**Plasma Processing for Tailoring the Surface Properties of Polymers**

Hisham M. Abourayana and Denis P. Dowling

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60927

#### **Abstract**

This chapter details how plasma treatments can be used to tailor the wettability of polymers. A plasma is an excited gas, and exposure of a polymer to a plasma discharge generally results in an enhancement in surface energy and associated with this is an increase in wettability. The effect however can be short lived due to hydrophobic recovery. In this review the use of both low and atmospheric plasmas for the activation of polymers will be discussed, as will the use of these plasmas for the deposition of plasma polymerised coatings. The latter can be used to produce polymer surfaces with tailored functionalities, thus achieving stable water contact angles ranging from superhydrophilic to superhydrophobic, as required.

This review briefly introduces plasmas and plasma processing and includes an overview of typical plasma treatment sources. This is followed by a review of the use of plasma discharges to treat polymers and in particular to enhance their surface energy, which is important for example in achieving enhanced adhesive bond strength. The final section of this chapter focuses on the deposition of plasma polymerised coatings and how these can be used to tailor both surface chemistry and morphology. Thus the wettability of polymer surfaces can be controlled.

**Keywords:** Plasma Treatments, Polymers, Water Contact Angle, Surface Acti‐ vation, PECVD

© 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.

## **1. Introduction**

In the mid-nineteenth century, the Czech physiologist Jan Evangelista Purkinje introduced the use of the Greek word *plasma* (meaning to be formed or moulded), to refer to the remains of corpuscular material in blood [1, 2]. In 1928 the American scientist Irving Langmuir proposed that electrons, ions and neutral species in an ionized gas are similar in arrangement to the corpuscular material in blood [2]. This gave rise to the use of the word plasma in physics. Plasmas are ionised gases, which consist of positive and negative ions, atoms and electrons, as well as neutral species [3].

Plasmas can be divided into either thermal or non-thermal [4], the thermal plasmas being characterised by high levels of ionisation [5]. Thermal plasmas are associated with joule heating and thermal ionisation, which enables the delivery of high power at high operating pressures [6]. They heat the entire gas stream during operation. Typical examples of thermal plasma sources include plasma torches, plasma spray and arc jets [7]. Non-thermal plasmas, which are often referred to as 'cold' plasmas or non-equilibrium plasmas are produced near room temperature or a little above this temperature. For these plasmas, electrons acquire higher energies than heavy particles (ions and molecules)—their energies ranging from 0.1 eV to some electron volts. Due to the low density of the gas, collisions with the other species are relatively rare and thermal equilibrium is not reached: the bulk temperature of the gas is comparable to room temperature [8]. Non-thermal plasmas are therefore applied for the treatment of polymers, and their use for controlling polymer wettability is the focus of this chapter.

A number of surface treatments have been applied to modify polymer surfaces in order to enhance properties such as adhesion, wettability and printability. Amongst these are mechan‐ ical or chemical treatments as well as exposure to flames, photons, ion beams and other types of radiation [9]. Mechanical treatment alone has limited effectiveness and due to health and environmental concerns the use of chemical treatments with solvents, oxidants such as chromates and permanganates, strong acids or bases, and sodium-liquid ammonia treatments for fluoropolymers are becoming increasingly unacceptable [10]. Furthermore, wet chemical treatments often give rise to problems of uniformity and reproducibility.

Amongst a range of different methods used to modifying polymer surfaces to improve wettability and adhesion, plasma treatment has proved to be one of the most effective, ensuring uniformity, besides being an environment-clean processing technology [11, 12]. Examples of some of these plasma treatment publications, carried out at both low and at atmospheric pressure, are given in Table 1.

#### **1.1. Flame and corona treatment**

As outlined earlier, the plasma processing of polymers generally involves technological plasmas, operating in the non-thermal regime. One type of thermal plasma that is routinely used to tailor polymer surfaces is a flame plasma [27]. These are formed by combining a flammable gas with air. Brief exposures to particles within the flame affect the distribution and density of electrons on the substrate and surface molecules are polarised through oxidation


**1. Introduction**

124 Surface Energy

as well as neutral species [3].

pressure, are given in Table 1.

**1.1. Flame and corona treatment**

In the mid-nineteenth century, the Czech physiologist Jan Evangelista Purkinje introduced the use of the Greek word *plasma* (meaning to be formed or moulded), to refer to the remains of corpuscular material in blood [1, 2]. In 1928 the American scientist Irving Langmuir proposed that electrons, ions and neutral species in an ionized gas are similar in arrangement to the corpuscular material in blood [2]. This gave rise to the use of the word plasma in physics. Plasmas are ionised gases, which consist of positive and negative ions, atoms and electrons,

Plasmas can be divided into either thermal or non-thermal [4], the thermal plasmas being characterised by high levels of ionisation [5]. Thermal plasmas are associated with joule heating and thermal ionisation, which enables the delivery of high power at high operating pressures [6]. They heat the entire gas stream during operation. Typical examples of thermal plasma sources include plasma torches, plasma spray and arc jets [7]. Non-thermal plasmas, which are often referred to as 'cold' plasmas or non-equilibrium plasmas are produced near room temperature or a little above this temperature. For these plasmas, electrons acquire higher energies than heavy particles (ions and molecules)—their energies ranging from 0.1 eV to some electron volts. Due to the low density of the gas, collisions with the other species are relatively rare and thermal equilibrium is not reached: the bulk temperature of the gas is comparable to room temperature [8]. Non-thermal plasmas are therefore applied for the treatment of polymers, and their use for controlling polymer wettability is the focus of this chapter.

A number of surface treatments have been applied to modify polymer surfaces in order to enhance properties such as adhesion, wettability and printability. Amongst these are mechan‐ ical or chemical treatments as well as exposure to flames, photons, ion beams and other types of radiation [9]. Mechanical treatment alone has limited effectiveness and due to health and environmental concerns the use of chemical treatments with solvents, oxidants such as chromates and permanganates, strong acids or bases, and sodium-liquid ammonia treatments for fluoropolymers are becoming increasingly unacceptable [10]. Furthermore, wet chemical

Amongst a range of different methods used to modifying polymer surfaces to improve wettability and adhesion, plasma treatment has proved to be one of the most effective, ensuring uniformity, besides being an environment-clean processing technology [11, 12]. Examples of some of these plasma treatment publications, carried out at both low and at atmospheric

As outlined earlier, the plasma processing of polymers generally involves technological plasmas, operating in the non-thermal regime. One type of thermal plasma that is routinely used to tailor polymer surfaces is a flame plasma [27]. These are formed by combining a flammable gas with air. Brief exposures to particles within the flame affect the distribution and density of electrons on the substrate and surface molecules are polarised through oxidation

treatments often give rise to problems of uniformity and reproducibility.

**Table 1.** Overview providing examples of previous studies on the use of both low and atmospheric plasmas for tailoring polymer surface properties (particularly wettability)

[28]. The high flame temperature (1000-2000 °C) and reaction with excited species in the flame lead to an increased oxygen concentration at the treated surface [29]. These 'hot' plasmas can interact with the polymer surface for some milliseconds, without thermally changing the substrate [8]. Flame treatment has been used in the polymer industry for over 40 years with considerable commercial success, particularly in the automotive industry for improving the bonding of adhesives and dyes to car panels and plastic containers [30].

Non-thermal plasmas can be generated at various operating pressures ranging from low to atmospheric pressure [31]. An example of non-thermal plasma used for surface treatment of polymers is corona discharge [32]. This a non-arcing, non-uniform plasma that ignites the region of the high electric field generated by the sharp points of the electrodes [33]. In order to prevent arcing, grounded surfaces cannot be near these field emission points, as a result the discharge is, by nature, non-uniform: plasma density drops off rapidly with increasing distance from the electrode [33]. In a similar mechanism to flame treatments, a corona treatment causes surface oxidation of polymers. Electrons, ions, excited species and photons, present in the discharge, react with the polymer surface to form radicals. These can in turn react rapidly with atmospheric oxygen [34]. The attraction of using flame treatment as opposed to corona discharge treatment rests with the ease with which non-uniform shapes can be treated and the perceived longevity of the treatment conferred in the flaming process. Indeed flame treatment is reported to provide better stability than corona treatment [35]. Amongst the advantages of corona and flame treatments are that these two processes can be used in continuous operation, and that they use relatively simple and cost effective equipment. The disadvantages of these treatments are that they are carried out in the open air, which often makes it difficult to control the uniformity or chemical nature of the modification, due to variations in ambient conditions such as humidity, contaminations and air pressure or temperature [36]. Examples of corona treatment and the glow formed using flame are shown in Figure 1.

**Figure 1.** Example of corona treatment (left) [37] and the glow formed using flame treatment (right) [38]

#### **1.2. Low pressure and atmospheric pressure plasmas**

Low pressure plasma treatment is used widely in material processing. For example for plasma etching in the semiconductors industry [39] as well as the deposition of coatings such as diamond like carbon (DLC) for tribological applications [40]. For polymer processing low pressure plasmas are used in applications ranging from achieving enhanced adhesion, for contaminant removal, and for coating deposition, i.e. in the medical device sector [12, 15, 41]. These plasmas however have several disadvantages including the requirement of vacuum processing equipment as well as limitations on the size of parts that can be placed into a vacuum chamber [42].

Plasmas can be generated by a number of discharge types including direct-current (DC) discharges, low-frequency discharges (e.g. corona treatment; kHz range), radio-frequency (rf) discharges (MHz range), and microwave discharges (GHz range) [43]. A schematic of a typical low pressure rf plasma system used for polymer treatments is given in Figure 2. This consists of a biased platin on which the polymer to be treated is located. The discharge can be monitored using optical emission spectroscopy to identify the active gaseous species.

to prevent arcing, grounded surfaces cannot be near these field emission points, as a result the discharge is, by nature, non-uniform: plasma density drops off rapidly with increasing distance from the electrode [33]. In a similar mechanism to flame treatments, a corona treatment causes surface oxidation of polymers. Electrons, ions, excited species and photons, present in the discharge, react with the polymer surface to form radicals. These can in turn react rapidly with atmospheric oxygen [34]. The attraction of using flame treatment as opposed to corona discharge treatment rests with the ease with which non-uniform shapes can be treated and the perceived longevity of the treatment conferred in the flaming process. Indeed flame treatment is reported to provide better stability than corona treatment [35]. Amongst the advantages of corona and flame treatments are that these two processes can be used in continuous operation, and that they use relatively simple and cost effective equipment. The disadvantages of these treatments are that they are carried out in the open air, which often makes it difficult to control the uniformity or chemical nature of the modification, due to variations in ambient conditions such as humidity, contaminations and air pressure or temperature [36]. Examples of corona treatment and the glow formed using flame are shown

**Figure 1.** Example of corona treatment (left) [37] and the glow formed using flame treatment (right) [38]

Low pressure plasma treatment is used widely in material processing. For example for plasma etching in the semiconductors industry [39] as well as the deposition of coatings such as diamond like carbon (DLC) for tribological applications [40]. For polymer processing low pressure plasmas are used in applications ranging from achieving enhanced adhesion, for contaminant removal, and for coating deposition, i.e. in the medical device sector [12, 15, 41]. These plasmas however have several disadvantages including the requirement of vacuum processing equipment as well as limitations on the size of parts that can be placed into a

Plasmas can be generated by a number of discharge types including direct-current (DC) discharges, low-frequency discharges (e.g. corona treatment; kHz range), radio-frequency (rf) discharges (MHz range), and microwave discharges (GHz range) [43]. A schematic of a typical

**1.2. Low pressure and atmospheric pressure plasmas**

in Figure 1.

126 Surface Energy

vacuum chamber [42].

**Figure 2.** Schematic of a capacitive coupled rf reactor. Note the window for optical emission spectroscopy (OES) ex‐ amination of the plasma

In contrast to the use of low pressure discharges the use of atmospheric plasmas offer a considerable level of flexibility. These sources typically generate plasmas at high frequencies (>1 kHz). This facilitates the formation of a homogeneous glow discharge via a Penning ionisation mechanism [44]. The homogeneity of the grounded discharges makes them ideal for surface treatments such as wettability enhancement, metal reduction, surface fluorination and film deposition. They can be applied as a continuous and cost-effective process [42]. Compared with corona plasmas the density of the atmospheric plasma is higher which enhances the rate and degree to which the ionised molecules are incorporated onto the polymer surface. An increased rate of ion bombardment occurs, which may result in stronger material bonding. Atmospheric plasma treatment technology also eliminates a possibility of treatment on a material's non-treated side, also known as backside treatment [17].

One widely used atmospheric pressure plasma source is the jet design. It typically consists of two concentric electrodes through which a mixture of helium, oxygen or other gases flow [45]. The discharge is ignited and operates on a feed stock gas, which flows between an outer grounded, cylindrical electrode and a central electrode, and produces a high velocity effluent stream of highly reactive chemical species. Once the gas exits the discharge volume, ions and electrons are rapidly lost by recombination, but the fast flowing effluent still contains neutral metastable species and radicals [45]. A schematic and photograph of an APP jet system operating at approx. 22 kHz is shown in Figure 3 [46].

**Figure 3.** Schematic (left) and photograph (right) of the Plasma Treat APP jet [46]

## **2. Plasma treatment of polymers**

Reviews on the treatment of polymers using low and atmospheric pressure plasmas have been reported previously by a number of authors [47, 48]. These studies demonstrate that plasmas have been used extensively, both to activate polymers and deposit plasma polymerised coatings. Plasma treatment has become an important industrial process for modifying polymer surfaces properties such as adhesion, friction, penetrability, wettability, dyeability and biocompatibility [49]. Plasma processing presents some major advantages: it is a dry, clean, and very fast process, having a very low specific consumption of chemicals and energy, while it affects only the surface and not the bulk material [50]. The surface modification techniques of polymer materials can be divided into three categories: (i) cleaning or etching by removal of material from the surface (ii) surface reactions producing functional groups and crosslinking and (iii) deposition of thin films on the surface [51].

#### **2.1. Plasma etching**

Plasma etching involves the removal of materials from a polymer surface by chemical reactions and physical etching at the surface to form volatile products [52]. Plasma etching is a partic‐ ularly important processing technology in the fabrication of semiconductor devices, for example for the removal of silicon [3]. In the case of polymeric substrates the energy used is lower and it normally involves the removal of organic contaminants from the polymer surface. This plasma etching can proceed through three different pathways [53]. Firstly, a polymer substrate is etched by chemical reaction of reactive plasma species (e.g. radicals, ions) with the surface, referred to as chemical etching. Secondly, ion bombardment of a polymer surface causes sputtering of the surface, which is a physical process. Finally, UV radiation from the plasma phase causes dissociation of chemical bonds, which leads to formation of low molecular weight (LMW) material. In general, these three etching mechanisms occur simultaneously during the plasma treatment of a polymer and induce a flow of volatile (LMW) products from the substrate to the plasma. This causes a gradual weight loss of the treated polymeric material. As a result of their exposure to a plasma of sufficiently high plasma power, the top layer on the polymer can be ablated. Chain-scission of the macromolecules is reported to be the main mechanism for this ablation process [54]. Even after short plasma exposure time ablation can occur, which also alters the surface topography resulting in an enhancement in wettability without modifying surface texture, but over-treatment can yield a very porous surface. Parameters that influence the effectiveness of this etching process are the type of polymer being treated, the applied power and the type of gas discharge formed. These processing parameters are considered individually as follows.

**Effect of discharge power** – The plasma etching rate of a given polymer increases with discharge power [55]. Upon higher energy input, the density of plasma reactive species as well as their acceleration towards the substrate will increase, resulting in more severe etching.

**Figure 3.** Schematic (left) and photograph (right) of the Plasma Treat APP jet [46]

linking and (iii) deposition of thin films on the surface [51].

Reviews on the treatment of polymers using low and atmospheric pressure plasmas have been reported previously by a number of authors [47, 48]. These studies demonstrate that plasmas have been used extensively, both to activate polymers and deposit plasma polymerised coatings. Plasma treatment has become an important industrial process for modifying polymer surfaces properties such as adhesion, friction, penetrability, wettability, dyeability and biocompatibility [49]. Plasma processing presents some major advantages: it is a dry, clean, and very fast process, having a very low specific consumption of chemicals and energy, while it affects only the surface and not the bulk material [50]. The surface modification techniques of polymer materials can be divided into three categories: (i) cleaning or etching by removal of material from the surface (ii) surface reactions producing functional groups and cross-

Plasma etching involves the removal of materials from a polymer surface by chemical reactions and physical etching at the surface to form volatile products [52]. Plasma etching is a partic‐

**2. Plasma treatment of polymers**

**2.1. Plasma etching**

128 Surface Energy

**Effect of polymer type** – The chemical structure and physical properties, e.g. melting tem‐ perature (Tm), glass transition temperature (Tg), crystallinity of polymers, have a major influence on their etching rate [53]. Many studies have been aimed at providing an increased understanding of the relationship between etch resistance and a polymer's chemical structure [18, 56]. One of the first comprehensive studies in this field was performed by Taylor and Wolf [53], who investigated the oxygen plasma etching behaviour of 40 different polymers. They reported that strong backbone bonds, aromatic and polar functional groups, and metallic atoms decrease etching rates. P. Slepicka et al. [18] studied the effect of argon plasma treatments on the roughness and the rate of etching of the polymers polyethylene terephthalate (PET), high-density polyethylene (HDPE), poly tetrafluoro-ethylene (PTFE) and poly L-lactic acid (PLLA)—the highest level of loss at 73 nm, was observed for the PLLA after a 240 seconds of treatment time. Under the same treatment conditions the thickness loss observed for PTFE was 39 nm and that for PET was 27 nm. Vesel et al. [56] compared the etching rates of different polymers (PMMA, PS, LDPE, HDPE, PVC and PTEF) using an oxygen plasma at a frequency of 27.12 MHz and a power of 200 W. They found that the polymer-etching rate increased linearly with treatment time with individual polymers etching at different rates and no correlation was obtained between the polymer chemical structure and its etching rate. As a general trend polymers with a lower melting temperature exhibit higher etching rates. The measured etching rates were roughly in the following order:

#### *PVC PMMA PE PET PTFE PS* > >> > >


A comparison of the physical characteristics of a range of different polymers and their etching rates is shown in Table 2.

**Table 2.** Comparison of the physical characteristics of the polymers shown and their etching rates [56]

**Effect of plasma gas type** – Probably, the most important discharge parameter in polymer etching is the type of plasma gas being used. Amongst those investigated have been oxygen, hydrogen, nitrogen, carbon dioxide, air, water, ammonia, tetrafluoromethane, the noble gases (e.g. helium, neon, argon), or mixtures (e.g. CF4/O2) [53]. Inert gases such as argon (Ar) or helium (He) generally induce relatively low etching rates compared to oxidative and fluori‐ nating plasmas. In general the rate of etching is in the following order:

$$Ar\_1 < \text{CF}\_4 < \text{CO}\_2 < air < \text{O}\_2.$$

Oxygen gas plasmas in particular are recognised to be very reactive etchants. Addition of CF4 to an oxygen plasma will further increase the etching rate of a polymer by increasing oxygen atom concentrations relative to those obtained in pure oxygen plasma [53]. Hsu et al. [57] studied the dependence of gas composition to the plasma etching chemistry of a poly‐ phenylene oxide (PPO). They found that the maximum etch rate was obtained at 20% CF4 and did not oincide with a maximum in atomic oxygen concentration. This indicates that the etch mechanism is not totally controlled by atomic oxygen and that atomic fluorine participates in the etching processes.

#### **2.2. Surface reactions**

In addition to the removal of material from a polymer surface during plasma treatments, significant chemical changes at the surface can occur. The surface chemistry and structure can be modified by the activated gaseous species [58]. Reactions between gas-phase species and the surface produce functional groups and cross-linking at the surface.

*PVC PMMA PE PET PTFE PS* > >> > >

A comparison of the physical characteristics of a range of different polymers and their etching

PVC 0.50 1.40 100 50–75 ~ 30 s 178 nm/s LDPE 1.00 0.92 110 50–90 ~ 100 s 31 nm/s HDPE 1.00 0.95 130 55–120 ~ 100 s 34 nm/s PMMA 0.50 1.19 160 50–90 / 6 nm/s PS 0.125 1.05 240 50–95 ~ 40 s 13 nm/s PETA 0.25 1.3-1.6 < 260 115–170 ~ 40 s 27 nm/s PET B 0.25 1.3-1.6 260 115–170 ~ 100 s 35 nm/s PTFE 0.20 2.20 327 180–260 / 18 nm/s

**Effect of plasma gas type** – Probably, the most important discharge parameter in polymer etching is the type of plasma gas being used. Amongst those investigated have been oxygen, hydrogen, nitrogen, carbon dioxide, air, water, ammonia, tetrafluoromethane, the noble gases (e.g. helium, neon, argon), or mixtures (e.g. CF4/O2) [53]. Inert gases such as argon (Ar) or helium (He) generally induce relatively low etching rates compared to oxidative and fluori‐

*Ar CF CO air O* 42 2 << < < .

Oxygen gas plasmas in particular are recognised to be very reactive etchants. Addition of CF4 to an oxygen plasma will further increase the etching rate of a polymer by increasing oxygen atom concentrations relative to those obtained in pure oxygen plasma [53]. Hsu et al. [57] studied the dependence of gas composition to the plasma etching chemistry of a poly‐ phenylene oxide (PPO). They found that the maximum etch rate was obtained at 20% CF4 and did not oincide with a maximum in atomic oxygen concentration. This indicates that the etch mechanism is not totally controlled by atomic oxygen and that atomic fluorine participates in

In addition to the removal of material from a polymer surface during plasma treatments, significant chemical changes at the surface can occur. The surface chemistry and structure can

**Max. working Temp. °C**

**Time when melting starts**

**Etching rate at 20 s of Treatment**

**Melting Temp. °C**

**Table 2.** Comparison of the physical characteristics of the polymers shown and their etching rates [56]

nating plasmas. In general the rate of etching is in the following order:

rates is shown in Table 2.

the etching processes.

**2.2. Surface reactions**

**Thickness (mm)**

**Density (g/cm3 )**

**Polymer**

130 Surface Energy

Helium, neon and argon are examples of inert gases that are widely used in plasma treatment. Due to its lower cost, argon is by far the most common inert gas used [52]. One of the conse‐ quences of inert gas plasma-irradiation is an effective energy transfer to the solid surface, a large amount of stable free radicals are created, so that even several seconds of plasma irradiation are sufficient to cause changes in the surface without affecting the bulk properties [59]. If a plasma reaction is to be carried out with a high system pressure, but a low reactive gas flow rate, an inert gas can serve as a diluent [60]. The exposure of the polymer to the inert gas plasma is sufficient to abstract hydrogen and to form free radicals at or near the surface. This can then interact to form the cross-linkages and unsaturated groups through chain scission. A further effect of the plasma is the removal of weakly bound low-molecular-weight materials or their conversion into a higher molecular-weight by cross-linking reactions [61]. This treatment has been known as CASING (cross-linking by activated species of inert gases).

It has been reported that [62] for oxygen-containing polymers, the oxygen to carbon ratio decreases during noble gas plasma treatment, probably due to the loss of CO or CO2. This is illustrated for PET, bis-phenol-A-polycarbonate (PC), and PMMA after Ar plasma treatment in Figure 4. The decrease in oxygen was measured by XPS. The rate of oxygen loss for PMMA and PET are nearly identical; however that for PC is much more rapid. This suggests that the carbonate oxygen of the PC exhibits a much more labile chemistry. All three polymer surfaces reach a steady-state value of ~28% oxygen loss, suggesting a steady-state surface composition as typically encountered in etched materials.

Unlike the case of the noble gas, only plasmas with the introduction of small amounts of a reactive gas to the noble gas can result in the formation of reactive functional groups on the polymer surface [62]. An example is shown in Table 3, where in addition to argon, mixtures of 1, 5 and 10% O2 in Ar as well as a pure oxygen plasma were used to modify several polymer surfaces. Significant amounts of oxygen are incorporated in all cases where oxygen is present, although the amount of incorporated oxygen is greatest with the pure O2 plasma. The amount of incorporated oxygen in the surface, was observed to correlate with the concentration of O2 in the plasma gas mixture, with the Ar/10% O2 approaching the value obtained with the pure O2 discharge. This observation is consistent with the improvement in adhesion observed for evaporated metals on polymers treated with Ar/O2 mixtures, as compared to that obtained for an Ar only discharge. It has been reported that the degree of incorporation of new functional groups with reactive/noble gas mixtures may depend on the efficiency of the VUV radiation emitted by the gases [62]. The efficiency approximately follows the sequence

$$\text{He} \rhd \text{Ne} \rhd \text{H}\_2 \rhd \text{Ar} \rightharpoonup \text{O}\_2 \lhd \text{N}\_2.$$

From this sequence it can be concluded that mixtures of the reactive gases such as O2 with He may be more effective at incorporating oxygen compared to mixtures of reactive gases with Ar.

**Figure 4.** X-ray photoelectron spectroscopy data illustrating the loss in surface oxygen as a function of Ar plasma treat‐ ment time for PMMA, PET and PC, treatment time in seconds [62]


**Table 3.** Atom percent of oxygen for PE, PS and PET surfaces as determined by XPS after the Ar, O2, and Ar/O2 gas plasma treatments. Note the increase in oxygen with the increase in the content of this gas in the plasma used to treat the individual polymers [62]

The use of inert gas plasma to improve wettability of polymer surface has been widely studied [18, 50] P. Slepicka et al. [18] investigated the surface properties of PET, HDPE, PTFE and PLLA polymers after treatment using DC argon plasma for different treatment times and discharge powers. The effect of the plasma was monitored based on water contact angle as shown in Figure 5. For PTFE the higher the plasma power applied the more pronounced decrease of contact angle was observed. Exposure to plasma leads to a partial defluorination by –C–F bond scission or polymer chain breakage. The –C–F may arise from the ion interaction, which can react with other radical on polymer surface, air oxygen, –C=C– bonds may be created on the plasma activated surface. The PTFE surface exhibits lower free radical count available for reaction with oxygen or nitrogen in comparison to other polymers [18]. PET exhibited a significantly higher decrease of contact angle after plasma treatment compared with PTFE. The decrease in contact angle is connected to changes in surface chemistry and indicates an increase of surface polarity. The interaction of PET with plasma leads to the –C–O– bond breakage in ester groups, resulting in a disruption in the polymer chain. Treatment of HDPE was reported to cause the creation of double bonds in the polymeric layer and forming of oxidised functional groups on the surface. These groups are created by the interaction of activated surface with gases from the atmosphere during the modification or, more often after the procedure [18].

**Plasma gas PE PS PET**

**Figure 4.** X-ray photoelectron spectroscopy data illustrating the loss in surface oxygen as a function of Ar plasma treat‐

**Table 3.** Atom percent of oxygen for PE, PS and PET surfaces as determined by XPS after the Ar, O2, and Ar/O2 gas plasma treatments. Note the increase in oxygen with the increase in the content of this gas in the plasma used to treat

The use of inert gas plasma to improve wettability of polymer surface has been widely studied [18, 50] P. Slepicka et al. [18] investigated the surface properties of PET, HDPE, PTFE and PLLA polymers after treatment using DC argon plasma for different treatment times and discharge powers. The effect of the plasma was monitored based on water contact angle as shown in Figure 5. For PTFE the higher the plasma power applied the more pronounced decrease of contact angle was observed. Exposure to plasma leads to a partial defluorination by –C–F bond scission or polymer chain breakage. The –C–F may arise from the ion interaction, which can react with other radical on polymer surface, air oxygen, –C=C– bonds may be created on the plasma activated surface. The PTFE surface exhibits lower free radical count available for

ment time for PMMA, PET and PC, treatment time in seconds [62]

Untreated Ar Ar/1% O2 Ar/5% O2 Ar/10% O2 O2

132 Surface Energy

the individual polymers [62]

**Figure 5.** Dependence of water contact angle on the plasma exposure time for plasma-treated PET, HDPE, PTFE and PLLA. Modified graph from data reported in [18]

Oxygen and oxygen-containing plasmas are probably the most widely used for polymer surface modification [19]. The oxygen plasma can react with the polymers to produce a variety of oxygen functional groups, including C-O, C=O, O-C=O, C-O-O and CO3. In an oxygen plasma, two processes occur simultaneously: etching of the polymer through the reactions of oxygen atoms with the surface carbon atoms, giving volatile reaction products. The other is the formation of oxygen rich functional groups at the polymer surface, obtained by reactions between the active species from the plasma and the surface atoms.

Nitrogen containing plasmas are also widely used to improve wettability, printability, bondability, electrical conductivity and biocompatibility of polymer surfaces [15]. Nitrogen plasmas are characterised not only by the appearance of highly vibrationally excited molecules, but also their molecules that can have a variety of electronically excited states, most of them being metastable, that make the plasma a rich source of excited nitrogen species [15]. As previously reported, changing the plasma gas or gas composition can be a possible option to improve the analytical performance of the glow discharge plasma [63].

Ita Junkar et al. [14] studied the effect of low pressure rf oxygen and nitrogen plasmas on the surface chemistry of polyethylene. They found that new functional groups are formed on the surface after plasma treatment as shown in Table 4. Interestingly, the saturation with nitrogen and oxygen was achieved after 3 seconds of nitrogen plasma treatment, as further treatment had only a minor effect on the chemical composition [14]. In contrast, oxygen plasma treatment showed saturation with oxygen after 30 seconds of treatment.


**Table 4.** Chemical composition of PET surface after treatment in oxygen and nitrogen plasma for the exposure times shown [14]

Ita Junkar et al. [14] also reported that plasma treatment had as expected altered the wettability of PET surface. They found that treating the PET for 3 seconds resulted in a decrease in water contact angle from 72° for the untreated polymer to 24° and 19° for nitrogen and oxygen plasma treatments respectively. Longer treatment times resulted in a further enhancement in wetta‐ bility, particularly after oxygen plasma treatments, with a contact angle value of approximately 3°, obtained after 90 seconds of treatment.

In addition to the type of gas discharge plasma, amongst the other plasma parameters affecting the wettability of polymer surfaces are treatment time and discharge power [61, 64]. Table 5 summarises the effect of discharge power and treatment time on the wettability of polyethy‐ lene (PE) using a microwave electron cyclotron resonance (ECR) plasma. From this table it is clear that the oxygen plasma is more effective than the argon plasma at reducing water contact angle. The authors also noted that both prolonged treatment times, as well as higher micro‐ wave power causes a deterioration in the polymer surfaces [61].


**Table 5.** Water contact angle of PS and PE treated with Ar and O2 plasma [61]

#### *2.2.1. Hydrophobic recovery*

Nitrogen containing plasmas are also widely used to improve wettability, printability, bondability, electrical conductivity and biocompatibility of polymer surfaces [15]. Nitrogen plasmas are characterised not only by the appearance of highly vibrationally excited molecules, but also their molecules that can have a variety of electronically excited states, most of them being metastable, that make the plasma a rich source of excited nitrogen species [15]. As previously reported, changing the plasma gas or gas composition can be a possible option to

Ita Junkar et al. [14] studied the effect of low pressure rf oxygen and nitrogen plasmas on the surface chemistry of polyethylene. They found that new functional groups are formed on the surface after plasma treatment as shown in Table 4. Interestingly, the saturation with nitrogen and oxygen was achieved after 3 seconds of nitrogen plasma treatment, as further treatment had only a minor effect on the chemical composition [14]. In contrast, oxygen plasma treatment

**PET surface Treatment time (s) C (at.%) O (at.%) N (at.%)**

**Table 4.** Chemical composition of PET surface after treatment in oxygen and nitrogen plasma for the exposure times

Ita Junkar et al. [14] also reported that plasma treatment had as expected altered the wettability of PET surface. They found that treating the PET for 3 seconds resulted in a decrease in water contact angle from 72° for the untreated polymer to 24° and 19° for nitrogen and oxygen plasma treatments respectively. Longer treatment times resulted in a further enhancement in wetta‐ bility, particularly after oxygen plasma treatments, with a contact angle value of approximately

In addition to the type of gas discharge plasma, amongst the other plasma parameters affecting the wettability of polymer surfaces are treatment time and discharge power [61, 64]. Table 5 summarises the effect of discharge power and treatment time on the wettability of polyethy‐ lene (PE) using a microwave electron cyclotron resonance (ECR) plasma. From this table it is clear that the oxygen plasma is more effective than the argon plasma at reducing water contact angle. The authors also noted that both prolonged treatment times, as well as higher micro‐

71.4 79.2 63.5 60.2 60.1 62.0 57.8 55.8 28.6 20.8 24.3 26.1 26.2 38.0 42.2 44.2 0 0 12.2 13.7 13.7 - - -

improve the analytical performance of the glow discharge plasma [63].

showed saturation with oxygen after 30 seconds of treatment.

3°, obtained after 90 seconds of treatment.

wave power causes a deterioration in the polymer surfaces [61].

Theoretical Untreated Nitrogen plasma Oxygen plasma

134 Surface Energy

shown [14]

Plasma activated polymer surfaces generally undergo a phenomenon known as hydrophobic recovery (aging); this involves a gradual increase in the water contact angle of polymers with time [65]. Several mechanisms for these observed changes in surface properties during hydrophobic recovery have been proposed, including the diffusion and reaction of free radicals, the diffusion or reorientation of polar surface groups toward the bulk and the recontamination of the plasma-cleaned surfaces. A longer and more intense plasma treatment is helpful to stabilise the hydrophilic properties [66]. This aging behaviour is usually strongly affected by environmental conditions. High temperature helps the polymer chain to move freely and accelerate the surface rearrangement. In the case of high humidity, the water molecules are adsorbed on the hydrophilic surface and these water molecules disturb the rotation or diffusion of polar groups [67].

An example of hydrophobic recovery is shown in Figure 6 [46]. In this case involving the air plasma treatment of polystyrene, almost complete hydrophobic recovery occurs one day after polymer activation. This figure demonstrates the effect of varying the pulsed plasma cycling time (PCT) on the water contact angle of polystyrene (PS) polymer. The PCT term determines the effective duty cycle. For example, a PCT of 50% equates to 50% of the power that the power supply can deliver for a given set voltage level [46]. The contact angle remained almost constant at all treatments between 5 and 70% PCT. The contact angle value then decreased to lower values with the more intense plasma obtained above 80% PCT values. After five days the water contact angle gradually increases to close to that obtained for the untreated polymer of 83°.

#### *2.2.2. Applications of plasma surface treatments*

Polymers are widely applied in fields ranging from biomaterials to automobile components [10]. Tailoring surface properties such as chemical composition, hydrophilicity, roughness, crystallinity, lubricity and cross-linking density are required for the success in these applica‐ tions [60]. While polymers have excellent bulk material and mechanical properties they often do not possess the surface properties needed for these applications. Plasma treatments are therefore applied to enhance surface properties, examples include the following.

**Figure 6.** Polystyrene water contact angle (recovery; time 1 h, 1 d and 5 d) versus plasma cycling time (PCT) (%). Treat‐ ment conditions: PWM 25 kHz, air volume = 76.6 l min-1 and gap distance 16 mm [46]

#### *2.2.2.1. Adhesion enhancement*

A particular focus of research on plasma-treated polymer base materials is related to adhesion enhancement [16, 68, 69]. The main factors affecting on the surface adhesion of polymer surface are the polymer hydrophilicity and surface roughness [55]. Example of the effect of atmos‐ pheric He plasma treatment on the surface roughness of PET polymer is shown in Figure 7.

**Figure 7.** AFM analysis of untreated (left) and He plasma treated APET (right). The roughness (Ra) increased from 0.4 to 0.9 nm after the plasma treatment [25]

Zhiqiang Gao et al. [55] investigated the effect of atmospheric pressure plasma (13.56 MHz) treatments of polyamids on their subsequent T-peel strength. As shown in Figure 8 it was found that the peel strength increases with longer plasma treatment but appeared to reach a maximum after approximately 120 seconds, under the conditions used. Other authors have shown that over plasma treatment of polymers can result in loss in adhesion, due to thermal damage of the treated surface [69].

**Figure 8.** Dependence of T-peel strength on He/O2 plasma treatment time [55]

#### *2.2.2.2. Heat-sealing*

*2.2.2.1. Adhesion enhancement*

136 Surface Energy

to 0.9 nm after the plasma treatment [25]

A particular focus of research on plasma-treated polymer base materials is related to adhesion enhancement [16, 68, 69]. The main factors affecting on the surface adhesion of polymer surface are the polymer hydrophilicity and surface roughness [55]. Example of the effect of atmos‐ pheric He plasma treatment on the surface roughness of PET polymer is shown in Figure 7.

**Figure 6.** Polystyrene water contact angle (recovery; time 1 h, 1 d and 5 d) versus plasma cycling time (PCT) (%). Treat‐

ment conditions: PWM 25 kHz, air volume = 76.6 l min-1 and gap distance 16 mm [46]

**Figure 7.** AFM analysis of untreated (left) and He plasma treated APET (right). The roughness (Ra) increased from 0.4

In addition to the activation of polymers prior to adhesive bonding, a further application of plasmas is to enhance heat-sealing efficiency. The basic sealing methodology is the bonding together of two polymer surfaces by bringing them into intimate contact while they are in a partially molten state [70]. Heat-sealed polymer trays are widely used for packaging food products, particularly meat and fish [25]. The advantage of plasmas pre-treating the polymers prior to heat sealing is a reduction in the required sealing temperature to achieve full bond strength [71]. For example, treatment of amorphous polyethylene terephthalate (APET) polymer used in food packaging using an atmospheric He plasma yielded up to a 25-fold increase in the heat-sealed polymer peel strength, compared to that obtained for the untreated polymer [25]. This was achieved at a temperature of 140°C, while normal heat-sealing takes place at about 180°C.

#### *2.2.2.3. Removal of contaminates*

In addition to the activation of polymers, contaminant layers can also be removed. An example is shown in Figure 9 where a thin layer of the mould release agent Frekote (approx. 8 nm thick) is removed from the surface of an epoxy composite [72]. Based on reflectance infra-red measurements the cured Frekote was fully broken down after 5 seconds of air plasma treat‐ ment. No thermal damage to the composite surface was observed. For this application it is critically important to provide sufficient energy to remove the organic contaminant but not to damage the composite surface.

**Figure 9.** The reflectance FTIR spectra demonstrate the decrease in the intensity of the peaks associated with Frekote on an epoxy composite, with duration of the air plasma exposure.

#### *2.2.2.4. Biomedical*

Plasma treatments have been used extensively to modify biomaterials [52]. An example of a polymer that has been investigated using plasma treatment is polymethylmethacrylate (PMMA). In a recent study Fatemeh Rezaei et al. [17] used an rf oxygen plasma to enhance the antibacterial and wettability properties of (PMMA) polymer for biomedical applications, especially ophthalmology. They investigate the antibacterial performance against *Escherichia coli* ATCC 25922 by using a modified plate-counting method. Up to a 2 log reduction in bacterial adhesion was observed on the plasma modified polymer. The effect of hydrophobic recovery on the antibacterial performance of the polymer was however not investigated. This study concluded that the bacterial adhesion mechanism is more highly dependent on the surface wettability and hydrophilicity compared to the surface roughness.

## **2.3. Plasma coating of polymer surfaces**

is removed from the surface of an epoxy composite [72]. Based on reflectance infra-red measurements the cured Frekote was fully broken down after 5 seconds of air plasma treat‐ ment. No thermal damage to the composite surface was observed. For this application it is critically important to provide sufficient energy to remove the organic contaminant but not to

**Figure 9.** The reflectance FTIR spectra demonstrate the decrease in the intensity of the peaks associated with Frekote

Plasma treatments have been used extensively to modify biomaterials [52]. An example of a polymer that has been investigated using plasma treatment is polymethylmethacrylate (PMMA). In a recent study Fatemeh Rezaei et al. [17] used an rf oxygen plasma to enhance the antibacterial and wettability properties of (PMMA) polymer for biomedical applications, especially ophthalmology. They investigate the antibacterial performance against *Escherichia coli* ATCC 25922 by using a modified plate-counting method. Up to a 2 log reduction in bacterial adhesion was observed on the plasma modified polymer. The effect of hydrophobic recovery on the antibacterial performance of the polymer was however not investigated. This study concluded that the bacterial adhesion mechanism is more highly dependent on the surface

on an epoxy composite, with duration of the air plasma exposure.

wettability and hydrophilicity compared to the surface roughness.

*2.2.2.4. Biomedical*

damage the composite surface.

138 Surface Energy

Plasma polymerisation has been defined as the formation of polymeric materials under the influence of plasma [29]. It refers to the deposition of polymer films through plasma dissoci‐ ation due to the excitation of an organic monomer gas and subsequent deposition and polymerisation of the excited species on the surface of a substrate [3]. The process of plasma polymerisation involves reactions between plasma species, between plasma and surface species, and between surface species [71]. In plasma polymerisation, the transformation of lowmolecular weight molecules (monomers) into high-molecular-weight molecules (polymers) is achieved due to the effect of energetic plasma species such as electrons, ions and radicals [52]. In this way plasma polymerisation is clearly chemically very different from conventional polymerisation as it involves radicals and ions [52]. Plasma polymers do not comprise repeating monomer units, but instead complicated units containing cross-linked, fragmented and rearranged units from the monomers. Unlike the case of plasma activated polymer where hydrophobic recovery causes increased contact angles to change with time after treatment, the chemistry of the plasma polymerisation controls and fixes the water contact angle of the coated polymer.

Polymeric thin films obtained using plasma-enhanced chemical vapour deposition (PECVD) have several advantages over films produced by conventional polymerisation. The resulting thin, pinhole-free films that are highly coherent and adherent to a variety of substrates may be prepared from monomers not polymerisable by conventional means. The deposited films can be tailored to exhibit properties such as chemically inertness, mechanically tough and thermally stable. They have thus been used in a wide variety of electrical, optical and bio‐ medical applications [73]. Additionally, plasma polymerised surfaces have economical advantage of a ''green'', environmentally benign, technology as compared to other processing methods [74].

Siloxane monomers provide a large number of possible reactants for plasma polymerisation reactions and are generally sufficiently volatile near room temperature, are nontoxic, non‐ flammable, commercially available, and exhibit safe handling besides being economical [71]. These compounds are preferentially used as monomers in low-pressure plasma deposition of silica (SiO2) and non-stoichiometric SiOx films, whereby the latter may have varying hydro‐ carbon contents [75, 76]. Besides silane (SiH4), commonly used monomers for the PECVD of SiO2 or SiOx films include tetraethoxysilane (TEOS), tetramethoxysilane (TMOS), tetrame‐ thylsilane (TMS), hexamethyldisiloxane (HMDSO) and hexamethyldisilazane (HMDS) [77, 78]. The presence of at least one organic group attached to the silicon atom (e.g., Si-CH3) facilitates the transition between a 'soft' polymeric surface and SiO2 by controlling the deposition process conditions. The carbon-silicon bond is very stable, nonpolar, and in the presence of an alkyl group it gives rise to low surface energy and hydrophobic effects [71].

The plasma polymerisation process is carried on usually in a low pressure, low temperature plasma such as those generated using direct current (dc), rf glow discharge (rfGD) and electron cyclotron resonance (ECR) sources [79, 80]. These plasma sources can generate large area uniform discharges with a well-controlled electron density [52]. An example of an oxygen rf plasma study to deposit silicon oxide films was that reported by K. Teshima et al. [80]. The precursor was tetramethoxysilane and it was found that by heating the substrate to 50°C enables carbon-free silicon oxide films to be deposited. Without this heating, during deposition carbon impurities which existed as Si-CH were obtained in the deposited films.

Plasma polymerised coatings have been extensively deposited on polymers in order to tailor surface energy, wettability and friction coefficient [79]. Many potential applications exist for these films in optics (antireflection coatings), food packaging gas diffusion barrier films and biomaterials engineering with respect to protein adsorption. A widely applied application of the silica films is their use for gas barriers applications in food packaging [81]. As a result there has been a strong demand for silica coatings on packaging polymers such as polyethylene terephthalate (PET), oriented polypropylene, polyethylene and oriented nylon. K. Teshima et al. [81] deposited silica films on PET, by low pressure low temperature PECVD using a mixture of tetramethoxysilane (TMOS) and oxygen. They reported that with the presence of active oxygen species, many types of contaminants in the film were largely eliminated, with the result that a dense silica film was obtained. Due to their good gas-barrier properties, applications include not only the manufacture of food packaging products, but also of organic electrolu‐ minescence displays and semiconductor devices.

## *2.3.1. Atmospheric plasma polymerised coatings*

The precursors used for the low pressure deposition of plasma polymerised coatings can also be used to deposit coatings at atmospheric pressure. As outlined earlier the advantages of the atmospheric plasma source are ease of use, with the absence of a requirement for a deposition chamber. A disadvantage for the coating deposition is that the control of coating chemistry can be somewhat more complicated due to the formation of the discharge containing the precursor in air. Nevertheless by selecting appropriate siloxane and fluorinated siloxane precursors, it has been demonstrated that coatings exhibiting controlled water contact angles (θ) ranging from hydrophilic (θ < 5°) to superhydrophobic (θ > 150°) can be obtained using these plasmas [82]. This is demonstrated in Figure 10 where coatings were deposited in a He jet discharge using TEOS, HMDSO, tetramethylcyclotetrasiloxane (TC) and perfluorooctyl‐ triethoxysilane precursors (FS). In addition to precursor type influencing the resulting water contact angle and surface energy, further deposition parameters that were important in influencing coatings chemistry and roughness were the precursor flow rate, jet source to substrate distance and discharge power.

In addition to fluorosiloxanes, fluoropolymers monomers have been extensively investigated as plasma polymerisable precursors for modifying material surfaces, due to their ability to control surface energy (and wettability), friction coefficient, chemical inertness, low dielectric constant and interactions with biological systems [71, 83]. Jacqueline Yim et al. [84] used atmospheric pressure plasma jet to investigate the developing hydrophobic thin film coatings on ultra-high molecular weight polyethylene (UHMWPE) films. Fluoroalkyl silanes, (CH3CH2O)3 SiCH2CH2 (CF2)7CF3 and (CH3O)3SiCH2CH2CF3 and fluoroaryl silane, F5Ar‐ Si(OCH2CH3)3 monomers were used as precursor materials and helium was used as the carrier gas. Optimal hydrophobic behaviour (contact angle of 110–116°) on the UHMWPE substrates was achieved using heptadecafluoro-1,1,2,2-tetrahydrodecyl triethoxysilane, owing to its long

**Figure 10.** Water contact angle and surface energy measurements of uncoated and plasma polymer coated silicon wa‐ fer substrates [82]

alkyl chain consisting of eight fluorocarbon (CF2 and CF3) groups. The properties of these polymers can be enhanced by producing mixed siloxane / fluoropolymer coatings [85]. In one study the anti-oil fouling performance of fluoropolymer/TEOS and fluorosiloxane/TEOS coatings were tested for 30 days at 95 °C on stainless steel separator discs in the engine of a passenger ferry [86]. In addition to demonstrating the good adhesion and durability of these approx. 100 nm thick coatings, they also exhibited significantly reduced levels of engine oil foulant adhesion onto the separator discs.

## *2.3.1.1. Superhydrophobic (SH) coatings*

precursor was tetramethoxysilane and it was found that by heating the substrate to 50°C enables carbon-free silicon oxide films to be deposited. Without this heating, during deposition

Plasma polymerised coatings have been extensively deposited on polymers in order to tailor surface energy, wettability and friction coefficient [79]. Many potential applications exist for these films in optics (antireflection coatings), food packaging gas diffusion barrier films and biomaterials engineering with respect to protein adsorption. A widely applied application of the silica films is their use for gas barriers applications in food packaging [81]. As a result there has been a strong demand for silica coatings on packaging polymers such as polyethylene terephthalate (PET), oriented polypropylene, polyethylene and oriented nylon. K. Teshima et al. [81] deposited silica films on PET, by low pressure low temperature PECVD using a mixture of tetramethoxysilane (TMOS) and oxygen. They reported that with the presence of active oxygen species, many types of contaminants in the film were largely eliminated, with the result that a dense silica film was obtained. Due to their good gas-barrier properties, applications include not only the manufacture of food packaging products, but also of organic electrolu‐

The precursors used for the low pressure deposition of plasma polymerised coatings can also be used to deposit coatings at atmospheric pressure. As outlined earlier the advantages of the atmospheric plasma source are ease of use, with the absence of a requirement for a deposition chamber. A disadvantage for the coating deposition is that the control of coating chemistry can be somewhat more complicated due to the formation of the discharge containing the precursor in air. Nevertheless by selecting appropriate siloxane and fluorinated siloxane precursors, it has been demonstrated that coatings exhibiting controlled water contact angles (θ) ranging from hydrophilic (θ < 5°) to superhydrophobic (θ > 150°) can be obtained using these plasmas [82]. This is demonstrated in Figure 10 where coatings were deposited in a He jet discharge using TEOS, HMDSO, tetramethylcyclotetrasiloxane (TC) and perfluorooctyl‐ triethoxysilane precursors (FS). In addition to precursor type influencing the resulting water contact angle and surface energy, further deposition parameters that were important in influencing coatings chemistry and roughness were the precursor flow rate, jet source to

In addition to fluorosiloxanes, fluoropolymers monomers have been extensively investigated as plasma polymerisable precursors for modifying material surfaces, due to their ability to control surface energy (and wettability), friction coefficient, chemical inertness, low dielectric constant and interactions with biological systems [71, 83]. Jacqueline Yim et al. [84] used atmospheric pressure plasma jet to investigate the developing hydrophobic thin film coatings on ultra-high molecular weight polyethylene (UHMWPE) films. Fluoroalkyl silanes, (CH3CH2O)3 SiCH2CH2 (CF2)7CF3 and (CH3O)3SiCH2CH2CF3 and fluoroaryl silane, F5Ar‐ Si(OCH2CH3)3 monomers were used as precursor materials and helium was used as the carrier gas. Optimal hydrophobic behaviour (contact angle of 110–116°) on the UHMWPE substrates was achieved using heptadecafluoro-1,1,2,2-tetrahydrodecyl triethoxysilane, owing to its long

carbon impurities which existed as Si-CH were obtained in the deposited films.

minescence displays and semiconductor devices.

*2.3.1. Atmospheric plasma polymerised coatings*

140 Surface Energy

substrate distance and discharge power.

Due to their self-cleaning and antistick properties there are a considerable range of potential applications of superhydrophobic surfaces. These properties are desirable for many industrial and biological applications such as self-cleaning windshields for automobiles, anti-biofouling paints for boats, antisticking of snow for antennas and windows, stain resistant textiles, antisoiling architectural coatings, the separation of water and oil. A particularly important potential application is in the textile industry such as in the manufacture of water-proof, fireretardant clothes [87].

Atmospheric pressure plasma have been used for the deposition of SH coatings, which generally exhibit a low polar chemistry in conjunction with a high surface roughness, such as the needle-like morphology shown in Figure 11 (right), the advantage of using plasmas for this application is firstly the relative speed of SH coating deposition as generally only a singlestep deposition process is required [71]. Superhydrophobic properties can also be obtained using non-fluorinated precursors. An example is the hexamethyldisiloxane (HMDSO) precursor, which as demonstrated in Figure 11 can be deposited as a low surface roughness hydrophobic coating (water contact angle 96°), or by tailoring the deposition conditions as a superhydrophobic coating (water contact angle 153°). The difference of 15 and 152 nm respectively in the coating roughness (Ra), as shown in Figure 11, was achieved by altering the jet orifice to substrate distance [85].

**Figure 11.** Optical profilometry images of the HMDSO hydrophobic coating (contact angle 96° - left) and superhydro‐ phobic coating (contact angle 153° - right) [85]

#### *2.3.1.2. Biomaterial applications*

Plasma polymerised coatings are increasingly being investigated for use in biomedical applications. These include surface modification of biomaterials to enhance implant integra‐ tion, the development of targeted drug delivery systems for more effective localised treatment of diseases, as well as therapeutic applications such as wound healing and sterilisation [71].

When an implant material is placed within the body, there are a number of interactions that occur. These interactions take place at the interface between the material surface and the biological environment. As a result, low-temperature plasma modification offers a potentially excellent route to alter the surface properties of an implant material to enhance integration, while retaining the operational functionality provided by the bulk material [71]. Table 6 lists some of the more common research areas and applications of plasma treatment in biomaterials. Low pressure rf plasmas for example have been used for deposited diglyme films on the medical grade polyurethane substrates in order to produce a water contact angle of 22° compared with 85° for the polymer itself to improve the coupling of polyurethanes with the living environment [88]. Atmospheric plasmas have also been used for the application of biofunctional coating to reduce inflammation, which may result in the formation of biofilms and bacteria and consequently cause the rejection of implant materials [71]. To enhance the hemocompatibility of blood contacting biomaterials, it is often beneficially to reduce the attachment of serum proteins, which can lead to the formation of thrombin, inflammation and implant rejection [66].

**Blood-compatible surfaces -** Vascular grafts, catheters, stents, heart-valves, membranes (e.g. for haemodialysis), filters (e.g. for blood cell separation), biomolecules immobilised on surfaces.

**Non-fouling surfaces -** Intraoculars (IOLs), contact lenses, wound healing, catheters, and biosensors.

**Tissue engineering and cell culture -** Cell growth, antibody production, essays, and vascular grafts.

**Biosensors -** Biomolecules immobilised on surfaces.

precursor, which as demonstrated in Figure 11 can be deposited as a low surface roughness hydrophobic coating (water contact angle 96°), or by tailoring the deposition conditions as a superhydrophobic coating (water contact angle 153°). The difference of 15 and 152 nm respectively in the coating roughness (Ra), as shown in Figure 11, was achieved by altering

**Figure 11.** Optical profilometry images of the HMDSO hydrophobic coating (contact angle 96° - left) and superhydro‐

Plasma polymerised coatings are increasingly being investigated for use in biomedical applications. These include surface modification of biomaterials to enhance implant integra‐ tion, the development of targeted drug delivery systems for more effective localised treatment of diseases, as well as therapeutic applications such as wound healing and sterilisation [71].

When an implant material is placed within the body, there are a number of interactions that occur. These interactions take place at the interface between the material surface and the biological environment. As a result, low-temperature plasma modification offers a potentially excellent route to alter the surface properties of an implant material to enhance integration, while retaining the operational functionality provided by the bulk material [71]. Table 6 lists some of the more common research areas and applications of plasma treatment in biomaterials. Low pressure rf plasmas for example have been used for deposited diglyme films on the medical grade polyurethane substrates in order to produce a water contact angle of 22° compared with 85° for the polymer itself to improve the coupling of polyurethanes with the living environment [88]. Atmospheric plasmas have also been used for the application of biofunctional coating to reduce inflammation, which may result in the formation of biofilms and bacteria and consequently cause the rejection of implant materials [71]. To enhance the hemocompatibility of blood contacting biomaterials, it is often beneficially to reduce the attachment of serum proteins, which can lead to the formation of thrombin, inflammation and

the jet orifice to substrate distance [85].

142 Surface Energy

phobic coating (contact angle 153° - right) [85]

*2.3.1.2. Biomaterial applications*

implant rejection [66].

**Barriers coatings -** Drug-release, gas-exchange membranes, device protection, corrosion protection, reduction of leaches (e.g. additives, catalysts, plasticisers, etc.)

**Table 6.** Examples of the potential use of plasma technology in the biomaterials industry [52, 66]

It is widely reported that proteins tend to adsorb more favourably onto surfaces with hydro‐ phobic properties [26]. Thus by deposition of plasma polymer films with specific chemical functionality, a reduction in the attachment of proteins, which can lead to biofilm formation, can be achieved. Through the deposition of siloxane films with varying water contact angle, it has been shown that cell attachment can be controlled as illustrated in Figure 12 [26]. For the siloxane coatings investigated in this study, the optimum MG63 (osteoblast) cell adhesion was observed at a water contact angle of approximately 64°. Surfaces which were more hydrophilic or hydrophobic led to a progressive reduction in the level of cell adhesion. The ability of superhydrophobic atmospheric plasma polymerised coatings to act as passive surfaces which resist bacterial (*S. Aureus*) adhesion has also been successfully demonstrated [82].

**Figure 12.** Influence of the plasma polymerised siloxane coated polystyrene water contact angle on osteoblast cell (MG63) cell adhesion [26]

For fluorinated siloxane coatings, the level of cell adhesion was found to be directly dependent on the level of fluorination. For example, a 13-fold decrease in cell adhesion was observed for the surface with a water contact angle of 155° compared with that obtained at 110° [26]. It is concluded from this and other studies that adhesion was also significantly influenced by cell type, and that compared with the surface roughness, the surface chemistry was found to exhibit a greater influence on cell adhesion.

A number of studies have highlighted the use of atmospheric plasma to deposit antithrom‐ bogenic coatings. For example, Osaka et al. [89] indicated that the TMCTS coated surfaces prevented blood plasma leakage, while also providing an improved antithrombogenic surface. Clarotti et al. [90] used a low-temperature plasma system to deposit fluorocarbon coatings on polymer membrane material to improve material biocompatibility and hemocompatibility. The thrombogenicity of the treated membranes was shown to reduce after fluorocarbon coating, while the filtering properties of the membranes remained unaffected.

## **3. Summary**

This chapter provided an overview of a range of treatments used to tailor the surface properties of polymers. In order to address their low surface energy a range of different treatments including flame, corona, low and atmospheric pressure plasmas have been successfully applied. Due to their controllability and speed of processing, plasmas are increasingly being selected as the method of choice for controlled industrial polymer surface treatments. The effect of the plasma-only treatments can be to remove contaminants, to enhance surface roughness and to produce 'active' polymer surfaces (i.e. generally oxygen rich). While these treatments are widely applied prior to adhesive bonding, the polymers may undergo hydro‐ phobic recovery. For more stable surfaces, which avoid this problem, it is necessary to deposit a plasma polymerised coating. These coatings have been extensively studied, and by tailoring coating chemistry and roughness surfaces with water contact angles from <10° to >150° can be obtained, the wettability being controlled by the deposited coating surface chemistry and roughness. These plasma polymerised coatings even at thickness levels of only 100 nm, have been shown to exhibit a surprisingly high level of robustness, particularly when mixed precursor monomers are used for coating deposition.

## **Author details**

Hisham M. Abourayana\* and Denis P. Dowling

\*Address all correspondence to: hisham.abourayana@ucdconnect.ie

University College Dublin, School of Mechanical and Materials Engineering, Ireland

## **References**

[1] Paul M. Bellan, editor. Fundamentals of Plasma Physics. Cambridge: Cambridge University Press; 2006. 631 p. DOI:10:0521821169

[2] R. N. Franklin and N. St. J. Braithwaite. 80 years of plasma. Plasma Sources Science and Technology. 2009;18:010201 (3 p). DOI:10.1088/0963-0252/18/1/010201

A number of studies have highlighted the use of atmospheric plasma to deposit antithrom‐ bogenic coatings. For example, Osaka et al. [89] indicated that the TMCTS coated surfaces prevented blood plasma leakage, while also providing an improved antithrombogenic surface. Clarotti et al. [90] used a low-temperature plasma system to deposit fluorocarbon coatings on polymer membrane material to improve material biocompatibility and hemocompatibility. The thrombogenicity of the treated membranes was shown to reduce after fluorocarbon

This chapter provided an overview of a range of treatments used to tailor the surface properties of polymers. In order to address their low surface energy a range of different treatments including flame, corona, low and atmospheric pressure plasmas have been successfully applied. Due to their controllability and speed of processing, plasmas are increasingly being selected as the method of choice for controlled industrial polymer surface treatments. The effect of the plasma-only treatments can be to remove contaminants, to enhance surface roughness and to produce 'active' polymer surfaces (i.e. generally oxygen rich). While these treatments are widely applied prior to adhesive bonding, the polymers may undergo hydro‐ phobic recovery. For more stable surfaces, which avoid this problem, it is necessary to deposit a plasma polymerised coating. These coatings have been extensively studied, and by tailoring coating chemistry and roughness surfaces with water contact angles from <10° to >150° can be obtained, the wettability being controlled by the deposited coating surface chemistry and roughness. These plasma polymerised coatings even at thickness levels of only 100 nm, have been shown to exhibit a surprisingly high level of robustness, particularly when mixed

coating, while the filtering properties of the membranes remained unaffected.

precursor monomers are used for coating deposition.

and Denis P. Dowling

University College Dublin, School of Mechanical and Materials Engineering, Ireland

[1] Paul M. Bellan, editor. Fundamentals of Plasma Physics. Cambridge: Cambridge

\*Address all correspondence to: hisham.abourayana@ucdconnect.ie

University Press; 2006. 631 p. DOI:10:0521821169

**3. Summary**

144 Surface Energy

**Author details**

**References**

Hisham M. Abourayana\*


Advances in Applied Science Research. 2012;3(3):1327-1334. ISSN: 0976-8610. Availa‐ ble online at www.pelagiaresearchlibrary.com


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## **DFT Investigations on the CVD Growth of Graphene**

Meicheng Li, Yingfeng Li and Joseph Michel Mbengue

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61031

#### **Abstract**

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152 Surface Energy

Modification of Polymeric Biomaterials. 1997;61:61-68

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The chemical vapor deposition technique is the most popular for preparing highquality graphene. Surface energy will dominate the nucleation process of graphene; thus, the surface energy problems involved in thin film growth are introduced first. The experimental tools to describe the growth process in detail are insufficient. So, a mass of simulation investigations, which can give out a very fine description of the surface atomic process, have been carried out on this topic. We mainly summarized the density functional theory works in unearthing the graphene nuclei process and mechanisms. In addition, some studies using molecular dynamics methods are also listed. Such a summary will be helpful to stimulate future experimental efforts on graphene synthesis.

**Keywords:** Surface energy, graphene, density functional theory, chemical vapor deposition

## **1. Introduction**

After the graphene has been prepared perfectly on a nickel surface by the chemical vapor deposition (CVD) method, [1] the 2D crystal formation process on a perfect cleavage plane suddenly becomes a very important issue that needs to be deeply understood and penetrated. Similar to the general surface absorption phenomenon, the basic physical laws under gra‐ phene's formation on a metal surface should be the minimization of surface energy. What's special is that the classic surface energy theory, to some extent, seems to be slightly "broad-

© 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.

brush." To explain and describe the perfect morphology of the obtained graphene crystals on a metal surface, we need to provide a very fine description of the process of graphene growth on a metal surface using CVD technology. This description should contain two main aspects:


The main results are listed in Table 1. The aim of this chapter is to introduce the specific surface energy problems in the formation of 2D crystal graphene on metal surfaces, which are helpful for materials selection and process optimization in the fabrication of 2D carbons and other materials.



**Table 1.** Summarization of researches on the surface process of graphene growth

brush." To explain and describe the perfect morphology of the obtained graphene crystals on a metal surface, we need to provide a very fine description of the process of graphene growth on a metal surface using CVD technology. This description should contain two main aspects: **1.** The real-time surface energy variations from the absorption of a single carbon atom on the metal surface, to the nucleation of graphene, to the formation of a large-scale single-

**2.** The stationary state on-surface atomic structures and morphologies of the carbon phase on the metal surface, as well as the surface energies of the different surface carbon

The main results are listed in Table 1. The aim of this chapter is to introduce the specific surface energy problems in the formation of 2D crystal graphene on metal surfaces, which are helpful for materials selection and process optimization in the fabrication of 2D carbons and other

> should mainly be CH*x* for graphene growth [2] DFT Identified a carbon atom approaching induced bridging-metal structure

DFT C atoms should be unstable on Cu surface but diffuse directly to the

DFT Chain configuration is superior and will dominate the Ni surface until the

DFT Linear C chain owns 6 atoms should be the representative structure on copper

DFT With increased concentration, C atoms will undergo a sinking and up-floating

DFT Graphene nucleation is very likely to start from the stepped regions, but can

nanoarches consisting of 3–13 atoms when compared to 2D compact islands of

by a C dissolving–precipitating process whereas it grows by a surface adsorption

DFT Revealed an energetic preference for the formation of stable 1D carbon

Exp. Analyzed the activation energy paths for graphene nucleation and growth

Theo. Paved the way for graphene growth on Cu based on Langmuir adsorption and

Exp. Using carbon isotope labeling, clearly verified that graphene growth on Ni occurs

MD On Ni surface, high C concentration leads to the formation of graphene island

and at ~1000 K, the graphene quality can be significantly improved [13]

formation on Cu [3]

number of C reaches 12 [5]

process on Cu surface [7]

easily grow over the step [8]

2D crystallization theory [11]

process on Cu [12]

subsurface [4]

surface [6]

equal sizes [9]

on Cu [10]

DFT Investigated the decomposition of CH4 on Cu, and declared the active species

layer graphene, and finally to the formation of multilayers of graphene

morphologies.

**Classification Method Brief descriptions**

materials.

154 Surface Energy

**Stationary state researches**

**Real-time kinetic researches**

By the present experimental technologies, it is still a great challenge to obtain the abovemen‐ tioned knowledge especially under high-temperature conditions. So, it naturally becomes the best choice to investigate the graphene on-surface growth process by the accurate, reliable theoretical approach: the density functional theory (DFT). [15] Except for some controllable numerical approximations, the DFT approach can be recognized as a rigorous accurate theory, and since it is based on the maximum advanced of physical theory today, the results obtained by the DFT approach is of great reliability. Using the DFT approach, the graphene on-surface growth process can be described even at the level of electron distribution. In recent years, DFT researches on this aspect have been in full swing and some key progresses have been obtained, e.g., the surface energy evolution curve with the carbon atom number increases during the graphene growth on cupper surface has been revealed in detail by Li et al. [6] Parts of these theoretical results have been verified in experiments, and thus can provide reliable guides to optimize the preparation of graphene.

In this chapter, the surface energy problems involved in thin film growth will be first intro‐ duced from the aspect of the classic surface energy theory. Then, we will introduce the approaches that have been exploited in describing the graphene CVD growth process from the energy aspect using the DFT approach. Thirdly, we will review the achievements using these approaches on the growth process of graphene.

## **2. Surface energy problems in thin film growth**

## **2.1. General fundamentals of surface energy**

Consider the atoms in the bulk and surface regions of a crystal, the atoms in the bulk possess lower energy since they are more tightly bound, while the ones on the surface will possess higher energy since they are less tightly bound. The sum of all the excess energies of the surface atoms is the surface energy. Therefore, surface energy is generally defined as the excess energy needed when a new surface is created. [16]

For a liquid, the surface energy density is identical to the surface tension (force per unit length), e.g., water has a surface energy density of 0.072 J/m2 and a surface tension of 0.072 N/m (the units are equivalent). For a solid, if we cut a body into pieces, it will consume energy. Under the hypothesis that the cutting process is reversible, according to the conservation of energy, the energy consumed by the cutting process will be equal to the energy inherent in the two new surfaces created. Therefore, the unit surface energy of a solid material would be half of its energy of cohesion. In practice, this is only an approximate description. Surfaces often change their form away from the simple "cleaved bond" model implied above, and readily rearrange or react to reduce their energy.

Surface energy is the essence of "energy." According to statistical thermodynamics, the surface energy can be described by the Gibbs isotherm. [17] From the expression of Gibbs free energy in differential form, *dG ≡ −SdT +VdP + γdA*, it can be defined as *<sup>γ</sup>* <sup>≡</sup>( <sup>∂</sup> <sup>G</sup> <sup>∂</sup> *<sup>A</sup>* )*<sup>T</sup>* ,*<sup>P</sup>*. Therefore, surface energy can be considered as a criterion at equilibrium. When a system is reaching the equili‐ brium state, it tends to reduce its free energy. In some cases, this stable state is achieved by the reduction of the surface energy. This principle of surface energy determines many physical phenomena. For example, the smaller drops will aggregate into larger ones; in the absence of gravity, a droplet will tend to become spherical to reduce its surface energy.

Most importantly, the relative magnitude of surface energy determines the wettability of one material on another material. A material having very low surface energy can easily wet a material having high surface energy and form a uniform adhesive layer on it. Conversely, if the deposition material has a higher surface energy, it readily forms an atomic group on the substrate with lower surface energy. Such a function of the surface energy has a wide range of practical applications. We can coat surface-modified materials (e.g., pigments) on the surface of buildings, automobiles or mechanical components to modify their surface energy and thus adapt to the working environment. A good example is waterproofing. Since organic material has low surface energy, coating wax on the surface of a vehicle can prevent the formation of water film when the automobile is wet with rain. Another important application, which is mainly discussed in this chapter (i.e., wettability), is that it determines the process of thin film growth and the quality of the samples obtained. This will be discussed in detail in Section 1.1.3.

#### **2.2. Determination of the surface energy**

To measure the surface energy of a liquid, commonly, there are two methods. The first one is the so-called stretching film method, as illustrated in Figure 1. By this method, the surface energy is measured by stretching a liquid membrane (which increases the surface area and hence the surface energy density). In that case, in order to increase the surface area of a mass of liquid by an amount, 2*δL* (the liquid membrane has two surfaces), a quantity of work, *Fδ*, is needed. The increase of the surface energy is 2*γδL* (where *γ* is the surface energy density of the liquid). So, 2*γδL* = *Fδ*, the surface energy density can be calculated by *γ* = *F*/2*L*.

The other commonly used method to measure the surface energy of a liquid is the capillary tube method, as illustrated in Figure 2. When inserting a capillary tube of greater surface energy into the liquid, the adhesive force of the liquid to the tube wall will point upward. Thus, to reduce the amount of energy, the liquid will rise along the tube till a new equilibrium is reached: *f* cos*θ* =*mg*. *f* is the adhesive force, which is equal to 2*πRγ* (*R* is the radius of the capillary, *γ* is the surface energy density of the liquid). θ is the contact angle between the liquid and the capillary. *mg* is the gravity of the liquid column, which equals to *πR*<sup>2</sup> *hρg* (*h* is the height of rise in the capillary and *ρ* is the density of the liquid). Therefore, the equality can be rewritten

**Figure 1.** A liquid membrane stretched by an external force.

new surfaces created. Therefore, the unit surface energy of a solid material would be half of its energy of cohesion. In practice, this is only an approximate description. Surfaces often change their form away from the simple "cleaved bond" model implied above, and readily

Surface energy is the essence of "energy." According to statistical thermodynamics, the surface energy can be described by the Gibbs isotherm. [17] From the expression of Gibbs free energy

energy can be considered as a criterion at equilibrium. When a system is reaching the equili‐ brium state, it tends to reduce its free energy. In some cases, this stable state is achieved by the reduction of the surface energy. This principle of surface energy determines many physical phenomena. For example, the smaller drops will aggregate into larger ones; in the absence of

Most importantly, the relative magnitude of surface energy determines the wettability of one material on another material. A material having very low surface energy can easily wet a material having high surface energy and form a uniform adhesive layer on it. Conversely, if the deposition material has a higher surface energy, it readily forms an atomic group on the substrate with lower surface energy. Such a function of the surface energy has a wide range of practical applications. We can coat surface-modified materials (e.g., pigments) on the surface of buildings, automobiles or mechanical components to modify their surface energy and thus adapt to the working environment. A good example is waterproofing. Since organic material has low surface energy, coating wax on the surface of a vehicle can prevent the formation of water film when the automobile is wet with rain. Another important application, which is mainly discussed in this chapter (i.e., wettability), is that it determines the process of thin film growth and the quality of the samples obtained. This will be discussed in detail in Section 1.1.3.

To measure the surface energy of a liquid, commonly, there are two methods. The first one is the so-called stretching film method, as illustrated in Figure 1. By this method, the surface energy is measured by stretching a liquid membrane (which increases the surface area and hence the surface energy density). In that case, in order to increase the surface area of a mass of liquid by an amount, 2*δL* (the liquid membrane has two surfaces), a quantity of work, *Fδ*, is needed. The increase of the surface energy is 2*γδL* (where *γ* is the surface energy density of

The other commonly used method to measure the surface energy of a liquid is the capillary tube method, as illustrated in Figure 2. When inserting a capillary tube of greater surface energy into the liquid, the adhesive force of the liquid to the tube wall will point upward. Thus, to reduce the amount of energy, the liquid will rise along the tube till a new equilibrium is reached: *f* cos*θ* =*mg*. *f* is the adhesive force, which is equal to 2*πRγ* (*R* is the radius of the capillary, *γ* is the surface energy density of the liquid). θ is the contact angle between the liquid

of rise in the capillary and *ρ* is the density of the liquid). Therefore, the equality can be rewritten

the liquid). So, 2*γδL* = *Fδ*, the surface energy density can be calculated by *γ* = *F*/2*L*.

and the capillary. *mg* is the gravity of the liquid column, which equals to *πR*<sup>2</sup>

<sup>∂</sup> *<sup>A</sup>* )*<sup>T</sup>* ,*<sup>P</sup>*. Therefore, surface

*hρg* (*h* is the height

in differential form, *dG ≡ −SdT +VdP + γdA*, it can be defined as *<sup>γ</sup>* <sup>≡</sup>( <sup>∂</sup> <sup>G</sup>

gravity, a droplet will tend to become spherical to reduce its surface energy.

rearrange or react to reduce their energy.

156 Surface Energy

**2.2. Determination of the surface energy**

as 2*πRγ*cos*θ* = *πR*<sup>2</sup> *hρg*, then the surface energy of the liquid can be calculated by *γ* = *Rρgh* / 2cos*θ*.

**Figure 2.** Illustrations for the capillary tube method in measuring the surface energy of a liquid.

For the measurement of the surface energy of a solid, the above two methods cannot be used. But there exists one way which is approximate to the capillary tube method in the case of liquids. This is called the zero creep method. At some high temperatures, the solid creeps and even though the surface area changes, the volume remains approximately constant. If over‐ hanging a cylindrical line of radius *r* and length *l*, at equilibrium, the variation of the total energy vanishes and we have

$$\text{d}E = 1/2\,\rho\text{g}\,\pi\left(2l^2rdr + 2r^2ldl\right) - 2\,\pi\gamma\left(rdl + ldr\right) = 0$$

where *ρ* is the density, and *γ* is the surface energy density of the solid line. Since the volume of the solid line remains constant, the variation of the volume is zero, i.e.

$$
\pi r^2 l = \pi \left( r + dr \right)^2 \left( l - dl \right)^2
$$

From these two equations, the expression of the surface energy for a solid can be deduced as *γ* = *rρgl*/2, which is similar as that of the liquid deduced from the capillary tube method. So, the surface energy density of the solid can be obtained by measuring the radius and length of a cylindrical line, at equilibrium.

This method is only valid for isotropic solids, whose surface energy is the same in all orienta‐ tions. Such a condition can be strictly satisfied only for amorphous solids. If the sample is a metal or made by powder sintering (like ceramics), isotropy is also a good approximation. In the case of single-crystal materials, which are obviously anisotropic, this method will become invalid. In addition, since the measurement conditions for the surface energy of a solid requires high temperature, the obtained results sometimes will be inaccurate and thus unreliable in practical applications. So, in determining the surface energy of a solid, theoretical methods are of special importance. The traditional theoretical methods in estimating the surface energy of a solid include the thermodynamics calculation and mechanical calculation methods.

In the thermodynamics calculation method, the surface energy of a solid at a given temperature is derived by the thermodynamic relations from the measured value under a melting state. So, the calculated surface energy is also only valid for isotropic solids. In the mechanical calcula‐ tion method, the surface energy of a solid is related to its Young's modulus. But since the Young's modulus for many materials is nearly the same, the obtained values are quite coarse with about six to seven multiples of errors. Additionally, both the thermodynamics and mechanical calculation methods can't reflect the relationships between the surface energy and the crystallographic orientations. So, they are mostly used for some particular systems or in cases that require less precision.

The third theoretical method is called the atomic calculation method. In this method, the surface energy is determined by multiplying the energy of one bond and the number of bonds being broken. According to the different approaches in obtaining the energy of one bond, this method can be split into two branches. In the first one, the energy of one bond is estimated by the sublimation energy. For the crystal owning one mole (*N*A) atoms, at least 0.5 *N*A bonds will be formed. In consideration of the coordination number *Z*, the number of bonds in one-mole crystal will be 0.5 *N*A\**Z*. So, the average energy per bond can be estimated as *<sup>ε</sup>* <sup>=</sup> *<sup>Δ</sup>Hs* 0.5*N*A\**<sup>Z</sup>* . *ΔHs* is the molar enthalpy of sublimation. In the other one, the energy of one bond is calculated by the interatomic potential, which can be calculat‐ ed using the modern molecular simulation method or the first principle method. Take the FCC crystal as an example, the coordination number of every atom is 12. While the atoms at the (111) plane only possess nine coordination atoms. This means that 3 bonds per atoms are broken during the formation of a (111) plane in the FCC crystal. So, the energy required to form one surface atom can be given as: *E*(111) = *ε*\*3<sup>≡</sup> *<sup>Δ</sup>Hs* <sup>2</sup>*N*<sup>A</sup> . The surface energy *γ* can be defined as *γ* ≡*E*(111)×number of surface atom / surface area. For the (111) plane in FCC crystal, the number of surface atom / surface area equals <sup>4</sup> 3*a*0 <sup>2</sup> . So, *<sup>γ</sup>* <sup>=</sup> *<sup>Δ</sup>H*<sup>s</sup> <sup>2</sup>*N*<sup>A</sup> ( <sup>4</sup> 3*a*0 <sup>2</sup> ) <sup>=</sup> *<sup>Δ</sup>H*<sup>s</sup> 3*N*A*a*<sup>0</sup> 2 .

#### **2.3. Thermokinetics process in thin film growth**

During the thin film growth process, an old surface will be covered and a new surface will be created. Thus, this process should be mainly controlled by the surface energy theory. There‐ fore, the growth thermokinetics as well as the quality of the obtained samples will be controlled by the surface energy. In the first, the critical size of the surface nucleation in thin film growth

1

and the nucleation rate are determined by the surface energy. In this section, the thermody‐ namic process of thin film growth on the flat surface is illustrated to introduce this determi‐ nation relationship.

In order to study step generation on a flat surface, we consider the case of forming a disc with radius *r* and height *a* (an atomic layer), as illustrated in Figure 3. We assume that the material of the disc is the same as the flat surface and the disc is grown epitaxially, the additional surface energy caused by the formation of the disc is only the surface energy on the side region of the disc, **Proof Corrections Form Author(s) Name(s): Meicheng Li Chapter Title: DFT Investigations on the CVD Growth of Graphene** 

$$E\_{\rm d} = 2\pi r a \gamma$$

This increased surface energy will exert a compressive force on the disc, 3 1 Could you please make the Bottom Edge Border of Table 1 have the same thickness?

**No. Delete Replace with** 

**Page No.** 

**Line**

7 11 Replace Figure 3 by a clearer version.

the surface energy density of the solid can be obtained by measuring the radius and length of

This method is only valid for isotropic solids, whose surface energy is the same in all orienta‐ tions. Such a condition can be strictly satisfied only for amorphous solids. If the sample is a metal or made by powder sintering (like ceramics), isotropy is also a good approximation. In the case of single-crystal materials, which are obviously anisotropic, this method will become invalid. In addition, since the measurement conditions for the surface energy of a solid requires high temperature, the obtained results sometimes will be inaccurate and thus unreliable in practical applications. So, in determining the surface energy of a solid, theoretical methods are of special importance. The traditional theoretical methods in estimating the surface energy of

a solid include the thermodynamics calculation and mechanical calculation methods.

In the thermodynamics calculation method, the surface energy of a solid at a given temperature is derived by the thermodynamic relations from the measured value under a melting state. So, the calculated surface energy is also only valid for isotropic solids. In the mechanical calcula‐ tion method, the surface energy of a solid is related to its Young's modulus. But since the Young's modulus for many materials is nearly the same, the obtained values are quite coarse with about six to seven multiples of errors. Additionally, both the thermodynamics and mechanical calculation methods can't reflect the relationships between the surface energy and the crystallographic orientations. So, they are mostly used for some particular systems or in

The third theoretical method is called the atomic calculation method. In this method, the surface energy is determined by multiplying the energy of one bond and the number of bonds being broken. According to the different approaches in obtaining the energy of one bond, this method can be split into two branches. In the first one, the energy of one bond is estimated by the sublimation energy. For the crystal owning one mole (*N*A) atoms, at least 0.5 *N*A bonds will be formed. In consideration of the coordination number *Z*, the number of bonds in one-mole crystal will be 0.5 *N*A\**Z*. So, the average energy per bond

the energy of one bond is calculated by the interatomic potential, which can be calculat‐ ed using the modern molecular simulation method or the first principle method. Take the FCC crystal as an example, the coordination number of every atom is 12. While the atoms at the (111) plane only possess nine coordination atoms. This means that 3 bonds per atoms are broken during the formation of a (111) plane in the FCC crystal. So, the energy required

defined as *γ* ≡*E*(111)×number of surface atom / surface area. For the (111) plane in FCC

During the thin film growth process, an old surface will be covered and a new surface will be created. Thus, this process should be mainly controlled by the surface energy theory. There‐ fore, the growth thermokinetics as well as the quality of the obtained samples will be controlled by the surface energy. In the first, the critical size of the surface nucleation in thin film growth

to form one surface atom can be given as: *E*(111) = *ε*\*3<sup>≡</sup> *<sup>Δ</sup>Hs*

crystal, the number of surface atom / surface area equals <sup>4</sup>

**2.3. Thermokinetics process in thin film growth**

0.5*N*A\**<sup>Z</sup>* . *ΔHs* is the molar enthalpy of sublimation. In the other one,

3*a*0

<sup>2</sup> . So, *<sup>γ</sup>* <sup>=</sup> *<sup>Δ</sup>H*<sup>s</sup>

<sup>2</sup>*N*<sup>A</sup> . The surface energy *γ* can be

<sup>2</sup> ) <sup>=</sup> *<sup>Δ</sup>H*<sup>s</sup> 3*N*A*a*<sup>0</sup> 2 .

<sup>2</sup>*N*<sup>A</sup> ( <sup>4</sup> 3*a*0

a cylindrical line, at equilibrium.

158 Surface Energy

cases that require less precision.

can be estimated as *<sup>ε</sup>* <sup>=</sup> *<sup>Δ</sup>Hs*

 **Figure 3.** (a) The disc nucleation on flat surface with height *a* and radius *r*; (b) schematic cross-sectional view of the disc (the side of the disc exerts a compressive force on it).

$$p = \frac{1}{A} \frac{dE\_d}{dr} = \frac{2\pi a \eta}{2\pi ra} = \frac{\mathcal{V}}{r}$$

where *A* is the surrounding area of the disc. Under such a compressive force, the energy of each atom in the disc will increase

$$p\Omega = \frac{\mathcal{Y}\Omega}{r}$$

where *Ω* is the atomic volume. Due to the energy increase, the atoms in the disc become much easier to sublimate than those in the flat substrate. The sublimation rate can be written as

$$\vec{J}\_c = N\_0 \nu\_s \exp\left(-\frac{\Delta G\_{\text{des}}}{kT} + \frac{\gamma \Omega}{rkT}\right) = J\_0 \times \exp\left(\frac{\gamma \Omega}{rkT}\right).$$

where *N*0 is the number of atoms being absorbed on the flat surface per unit area, *υ*<sup>s</sup> is the RMS velocity of atoms on the flat surface, Δ*G*des is the activation energy during the desorption process of the surface atom. At a given temperature, *J <sup>c</sup>* ' and *J*0 are both proportional to the pressure, so the pressure ratio on the disc and the flat surface is

$$\frac{p}{p\_0} = \exp\left(\frac{\mathcal{N}\Omega}{rkT}\right).$$

From this equation, the energy changes per atom from the gas phase to the solid phase can be calculated as *Δ<sup>μ</sup>* <sup>=</sup>*kT* ln( *<sup>p</sup> p*0 ), thus the sublimation heat per unit volume *ΔE*s can be calculated by *ΔE*s<sup>=</sup> *<sup>Δ</sup><sup>μ</sup> <sup>Ω</sup>* .

Consider the energy change from the gas phase to the solid phase during the disc growth, including the surface energy being increased and the sublimation heat being released,

$$
\Delta E = E\_s - V\Delta E\_s = 2\pi r a \chi - \pi r^2 a \Delta E\_s = 2\pi r a \chi - \pi r^2 a \frac{\Delta \mu}{\Omega}
$$

From this equation, the critical size (here means the critical radius *r*c) of the surface nucleation can be defined. Let *<sup>d</sup>Δ*<sup>E</sup> *dr* =0, we can obtain

$$r\_c = \frac{\mathcal{A}\Omega}{\Delta\mu}$$

If the radius of the disc reaches *r*c, the energy change *ΔE*c will equal

$$\Delta E\_{\text{c}} = \pi r\_{\text{c}} a \gamma$$

This energy is defined as the nucleation activation energy, which determines the nucleation rate

$$\text{Inucleation rate} \propto \exp\left(-\frac{\Delta E\_c}{kT}\right) = \exp\left(-\frac{\pi a \eta^2 \Omega}{kT \Delta \mu}\right)$$

In the second, the growth mode of thin film means that the layered growth or island growth is also controlled by the surface energy. Such control is illustrated in the heteroepitaxial growth of a thin film on a flat substrate, taking the (001) facet growth of simple cubic crystal as an example, and only the nearest-neighbor interactions are considered. Let thin film of material A grow on surface B, the interaction potential between two A atoms and two B atoms is indicated by *U*AA and *U*BB, respectively, and the interaction potential between atoms A and B is indicated by *U*AB. According to the definition of the surface energy, the surface energies of material A and B, and the interface energy between material A and B can be calculated as

process of the surface atom. At a given temperature, *J <sup>c</sup>*

*p*0

calculated as *Δ<sup>μ</sup>* <sup>=</sup>*kT* ln( *<sup>p</sup>*

*<sup>Ω</sup>* .

can be defined. Let *<sup>d</sup>Δ*<sup>E</sup>

rate

by *ΔE*s<sup>=</sup> *<sup>Δ</sup><sup>μ</sup>*

160 Surface Energy

pressure, so the pressure ratio on the disc and the flat surface is

*dr* =0, we can obtain

If the radius of the disc reaches *r*c, the energy change *ΔE*c will equal

*p*

*p rkT* <sup>0</sup>

From this equation, the energy changes per atom from the gas phase to the solid phase can be

Consider the energy change from the gas phase to the solid phase during the disc growth, including the surface energy being increased and the sublimation heat being released,

> *E E V E ra r a E ra r a* 2 2 s s <sup>s</sup> 2 2

<sup>D</sup> D= - D = - D = -

From this equation, the critical size (here means the critical radius *r*c) of the surface nucleation

m

W = D

*E ra* c c D = p g

This energy is defined as the nucleation activation energy, which determines the nucleation

In the second, the growth mode of thin film means that the layered growth or island growth is also controlled by the surface energy. Such control is illustrated in the heteroepitaxial growth of a thin film on a flat substrate, taking the (001) facet growth of simple cubic crystal as an example, and only the nearest-neighbor interactions are considered. Let thin film of material A grow on surface B, the interaction potential between two A atoms and two B atoms is

<sup>c</sup> nucleation rate exp exp

*r* c g

pg p

exp

Ω

æ ö g = ç ÷ è ø '

), thus the sublimation heat per unit volume *ΔE*s can be calculated

 pg p

*E a kT kT*

æ ö <sup>D</sup> æ ö <sup>W</sup> µ- =- ç ÷ ç ÷ è ø è ø <sup>D</sup>

2

m

p g

and *J*0 are both proportional to the

m

W

$$\begin{aligned} \mathcal{V}\_{\rm A} &= \boldsymbol{u}\_{\rm AA} \,/\, \mathbf{2}a^2 \\ \mathcal{V}\_{\rm B} &= \boldsymbol{u}\_{\rm BB} \,/\, \mathbf{2}a^2 \\ \mathcal{V}\_{\rm AB} &= \left[ \frac{\boldsymbol{u}\_{\rm AA}}{\mathbf{2}a^2} + \frac{\boldsymbol{u}\_{\rm BB}}{\mathbf{2}a^2} - \frac{\boldsymbol{u}\_{\rm AB}}{a^2} \right] \end{aligned}$$

where *a* is the lattice constant (the same for A and B). If *u*AB ≥*u*AA, which means *γ*<sup>B</sup> ≥*γ*<sup>A</sup> + *γ*AB (the film growth will reduce the energy of the system), the material A will wet the surface of material B completely, which results in a layered thin film growth process. If *u*AB <*u*AA, which means *γ*<sup>B</sup> <*γ*<sup>A</sup> + *γ*AB (the film growth will increase the energy of the system), material A can't completely wet material B, which results in an island thin film growth process.

In the initial stage of the thin film growth, there are only very few atoms. The concept of surface energy, which is a collection quantity for a given material, seems too big to be used in analyzing the growth process. So, in practice, for fine studies on the thin film nucleation process, energy evolution on the atomic and even on the electric level based on the theoretical method (specially the molecular simulation technology) is always used. **1.2 Approaches from energy aspect in investigating graphene growth**  Graphene is the first truly 2D crystal ever observed in nature,18 as shown in Figure

#### **3. Approaches from energy aspect in investigating graphene growth** inexistent in the past, due to the Mermin–Wagner theorem. This theorem states that a

opportunities for future devices and systems.

4. This is remarkable because 2D crystals were predicated to be unstable and thus

Graphene is the first truly 2D crystal ever observed in nature,[18] as shown in Figure 4. This is remarkable because 2D crystals were predicated to be unstable and thus inexistent in the past, due to the Mermin–Wagner theorem. This theorem states that a 2D crystal will melt at any temperature but zero due to thermal fluctuations. From its discovery, graphene has grabbed appreciable attention due to its exceptional electronic and optoelectronic properties: it is reported as one of the best electronic materials. The reported properties and applications of graphene have opened up new opportunities for future devices and systems. 2D crystal will melt at any temperature but zero due to thermal fluctuations. From its discovery, graphene has grabbed appreciable attention due to its exceptional electronic and optoelectronic properties: it is reported as one of the best electronic materials. The reported properties and applications of graphene have opened up new

 Figure 4. Illustration and the scanning probe microscopy image of graphene. (Haider I. Rasool, Emil B. Song, Matthew Mecklenburg, et al., JACS, 2011) **Figure 4.** Illustration and the scanning probe microscopy image of graphene. (Haider I. Rasool, Emil B. Song, Matthew Mecklenburg, et al., JACS, 2011)

Because of the great application potential of graphene, investigations on the

synthesis of single sheets of graphene have also attracted a large number of

researchers and companies. Till now, the synthesis routes of graphene can be broadly

categorized into five main different sections19: the exfoliation and cleavage route, the

chemical vapor deposition techniques, thermal decomposition of SiC or other

substrates, unzipping CNTs, and chemical methods. Among them, the chemical vapor

deposition technique is the most popular for preparing large-scale and high-quality

graphene samples. Most of the chemical vapor deposition growth of graphene uses

nickel, iron, and copper foils as the substrate. While nickel and iron have great carbon

solubility, the graphene growth will go through a carbon dissolving and precipitating

process.12 Therefore, on nickel and iron foils, the obtained graphene films are often

inhomogeneous with many defects and multilayer flakes. Such disadvantage can be

overcome by using copper foil as the substrate due to its low carbon solubility. The

growth process of graphene on copper foil is self-limited, thus large-scale high-quality

Because of the great application potential of graphene, investigations on the synthesis of single sheets of graphene have also attracted a large number of researchers and companies. Till now, the synthesis routes of graphene can be broadly categorized into five main different sec‐ tions[19]: the exfoliation and cleavage route, the chemical vapor deposition techniques, thermal decomposition of SiC or other substrates, unzipping CNTs, and chemical methods. Among them, the chemical vapor deposition technique is the most popular for preparing largescale and high-quality graphene samples. Most of the chemical vapor deposition growth of graphene uses nickel, iron, and copper foils as the substrate. While nickel and iron have great carbon solubility, the graphene growth will go through a carbon dissolving and precipitating process. [12] Therefore, on nickel and iron foils, the obtained graphene films are often inho‐ mogeneous with many defects and multilayer flakes. Such disadvantage can be overcome by using copper foil as the substrate due to its low carbon solubility. The growth process of graphene on copper foil is self-limited, thus large-scale high-quality single-layer samples can be obtained. So, here, we focus on the formation of graphene on copper substrate. To investi‐ gate the nucleation and growth mechanism of graphene on copper surface systematically is of great importance for exploiting and optimizing the fabrication of graphene by the chemical vapor deposition technique.

**Figure 5.** Growth mechanism of graphene on Cu surface. Methane is adsorbed on the surface and then decomposed to carbon adatoms. When the supersaturation of the carbon adatoms reaches a critical value (*C*nuc), graphene begins to nucleate and grow step by step.

Through experimental method, by characterizing the graphene nuclei grown on copper for different growth temperatures and times by high-resolution scanning electron microscope, Kim et al. [10] have analyzed the nucleation and growth mechanism of graphene on copper substrates (as shown in Figure 5). Methane molecules are first chemisorbed on the copper surface. Such adsorbed methane can be decomposed to carbon adatoms. The concentration of these carbon adatoms, *C*cu, increases with time increases, until a critical point, i.e., the super‐ saturation of the carbon adatoms reaches a critical value (*C*nuc). Now, graphene begins to nucleate. Such process and the growth of the nuclei will deplete the carbon surrounding them. So, *C*cu decreases quickly. In this decreasing process, the nucleation rate becomes negligible, while the growth of formed nuclei continues. Till the *C*cu is reduced to a stable level, *C*eq, the equilibrium between graphene, surface carbon, and CH4/H2 will be reached.

Analyses based on the experimental characterizations can give the framework of graphene growth similar to the existing theories for two-dimensional nucleation and growth of thin films. However, encumbered by the growth conditions of graphene and the lack of effective characterization methods, some fine messages, like the exact nature of the active carbon species adsorbed on the Cu surface, the adsorption and desorption energy of the carbon species on the Cu surface, the surface diffusion energy barrier, as well as the bonding process of the carbon species, cannot be well obtained yet. These messages are of great importance. The firstprinciple method, especially the density functional theory (DFT), is much suited for the investigation of such messages. By this method, a lot of simulation studies have been carried out on the atomic process of graphene growth on copper substrates.

Because of the great application potential of graphene, investigations on the synthesis of single sheets of graphene have also attracted a large number of researchers and companies. Till now, the synthesis routes of graphene can be broadly categorized into five main different sec‐ tions[19]: the exfoliation and cleavage route, the chemical vapor deposition techniques, thermal decomposition of SiC or other substrates, unzipping CNTs, and chemical methods. Among them, the chemical vapor deposition technique is the most popular for preparing largescale and high-quality graphene samples. Most of the chemical vapor deposition growth of graphene uses nickel, iron, and copper foils as the substrate. While nickel and iron have great carbon solubility, the graphene growth will go through a carbon dissolving and precipitating process. [12] Therefore, on nickel and iron foils, the obtained graphene films are often inho‐ mogeneous with many defects and multilayer flakes. Such disadvantage can be overcome by using copper foil as the substrate due to its low carbon solubility. The growth process of graphene on copper foil is self-limited, thus large-scale high-quality single-layer samples can be obtained. So, here, we focus on the formation of graphene on copper substrate. To investi‐ gate the nucleation and growth mechanism of graphene on copper surface systematically is of great importance for exploiting and optimizing the fabrication of graphene by the chemical

**Figure 5.** Growth mechanism of graphene on Cu surface. Methane is adsorbed on the surface and then decomposed to carbon adatoms. When the supersaturation of the carbon adatoms reaches a critical value (*C*nuc), graphene begins to

Through experimental method, by characterizing the graphene nuclei grown on copper for different growth temperatures and times by high-resolution scanning electron microscope, Kim et al. [10] have analyzed the nucleation and growth mechanism of graphene on copper substrates (as shown in Figure 5). Methane molecules are first chemisorbed on the copper surface. Such adsorbed methane can be decomposed to carbon adatoms. The concentration of these carbon adatoms, *C*cu, increases with time increases, until a critical point, i.e., the super‐ saturation of the carbon adatoms reaches a critical value (*C*nuc). Now, graphene begins to nucleate. Such process and the growth of the nuclei will deplete the carbon surrounding them. So, *C*cu decreases quickly. In this decreasing process, the nucleation rate becomes negligible, while the growth of formed nuclei continues. Till the *C*cu is reduced to a stable level, *C*eq, the

equilibrium between graphene, surface carbon, and CH4/H2 will be reached.

*i ii*

*iii*

*iv*

vapor deposition technique.

162 Surface Energy

nucleate and grow step by step.

DFT is a computational quantum mechanical modelling method, which is among the most popular and versatile methods available in physics, chemistry, and materials science. With this method, the properties of the system are determined by using functionals, i.e., functions of another function, which in this case is the spatially dependent electron density. DFT has broad applications in the chemical and material sciences for the interpretation and prediction of complex system behaviors. Specifically, DFT computational methods are applied for the study of systems exhibiting high sensitivity to synthesis and processing parameters. In this section, we will briefly introduce the primary approaches that have been exploited in investigating the growth mechanisms of graphene on copper surface.

## **3.1. The approaches that have been exploited in investigating graphene growth**

As mentioned above, the system tends to reduce its free energy as it reaches the equilibrium state. So, the most direct approach in investigating the growth process of graphene is the socalled geometry optimization approach, to study the geometry configuration evolution of the system with carbon atoms on copper surfaces by minimizing free energy. By DFT technology, during such evolution processes, the bond breaking and formation can be presented virtually, and the optimized configuration close to the real nucleation form can be obtained. For example, through carrying out configuration evolution calculations on the system containing 4–6 carbon atoms on the copper(111) surface, Li et al. [6] found that, at the very first stage, linear chains will be formed and dominate the copper surface, as illustrated in Figure 6.

**Figure 6.** Top and side views for the stable configuration of system containing 4–6 carbon atoms on copper(111) sur‐ face.

It is easy to imagine that, if several carbon atoms are absorbed on the copper surface, there will be some different nucleation forms, e.g., four carbon atoms will have four different forms as illustrated in Figure 7. These four configurations are obtained by geometry optimizations starting from different initial configurations with carbon atoms arranged on different locations. Depending on the laws of statistical thermodynamics, the occurrence probabilities of these different configurations will be dramatically determined by their configuration energy. So, calculating and comparing the stable energies of different possible configuration is also the commonly used approach in investigating the graphene growth process. carbon atoms arranged on different locations. Depending on the laws of statistical thermodynamics, the occurrence probabilities of these different configurations will be dramatically determined by their configuration energy. So, calculating and comparing the stable energies of different possible configuration is also the commonly used

Figure 6. Top and side views for the stable configuration of system containing 4–6 carbon atoms on copper(111) surface.

It is easy to imagine that, if several carbon atoms are absorbed on the copper

surface, there will be some different nucleation forms, e.g., four carbon atoms will

obtained by geometry optimizations starting from different initial configurations with

Figure 7. Different nucleation forms of four carbon atoms on Cu(111) surface. **Figure 7.** Different nucleation forms of four carbon atoms on Cu(111) surface.

approach in investigating the graphene growth process.

The growth process of graphene is a dynamic chemical reaction process, thus it is not only determined by the energies of the reactants (initial configurations) and products (stable configurations), but also deeply influenced by the activation energy. The transition state search technology in DFT method can offer these messages quite well. For example, Wu et al.3 have used the climbing image nudged elastic band method to search the transition state of a 1 + 1 (the bonding of two carbon atoms on The growth process of graphene is a dynamic chemical reaction process, thus it is not only determined by the energies of the reactants (initial configurations) and products (stable configurations), but also deeply influenced by the activation energy. The transition state search technology in DFT method can offer these messages quite well. For example, Wu et al. [3] have used the climbing image nudged elastic band method to search the transition state of a 1 + 1 (the bonding of two carbon atoms on Cu(111) surface) reaction, and identified the minimum energy path (MEP) of this reaction, as shown in Figure 8. First, the carbon atom remaining on the surface (carbon B) rotates around the bridging Cu to its neighboring site (Figure 8c), with a 0.51 eV barrier. Then, it rotates further toward carbon A with an activation energy of 0.64 eV. Finally, by conquering a 0.37 eV barrier, carbon B drags carbon A to the surface and forms a dimer (Figure 8e). This MEP with several barriers thus gives a very rugged part of the twoadatom potential energy surface.

Cu(111) surface) reaction, and identified the minimum energy path (MEP) of this reaction, as shown in Figure 8. First, the carbon atom remaining on the surface (carbon B) rotates around the bridging Cu to its neighboring site (Figure 8c), with a To reveal the realistic nucleation process of graphene on copper surface, the quantum me‐ chanics/molecular mechanics (QM/MM) method should be more suitable than the above approaches since it can consider the real reaction temperature and model the growth kinetics and nonequilibrium processes. However, since it contains quantum mechanics calculations, the computational efficiency is very low and thus this method can't handle large systems and can't model long enough times to reproduce the real reaction process. So, till now, few reports [2] using such approaches have been found.

The next best approach in revealing the dynamics nucleation process of graphene is the molecular dynamics (MD) method, based on empirical atomic force field. The MD method can simulate the real physical movements of every atom in a system of interacting atoms. The movement trajectories of every atom are determined by solving Newton's equations of motion numerically, where the interatom forces are defined by interatomic potentials (atomic force field). The precision and reliability of the MD method is much lower than the DFT method

**Figure 8.** Minimum energy path of the 1 + 1 carbon atom reaction on copper(111) surface.

It is easy to imagine that, if several carbon atoms are absorbed on the copper surface, there will be some different nucleation forms, e.g., four carbon atoms will have four different forms as illustrated in Figure 7. These four configurations are obtained by geometry optimizations starting from different initial configurations with carbon atoms arranged on different locations. Depending on the laws of statistical thermodynamics, the occurrence probabilities of these different configurations will be dramatically determined by their configuration energy. So, calculating and comparing the stable energies of different possible configuration is also the

carbon atoms arranged on different locations. Depending on the laws of statistical

thermodynamics, the occurrence probabilities of these different configurations will be

dramatically determined by their configuration energy. So, calculating and comparing

the stable energies of different possible configuration is also the commonly used

Figure 7. Different nucleation forms of four carbon atoms on Cu(111) surface.

The growth process of graphene is a dynamic chemical reaction process, thus it is not only determined by the energies of the reactants (initial configurations) and products (stable configurations), but also deeply influenced by the activation energy. The transition state search technology in DFT method can offer these messages quite well. For example, Wu et al. [3] have used the climbing image nudged elastic band method to search the transition state of a 1 + 1 (the bonding of two carbon atoms on Cu(111) surface) reaction, and identified the minimum energy path (MEP) of this reaction, as shown in Figure 8. First, the carbon atom remaining on the surface (carbon B) rotates around the bridging Cu to its neighboring site (Figure 8c), with a 0.51 eV barrier. Then, it rotates further toward carbon A with an activation energy of 0.64 eV. Finally, by conquering a 0.37 eV barrier, carbon B drags carbon A to the surface and forms a dimer (Figure 8e). This MEP with several barriers thus gives a very rugged part of the two-

The growth process of graphene is a dynamic chemical reaction process, thus it is

not only determined by the energies of the reactants (initial configurations) and

products (stable configurations), but also deeply influenced by the activation energy.

The transition state search technology in DFT method can offer these messages quite

method to search the transition state of a 1 + 1 (the bonding of two carbon atoms on

Cu(111) surface) reaction, and identified the minimum energy path (MEP) of this

To reveal the realistic nucleation process of graphene on copper surface, the quantum me‐ chanics/molecular mechanics (QM/MM) method should be more suitable than the above approaches since it can consider the real reaction temperature and model the growth kinetics and nonequilibrium processes. However, since it contains quantum mechanics calculations, the computational efficiency is very low and thus this method can't handle large systems and can't model long enough times to reproduce the real reaction process. So, till now, few reports

reaction, as shown in Figure 8. First, the carbon atom remaining on the surface

(carbon B) rotates around the bridging Cu to its neighboring site (Figure 8c), with a

The next best approach in revealing the dynamics nucleation process of graphene is the molecular dynamics (MD) method, based on empirical atomic force field. The MD method can simulate the real physical movements of every atom in a system of interacting atoms. The movement trajectories of every atom are determined by solving Newton's equations of motion numerically, where the interatom forces are defined by interatomic potentials (atomic force field). The precision and reliability of the MD method is much lower than the DFT method

have used the climbing image nudged elastic band

obtained by geometry optimizations starting from different initial configurations with

Figure 6. Top and side views for the stable configuration of system containing 4–6 carbon atoms on copper(111) surface.

It is easy to imagine that, if several carbon atoms are absorbed on the copper

surface, there will be some different nucleation forms, e.g., four carbon atoms will

have four different forms as illustrated in Figure 7. These four configurations are

commonly used approach in investigating the graphene growth process.

approach in investigating the graphene growth process.

**Figure 7.** Different nucleation forms of four carbon atoms on Cu(111) surface.

well. For example, Wu et al.3

164 Surface Energy

adatom potential energy surface.

[2] using such approaches have been found.

since they dramatically depend on the force field, which is fixed and thus cannot take the chemical conditions of atoms into account. While, just because of the coarse graining of the MD method compared with the DFT method, it can deal with systems consisting of a vast number (tens of thousands) of atoms. Using MD simulation based on the ReaxFF force-field, Ding et al. [13] have found that after 100 ps MD simulation at 1000 K, high C concentration leads to the formation of graphene islands, as shown in Figure 9.

**Figure 9.** Initial and final structures obtained in 100 ps MD simulations at 1000 K for 32 carbon atoms.

In summary, upon investigating the nucleation behaviors of carbon atoms to form graphene, four main approaches have been exploited. These approaches can provide intuitive images in the nucleation process of graphene, and some very useful messages in analyzing the surface reaction path. Besides these four approaches, the Monte Carlo simulation method[14, 20] has been also used. Since the Monte Carlo method provides similar messages as the DFT method with less accuracy, we did not discuss it here.

## **4. Achievements on investigations of graphene growth**

## **4.1. The exact nature of the active carbon species in graphene growth**

Hydrocarbon decomposition is the first step in the growth of graphene on copper surface, which determines the exact nature of the active carbon species. By the DFT calculations, Zhang et al. [2] investigated the decomposition process of CH4 on a five-layer *p*(3 × 3) copper slab by the transition state search technology. The initial state is an adsorbed CH4 molecule, and the final product is a C atom plus four H atoms on the surface. There are three intermediates, namely, methyl (CH3), methylene (CH2), and methylidyne (CH). As shown in Figure 10, all four dehydrogenation steps are endothermic, and the corresponding activation energy barriers are about 1.0–2.0 eV. The final product C + 4H is already 3.60 eV higher in energy than the adsorbed CH4, which suggests that atomic carbon is energetically very unfavorable on Cu surface. According to their results, the active species for graphene growth on the copper surface should not be carbon atoms but mainly CHx (especially CH). This is quite different from the case of other active metal surfaces, such as Pd, Ru (where the decomposition of CH4 is exothermic), and Ni (decomposition of CH4 is slightly endothermic).

Zhang's work is quite helpful to understand the growth mechanisms of graphene at the very initial stage. While, in spite of these insights, in most DFT investigations on the nucleation of graphene, atomic carbons are used. Surely, one of the main reasons for using atomic carbons is for simplicity (the situations will become very complicated if CHx is used as the active species). Besides, the more reasonable reason for using atomic carbons as the active species in graphene growth is that it is still hard to determine certain active carbon species for graphene growth on copper surface: since there exist complex surface morphologies on real copper substrates in experiments, the active site for the dehydrogenation of CHx might not be located at the plane copper surface but perhaps near the step regions, which should introduce significant influences on the dehydrogenation energy. In addition, to grow graphene on copper surfaces, dehydrogenation should finally be completed. To determine the exact nature of the active carbon species in graphene growth, further investigations are quite necessary.

#### **4.2. The stable configuration of 1-2 carbon atoms on the copper surface**

By experimental methods, the growth mechanism of graphene on copper substrate has been demonstrated to be a surface adsorption process. So, naturally, the carbon atoms should be more stable on the surface than in the bulk of the copper lattice. However, by comparing the absorption energy of carbon atoms on different locations in the 4 × 6 copper(111) slab, as shown

surface. According to their results, the active species for graphene growth on the

copper surface should not be carbon atoms but mainly CHx (especially CH). This is

quite different from the case of other active metal surfaces, such as Pd, Ru (where the

endothermic).

In summary, upon investigating the nucleation behaviors of carbon atoms to form graphene, four main approaches have been exploited. These approaches can provide intuitive images in the nucleation process of graphene, and some very useful messages in analyzing the surface reaction path. Besides these four approaches, the Monte Carlo simulation method[14, 20] has been also used. Since the Monte Carlo method provides similar messages as the DFT method

Hydrocarbon decomposition is the first step in the growth of graphene on copper surface, which determines the exact nature of the active carbon species. By the DFT calculations, Zhang et al. [2] investigated the decomposition process of CH4 on a five-layer *p*(3 × 3) copper slab by the transition state search technology. The initial state is an adsorbed CH4 molecule, and the final product is a C atom plus four H atoms on the surface. There are three intermediates, namely, methyl (CH3), methylene (CH2), and methylidyne (CH). As shown in Figure 10, all four dehydrogenation steps are endothermic, and the corresponding activation energy barriers are about 1.0–2.0 eV. The final product C + 4H is already 3.60 eV higher in energy than the adsorbed CH4, which suggests that atomic carbon is energetically very unfavorable on Cu surface. According to their results, the active species for graphene growth on the copper surface should not be carbon atoms but mainly CHx (especially CH). This is quite different from the case of other active metal surfaces, such as Pd, Ru (where the decomposition of CH4 is

Zhang's work is quite helpful to understand the growth mechanisms of graphene at the very initial stage. While, in spite of these insights, in most DFT investigations on the nucleation of graphene, atomic carbons are used. Surely, one of the main reasons for using atomic carbons is for simplicity (the situations will become very complicated if CHx is used as the active species). Besides, the more reasonable reason for using atomic carbons as the active species in graphene growth is that it is still hard to determine certain active carbon species for graphene growth on copper surface: since there exist complex surface morphologies on real copper substrates in experiments, the active site for the dehydrogenation of CHx might not be located at the plane copper surface but perhaps near the step regions, which should introduce significant influences on the dehydrogenation energy. In addition, to grow graphene on copper surfaces, dehydrogenation should finally be completed. To determine the exact nature of the

active carbon species in graphene growth, further investigations are quite necessary.

By experimental methods, the growth mechanism of graphene on copper substrate has been demonstrated to be a surface adsorption process. So, naturally, the carbon atoms should be more stable on the surface than in the bulk of the copper lattice. However, by comparing the absorption energy of carbon atoms on different locations in the 4 × 6 copper(111) slab, as shown

**4.2. The stable configuration of 1-2 carbon atoms on the copper surface**

with less accuracy, we did not discuss it here.

166 Surface Energy

**4. Achievements on investigations of graphene growth**

**4.1. The exact nature of the active carbon species in graphene growth**

exothermic), and Ni (decomposition of CH4 is slightly endothermic).

 Figure 10. Geometric structures of the initial state (I.S.), transition state (T.S.), and final state (F.S.) of the four steps of CH4 dehydrogenation on Cu(111) and Cu(100) surface (top); their energy profile is also shown (bottom). **Figure 10.** Geometric structures of the initial state (I.S.), transition state (T.S.), and final state (F.S.) of the four steps of CH4 dehydrogenation on Cu(111) and Cu(100) surface (top); their energy profile is also shown (bottom).

in Figure 11, Riikonen et al. [4] found that the HCP adsorption site is unstable. The FCC and BRI are also metastable sites; at finite temperatures, carbon diffuses directly to the subsurface A site. According to their analysis, the stabilization of carbon interstitials in the copper subsurface area can be understood with a few simple arguments. They state that, the copper atoms at the topmost layer are easily pushed toward the vacuum due to their low coordination numbers. Such greater flexibility of the topmost copper atoms compared with the bulk ones opens a gate to the carbon atoms, which can thus sink into the subsurface and form octahedrally symmetric copper surroundings. Zhang's work is quite helpful to understand the growth mechanisms of graphene at the very initial stage. While, in spite of these insights, in most DFT investigations on the nucleation of graphene, atomic carbons are used. Surely, one of the main reasons for using atomic carbons is for simplicity (the situations will become very

The occurrence of sinking carbon atoms on the copper subsurface has been also found in the work of Wu et al. [3] through transition state searches for two next nearest neighboring carbon atoms to form a dimer on the surface (Figure 8). In their report, an almost linear C-Cu-C configuration (Figure 8b) was formed. They named it the bridging-metal (BM) structure. Through geometry optimization for the system having two carbon atoms on the Cu(111) surface, Li et al. [7] also found this so-called BM structure, as shown in Figure 12. complicated if CHx is used as the active species). Besides, the more reasonable reason for using atomic carbons as the active species in graphene growth is that it is still hard to determine certain active carbon species for graphene growth on copper surface:

In conclusion, despite the growth mechanism of graphene on copper substrate being a surface adsorption process, the carbon atoms still have a chance to penetrate into the subsurface (solve in copper), especially under very low carbon atom concentrations. This means that under special process conditions, carbon atoms can also be implanted into the copper foil. Thus, since there exist complex surface morphologies on real copper substrates in experiments, the active site for the dehydrogenation of CHx might not be located at the plane copper surface but perhaps near the step regions, which should introduce

significant influences on the dehydrogenation energy. In addition, to grow graphene

**Figure 11.** The Cu(111) surface, top (a) and side (b) views; carbon energetics and minimum energy paths on the Cu(111) surface, subsurface and in the bulk (c). The small green and dark spheres denote the surface and octahedral adsorption sites, respectively. Surface adsorption sites contain four inequivalent styles: FCC, HCP, TET, and BRI. BRI′ is a neighboring equivalent site to BRI.

graphene can be formed by following high-temperature annealing, which results in the migration of implanted atoms to the surface and eventually bonding to each other. Such a technique has successfully been used.

In the usual fabrication process of graphene by CVD technology, such a "sinking" of carbon atoms into the copper subsurface will have nearly no influence on the surface adsorption growth of graphene, firstly because dimer formation and the subsequent graphene growth is by far the most favorable reaction in both energetic and kinetic terms. [12]. Secondly, Li et al. [7] have investigated the following behavior of the sunken carbon when more carbon atoms are absorbed around it. They found that, the sunken carbon atom will spontaneously form a dimer with one of the newly adsorbed carbon atoms, and the formed dimer will up-float on the top of the surface again, as shown in Figure 13.

**Figure 12.** Geometry optimization paths from two on-surface carbon atoms to the BM structure. The deformation elec‐ trodensities are mapped to characterize the bonding situations.

**Figure 13.** Geometry optimization paths for the system with one carbon atom absorbed near the BM structure.

#### **4.3. Configuration selectivity of the initial carbon clusters**

graphene can be formed by following high-temperature annealing, which results in the migration of implanted atoms to the surface and eventually bonding to each other. Such a

**Figure 11.** The Cu(111) surface, top (a) and side (b) views; carbon energetics and minimum energy paths on the Cu(111) surface, subsurface and in the bulk (c). The small green and dark spheres denote the surface and octahedral adsorption sites, respectively. Surface adsorption sites contain four inequivalent styles: FCC, HCP, TET, and BRI. BRI′

(c)

In the usual fabrication process of graphene by CVD technology, such a "sinking" of carbon atoms into the copper subsurface will have nearly no influence on the surface adsorption growth of graphene, firstly because dimer formation and the subsequent graphene growth is by far the most favorable reaction in both energetic and kinetic terms. [12]. Secondly, Li et al. [7] have investigated the following behavior of the sunken carbon when more carbon atoms are absorbed around it. They found that, the sunken carbon atom will spontaneously form a dimer with one of the newly adsorbed carbon atoms, and the formed dimer will up-float on

technique has successfully been used.

is a neighboring equivalent site to BRI.

168 Surface Energy

the top of the surface again, as shown in Figure 13.

Through DFT calculations, Gao et al. [5] have investigated the stable configurations of carbon clusters containing 1 to 24 atoms on the Ni(111) surface. For different configurations of the carbon clusters with the same size, they analyzed their stability by comparing the absorption energies (so-called formation energy), as given in Figure 14. They found that, within the entire size range of their calculations, carbon chains on the Ni(111) surface are always more stable than ring configurations of the same size. The crossover between the carbon chains and the Csp2 network occurs at *N* = 12, beyond which the energy difference between chain and sp2 configurations becomes larger and larger. This means that, during the graphene growth on Ni(111) surface, until *N* = 12, the C chain configuration is superior and will dominate the metal surface. A ground state structural transition from a C chain to a C-sp2 network (graphene island) occurs at *N* = 12.

**Figure 14.** Formation energies of chains, rings, and most stable sp2 networks on the Ni(111) surface versus the number of carbon atoms.

For the case of copper surfaces, Li et al. [6] have investigated the graphene nucleation path by importing carbon atoms step by -step. At every step, they exhausted all possible configurations and discussed their stability. Based on careful configuration and energy analyses, an overall path of graphene nucleation has been proposed in Figure 15. At the very first stage, the linear chains containing 4 to 10 carbon atoms will be formed and dominate the copper surface, while both the Y-type and circular carbon species are energetically repelled. Then, the growth of the carbon cluster encounters an energy barrier at about 0.25 eV. By conquering such a barrier, the carbon clusters will present Y-type (furcate) structures. Then, by adsorbing new carbon atoms step by step, ring-containing carbon structures and graphene nuclei will be formed, with energetic preference. Their results suggest that, it will be difficult to form furcate and ringcontaining carbon structures at the very initial stage of graphene nucleation, but it should be formed when the linear chains have grown to some length.

Based on analysis of the deformation electrodensity maps of the linear carbon chains contain‐ ing 4 to 10 atoms (Figure 16), Li et al. [6] have also discussed the bonding situation between the linear chain and the copper surface. The green color in Figure 16 indicates that net electrons remain and stable chemical bonds are formed. Through bonding situation analyses, they point out L6 should be a representative structure. In the linear carbon chains, when the number of carbon atoms is less than 6, not only the end- but also the mid-carbon atoms bond stably with the copper surface; if the number of carbon atoms reaches 6, the mid-carbon atoms are completely detached from the copper surface, and thus an arc is formed.

#### **4.4. Continuous growth of graphene over steps**

In the chemical vapor deposition fabrication of graphene on copper surface, it has been found that the growth of macroscopic pristine graphene is not limited by the underlying copper

**Figure 15.** Energy evolution curve of the overall nucleation path of graphene growth.

**Figure 14.** Formation energies of chains, rings, and most stable sp2 networks on the Ni(111) surface versus the number

For the case of copper surfaces, Li et al. [6] have investigated the graphene nucleation path by importing carbon atoms step by -step. At every step, they exhausted all possible configurations and discussed their stability. Based on careful configuration and energy analyses, an overall path of graphene nucleation has been proposed in Figure 15. At the very first stage, the linear chains containing 4 to 10 carbon atoms will be formed and dominate the copper surface, while both the Y-type and circular carbon species are energetically repelled. Then, the growth of the carbon cluster encounters an energy barrier at about 0.25 eV. By conquering such a barrier, the carbon clusters will present Y-type (furcate) structures. Then, by adsorbing new carbon atoms step by step, ring-containing carbon structures and graphene nuclei will be formed, with energetic preference. Their results suggest that, it will be difficult to form furcate and ringcontaining carbon structures at the very initial stage of graphene nucleation, but it should be

Based on analysis of the deformation electrodensity maps of the linear carbon chains contain‐ ing 4 to 10 atoms (Figure 16), Li et al. [6] have also discussed the bonding situation between the linear chain and the copper surface. The green color in Figure 16 indicates that net electrons remain and stable chemical bonds are formed. Through bonding situation analyses, they point out L6 should be a representative structure. In the linear carbon chains, when the number of carbon atoms is less than 6, not only the end- but also the mid-carbon atoms bond stably with the copper surface; if the number of carbon atoms reaches 6, the mid-carbon atoms are

In the chemical vapor deposition fabrication of graphene on copper surface, it has been found that the growth of macroscopic pristine graphene is not limited by the underlying copper

formed when the linear chains have grown to some length.

**4.4. Continuous growth of graphene over steps**

completely detached from the copper surface, and thus an arc is formed.

of carbon atoms.

170 Surface Energy

**Figure 16.** Deformation electrodensity maps for the linear carbon chains.

structure. Haider et al. [21, 22] have characterized the surface morphology of the copper substrate and the graphene grown by scanning tunneling microscopy (STM), as shown in Figure 17. They revealed that the atomic arrangement of graphene was not affected by the morphology and atomic arrangement of the copper substrate. This feature implies practical value for the mass production of high-quality graphene on rough copper substrates.

Inspired by this experimental phenomenon, Li et al. [8] have investigated the coalescence of carbon atoms over a copper monatomic step by the DFT calculations. They constructed a monatomic step as shown in Figure 18a, and carefully explored how the carbon atoms bond together over the step. Firstly, they put some carbon atoms on and under the steps separately.

**Figure 17.** (a) STM topograph of a highly corrugated region of the sample. (b) Atomic resolution STM topograph over a copper monatomic step.

In some special cases, as shown in Figure 18b, after geometric optimizations, the separated carbon atoms can successfully bond together. Additionally, this over-step coalescence of the carbon atoms is spontaneous as the energy evolution curve descends monotonically through‐ out all the geometry optimization steps. They attributed this success to the energy barrier preventing the bonding of the two carbon atoms, which is reduced significantly, since the two copper atoms between them are both shared by three carbon atoms and thus have weak interactions with the two bonded carbon atoms. However, the dimer formed finally moves up to the upper terrace but is not located on the over-step position. In their following DFT calculations, by importing another carbon atom to the "left hole" of the atom being drawn up to the upper terrace, they found that this over-step coalescence process is unrepeatable (Figure 18c). As a conclusion, the direct over-step coalescence of the carbon atoms separated by the steps is very difficult, and thus should not be the main pattern of graphene's continuous growth over the steps.

By importing additional carbon atoms between the existing ones separated by the steps, they found that the main way in which graphene grows over the steps continuously is that the carbon atoms, adsorbed additionally on the locations between the already existing ones which are separated by the steps, link them (these carbon atoms separated by the steps) together. They first imported one additional carbon atom, as illustrated in Figure 19a. The obtained configurations after geometry optimization show a positive trend to a successful over-step coalescence of carbon atoms. Then, one more carbon atom is imported again in the optimized configurations as shown in Figure 19b. Finally, the new carbon atom links the separated ones together, and a cambered over-step carbon chain was formed.

During the calculations of the absorption energies, they found that the adsorption energy of the single carbon atom near the steps (5.91–6.48 eV) is about 1.0 eV higher than that adsorbed on a flat copper surface (5.13–5.17 eV). This indicates that carbon nucleation should be very likely to start from the stepped regions. The thermodynamic reason is that around the step regions on the substrate, the surface energy is higher than that on the flat regions.

In some special cases, as shown in Figure 18b, after geometric optimizations, the separated carbon atoms can successfully bond together. Additionally, this over-step coalescence of the carbon atoms is spontaneous as the energy evolution curve descends monotonically through‐ out all the geometry optimization steps. They attributed this success to the energy barrier preventing the bonding of the two carbon atoms, which is reduced significantly, since the two copper atoms between them are both shared by three carbon atoms and thus have weak interactions with the two bonded carbon atoms. However, the dimer formed finally moves up to the upper terrace but is not located on the over-step position. In their following DFT calculations, by importing another carbon atom to the "left hole" of the atom being drawn up to the upper terrace, they found that this over-step coalescence process is unrepeatable (Figure 18c). As a conclusion, the direct over-step coalescence of the carbon atoms separated by the steps is very difficult, and thus should not be the main pattern of graphene's continuous

**Figure 17.** (a) STM topograph of a highly corrugated region of the sample. (b) Atomic resolution STM topograph over

By importing additional carbon atoms between the existing ones separated by the steps, they found that the main way in which graphene grows over the steps continuously is that the carbon atoms, adsorbed additionally on the locations between the already existing ones which are separated by the steps, link them (these carbon atoms separated by the steps) together. They first imported one additional carbon atom, as illustrated in Figure 19a. The obtained configurations after geometry optimization show a positive trend to a successful over-step coalescence of carbon atoms. Then, one more carbon atom is imported again in the optimized configurations as shown in Figure 19b. Finally, the new carbon atom links the separated ones

During the calculations of the absorption energies, they found that the adsorption energy of the single carbon atom near the steps (5.91–6.48 eV) is about 1.0 eV higher than that adsorbed on a flat copper surface (5.13–5.17 eV). This indicates that carbon nucleation should be very likely to start from the stepped regions. The thermodynamic reason is that around the step

regions on the substrate, the surface energy is higher than that on the flat regions.

together, and a cambered over-step carbon chain was formed.

**(a) (b)**

growth over the steps.

a copper monatomic step.

172 Surface Energy

**Figure 18.** (a) Side view of Cu(111) surface separated on terraces by monatomic steps. (b) Energy evolution curves and corresponding key configurations during the direct over-step coalescence of the carbon atoms. (c) The direct over-step coalescence of the carbon atoms is unrepeatable.

**Figure 19.** (a) Initial and optimized configurations after importing one additional carbon atoms on the step. (b) Those after importing the second additional carbon atoms on the step.

## **4.5. Molecular dynamics simulations on graphene growth**

Since graphene's growth is typical of a kinetic and nonequilibrium process. Molecular dynamics is a powerful tool to explore such processes at the atomic level. Based on the reactive force-field (ReaxFF), Ding et al. [13] have investigated the evolution of carbon structures and the growth kinetics of graphene on Ni(111) surface. Taking into account that the carbon concentration is raised gradually during the chemical vapor deposition experiments on graphene growth, they firstly investigate the effect of carbon concentration on the nucleation of graphene, as illustrated in Figure 20. By arranging 16 and 32 carbon atoms on the Ni surface, namely, 1/8 and 1/4 monolayers, they found that at the low concentration (16 carbon atoms), the carbon monomers readily enter the subsurface, which is identical to the DFT results above. As the carbon concentration increases, after 100 ps annealing, nearly all of the carbon atoms, which are arranged coincidentally to contain long chains or large polygonal rings, eventually form a sp2 network of pentagons, hexagons, and heptagons. As a summary, low concentrations do not allow the formation of large sp2 network, and high concentrations are required to induce the formation of graphene islands.

**Figure 20.** Initial and final structures obtained in 100 ps MD simulations at 1000 K for C16 and C32. Cyan and orange spheres represent Ni and C atoms, respectively.

Then, they turned to the influence of temperature on the formation of carbon structures. Under high carbon concentrations with 64 carbon atoms on the Ni surface, they analyzed the final configuration (Figure 21) after 100 ps molecular dynamics simulation at four temperatures 800, 1000, 1200, and 1400 K. They summarized the number of i-membered rings (MRs) (*i* = 3, 4,…, 9) in the C structures formed at different temperatures in Table 2. With the increases in temperature, the fact that the number of 3- and 4-MRs are greatly reduced indicates that they are very unstable; the increased numbers of 5-MRs and 7-MRs show that they are very stable. The number of 6-MRs denotes the quality of graphene fabricated. According to their simula‐ tion, the number of 6-MR reaches the maximum at 1000 K and decreases as the temperature further increases. Their results indicate that the optimal growth temperature of graphene should be around 1000 K, as most CVD experiments of graphene growth were applied.

**Figure 21.** Equilibrium configurations at 0, 800, 1000, 1200, and 1400 K.


**Table 1. Numbers of various polygons in the equilibrium configurations** 

**Table 2.** Number of various polygons in the equilibrium configurations

Through simulating the growth of graphene islands by adding carbon atoms around it, they found that graphene islands can grow larger by capturing deposited C atoms and forming more hexagons on the edge with its self-healing capabilities during growth.

## **5. Summary**

**4.5. Molecular dynamics simulations on graphene growth**

the formation of graphene islands.

174 Surface Energy

spheres represent Ni and C atoms, respectively.

Since graphene's growth is typical of a kinetic and nonequilibrium process. Molecular dynamics is a powerful tool to explore such processes at the atomic level. Based on the reactive force-field (ReaxFF), Ding et al. [13] have investigated the evolution of carbon structures and the growth kinetics of graphene on Ni(111) surface. Taking into account that the carbon concentration is raised gradually during the chemical vapor deposition experiments on graphene growth, they firstly investigate the effect of carbon concentration on the nucleation of graphene, as illustrated in Figure 20. By arranging 16 and 32 carbon atoms on the Ni surface, namely, 1/8 and 1/4 monolayers, they found that at the low concentration (16 carbon atoms), the carbon monomers readily enter the subsurface, which is identical to the DFT results above. As the carbon concentration increases, after 100 ps annealing, nearly all of the carbon atoms, which are arranged coincidentally to contain long chains or large polygonal rings, eventually form a sp2 network of pentagons, hexagons, and heptagons. As a summary, low concentrations do not allow the formation of large sp2 network, and high concentrations are required to induce

**Figure 20.** Initial and final structures obtained in 100 ps MD simulations at 1000 K for C16 and C32. Cyan and orange

Then, they turned to the influence of temperature on the formation of carbon structures. Under high carbon concentrations with 64 carbon atoms on the Ni surface, they analyzed the final The fundamental theory of surface energy and the corresponding problems involved in thin film growth have been briefly introduced in this chapter. For the special issue of graphene growth on metal surface under the frame of chemical vapor deposition technology, the growth process and the quality of samples obtained is also determined by the surface energy theory. But due to the high-temperature growth conditions of graphene and the lack of effective realtime characterization methods, the fine messages of key importance in analyzing the thermo‐ kinetics process of graphene growth are difficult to obtain by experimental measurements. Therefore, DFT investigations on the nucleation process of graphene under chemical vapor deposition growth have been carried out very prosperously. The key approaches being exploited in describing the graphene CVD growth process have been introduced. And some main achievements, on investigating the growth process of graphene, using the DFT method and the molecular dynamics method, have been reviewed. Till now, in spite of high-quality graphene samples being fabricated successfully using the chemical vapor deposition technol‐ ogy, to develop a wider range of applications, the preparation of graphene with special structures, like single crystal graphene sheets, graphene nanoflakes, graphene nanoribbons, graphene nanomesh, and graphene quantum dots, still needs further investigations on their growth mechanisms. We hope the above contents are helpful for the improvement in the fabrication and application of graphene.

## **Author details**

Meicheng Li\* , Yingfeng Li and Joseph Michel Mbengue

\*Address all correspondence to: mcli@ncepu.edu.cn

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Renewable Energy, North China Electric Power University, Beijing, China

## **References**


[8] Y. Li, M. Li, T. Gu, F. Bai, Y. Yu, T. Mwenya, Y. Yu, AIP Adv 3 052130 (2013).

process and the quality of samples obtained is also determined by the surface energy theory. But due to the high-temperature growth conditions of graphene and the lack of effective realtime characterization methods, the fine messages of key importance in analyzing the thermo‐ kinetics process of graphene growth are difficult to obtain by experimental measurements. Therefore, DFT investigations on the nucleation process of graphene under chemical vapor deposition growth have been carried out very prosperously. The key approaches being exploited in describing the graphene CVD growth process have been introduced. And some main achievements, on investigating the growth process of graphene, using the DFT method and the molecular dynamics method, have been reviewed. Till now, in spite of high-quality graphene samples being fabricated successfully using the chemical vapor deposition technol‐ ogy, to develop a wider range of applications, the preparation of graphene with special structures, like single crystal graphene sheets, graphene nanoflakes, graphene nanoribbons, graphene nanomesh, and graphene quantum dots, still needs further investigations on their growth mechanisms. We hope the above contents are helpful for the improvement in the

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,

[1] K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y.

[3] P. Wu, W. H. Zhang, Z. Y. Li, J. L. Yang, J. G. Hou, J Chem Phys 133 071101-1:4

[4] S. Riikonen, A. Krasheninnikov, L. Halonen, R. Nieminen, J Phys Chem C 116, 5802–

[5] J. F. Gao, Q. H. Yuan, H. Hu, J. J. Zhao, F. Ding, J Phys Chem C 115, 17695-17703

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[2] W. H. Zhang, P. Wu, Z. Y. Li, J. L. Yang, J Phys Chem C 115, 17782-17787 (2011).

School of Renewable Energy, North China Electric Power University, Beijing, China

fabrication and application of graphene.

, Yingfeng Li and Joseph Michel Mbengue

\*Address all correspondence to: mcli@ncepu.edu.cn

Choi, and B. H. Hong, Nature 457, 706 (2009).

**Author details**

Meicheng Li\*

176 Surface Energy

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