting that a low

With each finishing type, water contact angles are higher than with oil, in agreement with the results reported in the literature with other finishes on cotton [84, 94], although the values are lower than 150°, which is considered the lower limit for super hydrophobic surfaces showing the so-called Lotus effect. However, the UV-cured resins yielded oil contact angles mostly

X-ray photoelectron spectroscopy (XPS) analysis gives the chemical composition of the fabric surface and provides useful information on the fiber coating. Table 5 shows the relative peak intensities of C1s, O1s, F1s, and Cl2p in XPS measurements of untreated and finished cotton fabrics. For the untreated cotton, only two peaks corresponding to C and O are observed. F1s intensity was found to be about the same for samples that were thermally or UV cured, whereas

**Resin Curing C1s (%) O1s (%) F1s (%) Cl2p (%)**

UV 43.1 5.7 51.1 –

UV 46.0 8.7 43.5 1.7

UV 48.0 9.2 41.9 0.9

Untreated cotton – 60.6 39.4 – – Repellan EPF thermal 42.0 6.1 51.8 –

Repellan NFC thermal 44.7 10.7 43.3 1.3

Oleophobol CP-C thermal 46.4 7.7 44.7 1.3

**Table 5.** Relative intensities in the XPS spectra of untreated and resin-treated cotton fabrics (3% polymer add-on and

Information on how fluorine binds to the polymer surface can be obtained from the highresolution C1s signals. According to Selli et al. [91], the C1s spectrum was resolved into six components corresponding to the groups reported in Table 6 with the relative peak areas. For each resin, small differences arise from the comparison between thermal and UV curing, whereas higher differences can be observed between coatings of the different fluorocarbons. With Oleophobol CP-C, the coatings yielded the lowest percentage of the –CF2- groups and, conversely, the highest for the –CO- groups, although these differences did not affect water and oil repellency. However, in any case, a much lower concentration of the –CF3 groups was found. Such considerations suggest that the lower content of fluorine groups yielded by

Repellan NFC coating is enough to confer the requested surface properties to cotton.

In conclusion, UV curing of cotton with commercial perfluoro-alkyl-polyacrylates applied in water emulsion yielded water- and oil-repellent cotton fabrics like the thermal process. The polymerization yields as well as the contact angles with water and oil were of the same order of those obtained with thermal curing, even at low-resin add-ons. Moreover, the UV-cured resins yielded mostly super oil-repellent surfaces, whereas water and oil repellency was

polymer add-on is enough to modify the fiber surface.

higher than 120°, denoting super oil-repellent surfaces.

Repellan NFC showed the lowest values.

adequately maintained after washing.

60-s UV curing time).

152 Wetting and Wettability

There have been many articles in the literature on the improvement of hydrophobic properties of several kinds of fabrics using nanostructures achieved by nanotechnology. It was demon‐ strated that superhydrophobicity depends not only on surface chemistry but also on surface topology. Two theoretical models (Wenzel and Cassie–Baxter) have inspired how to engineer superhydrophobic surfaces by either roughening the same through microstructures or nanostructures or lowering the surface-free energy due to waxy materials applied on top of the rough structures, or both. An example is a microprocessing technique for producing rough surface and subsequent chemical treatment with silane- or fluorine-containing polymers to reduce the surface-free energy.

Roughened surfaces have commonly been obtained by the introduction of nano-size particles onto the pristine surface, and the sol–gel technique has been reported as a promising tool for the preparation of water-repellent coatings that is especially versatile for applications on glass, paper, and textile [95–100]. An exhaustive review on the application of sol–gel techniques to textiles has been published by Mahltig and Textor [101], and a series of selected articles is reported in Table 7.


**Table 7.** Selected articles on the surface modification of fabrics by sol–gel techniques.

In many research works, sol–gel formulations of fluoroalkylsilanes in combination with other silanes to obtain co-condensates are used. The solvents are mostly alcohols, but some waterbased systems have been described. In these nanocomposites, the organic and the inorganic networks are covalently bound and homogeneously intermingled at the nanometer scale so that the resulting coatings show enhanced mechanical stability [96].

These materials have a pronounced gradient structure, with a high concentration of fluoroalkyl groups at the coating–air interface so that only a small amount (1.7 mol%) of fluoroalkyl silane is necessary to obtain an effective repellency. Moreover, it accounts for an excellent adhesion of the coatings on various substrates such as glass, metals, and polymers. The gradient is due to the accumulation of surface-active fluorosilanol molecules and condensates at the interface.

Employing organically modified alkoxysilanes containing long-chained aliphatic or highly fluorinated groups, sol–gel offers far-reaching possibilities to prepare water- as well as oilrepellent textiles. A low required add-on is of great interest for textile applications; in fact, it keeps the typical hand and breathability of fabrics uncompromised. Furthermore, most fluorinated materials are very expensive and may often cause serious risks to the human health in case of skin contact and for the environment. Therefore, it is necessary to minimize the use of such substances.

**Fiber Topic Reference**

154 Wetting and Wettability

**Table 7.** Selected articles on the surface modification of fabrics by sol–gel techniques.

that the resulting coatings show enhanced mechanical stability [96].

In many research works, sol–gel formulations of fluoroalkylsilanes in combination with other silanes to obtain co-condensates are used. The solvents are mostly alcohols, but some waterbased systems have been described. In these nanocomposites, the organic and the inorganic networks are covalently bound and homogeneously intermingled at the nanometer scale so

These materials have a pronounced gradient structure, with a high concentration of fluoroalkyl groups at the coating–air interface so that only a small amount (1.7 mol%) of fluoroalkyl silane is necessary to obtain an effective repellency. Moreover, it accounts for an excellent adhesion of the coatings on various substrates such as glass, metals, and polymers. The gradient is due to the accumulation of surface-active fluorosilanol molecules and condensates at the interface.

Employing organically modified alkoxysilanes containing long-chained aliphatic or highly fluorinated groups, sol–gel offers far-reaching possibilities to prepare water- as well as oilrepellent textiles. A low required add-on is of great interest for textile applications; in fact, it keeps the typical hand and breathability of fabrics uncompromised. Furthermore, most

Nylon, PET/cotton Hydrorepellency Mahltig 2003 [102] Nylon Finishing of carpeting Satoh 2004 [103] Cotton Superhydrophobicity Daoud 2004 [104] Cotton Superhydrophobicity Yu 2007 [105] Wool, cotton, PET Superhydrophobicity Wang 2008 [106] Cotton Antimicrobial and repellency Tomšič 2008 [107] Cotton Superhydrophobicity Bae 2009 [108] Cotton Superhydrophobicity Erasmus 2009 [109] Cotton Durable hydrophobic finishing Roe 2009 [110] Cotton, PET Hydrorepellency Gao 2009 [111] PET, PET/cotton Hydrorepellency and antistaticity Textor 2010 [112] Cotton Superhydrophobicity Liu 2011 [113] Cotton Water and oil repellency, antimicrobial Simončič 2012 [114] Cotton Superhydrophobicity Shi 2012 [115] Cotton Superhydrophobicity and UV blocking Pan 2012 [116] Cotton Super hydro-oleophobicity, self-cleaning Vasiljević 2013 [117] Cotton Hydrorepellency Periolatto 2013 [118] Cotton Hydrorepellency and oil repellency Ferrero 2013 [119] Cotton, PET Hydrorepellency improved by plasma Montarsolo 2013 [120]

Periolatto et al. [118] obtained highly hydrophobic and oil-repellent cotton fabrics by a onestep deposition of a modified silica-based coatings by sol–gel prepared by co-hydrolysis and condensation in weakly acid medium of TEOS-based sols with low amounts of hydrophobic additives such as hexadecyltrimethoxysilane or fluorooctyltriethoxysilane. This work was further developed [119] with the aim of comparing the effect of the laboratory-grade fluori‐ nated reagent 1H,1H,2H,2H-Fluorooctyltriethoxy-silane (FOS) with that of a commercial product (Fluorolink S10). During the acid-catalyzed hydrolysis of TEOS or fluorinated alkoxysilanes, labile silanol groups are formed, which can first promote the silane adsorption onto the OH-rich cellulose structure of cotton fibers through hydrogen bonding. Successively, during the thermal curing step (120° for 1 h), the condensation reactions reported in Figure 5 can occur.

**Figure 5.** Grafting reactions of fluoromonomers on cotton [reprinted with permission from Elsevier: Ferrero F., Periolat‐ to M. Application of fluorinated compounds to cotton fabrics via sol–gel. Applied Surface Science 2013; 275, 201–207]

The procedure of preparation of the nanosols is illustrated in Figure 6.

The cotton samples were subjected to contact angle measurements by a Krüss DSA20E "Easydrop standard" drop shape analysis tensiometer using the sessile drop method for fitting. Measuring liquid drops were deposited from a glass syringe on the fabric's surface by means of software-controlled dosing. The contact angles were the average of at least five measurements for each sample, with a standard deviation of about 2–3%. The contact angles on untreated cotton were 0°C, whereas the drops are immediately absorbed. Moreover, the time necessary for the total absorption of both water and oil drops was measured. The results are summarized in Figure 7.

On samples finished with an impregnation time of 24 h, higher values of contact angles were measured (169°), denoting the importance of a deep penetration of the finishing agent inside the fibers.

A better behavior of Fluorolink-treated samples, with respect to the FOS-treated ones, was found: contact angles higher than 150 °C were measured, typical of super hydro- and oilrepellent surfaces. Absorption times higher than 2 h were measured with both water and oil drops, whereas on FOS-treated samples, the oil drop is absorbed in about 15 min, a good result but worse than Fluorolink's performance. This can be due to the molecular structure of Fluorolink, which is longer and more complex than FOS. The presence of TEOS seems to be ineffective.

**Figure 6.** Procedure of sol–gel preparation and its application to cotton fabrics to confer hydro and oil repellency.

The same measurements were made after five repeated washing cycles (at 40 °C for 30 min using 5-g/l ECE detergent according to ISO 105 C01 standard) to assess the durability of the treatments to laundering. The results are summarized in Figure 8.

fitting. Measuring liquid drops were deposited from a glass syringe on the fabric's surface by means of software-controlled dosing. The contact angles were the average of at least five measurements for each sample, with a standard deviation of about 2–3%. The contact angles on untreated cotton were 0°C, whereas the drops are immediately absorbed. Moreover, the time necessary for the total absorption of both water and oil drops was measured. The results

On samples finished with an impregnation time of 24 h, higher values of contact angles were measured (169°), denoting the importance of a deep penetration of the finishing agent inside

A better behavior of Fluorolink-treated samples, with respect to the FOS-treated ones, was found: contact angles higher than 150 °C were measured, typical of super hydro- and oilrepellent surfaces. Absorption times higher than 2 h were measured with both water and oil drops, whereas on FOS-treated samples, the oil drop is absorbed in about 15 min, a good result but worse than Fluorolink's performance. This can be due to the molecular structure of Fluorolink, which is longer and more complex than FOS. The presence of TEOS seems to be

**Fluorolink S10**

**NANOSOL**

15 mL Ethanol 1 ml HCl (0,01 N)

**Magnetic stirring for 24 h**

**Weight on: 5-10%**

**Drying and curing 1h at 120°C**

**Figure 6.** Procedure of sol–gel preparation and its application to cotton fabrics to confer hydro and oil repellency.

The same measurements were made after five repeated washing cycles (at 40 °C for 30 min using 5-g/l ECE detergent according to ISO 105 C01 standard) to assess the durability of the

1 mL HCl (0,01 N) 9 mL Fluorolink S10

treatments to laundering. The results are summarized in Figure 8.

**Fluorolink S10+ T EOS**

3,7 mL TEOS 2,5 mL Fluorolink S10 15 mL Ethanol 1 mL HCl (0,01 N)

> **Dipping in S10 or S10 + T EOS nanosol followed by 24 h impregnation**

are summarized in Figure 7.

**FOS** 

9 mL FOS 15 mL Ethanol

**Dipping in FOS nanosol followed by impregnation:**

•**1 min** •**2 h**  •**24 h**

the fibers.

156 Wetting and Wettability

ineffective.

**Figure 7.** Results of contact angle measurements and drop absorption time on cotton fabrics treated with sol–gel finish‐ es. From left to right; for FOS-finished samples add-on and impregnation time: 5% 1 min, 10% 1 min, 5% 2 h, 10% 2h, 5% 24 h, and 10% 24 h; for the other finishes: 5% 24 h and 10% 24 h.

**OIL (paraffin oil: 31.5 mN/ m surf. tension)**

**Figure 8.** Contact angle and drop absorption time measurements after five washing cycles (description of samples as shown in Figure 7).

On FOS samples after washing, a decrease in contact angles was observed, but the behavior was better with 24 h of impregnation, showing that a longer contact time enables better interpenetration of the finishing agent inside the cotton fibers. Instead, the samples finished by Fluorolink S10 showed the best performance, without the influence of TEOS. After washing, the drop absorption times of water strongly decreased, whereas the oil drop absorption time of 2 h was maintained by samples finished with Fluorolink S10.

The strong loss of hydrophobicity after washing can be due to a rearrangement of the fluori‐ nated chains with an orientation toward the internal part of the fibers. In fact, it is well known that fluorine-containing polymers are usually quite susceptible to rapid rearrangement when the polymer surface is contacted with water, in particular with short perfluorinated-side chains to minimize the interfacial free-energy response to the environmental media. This was confirmed by the increase in contact angle and water drop absorption time of the washed samples after ironing.

The results of XPS analysis confirmed the presence of finishing agents on the surface as evidenced by the content of F and Si. CF3 groups are present in the structure of FOS, whereas CF2 groups are present in FOS as well as in Fluorolink. In fact, the F content was higher on the FOS-treated samples (58.3% on the cotton finished with 10% FOS) than that finished with 10% Fluorolink (38.9%). These values were significantly reduced after washing (53.2% and 28.3%, respectively).

In conclusion, the application of a fluorinated alkoxysilane to cotton textiles by sol–gel is a promising textile finishing process to confer durable hydro and oil repellency. In fact, high contact angles and drop absorption time values were measured on treated cotton with both water and oil. Low add-ons (5%) are enough to confer the properties, unaffecting the fabric's characteristics. A prolonged impregnation time (24 h) significantly improves repellency and fastness to washing, whereas ironing of the washed samples can partially restore the hydro and oil repellency lost after washing.

The best performances were obtained with a commercial product (Fluorolink S10). This can allow the application of the treatment at the industrial level, taking into account that the sol– gel process can immediately be implemented on existing production lines of fabric finishing.

#### **5. Conclusions**

The modification of surface energy and wettability of textile fibers can be achieved by several techniques, such as plasma treatments, thermal or UV curing of suitable monomers and oligomers, and, finally, nanotechnology based on sol–gel processes.

LPPs are versatile, enabling various treatment types: etching, grafting of groups onto the surface, coating with polymers produced *in situ* from gaseous monomers or liquid oligomers previously impregnated, sputtering, and so on. Despite this flexibility, the apparatus is complex, cumbersome, expensive, and unsuitable for continuous fabric finishing. APP processes are preferable to this aim, but are limited with regard to utilizable gases and plasma polymerization. In any case, the major drawback of plasma activation aimed at improving the following processes is because most of the free radicals remaining on the treated fiber surface is extinguished when exposed to air oxygen; therefore, the time lapse between the plasma treatment and the exploitation of the effects should be as short as possible.

UV curing of suitable monomers or oligomers can be a valid alternative to traditional thermal curing for fabric water and oil repellency and other surface properties. It is a low-cost and environment-friendly process that can easily be introduced in the finishing processes.

Finally, sol–gel processes applied to fabric finishings allow for obtaining engineered surfaces with a great variety of applications arising from the properties of the nanostructures. If lowcost precursors will be found and the need for organic solvents will be reduced to a minimum amount, these techniques will show a significant development in the next years.

#### **Author details**

The strong loss of hydrophobicity after washing can be due to a rearrangement of the fluori‐ nated chains with an orientation toward the internal part of the fibers. In fact, it is well known that fluorine-containing polymers are usually quite susceptible to rapid rearrangement when the polymer surface is contacted with water, in particular with short perfluorinated-side chains to minimize the interfacial free-energy response to the environmental media. This was confirmed by the increase in contact angle and water drop absorption time of the washed

The results of XPS analysis confirmed the presence of finishing agents on the surface as evidenced by the content of F and Si. CF3 groups are present in the structure of FOS, whereas CF2 groups are present in FOS as well as in Fluorolink. In fact, the F content was higher on the FOS-treated samples (58.3% on the cotton finished with 10% FOS) than that finished with 10% Fluorolink (38.9%). These values were significantly reduced after washing (53.2% and 28.3%,

In conclusion, the application of a fluorinated alkoxysilane to cotton textiles by sol–gel is a promising textile finishing process to confer durable hydro and oil repellency. In fact, high contact angles and drop absorption time values were measured on treated cotton with both water and oil. Low add-ons (5%) are enough to confer the properties, unaffecting the fabric's characteristics. A prolonged impregnation time (24 h) significantly improves repellency and fastness to washing, whereas ironing of the washed samples can partially restore the hydro

The best performances were obtained with a commercial product (Fluorolink S10). This can allow the application of the treatment at the industrial level, taking into account that the sol– gel process can immediately be implemented on existing production lines of fabric finishing.

The modification of surface energy and wettability of textile fibers can be achieved by several techniques, such as plasma treatments, thermal or UV curing of suitable monomers and

LPPs are versatile, enabling various treatment types: etching, grafting of groups onto the surface, coating with polymers produced *in situ* from gaseous monomers or liquid oligomers previously impregnated, sputtering, and so on. Despite this flexibility, the apparatus is complex, cumbersome, expensive, and unsuitable for continuous fabric finishing. APP processes are preferable to this aim, but are limited with regard to utilizable gases and plasma polymerization. In any case, the major drawback of plasma activation aimed at improving the following processes is because most of the free radicals remaining on the treated fiber surface is extinguished when exposed to air oxygen; therefore, the time lapse between the plasma

UV curing of suitable monomers or oligomers can be a valid alternative to traditional thermal curing for fabric water and oil repellency and other surface properties. It is a low-cost and environment-friendly process that can easily be introduced in the finishing processes.

oligomers, and, finally, nanotechnology based on sol–gel processes.

treatment and the exploitation of the effects should be as short as possible.

samples after ironing.

158 Wetting and Wettability

and oil repellency lost after washing.

respectively).

**5. Conclusions**

Franco Ferrero\* and Monica Periolatto

\*Address all correspondence to: franco.ferrero@polito.it

Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy

#### **References**


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## **Surface Energy and Wetting in Island Films**

Sergei Dukarov, Aleksandr Kryshtal and Vladimir Sukhov

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60900

#### **Abstract**

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168 Wetting and Wettability

364.

The chapter describes the fundamental aspects of the effects of scale on surface phenomena in condensed films. Experimental and theoretical data for the size and temperature dependencies of the surface energy (including the solid phase); wetting of solid surfaces and free thin films by small metal particles are discussed. Several modern methods of contact angle measurement in small-sized systems based on the optical and electron microscopy methods are described.

**Keywords:** surface energy, small particles, thin films, wetting, size effects

#### **1. Introduction**

Surface energy is one of the most important characteristics of condensed matter. While methods available for the liquid phase enable to determine reliably not only the value but also the temperature dependence of surface energy [1–3], for the solid phase the accuracy of existing methods, as a rule, does not allow to trace its temperature dependence [4, 5]. Therefore, the following approach is justified: what information can be obtained about surface energy of the condensed matters on studies of various properties and processes in small size samples [6–9]. This article considers mainly the investigations of temperature and size dependence of surface energy of condensed matter based on the analysis of surface phenomena and phase transitions in nano-sized systems.

Wetting of solid surfaces with a liquid as well as spreading of a liquid over solid surfaces as a manifestation of interaction between the solid and liquid phases is one of the universal

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

phenomena and covers a wide variety of both fundamental and technological processes. Despite their crucial importance, these processes are still unclear [1, 2, 10]. Therefore, this paper focuses on effects of wetting in nanodispersed systems and considers various physical and chemical factors affecting it. Such statement of the problems seems actual since these details are important to describe a wide range of processes and phenomena, whereas the available data are disembodies and often ambiguous or even lacking.

#### **2. The surface energy of nanoparticles**

#### **2.1. The size dependence of the surface energy of nanoparticles**

In the framework of the Gibbs thermodynamics of heterophase systems, the size dependence of surface energy is due to the curvature of the phase interface. The Gibbs method applied to interfaces with a small curvature radius was first developed by Tolman [11], who derived the equation relating the surface energy σ of a spherical particle with its radius *R*

$$\frac{1}{\sigma} \frac{d\sigma}{dR} = \frac{\left(2\,\delta/R^2\right)\left(1+\delta/R+\delta^2/3R^2\right)}{1+\left(2\,\delta/R\right)\left(1+\delta/R+\delta^2/3R^2\right)}\tag{1}$$

where δ is the difference between the radii of equimolecular surface and surface of tension. Since the function δ = δ(*R*) is unknown, at δ << *R* the variable δ can be considered constant and equal to the value for plane interface, that is, δ ≈ δ∞. Under this assumption approximate solution to equation (1) was obtained in [11] known in literature as the Tolman formula:

$$
\sigma/\sigma\_{\circ} = 1/\left(1 + 2\delta\_{\circ}/R\right),
$$

For particles with *R* >> δ∞ the first term of the expansion will be sufficient

$$
\sigma = \sigma\_{\circ} \left( 1 - \alpha / \mathbb{R} \right). \tag{2}
$$

In this approach the parameter α = 2δ∞ has a definite physical meaning as a width of the respective phase interface for any condensed phases. Character of the dependence σ(*R*) is determined by the sign of the parameter δ∞. In the case when δ∞ > 0, surface energy of micro‐ particles will decrease, and at δ∞ < 0, conversely, increase of σ with decrease of *R*. Since the sign and value of parameter δ∞ cannot be obtained based on thermodynamic prerequisites, determination of the type of the dependence σ(*R*) calls for the use of the model of the structure of the transition layer for real systems or experimental results. In [3] this problem is solved for a simple idealized fluid using correlation function methods and it is shown that in this system the transition layer has a layered structure corresponding to some orderliness of particles therein. This is essential for many phenomena in surface physics.

Calculations of δ∞ for plane liquid–vapor interfaces made by statistical methods [12] has shown that the quantity δ∞ > 0 and has a value of approximately a few tenth of nanometer (e.g., according to [12] for argon at 90 K δ∞ = 0.36 nm). Further research with use of a computer simulation [13–17], electron theory of surface energy of metals [18, 19], the thermodynamic perturbation theory [20, 21] is consistent with the results in terms of the type of the dependence σ(*R*).

phenomena and covers a wide variety of both fundamental and technological processes. Despite their crucial importance, these processes are still unclear [1, 2, 10]. Therefore, this paper focuses on effects of wetting in nanodispersed systems and considers various physical and chemical factors affecting it. Such statement of the problems seems actual since these details are important to describe a wide range of processes and phenomena, whereas the available

In the framework of the Gibbs thermodynamics of heterophase systems, the size dependence of surface energy is due to the curvature of the phase interface. The Gibbs method applied to interfaces with a small curvature radius was first developed by Tolman [11], who derived the

> ( )( ) ( )( )

 dd

where δ is the difference between the radii of equimolecular surface and surface of tension. Since the function δ = δ(*R*) is unknown, at δ << *R* the variable δ can be considered constant and equal to the value for plane interface, that is, δ ≈ δ∞. Under this assumption approximate solution to equation (1) was obtained in [11] known in literature as the Tolman formula:

> a

In this approach the parameter α = 2δ∞ has a definite physical meaning as a width of the respective phase interface for any condensed phases. Character of the dependence σ(*R*) is determined by the sign of the parameter δ∞. In the case when δ∞ > 0, surface energy of micro‐ particles will decrease, and at δ∞ < 0, conversely, increase of σ with decrease of *R*. Since the sign and value of parameter δ∞ cannot be obtained based on thermodynamic prerequisites, determination of the type of the dependence σ(*R*) calls for the use of the model of the structure of the transition layer for real systems or experimental results. In [3] this problem is solved for a simple idealized fluid using correlation function methods and it is shown that in this system the transition layer has a layered structure corresponding to some orderliness of particles

 dd

12 1 3 *d R RR dR R RR*

2 2 2

 d¥ ¥ = + 11 2 ( ) *R*

2 2

= - ¥ ( ) 1 . *R* (2)

(1)

data are disembodies and often ambiguous or even lacking.

**2.1. The size dependence of the surface energy of nanoparticles**

equation relating the surface energy σ of a spherical particle with its radius *R*

d

ss

For particles with *R* >> δ∞ the first term of the expansion will be sufficient

ss

therein. This is essential for many phenomena in surface physics.

d

s

s

21 3 1

+ + <sup>=</sup> + ++

**2. The surface energy of nanoparticles**

170 Wetting and Wettability

Qualitatively, the decrease in the surface energy of small particles can be explained as follows. For the condensed phase being in equilibrium with its own vapor, the interface surface energy at first approximation is proportional to the difference between the number of atoms (mole‐ cules) per unit volume of the condensed and vapor phases. With decreasing particle size of the condensed phase vapor pressure increases, and, consequently, its density increases, which causes decrease of the surface energy of the particle – saturated vapor interface approximately in inverse proportion to the particle radius.

In this way, theoretical studies suggest the existence of the size dependence of surface energy in the nanodispersed systems. According to estimates made using different methods, depend‐ encies of σ on size for particles and films are manifested as a monotone decrease with de‐ creasing size starting from a radius of less than 20 nm for particles and a thickness of < 5 nm for films.

#### **2.2. Experimental foundations for the determination of surface energy of nanoparticles**

Experimental determination of surface energy of solid bodies is a challenging task. Experi‐ mental methods available to scientists today offer the measurement of values of surface energy of liquid-phase matters with a reasonable degree of accuracy and in a broad temperature band, which is not the case for the crystalline phase. Known experimental methods for the determi‐ nation of the surface energy for the crystalline phase are limited, and, as a rule, have a very narrow range of pre-melting temperatures and provide precision of not more than 10–20% [4]. This is largely due to the fact that surface energy is not a directly measurable value, but in most cases it is estimated as an adjustable parameter in various processes such as, for example, wetting, spreading, melting, crystallization, dissolution, analysis of high-temperature creep, electronic work function, etc. Among the best-known methods are the following: the crystal cleavage method, the dispersed powder dissolution method, the "neutral" droplet method, the multiphase equilibrium method, the growth and evaporation steps method, the "healing" scratch method, and, finally, the zero creep method [4]. Surface energy may also be evaluated by the measurement of electronic work function [18, 19]. However, the analysis of these methods shows that they are not applicable to the measurement of surface energies of small particles.

#### *2.2.1. Kinetics of evaporation of small particles and surface energy*

Surface energy of small particles can be determined by kinetics of evaporation in vacuum at a constant temperature [6]. The method is based on the concepts of the molecular-kinetic theory that supposes that the rate of evaporation from a unit of free surface in vacuum is defined by the expression

$$\frac{dM}{dt} = \left(\frac{m}{2\pi kT}\right)^{\sharp 2} P(T)\_r$$

where *m* is mass of atom (molecule), *k* is Boltzmann constant, *Р* is pressure of saturated vapor at temperature *Т*. For the particle with the radius *R* saturated vapor pressure is linked to the vapor pressure over a flat surface *P*∞(*Т*) with the Kelvin equation

$$P\left(T,R\right) = P\_{\text{av}}\left(T\right)\exp\left(\frac{2\text{v}\_{\text{a}}}{kT}\frac{\sigma}{R}\right). \tag{3}$$

(va is atomic volume). The evaporation rate will be equal to

$$\frac{dM}{dt} = \left(\frac{m}{2\pi kT}\right)^{1/2} P\_\circ \left(T\right) \exp\left(\frac{2\mathbf{v}\_s}{kT}\frac{\sigma}{R}\right). \tag{4}$$

For an array of particles on the substrate it is more practicable to measure not the evaporation rate *dM/dt*, but the dependence of the particle radius on its evaporation time *t* at a constant temperature. From the relation of *R* to *t* one can determine the variation of the particle radius *dR/dt* at different *R* and, consequently, find σ. Indeed, as it follows from (4)

$$\left|\frac{d\mathcal{R}}{dt}\right| = \frac{1}{\rho}\frac{dM}{dt} = \frac{1}{\rho}\left(\frac{m}{2\pi kT}\right)^{1/2}P\_o\exp\left(\frac{2\mathbf{v}\_s}{kT}\frac{\sigma}{R}\right)\text{or}\ln\left|\frac{d\mathcal{R}}{dt}\right| = \ln A + \frac{B\sigma}{R}\tag{5}$$

where

$$A = \frac{1}{\rho} \left(\frac{m}{2\pi kT}\right)^{1/2} P\_{\text{o}}\left(T\right) \text{ and } B = \frac{2\text{v}\_{\text{o}}}{kT}.\tag{6}$$

According to (5) and (6), knowing the temperature, particle size reduction rate *dR/dt*, and *Р*∞(*Т*), one can determine the value of σ. These expressions adequately describe evaporation kinetics of liquid Pb particles and crystalline Ag particles [6] at values of σ close to handbook ones.

Electron microscope investigation of the kinetics of particle evaporation was later used to register the melting temperature of small crystalline Au particles by breaks in dependencies *R*(*t*) [7]. This effect is due to the difference in evaporation rates for crystalline and liquid states. The melting temperature lowering data obtained for small Au particles from their evaporation kinetics [7] correlate well with similar results established later using electron diffraction analysis [22]. Investigating the kinetics of evaporation of silver particles on carbon substrates has shown that the observed sublimation temperature generally decreased with decreasing particle size [23], in agreement with the predictions from the Kelvin equation. However, sublimation of smaller nanoparticles was often observed to occur in discrete steps, which led to faceting of the nanoparticles.

This method was used to determine the surface energy of small particles in Bi, Pb, and Au island films [8, 9]. The sample film was heated in the electron microscope by electron beam up to the onset temperatures of evaporation. The temperature and, hence, evaporation rate was controlled with beam density. The particles radius variation rate ∆*R*/∆*t* during evaporation was established by the analysis of a series of successive electron micrographs taken at fixed time intervals. These data allowed to establish the temperature of particles heated by the electron beam. For this purpose, expression (6) at *R* → ∞ should be represented in the form

$$\mathbf{1g}\,P\_{\ll}\begin{pmatrix}T\\ \end{pmatrix}=\mathbf{1g}\,\mathbf{C}+\mathbf{1}\not\mathbf{1}\prime\prime\prime\tag{7}$$

Where *<sup>C</sup>* <sup>=</sup>*ρ*( <sup>2</sup>*π<sup>k</sup> <sup>m</sup>* ) 1/2 (*dR* / *dt*) <sup>R</sup>→*<sup>∞</sup>*.

that supposes that the rate of evaporation from a unit of free surface in vacuum is defined by

æ ö <sup>=</sup> ç ÷ è ø

where *m* is mass of atom (molecule), *k* is Boltzmann constant, *Р* is pressure of saturated vapor at temperature *Т*. For the particle with the radius *R* saturated vapor pressure is linked to the

æ ö = ç ÷

( ) () <sup>a</sup> 2v *P T,R P T* exp . *kT R*

( ) 1 2

æ ö æ ö <sup>=</sup> ç ÷ ç ÷ è ø è ø

*<sup>a</sup> dM m P T dt kT kT R*

p¥

*dR/dt* at different *R* and, consequently, find σ. Indeed, as it follows from (4)

1 2

¥

2

è ø

r p

r

where

 rp exp . <sup>2</sup>

For an array of particles on the substrate it is more practicable to measure not the evaporation rate *dM/dt*, but the dependence of the particle radius on its evaporation time *t* at a constant temperature. From the relation of *R* to *t* one can determine the variation of the particle radius

> 1 1 2v exp or ln ln , <sup>2</sup> *<sup>a</sup> dR dM m dR B P A dt dt kT kT R dt R*

> > ( )

*kT kT* ¥

According to (5) and (6), knowing the temperature, particle size reduction rate *dR/dt*, and *Р*∞(*Т*), one can determine the value of σ. These expressions adequately describe evaporation kinetics of liquid Pb particles and crystalline Ag particles [6] at values of σ close to handbook ones.

Electron microscope investigation of the kinetics of particle evaporation was later used to register the melting temperature of small crystalline Au particles by breaks in dependencies *R*(*t*) [7]. This effect is due to the difference in evaporation rates for crystalline and liquid states.

<sup>1</sup> 2v and .

*<sup>m</sup> <sup>a</sup> <sup>A</sup> PT B*

æ ö = = ç ÷

1/2

æ ö æ ö = = ç ÷ ç ÷ = + è ø è ø

s

¥

vapor pressure over a flat surface *P*∞(*Т*) with the Kelvin equation

(va is atomic volume). The evaporation rate will be equal to

1 2 , <sup>2</sup> *dM m P(T) dt kT* p

> s

2v

s

è ø (3)

 s (4)

(5)

(6)

the expression

172 Wetting and Wettability

Tabular data are available for the function *Р*∞(*T*), while the value (*dR/dt*)*<sup>R</sup>*→∞ is to be determined experimentally from the results of change of the radius of the particles during their evaporation represented in accordance with (5) and (6) in the coordinates "ln |∆*R*/∆*t*| — 1/*R*." Equation (7) can be solved graphically for *Т* and, thus, the temperature of the observed object can be found.

Figure 1а presents an example of a series of successive micrographs of Bi island films ob‐ tained in the process of their evaporation with the time interval of 15 s, and Figure 1b, c present the results of analysis of evaporation of Au island films. These data were used to find values of ∆*R* for different-sized particles at fixed time intervals ∆*t*. Resulting dependencies for the ensemble of particles in Au island films (the size range of 10–50 nm) are presented in Figure 1c in the coordinates "ln |∆*R*/∆*t*|— 1/*R*." Since these dependencies are linear, according to (5) and (6) they allow us to establish σ and values of (*dR*/*dt*)*R*→∞. The range of particle sizes in experi‐ ments [8, 9] made 10–150 nm. For Pb and Bi temperatures of particle evaporation were higher than melting temperatures, whereas for Au island films data on evaporation rates both in liquid and crystalline state were obtained.

Values of surface energies σ for Au, Pb, and Bi found as a result of the preceding experiments are presented in Table 1, which also presents available literature data for σ at similar temper‐ atures. Comparison of values of σ obtained by kinetics of evaporation of small particles with available data for bulk samples shows their satisfactory fit.

*Figure 1. Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are*  **Figure 1.** Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are given in the charts) (b), and relations of evaporation rate to reciprocal size of particles for gold island films on carbon substrates (c)


740 452 730 439 [7] **Table 1.** Comparison of surface energy values for Au, Pb, and Bi [8]

Bi 650 386 509–518 501 [5]

*1.2.2. Dependence of surface energy on particle size* 

770 447

750 450 748 436 [7]

Table 1. Comparison of surface energy values for Au, Pb, and Bi [8]

regarding the sign of the size dependence of the surface energy of small particles.

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions

The preceding paragraph demonstrates that the surface energy of small particles can be

directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the

6

Ме

Au

Pb

2 2

1

#### *2.2.2. Dependence of surface energy on particle size* 3 5 0.36 нм 0.36 nm

=

Proof Corrections Form

PROOF CORRECTIONS FORM

No. Delete Replace with

2 2

σ≈σ <sup>∞</sup> δ− <sup>∞</sup> <sup>∞</sup> RR +δ+ ( <sup>R</sup>) <sup>∞</sup> <sup>∞</sup> <sup>σ</sup> <sup>σ</sup> <sup>=</sup> <sup>11</sup> <sup>+</sup> <sup>2</sup><sup>δ</sup>

2 3

Author(s) Name(s): Sergei Dukarov, Aleksandr Kryshtal and 4 Vladimir Sukhov

( )( )

+ +

12 1 3

Chapter Title: Surface Energy and Wetting in Island Films

1 21 3

σ δ δδ

σ δ δδ

d R RR

Some characters are not recognized on the figure! Could you please replace it with a higher quality

8 35 = 0.24 nm α = 0.24 nm

9 18 ν – creep data – creep data

9 19 ο – data for Fe – data for Fe

12 2 energy σl energy σ<sup>l</sup>

9 16 Could you please replace fig 4 with a higher quality

dR R RR

+ ++

<sup>2</sup>Eq(1) ( )( )

=

<sup>2</sup>17 ( <sup>21</sup> (<sup>2</sup> ) ...) <sup>2</sup>

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions regarding the sign of the size dependence of the surface energy of small particles. 3 17 decencies dependencies

( )( )

+ +

12 1 3

1 21 3

σ δ δδ

σ δ δδ

d R RR

dR R RR

+ ++

( )( )

2 2 2

The preceding paragraph demonstrates that the surface energy of small particles can be directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the results of such experiments for nanoparticles over 20 nm in size. At the same time, the kinetics of evaporation of Pb and Au nanoparticles with the size below 20 nm both in liquid and crystalline state was investigated in works [6, 7]. The authors of these studies used these results to test the applicability of the Kelvin equation (3) and to estimate values of σ at temperatures at which the evaporation of particles is observed. However, the authors [6, 7] did not analyze the dependence of particle evaporation rates on particle size. Such analysis was offered by the authors in [8, 9], where they demonstrate that for particles with a size of less than 10 nm their surface energy decreases. Figure 2а presents an example of the plot of *R*(*t*) for Pb particles at different temperatures, and Figure 2b presents particle size reduction rate in the coordinates "ln|Δ*R* /Δ*t* | −1 / *R*" plotted using these data. 4 13 Р<sup>∞</sup> Р∞(Т), 5 26 Figure Figure 1c

7 23 equation equation (2) **Figure 2.** Change of the radius of Pb particles in the process of evaporation (a) and the plot of their evaporation rate against size on the coordinate "ln│*∆*R/*∆*t│ — 1/R" (b) (calculated using data [7]). Curves 1, 2 correspond to particles of different initial size at Т = 720 K

1/3 α = 0.916v<sup>a</sup> 1/3 It is evident that at sizes of particles less than 10 nm significant deviation of the preced‐ ing relationship from linear is observed, which in accordance to (5) is an evidence of decreasing σ. Values of σ calculated using expression (5) are presented in Figure 3 (Curve 5), which also shows calculation data of the relation σ(*R*) for Pb microparticles using the Tolman equation (2) with the parameter α = 0.29 nm, which value is determined from the empirical relation α = 0.916v*<sup>a</sup>* 1/3 [26] (Curve 4). The same figure presents the results of calculation of values of gold and lead nanoparticles surface energy at different tempera‐ tures (Curves 2, 3, 5) obtained from the data of analysis of particle evaporation kinetics given in [6, 7].

8 33 Could you please replace fig 3 with a higher quality Comparison of these dependencies produces qualitatively the same result, that is, the surface energy of small particles decreases with decrease of their size, but nanoparticles evaporation experiments suggest a stronger relationship σ(*R*).

6

*Figure 1. Electron micrographs of successive stages of evaporation of Bi island films on* 

**Figure 1.** Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are given in the charts) (b), and relations of evaporation

*amorphous Si films (а); change of particle size in the process of evaporation (temperatures are* 

*given in the charts) (b), and relations of evaporation rate to reciprocal size of particles for gold* 

figure?

139080 [5]

*island films on carbon substrates (c)* 

174 Wetting and Wettability

Page No.

Line

1510 1160

770 447

Evaporation kinetics [8, 9] Literature data

rate to reciprocal size of particles for gold island films on carbon substrates (c)

7 16

1260 1430 1176–

1510 1160

770 447

*Т*, K , mJ/m2 *Т*, K , mJ/m2

**Evaporation kinetics [8, 9] Literature data**

4 14 (Т),

5 27 1c

1245 141020 1240 1410 [5]

1310 1320100 1297 1137 [6]

7 24 (2)

7 24 α =

1350 1230100 1348 1135 [6]

670 385 557–589 560 [5]

720 484 735 438 [7]

Bi 650 386 509–518 501 [5]

7 25 0.916v<sup>a</sup>

740 452 730 439 [7]

750 450 748 436 [7]

8 34 α

Table 1. Comparison of surface energy values for Au, Pb, and Bi [8]

regarding the sign of the size dependence of the surface energy of small particles.

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions

image?

image?

The preceding paragraph demonstrates that the surface energy of small particles can be

directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the

Bi 650 386 509–518 501 [5]

**Table 1.** Comparison of surface energy values for Au, Pb, and Bi [8]

*1.2.2. Dependence of surface energy on particle size* 

1306

 385 557–589 560 [5] 484 735 438 [7] 452 730 439 [7] 450 748 436 [7]

*Т*, K σ, mJ/m<sup>2</sup> *Т*, K σ, mJ/m<sup>2</sup>

 1410±20 1240 1410 [5] 1430 1176–1306 1390±80 [5] 1320±100 1297 1137 [6] 1230±100 1348 1135 [6]

Ме

Ме

Au

Pb

Au

Pb

8

(ρl/ρS)

Figure 3. The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at α = 0.24 nm, 2 and 3 – using microparticles evaporation data at **Figure 3.** The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at *α* = 0.24 nm, 2 and 3 – using microparticles evaporation data at Т = 1348 K and Т = 1316 K); b – Pb (4 – calcula‐ tion using the Tolman equation at *α* =0.29 nm, 5 – particle evaporation data at Т = 735 K)

#### *2.2.3. Decrease in small particles melting temperature and surface energy* Т = 1348 K and Т = 1316 K); b – Pb (4 – calculation using the Tolman equation at α =0.29 nm,

 

S RS It is common knowledge that melting temperature of small particles, thin metal, and alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for the size dependence of melting temperature 5 – particle evaporation data at Т = 735 K) Comparison of these dependencies produces qualitatively the same result, that is, the surface energy of small particles decreases with decrease of their size, but nanoparticles evaporation experiments suggest a stronger relationship σ(R).

$$\frac{T\_s - T\_\text{R}}{T\_\text{S}} = \frac{3}{\lambda R} \left( \sigma\_\text{s} - \sigma\_\text{s} \left( \bigvee\_s \rho\_\text{s} \right)^{\text{Q3}} \right) \tag{8}$$

where *ТS* and *Т<sup>R</sup>* are the melting temperatures of a bulk sample and a particle with the radius *R*, λ is melting heat, σ and *ρ* are surface energies and densities of crystalline (*s*) and liquid (*l*) phases, respectively. As it is seen from (8) using experimental data *ТR*(*R*), one can establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σ*S*–σ*<sup>l</sup>* (*ρ<sup>l</sup>* /*ρS*) 1/3, and given known values of σ*<sup>l</sup>* find σ*S*. The possibility of determining surface energy in solid phase and its temperature dependence using experimental data *ТR*(*R*) are detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but changes in accordance to variation of σ*S* and σ*<sup>l</sup>* . Considering this, the expression for the melting temperature of small particles can be represented in the following form alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for the size dependence of melting temperature

where ТS and ТR are the melting temperatures of a bulk sample and a particle with the radius

R, λ is melting heat, σ and ρ are surface energies and densities of crystalline (s) and liquid

(l) phases, respectively. As it is seen from (8) using experimental data ТR(R), one can

establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σS−σ<sup>l</sup>

energy in solid phase and its temperature dependence using experimental data ТR(R) are

detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but

1/3, and given known values of σ<sup>l</sup> find σS. The possibility of determining surface

$$\frac{T\_s - T\_r}{T\_s} = \frac{3\Delta\Omega\_0}{\lambda \left(R - \Delta R\right)^{\prime}}\tag{9}$$

where ∆Ω0 = *σ<sup>s</sup>* <sup>0</sup> <sup>−</sup>*σ<sup>l</sup>* 0 (1 + *δ<sup>V</sup>* / 3) is the variation of surface energy during melting at temperature *Ts*; ∆*R* = 3*Ts*[γ*<sup>l</sup>* (1 + δ*V*/3) – γ*s*]/λ*ρs*, γ*<sup>l</sup>* = ∂σ*<sup>l</sup>* /∂*T* is the temperature coefficient of liquid phase surface energy; γ*s* = ∂σ*s*/∂*T* is the temperature coefficient of solid phase surface energy, σ<sup>0</sup> is surface energy of relevant phase at bulk sample melting temperature *Тs*, δ*<sup>V</sup>* is relative variation of volume during melting.

It follows from (9) that using the experimental relation *ТR*(*R*) one can calculate ∆Ω at different temperatures and, provided known type of temperature dependence of liquid phase surface energy σ*<sup>l</sup>* (*Т*) below *Тs*, find dependence σ*s*(*Т*). This approach allowed to evaluate relations ∆Ω(*Т*) and σ*s*(*Т*) over a broad temperature interval using experimental data of *ТR*(*R*) for Sn and In [31, 32]. The validity of linear extrapolation of values of liquid phase surface energy σ*<sup>l</sup>* to the region of significant supercooling was substantiated in works [9, 38].

Considering the preceding, we calculated values of surface energies for a number of metals (In, Sn, Bi, Pb, Al, Au) in crystalline state over the temperature interval of (0.6–1)*Тs*. The obtained results are presented in Figure 4. These values agree well with available literature data on σ*s* for bulk samples obtained by other methods. the coordinates "ln(∆σ/σ) – 1/T" the paper also estimated the vacancy formation energy E<sup>V</sup> that yielded the following values: In – 0.5 eV, Sn – 0.62 eV and Pb – 0.6 eV. Close values of the values of EV support vacancy mechanism of nonlinear temperature dependence of

solid phase surface energy in the premelting temperature band.

*2.2.3. Decrease in small particles melting temperature and surface energy*

tion using the Tolman equation at *α* =0.29 nm, 5 – particle evaporation data at Т = 735 K)

the size dependence of melting temperature

5 – particle evaporation data at Т = 735 K)

176 Wetting and Wettability

known values of σ*<sup>l</sup>*

be represented in the following form

S RS

of σ*S* and σ*<sup>l</sup>*

8

(ρl/ρS)

*T T*

evaporation experiments suggest a stronger relationship σ(R).

*T R*

l

difference of surface energies of solid and liquid phases, that is, ∆Ω=σ*S*–σ*<sup>l</sup>*

*s T T T*

S

<sup>ρ</sup> σ−σ <sup>λ</sup> <sup>=</sup> <sup>−</sup> <sup>31</sup> <sup>3</sup>

 

<sup>l</sup> RT

It is common knowledge that melting temperature of small particles, thin metal, and alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for

surface energy of small particles decreases with decrease of their size, but nanoparticles

Figure 3. The plot of surface energy against microparticles size: a – Au (1 – calculation using

**Figure 3.** The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at *α* = 0.24 nm, 2 and 3 – using microparticles evaporation data at Т = 1348 K and Т = 1316 K); b – Pb (4 – calcula‐

the Tolman equation at α = 0.24 nm, 2 and 3 – using microparticles evaporation data at

Т = 1348 K and Т = 1316 K); b – Pb (4 – calculation using the Tolman equation at α =0.29 nm,

<sup>3</sup> , *<sup>l</sup>*

where *ТS* and *Т<sup>R</sup>* are the melting temperatures of a bulk sample and a particle with the radius *R*, λ is melting heat, σ and *ρ* are surface energies and densities of crystalline (*s*) and liquid (*l*) phases, respectively. As it is seen from (8) using experimental data *ТR*(*R*), one can establish the

alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of

thermodynamics, there exist several models to describe the size dependence of melting

temperature of small particles [27]; however, as the quantitative analysis of experimental

data shows, the triple point model proves to be the most feasible. Within the framework of

this model the problem of the melting temperature of the small particle was first solved by

 ρ

where ТS and ТR are the melting temperatures of a bulk sample and a particle with the radius

R, λ is melting heat, σ and ρ are surface energies and densities of crystalline (s) and liquid

(l) phases, respectively. As it is seen from (8) using experimental data ТR(R), one can

establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σS−σ<sup>l</sup>

energy in solid phase and its temperature dependence using experimental data ТR(R) are

detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but

1/3, and given known values of σ<sup>l</sup> find σS. The possibility of determining surface

s l

its temperature dependence using experimental data *ТR*(*R*) are detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but changes in accordance to variation

( ) <sup>0</sup> <sup>3</sup> , *s r*

l*R R*

Pavlov [37], who obtained expression for the size dependence of melting temperature

è ø è ø

r

It is common knowledge that melting temperature of small particles, thin metal, and

Comparison of these dependencies produces qualitatively the same result, that is, the

r

*S R <sup>l</sup> <sup>S</sup> <sup>s</sup> <sup>S</sup>*

1.2.3. Decrease in small particles melting temperature and surface energy

s s


1 3

find σ*S*. The possibility of determining surface energy in solid phase and


. Considering this, the expression for the melting temperature of small particles can

 

TT , (8)

(8)

10

1/3, and given

 (*ρ<sup>l</sup>* /*ρS*)

data [6, 7, 22, 31–36] (the dotted lines are extrapolation of dependencies σl(T) to the area of supercooling state) – creep data [5], ⊕ – small particles evaporation data [7], – data for **Figure 4.** Surface energy temperature dependence for different metals according to the TR(R) data [6, 7, 22, 31–36] (the dotted lines are extrapolation of dependencies *σ*<sup>l</sup> (T) to the area of supercooling state) ■ – creep data [5], ⊕ – small par‐ ticles evaporation data [7], □ – data for Fe [39]

Figure 4. Surface energy temperature dependence for different metals according to the TR(R)

Fe [39] 2. Wetting in condensed films Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for It is evident that there is a common tendency observed for all of the preceding metals mani‐ fested in the fact that the values of σ*<sup>s</sup>* have nonlinear temperature dependence. With relative temperatures below *T/Ts* ≤ (0.85–0.9) the temperature coefficient for these metals becomes approximately constant and makes module (0.3–0.4) mJ/m2 K (Figure 4). Nonlinear decrease in σ*s* at *Т* → *Т<sup>s</sup>* is probably common for metals. The result of work [39] supports this assumption. In this work, surface energy of macroscopic iron samples is determined using the method of wetted solid surface deformation over the range of temperatures (1580–1790) K (Figure 4).

the determination of the wetting contact angles θ shows that the use of traditional methods

[1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new

methods [41, 42] were developed that allowed to investigate wetting in ultradispersed

systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for

method on solid substrates, which, as a rule, were prepared using vacuum condensation as

well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate

temperature that ensured condensation of the metal into liquid phase. The obtained films

were cooled in vacuum to room temperature and the crystallized particles were further

analyzed using the methods of optical, scanning, and transmission electron microscopy.

According to the estimates and data of experimental research [42–44] (Figure 5) contact

Test samples were island films of various metals condensed in vacuum by vapor–liquid

θ > 90°), with typical phase size changing over a broad range.

The nonlinear increment effect │∂σ*S*/∂*Τ*│at *Т* → *Т<sup>S</sup>* was considered for In and Sn and supported by case study calculations of σ*S*, made for Bi, Pb, Al, Au in work [9]. A detailed analysis of nonlinear relation of the temperature coefficient ∂σ*S*/∂*Τ* in premelting temperature band showed its vacancy nature [9]. Based on the analysis of data on σ*S*(*T*) in the coordinates "ln(∆σ/σ) – 1/*T*" the paper also estimated the vacancy formation energy *EV* that yielded the following values: In – 0.5 eV, Sn – 0.62 eV and Pb – 0.6 eV. Close values of the values of *EV* support vacancy mechanism of nonlinear temperature dependence of solid phase surface energy in the premelting temperature band.

### **3. Wetting in condensed films**

Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for the determination of the wetting contact angles θ shows that the use of traditional methods [1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new methods [41, 42] were developed that allowed to investigate wetting in ultradispersed systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for θ > 90°), with typical phase size changing over a broad range.

Test samples were island films of various metals condensed in vacuum by vapor–liquid method on solid substrates, which, as a rule, were prepared using vacuum condensation as well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate temperature that ensured condensation of the metal into liquid phase. The obtained films were cooled in vacuum to room temperature and the crystallized particles were further analyzed using the methods of optical, scanning, and transmission electron microscopy. According to the estimates and data of experimental research [42–44] (Figure 5) contact angle measurement error due to changing droplet volume during its solidification on the substrate is not more than 2°. In this way one can discard the variation of the angle during crystallization of liquid droplets and relate the values of θ found for crystallized particles to values of the contact angles of liquid droplets at the temperature of their formation.

**Figure 5.** Electron microscope images of crystalline (a) and liquid (b) lead particles on a carbon substrate and a sche‐ matic representation of a liquid droplet on a solid substrate (c)

In the case when the gravity effect can be disregarded, the shape of small droplets is a segment of a sphere (estimations show that this is knowingly true for metals with particle size below 105 nm). To find the angle θ it is sufficient to measure any two of the three quantities that define droplets on the substrate: the radius of droplet surface curvature *R*, the diameter of its base *d* (*d =* 2*r*), and the height *H* (Figure 5c).

The methods suggested in [41, 42] differ in approaches to measure geometric parameters of droplets. The most frequently used cleavage and convolution methods are based on measure‐ ment of the said parameters during direct observation of droplet profiles with an optical or electron microscope [41, 42]. In this case, the contact angle is determined from the relations

$$\theta = 2 \operatorname{arctg} \frac{2H}{d} = \arccos \left( 1 - \frac{H}{R} \right) = \begin{cases} \arcsin \frac{d}{2R}, & \theta < 90^{\circ}, \\ 180^{\circ} - \arcsin \frac{d}{2R}, & \theta > 90^{\circ}. \end{cases}$$

The developed complex of methods [41, 42] makes it possible to investigate the wetting of surfaces with small droplets, with the size of the latter ranging within 3–105 nm.

#### **3.1. Size effect in wetting**

The nonlinear increment effect │∂σ*S*/∂*Τ*│at *Т* → *Т<sup>S</sup>* was considered for In and Sn and supported by case study calculations of σ*S*, made for Bi, Pb, Al, Au in work [9]. A detailed analysis of nonlinear relation of the temperature coefficient ∂σ*S*/∂*Τ* in premelting temperature band showed its vacancy nature [9]. Based on the analysis of data on σ*S*(*T*) in the coordinates "ln(∆σ/σ) – 1/*T*" the paper also estimated the vacancy formation energy *EV* that yielded the following values: In – 0.5 eV, Sn – 0.62 eV and Pb – 0.6 eV. Close values of the values of *EV* support vacancy mechanism of nonlinear temperature dependence of solid phase surface

Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for the determination of the wetting contact angles θ shows that the use of traditional methods [1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new methods [41, 42] were developed that allowed to investigate wetting in ultradispersed systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for θ > 90°), with

Test samples were island films of various metals condensed in vacuum by vapor–liquid method on solid substrates, which, as a rule, were prepared using vacuum condensation as well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate temperature that ensured condensation of the metal into liquid phase. The obtained films were cooled in vacuum to room temperature and the crystallized particles were further analyzed using the methods of optical, scanning, and transmission electron microscopy. According to the estimates and data of experimental research [42–44] (Figure 5) contact angle measurement error due to changing droplet volume during its solidification on the substrate is not more than 2°. In this way one can discard the variation of the angle during crystallization of liquid droplets and relate the values of θ found for crystallized particles to values of the contact angles

**Figure 5.** Electron microscope images of crystalline (a) and liquid (b) lead particles on a carbon substrate and a sche‐

energy in the premelting temperature band.

typical phase size changing over a broad range.

of liquid droplets at the temperature of their formation.

matic representation of a liquid droplet on a solid substrate (c)

**3. Wetting in condensed films**

178 Wetting and Wettability

Wetting in the liquid–solid system is defined by the equilibrium contact angle θ, which is related to surface energies of contact phases with Young's equation

$$\cos \theta = \left(\sigma\_u - \sigma\_{ul}\right) / \sigma\_{1'} \tag{10}$$

where the indices *u* and *l* refer to solid (substrate) and liquid (particle) phase, respectively. One would expect that the size dependence of surface energy will cause a difference of wetting patterns in nanodispersed systems from known ones for macroscopic objects. This may change the contact angle with increasing dispersity of both liquid and solid phases. In order to provide a theoretical description of these phenomena, it is necessary to solve the problem of the equilibrium shape of the microdroplet and its contact angle, that is, obtain an equation analogous to Young's equation (10) with regard for the relationship σ(*R*).

Consider, following [42, 43, 45], a small droplet of liquid on a flat solid surface. The total free energy of the system *F* is comprised of the hydrostatic energy *pV* (here, pressure p may be regarded as the undetermined Lagrange multiplier that accounts the constant droplet volume V) and surface forces energy

$$F = -pV + \int\_{\mathcal{S}\_l} \sigma\_l dS + \int\_{\mathcal{S}\_{ul}} (\sigma\_{ul} - \sigma\_u) dS\_\prime \tag{11}$$

where S is the interfacial area.

In accordance with existing concepts [11, 45] the surface energy σ<sup>l</sup> is viewed as dependent on the average surface curvature C at a given point

$$
\sigma\_l = \sigma\_l^\circ \left(1 - a\mathbb{C}\right). \tag{12}
$$

For spherical surface (*C* = 1/*R*) relation (12) agrees with expression (2) known in the literature as the Tolman formula.

When finding equilibrium conditions, one should take account of the size dependence of the interfacial energy of droplet – substrate boundary σul. It would be natural to consider this dependence as a relation not to the radius of the surface curvature *R*, but to the radius of the wetted perimeter r [42, 45], that is, for σul use relationship in the form

$$
\sigma\_{ul} = \sigma\_{ul}^{\circ} \left( 1 - \beta / r \right). \tag{13}
$$

Expressions (12) and (13) apply at 1/*C* >> α and *r* >> β. Finding equilibrium characteristics of the droplet does not require any assumptions as to the sign and value of parameters α and β.

Due to the axiality of the problem, it can be solved using polar coordinates with their origin in the center of the circle of the wetted perimeter and the vertical axis *z* perpendicular to the substrate plane. The profile of the free surface of the droplet is defined by the function *z*(*ρ*)*.* Without loss of generality, one can regard *z*(*ρ*) function as single-valued, that is, consider the case of θ < 90° (it can be shown that the obtained results will be valid on the whole range of angles θ, if *z* is chosen as an independent variable and the droplet surface is set single-valued at any θ using the function *ρ*(*z*)).

The equilibrium shape of the droplet is found by minimizing the functional (11), which, with regard to relations for droplet volume and areas of its boundary surfaces, is written as follows:

$$\begin{split} F &= 2\pi \Big[ \Big[ -pz + \sigma\_{\!} \Big( \mathbf{C} \big) \Big( 1 + z'^2 \big)^{\mathbb{X}} + \sigma\_{\!} \Big( r \big) - \sigma\_{\!} \Big] \rho d\rho, \\ C &= -\frac{1}{2} \Big[ z'' \big( 1 + z'^2 \big)^{-\frac{\mathsf{X}}{\mathsf{X}}} + \frac{z'}{\rho} \Big( 1 + z'^2 \big)^{-\frac{\mathsf{X}}{\mathsf{X}}} \Big]. \end{split} \tag{14}$$

The summand (σ*ul*(*r*) – σ*u*)*ρ* in the expression under the integral sign does not contain *z*(*ρ*) and its derivatives, that is, the relation σ*ul*(*r*) defines only boundary conditions and has no effect on the shape of the droplet.

Functional variation (14) in δ*z* gives the Euler equation, which after term-by-term integration takes on the form

$$-\frac{p\rho^2}{2} = \rho \left(1 + z'^2\right)^{\underline{\chi}'} \frac{d\sigma\_l}{d\mathbb{C}} \frac{\partial\mathbb{C}}{\partial z'} + \frac{\sigma\_l \rho z'}{\left(1 + z'^2\right)^{\underline{\chi}'}} - \frac{d}{d\rho} \left[\rho \left(1 + z'^2\right)^{\underline{\chi}'} \frac{d\sigma\_l}{d\mathbb{C}} \frac{\partial\mathbb{C}}{\partial z''}\right].\tag{15}$$

The integration constant in (15) is equal to zero from the equal-zero condition of one of the non-integral summands δF at the point *ρ* = 0. The complexity of equation (15) makes its general solution unlikely, which fact urges us to use specification of relation σl(C) in the form (12). Substitution in (15) of relation (12) and expressions for derivatives *dσ<sup>l</sup>* / *dC*, ∂*<sup>C</sup>* / <sup>∂</sup> *<sup>z</sup>* ′ and ∂*C* / ∂ *z* ″ yields a nonlinear differential first-order equation

$$
\left[z'\left(1+z'^2\right)^{-\aleph\_z'}\right]^2 + \frac{2\rho}{\alpha} \left[z'\left(1+z'^2\right)^{-\aleph\_z'}\right] + \frac{p\rho^2}{\alpha\sigma\_l} = 0\,,
$$

which solution by separation of variables gives equilibrium shape of the droplet surface in the form of a sphere truncated by plane *z* = 0:

$$\left(\left(z-z\_{0}\right)^{2}+\rho^{2}=\mathbb{R}^{2}.\tag{16}$$

The sphere radius satisfies the relation

where S is the interfacial area.

180 Wetting and Wettability

as the Tolman formula.

at any θ using the function *ρ*(*z*)).

on the shape of the droplet.

takes on the form

0

ò

*r*

p

2

In accordance with existing concepts [11, 45] the surface energy σ<sup>l</sup>

ss

wetted perimeter r [42, 45], that is, for σul use relationship in the form

ss

( ) 1 .

For spherical surface (*C* = 1/*R*) relation (12) agrees with expression (2) known in the literature

When finding equilibrium conditions, one should take account of the size dependence of the interfacial energy of droplet – substrate boundary σul. It would be natural to consider this dependence as a relation not to the radius of the surface curvature *R*, but to the radius of the

( ) 1 . *ul ul*

 b

Expressions (12) and (13) apply at 1/*C* >> α and *r* >> β. Finding equilibrium characteristics of the droplet does not require any assumptions as to the sign and value of parameters α and β.

Due to the axiality of the problem, it can be solved using polar coordinates with their origin in the center of the circle of the wetted perimeter and the vertical axis *z* perpendicular to the substrate plane. The profile of the free surface of the droplet is defined by the function *z*(*ρ*)*.* Without loss of generality, one can regard *z*(*ρ*) function as single-valued, that is, consider the case of θ < 90° (it can be shown that the obtained results will be valid on the whole range of angles θ, if *z* is chosen as an independent variable and the droplet surface is set single-valued

The equilibrium shape of the droplet is found by minimizing the functional (11), which, with regard to relations for droplet volume and areas of its boundary surfaces, is written as follows:

( )( ) ( )

2

21 ,

<sup>3</sup> <sup>1</sup> 2 2

The summand (σ*ul*(*r*) – σ*u*)*ρ* in the expression under the integral sign does not contain *z*(*ρ*) and its derivatives, that is, the relation σ*ul*(*r*) defines only boundary conditions and has no effect

Functional variation (14) in δ*z* gives the Euler equation, which after term-by-term integration


1 2

s

 s rr

( ) ( )

<sup>1</sup> 1 1.

ì ü ¢ =- + + + í ý ¢¢ ¢ ¢ î þ

*<sup>z</sup> C zz z*

 s

2 2

r

*<sup>l</sup> ul u F pz C z r d*

é ù = -+ + + - ¢ ê ú ë û

 a

the average surface curvature C at a given point

is viewed as dependent on

(14)

*l l C* ¥ = - (12)

*r* ¥ = - (13)

$$p = \frac{2\sigma\_l^{\circ}}{R} \left(1 - \frac{a}{2R}\right)^{\circ}$$

which shows that the undetermined Lagrange multiplier p is nothing, but the Laplace pressure adjusted for the dependence σ(*R*). Integration constant *z*<sup>0</sup> = ± *<sup>R</sup>* <sup>2</sup> <sup>−</sup>*<sup>r</sup>* <sup>2</sup> has the meaning of zcoordinate of the sphere center (16) and is determined from the condition *z*(*r*) = 0.

The wetting angle θ can be found from the boundary condition or, since function *z*(*ρ*) is defined, from the condition of minimum free energy of the droplet at a constant volume. For this purpose the surface energy of the droplet must be expressed in terms of *R* and θ

$$F\_s = \pi R^2 \left\{ 2\sigma\_l \left( R \right) \left( 1 - \cos \theta \right) + \left[ \sigma\_{ul}(r) - \sigma\_u \right] \sin^2 \theta \right\}.$$

By setting the derivative *dFs/dR* to zero we can obtain the equation, which, considering constant volume, gives the equilibrium condition of a microdroplet on a substrate

$$\cos\theta = \left(\sigma\_u - \sigma\_{ul} - R\frac{d\sigma\_l}{dR} - \frac{r}{2}\frac{d\sigma\_{ul}}{dr}\right) \bigg/ \left(\sigma\_l + R\frac{d\sigma\_l}{dR}\right). \tag{17}$$

Equation (17), naturally, is different from Young's equation (10) by presence of summands containing surface energy derivatives with respect to size.

By using expressions (12) and (13) for σ*<sup>l</sup>* (*R*) and σ*ul*(*R*), we can write the relation for the contact angle of the microparticle through the parameters α and β that define the size dependence of respective surface energies as follows [42, 45]:

$$\cos\theta = \cos\theta\_{\circ} - \frac{a}{R} + \frac{\beta}{2R} \frac{\sigma\_{\circ}^{\circ}}{\sigma\_{\circ}^{\circ}} \frac{1}{\sin\theta}.\tag{18}$$

Naturally, in the extreme case at σ → σ∞ (α/*R* → 0, β/*R* → 0) all the expressions received go into known relations of the capillary theory. It should be further noted that equation (18) agrees by the type of functional dependence on size with relations received in the scope of the line tension model [46, 47].

#### *3.1.1. Contact angle size dependencies and surface energy of the solid–liquid interface*

The size effect in wetting of the flat surface of the solid substrate with small metal droplets was first found for vacuum-condensed island tin and indium on an amorphous carbon substrate [42–44]. A combination of optical and electron microscopy [41, 42] allowed to determine wetting contact angles over the range of particles of 1–104 nm. According to measurements using optical microscopy the contact angle in the Sn/C system for micron-sized droplets is constant and makes 151°±2°, which fact agrees with the known data for the tincarbon system. For measurement of contact angle in islands of smaller size we applied the methods of convolution and photometric analysis of electron microscope pictures.

The results of measurement of θ for tin on carbon substrate are presented in Figure 6а, which demonstrates that for big particles (*R >* 30 nm) values obtained are close to respective values of micron-sized droplets. As the size of the particles decreases (*R <* 30 nm) one can observe decrease of the contact angle.

Figure 6. The plots of the contact angle against the radius of particles of tin (a), bismuth (b), and led (c) on a carbon substrate ( – data using convolution method, – using photometric **Figure 6.** The plots of the contact angle against the radius of particles of tin (a), bismuth (b), and led (c) on a carbon substrate (O – data using convolution method, ● – using photometric measurement of electron microscope pictures) [9, 42–44]

The preceding research was followed later by the study of wetting in the systems of

"island metal (Bi, Pb, Au) film–amorphous carbon film" and "Pb–amorphous silicon film"

depending on the size of particles [9, 42–44]. For all investigated systems it was obtained

that with particle sizes R > 100 nm and thicknesses of carbon and silicon films t > 20 nm,

contact angles of liquid droplets in island films well agree with data of respective contact

systems in bulk state. With particle sizes R < 30 nm the value � decreases so that ∆θ = θ∞ –

θ ≈ (20°–25°) at R = (4–5) nm (Figure 6). The conclusion regarding reduction of the contact

angles of nanosized droplets to the extent of their spreading was obtained in [48] by

gold–carbon system was discussed in detail in [50]. It showed that the amount of pressure of

residual gases during the preparation of gold island films has no effect on the values of

surface energies corresponding to the bulk state, though it has a slight impact on their size

separate interest, in particular, for some practical applications (e.g., the formation of ordered

nanostructures by film melting [51–53]), but at the same time allow to obtain new physical

information regarding properties of microparticles. Thus, using the experimental relations

�(R) and σl(R) one can establish the size dependence of interfacial energy of the

used, from which, using the relation �(R) at known quantities of the parameter � and the

value of the surface energy �u, the value of the interfacial energy of the microparticle–

substrate boundary and its size dependence were found. The parameter � can be found from

data on the kinetics of evaporation of small particles [8]. It may be evaluated using the

For analysis of results of the size effect of wetting in island films expression (18) was

The results of the study of wetting obtained [9, 42–44] and presented in Figure 6 are of

Influence of sample preparation conditions on the contact angles of microparticles in the

measurement of electron microscope pictures) [9, 42–44]

modeling using the molecular dynamics method.

microparticle–substrate boundary σul.

dependence.

15

The preceding research was followed later by the study of wetting in the systems of "island metal (Bi, Pb, Au) film–amorphous carbon film" and "Pb–amorphous silicon film" depending on the size of particles [9, 42–44]. For all investigated systems it was obtained that with particle sizes *R* > 100 nm and thicknesses of carbon and silicon films t > 20 nm, contact angles of liquid droplets in island films well agree with data of respective contact systems in bulk state. With particle sizes *R <* 30 nm the value θ decreases so that ∆θ = θ∞ – θ ≈ (20°–25°) at *R* = (4–5) nm (Figure 6). The conclusion regarding reduction of the contact angles of nanosized droplets to the extent of their spreading was obtained in [48] by modeling using the molecular dynamics method.

Equation (17), naturally, is different from Young's equation (10) by presence of summands

angle of the microparticle through the parameters α and β that define the size dependence of

*<sup>l</sup> R R*

Naturally, in the extreme case at σ → σ∞ (α/*R* → 0, β/*R* → 0) all the expressions received go into known relations of the capillary theory. It should be further noted that equation (18) agrees by the type of functional dependence on size with relations received in the scope of the line tension

The size effect in wetting of the flat surface of the solid substrate with small metal droplets was first found for vacuum-condensed island tin and indium on an amorphous carbon substrate [42–44]. A combination of optical and electron microscopy [41, 42] allowed to determine wetting contact angles over the range of particles of 1–104 nm. According to measurements using optical microscopy the contact angle in the Sn/C system for micron-sized droplets is constant and makes 151°±2°, which fact agrees with the known data for the tincarbon system. For measurement of contact angle in islands of smaller size we applied the

The results of measurement of θ for tin on carbon substrate are presented in Figure 6а, which demonstrates that for big particles (*R >* 30 nm) values obtained are close to respective values of micron-sized droplets. As the size of the particles decreases (*R <* 30 nm) one can observe

Figure 6. The plots of the contact angle against the radius of particles of tin (a), bismuth (b), and led (c) on a carbon substrate ( – data using convolution method, – using photometric

**Figure 6.** The plots of the contact angle against the radius of particles of tin (a), bismuth (b), and led (c) on a carbon substrate (O – data using convolution method, ● – using photometric measurement of electron microscope pictures)

The preceding research was followed later by the study of wetting in the systems of

"island metal (Bi, Pb, Au) film–amorphous carbon film" and "Pb–amorphous silicon film"

depending on the size of particles [9, 42–44]. For all investigated systems it was obtained

that with particle sizes R > 100 nm and thicknesses of carbon and silicon films t > 20 nm,

contact angles of liquid droplets in island films well agree with data of respective contact

systems in bulk state. With particle sizes R < 30 nm the value � decreases so that ∆θ = θ∞ –

θ ≈ (20°–25°) at R = (4–5) nm (Figure 6). The conclusion regarding reduction of the contact

angles of nanosized droplets to the extent of their spreading was obtained in [48] by

gold–carbon system was discussed in detail in [50]. It showed that the amount of pressure of

residual gases during the preparation of gold island films has no effect on the values of

surface energies corresponding to the bulk state, though it has a slight impact on their size

separate interest, in particular, for some practical applications (e.g., the formation of ordered

nanostructures by film melting [51–53]), but at the same time allow to obtain new physical

information regarding properties of microparticles. Thus, using the experimental relations

�(R) and σl(R) one can establish the size dependence of interfacial energy of the

used, from which, using the relation �(R) at known quantities of the parameter � and the

value of the surface energy �u, the value of the interfacial energy of the microparticle–

substrate boundary and its size dependence were found. The parameter � can be found from

data on the kinetics of evaporation of small particles [8]. It may be evaluated using the

For analysis of results of the size effect of wetting in island films expression (18) was

The results of the study of wetting obtained [9, 42–44] and presented in Figure 6 are of

Influence of sample preparation conditions on the contact angles of microparticles in the

cos cos . 2 sin

 q

*3.1.1. Contact angle size dependencies and surface energy of the solid–liquid interface*

methods of convolution and photometric analysis of electron microscope pictures.

a b s 1

q

¥ ¥ = -+ (18)

*ul*

¥

s

(*R*) and σ*ul*(*R*), we can write the relation for the contact

15

containing surface energy derivatives with respect to size.

q

By using expressions (12) and (13) for σ*<sup>l</sup>*

model [46, 47].

182 Wetting and Wettability

decrease of the contact angle.

measurement of electron microscope pictures) [9, 42–44]

modeling using the molecular dynamics method.

microparticle–substrate boundary σul.

dependence.

[9, 42–44]

respective surface energies as follows [42, 45]:

Influence of sample preparation conditions on the contact angles of microparticles in the gold– carbon system was discussed in detail in [50]. It showed that the amount of pressure of residual gases during the preparation of gold island films has no effect on the values of surface energies corresponding to the bulk state, though it has a slight impact on their size dependence.

The results of the study of wetting obtained [9, 42–44] and presented in Figure 6 are of separate interest, in particular, for some practical applications (e.g., the formation of ordered nano‐ structures by film melting [51–53]), but at the same time allow to obtain new physical infor‐ mation regarding properties of microparticles. Thus, using the experimental relations θ(R) and σ*l* (R) one can establish the size dependence of interfacial energy of the microparticle–substrate boundary σ*ul*.

For analysis of results of the size effect of wetting in island films expression (18) was used, from which, using the relation θ(R) at known quantities of the parameter α and the value of the surface energy σu, the value of the interfacial energy of the microparticle–substrate boundary and its size dependence were found. The parameter α can be found from data on the kinetics of evaporation of small particles [8]. It may be evaluated using the rela‐ tion α ≈ 0.916*va* 1/3 (va – atomic volume) too [26]. Calculation of α using this relation yields the value of α(Pb) = 0.27 and α(Au) = 0.23 nm, that is, quantities close to those found experimentally in [8]. This allows to use at first approximation the preceding relation to estimate the parameter α for metals that lack experimental data for the relation σ*<sup>l</sup>* (R). The value of the surface energy of carbon film was determined and presented in work [9, 43] from the data on wetting of free films of different thickness with microdroplets of indi‐ um, tin, and lead, which makes σ*u* = 120±30 mJ/m<sup>2</sup> .

Using these data authors of work [45] found values of σul and the parameter β, which are presented for the investigated metal-carbon systems in Table 2.

The parameters α and β are positive, which is an evidence of decreasing surface energy of microparticles and interfacial energy at the substrate boundary with a decrease of the radius. Values of α approximately correspond to the thickness of the surface layer at the liquid– vacuum boundary. The value β, which defines the width of the transition zone between the liquid particle and the substrate and depends on the nature of contacting phases, is 2–4 times as big as α.


**Table 2.** Results of wetting size effect in metal-carbon systems [42, 43, 45]

#### *3.1.2. Wetting hysteresis in condensed microdroplets*

The observed reduction of the contact angle θ with decreasing radius of the droplet is accounted for by the size dependence σ*l* and σ*lu*, due to the growing relative contribution of interface regions. However, wetting parameters are also subject to the influence of substrate elastic deformation, which was disregarded earlier when deriving equations (17) and (18). The effect of deformation on angle θ in the case when substrate is a thin film was dealt in detail in [54], for elastic half-space in [55], but because of approximation, the results presented in [55] cannot be applied to droplets with the size below 20–50 nm, that is, when wetting size effect is observed. Works [42, 56] offer solutions of the problem of determina‐ tion of the value of the equilibrium wetting angle θ for the microdroplet with a radius of less than 50 nm with regard to elastic deformation of the substrate. On assumption that the force of liquid tension along the wetting perimeter is uniformly distributed along the ring of finite width, it was shown that elastic deformation effect is insufficient (1–2° for the systems considered earlier), and, hence, reduction of the contact angle is primarily de‐ fined by the size dependence of specific energies of interface surfaces. Nevertheless, for substrates with low value of Young's modulus (*E* ~ 109 N/m2 ) additional deflection of contact angle for small droplets reaches 5–6°.

At the same time, as a result of the small size of droplets and increased diffusion coefficients in nanodispersed systems [57–59], the wetting perimeter under the action of surface tension forces may experience irreversible changes, which may be registered with electron microscopy as circular traces on the substrate left after evaporated droplets. In addition, the plot of the radius of evaporating droplet against time at constant temperature, as a rule, has periodic deviations of experimental points from the continuous curve. Works dedicated to direct measurement of the wetting contact angle also demonstrate fluctuations ∆θ ≈ 10–15°, while the precision of the convolution and photometry methods makes 3–5° [41, 42]. In both cases these deviations may be accounted for by wetting hysteresis. This phenomenon consists in fixation of the wetting perimeter, which under certain conditions, for example, during evaporation, significantly changes the behavior of the liquid droplet. Work [60] examines the reasons causing this effect in microdroplets, it analyses the effect of wetting hysteresis on parameters of the droplet–substrate system.

A number of works were concerned with wetting hysteresis, for example [46, 61], and the commonest causes of this effect are considered to be microroughness and inhomogeneity of the substrate. However, many assumptions underlying these works, for example, the rough‐ ness height of ~ 1 µm cannot be applied to microdroplets. In several systems fixation of the wetting perimeter is achieved by partial mutual dissolution of solid and liquid phases. Nevertheless, hysteresis may be as well observed for systems with minor mutual solubility, such as Au/C. Some authors noted that at high temperatures under the action of liquid surface tension forces, the substrate may be subject to inelastic deformation. In this case the triple contact area develops a prominent welt. Comparison of different mechanisms of mass transfer at small (~10-8 m) distances implies a conclusion about the defining role of surface diffusion. As follows from estimations made in work [60] characteristic time of deformation in the Au/C systems makes about 0.1 s. Since the time of condensation of films is about 102 s, in the process of droplet growth the welt has enough time to form even with quite frequent jumps of the wetting perimeter, that is, the droplet creates substrate roughness itself.

**Metal** *<sup>σ</sup><sup>l</sup>*

184 Wetting and Wettability

*∞* **, mJ/m2**

**Table 2.** Results of wetting size effect in metal-carbon systems [42, 43, 45]

substrates with low value of Young's modulus (*E* ~ 109 N/m2

angle for small droplets reaches 5–6°.

parameters of the droplet–substrate system.

*3.1.2. Wetting hysteresis in condensed microdroplets*

**α, nm** *<sup>σ</sup>ul*

Calculated Experiment [8]

Au 1130 0.24 0.23 955 1.0 138.4 Sn 531 0.28 - 574 0.53 152.4 Pb 450 0.29 0.27 463 0.91 140.9 Bi 376 0.30 - 407 0.5 141.0 In 559 0.27 - 566 0.55 143

The observed reduction of the contact angle θ with decreasing radius of the droplet is accounted for by the size dependence σ*l* and σ*lu*, due to the growing relative contribution of interface regions. However, wetting parameters are also subject to the influence of substrate elastic deformation, which was disregarded earlier when deriving equations (17) and (18). The effect of deformation on angle θ in the case when substrate is a thin film was dealt in detail in [54], for elastic half-space in [55], but because of approximation, the results presented in [55] cannot be applied to droplets with the size below 20–50 nm, that is, when wetting size effect is observed. Works [42, 56] offer solutions of the problem of determina‐ tion of the value of the equilibrium wetting angle θ for the microdroplet with a radius of less than 50 nm with regard to elastic deformation of the substrate. On assumption that the force of liquid tension along the wetting perimeter is uniformly distributed along the ring of finite width, it was shown that elastic deformation effect is insufficient (1–2° for the systems considered earlier), and, hence, reduction of the contact angle is primarily de‐ fined by the size dependence of specific energies of interface surfaces. Nevertheless, for

At the same time, as a result of the small size of droplets and increased diffusion coefficients in nanodispersed systems [57–59], the wetting perimeter under the action of surface tension forces may experience irreversible changes, which may be registered with electron microscopy as circular traces on the substrate left after evaporated droplets. In addition, the plot of the radius of evaporating droplet against time at constant temperature, as a rule, has periodic deviations of experimental points from the continuous curve. Works dedicated to direct measurement of the wetting contact angle also demonstrate fluctuations ∆θ ≈ 10–15°, while the precision of the convolution and photometry methods makes 3–5° [41, 42]. In both cases these deviations may be accounted for by wetting hysteresis. This phenomenon consists in fixation of the wetting perimeter, which under certain conditions, for example, during evaporation, significantly changes the behavior of the liquid droplet. Work [60] examines the reasons causing this effect in microdroplets, it analyses the effect of wetting hysteresis on

*∞* **, mJ/m2**

**β, nm** *θ∞*

) additional deflection of contact

The values of the contact angles corresponding to perimeter breakdown with changing volume of the droplet were received [60] from the condition of the system's minimum free energy taking into account elastic deformations of the substrate and their partial relaxa‐ tion in the triple contact area trough surface diffusion. According to [60] the contribution of relaxed elastic deformation energy reaches significant values, for example, for the Au/C system the wetting hysteresis, that is, difference between advancing θ*a* and receding θ*<sup>r</sup>* contact angles makes about 3°.

In this way, with changes of the volume of the droplet, for example, during evaporation, its wetting perimeter will be fixed until the contact angle is reduced to the critical value θ*r*. Upon this wetting the perimeter will break, and the droplet will take the position corresponding to equilibrium (Young's) value θ0. In this position the wetted perimeter develops a new welt and the process recurs. It may be noted that for sufficiently big droplets (with their base radius considerably larger than the width of the welt) the dependence of values of the angles θ*r* and θ*<sup>a</sup>* on the size is small. Thus, for the Au/C system with the droplet radius growing from 20 to 1000 nm the value of these angles changes by 1° due to the increase of elastic energy contri‐ bution.

Considerable amount of Laplace pressure in very small (less than 10 nm) droplets results in elastic deformation being able to relax not only in the triple contact area, but also directly under the droplet. In this case, along with the welt along the wetted perimeter dimples may form under the droplet, which causes higher hysteresis value, with the difference θ0 – θ*r* growing much faster than θ*a* – θ0, that is, the minimum contact angles diverge from the equilibrium value more than the maximum ones. Taking into account the decrease of the value of the contact angle, one may conclude that, for example, for the same Au/C system the contact angle of small (2–5 nm) droplets may reach 65–70° at θ0 = 138°.

#### **3.2. Wetting in droplet–thin film–substrate systems**

Among the factors that define wetting in dispersed metal–metal systems, in addition to size effect of wetting, one can single out the following: discontinuity of intermediate film and resulting heterogeneity of the substrate, mutual solubility of components in each other, formation of chemical compounds at the solid and liquid phase interface, and oxidation of the metal film. Therefore, wetting processes in ultradispersed systems are defined by a number of parameters, which are quite inseparable.

A case study research of the influence of fineness of the solid phase on the contact angle is presented in work [62], which investigated wetting of thin films of different thickness depos‐ ited on bulk substrate. It showed that in the melt (Ag, Cu, Sn, Pb)–metal film (Mo, V, Fe)– nonmetal substrate (sapphire, quartz, graphite) system the contact angle is subject to linear variation within the range of values corresponding to wetting of clean substrate (at thickness of film *t* → 0) and wetting of film substance in compact state (at *t > tc*). The values of critical thicknesses tc, below which change of the contact angle is observed for the investigated systems is in the range of 20–50 nm. At the same, when carbon film covered germanium is wetted with tin the change of the contact angle is observed up to a thickness of 3 nm, while remaining unchanged further, and corresponds to the wetting of compact graphite. The authors explain the obtained results by discontinuity of carbon films at t < 3 nm.

Wetting in triple systems Pb/Ni/[NaCl, Si, GaAs], Sn/[C, Al, Al2O3]/KCl, Bi/Fe/KCl as a function of metal film thickness (2 nm < t < 200 nm) was investigated in [9, 42–44, 63]. These systems substantially differ by interaction behaviors: Sn–C, Sn–Al2O3, Bi–Fe – complete insolubility in solid and liquid states; Sn–Al – solubility 0.5 wt. % Al in Sn; and Pb–Ni – up to 4 wt. % Ni in Pb. Test samples were prepared as follows. Variable thickness intermediate film (Al, Fe, Ni, C, Al2O3) was condensed on monocrystal substrates (KCl, NaCl, Si, GaAs) in a vacuum of 10-6– 10-8 mm Hg. The studied metal (Sn, Bi, Pb) was condensed on this film by the vapor–liquid mechanism without deterioration in vacuum. The substrate temperature during condensation was 653 K for Pb, 523 K for Sn, and 560 K for Bi.

In all investigated systems degree of wetting strongly depends on intermediate film thickness, though the range of thicknesses, on which change of θ occurs is different. The common feature for the analyzed systems is that the contact angle is defined at a fist approximation by heterogeneity of the wetted surface and changes within extreme limits corresponding to wetting of clean substrate (*t* → 0) and intermediate film material in bulk state (*t* > *tc*). The critical thickness *tc*, at which complete screening of a bulk substrate by a thin film is observed, depends on the character of interaction of the systems' components and varies from nanometers (no interaction) to tens and hundreds of nanometers (dissolution of the film in the melt, formation of chemical compounds). The analysis of the obtained results together with data [62] allowed to classify the main types of the relations θ(*t*) for wetting with a melt of thin film on the surface of a bulk substrate (Figure 7):

**a. Noninteracting systems** – Figure 7a. The value *tk* in such systems is defined by the microstructure of intermediate film and to some extent may depend on technological parameters of its production (substrate temperature, condensation rate, etc.). The varia‐ tion of the contact angle is defined by transition from discontinuous to continuous film and the dependence of its surface energy on thickness. Sn/C/KCl (Figure 8a), Sn/Al2O3/ KCl, Sn/C/Ge [62] may serve as examples of such systems. Since wetting angle in such systems changes for intermediate film thinner than 10 nm, effects related to size variation

Figure 7. Main types of dependencies θ(t) for systems melt – film – substrate:

a) noninteracting systems; b) systems with dissolution of film in the melt; c) systems with chemical interaction at the

film–substrate interface

are also possible. Thus, in the Sn/C/KCl system variation of θ is observed in the range of 2 < t

Figure 8. Wetting angle against thickness of intermediary film for systems Sn/C/KCl (а);

material of intermediate film in liquid droplets causes considerable displacement of t<sup>k</sup>

b) Systems with dissolution of film in liquid metal – Figure 7b. Dissolution of the

Bi/Fe/KCl (1), Sn/Al/KCl (2), Pb/Ni/NaCl (3) (b); and Pb/Ni/GaAs (c) [9, 42–44, 63]

wetting with a melt of thin film on the surface of a bulk substrate (Figure 7):

film–substrate interface

results together with data [62] allowed to classify the main types of the relations θ(t) for

Figure 7. Main types of dependencies θ(t) for systems melt – film – substrate:

a) noninteracting systems; b) systems with dissolution of film in the melt; c) systems with chemical interaction at the

wetting with a melt of thin film on the surface of a bulk substrate (Figure 7):

resulting heterogeneity of the substrate, mutual solubility of components in each other, formation of chemical compounds at the solid and liquid phase interface, and oxidation of the metal film. Therefore, wetting processes in ultradispersed systems are defined by a number of

A case study research of the influence of fineness of the solid phase on the contact angle is presented in work [62], which investigated wetting of thin films of different thickness depos‐ ited on bulk substrate. It showed that in the melt (Ag, Cu, Sn, Pb)–metal film (Mo, V, Fe)– nonmetal substrate (sapphire, quartz, graphite) system the contact angle is subject to linear variation within the range of values corresponding to wetting of clean substrate (at thickness of film *t* → 0) and wetting of film substance in compact state (at *t > tc*). The values of critical thicknesses tc, below which change of the contact angle is observed for the investigated systems is in the range of 20–50 nm. At the same, when carbon film covered germanium is wetted with tin the change of the contact angle is observed up to a thickness of 3 nm, while remaining unchanged further, and corresponds to the wetting of compact graphite. The authors explain

Wetting in triple systems Pb/Ni/[NaCl, Si, GaAs], Sn/[C, Al, Al2O3]/KCl, Bi/Fe/KCl as a function of metal film thickness (2 nm < t < 200 nm) was investigated in [9, 42–44, 63]. These systems substantially differ by interaction behaviors: Sn–C, Sn–Al2O3, Bi–Fe – complete insolubility in solid and liquid states; Sn–Al – solubility 0.5 wt. % Al in Sn; and Pb–Ni – up to 4 wt. % Ni in Pb. Test samples were prepared as follows. Variable thickness intermediate film (Al, Fe, Ni, C, Al2O3) was condensed on monocrystal substrates (KCl, NaCl, Si, GaAs) in a vacuum of 10-6– 10-8 mm Hg. The studied metal (Sn, Bi, Pb) was condensed on this film by the vapor–liquid mechanism without deterioration in vacuum. The substrate temperature during condensation

In all investigated systems degree of wetting strongly depends on intermediate film thickness, though the range of thicknesses, on which change of θ occurs is different. The common feature for the analyzed systems is that the contact angle is defined at a fist approximation by heterogeneity of the wetted surface and changes within extreme limits corresponding to wetting of clean substrate (*t* → 0) and intermediate film material in bulk state (*t* > *tc*). The critical thickness *tc*, at which complete screening of a bulk substrate by a thin film is observed, depends on the character of interaction of the systems' components and varies from nanometers (no interaction) to tens and hundreds of nanometers (dissolution of the film in the melt, formation of chemical compounds). The analysis of the obtained results together with data [62] allowed to classify the main types of the relations θ(*t*) for wetting with a melt of thin film on the surface

**a. Noninteracting systems** – Figure 7a. The value *tk* in such systems is defined by the microstructure of intermediate film and to some extent may depend on technological parameters of its production (substrate temperature, condensation rate, etc.). The varia‐ tion of the contact angle is defined by transition from discontinuous to continuous film and the dependence of its surface energy on thickness. Sn/C/KCl (Figure 8a), Sn/Al2O3/ KCl, Sn/C/Ge [62] may serve as examples of such systems. Since wetting angle in such systems changes for intermediate film thinner than 10 nm, effects related to size variation

parameters, which are quite inseparable.

186 Wetting and Wettability

the obtained results by discontinuity of carbon films at t < 3 nm.

was 653 K for Pb, 523 K for Sn, and 560 K for Bi.

of a bulk substrate (Figure 7):

are also possible. Thus, in the Sn/C/KCl system variation of θ is observed in the range of 2 < t < 7 nm. At the same time, electron microscope analysis of clean carbon films suggests their а) Noninteracting systems – Figure 7a. The value tk in such systems is defined by the **Figure 7.** Main types of dependencies *θ*(t) for systems melt – film – substrate: a) noninteracting systems; b) systems with dissolution of film in the melt; c) systems with chemical interaction at the film–substrate interface

of film surface energy are also possible. Thus, in the Sn/C/KCl system variation of θ is observed in the range of 2 < *t* < 7 nm. At the same time, electron microscope analysis of clean carbon films suggests their continuity with decrease of thickness down to 1.5–2 nm. This gives ground to assumption that apart from discontinuity of carbon film the relation θ(*t*) in the Sn/C/KCl system is also stipulated by their surface energy. Since with decreas‐ ing *t* changes not only σ*u*, but also interface energies of the film–particle interface σ*lu* and film–bulk substrate, the said relation, strictly speaking, reflects changes in adhesion tension σ*u*–σ*lu* with decrease of thickness of carbon film on the surface of macroscopic KCl monocrystal. continuity with decrease of thickness down to 1.5–2 nm. This gives ground to assumption that apart from discontinuity of carbon film the relation θ(t) in the Sn/C/KCl system is also stipulated by their surface energy. Since with decreasing t changes not only σu, but also interface energies of the film–particle interface σlu and film–bulk substrate, the said relation, strictly speaking, reflects changes in adhesion tension σu–σlu with decrease of thickness of carbon film on the surface of macroscopic KCl monocrystal. microstructure of intermediate film and to some extent may depend on technological parameters of its production (substrate temperature, condensation rate, etc.). The variation of the contact angle is defined by transition from discontinuous to continuous film and the dependence of its surface energy on thickness. Sn/C/KCl (Figure 8a), Sn/Al2O3/KCl, Sn/C/Ge [62] may serve as examples of such systems. Since wetting angle in such systems changes for intermediate film thinner than 10 nm, effects related to size variation of film surface energy

Figure 8. Wetting angle against thickness of intermediary film for systems Sn/C/KCl (а); Bi/Fe/KCl (1), Sn/Al/KCl (2), Pb/Ni/NaCl (3) (b); and Pb/Ni/GaAs (c) [9, 42–44, 63] **Figure 8.** Wetting angle against thickness of intermediary film for systems Sn/C/KCl (а); Bi/Fe/KCl (1), Sn/Al/KCl (2), Pb/Ni/NaCl (3) (b); and Pb/Ni/GaAs (c) [9, 42–44, 63] interface energies of the film–particle interface σlu and film–bulk substrate, the said relation, strictly speaking, reflects changes in adhesion tension σu–σlu with decrease of thickness of

b) Systems with dissolution of film in liquid metal – Figure 7b. Dissolution of the material of intermediate film in liquid droplets causes considerable displacement of t<sup>k</sup> **b. Systems with dissolution of film in liquid metal** – Figure 7b. Dissolution of the materi‐ al of intermediate film in liquid droplets causes considerable displacement of *tk* toward the region of higher thickness values; examples of change of the wetting contact angle in such systems are given in Figure 8b. In this case the dependence features another typical thickness *ts*, by which the intermediary film completely dissolves in the melt. The value *ts* depends on the solubility of the film material in liquid metal at given temperature. A partial dissolution of film in liquid metal is observed within the interval of thickness *ts < t < tc*, which causes its discontinuity, that is, the substrate becomes heterogeneous. Since solubility of film material in the melt for the investigated systems is limited, the degree of substrate carbon film on the surface of macroscopic KCl monocrystal.

20

20

heterogeneity is a function of film thickness, which fact accounts for the observed depend‐ ence θ(*t*). Dependencies of this type are observed in Pb/Ni/NaCl, Bi/Fe/KCl, Sn/Al/KCl systems (Figure 8b) and for a number of systems studied in [62]: [Cu, Ag, Pb, Sn]/[Mo, V, Fe]/[quartz, sapphire, graphite];

**c. Systems with chemical interaction of film with substrate**– Figure 7c (Pb/Ni/Si и Pb/Ni/ GaAs [42, 63], Figure 8c). As could be seen from Figure 8c, in the Pb/Ni/GaAs system changes in wetting occur in two stages. First, the contact angle decreases to intermediary θ ≈ 75°, then over the range of thickness 6 < *t* < 14 nm the plot θ(*t*) features a plateau, which has never been observed in similar systems investigated earlier, and further the contact angle changes again until it reaches a value corresponding to the Pb/Ni system. This variation of θ(*t*) directly suggests the presence of at least two mechanisms of wetting variation with film thickness, one of which occurs on the interval 0 < *t* < 14 nm, and the other one at *t* > 14 nm. Hence, this type of system can be divided into two subsystems, and, accordingly, is specified by the two values of critical thickness. The second subsystem (regions B, C, D in Figure 8c) belongs to type (a) or (b). In the first subsystem substrate heterogeneity on the transition segment 0 < *t* < *tc1* (region А in Figure 8c) is caused by the growth of new phase island – a chemical combination of film with substrate (results of phase analysis of double-layer Ni–GaAs films produced in different conditions are presented in works [64, 65]), and the value *tc1*, which corresponds to the formation of continuous film of the compound, is defined by the mechanism of interaction of inter‐ mediate layer with substrate.

It should be noted that plots presented in Figure 7 are simplest and influence other factors, for example, interaction with the residual atmosphere (Sn/Al/KCl [42]) may cause a more complex variation of the contact angle with changing thickness of the intermediary film.

#### **3.3. Wetting of thin free films**

When interpreting results of wetting in three-component systems liquid–thin film–bulk substrate, it is difficult to separate effects due to film thickness itself and the influence of bulk substrate. Therefore, it was considered expedient to investigate wetting of thin free films depending on their thickness [42–44]. The obtained results did not make it possible to find size dependence of surface energies of thin carbon films. However, these results are of interest in themselves because it is possible for highly dispersed systems, when liquid particles wet not the surface of bulk solid bodies, but that of free thin films. In this case, specific effects connected to deformation of film under the liquid droplet are observed.

A theory of half-space wetting was constructed in [55]. It suggests that the droplet deforms the region near the line of contact of three phases to form a welt. In case of thin films defor‐ mation may be significant that makes it possible to find it by experiment. Therefore, in the following text we give an outline theoretical analysis of wetting of thin free films on assump‐ tion of constant surface energies σ*<sup>l</sup>* , σ*u* and σ*ul*, made in work [54], and respective experimental results of the research [42–44].

#### *3.3.1. Wetting of elastically deformed film with small droplets* with introduction to the expression of which a summand corresponding to energy of the

2.3.1. Wetting of elastically deformed film with small droplets

respective experimental results of the research [42–44].

2.3. Wetting of thin free films

heterogeneity is a function of film thickness, which fact accounts for the observed depend‐ ence θ(*t*). Dependencies of this type are observed in Pb/Ni/NaCl, Bi/Fe/KCl, Sn/Al/KCl systems (Figure 8b) and for a number of systems studied in [62]: [Cu, Ag, Pb, Sn]/[Mo, V,

**c. Systems with chemical interaction of film with substrate**– Figure 7c (Pb/Ni/Si и Pb/Ni/ GaAs [42, 63], Figure 8c). As could be seen from Figure 8c, in the Pb/Ni/GaAs system changes in wetting occur in two stages. First, the contact angle decreases to intermediary θ ≈ 75°, then over the range of thickness 6 < *t* < 14 nm the plot θ(*t*) features a plateau, which has never been observed in similar systems investigated earlier, and further the contact angle changes again until it reaches a value corresponding to the Pb/Ni system. This variation of θ(*t*) directly suggests the presence of at least two mechanisms of wetting variation with film thickness, one of which occurs on the interval 0 < *t* < 14 nm, and the other one at *t* > 14 nm. Hence, this type of system can be divided into two subsystems, and, accordingly, is specified by the two values of critical thickness. The second subsystem (regions B, C, D in Figure 8c) belongs to type (a) or (b). In the first subsystem substrate heterogeneity on the transition segment 0 < *t* < *tc1* (region А in Figure 8c) is caused by the growth of new phase island – a chemical combination of film with substrate (results of phase analysis of double-layer Ni–GaAs films produced in different conditions are presented in works [64, 65]), and the value *tc1*, which corresponds to the formation of continuous film of the compound, is defined by the mechanism of interaction of inter‐

It should be noted that plots presented in Figure 7 are simplest and influence other factors, for example, interaction with the residual atmosphere (Sn/Al/KCl [42]) may cause a more complex

When interpreting results of wetting in three-component systems liquid–thin film–bulk substrate, it is difficult to separate effects due to film thickness itself and the influence of bulk substrate. Therefore, it was considered expedient to investigate wetting of thin free films depending on their thickness [42–44]. The obtained results did not make it possible to find size dependence of surface energies of thin carbon films. However, these results are of interest in themselves because it is possible for highly dispersed systems, when liquid particles wet not the surface of bulk solid bodies, but that of free thin films. In this case, specific effects connected

A theory of half-space wetting was constructed in [55]. It suggests that the droplet deforms the region near the line of contact of three phases to form a welt. In case of thin films defor‐ mation may be significant that makes it possible to find it by experiment. Therefore, in the following text we give an outline theoretical analysis of wetting of thin free films on assump‐

, σ*u* and σ*ul*, made in work [54], and respective experimental

22

film:

 

L

0

function.

variation of the contact angle with changing thickness of the intermediary film.

to deformation of film under the liquid droplet are observed.

Fe]/[quartz, sapphire, graphite];

188 Wetting and Wettability

mediate layer with substrate.

**3.3. Wetting of thin free films**

tion of constant surface energies σ*<sup>l</sup>*

results of the research [42–44].

According to [42–44, 54], the equilibrium characteristic of the system comprised of free elastically deformed film with the thickness *t* and the wetting droplet (Figure 9) is found in the same way as in the problem discussed earlier – from the minimum free energy condition, with introduction to the expression of which a summand corresponding to energy of the film: ( ) ( ) ( ) ( ) <sup>ρ</sup> Θρ ρσ+ρ− <sup>+</sup> ′ ψ+ζ ζ′ <sup>ζ</sup> ′′ ′ <sup>ρ</sup> π= <sup>−</sup> σ+ζ− <sup>−</sup> ′ σ−σ+ <sup>+</sup> ζ′ ∫ <sup>F</sup> zp <sup>z</sup> <sup>r</sup> <sup>u</sup> uu <sup>d</sup> <sup>l</sup> uul 2 1 1 12 ,,,, <sup>2</sup> 2 2 (19)

When interpreting results of wetting in three-component systems liquid–thin film–bulk

substrate, it is difficult to separate effects due to film thickness itself and the influence of

bulk substrate. Therefore, it was considered expedient to investigate wetting of thin free

films depending on their thickness [42–44]. The obtained results did not make it possible to

find size dependence of surface energies of thin carbon films. However, these results are of

interest in themselves because it is possible for highly dispersed systems, when liquid

particles wet not the surface of bulk solid bodies, but that of free thin films. In this case,

deforms the region near the line of contact of three phases to form a welt. In case of thin

films deformation may be significant that makes it possible to find it by experiment.

Therefore, in the following text we give an outline theoretical analysis of wetting of thin

free films on assumption of constant surface energies σl, σu и σul, made in work [54], and

According to [42–44, 54], the equilibrium characteristic of the system comprised of free

elastically deformed film with the thickness t and the wetting droplet (Figure 9) is found in

A theory of half-space wetting was constructed in [55]. It suggests that the droplet

specific effects connected to deformation of film under the liquid droplet are observed.

$$\begin{split} F &= 2\pi \Big[ \Big( \Big[ -p\left( z - \zeta \right) + \sigma \sqrt{1 - z'^2} + \left( \sigma\_{ul} - \sigma\_{\upsilon} \right) \sqrt{1 + \zeta^2} \Big] \Big) \rho \Theta \Big( r - \rho \Big) + \\ &+ 2\sigma\_{\upsilon} \rho \sqrt{1 + \zeta^{\*2}} + \nu \Big( \zeta \gamma , \zeta ^\*, u, u', \rho \big) \Big] d\rho, \end{split} \tag{19}$$

where *L* is the radius of the film fixation circle, functions ζ(*ρ*) and *z*(*ρ*) define the radial profile of the surfaces of the film and the droplet, respectively; Θ(*x*) is the Heaviside step function.

Figure 9. Schematic diagram of a liquid droplet on a thin elastic film **Figure 9.** Schematic diagram of a liquid droplet on a thin elastic film

The function ψ is equal to the sum of contributions of elastic energies of pure bending ψ1 and longitudinal extension of the film ψ2, written, according to [66], with regard to axiality in the following form:

$$\begin{split} \boldsymbol{\nu}\_{1} &= \frac{1}{2} D \rho \Big( \boldsymbol{\zeta}^{\prime} + \frac{2\nu}{\rho} \boldsymbol{\zeta}^{\prime} \boldsymbol{\zeta}^{\prime} + \frac{1}{\rho^{2}} \boldsymbol{\zeta}^{\prime 2} \Big), \\ \boldsymbol{\nu}\_{2} &= \frac{6}{t^{2}} D \rho \Big( \boldsymbol{\nu}^{\prime 2} + \frac{2\nu}{\rho} \boldsymbol{\nu}^{\prime} \boldsymbol{\nu} + \frac{\boldsymbol{u}^{2}}{\rho^{2}} + \frac{1}{4} \boldsymbol{\zeta}^{\prime 4} + \boldsymbol{u}^{\prime} \boldsymbol{\zeta}^{\prime 2} + \frac{\nu}{\rho} \boldsymbol{u} \boldsymbol{\zeta}^{\prime 2} \Big), \end{split} \tag{20}$$

where ν is Poisson's ratio, *u* is the radial component of two-dimensional displacement vector, *D* =*Et* <sup>3</sup> / 12(1−*ν* 2) is the stiffness factor (*E* is Young's modulus).

The shape of the free surface of liquid is found by variation of the functional *F* in δ*z* on 0≤*ρ* ≤*r*. Upon double integration, the relevant Euler equation yields function *z*(*ρ*) as a sphere (16) with the radius *R* = 2σ*<sup>l</sup>* /*p*.

Variation of *F* in δξ and δ*u* allows to obtain equations to define film deformation, which, after partial integration and substitution of the ψ1 and ψ2 from (20), assume the form

$$\begin{split} \zeta'' &+ \frac{1}{\rho} \zeta'' - \frac{1}{\rho^2} \zeta' - \frac{12}{t^2} \Big( u' + \frac{\nu}{\rho} u + \frac{1}{2} \zeta'^2 \Big) - \\ &- \frac{1}{D} \Big[ (\sigma\_{ul} - \sigma\_u) \Theta (r - \rho) + 2\sigma\_u \Big] \frac{\zeta'}{\sqrt{1 + \zeta'^2}} = -\frac{pr}{2D} \Theta (r - \rho); \end{split} \tag{21}$$

$$
\mu'' + \frac{1}{\rho}\mu' - \frac{1}{\rho^2}\mu = -\zeta'\zeta'' - \frac{1-\nu}{2\rho}\zeta'^2. \tag{22}
$$

The boundary conditions for equations (21) and (22) follow from non-integral summands of the variation δ*F* going to zero. Two of them were used to draw equations (21), (22), and the rest may be written as follows: *u*(0) = 0*;* ξ'(0) = 0; ξ(*L*) = 0; ξ'(*L*) = 0; *u*(*L*) = 0; besides that, the point *ρ* = *r* shall require continuity of the functions ζ(*ρ*), ζ'(*ρ*), *u*(*ρ*), ζ''(*ρ*), and *u*'(*ρ*).

The condition of equilibrium value of the contact angle θ may be determined by variation of functional (19) with δ*r.* Here we obtain an expression, which is Young's equation written along the tangent line to the film surface at point *ρ* = *r*: *σ<sup>l</sup>* cos(*θ* −*ϕ*)=*σ<sup>u</sup>* −*σul*, where ϕ = arctgζ'(*r*) – film inclination angle at the point *ρ* = *r.* The same Young's equation corrected for elastic surface inclination angle was obtained in [55].

Another relation connecting ϕ and θ follows from equation (21) and boundary conditions at the point *ρ* = *r*:

$$
\sigma\_l \cdot \sin \theta = \left(\sigma\_{ul} - \sigma\_u\right) \sin \phi + D \left[\angle^{\text{'''}}(r+0) - \zeta^{\text{'''}}(r-0)\right].\tag{23}
$$

As it is seen from (21) and (23), the contact angle depends on film deformation and is deter‐ mined by the jump of the third derivative ζ(*ρ*) on the line of three-phase contact.

Features of deformation for small and big film deflections, that is, with prevailing bending and tensile deformation, respectively, were evaluated in [54]. In the case when the maximum film deflection δ is less than its thickness, equations (21) and (22) become linear, and their solution yields the following expression

$$\frac{E}{1-\nu^2} = \frac{9\sigma\_l \cdot \sin\theta\_o}{8t^3} \left(\lim\_{r \to 0} \frac{\delta}{r^3}\right)^{-1}, \qquad \phi \sim \frac{4}{3}\frac{\delta}{r},\tag{24}$$

which relates Young's module to parameters measurable by experiment. At greater film bends (δ > *t*), approximate solutions of equations (21) and (22) can be obtained resulting in the estimation

#### Surface Energy and Wetting in Island Films http://dx.doi.org/10.5772/60900 191

$$\frac{\delta}{r} \sim \left(2\sigma\_l \cdot \sin \theta\_o / Et\right)^{\frac{1}{3}}.\tag{25}$$

In the case of a very thin film *t* ≤ 10σ/*E* (this can be the case for films with low elastic modulus) its shape under the droplet tends to sphere with the radius *Rul* =*r*(*σ<sup>u</sup>* + *σul*)/ *σ<sup>l</sup>* sin*θ* and remains flat outside the droplet. Smooth transition from one shape to another takes place in a narrow region with the width of the order of film thickness, and the value of the contact angle *θ* =lim*t*→0 *θ*(*t*)

is defined only by surface phase energies in accordance with the equations

$$\begin{aligned} \sigma\_l \cos \theta\_0 + \left(\sigma\_u + \sigma\_{ul}\right) \cos \phi &= 2\sigma\_u; \\ \sigma\_l \sin \theta\_0 = \left(\sigma\_u + \sigma\_{ul}\right) \sin \phi. \end{aligned} \tag{26}$$

#### *3.3.2. Wetting of free carbon films with metal droplets*

( )( ) ( )

11 1 . <sup>2</sup>

zz

The boundary conditions for equations (21) and (22) follow from non-integral summands of the variation δ*F* going to zero. Two of them were used to draw equations (21), (22), and the rest may be written as follows: *u*(0) = 0*;* ξ'(0) = 0; ξ(*L*) = 0; ξ'(*L*) = 0; *u*(*L*) = 0; besides that, the

The condition of equilibrium value of the contact angle θ may be determined by variation of functional (19) with δ*r.* Here we obtain an expression, which is Young's equation written along

inclination angle at the point *ρ* = *r.* The same Young's equation corrected for elastic surface

Another relation connecting ϕ and θ follows from equation (21) and boundary conditions at

sin ( ) sin () () 0 0.

 z

As it is seen from (21) and (23), the contact angle depends on film deformation and is deter‐

Features of deformation for small and big film deflections, that is, with prevailing bending and tensile deformation, respectively, were evaluated in [54]. In the case when the maximum film deflection δ is less than its thickness, equations (21) and (22) become linear, and their solution

> 0 9 sin <sup>4</sup> lim , ~ , 1 8 <sup>3</sup>

which relates Young's module to parameters measurable by experiment. At greater film bends (δ > *t*), approximate solutions of equations (21) and (22) can be obtained resulting in the

d

*t r r*

*r*

®

è ø

1


 z*<sup>l</sup>* × = - + +- - *ul u Dr r* é ù ¢¢¢ ¢¢¢ ë û (23)

> d

f

 f

mined by the jump of the third derivative ζ(*ρ*) on the line of three-phase contact.

23 3

 q

æ ö <sup>×</sup> <sup>=</sup> ç ÷ - ç ÷

¥

*l*

s

*E*

n

è ø

<sup>1</sup> 2 ; <sup>2</sup> <sup>1</sup> *ul u <sup>u</sup>*

*u u*

 s

¢ - - Q- + é ù =- Q - ë û

n

> r

*D D*

2

point *ρ* = *r* shall require continuity of the functions ζ(*ρ*), ζ'(*ρ*), *u*(*ρ*), ζ''(*ρ*), and *u*'(*ρ*).

r

2 2

 z

r

ss

the tangent line to the film surface at point *ρ* = *r*: *σ<sup>l</sup>*

qss

inclination angle was obtained in [55].

s

yields the following expression

the point *ρ* = *r*:

estimation

zz

190 Wetting and Wettability

r

1 1 12 1

æ ö ¢¢¢ ¢¢ ¢ ¢ ¢ + - - ++ - ç ÷

*t*

*uu u*

r

 r 2

z

2

*pr r r*

z

2

2


n

 r  z

z

+ ¢

r

cos(*θ* −*ϕ*)=*σ<sup>u</sup>* −*σul*, where ϕ = arctgζ'(*r*) – film

(21)

(24)

As already noted, experimental research of wetting of free amorphous carbon films of different thickness with island vacuum condensates aimed at obtaining data on surface energy of films was made in [42–44]. The research used test metals (In, Sn, Pb), which are inert to carbon films and forming with carbon films contact angles of 140°–150°.

Test samples were prepared by evaporation and condensation of carbon and metal in a vacuum of 10–6 mm Hg on carbon films of different thickness located on copper grids with the mesh size of 60 µm. During the experiment the temperature was kept above the melting point for the relevant metal. Carbon film thickness varied on the range of 4–30 nm, and the size of liquid metal particles was 30–500 nm and was limited, on the one hand, by the need to exclude size effect due to dispersity of the liquid phase, and by strength of carbon films on the other.

Electron microscope examination of profiles of crystallized metal droplets (Figure 10) revealed substantial difference in the shape of the interphase boundary droplet–substrate for micro‐ particles condensed on free films and films on a solid surface. The difference is that when the film is thin enough it gets deformed by the droplet (Figure 10), while in particles condensed on a solid surface, liquid–substrate interface remained flat.

For the analyzed systems it was determined that at *t* < 30 nm the contact angle decreases with film thickness (Figure 11). At *t* > 30 nm the angle θ approaches the constant value θ∞ that corresponds to wetting of bulk material. Analysis of profiles of droplets on free films showed that the film is deformed by the droplet, with the degree of deflection being a function of thickness and becoming a factor at *t* < 10 nm.

The obtained results were interpreted in [42–44] within the framework of wetting of elastically deformable carbon films [54], whose basic concepts were given earlier. As follows from relations (24) and (25), at *t* = const the relation of maximum film deflection δ to the droplet base radius *r* will be different for cases with prevailing deformation of bending (δ ~ *r*<sup>3</sup> at δ < *t*) and stretching (δ ~ *r* at δ > *t*).

δ < t on the coordinates "r

26

expression

thickness and becoming a factor at t < 10 nm.

Electron microscope examination of profiles of crystallized metal droplets (Figure 10)

revealed substantial difference in the shape of the interphase boundary droplet–substrate for

microparticles condensed on free films and films on a solid surface. The difference is that

when the film is thin enough it gets deformed by the droplet (Figure 10), while in particles

with film thickness (Figure 11). At t > 30 nm the angle θ approaches the constant value θ∞ that

corresponds to wetting of bulk material. Analysis of profiles of droplets on free films showed

that the film is deformed by the droplet, with the degree of deflection being a function of

elastically deformable carbon films [54], whose basic concepts were given earlier. As follows

droplet base radius r will be different for cases with prevailing deformation of bending (δ ~ r

The obtained results were interpreted in [42–44] within the framework of wetting of

For the analyzed systems it was determined that at t < 30 nm the contact angle decreases

condensed on a solid surface, liquid–substrate interface remained flat.

**Figure 10.** Micrographs of tin droplets on free carbon films with the thickness of 20 (a) и 10 (b) nm

Experimental relations δ(*r*) for the Sn/C system at *t* = 10 nm (Figure 12) corroborate this conclusion. It is apparent from the chart that the linear dependence δ(*r*) is observed at δ < *t* on the coordinates "*r*<sup>3</sup> — δ," and at δ > *t* – on the coordinates "*r* — δ." Experimental relations δ(r) for the Sn/C system at t = 10 nm (Figure 12) corroborate this conclusion. It is apparent from the chart that the linear dependence δ(r) is observed at 3

— δ," and at δ > t – on the coordinates "r — δ."

Figure 11. Dependence of the angle of wetting of free carbon films with tin (a), lead (b), and indium (c) on their thickness [42–44] **Figure 11.** Dependence of the angle of wetting of free carbon films with tin (a), lead (b), and indium (c) on their thick‐ ness [42–44]

It follows from the same charts that <sup>r</sup> <sup>t</sup> <sup>r</sup> <sup>→</sup> <δ <sup>δ</sup> )(lim 3 <sup>0</sup> = 7.5⋅10–6 nm–2 and ( ) <sup>t</sup> <sup>r</sup> >δ <sup>δ</sup> = 0.11. Since Poisson's ratio is usually within the limits 1/4 < ν < 1/2, then from relation (24) one can It follows from the same charts that lim *r*→0 (*δ* /*r* <sup>3</sup> )| *<sup>δ</sup>*<*<sup>t</sup>* = 7.5⋅10–6 nm–2 and (*δ* /*r*)| *<sup>δ</sup>*>*<sup>t</sup>* = 0.11. Since Poisson's ratio is usually within the limits 1/4 < ν < 1/2, then from relation (24) one can estimate Young's modulus for carbon film, which turns out to be equal to *E* ≈ (3,4–4,2)⋅1010 N/m2 . With regard to this value from (25) one gets (*δ* /*r*)| *<sup>δ</sup>*>*<sup>t</sup>* ≈ 0.10 ± 0.01, which agrees well with the experiment. Theoretical prediction of the contact angle at *t* = 10 nm, too, gives the value of θ = (140 ± 1)°, close to the experimental one of θ ≈ 138° . estimate Young's modulus for carbon film, which turns out to be equal to E ≈ (3,4– 4,2)⋅10<sup>10</sup> N/m<sup>2</sup> . With regard to this value from (25) one gets ( ) <sup>t</sup> <sup>r</sup> >δ <sup>δ</sup> ≈ 0.10 ± 0.01, which agrees well with the experiment. Theoretical prediction of the contact angle at t = 10 nm, too, gives the value of θ = (140 ± 1)°, close to the experimental one of θ ≈ 138° .

25

. Since

) reported in literature, as a rule, refer

gives values (130, 140 и 135° for In, Sn,

3

Figure 12. The relation δ(r) on the coordinates "r – δ" (a) and "r<sup>3</sup> – δ" (b) for tin droplets on a free carbon film with the thickness of 10 nm [42–44] **Figure 12.** The relation *δ*(r) on the coordinates "r – *δ*" (a) and "r<sup>3</sup> – *δ*" (b) for tin droplets on a free carbon film with the thickness of 10 nm [42–44]

The results of theoretical consideration for very thin films were used to evaluate the

( ) σ=σ <sup>θ</sup><sup>∞</sup> −θ <sup>θ</sup><sup>∞</sup> sin 4/ coscos lu <sup>0</sup> . (27)

The range of free films thickness on which this relation is satisfied is not attainable

experimentally (t < 1 nm); however, the angle θ0 may be found by extrapolation of the

relation θ(t). The values of carbon films surface energy estimated with the help of (27) from

data regarding surface energy of amorphous carbon films are unavailable, works [42–44]

compare obtained values of σu with surface energy data for different modifications of

carbon. Values of σu for carbon found by different authors quite well agree with the results

to high temperature and crystalline modifications of carbon. It should be noted that great

values of σu most likely cannot be taken as characteristics of amorphous carbon film

Variation of θ with thickness of free films as a result of theoretically predicted size

dependence of their surface energy is about an order of magnitude smaller than the change

in the contact angle due to deformation. Hence, the studies did not allow to trace the

experimental data for the In/C, Sn/C, and Pb/C system make about 120 ± 30 mJ/m<sup>2</sup>

[42–44], whereas large values of σu (500–2500 mJ/m<sup>2</sup>

because calculation of θ<sup>0</sup> even at σ<sup>u</sup> = 350 mJ/m<sup>2</sup>

and Pb, respectively) that exceed those measured experimentally.

surface energy of carbon films. As follows from (26) and (10), in the case when deformation

energy in comparison with surface ones may be neglected, the quantity σu is defined by the

The results of theoretical consideration for very thin films were used to evaluate the surface energy of carbon films. As follows from (26) and (10), in the case when deformation energy in comparison with surface ones may be neglected, the quantity σ*u* is defined by the expression

$$
\sigma\_u = \sigma\_l \sin \theta\_o \Big/ \mathbf{4} \left( \cos \theta\_0 - \cos \theta\_u \right). \tag{27}
$$

The range of free films thickness on which this relation is satisfied is not attainable experimentally (*t* < 1 nm); however, the angle θ0 may be found by extrapolation of the relation θ(*t*). The values of carbon films surface energy estimated with the help of (27) from experimental data for the In/C, Sn/C, and Pb/C system make about 120 ± 30 mJ/m2 . Since data regarding surface energy of amorphous carbon films are unavailable, works [42–44] compare obtained values of σ*u* with surface energy data for different modifications of carbon. Values of σ*u* for carbon found by different authors quite well agree with the results [42–44], whereas large values of σ*u* (500–2500 mJ/m2 ) reported in literature, as a rule, refer to high temperature and crystalline modifications of carbon. It should be noted that great values of σ*u* most likely cannot be taken as characteristics of amorphous carbon film because calculation of θ0 even at σ*u* = 350 mJ/m2 gives values (130, 140 и 135° for In, Sn, and Pb, respectively) that exceed those measured experimentally.

Variation of θ with thickness of free films as a result of theoretically predicted size dependence of their surface energy is about an order of magnitude smaller than the change in the contact angle due to deformation. Hence, the studies did not allow to trace the dependence of σ(*t*) for free carbon films, though they made it possible to determine the value of surface energy for them.

#### **3.4. Wetting in supercooled island condensates**

25

. Since

. With

.

– δ" (b) for tin droplets on

) reported in literature, as a rule, refer

gives values (130, 140 и 135° for In, Sn,

3

**Figure 10.** Micrographs of tin droplets on free carbon films with the thickness of 20 (a) и 10 (b) nm

the coordinates "*r*<sup>3</sup>

indium (c) on their thickness [42–44]

It follows from the same charts that lim

3

It follows from the same charts that <sup>r</sup> <sup>t</sup> <sup>r</sup> <sup>→</sup> <δ <sup>δ</sup> )(lim

= (140 ± 1)°, close to the experimental one of θ ≈ 138°

Figure 12. The relation δ(r) on the coordinates "r – δ" (a) and "r<sup>3</sup>

a free carbon film with the thickness of 10 nm [42–44]

**Figure 12.** The relation *δ*(r) on the coordinates "r – *δ*" (a) and "r<sup>3</sup>

[42–44], whereas large values of σu (500–2500 mJ/m<sup>2</sup>

because calculation of θ<sup>0</sup> even at σ<sup>u</sup> = 350 mJ/m<sup>2</sup>

and Pb, respectively) that exceed those measured experimentally.

δ < t on the coordinates "r

ness [42–44]

4,2)⋅10<sup>10</sup> N/m<sup>2</sup>

expression

thickness of 10 nm [42–44]

26

Experimental relations δ(*r*) for the Sn/C system at *t* = 10 nm (Figure 12) corroborate this conclusion. It is apparent from the chart that the linear dependence δ(*r*) is observed at δ < *t* on

this conclusion. It is apparent from the chart that the linear dependence δ(r) is observed at

Figure 11. Dependence of the angle of wetting of free carbon films with tin (a), lead (b), and

**Figure 11.** Dependence of the angle of wetting of free carbon films with tin (a), lead (b), and indium (c) on their thick‐

3

*r*→0 (*δ* /*r* <sup>3</sup>

too, gives the value of θ = (140 ± 1)°, close to the experimental one of θ ≈ 138°

Poisson's ratio is usually within the limits 1/4 < ν < 1/2, then from relation (24) one can

regard to this value from (25) one gets (*δ* /*r*)| *<sup>δ</sup>*>*<sup>t</sup>* ≈ 0.10 ± 0.01, which agrees well with the experiment. Theoretical prediction of the contact angle at *t* = 10 nm, too, gives the value of θ

agrees well with the experiment. Theoretical prediction of the contact angle at t = 10 nm,

.

The results of theoretical consideration for very thin films were used to evaluate the

( ) σ=σ <sup>θ</sup><sup>∞</sup> −θ <sup>θ</sup><sup>∞</sup> sin 4/ coscos lu <sup>0</sup> . (27)

The range of free films thickness on which this relation is satisfied is not attainable

experimentally (t < 1 nm); however, the angle θ0 may be found by extrapolation of the

relation θ(t). The values of carbon films surface energy estimated with the help of (27) from

data regarding surface energy of amorphous carbon films are unavailable, works [42–44]

compare obtained values of σu with surface energy data for different modifications of

carbon. Values of σu for carbon found by different authors quite well agree with the results

to high temperature and crystalline modifications of carbon. It should be noted that great

values of σu most likely cannot be taken as characteristics of amorphous carbon film

Variation of θ with thickness of free films as a result of theoretically predicted size

dependence of their surface energy is about an order of magnitude smaller than the change

in the contact angle due to deformation. Hence, the studies did not allow to trace the

experimental data for the In/C, Sn/C, and Pb/C system make about 120 ± 30 mJ/m<sup>2</sup>

surface energy of carbon films. As follows from (26) and (10), in the case when deformation

energy in comparison with surface ones may be neglected, the quantity σu is defined by the

. With regard to this value from (25) one gets ( ) <sup>t</sup> <sup>r</sup> >δ <sup>δ</sup> ≈ 0.10 ± 0.01, which

Poisson's ratio is usually within the limits 1/4 < ν < 1/2, then from relation (24) one can estimate Young's modulus for carbon film, which turns out to be equal to *E* ≈ (3,4–4,2)⋅1010 N/m2

estimate Young's modulus for carbon film, which turns out to be equal to E ≈ (3,4–

Experimental relations δ(r) for the Sn/C system at t = 10 nm (Figure 12) corroborate

— δ," and at δ > t – on the coordinates "r — δ."

Electron microscope examination of profiles of crystallized metal droplets (Figure 10)

revealed substantial difference in the shape of the interphase boundary droplet–substrate for

microparticles condensed on free films and films on a solid surface. The difference is that

when the film is thin enough it gets deformed by the droplet (Figure 10), while in particles

with film thickness (Figure 11). At t > 30 nm the angle θ approaches the constant value θ∞ that

corresponds to wetting of bulk material. Analysis of profiles of droplets on free films showed

that the film is deformed by the droplet, with the degree of deflection being a function of

elastically deformable carbon films [54], whose basic concepts were given earlier. As follows

from relations (24) and (25), at t = const the relation of maximum film deflection δ to the

droplet base radius r will be different for cases with prevailing deformation of bending (δ ~ r

The obtained results were interpreted in [42–44] within the framework of wetting of

Figure 10. Micrographs of tin droplets on free carbon films with the thickness of 20 (a) и 10 (b) nm

<sup>0</sup> = 7.5⋅10–6 nm–2 and ( ) <sup>t</sup> <sup>r</sup> >δ <sup>δ</sup> = 0.11. Since

– *δ*" (b) for tin droplets on a free carbon film with the

)| *<sup>δ</sup>*<*<sup>t</sup>* = 7.5⋅10–6 nm–2 and (*δ* /*r*)| *<sup>δ</sup>*>*<sup>t</sup>* = 0.11. Since

For the analyzed systems it was determined that at t < 30 nm the contact angle decreases

condensed on a solid surface, liquid–substrate interface remained flat.

thickness and becoming a factor at t < 10 nm.

at δ < t) and stretching (δ ~ r at δ > t).

192 Wetting and Wettability

— δ," and at δ > *t* – on the coordinates "*r* — δ."

It is known that above the melting temperature the surface energy σ<sup>l</sup> decreases linearly with increase of temperature. However, existing knowledge and experimental data on temperature dependence of surface energy of supercooled liquids are ambiguous [67]. According to [67] at significant supercooling values, one may expect inversion of the temperature dependence σ*l* (*T*).

The temperature dependence of the surface energy of metals (Ga, In, Sn, Bi, Pb) [68] has been studied only in the rage of small supercoolings down to 0.1*Ts*. Using containerless electrostatic levitation techniques [69–71] for a number of refractory metals supercoolings (0.12–0.18)*Ts* were reached and it was determined that the dependence σ*<sup>l</sup>* (*T*) is linear (*d*σ*<sup>l</sup>* /*dT<*0) in the supercooled region.

Measurement of surface energy of supercooled melts is hard to make because considerable supercoolings are normally obtained in microvolumes, and traditional methods to determine σl require large amount of melt [1, 40]. However, temperature dependence of surface energy on at *T* < *Ts* can be estimated by analyzing wetting of the solid substrate with supercooled droplets.

#### *3.4.1. Inversion of wetting temperature dependence in island films*

Contact pairs being island films of tin, indium, bismuth, and copper on amorphous carbon substrates and indium on aluminum substrate were investigated in [42, 43, 72]. The test samples were prepared by condensation in a vacuum of 5⋅10–6–2⋅10–8 mm Hg on the circular substrate with temperature gradient (200–900 K) set along it. As a result, condensation to equilibrium or supercooled phase with the formation of microdroplets occurred according to the condensation diagram [73–76]. The obtained samples were cooled to room temperature and then wetting contact angles on crystallized droplets condensed at different substrate temperatures were measured. Due to wetting hysteresis, which occurs even on an absolutely smooth and uniform surface because of deformation of the substrate in the region of triple contact [60], the droplet base radius remains constant during cooling. The contract angles were measured on electron microscope pictures of droplet profiles (Figure 13) and averaged for 10– 20 droplets. As long as condensation takes place on a substrate with temperature gradient, the relation θ(*T*) can be measured in single experiment on a wide range of temperatures with arbitrarily small temperature step.

**Figure 13.** Micrographs of tin particles condensed in a vacuum of 5⋅10-6 mm Hg at temperatures 400 K (a), 570 K (b), and 730 K (c) [72]

The results of measurement of wetting angles in the Sn/C and In/C systems [72] are presented in Figure 14a, b. The obtained dependencies are characterized by the maximum at tempera‐ tures 550 and 500 K for tin and indium, respectively. Below *Ts* the wetting angle gradually decreases with decrease of temperature. Decrease of θ for the investigated systems makes about 25° at maximum achieved supercoolings ∆*T*Sn = 160 K и ∆*T*In = 100 K. Better wetting is also observed above *Ts* at growing temperature, where for indium and tin θ decreases on the same temperature range: 550 < *T* < 650 K. Over 700 K the contact angle in the Sn/C system shows behavior typical for noninteracting systems consisting in small decrease θ with the growth of temperature. Here the relation θ(*T*) is close to linear with the slope coefficient *d*(cosθ)/*dT* ≈ 0.0001 K–1.

In the Bi/C system temperature dependence of wetting, similarly to the In/C and Sn/C systems considered earlier, is nonmonotonic and is characterized by considerable de‐ crease of the contact angle when approaching the temperature of maximum supercooling (Figure 14c). However, the maximum value of θ for bismuth is achieved at *T* = 430 K, that is, in supercooled state unlike tin and indium, for which the maximum θ(*T*) is above the melting temperature. The temperature range where the wetting angle decreases appears

gradient, the relation θ(T) can be measured in single experiment on a wide range of

Figure 13. Micrographs of tin particles condensed in a vacuum of 5⋅10-6 mm Hg at

presented in Figure 14a, b. The obtained dependencies are characterized by the maximum at

temperatures 550 and 500 K for tin and indium, respectively. Below T<sup>s</sup> the wetting angle

gradually decreases with decrease of temperature. Decrease of � for the investigated

systems makes about 25° at maximum achieved supercoolings �TSn = 160 K и

�TIn = 100 K. Better wetting is also observed above Ts at growing temperature, where for

indium and tin � decreases on the same temperature range: 550 < T < 650 K. Over 700 K

the contact angle in the Sn/C system shows behavior typical for noninteracting systems

The results of measurement of wetting angles in the Sn/C and In/C systems [72] are

temperatures with arbitrarily small temperature step.

temperatures 400 K (a), 570 K (b), и 730 K (c) [72]

*3.4.1. Inversion of wetting temperature dependence in island films*

arbitrarily small temperature step.

and 730 K (c) [72]

194 Wetting and Wettability

*d*(cosθ)/*dT* ≈ 0.0001 K–1.

Contact pairs being island films of tin, indium, bismuth, and copper on amorphous carbon substrates and indium on aluminum substrate were investigated in [42, 43, 72]. The test samples were prepared by condensation in a vacuum of 5⋅10–6–2⋅10–8 mm Hg on the circular substrate with temperature gradient (200–900 K) set along it. As a result, condensation to equilibrium or supercooled phase with the formation of microdroplets occurred according to the condensation diagram [73–76]. The obtained samples were cooled to room temperature and then wetting contact angles on crystallized droplets condensed at different substrate temperatures were measured. Due to wetting hysteresis, which occurs even on an absolutely smooth and uniform surface because of deformation of the substrate in the region of triple contact [60], the droplet base radius remains constant during cooling. The contract angles were measured on electron microscope pictures of droplet profiles (Figure 13) and averaged for 10– 20 droplets. As long as condensation takes place on a substrate with temperature gradient, the relation θ(*T*) can be measured in single experiment on a wide range of temperatures with

**Figure 13.** Micrographs of tin particles condensed in a vacuum of 5⋅10-6 mm Hg at temperatures 400 K (a), 570 K (b),

The results of measurement of wetting angles in the Sn/C and In/C systems [72] are presented in Figure 14a, b. The obtained dependencies are characterized by the maximum at tempera‐ tures 550 and 500 K for tin and indium, respectively. Below *Ts* the wetting angle gradually decreases with decrease of temperature. Decrease of θ for the investigated systems makes about 25° at maximum achieved supercoolings ∆*T*Sn = 160 K и ∆*T*In = 100 K. Better wetting is also observed above *Ts* at growing temperature, where for indium and tin θ decreases on the same temperature range: 550 < *T* < 650 K. Over 700 K the contact angle in the Sn/C system shows behavior typical for noninteracting systems consisting in small decrease θ with the growth of temperature. Here the relation θ(*T*) is close to linear with the slope coefficient

In the Bi/C system temperature dependence of wetting, similarly to the In/C and Sn/C systems considered earlier, is nonmonotonic and is characterized by considerable de‐ crease of the contact angle when approaching the temperature of maximum supercooling (Figure 14c). However, the maximum value of θ for bismuth is achieved at *T* = 430 K, that is, in supercooled state unlike tin and indium, for which the maximum θ(*T*) is above the melting temperature. The temperature range where the wetting angle decreases appears

Figure 14. Temperature dependencies of wetting for island condensates of metals on different substrates. On the left – Sn/C (a) (base substrate: – NaCl; – Al2O3; vacuum 5⋅10-6 mm **Figure 14.** Temperature dependencies of wetting for island condensates of metals on different substrates. On the left – Sn/C (a) (base substrate: O – NaCl; ● – Al2O3; vacuum 5 10-6 mm Hg) and In/C (b), on the right – Bi/C (c), and In/Al (d) [42, 43, 72]

quite narrow: 400 < *T* < 420 K. On these interval θ decreases by 25°, this corresponds to reduction of adhesion tension by 50%. Hg) and In/C (b), on the right – Bi/C (c), and In/Al (d) [42, 43, 72]

Nonmonotonic dependence of the contact angle on temperature is also a feature of In/Al system (Figure 14d). This is similar to the relation θ(*T*) in the Sn/C system, but is almost completely above the melting temperature for indium. For In/Al relatively low supercool‐ ings (∆*T/Ts ≈* 0.05) were received, which is generally typical for metal condensates on metal substrates [73, 74, 76]. Starting with the temperature *T* = 420 K (θ = 60°), the contact angle is growing with the growth of temperature, and at *T* = 490 K takes the maximum value of θ = 143°. It is followed by fast reduction of θ, and at *T* > 500 K the contact angle is constant with the value θ = 120°. Characteristically, at the melting temperature and below, in supercooled state, indium wets aluminum substrate. Transition from wetting to nonwet‐ ting, that is, the change of sign of adhesion tension, in the In/Al system is observed at *T* = 440 K.

28

For the Cu/C system wetting temperature dependence does not have any peculiarities: on the interval 1200 < *T* < 1300 K decrease of the contact angle is observed with growing temperature (*d*(cosθ)/*dT* ≈ 0.001 K–1). This, on the one hand, is similar to the behavior of θ(*T*) for the Bi/C system with the same values of relative supercoolings, and on the other the linear relation θ(*T*) is typical for contact systems with noninteracting components [1, 40].

Observed changes of the contact angle in the supercooled region, as noted in [42, 43, 72], is probably stipulated by abnormal behavior of either liquid metal surface energy or interface energy of the metal–carbon boundary. If σ*ul* is assumed to be constant or growing with decrease of temperature, then according to Young's equation experimental data for θ(*T*) is an evidence of sharp increase in liquid metal surface energy. Thus, for tin at *T* ≤ 400 K the variable σ*<sup>l</sup>* , found

30

residual atmosphere.

under assumption of constant adhesion tension, exceeds the relevant quantity for solid metal. Hence, crystallization of tin at *T* < 400 K will be accompanied by decreasing surface energy, which is not in agreement with existing theoretical models and experimental data. In this way, the assumption regarding constant let alone growing σ*ul* with increasing supercooling leads to a contradiction. Therefore, the data for wetting in supercooled stated most likely suggest significant decrease of interfacial energy of the supercooled droplet–substrate boundary with decreasing temperature. The relations σ*ul*(*T*), calculated using linear extrapolation of the data for surface energy temperature dependence of liquid tin and indium [68] to the supercooling region, are presented in Figure 15. alone growing �ul with increasing supercooling leads to a contradiction. Therefore, the data for wetting in supercooled stated most likely suggest significant decrease of interfacial energy of the supercooled droplet–substrate boundary with decreasing temperature. The relations σul(T), calculated using linear extrapolation of the data for surface energy temperature dependence of liquid tin and indium [68] to the supercooling region, are presented in Figure 15.

Figure 15. The plots of liquid phase surface energy [68] and interfacial energy of the droplet– substrate boundary against temperature for Sn/C (a) и In/C (b). **Figure 15.** The plots of liquid phase surface energy [68] and interfacial energy of the droplet–substrate boundary against temperature for Sn/C (a) and In/C (b).

Among the reasons causing such a significant decrease in interfacial energy works [42, 43, 72] cite adsorption of gaseous impurities, which value increases with decrease of temperature or inversion of the surface energy of metal in supercooled state. However, considering the fact that for a number of analyzed metals (In, Sn, Bi) inversion of wetting temperature dependence occurs within approximately the same temperature range, while in the Cu/C system at high temperature it was not found at all, one should probably consider the adsorption of impurities from residual gases that grows at such temperatures crucial and Among the reasons causing such a significant decrease in interfacial energy works [42, 43, 72] cite adsorption of gaseous impurities, which value increases with decrease of temperature or inversion of the surface energy of metal in supercooled state. However, considering the fact that for a number of analyzed metals (In, Sn, Bi) inversion of wetting temperature depend‐ ence occurs within approximately the same temperature range, while in the Cu/C system at high temperature it was not found at all, one should probably consider the adsorption of impurities from residual gases that grows at such temperatures crucial and causing decrease of interfacial energy on the carbon substrate boundary with increased supercooling, and hence, better wetting observed experimentally. The increase of temperature of the substrate above 500–600 K increases σ*u* of carbon film due to sharp reduction of absorption of gases on its surface, which results in better wetting.

#### causing decrease of interfacial energy on the carbon substrate boundary with increased *3.4.2. Influence of pressure of residual gases on wetting of carbon substrate with tin*

supercooling, and hence, better wetting observed experimentally. The increase of temperature of the substrate above 500–600 K increases �<sup>u</sup> of carbon film due to sharp reduction of absorption of gases on its surface, which results in better wetting. 2.4.2. Influence of pressure of residual gases on wetting of carbon substrate with tin The experimental relations θ(*T*) (Figure 14) may not be explained by linear change of surface energies of the contacting phases. In addition, one of the possible explanations of nonmonot‐ onous behavior of θ(*T*) is the influence of adsorbed gaseous impurities. For this reason, the works [42, 43, 77] investigated temperature dependencies of contact angles for island films of tin on carbon substrates, condensed under the controlled composition of the residual atmos‐ phere.

The experimental relations θ(T) (Figure 14) may not be explained by linear change of surface energies of the contacting phases. In addition, one of the possible explanations of The samples were prepared using the technique described earlier [72] at the pressure of residual gases of 10–7–10–9 mm Hg. A mass spectrometer was employed to control residual atmosphere, and its content was changed by leaking gas into the unit pumped to a pressure

nonmonotonous behavior of θ(T) is the influence of adsorbed gaseous impurities. For this

reason, the works [42, 43, 77] investigated temperature dependencies of contact angles for

island films of tin on carbon substrates, condensed under the controlled composition of the

residual gases of 10–7–10–9 mm Hg. A mass spectrometer was employed to control residual

The samples were prepared using the technique described earlier [72] at the pressure of

of 10–9 mm Hg. The wetting contact angles were measured on micrographs of particle profiles on rolled-up (Figure 16) or inclined (Figure 17) spots of carbon film (convolution and angular observation methods [41, 42]); the quantity θ for a fixed temperature was found by averaging the contact angle values for 10–20 microparticles.

under assumption of constant adhesion tension, exceeds the relevant quantity for solid metal. Hence, crystallization of tin at *T* < 400 K will be accompanied by decreasing surface energy, which is not in agreement with existing theoretical models and experimental data. In this way, the assumption regarding constant let alone growing σ*ul* with increasing supercooling leads to a contradiction. Therefore, the data for wetting in supercooled stated most likely suggest significant decrease of interfacial energy of the supercooled droplet–substrate boundary with decreasing temperature. The relations σ*ul*(*T*), calculated using linear extrapolation of the data for surface energy temperature dependence of liquid tin and indium [68] to the supercooling

alone growing �ul with increasing supercooling leads to a contradiction. Therefore, the data

for wetting in supercooled stated most likely suggest significant decrease of interfacial

energy of the supercooled droplet–substrate boundary with decreasing temperature. The

relations σul(T), calculated using linear extrapolation of the data for surface energy

temperature dependence of liquid tin and indium [68] to the supercooling region, are

Figure 15. The plots of liquid phase surface energy [68] and interfacial energy of the droplet–

**Figure 15.** The plots of liquid phase surface energy [68] and interfacial energy of the droplet–substrate boundary

Among the reasons causing such a significant decrease in interfacial energy works [42, 43, 72] cite adsorption of gaseous impurities, which value increases with decrease of temperature or inversion of the surface energy of metal in supercooled state. However, considering the fact that for a number of analyzed metals (In, Sn, Bi) inversion of wetting temperature depend‐ ence occurs within approximately the same temperature range, while in the Cu/C system at high temperature it was not found at all, one should probably consider the adsorption of impurities from residual gases that grows at such temperatures crucial and causing decrease of interfacial energy on the carbon substrate boundary with increased supercooling, and hence, better wetting observed experimentally. The increase of temperature of the substrate above 500–600 K increases σ*u* of carbon film due to sharp reduction of absorption of gases on its surface,

Among the reasons causing such a significant decrease in interfacial energy works [42,

43, 72] cite adsorption of gaseous impurities, which value increases with decrease of

temperature or inversion of the surface energy of metal in supercooled state. However,

considering the fact that for a number of analyzed metals (In, Sn, Bi) inversion of wetting

temperature dependence occurs within approximately the same temperature range, while in

the Cu/C system at high temperature it was not found at all, one should probably consider

the adsorption of impurities from residual gases that grows at such temperatures crucial and

causing decrease of interfacial energy on the carbon substrate boundary with increased

supercooling, and hence, better wetting observed experimentally. The increase of

The experimental relations θ(*T*) (Figure 14) may not be explained by linear change of surface energies of the contacting phases. In addition, one of the possible explanations of nonmonot‐ onous behavior of θ(*T*) is the influence of adsorbed gaseous impurities. For this reason, the works [42, 43, 77] investigated temperature dependencies of contact angles for island films of tin on carbon substrates, condensed under the controlled composition of the residual atmos‐

temperature of the substrate above 500–600 K increases �<sup>u</sup> of carbon film due to sharp

2.4.2. Influence of pressure of residual gases on wetting of carbon substrate with tin

The samples were prepared using the technique described earlier [72] at the pressure of residual gases of 10–7–10–9 mm Hg. A mass spectrometer was employed to control residual atmosphere, and its content was changed by leaking gas into the unit pumped to a pressure

surface energies of the contacting phases. In addition, one of the possible explanations of

nonmonotonous behavior of θ(T) is the influence of adsorbed gaseous impurities. For this

reason, the works [42, 43, 77] investigated temperature dependencies of contact angles for

island films of tin on carbon substrates, condensed under the controlled composition of the

residual gases of 10–7–10–9 mm Hg. A mass spectrometer was employed to control residual

The samples were prepared using the technique described earlier [72] at the pressure of

The experimental relations θ(T) (Figure 14) may not be explained by linear change of

reduction of absorption of gases on its surface, which results in better wetting.

*3.4.2. Influence of pressure of residual gases on wetting of carbon substrate with tin*

substrate boundary against temperature for Sn/C (a) и In/C (b).

region, are presented in Figure 15.

against temperature for Sn/C (a) and In/C (b).

which results in better wetting.

presented in Figure 15.

196 Wetting and Wettability

30

residual atmosphere.

phere.

**Figure 16.** Micrographs of crystallized tin droplets condensed in a vacuum of 2⋅10–8 mm Hg on carbon substrates at temperatures 350 K (a), 410 K (b), and 500 K (c) [42, 43, 77]

The results of measurement of θ(*T*) for tin droplets obtained under different vacuum are presented in Figure 18. Comparison of experimental data on wetting in tin films prepared in a vacuum of 10–6 и 10–8 mm Hg shows that they are different, firstly, by absence of a maximum in dependence θ(*T*) (pressure 10–8 mm Hg) and, secondly, by the fact that with better vacuum this dependence shifts to the region of smaller values of wetting angles (for pressure of 10–8 mm Hg this displacement makes 20–30°).

At substrate temperatures *T* > 500 K for films prepared in a vacuum of 10–8 mm Hg, relation θ(*T*) goes constant, and the contact angles become approximately equal to the angles θ for films produced at *p* = 10–5 mm Hg, but at temperatures above 650 K. This suggests that the maximum on the wetting temperature dependence for island condensates of tin, indium, and bismuth obtained in a vacuum of 10–5–10–6 mm Hg [72] is defined by the influence of gaseous impurities adsorbed from residual atmosphere, which respectively modify surface energies of the contacting phases. It is typical that the relation θ(*T*) for films condensed in a vacuum of 10–7 mm Hg assumes intermediate position between the values obtained for samples at *p* = 10–6 and 10–8 mm Hg.

It is worth noting that for a supercooled state of tin decrease of temperature in all cases leads to a decrease of the contact angles. At the pressure of residual gases of 10–8 mm Hg improve‐ ment of wetting gets quite significant and makes ∆θ ≈ 50°. Variation of wetting with temper‐ ature is well illustrated by micrographs of particle profiles (Figure 16) and inclined spots of film near the temperature of maximum supercooling (Figure 17). In this case, as could be seen from the chart (Figure 18, Curve 3) and micrographs (Figs. 16, 17), transition from nonwetting (θ > 90°, i.e., σ*ul* > σ*u*) to wetting (θ < 90°, σ*ul* < σ*u*) is observed in the region of deep supercoolings (at *T* < 350 K). Existence of such transition, which is essentially a change of sign of the adhesion tension σ*u*–σ*ul* directly corroborates the conclusion about significant decrease in interfacial energy of the droplet–substrate supercooling boundary with temperature, which is deter‐ mined by adsorption of impurities from residual gases growing with decrease of temperature [42, 43, 72]. The results in work [77] give reason to assume that nonmonotonous wetting hetero-ion pumping system.

32

(θ = 82°)

dependence in the Sn/C system is due to the interaction of methane group gases produced in the process of operation of the hetero-ion pumping system.

**Figure 17.** Micrographs of tin island film condensed in a vacuum of 2⋅10–8 mm Hg on a carbon substrate at the temper‐ ature of 315 K (θ = 82°) due to the interaction of methane group gases produced in the process of operation of the

Figure 17. Micrographs of tin island film condensed in a vacuum of 2⋅10–8 mm Hg on a Figure 18. Temperature dependence of the contact angle **Figure 18.** Temperature dependence of the contact angle of wetting of carbon substrates with tin islands prepared un‐ der different pressure of residual gases: 1 – 5⋅10–6 mm Hg [72], 2 – 3⋅10–7 mm Hg, and 3 – 2⋅10–8 mm Hg. [42, 43, 77]

carbon substrate at the temperature of 315 K of wetting of carbon substrates with tin islands prepared under different pressure of residual gases: 1 – 5⋅10–6 mm Hg [72], 2 – The analysis of the outlined results allows us to assume that the supercooled state of the metal itself is not the main cause of sharp improvement of wetting with decrease of temperature for fusible metals. This is also suggested by the fact that inversion of wetting temperature dependence is observed both above (Sn/C, In/C, In/Al) and below (Bi/C) of melting point, while for the Cu/C system there is no inversion at all. However, this conclusion may not be consid‐

mm

3⋅10–7 mm Hg, and 3 – 2⋅10–8

Hg. [42, 43, 77]

The analysis of the outlined results allows us to assume that the supercooled state of the

metal itself is not the main cause of sharp improvement of wetting with decrease of

temperature for fusible metals. This is also suggested by the fact that inversion of wetting

temperature dependence is observed both above (Sn/C, In/C, In/Al) and below (Bi/C) of

melting point, while for the Cu/C system there is no inversion at all. However, this

conclusion may not be considered final since for the Cu/C system the relation θ(T) was

studied at insignificant relative supercoolings (∆T/T<sup>s</sup> ≈ 0.12), and, probably, this is why

wetting inversion was not detected. In this way, data available now suggest the generality of

Figure 19. The plot of wetting angle against the radius of supercooled (1 – Т = 400 K, 2 – T = 400 K [72, 78]) and equilibrium (3 – Т = 520 K [9, 42–44]) tin microdroplets

typical for the contact systems investigated earlier [9, 42–44]. Since extrapolation of surface

wetting inversion, though they are not sufficient to give a definite answer to the question

33

ered final since for the Cu/C system the relation θ(*T*) was studied at insignificant relative supercoolings (∆*T/Ts ≈* 0.12), and, probably, this is why wetting inversion was not detected. In this way, data available now suggest the generality of wetting inversion, though they are not sufficient to give a definite answer to the question regarding its mechanism. Pb/Si) as a case study, wetting of amorphous neutral substrates with liquid metals is improving with decrease of the size of microdroplets [9, 42–44]. This effect is a result of decrease in surface energy of metal droplets σl themselves and droplet–substrate interfacial

regarding its mechanism.

#### *3.4.3. Size effect in wetting in supercooled droplets* energy and has been only investigated for temperatures above the melting point of the metal.

dependence in the Sn/C system is due to the interaction of methane group gases produced in

**Figure 17.** Micrographs of tin island film condensed in a vacuum of 2⋅10–8 mm Hg on a carbon substrate at the temper‐

Figure 18. Temperature

dependence of the contact angle of wetting of carbon substrates with tin islands prepared under different pressure of residual

**Figure 18.** Temperature dependence of the contact angle of wetting of carbon substrates with tin islands prepared un‐ der different pressure of residual gases: 1 – 5⋅10–6 mm Hg [72], 2 – 3⋅10–7 mm Hg, and 3 – 2⋅10–8 mm Hg. [42, 43, 77]

The analysis of the outlined results allows us to assume that the supercooled state of the metal itself is not the main cause of sharp improvement of wetting with decrease of temperature for fusible metals. This is also suggested by the fact that inversion of wetting temperature dependence is observed both above (Sn/C, In/C, In/Al) and below (Bi/C) of melting point, while for the Cu/C system there is no inversion at all. However, this conclusion may not be consid‐

gases: 1 – 5⋅10–6 mm Hg [72], 2 –

mm

3⋅10–7 mm Hg, and 3 – 2⋅10–8

Hg. [42, 43, 77]

The analysis of the outlined results allows us to assume that the supercooled state of the

metal itself is not the main cause of sharp improvement of wetting with decrease of

temperature for fusible metals. This is also suggested by the fact that inversion of wetting

temperature dependence is observed both above (Sn/C, In/C, In/Al) and below (Bi/C) of

melting point, while for the Cu/C system there is no inversion at all. However, this

conclusion may not be considered final since for the Cu/C system the relation θ(T) was

studied at insignificant relative supercoolings (∆T/T<sup>s</sup> ≈ 0.12), and, probably, this is why

wetting inversion was not detected. In this way, data available now suggest the generality of

the process of operation of the hetero-ion pumping system.

transition from nonwetting (θ > 90°, i.e., σul > σu) to wetting (θ < 90°, σul < σu) is observed

in the region of deep supercoolings (at T < 350 K). Existence of such transition, which is

essentially a change of sign of the adhesion tension σu–σul directly corroborates the

conclusion about significant decrease in interfacial energy of the droplet–substrate

supercooling boundary with temperature, which is determined by adsorption of impurities

from residual gases growing with decrease of temperature [42, 43, 72]. The results in work

[77] give reason to assume that nonmonotonous wetting dependence in the Sn/C system is

due to the interaction of methane group gases produced in the process of operation of the

ature of 315 K (θ = 82°)

198 Wetting and Wettability

hetero-ion pumping system.

Figure 17. Micrographs of tin island film

condensed in a vacuum of 2⋅10–8 mm Hg on a

carbon substrate at the temperature of 315 K

32

(θ = 82°)

As it has been shown earlier using the contact systems (Sn/C, In/C, Bi/C, Pb/C, Au/C, Pb/Si) as a case study, wetting of amorphous neutral substrates with liquid metals is improving with decrease of the size of microdroplets [9, 42–44]. This effect is a result of decrease in surface energy of metal droplets σ*<sup>l</sup>* themselves and droplet–substrate interfacial energy and has been only investigated for temperatures above the melting point of the metal. At the same time it is known that crystallization of small particles takes place at significant supercoolings [73–76], and for description of this process we must know both absolute values of the contact angles at relevant temperatures and their size dependence. At the same time it is known that crystallization of small particles takes place at significant supercoolings [73–76], and for description of this process we must know both absolute values of the contact angles at relevant temperatures and their size dependence. Such investigations for island tin films on amorphous carbon substrate were made in [72, 78]. The results of measurement of contact angles in the Sn/C system at temperatures 400 K and 315 K are presented in Figure 19, which shows that for supercooled droplets as

Such investigations for island tin films on amorphous carbon substrate were made in [72, 78]. The results of measurement of contact angles in the Sn/C system at temperatures 400 K and 315 K are presented in Figure 19, which shows that for supercooled droplets as well as for equilibrium ones (see Figure 6a) the contact angle decreases with decrease of droplets size. However, numerical values of the contact angles for droplets of equal size turn out to be different, and the relation θ(*R*) (*R* is the droplet radius) for supercooled droplets is displaced to the region of lower values of θ by quantity ∆θ ≈ 15° and 55° for 400 K and 315 K, respectively. well as for equilibrium ones (see Figure 6a) the contact angle decreases with decrease of droplets size. However, numerical values of the contact angles for droplets of equal size turn out to be different, and the relation θ(R) (R is the droplet radius) for supercooled droplets is displaced to the region of lower values of θ by quantity ∆θ ≈ 15° and 55° for 400 K and 315

K, respectively.

Comparison with known results regarding the size effect of wetting at T > Ts [9, 42–44] provides grounds to believe that the mechanism of the effect for metastable droplets (at T < **Figure 19.** The plot of wetting angle against the radius of supercooled (1 – Т = 315 K, 2 – T = 400 K [72, 78]) and equili‐ brium (3 – Т = 520 K [9, 42–44]) tin microdroplets

Ts) is the same as for equilibrium ones, that is, it is defined by the dependence of the droplet–substrate interfacial energy on the size the droplet itself. This is also supported by the fact that obtained dependencies θ(R) are linear in the coordinates "cosθ – 1/R," which is Comparison with known results regarding the size effect of wetting at *T > Ts* [9, 42–44] provides grounds to believe that the mechanism of the effect for metastable droplets (at *T < Ts*) is the same as for equilibrium ones, that is, it is defined by the dependence of the droplet–substrate interfacial energy on the size the droplet itself. This is also supported by the fact that obtained

dependencies θ(*R*) are linear in the coordinates "cosθ – 1/*R*," which is typical for the contact systems investigated earlier [9, 42–44]. Since extrapolation of surface energies to such signifi‐ cant supercoolings looks unjustified, it is not possible to numerically estimate size dependen‐ cies of surface and interface energies in the contact system. At the same time, the full similarity of relations θ(*R*) for equilibrium and supercooled particles offers grounds to argue that they are driven by the same laws.

#### **4. Conclusions**

The experimental data and their analysis outlined herein show that the application of island vacuum condensates to study surface energy and wetting allowed to obtain a number of general results of crucial importance for physics and chemistry of surface phenomena.

Quantitative data of surface energies of solid Au, Pb, and Bi nanoparticles and parameters that define size dependence of surface energy of small particles have been obtained from the investigations of evaporation processes in condensed films.

Options for measuring surface energy in the solid phase and its temperature dependence are discussed and are based on the data regarding the decrease of melting temperature of small metal particles. Temperature dependencies of surface energy for In, Sn, Bi, Pb, Al, Au, and Pt have been calculated on the basis of the preceding consideration. The significant reduction of surface energy for all metals studied when approaching melting temperature has been shown.

The detailed investigation and theoretical description of the size effect of wetting, which consists in the decrease of the wetting angle with the decrease of particles size, have been provided. Size dependencies of wetting angle in In/C, Sn/C, Bi/C, Pb/C, Pb/Si, and Au/C have been obtained for equilibrium and supercooled (Sn/C) liquid microdroplets. On the basis of these studies, size dependencies of interfacial energy of In/C, Sn/C, Bi/C, Pb/C, Au/C couples were obtained.

Experimental data and theoretical description of the effect of thickness of free carbon film on wetting angle have been obtained for In/C, Sn/C, and Pb/C couples. These studies enabled to determine the surface energy of thin carbon films, which makes σu = 120±30 mJ/m<sup>2</sup> .

Temperature dependencies of contact angle in In/C, Sn/C, Bi/C, In/Al, and Cu/C couples have been obtained for equilibrium and supercooled liquid microdroplets.

### **Author details**

Sergei Dukarov, Aleksandr Kryshtal\* and Vladimir Sukhov

\*Address all correspondence to: aleksandr.p.kryshtal@univer.kharkov.ua

V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

#### **References**

dependencies θ(*R*) are linear in the coordinates "cosθ – 1/*R*," which is typical for the contact systems investigated earlier [9, 42–44]. Since extrapolation of surface energies to such signifi‐ cant supercoolings looks unjustified, it is not possible to numerically estimate size dependen‐ cies of surface and interface energies in the contact system. At the same time, the full similarity of relations θ(*R*) for equilibrium and supercooled particles offers grounds to argue that they

The experimental data and their analysis outlined herein show that the application of island vacuum condensates to study surface energy and wetting allowed to obtain a number of general results of crucial importance for physics and chemistry of surface phenomena.

Quantitative data of surface energies of solid Au, Pb, and Bi nanoparticles and parameters that define size dependence of surface energy of small particles have been obtained from the

Options for measuring surface energy in the solid phase and its temperature dependence are discussed and are based on the data regarding the decrease of melting temperature of small metal particles. Temperature dependencies of surface energy for In, Sn, Bi, Pb, Al, Au, and Pt have been calculated on the basis of the preceding consideration. The significant reduction of surface energy for all metals studied when approaching melting temperature has been shown. The detailed investigation and theoretical description of the size effect of wetting, which consists in the decrease of the wetting angle with the decrease of particles size, have been provided. Size dependencies of wetting angle in In/C, Sn/C, Bi/C, Pb/C, Pb/Si, and Au/C have been obtained for equilibrium and supercooled (Sn/C) liquid microdroplets. On the basis of these studies, size dependencies of interfacial energy of In/C, Sn/C, Bi/C, Pb/C, Au/C couples

Experimental data and theoretical description of the effect of thickness of free carbon film on wetting angle have been obtained for In/C, Sn/C, and Pb/C couples. These studies enabled to

Temperature dependencies of contact angle in In/C, Sn/C, Bi/C, In/Al, and Cu/C couples have

and Vladimir Sukhov

.

determine the surface energy of thin carbon films, which makes σu = 120±30 mJ/m<sup>2</sup>

been obtained for equilibrium and supercooled liquid microdroplets.

\*Address all correspondence to: aleksandr.p.kryshtal@univer.kharkov.ua

V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

investigations of evaporation processes in condensed films.

are driven by the same laws.

**4. Conclusions**

200 Wetting and Wettability

were obtained.

**Author details**

Sergei Dukarov, Aleksandr Kryshtal\*


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204 Wetting and Wettability


## **Wettability of Nanostructured Surfaces**

L. Duta, A.C. Popescu, I. Zgura, N. Preda and I.N. Mihailescu

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60808

#### **Abstract**

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206 Wetting and Wettability

There are many studies in literature concerning contact angle measurements on different materials/substrates. It is documented that textiles can be coated with multifunctional materials in form of thin films or nanoparticles to acquire character‐ istics that can improve the protection and comfort of the wearer. The capacity of oxide nanostructures to inhibit fungal development and neutralize bacteria is a direct consequence of their wetting behavior [1–6]. Moreover, the radical modification of wetting behavior of nanostructures from hydrophilic to hydrophobic when changing the pulsed laser deposition (PLD) ambient will be thoroughly discussed.

When an implant is introduced inside the human body, its surface is first wetted by the physiological fluids. This further controls the proteins adsorption followed by the attachment of cells to the implant surface. Hence, surface wettability is considered an important criterion that dictates biocompatibility of the implant and could stand for a decisive factor for its long-term stability inside the human body.

In Section 1 of this chapter, the reader is briefly introduced to wetting phenomenon, and correlations between well-known Young, Cassie, and Wenzel approaches are made. Next, one of the most spread techniques to measure the wettability of surface, the contact angle measurement, is thoroughly explained and relevant examples are given.

Section 2 begins with a summarized table about previous works on synthesis of hydrophobic or hydrophilic nanostructures with a special focus on ZnO, SiOx, TiO2, and DLC materials. A short presentation of the advantages of their synthesis by PLD, sol-gel, thermal evaporation, solution based on chemical approaches, sputtering, and plasma enhanced chemical vapor deposition will be introduced.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Sections 3 includes a brief literature overview on results regarding synthesis by aforementioned techniques of different oxides (ZnO, TiO2, and SiOx) and DLC nanostructures onto textile (polyester, polyamide, cotton/polyester, and poly(lactic acid)) or metallic substrates for medical purposes.

The chapter ends with conclusions and references, which include books and review articles relevant to the topics.

**Keywords:** Wettability, contact angle measurements, oxide and diamond like car‐ bon nanostructures, textile functionalization, medical applications, pulsed laser deposition, sol-gel, combined radio frequency plasma enhanced chemical vapor deposition, magnetron sputtering

#### **1. Introduction**

Wetting is the ability of liquids to keep in contact with solid surfaces. It is a direct result of intermolecular interactions, which occur when two media (liquid and solid) are brought together. Wettability studies usually involve the measurements of contact angle (CA), which indicates the degree of wetting when a solid and liquid interact. A low CA (<90°) corresponds to high wettability, and the fluid will spread over a large area of the surface. A high CA (>90°) corresponds to low wettability, and the fluid will minimize contact with the surface and form a compact liquid droplet. CA>150° indicates minimal contact between the liquid droplet and the surface and corresponds to a superhydrophobic behavior.

In the case of a liquid droplet on an ideal solid surface (which is flat, rigid, perfectly smooth, chemically homogeneous, and has zero CA hysteresis), which forms a CA (*θ*), the general formula of the well-known Young's equation (which assumes a perfectly flat and rigid surface) [7] that describes the balance (Figure 1a) between the surface tension of the liquid/vapor *γ*SV and that of the liquid/vapor *γ*LV and the interfacial tension of the solid/liquid *γ*LS is as follows:

$$\cos \theta = \left(\chi\_{\rm SV} - \chi\_{\rm LS}\right) / \chi\_{\rm LV} \tag{1}$$

**Figure 1.** Wetting behavior of solid substrates: (a) Young, (b) Wenzel, (c) Cassie, and (d) intermediate state between Wenzel and Cassie regimes.

In reality, only a few solid surfaces are actually flat. The surface roughness is therefore one important parameter that should be taken into consideration when assessing the wetting behavior of a surface [8, 9]. This influence can prove significant for static and dynamic wetting.

Besides Young's theory, the Wenzel (Figure 1b) and Cassie (Figure 1c) regimes [9, 10], or an intermediate state between these two models (Figure 1d) [11], are generally used to correlate the roughness of the surface with the apparent CA of a liquid.

Several authors modeled the effect of surface roughness over CA [12–14]. The basic idea was to account for roughness through *r*, which is the ratio of the actual to projected area. Thus, *A*LS =*r* ⋅ *ALSapp* and *A*SV =*r* ⋅ *A*SVapp where *ALS* and ASV are the liquid-solid and solid-vapor areas, ALSapp and *A*SVapp are the liquid-solid and solid-vapor areas. In this case, Eq. (1) becomes

$$\cos \theta\_{\text{rough}} = r \cos \theta\_{\text{true}} \tag{2}$$

Due to surface roughness, for CA <90°, the apparent CA will decrease, while for CA>90°, its value will increase. This corresponds to the Wenzel case, as illustrated in Figure 1b, where the liquid completely fills the air pockets of the rough surface at the contact site. If the CA is large and the surface rough, the liquid may trap air. As a consequence, a composite surface effect will appear, as illustrated in Figure 1c.

In the Cassie model [15], it is presumed that in the grooves the air is trapped under the liquid droplet. This determines the appearance of a composite surface (Figure 1c). The chemical heterogeneity of a rough surface can be related, in this model, to the apparent CA, *θ*app, through the following formula:

$$
\cos\theta\_{\rm app} = f\_{\rm S}\cos\theta\_{\rm S} + f\_{\rm V}\cos\theta\_{\rm V} \tag{3}
$$

with *f*S and *f*V as the area fractions of the solid and vapor on the surface, respectively. Since *f* <sup>S</sup> + *f* <sup>V</sup> =1, *θ*S = *θ*, and *θ*V = 180°, Eq. (3) can be written as follows:

$$\cos \theta\_{\rm app} = -1 + f\_{\rm S} \left( \cos \theta\_{\rm true} + 1 \right) \tag{4}$$

where *θ*true is the CA on a smooth surface [15].

Sections 3 includes a brief literature overview on results regarding synthesis by aforementioned techniques of different oxides (ZnO, TiO2, and SiOx) and DLC nanostructures onto textile (polyester, polyamide, cotton/polyester, and poly(lactic

The chapter ends with conclusions and references, which include books and review

**Keywords:** Wettability, contact angle measurements, oxide and diamond like car‐ bon nanostructures, textile functionalization, medical applications, pulsed laser deposition, sol-gel, combined radio frequency plasma enhanced chemical vapor

Wetting is the ability of liquids to keep in contact with solid surfaces. It is a direct result of intermolecular interactions, which occur when two media (liquid and solid) are brought together. Wettability studies usually involve the measurements of contact angle (CA), which indicates the degree of wetting when a solid and liquid interact. A low CA (<90°) corresponds to high wettability, and the fluid will spread over a large area of the surface. A high CA (>90°) corresponds to low wettability, and the fluid will minimize contact with the surface and form a compact liquid droplet. CA>150° indicates minimal contact between the liquid droplet and

In the case of a liquid droplet on an ideal solid surface (which is flat, rigid, perfectly smooth, chemically homogeneous, and has zero CA hysteresis), which forms a CA (*θ*), the general formula of the well-known Young's equation (which assumes a perfectly flat and rigid surface) [7] that describes the balance (Figure 1a) between the surface tension of the liquid/vapor *γ*SV and that of the liquid/vapor *γ*LV and the interfacial tension of the solid/liquid *γ*LS is as follows:

> ( ) SV LS LV cosqg

 g

**Figure 1.** Wetting behavior of solid substrates: (a) Young, (b) Wenzel, (c) Cassie, and (d) intermediate state between

 g

= - / (1)

acid)) or metallic substrates for medical purposes.

the surface and corresponds to a superhydrophobic behavior.

articles relevant to the topics.

deposition, magnetron sputtering

**1. Introduction**

208 Wetting and Wettability

Wenzel and Cassie regimes.

From Eq. (4), it follows that in case of a true value of CA >90°, the surface roughness will determine an increase of CA's apparent value. In contradiction to Wenzel regime, in the Cassie mode, the CA value will increase even for CA values <90º due to the air pockets trapped under the liquid droplet [9]. It was shown that, when applying a physical deformation to a spherical droplet, a variation from the Cassie to Wenzel state can be achieved [16, 17] (Figure 1d). In some cases, a transition between these two modes can also occur [18–20]. Therefore, the droplet will fill the air pockets of the rough substrate resulting in a decrease of the apparent value of CA. In these cases, for the estimation of CA values, Eqs. (2) and (4) can be used before and after the transition, respectively. Taking into account these results, the following equation can be written [11]:

$$\cos \theta\_{\rm th} = \left(f\_{\rm S} - 1\right) / \left(r - f\_{\rm S}\right) \tag{5}$$

where *θ*th represents a threshold value between Wenzel and Cassie states.

#### **1.1. CA measurements of nanostructured surfaces**

Immediately after an implant is introduced inside the human body, the first events that occur are the wetting of the material by the physiological fluids, followed by attachment of cells to the implant surface [21]. In order to evaluate the wetting behavior of a system, plenty of quantitative (CA, imbibition, and forced displacement, and electrical resistivity wettability) and qualitative (imbibition rates, microscope examination, flotation, glass slide, relative permeability curves, permeability/saturation relationships, capillary pressure curves, capil‐ larimetric method, displacement capillary pressure, reservoir logs, nuclear magnetic reso‐ nance, and dye adsorption) methods have been developed [22]. Among these, CA measurement is probably the most adopted technique to investigate the average wettability of a surface [23]. Moreover, this type of investigation has been extensively applied to assess the wetting behavior of different nanostructured surfaces, used for various medical applica‐ tions. Some relevant literature examples limited to oxides (ZnO, TiO2, SiO*x*) and diamond-like carbon (DLC) structures are briefly summarized in Table 1.


**Table 1.** CA measurements of hydrophobic/hydrophilic ZnO, SiO*x*, TiO2, and DLC nanostructures used for medical applications.

CA can be classified into static or dynamic. Static CA is measured when liquid droplet is standing alone on the surface, without needle insertion, and the solid/liquid/air boundary is not moving. These measurements are used in quality control and research and product development. One can measure the dynamic CA when the solid/liquid/air boundary is moving. In this way, advancing and receding CA are measured. CA hysteresis, which represents the difference between these two angles, comes from surface chemical and topo‐ graphical heterogeneities, solution impurities absorbing on the surface, or swelling, rear‐ rangement or alteration of the surface by the solvent [41, 42].

The hydrophobic behavior of a surface is generally assessed by the apparent water CA, in static measurements. Moreover, when evaluating a surface repellency, one should take into consid‐ eration the sliding-down (which is evaluated by measuring the sliding angle, *α*, at which a liquid droplet begins to slide down an inclined plate) and rolling-off behaviors of liquid droplets [9]. Due to the CA hysteresis [43, 44], the liquid droplets do not slide off easily on a surface presenting a high value of static CA. Eq. (6) [43, 45] quantitatively describes the relationship between the hysteresis and the sliding angle:

$$
\log\left(\sin a\right) / \,\mathrm{w} = \mathbb{Y}\_{\mathrm{LV}}\left(\cos \theta\_{\mathrm{R}} - \cos \theta\_{\mathrm{A}}\right) \tag{6}
$$

where *θ*A and *θ*<sup>R</sup> are the advancing and receding CAs, respectively (Figure 2), *g* is the gravi‐ tational force, *m* is the mass, and *w* is the width of the droplet.

**Figure 2.** Illustration of the advancing and receding CAs.

th S ( )( ) <sup>S</sup> cos 1 /

Immediately after an implant is introduced inside the human body, the first events that occur are the wetting of the material by the physiological fluids, followed by attachment of cells to the implant surface [21]. In order to evaluate the wetting behavior of a system, plenty of quantitative (CA, imbibition, and forced displacement, and electrical resistivity wettability) and qualitative (imbibition rates, microscope examination, flotation, glass slide, relative permeability curves, permeability/saturation relationships, capillary pressure curves, capil‐ larimetric method, displacement capillary pressure, reservoir logs, nuclear magnetic reso‐ nance, and dye adsorption) methods have been developed [22]. Among these, CA measurement is probably the most adopted technique to investigate the average wettability of a surface [23]. Moreover, this type of investigation has been extensively applied to assess the wetting behavior of different nanostructured surfaces, used for various medical applica‐ tions. Some relevant literature examples limited to oxides (ZnO, TiO2, SiO*x*) and diamond-like

**Material Envisaged application Cited reference**

Temporary blood-contacting medical devices (cardiovascular and interventional

**Table 1.** CA measurements of hydrophobic/hydrophilic ZnO, SiO*x*, TiO2, and DLC nanostructures used for medical

Self-cleaning coatings and antifogging materials [24]

Antibacterial properties [25, 26] Environmental sensing [27] Micro/nanodevices [28]

Antibacterial properties [29] Cells migration on artificial surfaces [30] Bioactive properties [31] Superoleophobic surfaces [32]

Antibacterial properties [25] Microbial fuel cells and bioremediations [33] Blood-contacting biomaterials [34]

devices, artificial organs, pacemakers) [35, 36]

Resistance to microbial adhesion [40]

Resistance to corrosion [38] Antifogging [39]

Femoral head and the acetabulum hip joint components [37]

=- - *f rf* (5)

q

**1.1. CA measurements of nanostructured surfaces**

carbon (DLC) structures are briefly summarized in Table 1.

ZnO

210 Wetting and Wettability

SiO*<sup>x</sup>*

TiO2

DLC

applications.

where *θ*th represents a threshold value between Wenzel and Cassie states.

Advancing and receding CA represent the maximum and minimum values that can be measured on the surface for the static CA. Due to the increasing interest on smart materials (self-cleaning and superhydrophobic), the dynamic CAs and CA hysteresis are highly applied [46, 47]. For self-cleaning applications, it is important that sliding angles (angle of the substrate which has to be tilted in order to move the droplet) to present small values.

From Eq. (6), it can be inferred that a lower droplet mass and smaller difference between the advancing and receding CAs will result in a smaller angle α. It is worthy to note that the surface roughness has a strong effect on the CA hysteresis [43].

Zisman observed for the first time that cos*θ* increases linearly as the surface tension of the liquid (*γ*LV) decreases [48, 49]. He investigated the wettability of solids by determining the critical surface tension using CA. This method is used to determine the so-called critical surface free energy (*γc*), that differs from the solid surface free energy, *γ<sup>S</sup>* . According to his method, the value of *γC* of a solid is equal to the value of *γ*L of a liquid, which is in contact with the solid and for which the CA is zero. The value for *γ*c is determined from empirical investigations, consisting of the CA measurements for the studied solid and the liquids of a homologous series of organic compounds like *n*-alkanes. The values are plotted with the *y*-axis corresponding to the cosine values of the CA (θ) and the *x*-axis relating to the *γ*L values for the studied liquids. The values of cos*θ* for the liquids of a series of *n*-alkanes form approximately a straight line. Extrapolation of this line to the point of cos*θ* =1 yields the value of *γC* equal to *γ*L.

Despite the fact that *γC* is not the solid surface free energy, the critical surface tension has been shown to correlate with the known surface chemistry of several solids.

The Zisman method has been widely used to assess the critical surface tension *γC* of different organic films or low-energy solids deposited on high-energy solids (e.g., metals, glass [50, 51]). In this approach, by using series of homologous nonpolar liquids (e.g., *n*-alkanes), one can obtain the total solid surface energy of a nonpolar solid and the dispersion component (*γ<sup>S</sup> <sup>d</sup>* ) of the total surface energy of a polar solid. We note that, when using polar liquids on polar and nonpolar solids, one can obtain the deviation from rectilinear relation. Also by using polar liquids, the determination of any component of the solid free energy it is not possible.

### **2. Alternative deposition techniques employed for the synthesis of hydrophobic/hydrophilic nanostructured surfaces (thin films or nanoparticles)**

Many methods were employed to synthesize hydrophobic or hydrophilic nanostructures (thin films, TFs, and nanoparticles, NPs), and some literature examples limited to ZnO, SiO*x*, TiO2, and DLC are summarized in Table 2.

Among these methods, pulsed laser deposition (PLD), sol-gel (SG), thermal evaporation (TE), solution based on chemical approaches, sputtering, and plasma enhanced chemical vapor deposition (PECVD) will be briefly described hereinafter. They are easy to use, low cost, and yield high throughput of micro- and nanostructures.



critical surface tension using CA. This method is used to determine the so-called critical surface free energy (*γc*), that differs from the solid surface free energy, *γ<sup>S</sup>* . According to his method, the value of *γC* of a solid is equal to the value of *γ*L of a liquid, which is in contact with the solid and for which the CA is zero. The value for *γ*c is determined from empirical investigations, consisting of the CA measurements for the studied solid and the liquids of a homologous series of organic compounds like *n*-alkanes. The values are plotted with the *y*-axis corresponding to the cosine values of the CA (θ) and the *x*-axis relating to the *γ*L values for the studied liquids. The values of cos*θ* for the liquids of a series of *n*-alkanes form approximately a straight line.

Despite the fact that *γC* is not the solid surface free energy, the critical surface tension has been

The Zisman method has been widely used to assess the critical surface tension *γC* of different organic films or low-energy solids deposited on high-energy solids (e.g., metals, glass [50, 51]). In this approach, by using series of homologous nonpolar liquids (e.g., *n*-alkanes), one can obtain the total solid surface energy of a nonpolar solid and the dispersion component

*<sup>d</sup>* ) of the total surface energy of a polar solid. We note that, when using polar liquids on polar and nonpolar solids, one can obtain the deviation from rectilinear relation. Also by using polar liquids, the determination of any component of the solid free energy it is not possible.

**2. Alternative deposition techniques employed for the synthesis of hydrophobic/hydrophilic nanostructured surfaces (thin films or**

Many methods were employed to synthesize hydrophobic or hydrophilic nanostructures (thin films, TFs, and nanoparticles, NPs), and some literature examples limited to ZnO, SiO*x*, TiO2,

Among these methods, pulsed laser deposition (PLD), sol-gel (SG), thermal evaporation (TE), solution based on chemical approaches, sputtering, and plasma enhanced chemical vapor deposition (PECVD) will be briefly described hereinafter. They are easy to use, low cost, and

**Material Structure type Deposition technique Cited reference**

TFs SG [52] TFs Metal-organic vapor deposition [53] NPs Microwave plasma [54] TFs Magnetron sputtering, MS [55] TFs Electrodeposition [56]

Extrapolation of this line to the point of cos*θ* =1 yields the value of *γC* equal to *γ*L.

shown to correlate with the known surface chemistry of several solids.

(*γ<sup>S</sup>*

212 Wetting and Wettability

**nanoparticles)**

ZnO

and DLC are summarized in Table 2.

yield high throughput of micro- and nanostructures.

**Table 2.** Different deposition techniques used for the synthesis of hydrophobic/hydrophilic ZnO, SiO*x*, TiO2, and DLC nanostructures.

In the field of TFs growth, PLD has proven to be among the most versatile methods [59], with features superior to conventional deposition techniques (fast processing, reliability and low production cost). In this technique, high power laser energies are used. They are focused onto a target in order to evaporate its surface under vacuum or different gas ambient atmospheres. The vaporized material consisting of ions, atoms, or molecules is subsequently deposited onto a generally parallel substrate. Repeated laser pulses will result in the deposition of the TFs in form of a coating on the substrate.

One important advantage of PLD method is the stoichiometric transfer of different materials from the targets in the deposited films [59, 90, 91]. This represents a direct consequence of the high ablation rate that allows all elements to evaporate simultaneously [92]. This technique ensures an excellent adherence of the deposited structure to substrates, the high accuracy control of the growth rate (10–2–10–1 Å/pulse), the absence of contamination, the simplified growth of materials and combinations of materials of technological interest [93], and the good control of the final crystalline state of the coatings [59, 94].

The SG process is a synthesis route consisting in the preparation of a sol and successive gelation and solvent removal. This technique represents one of the simplest approaches to produce TFs. It presents many advantages in comparison with traditional deposition techniques, such as low working temperature, possibility to cover large surfaces, and high purity of the working conditions.

Compared to the physical route where harsh conditions such as high temperature or special equipment are usually required and consequently generating high costs, the solution based on chemical approaches [95–97] presents several advantages, including the simplicity in operation, low fabrication costs, low process temperatures (below 90 °C), and ambient pressure processing.

Thermal vacuum deposition or TE method is used to fabricate TFs under a high vacuum environment. In this method, an electron beam (e-beam) or resistive heating is usually used to evaporate the desired material inside the vacuum chamber, which then adheres to a substrate positioned above it.

The uniformity, high quality, and adherence of the deposited materials on large areas; the high deposition rate; and the versatility of sputtering techniques have made them attractive for the production of TFs [98–101]. In plasma sputtering deposition, plasma is used as the source of ions. These ions bombard a solid material, commonly known as the cathode or the target, with a typical kinetic energy of several hundreds electron volts. The ion bombardment produces the emission and acceleration of the secondary electrons, which play an important role in maintaining the plasma around the cathode [102]. The ionizing energetic electrons are confined close to the cathode allowing operation at high plasma densities and low pressures.

### **3. Synthesis of hydrophobic/hydrophilic oxides and DLC nanostructures onto textiles and metallic medical substrates**

A brief literature review on results regarding oxide (ZnO, TiO2, SiO*x*) and DLC nanostructures synthesized by PLD, SG, TE, solution based on chemical approaches, sputtering, and PECVD onto textile or metallic substrates will be presented hereinafter. Polyester, cotton/polyester, and poly(lactic acid) woven fabrics can be coated with multifunctional oxide materials in form of TFs or NPs to get properties that increase the protection and comfort of the wearer. When covering the surface with NPs, a new roughness is added leading thus to a dual-size surface roughness. Therefore, the study of wettability properties is a tool to test the surface function‐ alization [103]. It is well known that wetting of a surface by a liquid is affected by surface roughness [104]. In the case of textile materials, the roughness is related to the geometry which is very complex [105]. Due to the fiber topography, the construction of the yarn, and the construction of the fabric, polymer, natural, and synthetic fibers might be made from porous materials that can absorb water from the environment. Fabrics have thus pronounced texture, porosity, and also (oriented) in-plane capillarity along the threads [103]. CAs on textile substrates can be useful quantities for comparative measurements in order to characterize the effects of surface modification, especially if the textile is distinctly hydrophobic [105]. Titanium (Ti) stands for the most used metallic material for medical applications due to its unique properties such as biocompatibility, excellent mechanical properties in bulk, relative to the low mass density, and high corrosion and ductility resistance [106].

#### **3.1. ZnO**

The SG process is a synthesis route consisting in the preparation of a sol and successive gelation and solvent removal. This technique represents one of the simplest approaches to produce TFs. It presents many advantages in comparison with traditional deposition techniques, such as low working temperature, possibility to cover large surfaces, and high purity of the working

Compared to the physical route where harsh conditions such as high temperature or special equipment are usually required and consequently generating high costs, the solution based on chemical approaches [95–97] presents several advantages, including the simplicity in operation, low fabrication costs, low process temperatures (below 90 °C), and ambient pressure

Thermal vacuum deposition or TE method is used to fabricate TFs under a high vacuum environment. In this method, an electron beam (e-beam) or resistive heating is usually used to evaporate the desired material inside the vacuum chamber, which then adheres to a

The uniformity, high quality, and adherence of the deposited materials on large areas; the high deposition rate; and the versatility of sputtering techniques have made them attractive for the production of TFs [98–101]. In plasma sputtering deposition, plasma is used as the source of ions. These ions bombard a solid material, commonly known as the cathode or the target, with a typical kinetic energy of several hundreds electron volts. The ion bombardment produces the emission and acceleration of the secondary electrons, which play an important role in maintaining the plasma around the cathode [102]. The ionizing energetic electrons are confined

close to the cathode allowing operation at high plasma densities and low pressures.

**onto textiles and metallic medical substrates**

**3. Synthesis of hydrophobic/hydrophilic oxides and DLC nanostructures**

A brief literature review on results regarding oxide (ZnO, TiO2, SiO*x*) and DLC nanostructures synthesized by PLD, SG, TE, solution based on chemical approaches, sputtering, and PECVD onto textile or metallic substrates will be presented hereinafter. Polyester, cotton/polyester, and poly(lactic acid) woven fabrics can be coated with multifunctional oxide materials in form of TFs or NPs to get properties that increase the protection and comfort of the wearer. When covering the surface with NPs, a new roughness is added leading thus to a dual-size surface roughness. Therefore, the study of wettability properties is a tool to test the surface function‐ alization [103]. It is well known that wetting of a surface by a liquid is affected by surface roughness [104]. In the case of textile materials, the roughness is related to the geometry which is very complex [105]. Due to the fiber topography, the construction of the yarn, and the construction of the fabric, polymer, natural, and synthetic fibers might be made from porous materials that can absorb water from the environment. Fabrics have thus pronounced texture, porosity, and also (oriented) in-plane capillarity along the threads [103]. CAs on textile substrates can be useful quantities for comparative measurements in order to characterize the effects of surface modification, especially if the textile is distinctly hydrophobic [105]. Titanium

conditions.

214 Wetting and Wettability

processing.

substrate positioned above it.

ZnO is an *n*-type metal oxide semiconductor having a wide band gap, high electron mobility, and thermal conductivity. It mainly crystallizes in the wurtzite phase, being intrinsically polar, and thus exhibiting interesting piezoelectric properties. In addition, in the form of TFs or NPs, ZnO possesses promising antibacterial and antifungal, photocatalytic, electrical, electronic, and optical properties [107–115]. Recently, combinations ZnO-organic were tested for various applications requiring antimicrobial properties [116, 117]. Also, ZnO has probably the richest family of structures' morphology including rods, prisms, wires, whiskers, or tubes [95–97, 118– 123]. Moreover, morphology influences other properties such as wettability, another signifi‐ cant characteristic of ZnO covered surfaces bringing great advantages in a wide variety of applications in industry and daily life [124–127]. For example, wettability is critical in cosmetics and textile fields where ZnO can be used due to its biocompatibility property.

Hydrophobins are a class of small-size cysteine-rich proteins synthesized by filamentous fungi [128]. They form ~5–10 nm thick self-assembled monolayers [129] on different substrates, changing their surface wetting properties. Namely, hydrophobic surfaces can be turned to hydrophilic, while hydrophilic materials become hydrophobic [130] after immersion in an aqueous solution of hydrophobin. Textile materials can be finished with various functionali‐ zation agents, such as chitosan microcomposites [131] or nanocomposites [132, 133], medicinal herbs [134], nisin [135], polyhexamethylene biguanide [136], or PMMA nanocomposites [137], in order to obtain new surface properties like antimicrobial, hydrophobicity, resistance to laundering, or protection against decoloration. Due to exceptional surface properties and to the tuning opportunities, their use is envisaged in cosmetic industry, polymer emulsion synthesis, and biosensing [138].

#### *3.1.1. ZnO nanostructures synthesized by PLD onto cotton/polyester textiles*

Yang et al. [139] and Papadopoulou et al. [140] demonstrated that the structures synthesized by PLD can be controlled in terms of wetting behavior. Therefore, ZnO structures showed a hydrophilic behavior after exposure to UV and were converted to hydrophobic after thermal treatment or storage in complete darkness. In this respect, a one-step PLD procedure to obtain either hydrophobic or hydrophilic ZnO structures (TFs or NPs), without any complementary post-deposition treatments of the surface, was recently proposed [141]. Depending on the number of applied laser pulses, well-separated NPs (for 10 pulses) or compact TFs (for 100 pulses) were synthesized. By varying the ambient gas nature and pressure inside reaction chamber, hydrophilic or hydrophobic surfaces were obtained. The expected properties of the textiles coated with ZnO were evaluated at room temperature (RT) by static CA measurements.

The TFs deposited on textiles (Figure 3) in a flux of 13 Pa oxygen were highly transparent and had a hydrophilic behavior (Figure 3a), while those obtained in vacuum were opaque and showed a hydrophobic behavior (Figure 3b).

**Figure 3.** Textiles coated with ZnO nanostructures: (a) hydrophilic TF deposited in 13 Pa oxygen, (b) hydrophobic TF deposited in vacuum, and (c) hydrophobic NPs deposited in vacuum.

A CA of 157° (Figure 4) was measured, which qualified these films as superhydrophobic.

**Figure 4.** SEM micrograph of the superhydrophobic textile coated with ZnO TF in vacuum. Inset: water droplet in stat‐ ic mode with the CA of 157°.

In the case of NP samples, eye examination confirmed a hydrophilic behavior for the structures deposited in the oxygen flux and a hydrophobic one after deposition in vacuum (Figure 3c).

The macroscopic and microscopic observations have revealed a smoother surface in case of TFs deposited in vacuum characterized by a six times smaller RMS and negative values for surface skewness (*S*sk) and kurtosis (*S*ku) (Table 3).


**Table 3.** Amplitude parameters for ZnO TFs deposited in 13 Pa oxygen flux and vacuum. Reproduced from Popescu et al. [141].

Figure 5 shows two-dimensional AFM images of the TFs deposited in 13 Pa oxygen flux and vacuum. The grains (of ~140 nm) visualized by AFM (Figure 5b, d) were in fact consisting of very small crystallites (of ≤10 nm), as proved by the XRD patterns.

**Figure 3.** Textiles coated with ZnO nanostructures: (a) hydrophilic TF deposited in 13 Pa oxygen, (b) hydrophobic TF

**Figure 4.** SEM micrograph of the superhydrophobic textile coated with ZnO TF in vacuum. Inset: water droplet in stat‐

In the case of NP samples, eye examination confirmed a hydrophilic behavior for the structures deposited in the oxygen flux and a hydrophobic one after deposition in vacuum (Figure 3c).

The macroscopic and microscopic observations have revealed a smoother surface in case of TFs deposited in vacuum characterized by a six times smaller RMS and negative values for

RMS (nm) 36.817 36.793 6.578 5.796 *S*sk 0.404 0.421 –0.113 –0.0731 *S*ku 0.0274 0.24 –0.375 –0.357

**Table 3.** Amplitude parameters for ZnO TFs deposited in 13 Pa oxygen flux and vacuum. Reproduced from Popescu et

**Sample type/scanning area** TFs oxygen/10×10 µm2 TFs oxygen/2×2 µm2 TFs vacuum/10×10 µm2 TFs vacuum/2×2 µm2

A CA of 157° (Figure 4) was measured, which qualified these films as superhydrophobic.

deposited in vacuum, and (c) hydrophobic NPs deposited in vacuum.

surface skewness (*S*sk) and kurtosis (*S*ku) (Table 3).

ic mode with the CA of 157°.

216 Wetting and Wettability

**Amplitude parameters**

al. [141].

**Figure 5.** Two-dimensional AFM topography images of the TFs deposited in (a, c) a 13-Pa oxygen flux and (b, d) vac‐ uum at different scales: (a, b) (10 × 10) µm2 and (c, d) (2 × 2) µm2 . Reproduced from Popescu et al. [141].

In order to account for the significant difference observed in the wetting behavior of the TFs and NPs deposited in a flux of oxygen and in vacuum, a model was proposed for surface wetting. The numerous gaps between crystallites are filled with air acting as a support "buffer" for the water droplet, in contact to the surface in a few small nanometric sites only. Conversely, the TFs deposited in an oxygen flux (Figure 5a, c) consist of larger crystallites and a few intergranular pores only. Thus, the air "buffer" is rarefied, so the contact between the water droplet and the ZnO surface is extending over a larger area (Figure 6). The droplet weight prevails over the counter pressure exerted by the ZnO surface and eventually collapses under its own weight. Figure 6 shows schematically the water droplet in contact with ZnO structures synthesized in vacuum (Figure 6a) and oxygen flux (Figure 6b).

**Figure 6.** Schematic of the water droplet in contact with ZnO surface deposited in (a) vacuum and (b) 13 Pa oxygen flux. Reproduced from Popescu et al. [141].

The NP depositions in vacuum consist of a large number of small crystallites, which include a huge amount of vapor pockets. Their action cumulates with the effect of the air, which is present in the space between NPs to more efficiently support the droplet weight. This model is in accordance with other studies on hydrophobic plant leaf surfaces [142]. Accordingly, the largest contact area between the water droplet and the leaf surface corresponds to flat and microstructured surfaces but is generated in case of nanostructures as an effect of vapor pockets entrapment.

The electric charging of the surface should be considered when explaining the affinity or repellency to water of ZnO structures. XRD investigations demonstrated that the ambience in the interaction chamber also showed the combinations between Zn and O atoms in the crystalline lattice [141]. In case of structures deposited in vacuum, there is a mix in each crystalline plane of positive and negative charges. One should note that the water droplet is neutral from the electrical point of view. Accordingly, the deposited structures do not interact electrically with the water droplet. Oppositely, the structures deposited in an oxygen flux have only one type of atoms per plane that induce a positive (Zn) or negative (O) charging of surface [141]. The synthesized structures interact electrically with the droplet to reach the neutral status, thus attracting the water bubble toward the ZnO surface causing supplementary stress that contributes to the collapse of the bubble.

In a parallel study, the capacity of these oxide nanostructures to completely inhibit fungal development and neutralize bacteria was found to be a direct consequence of their wetting behavior [1-6].

The intercalation of a hydrophobin nanolayer between substrate and ZnO film, which can boost the oxide efficiency against microorganisms with a higher natural resistance, was recently studied and an explanation of the observed phenomena was proposed [143]. In case of ZnO TFs deposited on bare textiles, the adhesion is governed by physical mechanisms only (as e.g., mechanical or dispersion adhesion [144]), while in case of a buffer layer of hydrophobin interposed between textile and ZnO, chemical bonding occurs, the fastening between the ZnO and the textile substrate becoming much stronger. When used alone, the hydrophobin had no effect on both *Candida albicans* colonies and six strains of filamentous fungi. In case of simple finishing with ZnO, the reduction rate was of 50% and 70% of the colonies in 24 h (Figure 7a, b).

**Figure 7.** Percentage and logarithmic reduction of (a) *C. albicans* population and (b) mold mix inoculum after 24 h culti‐ vation on untreated and ZnO treated textiles. Reproduced from Popescu et al. [143].

In order to improve ZnO efficiency against resistant fungi, the oxygen concentration on films' surface was increased by covering the textile fibers with hydrophobin and then adding an upper layer of ZnO. As an effect, the orientation and shape of ZnO crystallites were changed, the (001) film texturing becoming more pronounced and nanocrystallites elongated, with more polar planes (001) parallel to the surface (Figure 8a). Depending on the orientation of the *c*axis, these planes may contain oxygen atoms only (Figure 8b). The ZnO film deposited on hydrophobin proved in this case 100% efficient in reducing colonies of both *C. albicans* and a mold mix of filamentous fungi (Figure 7a, b). This significant enhancement was attributed to the higher texturing of the oxide film when growing on hydrophobin interlayer, resulting in an increased presence of oxygen species on surface.

The NP depositions in vacuum consist of a large number of small crystallites, which include a huge amount of vapor pockets. Their action cumulates with the effect of the air, which is present in the space between NPs to more efficiently support the droplet weight. This model is in accordance with other studies on hydrophobic plant leaf surfaces [142]. Accordingly, the largest contact area between the water droplet and the leaf surface corresponds to flat and microstructured surfaces but is generated in case of nanostructures as an effect of vapor

The electric charging of the surface should be considered when explaining the affinity or repellency to water of ZnO structures. XRD investigations demonstrated that the ambience in the interaction chamber also showed the combinations between Zn and O atoms in the crystalline lattice [141]. In case of structures deposited in vacuum, there is a mix in each crystalline plane of positive and negative charges. One should note that the water droplet is neutral from the electrical point of view. Accordingly, the deposited structures do not interact electrically with the water droplet. Oppositely, the structures deposited in an oxygen flux have only one type of atoms per plane that induce a positive (Zn) or negative (O) charging of surface [141]. The synthesized structures interact electrically with the droplet to reach the neutral status, thus attracting the water bubble toward the ZnO surface causing supplementary stress

In a parallel study, the capacity of these oxide nanostructures to completely inhibit fungal development and neutralize bacteria was found to be a direct consequence of their wetting

The intercalation of a hydrophobin nanolayer between substrate and ZnO film, which can boost the oxide efficiency against microorganisms with a higher natural resistance, was recently studied and an explanation of the observed phenomena was proposed [143]. In case of ZnO TFs deposited on bare textiles, the adhesion is governed by physical mechanisms only (as e.g., mechanical or dispersion adhesion [144]), while in case of a buffer layer of hydrophobin interposed between textile and ZnO, chemical bonding occurs, the fastening between the ZnO and the textile substrate becoming much stronger. When used alone, the hydrophobin had no effect on both *Candida albicans* colonies and six strains of filamentous fungi. In case of simple finishing with ZnO, the reduction rate was of 50% and 70% of the colonies in 24 h (Figure 7a, b).

**Figure 7.** Percentage and logarithmic reduction of (a) *C. albicans* population and (b) mold mix inoculum after 24 h culti‐

vation on untreated and ZnO treated textiles. Reproduced from Popescu et al. [143].

pockets entrapment.

218 Wetting and Wettability

behavior [1-6].

that contributes to the collapse of the bubble.

**Figure 8.** XRD patterns of ZnO TFs (a); the orientation of the (001) ZnO crystallites grown on hydrophobin, resulting in outer termination either in O or in Zn atoms only (b). Reproduced from Popescu et al. [143].

ZnO is recognized to possess antibacterial and antifungal properties. Nair et al. [109] assessed the microbiological activity of ZnO against a mold mix of microbes and associated the high reduction ratio to the generation of surface oxygen species. Sawai et al. [110] and Premanathan et al. [111] suggested that these oxide species form in wet media hydroxyl radicals and hydrogen peroxide. As known, the hydroxyl radical is the most reactive one, able to interact with almost every type of molecule of the living cells of bacteria and fungi, causing irreversible damage to cellular components and eventual apoptosis. Applerot et al. [112] advanced a mechanism for the reactive oxygen species formation on ZnO surface. The oxygen atoms present on surface interact with water molecules, forming OH‒ radicals. A chain reaction occurs, resulting in exponential multiplication of these radicals on surface.

We note that no negative side effects of hydrophobins when in contact with human tissue were reported [145], and to the benefit of biomedical applications, they were able to form, in specific cases, resistant monolayers with antimicrobial activity [146]. Moreover, the proposed antimi‐ crobial finishing procedure of fabrics with a conjunction of a thin layer of hydrophobin and a ZnO layer can find applications in the medical field, where solutions are constantly required for elimination of microbial contamination, thus reducing the risks of infections during surgery.

#### *3.1.2. ZnO nanostructures synthesized by solution based on chemical approaches onto solid (glass) substrates*

In the synthesis process of ZnO nanostructures using solution based on chemical approaches, a zinc salt and a basic compound are brought together. The involved chemical reactions can be described as follows:

**i.** Using a weak base ((CH2)6N4)

$$\begin{aligned} \text{Zn}(\text{NO}\_3\text{})\_2 &\rightarrow \text{Zn}^{2+} + 2\text{NO}\_3^- \\ \text{(CH}\_2\text{)}\_6\text{N}\_4 + 6\text{H}\_2\text{O} &\rightarrow 6\text{HCHO} + 4\text{NH}\_3 \\ \text{NH}\_3 + \text{H}\_2\text{O} &\rightarrow \text{NH}\_4^+ + \text{HO}^- \\ \text{Zn}^{2+} + 3\text{NH}\_4^+ &\rightarrow \left[\text{Zn}\left(\text{NH}\_3\right)\_4\right]^{2+} \\ \left[\text{Zn}\left(\text{NH}\_3\right)\_4\right]^{2+} &\text{HO}^- \rightarrow \text{Zn}\left(\text{OH}\right)\_2 + 4\text{NH}\_3 \\ \text{Zn}\left(\text{OH}\right)\_2 &\rightarrow \text{ZnO}\downarrow + \text{H}\_2\text{O} \end{aligned}$$

**ii.** Using a strong base (NaOH)

$$\begin{aligned} \text{Zn}(\text{NO}\_3\text{}\_2)\_2 &\rightarrow \text{Zn}^{2+} + 2\text{NO}\_3^-\\ \text{Zn}^{2+} + 2\text{HO}^- &\rightarrow \text{Zn(OH)}\_2\\ \text{Zn(OH)}\_2 + 2\text{HO}^- &\rightarrow \left[\text{Zn(OH)}\_4\right]^{2-}\\ \left[\text{Zn(OH)}\_4\right]^{2-} &\rightarrow \text{ZnO}\downarrow + 2\text{HO}^- + \text{H}\_2\text{O} \end{aligned}$$

**iii.** Using a reducing agent ((CH3)2NHBH3) [147]

$$\begin{aligned} \text{Zn}(\text{NO}\_3\text{})\_2 &\rightarrow \text{Zn}^{2+} + 2\text{NO}\_3^-\\ \text{(CH}\_3\text{)}\_2\text{NHBH}\_3 + 2\text{H}\_2\text{O} &\rightarrow \text{HBO}\_2 + \text{(CH}\_3\text{)}\_2\text{NH}\_2^+ + 5\text{H}^+ + 6\text{e}^-\\ \text{NO}\_3^- + \text{H}\_2\text{O} + 2\text{e}^- &\rightarrow \text{NO}\_2^- + 2\text{HO}^-\\ \text{Zn}^{2+} + 2\text{HO}^- &\rightarrow \text{Zn}(\text{OH})\_2\\ \text{Zn}(\text{OH})\_2 &\rightarrow \text{ZnO} \downarrow + \text{H}\_2\text{O} \end{aligned}$$

with almost every type of molecule of the living cells of bacteria and fungi, causing irreversible damage to cellular components and eventual apoptosis. Applerot et al. [112] advanced a mechanism for the reactive oxygen species formation on ZnO surface. The oxygen atoms present on surface interact with water molecules, forming OH‒ radicals. A chain reaction

We note that no negative side effects of hydrophobins when in contact with human tissue were reported [145], and to the benefit of biomedical applications, they were able to form, in specific cases, resistant monolayers with antimicrobial activity [146]. Moreover, the proposed antimi‐ crobial finishing procedure of fabrics with a conjunction of a thin layer of hydrophobin and a ZnO layer can find applications in the medical field, where solutions are constantly required for elimination of microbial contamination, thus reducing the risks of infections during

*3.1.2. ZnO nanostructures synthesized by solution based on chemical approaches onto solid*

In the synthesis process of ZnO nanostructures using solution based on chemical approaches, a zinc salt and a basic compound are brought together. The involved chemical reactions can

2+ –

24 2 3 6 + –

CH N + 6H O 6HCHO + 4NH

®

( )

é ù ë û

3 3 4 2

( ) ( )

Zn NH + HO Zn OH + 4NH

®

( )

2 4 2– – 2 4

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Zn OH ZnO 2HO + H O

2 2– –

é ù ë û

2+ –

2 2

( ) ( )

Zn OH + 2HO Zn OH

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<sup>é</sup> <sup>ù</sup> <sup>+</sup> ë û ¯

3 3 2

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Zn OH ZnO H O

Zn NO Zn + 2NO Zn + 2HO Zn OH

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3 3 2

2+ 2+ <sup>+</sup> 4 3 4 2+ –

32 4

NH + H O NH + HO Zn + 3NH Zn NH

®

®

Zn NO Zn + 2NO

®

occurs, resulting in exponential multiplication of these radicals on surface.

surgery.

220 Wetting and Wettability

*(glass) substrates*

be described as follows:

**i.** Using a weak base ((CH2)6N4)

**ii.** Using a strong base (NaOH)

( )

( )

( )

2+ –

( )

**iii.** Using a reducing agent ((CH3)2NHBH3) [147]

é ù ë û

( )

The ZnO structures were examined by XRD (Figure 9). The diffraction peaks observed at 2*θ* = (31.8°, 34.5°, 36.3°, 47.5°, 56.6°, 63.0°, 66.4°, 68.0°, and 69.1°) are characteristic to ZnO hexagonal wurtzite phase (JCPDS file no. 36-1451), with corresponding Miller indexes at (100), (002), (101), (102), (110), (103), (200), (112), and (201). The strong and sharp diffraction patterns suggest that the as-obtained structures are well crystallized.

**Figure 9.** XRD patterns of ZnO samples synthesized in the presence of (a) (CH2)6N4, (b) NaOH, and (c) (CH3)2NHBH3.

SEM images of the samples (Figure 10) revealed the following morphologies for the ZnO micro/ nanostructured TFs: rods (4.5 µm in length and 330 nm in diameter; Figure 10a, b), flowers (1– 2 µm in dimension; Figure 10c, d), and hexagonal prisms (400 nm in length and 200 nm in diameter; Figure 10e, f). Insets to Figure 10 show the influence of the ZnO surface morphology on wetting behavior. The corresponding CA values of the ZnO samples are 164.8° (rods), 94.3° (flowers), and 79.4° (prisms). An explanation for the different values of CA can be related to the numerous gaps between the ZnO structures filled with air. For this reason, the film containing a higher volume of air trapped between the ZnO structures at the solid/water interface has a superhydrophobic behavior. The CA results were confirmed by AFM meas‐ urements (Figure 11). The RMS values were as follows: 390 nm (rods), 120 nm (flowers), and 50 nm (prisms).

Due to their morphology, the ZnO structures present different degrees of compactness, trapping more or less air in-between. In this way, the CA value is linked to the RMS value of the sample.

**Figure 10.** SEM images, at different magnification, of the ZnO samples synthesized in the presence of (a, b) (CH2)6N4, (c, d) NaOH, and (e, f) (CH3)2NHBH3. Insets: optical photographs of the water droplets shape on the ZnO surfaces with the corresponding CA values.

**Figure 11.** AFM images of the ZnO samples synthesized in the presence of (a) NaOH and (b) (CH3)2NHBH3.

#### **3.2. TiO2**

Titanium dioxide (TiO2) is a transition metal oxide with UV absorbing properties with many technological applications [148, 149]. High photocatalytic efficiency, great stability, and low cost of production are in favor of TiO2's photocatalytic properties [149]. In addition to bulk applications, TiO2 TFs were obtained for UV blocking, antibacterial or/and photocatalytic properties [149].


#### *3.2.1. TiO2 structures synthesized by SG and sputtering onto textile substrates*

Some properties of the substrates used in the experiments are summarized in Table 4.

**Table 4.** Characteristics of different textiles functionalized with TiO2.

**Figure 10.** SEM images, at different magnification, of the ZnO samples synthesized in the presence of (a, b) (CH2)6N4, (c, d) NaOH, and (e, f) (CH3)2NHBH3. Insets: optical photographs of the water droplets shape on the ZnO surfaces with

**Figure 11.** AFM images of the ZnO samples synthesized in the presence of (a) NaOH and (b) (CH3)2NHBH3.

Titanium dioxide (TiO2) is a transition metal oxide with UV absorbing properties with many technological applications [148, 149]. High photocatalytic efficiency, great stability, and low cost of production are in favor of TiO2's photocatalytic properties [149]. In addition to bulk applications, TiO2 TFs were obtained for UV blocking, antibacterial or/and photocatalytic

the corresponding CA values.

222 Wetting and Wettability

**3.2. TiO2**

properties [149].

XRD and SEM investigations [103] indicated, for both deposition techniques, that TiO2 NPs were amorphous. Sputtered layers consisted of aggregates randomly distributed on substrate, while the SG layers showed a uniform distribution of NPs, with a mosaic-like structure. SEM images (Figure 12) suggest the formation of NPs, which are not singularly distinguishable. The sputtered layers consist of NP aggregates (in coalescence) with less than 20 nm diameter, randomly scattered on substrate. In the case of the SG layer, there are bridge-aggregated NPs leading both to a mosaic-like structure and to cracks and interfiber bonds [150].

**Figure 12.** SEM images of TiO2 samples deposited on P2 substrates by (a) SG and (b) sputtering.

A highly polar liquid–water was recommended [151] as testing liquid in CA measure‐ ments, for estimating the wettability of polar solids as polyester materials. The water repellency was thus regarded as indicating the performances of the coated layers and was evaluated by measuring static (equilibrium) CAs at RT [152]. In order to have a general idea of the samples' wetting behavior, different measurement points on each sample were thus considered (Figure 13).

**Figure 13.** Water droplets on TiO2 deposited on P2 samples by (a) SG and (b) sputtering.


\* *θ*0 = 84° (for raw), 89.4° (for SG), and 62.1° (for sputtered) samples.

**Table 5.** Water CA values measured onto different investigated surfaces.

From Table 5, one can see that the CAs increase more by fabric modification (after Titania deposition). CAs were influenced by air, water droplet, and surface of fabric, which formed a nanorough substrate. One sample (P28) is hydrophilic meaning that water passes through it; this sample has voids large enough, and the margins become hydrophilic by deposition of hydrophilic particles. The behavior might be approximated by the Cassie–Baxter equation:

$$
\cos \theta\_c = f \cos \theta\_0 - (1 - f) \tag{7}
$$

Here, *θ*C is the composite CA formed on the treated fabric and *θ*0 is the CA formed on untreated fabric [153]. The parameter *f* represents the fraction of the surface in contact with the water droplet. Knowing the corresponding CAs, its values can be calculated for each raw-treated pair of samples, using the following equation:

$$f = (1 + \cos \theta\_{\circ}) / (1 + \cos \theta\_{\circ}) \tag{8}$$

These values are summarized in Table 5. However, it seems that Cassie–Baxter equation (or Wenzel equation) should be applied to superhydrophobic surfaces with caution [154]. TiO2 can be used to obtain hydrophobic surfaces by producing artificial roughness via micro structuring [155].

#### **3.3. SiO***<sup>x</sup>*

idea of the samples' wetting behavior, different measurement points on each sample were

**Figure 13.** Water droplets on TiO2 deposited on P2 samples by (a) SG and (b) sputtering.

\* *θ*0 = 84° (for raw), 89.4° (for SG), and 62.1° (for sputtered) samples.

**Table 5.** Water CA values measured onto different investigated surfaces.

The mean CA values of the raw or coated samples are summarized in Table 5.

**Sample code CA (°)** *<sup>f</sup>* **<sup>=</sup> 1 + cos***θ***<sup>c</sup>**

P2 136.9 0.244 P3 138.1 0.231 P28 152.1 0.105 P30 124.8 0.389 PLA 129.6 0.328 TiO2 SG/P2 169.3 0.017 TiO2 SG/P3 169.7 0.016 TiO2 SG/P28 152.7 0.110 TiO2 SG/P30 158.9 0.067 TiO2 SG/PLA 140.6 0.225 TiO2 SP4/P2 133.8 0.209 TiO2 SP4/P3 166.0 0.020 TiO2 SP4/P28 Hydrophilic 0.681 TiO2 SP4/P30 155.8 0.059 TiO2 SP4/PLA 150.3 0.089

**1 + cos***θ***<sup>0</sup>**

 **\***

thus considered (Figure 13).

224 Wetting and Wettability

Silicon oxide was deposited onto polymeric substrates as a viable alternative to metallic depositions used for packing materials due to their transparency, recyclability, microwave use, and impressive barrier properties [156], to produce textiles with hydrophobic properties [157]. In addition, silica NPs immobilized on textiles can lead to flame retardant properties [158]. SGdeposited layer can be compared to the one deposited in vacuum at low angle because in both cases the deposit is awaited (super) hydrophilization evidence since SiO2 brings its OH groups which print to the media hydrophilic properties. However, due to the columnary nanostruc‐ tured relief of deposited layer, it was expected that the roughness of the textile surface would be increased. In addition, information was acquired on vacuum deposition at small angle [159– 162]. Thus, we preferred this technique for a SiO*x* deposition onto textile materials [163].

*3.3.1. SiOx structures synthesized by thermal evaporation at small angles onto polyester (P), polyamide (PA), poly(lactic acid) (PLA), and natural cellulosic hemp (H) substrates*

The differences between the investigated textiles [163] are summarized in Table 6.


**Table 6.** Different functionalized textiles and their corresponding static CA values.

The XRD diffractograms pointed to an amorphous phase of the SiO*x* deposited layers [163].

SEM morphologies of SiO*x* particles synthesized on fabrics are presented in Figure 14. The raw material images showed defects like kink bands, dislocations, nodes, and slip planes, which are common characteristics of hemp materials [164]. SEM images of synthesized samples showed that SiO*x* particles were grown on the fiber surfaces in a continuous and noncolumnar layer (Figure 14). Apparently, each individual fiber of samples looks uniformly covered by an amorphous layer [163].

**Figure 14.** SEM images of SiOx layers deposited on (a, a′) P2 and (b, b′) H substrates, at two different magnifications.

The wettability properties were evaluated by measuring static (equilibrium) CAs. The measurements were carried out at RT [152]. The images were processed using specific programs to fit the profile with the Young–Laplace equation in order to obtain the value of static CA.

**Sample code Textile 2D element/thread Nature of the fibers Color**

**Table 6.** Different functionalized textiles and their corresponding static CA values.

Polyester

P2 Knitted/interlock/Nm 50/1 138.1 128.9 P3 Knitted/glat/Nm 50/1 158.2 154.9 P4 Fabric/Nm 70/2 + Nm 40/2 136.9 139.2 P27 Fabric Hydrophilic Hydrophilic P28 Fabric 152.1 105.3 P30 Fabric 124.8 75.5 PA Knitted Polyamide 165.1 97.6 PLA Nonwoven Poly(lactic acid) 129.6 Hydrophilic H Fabric Hemp Beige 126.9 135.0

The XRD diffractograms pointed to an amorphous phase of the SiO*x* deposited layers [163].

SEM morphologies of SiO*x* particles synthesized on fabrics are presented in Figure 14. The raw material images showed defects like kink bands, dislocations, nodes, and slip planes, which are common characteristics of hemp materials [164]. SEM images of synthesized samples showed that SiO*x* particles were grown on the fiber surfaces in a continuous and noncolumnar layer (Figure 14). Apparently, each individual fiber of samples looks uniformly covered by an

**Figure 14.** SEM images of SiOx layers deposited on (a, a′) P2 and (b, b′) H substrates, at two different magnifications.

White

P1 Knitted/interlock/Nm 70/1

226 Wetting and Wettability

amorphous layer [163].

**CA (°) Raw textile SiOx/textile**

136.9 139.2

In Figure 15, the image of the water droplet onto the deposited P2 sample and the correspond‐ ing CA is represented. The measurements were performed for a direction parallel to the privileged one of the knitted matter (vertically advance geometry). When following a direction perpendicular to the privileged one, the measurements evidence differences of few degrees only.

**Figure 15.** Water droplets on SiO*x* TFs deposited on (a) P2 and (b) H samples. Reproduced from Frunza et al. [163].

From Figure 15, one can observe that the investigated surfaces are not flat, smooth, or homo‐ geneous. These characteristics of the samples make it difficult to apply a specific model algorithm. Moreover, wetting of fabric surfaces is complicated by the heterogeneity, the diffusion of liquid into the fiber, and the capillary action of the fiber assembly. Under these conditions, the experimentally measured CA is an apparent one and can differ considerably from the actual value [163].

The mean CA values of the raw and deposited samples are summarized in Table 6. One can observe that the CA generally decreases after surface functionalization with SiO*x*, in a range of few up to several tens of degrees. As expected, the presence of SiO*x* NPs onto the fiber surface confers to the textiles a hydrophilic behavior (see Table 6).

#### *3.3.2. Surface free energy of SiO2 (quartz) inferred from CA measurements*

Starting from known values of the dispersive and polar parts of the probe liquids' surface tension and obtained values of the CAs, the dispersive and polar parts of the surface tension of the solid (fused quartz) were estimated either by minimization of the equation system using the least square method or by solving the equations taken for combinations of two probe liquids [165].

Eq. (9) is a relation between the dispersive and polar parts of the solid substrate's surface tension and the same quantities of the surface tension of the wetting liquid and the corre‐ sponding CA:

$$\gamma\_{\perp}(1+\cos\theta) = 2\sqrt{\gamma\_{\rm S}^{d}}\sqrt{\gamma\_{\perp}^{d}} + 2\sqrt{\gamma\_{\rm S}^{p}}\sqrt{\gamma\_{\perp}^{p}} \tag{9}$$

The values *γ*<sup>S</sup> d and *γ*<sup>S</sup> p were obtained by averaging the dispersive and polar components of *γ*<sup>S</sup> resulted from solving Eq. (9) for all pairs of liquids that have the condition number of system matrix low enough (as defined in [166]).

CAs of water on fused silica can vary in a large interval. This behavior is in agreement with the one described in the literature, for example, with a 20º to 80º range obtained on quartz dehydroxylated by heating, slightly contaminated, or deliberately methylated [167]. The values we found can be interpreted in terms of the dependence of water CAs on sample purity; the presence of amorphous materials, chemicals, heating, and other pretreatments; and contamination by adsorption of substances from laboratory ambient. All these factors could have an influence over the increasing values of the CA. The obtained values were supposed to depend on the amounts of silanol groups and physically adsorbed water molecules on the quartz/silica surface. The investigation of "cleaner" surfaces obtained by a thermal treatment removing the hydroxyl groups at temperatures of the beginning and ending of the dehydrox‐ ylation process [168] was carried out.


The components of surface free energy of fused silica were determined by CA measurements of several liquids (see Table 7).

**Table 7.** Values of CA (°) of different liquids on fused quartz treated at two different temperatures.

The fused silica plate samples were heated in atmosphere in order to remove water adsorbed on surface and most of the silanol groups. Measurements of CA on solid substrate were performed by analysis of the profile images of symmetric static liquid drops using the Drop Shape Analysis System (model DSA 100, from Krüss) [141, 152]. The samples were placed on a stage, under the tip of liquid-dispensing disposable blunt-end stainless steel needle with an outer diameter of 0.5 mm. The fixed needle was attached to a syringe pump, which was controlled by the computer for drop delivery. The volume of the drops was of ~ 2–3 µl. The CAs were determined by fitting the shape of the sessile drop with a smooth curve and then calculating the slope of the tangent to the drop at the liquid–solid–vapor interface. Low CAs (*θ* < 30º) were determined by fitting the shape of the sessile drop with a circle, whereas larger CAs were estimated by fitting the drop shape with a polynomial equation of second degree or a circle equation. The camera was positioned to observe the droplet under an angle of about 2°–3° in respect to the sample surface supporting the droplet. The tests were carried out at RT. CAs were obtained with an uncertainty of ±2° due to combined effects of drop asymmetry, surface heterogeneity, and variation in drop position on the plate.

Representative images of the observed water droplets on plates are given in Figure 16.

d d p p

 gg(1 cos ) 2 2 += + (9)

p were obtained by averaging the dispersive and polar components of *γ*<sup>S</sup>

glycol Dimethyl sulfoxide

L SL SL

resulted from solving Eq. (9) for all pairs of liquids that have the condition number of system

CAs of water on fused silica can vary in a large interval. This behavior is in agreement with the one described in the literature, for example, with a 20º to 80º range obtained on quartz dehydroxylated by heating, slightly contaminated, or deliberately methylated [167]. The values we found can be interpreted in terms of the dependence of water CAs on sample purity; the presence of amorphous materials, chemicals, heating, and other pretreatments; and contamination by adsorption of substances from laboratory ambient. All these factors could have an influence over the increasing values of the CA. The obtained values were supposed to depend on the amounts of silanol groups and physically adsorbed water molecules on the quartz/silica surface. The investigation of "cleaner" surfaces obtained by a thermal treatment removing the hydroxyl groups at temperatures of the beginning and ending of the dehydrox‐

The components of surface free energy of fused silica were determined by CA measurements

The fused silica plate samples were heated in atmosphere in order to remove water adsorbed on surface and most of the silanol groups. Measurements of CA on solid substrate were performed by analysis of the profile images of symmetric static liquid drops using the Drop Shape Analysis System (model DSA 100, from Krüss) [141, 152]. The samples were placed on a stage, under the tip of liquid-dispensing disposable blunt-end stainless steel needle with an outer diameter of 0.5 mm. The fixed needle was attached to a syringe pump, which was controlled by the computer for drop delivery. The volume of the drops was of ~ 2–3 µl. The CAs were determined by fitting the shape of the sessile drop with a smooth curve and then calculating the slope of the tangent to the drop at the liquid–solid–vapor interface. Low CAs (*θ* < 30º) were determined by fitting the shape of the sessile drop with a circle, whereas larger CAs were estimated by fitting the drop shape with a polynomial equation of second degree or a circle equation. The camera was positioned to observe the droplet under an angle of about 2°–3° in respect to the sample surface supporting the droplet. The tests were carried out at RT.

240 5.3 14.2 24.9 8.3 0 1000 33.6 14.8 24 0 6.5

**Table 7.** Values of CA (°) of different liquids on fused quartz treated at two different temperatures.

 gg

 q

**Treatment temperature (°C) CA for different liquids (°)**

Water Glycerol NP5 Ethylene

g

The values *γ*<sup>S</sup>

228 Wetting and Wettability

d and *γ*<sup>S</sup>

matrix low enough (as defined in [166]).

ylation process [168] was carried out.

of several liquids (see Table 7).

**Figure 16.** Water droplets on the SiOx plates treated at (a) 240°C and (b) 1000°C, and the corresponding CAs.

Based on literature values [169–171] of the polar and dispersion parts of the liquid surface tension (see Table 8) and using the methods of geometric or harmonic mean for the interaction term, the calculation of the two components for fused silica (see Table 9) gave some differences, but their sum did not differ much. Moreover, our tests seem to indicate the method of harmonic mean as better than that one of Owens–Wendt [165].


**Table 8.** Physical properties of different liquids used as samples.


**Table 9.** The surface tension components (dispersive *γ*<sup>s</sup> d and polar *γ*<sup>s</sup> p parts) of fused silica obtained by different calculation methods.

The polar part of the surface free energy of fused silica thermally treated is higher than the dispersive part as resulting from both methods (geometrical and harmonic mean). This might be an indication that, at the measurement moment, the plate surface was not (totally) covered by water vapors from environment.

In agreement with the decreasing number of silanol groups by the thermal treatment, the polar part of the surface tension shows a decreasing trend when increasing the pretreatment temperature.

The indirect method of CA measurements applied for the set of liquids chosen to have complementary interactions with quartz surface, allowed for obtaining values for the compo‐ nents of the surface free energy.

#### **3.4. Effects of proteins from blood plasma on the hydrophobicity of DLC films**

The amorphous phase of sp3 bonded C atoms is known as DLC [82, 172, 173]. Beside high wear resistance coatings for metallic parts, DLC also proved useful in coating implants due to specific surface properties (low surface energy values and chemical inertness) that prevent blood coagulation and favor osteoblasts adhesion [90, 172]. In the biomedical field, the main necessity for DLC coatings comes from vascular prostheses. In the case of interaction with blood, it seems that DLC quality has a major influence upon clotting time. During the blood flow through these tubes, the erythrocytes and thrombocytes (platelets) aggregate in certain spots and may eventually block the blood passage. To compensate for this general weakness of vascular prostheses, DLC films can bind albumin molecules from the sanguine plasma forming a passive layer that makes the surfaces less adhesive for blood platelets [174].

The blood compatibility with carbon-based films is extremely complex and for the moment there is no relation found between hemocompatibility and surface properties such as surface energy, atomic bond structure of carbon, or composition of material. Contradictory data have been reported regarding the behavior of the material in terms of blood clotting, the adherence of platelets, or protein adsorption to surfaces. The relationship between the sp3 bonds content of DLC and its antithrombogenicity properties is still not well understood. In vitro [82] and in vivo [88, 175] studies indicate that better results can be obtained for a higher sp3 content.

Kwok et al. [176] pointed out that a higher surface energy of phosphorous doped a-C:H films is associated with a low adsorption of proteins, among them the albumin being the preferential one. Similar findings in terms of protein adsorption were presented by Ma et al. [177], who reported a higher albumin to fibrinogen adsorption ratios on surfaces with higher surface energy.

Jones et al. [178] explored platelet attachment on Ti, TiN, TiC, and DLC surfaces and reported that the more hydrophilic surfaces present a greater platelet spreading and fibrinogen adsorption. They suggested that the better hemocompatibility of DLC surface is linked to its low surface energy and thus high hydrophobicity. Okpalugo et al. [179] also noted that improved blood compatibility can be obtained when surface energy is lowered in silicon doped a-C:H films.

Recently, the correlation between activated partial thromboplastin time (aPTT) and surface energy of DLC structures with different sp3 /sp2 bonds ratio was studied. Attention was paid to the investigation of protein adsorption and platelets adherence to the surface, both acting as crucial factors for material hemocompatibility [84].

#### *3.4.1. Types of bonds in the films*

The polar part of the surface free energy of fused silica thermally treated is higher than the dispersive part as resulting from both methods (geometrical and harmonic mean). This might be an indication that, at the measurement moment, the plate surface was not (totally) covered

In agreement with the decreasing number of silanol groups by the thermal treatment, the polar part of the surface tension shows a decreasing trend when increasing the pretreatment

The indirect method of CA measurements applied for the set of liquids chosen to have complementary interactions with quartz surface, allowed for obtaining values for the compo‐

resistance coatings for metallic parts, DLC also proved useful in coating implants due to specific surface properties (low surface energy values and chemical inertness) that prevent blood coagulation and favor osteoblasts adhesion [90, 172]. In the biomedical field, the main necessity for DLC coatings comes from vascular prostheses. In the case of interaction with blood, it seems that DLC quality has a major influence upon clotting time. During the blood flow through these tubes, the erythrocytes and thrombocytes (platelets) aggregate in certain spots and may eventually block the blood passage. To compensate for this general weakness of vascular prostheses, DLC films can bind albumin molecules from the sanguine plasma forming a passive layer that makes the surfaces less adhesive for blood platelets [174].

The blood compatibility with carbon-based films is extremely complex and for the moment there is no relation found between hemocompatibility and surface properties such as surface energy, atomic bond structure of carbon, or composition of material. Contradictory data have been reported regarding the behavior of the material in terms of blood clotting, the adherence

of DLC and its antithrombogenicity properties is still not well understood. In vitro [82] and in

Kwok et al. [176] pointed out that a higher surface energy of phosphorous doped a-C:H films is associated with a low adsorption of proteins, among them the albumin being the preferential one. Similar findings in terms of protein adsorption were presented by Ma et al. [177], who reported a higher albumin to fibrinogen adsorption ratios on surfaces with higher surface

Jones et al. [178] explored platelet attachment on Ti, TiN, TiC, and DLC surfaces and reported that the more hydrophilic surfaces present a greater platelet spreading and fibrinogen adsorption. They suggested that the better hemocompatibility of DLC surface is linked to its low surface energy and thus high hydrophobicity. Okpalugo et al. [179] also noted that improved blood compatibility can be obtained when surface energy is lowered in silicon doped

of platelets, or protein adsorption to surfaces. The relationship between the sp3

vivo [88, 175] studies indicate that better results can be obtained for a higher sp3

bonded C atoms is known as DLC [82, 172, 173]. Beside high wear

bonds content

content.

**3.4. Effects of proteins from blood plasma on the hydrophobicity of DLC films**

by water vapors from environment.

nents of the surface free energy.

The amorphous phase of sp3

temperature.

230 Wetting and Wettability

energy.

a-C:H films.

XPS analysis, indicating the C 1s core level variation, was used in order to assess the amount of sp2 and sp3 bonded C in three types of samples (D20, D60, and D100; see Table 10).


**Table 10.** XPS peak separation data for the C 1s line of DLC films. Reproduced from Popa et al. [84].

From the XPS analysis, the amount of sp3 -bonded C and sp2 -C, as the ratio between the integral intensities of each component, could be extracted. The XPS spectra exhibited a very complex shape pointing to the existence of different chemical states for C 1s (Figure 17).

Three components were needed in order to assure a good fit, associated with the sp3 -C (286 eV) and sp2 -C (284.3 eV) contributions, as well as to C–O, C=O, and/or O–C=O bonds (287.5– 289.9 eV) owing most probably to the contamination of the sample surface [180–182]. The deconvolution studies of the C 1s spectra generally reveal two main distinct peaks assignable to sp2 - and sp3 -C hybridization [182]. The peak placed at a higher binding energy (BE) is assigned to sp3 -bonded carbon (C–C and C–H), and that at lower BE corresponds to the sp2 hybridization state of carbon. From the analysis of the main components of C 1s core level spectra, one could assume that the amount of sp2 bonded C decreases from 36% in D20 sample to about 10% in D100. When the methane dilution is increased (D60 and D100), the sp3 -C concentration strongly increases (to ~78 and 87%, respectively).

The increase in the sp3 content with the augmentation of the methane concentration has been confirmed both by Raman and XPS. A significant sp3 content augmentation from sample D20 to D100 was measured. This could be the effect of the initial sp3 hybridization of carbon in the methane molecule. Bugaev et al. [183] also reported that high-quality DLC films can be obtained from pure methane, their results pointing that most probably methyl mechanism is favoring diamond-like bonds formation. It is known that CH3 are the most abundant species in pure methane discharges, while carbon dimer C2 is the most abundant in methane highly diluted in argon discharges [184, 185].

**Figure 17.** High-resolution XPS spectra for C 1s core level photoelectron after sputter cleaning: samples (a) D20, (b) D60 and (c) D100. Reproduced from Popa et al. [84].

#### *3.4.2. Surface energy*

Using deionized water and formamide as standard solvents, solid surface energy calculations based on CA measurements were performed. The measurements of the prepared DLC structures were carried out using the goniometric method, the two solvents being dropped onto the surface and the CA estimated. The drop size and the drip distance were kept constant in all cases. The CA values were determined by the evaluation of the tangent angle of a sessile liquid drop on the DLC solid surface. The surface energy was calculated using the Owens– Wendt approximation [186, 187].

The surface energy values recorded for DLC/Ti structures were lower than those of the bare medical grade Ti and PMMA control substrates (see Table 11).


**Table 11.** Surface energy values recorded for the DLC TFs, and for the Ti and PMMA controls. Reproduced from Popa et al. [84].

One notices a decrease of the surface energy with the increase of methane dilution in the reactor chamber (Table 11). The two tailed *t*-testing showed statistically significant differences (*p* < 0.05) between the surface energy values recorded for all samples. An important decrease (with ~25%) of the surface energy was obtained when applying the DLC coating: from 37.85 ± 0.94 mJ/m2 for the bare Ti substrate down to 28.7 ± 0.34 mJ/m2 for the D100 structure.

#### *3.4.3. DLC films interaction with blood*

**Figure 17.** High-resolution XPS spectra for C 1s core level photoelectron after sputter cleaning: samples (a) D20, (b)

D60 and (c) D100. Reproduced from Popa et al. [84].

232 Wetting and Wettability

Platelets were obtained by centrifugation of whole blood and their adherence to the DLC films surface was investigated by Western blot method. The detailed procedures for platelets isolation and for the Western blot technique are described in Ref. [84].

The obtained signal is proportional to the amount of beta-actin, a structural protein present in all cells and, therefore, to the number of platelets adhered on the sample surface at the moment of lysis. As visible from Figure 18, there was almost the same number of platelets present on the surface of bare titanium and D20 samples.

The number of platelets adhered on D60 and D100 was significantly lower. The DLC coatings ensure conditions for a weaker platelet–surface interaction, which in vivo can conduct to a lower platelet activation and subsequently a prolonged time of coagulation. One can assert that this effect derives from the fact that all cells have a negatively charged cellular membrane,

**Figure 18.** (a) Western blot analysis of beta-actin and aprotinin present in platelets adhered on DLC and bare Ti sam‐ ples; (b) optical density histograms of normalized quantity of beta-actin present in platelets adhered on DLC and bare Ti samples. Reproduced from Popa et al. [84].

which tends to interact/adhere to positively charged surfaces (hydrophilic surfaces) rather than to hydrophobic ones.

The polyvinylidene fluoride membranes were also probed with aprotinin (a protease inhibitor with proteic structure and a mass of ~6 kDa), which was present in the same concentration in all samples, since it was added to the lysis buffer formulation. This is an internal quality control which ensures that all steps of the technique are properly done.

The results of protein adsorption on the DLC surfaces are shown in Figure 19.

Figure 19a shows that serum albumin was adsorbed in greater quantities on all DLC surfaces than on the bare titanium surface [albumin molecular weight (MW) ~66,483 Da]. Other proteins (G immunoglobulins) presented a roughly similar pattern (G immunoglobulins MW ~134,350 Da). Another important peak is that of 28,900 Da, which can be assigned to the factor XIIa light chain and is more prominent on the titanium sample (Figure 19b). The factor XII, the activator of surface contact coagulation cascade, could not be identified because it had a mass similar to that of albumin (factor XII MW ~67,792 Da).

Albumin is a protein that has hydrophobic moieties, being a blood carrier for many hydro‐ phobic molecules. Since our DLC surfaces tend to be more hydrophobic, it is expected to find more adsorbed albumin than on titanium as confirmed by mass spectroscopy spectra. The vast majority of proteins in blood are glycosylated, which makes them more hydrophilic and more susceptible to polar interactions. The quantity of albumin adsorbed on the surface shields the surface of the sample, making it difficult for the different proteins and coagulation factors to

which tends to interact/adhere to positively charged surfaces (hydrophilic surfaces) rather than

**Figure 18.** (a) Western blot analysis of beta-actin and aprotinin present in platelets adhered on DLC and bare Ti sam‐ ples; (b) optical density histograms of normalized quantity of beta-actin present in platelets adhered on DLC and bare

The polyvinylidene fluoride membranes were also probed with aprotinin (a protease inhibitor with proteic structure and a mass of ~6 kDa), which was present in the same concentration in all samples, since it was added to the lysis buffer formulation. This is an internal quality control

Figure 19a shows that serum albumin was adsorbed in greater quantities on all DLC surfaces than on the bare titanium surface [albumin molecular weight (MW) ~66,483 Da]. Other proteins (G immunoglobulins) presented a roughly similar pattern (G immunoglobulins MW ~134,350 Da). Another important peak is that of 28,900 Da, which can be assigned to the factor XIIa light chain and is more prominent on the titanium sample (Figure 19b). The factor XII, the activator of surface contact coagulation cascade, could not be identified because it had a mass similar

Albumin is a protein that has hydrophobic moieties, being a blood carrier for many hydro‐ phobic molecules. Since our DLC surfaces tend to be more hydrophobic, it is expected to find more adsorbed albumin than on titanium as confirmed by mass spectroscopy spectra. The vast majority of proteins in blood are glycosylated, which makes them more hydrophilic and more susceptible to polar interactions. The quantity of albumin adsorbed on the surface shields the surface of the sample, making it difficult for the different proteins and coagulation factors to

which ensures that all steps of the technique are properly done.

to that of albumin (factor XII MW ~67,792 Da).

The results of protein adsorption on the DLC surfaces are shown in Figure 19.

to hydrophobic ones.

234 Wetting and Wettability

Ti samples. Reproduced from Popa et al. [84].

**Figure 19.** (a) SELDI-ToF complete spectra of proteins adsorbed on DLC and bare Ti samples from fresh blood plasma; (b) SELDI-ToF detailed spectra in MW range 8000–30,000 Da. Reproduced from Popa et al. [84].

reach the sample and activate the coagulation cascade (Figure 19b). These findings are in line with Liu et al. [188], who showed that the albumin adsorption on DLC inactivates the surface for blood clotting. One can state that the coagulation time for each material is in line with surface energy data, with the platelet–surface adherence properties and protein adsorption profiles, and so advocates for a cause–effect relationship between these factors.

#### **4. Conclusions**

Wettability of solid substrates represents an important phenomenon for many natural systems and can play a key role in a wide range of applications such as coatings, tunable surfaces, design of hydrophobic/superhydrophobic, or hydrophilic surfaces. It is well known that the wettability of a solid surface is governed by both surface structure and chemistry. After a brief introduction on wettability of nanostructures and the possibility to investigate it by contact angle (CA) measurements, this chapter focused on hydrophobic and hydrophilic structures (oxide and DLC TFs or NPs) synthesized by various deposition techniques (PLD, SG, TE, solution based on chemical approaches, sputtering, and PECVD).

The possibility of tuning the wetting behavior of textile materials by their functionalization with oxide TFs or NPs was reviewed. Depending on the deposition ambience, the TFs can change their behavior from hydrophilic when obtained in an oxygen flux to superhydrophobic when deposited in vacuum. The hydrophobicity was found consistent with the organization of the deposits in vacuum consisting of nanometric crystallites. The subsequent treatment with a TF of a fusion hydrophobin, deposited by soaking in solution, and a ZnO TF finishing in vacuum boosted the antifungal efficiency of the structure by 100%. This significant enhance‐ ment was attributed to the higher texturing of the oxide film when growing on hydrophobin interlayer, resulting in an increased presence of oxygen species on surface. In complementary studies, fabrics functionalized with oxide layers showed improved UV protective performan‐ ces. These results might offer guidance for laser manufacturing in one technological step of stable superhydrophobic and antifungal textile surfaces, used for everyday garments and medical clothing.

ZnO structures can present different degrees of compactness, and as a consequence, they can trap more or less air. This result can be explained by the Cassie–Baxter model. Due to the morphology of the deposited ZnO structure, which is made of a large number of small prisms, the roughness presents high values. The apparent CA is therefore enhanced as compared to the one measured on a similar smooth surface. When the space between the ZnO structures is large enough, the water droplet can penetrate, and an explanation of the phenomenon can be based on the Wenzel model. There exists also the possibility to obtain a transition between these two regimes, and the apparent CA could be different than the one inferred for a smooth surface.

CA measurements confirmed that the presence of SiO*<sup>x</sup>* particles on fiber surfaces can change the wetting behavior of the structure. Since it brings OH groups to the surface, the deposition of SiO*x* is therefore expected to provide hydrophilic properties to the textiles.

Although bulk polyester is hydrophobic, water droplets can be sucked into the fibers due to high porosity (void areas) of the material. The void areas were drastically reduced by the addition of TiO2 particles. They decrease the voids and concomitantly increase the sample hydrophobicity. Under these complex conditions, one cannot use the traditional equations like Cassie–Baxter or Wenzel to model the wettability behavior of the heterogeneous and rough samples.

Protein adsorption using fresh blood plasma from healthy patients was also studied. In the case of DLC films with the highest sp3 content, albumin was preferentially adsorbed (due to the affinity between the surface and the hydrophobic moieties of the protein), thus shielding the surface and preventing the immobilization of coagulation factors.

The results reviewed in this chapter are devoted to improve the understanding of the wetta‐ bility of nanostructured surfaces. Understanding the importance of surface wettability and succeeding to control this phenomenon at nanometric scale will hopefully facilitate the fabrication of devices with improved characteristics for top applications, especially in nano‐ technology.

### **Acknowledgements**

reach the sample and activate the coagulation cascade (Figure 19b). These findings are in line with Liu et al. [188], who showed that the albumin adsorption on DLC inactivates the surface for blood clotting. One can state that the coagulation time for each material is in line with surface energy data, with the platelet–surface adherence properties and protein adsorption

Wettability of solid substrates represents an important phenomenon for many natural systems and can play a key role in a wide range of applications such as coatings, tunable surfaces, design of hydrophobic/superhydrophobic, or hydrophilic surfaces. It is well known that the wettability of a solid surface is governed by both surface structure and chemistry. After a brief introduction on wettability of nanostructures and the possibility to investigate it by contact angle (CA) measurements, this chapter focused on hydrophobic and hydrophilic structures (oxide and DLC TFs or NPs) synthesized by various deposition techniques (PLD, SG, TE,

The possibility of tuning the wetting behavior of textile materials by their functionalization with oxide TFs or NPs was reviewed. Depending on the deposition ambience, the TFs can change their behavior from hydrophilic when obtained in an oxygen flux to superhydrophobic when deposited in vacuum. The hydrophobicity was found consistent with the organization of the deposits in vacuum consisting of nanometric crystallites. The subsequent treatment with a TF of a fusion hydrophobin, deposited by soaking in solution, and a ZnO TF finishing in vacuum boosted the antifungal efficiency of the structure by 100%. This significant enhance‐ ment was attributed to the higher texturing of the oxide film when growing on hydrophobin interlayer, resulting in an increased presence of oxygen species on surface. In complementary studies, fabrics functionalized with oxide layers showed improved UV protective performan‐ ces. These results might offer guidance for laser manufacturing in one technological step of stable superhydrophobic and antifungal textile surfaces, used for everyday garments and

ZnO structures can present different degrees of compactness, and as a consequence, they can trap more or less air. This result can be explained by the Cassie–Baxter model. Due to the morphology of the deposited ZnO structure, which is made of a large number of small prisms, the roughness presents high values. The apparent CA is therefore enhanced as compared to the one measured on a similar smooth surface. When the space between the ZnO structures is large enough, the water droplet can penetrate, and an explanation of the phenomenon can be based on the Wenzel model. There exists also the possibility to obtain a transition between these two regimes, and the apparent CA could be different than the one inferred for a smooth

CA measurements confirmed that the presence of SiO*<sup>x</sup>* particles on fiber surfaces can change the wetting behavior of the structure. Since it brings OH groups to the surface, the deposition

of SiO*x* is therefore expected to provide hydrophilic properties to the textiles.

profiles, and so advocates for a cause–effect relationship between these factors.

solution based on chemical approaches, sputtering, and PECVD).

**4. Conclusions**

236 Wetting and Wettability

medical clothing.

surface.

LD and INM acknowledge project no. 7-083/2014 (CARLA). IZ acknowledges the financial support of the Romanian Ministry of Education and Research under the Project IDEI 281/2011. ACP acknowledges the funding of this research by the Romanian National Authority for scientific research through PNII-RU-TE-2012-3-0379 (TE 16/2013).

#### **Author details**

L. Duta1 , A.C. Popescu1 , I. Zgura2 , N. Preda2 and I.N. Mihailescu1\*

\*Address all correspondence to: ion.mihailescu@inflpr.ro

1 National Institute for Lasers, Plasma, and Radiation Physics, Magurele, Romania

2 National Institute of Materials Physics, Magurele, Romania

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### **Wetting Behavior of Dental Implants**

In-Hye Kim, Tae-Yup Kwon and Kyo-Han Kim

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61098

#### **Abstract**

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Titanium (Ti) and titanium alloys are widely used in biomedical devices and components, because of their desirable properties, such as relatively low modulus, good fatigue strength, formability, machinability, corrosion resistance, and biocom‐ patibility. However, Ti and its alloys cannot meet all of the clinical requirements. Therefore, surface modification of Ti has been often performed to improve the biological, chemical, and mechanical properties. Various modifications of surface properties have been investigated to predictably improve the osseointegration of Ti implants. The rate and quality of osseointegration in Ti implants are related to their surface properties. A multiplicity of implant surface forms exist engineered with mechanical features that physically interlock the implant with bone. Various strategies have been utilized to improve bone integration of Ti-based implants. For example, surface grit blasting, acid-etching and anodization methods enhance cell growth, improving implant fixation through increases in interlocking surface area and alterations of oxide thickness. On the other hand, surface composition and hydrophi‐ licity are parameters that may play a role in implant-tissue interaction and osseoin‐ tegration. Highly hydrophilic surfaces seem more desirable than hydrophobic ones in view of their interactions with biological fluids, cells and tissues. Several recent studies have shown that the surface energy of biomaterials strongly has influence the initial cell attachment and spreading of osteoblastic cells on the biomaterial surfaces. Hallab et al. said that surface energy might be a more important determinant of cell adhesion and proliferation, and might be more useful than surface roughness for generating cell adhesion and cell. It may have the influence on protein adsorption and the structural rearrangement of the proteins on the material. Therefore, understanding the relationship between surface energy and cell adhesion on different biomaterials will facilitate the design of optimized implant material surfaces and subsequently the

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

cell attachment. Surface energy is an important parameter of the material surface. It is affected by several surface characteristics, such as chemical composition, surface charge, and microstructural topography. Many papers reported that surface energy is one of important surface characteristics parameter of modified titanium surfaces. Given the importance of surface wettability of dental implants surfaces in the achievement of osseointegration, the surface free energy values for a given material, obtained by various methods and with use of different measuring liquids, are not consistent. Thus, we provided a review article of the surface modification on titanium surface and the surface wettability. The relationship between CAs and surface preparations was determined in this review.

**Keywords:** surface free energy, contact angle, dental implant

#### **1. Introduction**

Titanium (Ti) and titanium alloys are widely used in biomedical devices and components because of their desirable properties, such as relatively low modulus, good fatigue strength, formability, machinability, corrosion resistance, and biocompatibility. [1] However, Ti and its alloys cannot meet all of the clinical requirements. Therefore, the surface modification of Ti has been often performed to improve the biological, chemical, and mechanical properties. [2] Various modifications of surface properties have been investigated to significantly improve the osseointegration of Ti implants. [3] The rate and the quality of osseointegration in Ti implants are related to their surface properties. A multiplicity of implant surface forms exists, which are engineered with mechanical features that physically interlock the implant with bone. Various strategies have been implemented to improve bone integration of Ti-based implants. [4, 6] For example, surface grit blasting, acid etching, and anodization methods enhance cell growth, improving implant fixation and thereby increasing interlocking surface area and altering oxide thickness.

On the other hand, surface composition and hydrophilicity are parameters that play an important role in implant–tissue interaction and osseointegration. [7] Radiofrequency glow discharge has been implemented to increase surface energy and to enhance cell binding. Highly hydrophilic surfaces seem more desirable than hydrophobic ones in view of their interactions with biological fluids, cells, and tissues. [8] Recent studies have shown that the surface energy of biomaterials strongly has influence on the initial cell attachment and spreading of osteoblastic cells on the biomaterial surfaces. [9, 10] Hallab et al. [11] suggested that surface energy may be a more important determinant of cell adhesion and proliferation and may be more useful than surface roughness for generating cells. It may have the influence on protein adsorption and the structural rearrangement of the proteins on the material. Therefore, understanding the relationship between surface energy and cell response on different biomaterials will facilitate the design of optimized implant surfaces and subsequently enhance cell responses. [12]

Surface energy is an important parameter of the material surface. [12] It is affected by several surface characteristics, such as chemical composition, surface charge, and microstructural topography. [13, 14] It has been reported that surface energy is one of important surface characteristic of modified titanium surfaces. [7, 15, 17] The relationship among surface factors, including surface roughness, surface energy, contact angle (CA) values, and cell adhesion to biomaterial surfaces, is presented in Figure 1. Each relationship was supported by a number of studies, which are referenced in the diagram. The understanding of surface factors, cell adhesion, and their relationships is mandatory for better understanding of the bone-implant interface.

cell attachment. Surface energy is an important parameter of the material surface. It is affected by several surface characteristics, such as chemical composition, surface charge, and microstructural topography. Many papers reported that surface energy is one of important surface characteristics parameter of modified titanium surfaces. Given the importance of surface wettability of dental implants surfaces in the achievement of osseointegration, the surface free energy values for a given material, obtained by various methods and with use of different measuring liquids, are not consistent. Thus, we provided a review article of the surface modification on titanium surface and the surface wettability. The relationship between CAs and surface

Titanium (Ti) and titanium alloys are widely used in biomedical devices and components because of their desirable properties, such as relatively low modulus, good fatigue strength, formability, machinability, corrosion resistance, and biocompatibility. [1] However, Ti and its alloys cannot meet all of the clinical requirements. Therefore, the surface modification of Ti has been often performed to improve the biological, chemical, and mechanical properties. [2] Various modifications of surface properties have been investigated to significantly improve the osseointegration of Ti implants. [3] The rate and the quality of osseointegration in Ti implants are related to their surface properties. A multiplicity of implant surface forms exists, which are engineered with mechanical features that physically interlock the implant with bone. Various strategies have been implemented to improve bone integration of Ti-based implants. [4, 6] For example, surface grit blasting, acid etching, and anodization methods enhance cell growth, improving implant fixation and thereby increasing interlocking surface area and

On the other hand, surface composition and hydrophilicity are parameters that play an important role in implant–tissue interaction and osseointegration. [7] Radiofrequency glow discharge has been implemented to increase surface energy and to enhance cell binding. Highly hydrophilic surfaces seem more desirable than hydrophobic ones in view of their interactions with biological fluids, cells, and tissues. [8] Recent studies have shown that the surface energy of biomaterials strongly has influence on the initial cell attachment and spreading of osteoblastic cells on the biomaterial surfaces. [9, 10] Hallab et al. [11] suggested that surface energy may be a more important determinant of cell adhesion and proliferation and may be more useful than surface roughness for generating cells. It may have the influence on protein adsorption and the structural rearrangement of the proteins on the material. Therefore, understanding the relationship between surface energy and cell response on different biomaterials will facilitate the design of optimized implant surfaces and subsequently

preparations was determined in this review.

**1. Introduction**

254 Wetting and Wettability

altering oxide thickness.

enhance cell responses. [12]

**Keywords:** surface free energy, contact angle, dental implant

**Figure 1.** The relationship among contact angle, surface preparation, surface energy, roughness, and cell adhesion.

Given the importance of surface wettability of dental implants in the achievement of osseoin‐ tegration, the surface free energy (SFE) values for a given material obtained by various methods using different measuring liquids are not consistent. Thus, the current review article deals with the relationship between CAs and surface preparations.

#### **2. Surface Free Energy (SFE) and Contact Angle (CA)**

Surface free energy (SFE) is defined as the work required for increasing the surface area of a substance per unit area. SFE is induced from the unfulfilled bonding potential of molecules at a surface,. These are different molecules within a material, which have less energy because they are affected by interactions with like molecules in all directions. Moreover, SFE is dictated by the surface roughness, topography, and composition of the implant and is crucial in determining which proteins are absorbed onto the surface. Surface energy, which is intimately related to wettability, [18] is a useful quantity that has often correlated strongly with biological interaction. Thus, it is usually reported that biomaterial surfaces with moderate hydrophilicity improves cell growth and higher biocompatibility. [19] This points out to the existence of a range of optimal surface energies. [20]

SFE can be determined by measuring the contact angle formed by a range of liquids on a given surface, using several diverse approaches. [21] The most useful methods for characterizing wettability on solid surfaces are static CA measurements. CA measurements are quantifiable, readily acquired using relatively low-cost instruments and simple procedures, amenable for use in environments from academic research laboratories to industrial manufacturing facilities, and an extremely powerful method for characterizing surfaces. A drop of liquids in contact with a surface will display a contact angle, traditionally measured through the liquid. Thus, examination of wetting behavior draws the conclusion that a liquid usually shows a wide range of angles on a measured solid surface. [22] The physical surface properties and the surface energy can be quantified by the wettability and by the CA of liquids with the surface. [23] The values of the CA indicate whether the surface is hydrophilic or hydrophobic. [24] Several authors have suggested that CA measurements give values ranging from 0° (hydro‐ philic) to 140° (hydrophobic) for titanium implant surfaces. [25, 26]

#### **3. Calculations of surface free energy**

The modified form of the Young equation is as follows:

$$
\gamma\_s = \gamma\_{sl} + \gamma\_l \cos \Theta \tag{1}
$$

where *Θ* is the contact angle and *γ*s, *γ*sl, and *γ*<sup>l</sup> are the surface tensions of the solid, solid–liquid, and liquid surfaces, respectively. The quantities *γ*<sup>l</sup> and *Θ*, appearing in Eq. 1, can be measured. However, the quantity *γ*sl remains unknown. The effect of adsorption of the measuring liquid on the surface of a solid should also be taken into account. Therefore, some additional assumptions concerning the relations between *γ*s, *γ*<sup>l</sup> , and *γ*sl need to be made in order to solve Eq. 1.

The idea of the partition of the surface free energy into singular components includes the assumption that the quantity *γ*sl is determined by dissimilar interfacial interactions that rely on the properties of both the measuring liquid and the *γ*sl of the solid. Fowkes [27] assumed that the SFE of a solid (and of a liquid) is a sum of independent components, associated with specific interactions:

$$\boldsymbol{\gamma}\_{s} = \boldsymbol{\gamma}\_{s}^{\mathrm{d}} + \boldsymbol{\gamma}\_{s}^{\mathrm{p}} + \boldsymbol{\gamma}\_{s}^{\mathrm{h}} + \boldsymbol{\gamma}\_{s}^{\mathrm{i}} + \boldsymbol{\gamma}\_{s}^{\mathrm{ab}} + \boldsymbol{\gamma}\_{s}^{\mathrm{o}} \tag{2}$$

where *γ*<sup>s</sup> p, *γ*<sup>s</sup> d , *γ*<sup>s</sup> ab, *γ*<sup>s</sup> h, and *γ*<sup>s</sup> i are the polar, dispersion, acid–base components, hydrogen (related to hydrogen bonds), and inductions, respectively, while *γ*<sup>s</sup> <sup>o</sup> refers to all interactions. Moreover, the dispersion component of the surface free energy is related with the London force interactions, resulting from the electron dipole instability according to the theory. These interactions occur normally between neighboring atoms and molecules. The forces depend on the kind of similarly attracting elements of the matter but are independent of other types of interactions. The remaining van der Waals interactions have been regarded by Fowkes [27] as a division of the generation interactions. He investigated a solid or liquid in which the dispersion interactions appear. Considering such systems, he found out the surface free energy corresponding to the interface of a solid and liquid as follows:

$$
\gamma\_s \gamma\_d = \gamma\_s + \gamma\_1 - \left(2\left(\gamma\_s^{\;d} \gamma\_1^{\;d}\right)^{0.5}\right)^{0.5} \tag{3}
$$

Eq. 3 is limited to the interfacial London interactions.

SFE can be determined by measuring the contact angle formed by a range of liquids on a given surface, using several diverse approaches. [21] The most useful methods for characterizing wettability on solid surfaces are static CA measurements. CA measurements are quantifiable, readily acquired using relatively low-cost instruments and simple procedures, amenable for use in environments from academic research laboratories to industrial manufacturing facilities, and an extremely powerful method for characterizing surfaces. A drop of liquids in contact with a surface will display a contact angle, traditionally measured through the liquid. Thus, examination of wetting behavior draws the conclusion that a liquid usually shows a wide range of angles on a measured solid surface. [22] The physical surface properties and the surface energy can be quantified by the wettability and by the CA of liquids with the surface. [23] The values of the CA indicate whether the surface is hydrophilic or hydrophobic. [24] Several authors have suggested that CA measurements give values ranging from 0° (hydro‐

philic) to 140° (hydrophobic) for titanium implant surfaces. [25, 26]

cos *s sl l* gg

 g

However, the quantity *γ*sl remains unknown. The effect of adsorption of the measuring liquid on the surface of a solid should also be taken into account. Therefore, some additional

The idea of the partition of the surface free energy into singular components includes the assumption that the quantity *γ*sl is determined by dissimilar interfacial interactions that rely on the properties of both the measuring liquid and the *γ*sl of the solid. Fowkes [27] assumed that the SFE of a solid (and of a liquid) is a sum of independent components, associated with

> d p h i ab o ss s s s s s

Moreover, the dispersion component of the surface free energy is related with the London force interactions, resulting from the electron dipole instability according to the theory. These interactions occur normally between neighboring atoms and molecules. The forces depend on the kind of similarly attracting elements of the matter but are independent of other types of

 g= + + ++ + (2)

are the polar, dispersion, acid–base components, hydrogen

=+ Q (1)

are the surface tensions of the solid, solid–liquid,

and *Θ*, appearing in Eq. 1, can be measured.

, and *γ*sl need to be made in order to solve

<sup>o</sup> refers to all interactions.

**3. Calculations of surface free energy**

where *Θ* is the contact angle and *γ*s, *γ*sl, and *γ*<sup>l</sup>

Eq. 1.

256 Wetting and Wettability

where *γ*<sup>s</sup>

specific interactions:

p, *γ*<sup>s</sup> d , *γ*<sup>s</sup> ab, *γ*<sup>s</sup>

and liquid surfaces, respectively. The quantities *γ*<sup>l</sup>

assumptions concerning the relations between *γ*s, *γ*<sup>l</sup>

gg

h, and *γ*<sup>s</sup> i  g g g g

(related to hydrogen bonds), and inductions, respectively, while *γ*<sup>s</sup>

The modified form of the Young equation is as follows:

Owens and Wendt [28] changed the Fowkes idea while assuming that the sum of all the components occurring on the right-hand side of Eq. 2, except *γ*<sup>s</sup> d, can be considered as associated with the polar interaction (*γ*<sup>s</sup> p). Thus, they suggested the following equation:

$$
\gamma\_{s1} = \gamma\_s + \gamma\_1 - \left(\mathcal{I}\left(\boldsymbol{\gamma}\_s^d \boldsymbol{\gamma}\_1^d\right)^{0.5} - \mathcal{I}\left(\boldsymbol{\gamma}\_s^p \boldsymbol{\gamma}\_1^p\right)^{0.5}\right)^{0.5} \tag{4}
$$

Because the polar interaction definition by Fowkes [27] differs from that by Owens and Wendt, the meanings of *γ*<sup>s</sup> p and *γ*<sup>l</sup> p in Eq. 2 are different than those in Eq. 4.

The latest idea of the partition of surface free energy of solids and liquids into components is that presented by van Oss, Chaudhury, and Good. [29] The authors separated *γ*s into two components, one containing the long-range interactions (London, Debye, and Keesom) called the Lifshitz–van der Waals component (*γ*LW) and the other that includes the short-range interactions called the acid–base component (*γ*AB). The latter component associated with the acid–base interactions is equal 2(*γ*<sup>+</sup> *γ*− ) 0.5, where *γ*<sup>+</sup> and *γ*<sup>−</sup> mean the acidic and basic components, respectively. Consequently, the following relationship was created:

$$\mathcal{I}\_{sl} = \left\{ \left( \boldsymbol{\chi}\_{s}^{\rm LW} \right)^{0.5} - \left( \boldsymbol{\chi}\_{1}^{\rm LW} \right)^{0.5} \right\} \mathbf{2} + \mathbf{2} \left\{ \left( \boldsymbol{\chi}\_{s}^{\rm s} \right)^{0.5} - \left( \boldsymbol{\chi}\_{1}^{\rm s} \right)^{0.5} \right\} \cdot \left\{ \left( \boldsymbol{\chi}\_{s}^{\cdot} \right)^{0.5} - \left( \boldsymbol{\chi}\_{1}^{\cdot} \right)^{0.5} \right\} \tag{5}$$

#### **4. Owens–Wendt method**

In the Owens–Wendt method, [30] they made the assumptions similar to those in the Fowkes method. The two methods, being identical in the mathematical aspect, differ slightly in the way of calculating the surface free energy. The combination of Eq. 1 with Eq. 4 leads to the following relationship:

$$\left(\left(\boldsymbol{\chi}\_{s}^{\mathrm{d}}\boldsymbol{\chi}\_{\mathrm{l}}^{\mathrm{d}}\right)^{0.5} + \left(\boldsymbol{\chi}\_{s}^{\mathrm{p}}\boldsymbol{\chi}\_{\mathrm{l}}^{\mathrm{p}}\right)^{0.5} = \boldsymbol{\chi}\_{\mathrm{l}}\left(1 + \cos\Theta\right)\tag{6}$$

#### **5. van Oss–Chaudhury–Good method**

The component *γ*ab is equal 2(*γ*<sup>+</sup> *γ*− ) 0.5 and combining Eq. 1 with Eq. 5, van Oss, Chaudhury, and Good obtained the following relationship: [30]

$$\left(\left(\boldsymbol{\gamma}\_{s}^{\text{LW}}\boldsymbol{\gamma}\_{1}^{\text{LW}}\right)^{0.5} + \left(\boldsymbol{\gamma}\_{s}^{\text{+}}\boldsymbol{\gamma}\_{1}^{\text{-}}\right)^{0.5} + \left(\boldsymbol{\gamma}\_{s}^{\text{-}}\boldsymbol{\gamma}\_{1}^{\text{+}}\right)^{0.5} = 0.5\left(1 + \cos\Theta\right) \tag{7}$$

Since three unknowns, *γ*<sup>s</sup> LW, *γ*<sup>s</sup> + , and *γ*<sup>s</sup> − , appear in Eq. 7, the solution of a system of three independent linear equations is needed to establish these quantities. When three different liquids are used to measure the contact angle of a material, such a system is obtained. More‐ over, two bipolar and one non polar liquid should form the set of the three measuring liquids. The values of the coefficients appearing in such a scheme of equations have been given somewhere else. The key of the scheme of three equations shown, as used in the van Oss– Chaudhury–Good method, cannot always be appropriate and undoubtedly interpreted. This follows from the presumed conditions and limitations, related with both the selected meas‐ uring liquids and the methods of determination of the surface free energy components such as *γ*<sup>l</sup> LW, *γ*<sup>l</sup> + , and *γ*<sup>l</sup> − .

#### **6. Methods based on determination of the contact angle hysteresis**

This approach is one of the latest methods for calculating the SFE of polymeric materials. [31, 32] It consists of the measurements of both the advancing CA (*Θ*a) and the receding one (*Θ*r) by using the same measuring liquid of a known value of *r*<sup>l</sup> . The surface free energy of a tested solid can be calculated from the following equation:

$$r\_s = r\_{\rm i} (\cos \Theta\_{\rm r} - \cos \Theta\_{\rm a}) \left| \begin{pmatrix} 1 + \cos \Theta\_{\rm a} \\ \end{pmatrix} 2 \right| \left| \begin{pmatrix} 1 + \cos \Theta\_{\rm r} \\ \end{pmatrix} 2 - \begin{pmatrix} 1 + \cos \Theta\_{\rm a} \\ \end{pmatrix} 2 \right| \tag{8}$$

Unlike the approaches presented above, Eq. 8 takes into account adsorption at the interface. The contact angle appearing in Eq. 1 is the advancing contact angle. Thus, this equation transforms into the following one:

$$r\_{\rm s} = r\_{\rm sl} + r\_{\rm l} \cos \Theta\_{\rm a} \tag{9}$$

The SFE of a solid (*r*sf), which considers adsorption occurring during the measurement of *Θ*r, can be expressed by the following relationship:

$$r\_{\rm sf} = r\_{\rm sl} + r\_{\rm l} \cos \Theta\_{\rm r} \tag{10}$$

The following relation is valid:

**5. van Oss–Chaudhury–Good method**

Good obtained the following relationship: [30]

g g *γ*− )

s l s l sl

 g g

LW, *γ*<sup>s</sup> + , and *γ*<sup>s</sup> −

by using the same measuring liquid of a known value of *r*<sup>l</sup>

solid can be calculated from the following equation:

*r r*

transforms into the following one:

can be expressed by the following relationship:

( )( )( ) ( ) 0.5 0.5 0.5 LW LW + - - +

**6. Methods based on determination of the contact angle hysteresis**

sl r a = cos – cos 1+cos 2/ 1+cos 2– 1 + cos 2 ( QQ Q Q Q )( ) ( ) ( ) { <sup>a</sup> é ù

s sl l a

sf sl l r

This approach is one of the latest methods for calculating the SFE of polymeric materials. [31, 32] It consists of the measurements of both the advancing CA (*Θ*a) and the receding one (*Θ*r)

Unlike the approaches presented above, Eq. 8 takes into account adsorption at the interface. The contact angle appearing in Eq. 1 is the advancing contact angle. Thus, this equation

The SFE of a solid (*r*sf), which considers adsorption occurring during the measurement of *Θ*r,

 gg

independent linear equations is needed to establish these quantities. When three different liquids are used to measure the contact angle of a material, such a system is obtained. More‐ over, two bipolar and one non polar liquid should form the set of the three measuring liquids. The values of the coefficients appearing in such a scheme of equations have been given somewhere else. The key of the scheme of three equations shown, as used in the van Oss– Chaudhury–Good method, cannot always be appropriate and undoubtedly interpreted. This follows from the presumed conditions and limitations, related with both the selected meas‐ uring liquids and the methods of determination of the surface free energy components such

0.5 and combining Eq. 1 with Eq. 5, van Oss, Chaudhury, and

+ + = 0.5 1 + cosQ (7)

, appear in Eq. 7, the solution of a system of three

. The surface free energy of a tested

ë û <sup>r</sup> <sup>a</sup> } (8)

*rrr* =+ Q cos (9)

*rrr* = + cosQ (10)

The component *γ*ab is equal 2(*γ*<sup>+</sup>

258 Wetting and Wettability

Since three unknowns, *γ*<sup>s</sup>

as *γ*<sup>l</sup> LW, *γ*<sup>l</sup> + , and *γ*<sup>l</sup> − .

$$r\_{sl} = r\_{sl} + \pi \tag{11}$$

where π is the equilibrium pressure of the surfaces of the measuring liquid. The adhesion can be determined from the following equation:

$$\mathcal{W}\_{\rm sl} = r\_{\rm s} + r\_{\rm l} - r\_{\rm sl} \tag{12}$$

in which *Θ*a or *Θ*r is used, depending on the kind of the interfacial system.

When applying the Young and Dupre equations, the parameter Φ defined by Girifalco and Good as well as making suitable substitutions. While finding this relationship, its authors neither asked nor confirmed the basics of the knowledge in this area. Finding new relations are unquestionable contribution of the authors of this method.

The determination of the polymeric material surface energy with the use of Eq. 8 needs the measurements of *Θ*a and *Θ*<sup>r</sup> and the information of *r*<sup>l</sup> of the measuring liquid. Nonetheless, as the authors of the method highlighted, the calculated values of the surface free energy rely on the tested measuring liquid. Therefore, they verify the results of studies regarding other methods for calculating the surface free energy of polymeric materials. [33, 34]

### **7. Analysis methods of wetting behavior of different dental implant surfaces**

There are a number of techniques to measure the contact angle of a liquid on a substrate, including optical reflectometry, contrast interferometry, capillary rise technique, Wilhelmy plate tensiometry, and various goniometric methods (Table 1).



**Table 1.** Contact angle and surface free energy calculation analysis of various treated dental implants on previous studies.

#### **7.1. Static drop method**

The most commonly employed technique for measuring the contact angle of drops on liquid repellent surfaces is the sessile drop method coupled with digital image analysis. A liquid drop of a volume (calculated) is silently dropped on the substrate and a camera captured the boundary of the drop. Many imaging analysis algorithms can be utilized to estimate the contact angle from the drop outline, such as rough spherical cap calculations [43] or direct fitting to arithmetical keys of the Young Laplace equation. [44]

#### **7.2. Advancing and receding angle**

The advancing contact angles of water and other liquids (diiodomethane, formamide, etc.) were measured after settling 6 µL droplets on the surface. Then after sucking of 2 µL from the droplet into the syringe, the receding contact angle was measured. On the other hand, a drop on a tilted plate is shown schematically, in which the front angle is close to the advancing angle and the rear angle is close to the receding angle on the drop before descending. When the hysteresis is small, the droplet is close to a spherical cap. Moreover, the contact angle passes from the advancing value to the receding one along the contact line. Because these angles are considered to be close to each other, it just is written that the upper half of the droplet makes the angle *Θ*r, while the lower half meets the angle *Θ*a.

#### **7.3. Captive air bubble method**

**Surface modifications**

260 Wetting and Wettability

Physical vapor deposition

Acid, sandblasted, and anodized treatment

Acid, blasted, and blasted + etched

Plasma immersion ion implantation

RGDS-coated

**7.1. Static drop method**

studies.

Thermal oxidation N/A

**Conditions of measurement**

Benzylethanol, diiodmethane, formamide, and water

N/A Water, Dulbecco's

N/A Water, NaCl, DMSO, and

None N/A Water, formamide, and

N/A

arithmetical keys of the Young Laplace equation. [44]

**7.2. Advancing and receding angle**

**Time Liquid Method Surface energy**

modified Eagle's medium Dynamic contact angle – [37]

1–2 s Water Sessile drop Wenzel law [39]

Plasma spray 10 s–20 min Water, diiodomethane Sessile drop Owens and Wendt [5]

anodized Ti 1 µL/s Water Sessile drop N/A [42]

The most commonly employed technique for measuring the contact angle of drops on liquid repellent surfaces is the sessile drop method coupled with digital image analysis. A liquid drop of a volume (calculated) is silently dropped on the substrate and a camera captured the boundary of the drop. Many imaging analysis algorithms can be utilized to estimate the contact angle from the drop outline, such as rough spherical cap calculations [43] or direct fitting to

The advancing contact angles of water and other liquids (diiodomethane, formamide, etc.) were measured after settling 6 µL droplets on the surface. Then after sucking of 2 µL from the droplet into the syringe, the receding contact angle was measured. On the other hand, a drop on a tilted plate is shown schematically, in which the front angle is close to the advancing angle and the rear angle is close to the receding angle on the drop before descending. When the

**Table 1.** Contact angle and surface free energy calculation analysis of various treated dental implants on previous

Glycol, glycerol, water, formamide, methylene iodide, and tricresyl phosphate

human blood Static drop – [38]

diiodomethane Captive air bubble van Oss–Good [40]

**Ref.**

**calculation**

Static drop Owens and Wendt [3, 6]

Static drop Owens and Wendt [41]

Although most studies addressing (super)hydrophobic behaviors have so far dealt with the wetting of low surface energy and textured substrates in air environment, the captive air bubble method, the so-called two liquid phase method, is a totally novel system and configu‐ ration involving the wetting of highly hydrophilic, textured metallic materials in liquid alkane medium.

#### **7.4. Wilhelmy plate method**

The dynamic contact angle measurements are performed on the basis of the Wilhelmy plate technique. The force acting on plates immerse (wetting) and emerge (dewetting) in a liquid is recorded by means of an electrobalance. The hysteresis force loops are used to calculate advancing and receding contact angles (CAs) during immersion and emersion according to the following equation:

$$\text{loss}\Theta\_- = \text{F} / L\_\gamma \tag{13}$$

where *Θ* is the advancing or receding CA, *F* is the wetting force, *L* is the wetted length (sample perimeter), and *γ* is the surface tension of the wetting liquid. Thus, the CA and the wettability of a solid can be determined from the known surface tension and the measured weight of the liquid meniscus. *F*/*L* is the so-called wetting tension and equals to the product of cos*Θ* and *γ*, which is itself part of the fundamental Young equation for sessile drops in thermodynamic equilibrium. The difference between the advancing and the receding CAs is referred to as CA hysteresis. [45]

The hysteresis force loops are qualitatively described in terms of thermodynamic and kinetic hysteresis. For CA calculations, linear portions of the respective *F*/*L* lines are extrapolated to zero immersion depth by linear regression. Before each tensiometry wetting experiment, water surface tension *γ* was measured by means of the Wilhelmy method using a standard rough‐ ened platinum Wilhelmy plate. [46]

#### **8. Influence of surface cleaning on contact angle analyzing**

Surface cleaning method has a quantitative and qualitative influence on the results of contact angle (CA) measurements. An author studied the evolution of contact angle values versus the roughness for the three different cleaning methods [47]:

**Type 0:** water rinsing followed by nitrogen drying

**Type I:** successive soakings in ultrasonic baths of acetone, cyclohexane, and acetone, followed by water rinsing and nitrogen drying

**Type II:** "Type I" cleaning followed by an argon plasma cleaning

Based on the study, CAs around 150° was observed with type 0 cleaning, and no trivial correlation with the roughness was found. Type 0 cleaned surfaces are still covered by usual organic contaminants from ambient air, and no significant influence of the roughness on CA values is observed. The contact angle remained even around 140° in the roughness range between 2.5 and 12 µm, before it begin to reduce for *Ra* higher than 12 µm. Finally, type II cleaning strongly decreased contact angle values [48] compared to type I and type 0 ones. When the roughness increased up to a threshold value *Ra* = 10 µm, an increase in contact angle was detected. Above this threshold, the contact angle remained constant at 120°.

It thus clearly appears from these results that the more efficient the surface cleaning, the more strong and measurable the correlation between CA and roughness. To determine the Young equilibrium angle, CAs were measured on mirror polished titanium surfaces in the "two liquid phase" configuration, after the three different cleaning methods.

**Figure 2.** Ti surfaces of the untreated (a) and plasma-treated (b) for cleaning. Reproduced with permission from Kim et al. (49).

Plasma treatment also can be used as a cleaning method. Appropriate plasma processes render the surfaces more hydrophilic and modify the oxide layer. [49] Also, the application of plasma to metal implants can clean the surface of materials as shown in Figure 2. Among the wide range of plasma techniques, atmospheric plasma is one of the simplest and most efficient processes. We studied to evaluate the effects of atmospheric pressure plasma on the Ti surface. In this study, the plasma treatment did not affect the surface roughness. Therefore, atmos‐ pheric plasma is a powerful way of creating a functionalized hydrophilic surface of Ti implants as a simple and highly efficient method. An atmospheric plasma treatment has the potential as a surface modifying technique to clean the Ti implant surface.

#### **9. Surface roughness and contact angle**

The surface roughness is also an important parameter to be considered. To enhance our understanding of liquids in contact with rough surfaces, a systematic study was carried out in which water contact angle measurements were performed on a wide variety of rough surfaces with precisely controlled surface chemistry.

A uniform surface (*Θ*Y) does have a unique value only if perfectly flat. On genuine surfaces, depending on how a drop is deposited, the contact angle can differ from advancing and receding contact angles. This hysteresis can be attributed to inhomogeneities in the division of adsorbents or the existence of contaminants, to surface roughness, or to time-dependent surface reorganizations. [50] The value of *Θ* is strongly influenced on the surface morphology on rough surfaces. On rough and hydrophobic surfaces, the liquid can either go after the surface topography or show strong pinning or can connect from sharpness to asperity while surrounding air below and presenting almost no hysteresis in the contact angle.

#### **9.1. Wenzel**

**Type 0:** water rinsing followed by nitrogen drying

**Type II:** "Type I" cleaning followed by an argon plasma cleaning

detected. Above this threshold, the contact angle remained constant at 120°.

phase" configuration, after the three different cleaning methods.

by water rinsing and nitrogen drying

262 Wetting and Wettability

al. (49).

**Type I:** successive soakings in ultrasonic baths of acetone, cyclohexane, and acetone, followed

Based on the study, CAs around 150° was observed with type 0 cleaning, and no trivial correlation with the roughness was found. Type 0 cleaned surfaces are still covered by usual organic contaminants from ambient air, and no significant influence of the roughness on CA values is observed. The contact angle remained even around 140° in the roughness range between 2.5 and 12 µm, before it begin to reduce for *Ra* higher than 12 µm. Finally, type II cleaning strongly decreased contact angle values [48] compared to type I and type 0 ones. When the roughness increased up to a threshold value *Ra* = 10 µm, an increase in contact angle was

It thus clearly appears from these results that the more efficient the surface cleaning, the more strong and measurable the correlation between CA and roughness. To determine the Young equilibrium angle, CAs were measured on mirror polished titanium surfaces in the "two liquid

**Figure 2.** Ti surfaces of the untreated (a) and plasma-treated (b) for cleaning. Reproduced with permission from Kim et

A roughness factor, describing the roughness influenced on *Θ* (Eq. 11), was introduced by Wenzel, as follows [51]:

$$\cos \Theta^{\mathsf{W}} = r \cdot \cos \Theta^{\mathsf{r}} \tag{14}$$

where *r* is calculated by dividing the actual roughness-enhanced surface area by its projection. This behavior is often referred to as Wenzel-type wetting.

#### **9.2. Cassie–Baxter**

For the second case, Cassie and Baxter [52] modified Wenzel's equation by introducing the fractions *f*1 and *f*2, where *f*1 corresponds to the area in contact with the liquid divided by the projected area and *f*<sup>2</sup> to the area in contact with the air trapped beneath the drop, also divided by the projected area:

$$\mathbf{f}\cos\Theta^{\text{CB}} = \mathbf{f}\_1\mathbf{\hat{cos}}\Theta^{\text{Y}} - \mathbf{f}\_2 \tag{15}$$

Structured surfaces that exhibit superhydrophobicity can also show an effect known as hemiwicking [53] or superwetting if they are surface-chemically functionalized to be hydro‐ philic. Hemiwicking is a complete wetting due to the presence of capillary forces in two dimensions. [54]

When the surface energy is high, the surface roughness indeed enhances wettability, causing hemiwicking in many cases caused by capillary forces. The pinning of the contact line results in a move to more hydrophobic *θ* values at lower surface energies. It was found that the surface topography outlines the pinning strength and with it the energy barrier working against the wetting behavior of the drop.

#### **10. Contact angle and roughness of modified Ti implant surfaces**

Although the increasing contact angle is in accordance with roughness on nontreated surfaces, modified surfaces have shown different consequences. In physical states, grit-blasting and etching treatments decrease the contact angle of the surfaces, except sandblasting and the acidetching (SLA) treatment (Table 2). SLA-treated surface has nanosized features. This surface also contains two major roughness scales. The microscale roughness originates from the sandblasting step, leading to troughs. The superimposed nanoscale roughness was created by the acid-etching process. Thus, the apparent contact angle on the SLA surface is hydrophobic. This phenomenon can be explained by pinning the contact line. [48] On the other hand, anodizing treatment makes surface hydrophilic.



**Table 2.** Surface contact angle and roughness value of modified titanium surfaces.

#### **11. Conclusions**

CB Y

dimensions. [54]

264 Wetting and Wettability

Physical state

wetting behavior of the drop.

anodizing treatment makes surface hydrophilic.

Nontreated (ground surfaces)

Etching

Sandblast with large grit and acid etch (SLA)

Thermal spray

Structured surfaces that exhibit superhydrophobicity can also show an effect known as hemiwicking [53] or superwetting if they are surface-chemically functionalized to be hydro‐ philic. Hemiwicking is a complete wetting due to the presence of capillary forces in two

When the surface energy is high, the surface roughness indeed enhances wettability, causing hemiwicking in many cases caused by capillary forces. The pinning of the contact line results in a move to more hydrophobic *θ* values at lower surface energies. It was found that the surface topography outlines the pinning strength and with it the energy barrier working against the

Although the increasing contact angle is in accordance with roughness on nontreated surfaces, modified surfaces have shown different consequences. In physical states, grit-blasting and etching treatments decrease the contact angle of the surfaces, except sandblasting and the acidetching (SLA) treatment (Table 2). SLA-treated surface has nanosized features. This surface also contains two major roughness scales. The microscale roughness originates from the sandblasting step, leading to troughs. The superimposed nanoscale roughness was created by the acid-etching process. Thus, the apparent contact angle on the SLA surface is hydrophobic. This phenomenon can be explained by pinning the contact line. [48] On the other hand,

**10. Contact angle and roughness of modified Ti implant surfaces**

**Modifications of surface Degrees of water contact**

85.2 ± 3.6 76.3 ± 3.0 55.4 ± 4.1 43.0 ± 2.0

Grit-blasting 32.5 ± 3.5 1.64 [55]

69.3 ± 3.0 96.2 ± 9.2

138.3 ± 4.2 120.1 ± 15.2

> 57.4 ± 3.2 0.0

Chemical state Electro chemical deposition 75.0 ± 1.0 3.50 [37]

1 2 cos = cos – Q Q *f f* (15)

**angle (°) Surface roughness (μm) Ref.**

0.65 0.45 0.26 0.23

0.37

2.40

1.06

0.51 [38]

3.12 [6]


[38] [7]

Surface composition and hydrophilicity are parameters that play a major role in implant–tissue interaction and osseointegration. In biological state, interfacial reactions *in vivo* change relevant physical and chemical surface parameters, such as the surface energy, affecting the long-term stability of implants. [61] In addition to surface topography, the properties of implant materials that affect cellular behavior include mechanical rigidity and wettability (SFE). The wettability of the surface plays an important role with respect to protein adsorption, cell attachment, and spreading. [62, 63] In some recent works, surfaces with a high surface free energy are reported to be more adhesive than those with a low surface free energy. [36] Thus, the understanding of surface factors, particularly surface wettability, is mandatory for better understanding of the bone implant biomaterial interface.

#### **Author details**

In-Hye Kim1\*, Tae-Yup Kwon2,3 and Kyo-Han Kim2,3

\*Address all correspondence to: hotsoul7@knu.ac.kr

1 Department of Dental Science, Graduate School of Kyungpook National University, Daegu, Korea

2 Department of Dental Biomaterials, School of Dentistry, Kyungpook National University, Daegu, Korea

3 Institute for Biomaterials Research and Development Dental Materials Testing and Evaluation Center, Kyungpook National University, Daegu, Korea

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