**Aspects Regarding Radiation Crosslinking of Elastomers**

Elena Manaila, Maria Daniela Stelescu and Gabriela Craciun

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/47747

## **1. Introduction**

Elastomers or rubbers are materials used in a large range of industrial and household applications. A common physical-chemical treatment is curing (crosslinking), imparting the rubber mechanical and thermal stability. Elastomers show low thermal conductivity values, and therefore, require complex and high cost heating methods; thus, the ionizing (accelerated electrons) method shows high interest for the grafting and crosslinking processes. In addition to the lack of environmental impact, reliability, flexibility and low costs render the radiation technologies especially attractive.

Vulcanisation is the process by which rubber is changed from essentially a plastic material to either an elastic or a hard material (Stelescu et al., 2010). In this process, an elastomer is transformed from a 'plastic', 'formable' material into an 'elastic' material by the formation of a three-dimensional network with different types of junctions. The word vulcanisation derives from *Vulcan*, the Roman God of fire. Not accidentally, it also means volcano, a hot place where quite some sulphur species can be found. The term vulcanisation was therefore originally exclusively applied to the crosslinking reaction achieved by sulphur at high temperatures.

Nowadays this term is also applied to refer to other crosslinking processes, such as peroxide cure. There are several possibilities for the crosslinking of rubber. The already mentioned sulphur vulcanisation was the first to be discovered and still is today's most common cure system. The sulphur vulcanisation process requires the presence of carbon-carbon unsaturation in the polymer and it leads to a three-dimensional rubber network in which the polymer chains are linked to each other by sulphur bridges. As a result, sulphur cured articles have good tensile and tear strength, good dynamic properties, but poor high temperature properties like ageing, for instance (Alvarez Grima, 2007; Dluzneski, 2001).

© 2012 Manaila et al., licensee InTech. This is an open access chapter 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. © 2012 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.

Other vulcanisation systems, i.e. peroxides, ultraviolet light, electron beam, microwave, resins, etc. were later discovered and gained more importance with the progressive development of synthetic rubbers.

The use of organic peroxides as crosslinking agents for rubber was first reported by Ostromislenski in 1915 (Alvarez Grima, 2007) and at present it is the only vulcanization method that can compete with accelerated sulphur cure, with respect to vulcanization rate. Interest in the industrial use of peroxides as curing agents increased with the introduction of a number of fully saturated elastomers, such as ethylene-propylene rubber (EPM), fluoro elastomers (FKM), etc., which cannot be cured by sulphur vulcanization (Alvarez Grima, 2007). Peroxide vulcanisation leads to a rubber network in which the polymer chains are linked to each other by very stable covalent carbon-carbon bonds. Peroxide cured vulcanisates have therefore good high temperature properties, like heat ageing and compression set, compared to sulphur cured articles (Alvarez Grima, 2007; Dluzneski, 2001)

In addition, peroxide cure allows vulcanisation of both unsaturated and saturated polymers, which is not possible with sulphur vulcanisation. On the other hand, some mechanical properties of peroxide cured articles are inferior to those achieved by sulphur cure, i.e. tensile strength, dynamic properties, and therefore entail a limitation on the use of this vulcanization system. Another serious problem with peroxides is the lack of sufficient scorch time. Scorch time: the time elapsed until vulcanisation starts, is of major importance in order to control the vulcanisation reaction. The term scorch safety refers to a certain scorch time which is enough to provide good processing of the material before it starts vulcanising; this is of great importance especially in industry. Upon reaching the typical dissociation temperature of a peroxide, the crosslinking reaction immediately proceeds at full speed, leaving the processor little or no time for shaping of the rubber article. The addition of certain scorch-retarders is sometimes of help, but this usually goes at the expense of crosslink density obtained: a waste of money (Alvarez Grima, 2007).

### **2. Electron beam and microwaves vulcanization**

Radiation curing has historically been used as an alternative to peroxides in applications where the curatives themselves or sideproducts of vulcanization are viewed as impurities in the final product. Peroxide cure progresses through a series of radical intermediates, each of which can undergo side reactions which may not necessarily contribute to crosslink density. Radiation cure, on the other hand, has been promoted as a cleaner and more homogeneous cure process. Electron beam irradiation has been used in the wire and cable industry for longer than 30 years and applied to a wide range of commodity and specialty elastomers. A survey of the types of elastomers susceptible to radiation curing is available, as are review articles describing the electron-beam curing of commercially significant grades (Bhowmick & Vijayabaskar, 2006; Henning, 2008). Variables such as radiation dosage and the effect of polymer microstructure and chemical additives on the efficiency of electron beam cure have been studied. Some researchers (Zaharescu et al., 2000; Chowdhury & Banerji, 2005) studied radiation-induced crosslinking in thermoplastic elastomers based on ethylene-propylene rubber (EPDM) and polyethylene (PE) or polypropylene (PP) plastics.

Elastomer crosslinking by means of electron beam (EB) is done without heating and in the absence of vulcanization agents. The reaction mechanism is similar to crosslinking with peroxides, but in this case, reaction initiation is due to the action of EB and in the presence of the polyfunctional monomers. Ionizing radiation produces an excitation of polymer molecules. The energies associated with the excitation are dependent on the irradiation dosage of electrons. The interaction results in formation of free radicals formed by dissociation of molecules in the excited state or by interaction of molecular ions. The free radicals or molecular ions can react by connecting the polymer chains directly or initiating grafting reactions.

4 Advanced Elastomers – Technology, Properties and Applications

development of synthetic rubbers.

Other vulcanisation systems, i.e. peroxides, ultraviolet light, electron beam, microwave, resins, etc. were later discovered and gained more importance with the progressive

The use of organic peroxides as crosslinking agents for rubber was first reported by Ostromislenski in 1915 (Alvarez Grima, 2007) and at present it is the only vulcanization method that can compete with accelerated sulphur cure, with respect to vulcanization rate. Interest in the industrial use of peroxides as curing agents increased with the introduction of a number of fully saturated elastomers, such as ethylene-propylene rubber (EPM), fluoro elastomers (FKM), etc., which cannot be cured by sulphur vulcanization (Alvarez Grima, 2007). Peroxide vulcanisation leads to a rubber network in which the polymer chains are linked to each other by very stable covalent carbon-carbon bonds. Peroxide cured vulcanisates have therefore good high temperature properties, like heat ageing and compression set, compared to sulphur cured articles (Alvarez Grima, 2007; Dluzneski, 2001) In addition, peroxide cure allows vulcanisation of both unsaturated and saturated polymers, which is not possible with sulphur vulcanisation. On the other hand, some mechanical properties of peroxide cured articles are inferior to those achieved by sulphur cure, i.e. tensile strength, dynamic properties, and therefore entail a limitation on the use of this vulcanization system. Another serious problem with peroxides is the lack of sufficient scorch time. Scorch time: the time elapsed until vulcanisation starts, is of major importance in order to control the vulcanisation reaction. The term scorch safety refers to a certain scorch time which is enough to provide good processing of the material before it starts vulcanising; this is of great importance especially in industry. Upon reaching the typical dissociation temperature of a peroxide, the crosslinking reaction immediately proceeds at full speed, leaving the processor little or no time for shaping of the rubber article. The addition of certain scorch-retarders is sometimes of help, but this usually goes at the

expense of crosslink density obtained: a waste of money (Alvarez Grima, 2007).

Radiation curing has historically been used as an alternative to peroxides in applications where the curatives themselves or sideproducts of vulcanization are viewed as impurities in the final product. Peroxide cure progresses through a series of radical intermediates, each of which can undergo side reactions which may not necessarily contribute to crosslink density. Radiation cure, on the other hand, has been promoted as a cleaner and more homogeneous cure process. Electron beam irradiation has been used in the wire and cable industry for longer than 30 years and applied to a wide range of commodity and specialty elastomers. A survey of the types of elastomers susceptible to radiation curing is available, as are review articles describing the electron-beam curing of commercially significant grades (Bhowmick & Vijayabaskar, 2006; Henning, 2008). Variables such as radiation dosage and the effect of polymer microstructure and chemical additives on the efficiency of electron beam cure have been studied. Some researchers (Zaharescu et al., 2000; Chowdhury & Banerji, 2005) studied radiation-induced crosslinking in thermoplastic elastomers based on ethylene-propylene

**2. Electron beam and microwaves vulcanization** 

rubber (EPDM) and polyethylene (PE) or polypropylene (PP) plastics.

EB vulcanization has demonstrated extremely positive results compared to the conventional curing system such as: no polymer degradation due to high temperature as EB crosslinking occurs at room temperature, no oxidative degeneration in polymers as observed in classical crosslinking, direct crosslinking by C-C linkage by EB, extremely strong bonds, high degree of crosslinking, extremely short curing cycles, zero blooming effects; extremely high tensile strength; extremely high resistance to compression set; extremely high resistance to oils, grease, lubricants; highly improved accelerated ageing properties, very high productivity, perfect for thin products, lower material waste (MGM Rubber Company-Research and Development, 2007). However, the radiation crosslinking of rubbers was not used in larger technical applications because of the high cost of irradiation to bring about vulcanization, but could become an industrial process when the radiation dose decreased with the use of some sensitizers.

Modification of thermoplastic and rubbery materials by EB and microwave (MW) radiations is a potential method for the development of new materials like polymers and composites. Interaction of each of the two physical systems, EB and MW, with a substance has revealed their ability for changing physical and chemical proprieties of the treated substance.

Therefore, the physical and chemical effects of the EB and MW radiation have drawn high interest, resulting in a large industrial application range of the new materials with improved characteristics. A comparative study of the effects of separate interaction of EB and MW with the substance, effects on which the modern processes for the production of new materials with special characteristics have been developed, has revealed the following: (a) production of materials by EB (ionizing) radiation is based on the coulomb interaction of accelerated electrons with the atoms of the substances they are penetrating. From this interaction, secondary electrons, excited molecules, free ions and radicals result, which are precursors of some chemical reactions resulting in new materials; (b) production of materials by MW (non-ionizing) radiation is based on thermal effects (dielectric heating) of the interaction of the electromagnetic waves with the substance. MW energy absorbed within the substance is dependent on the molecule characteristics, that is on the permittivity and magnetic permeability resulting in a high selectivity level for the chemical reactions induced by MW interaction with the constituents of the material they are penetrating; (c) by separate/ combined EB and MW irradiation, materials with single characteristics are obtained with high yields, inaccessible by the traditional curing methods.

Radiation (EB-ionizing radiation and MWs-non-ionizing radiation) are used successfully instead of the traditional methods and, in addition, provides new possibilities like as

crosslinking in thick polymer articles, in complex sections or production of recycled rubbers of high quality.

The high-molecular compounds (elastomers) are made up of a large number of elementary molecules – monomers. These molecules can be of the same class or of different classes, resulting thus homopolymers and copolymers, respectively. The radiation acts on the highmolecular compounds as follows: (1) at a relatively low radiation dose (radiation dose = the energy absorbed per unit of mass of the irradiated material; it is measured in J/Kg; unit of measure for the absorbed dose is a gray: 1Gy = 1 J/kg), only "pure polymerization" occurs. With the linear increase in the radiation dose, the linear polymer chains increase progressively by addition of a molecule from a blend with low molecular weight to a radical at the end of an increasing chain; (2) with the dose increase during the pure polymerization, a new process named "grafting" takes place. By this process side chains are made in the polymer, resulting in modified surface properties in some materials, like as: biocompatibility, moisture-absorbent and moisture-repellent, and mechanical, chemical and thermal characteristics. This process is very promising for the biomaterial synthesis. (3) with the further increase in radiation dose, the "crosslinking" process takes place, when links are formed between polymer chains resulting in two- and three-dimensional structures. During this process insignificant chemical changes occur but significant structural changes. Simultaneously degradation occurs. Crosslinking and degradation (through chain scission) are two competing processes that always co-exist under radiation. Both processes have many applications in the field of new materials with improved characteristics, like as elastomer crosslinking. (4) the combined effects of the two processes are used in many industry processes, being known as "radiation curing". Three radiation induced processes are used in "radiation curing": monomer polymerization, polymer chain crosslinking and chemical bonding between polymer and substrate molecules.

Use of ionizing and non-ionizing radiation to obtain materials with improved characteristics is based on their advantages like as: *(I) electrons beam (EB):* (I.1.) accelerate the polymerization/vulcanization process, thus reducing the preparation time with tens to hundreds times; (I.2.) increase the conversion of raw material into the finished material up to a 100% yield and, therefore, the percentage of the residual monomer is nearly 0%, which is very important with noxious monomers; (I.3.) reduce the energy required in crosslinking and grafting with 5 –10 times as compared with the traditional method; *(II) microwaves (MW):* (II.1.) promote a narrow distribution of the molecular masses, as the crosslinking and grafting occurs simultaneously in the bulk due to the rapid energy transfer, volumetric and selective properties of MW dielectric heating , (II.2.) promote fast crosslinking and grafting processes, by tens to hundreds times faster than in classical procedure because the electromagnetic energy is directly transferred from the MW to the atoms or molecules of the irradiated material

### **3. Polyfunctional monomers (co-agents)**

Reported papers suggest that appropriate polyfunctional monomers (co-agents) in polymer matrix (Vijayabaskar & Bhowmick, 2005; Yasin et al., 2005) could be used to obtain desired rubber physical properties at lower irradiation doses (Hafezi et al., 2006; Stelescu et.al., 2011; Stelescu et al., 2012). Co-agents are multi-functional organic molecules which are highly reactive towards free radicals (Alvarez Grima, 2007). They are used as reactive additives to boost the vulcanization efficiency (Endstra, 1990). The most used coagents are molecules with maleimide groups, (meth)acrylate groups, or allylic groups, (Dikland et al., 1993) but polymeric materials with a high vinyl content, i.e. 1,2-polybutadiene, can also act as coagents.

The co-agents can be divided into two groups: Type I and Type II co-agents.

6 Advanced Elastomers – Technology, Properties and Applications

chemical bonding between polymer and substrate molecules.

**3. Polyfunctional monomers (co-agents)** 

of high quality.

irradiated material

crosslinking in thick polymer articles, in complex sections or production of recycled rubbers

The high-molecular compounds (elastomers) are made up of a large number of elementary molecules – monomers. These molecules can be of the same class or of different classes, resulting thus homopolymers and copolymers, respectively. The radiation acts on the highmolecular compounds as follows: (1) at a relatively low radiation dose (radiation dose = the energy absorbed per unit of mass of the irradiated material; it is measured in J/Kg; unit of measure for the absorbed dose is a gray: 1Gy = 1 J/kg), only "pure polymerization" occurs. With the linear increase in the radiation dose, the linear polymer chains increase progressively by addition of a molecule from a blend with low molecular weight to a radical at the end of an increasing chain; (2) with the dose increase during the pure polymerization, a new process named "grafting" takes place. By this process side chains are made in the polymer, resulting in modified surface properties in some materials, like as: biocompatibility, moisture-absorbent and moisture-repellent, and mechanical, chemical and thermal characteristics. This process is very promising for the biomaterial synthesis. (3) with the further increase in radiation dose, the "crosslinking" process takes place, when links are formed between polymer chains resulting in two- and three-dimensional structures. During this process insignificant chemical changes occur but significant structural changes. Simultaneously degradation occurs. Crosslinking and degradation (through chain scission) are two competing processes that always co-exist under radiation. Both processes have many applications in the field of new materials with improved characteristics, like as elastomer crosslinking. (4) the combined effects of the two processes are used in many industry processes, being known as "radiation curing". Three radiation induced processes are used in "radiation curing": monomer polymerization, polymer chain crosslinking and

Use of ionizing and non-ionizing radiation to obtain materials with improved characteristics is based on their advantages like as: *(I) electrons beam (EB):* (I.1.) accelerate the polymerization/vulcanization process, thus reducing the preparation time with tens to hundreds times; (I.2.) increase the conversion of raw material into the finished material up to a 100% yield and, therefore, the percentage of the residual monomer is nearly 0%, which is very important with noxious monomers; (I.3.) reduce the energy required in crosslinking and grafting with 5 –10 times as compared with the traditional method; *(II) microwaves (MW):* (II.1.) promote a narrow distribution of the molecular masses, as the crosslinking and grafting occurs simultaneously in the bulk due to the rapid energy transfer, volumetric and selective properties of MW dielectric heating , (II.2.) promote fast crosslinking and grafting processes, by tens to hundreds times faster than in classical procedure because the electromagnetic energy is directly transferred from the MW to the atoms or molecules of the

Reported papers suggest that appropriate polyfunctional monomers (co-agents) in polymer matrix (Vijayabaskar & Bhowmick, 2005; Yasin et al., 2005) could be used to obtain desired *Type I: Addition and hydrogen abstraction reactions*: these co-agents consist of rather polar molecules with a low molecular weight and activated double bonds. Their main characteristic is that they are highly reactive towards radicals, so scorch takes place very fast, which sometimes can be a disadvantage. By using this kind of coagents not only the rate of cure is increased but also the crosslink density or state of cure. A disadvantage that may be present when using this type of co-agents is that, due to polarity, the compatibility of these co-agents with the polymer matrix is limited. Some examples of Type I co-agents are: acrylates, methacrylates, bismaleimides and zinc salts.

*Type II: Addition reactions*: these co-agents are, in general, less polar molecules, which form more stable free radicals, so scorch does not take place as fast as with the previous type of co-agents. The use of these co-agents leads to an increase in crosslink density of the vulcanisate but, unlike Type I, they are not capable of increasing the cure rate. Due to their low polarity, these co-agents have a good compatibility with many elastomers. Some examples are: high-vinyl 1,2-polybutadiene, divinylbenzene, allyl esters of cyanurates, isocyanurates and sulphur.

This review gives an overview about our research (Stelescu & Manaila, 2007; Zuga et al., 2007; Zuga, Miu et al., 2007; Manaila et al., 2008; Stelescu et al., 2010; Manaila, Martin, Stelescu et al., 2009; Stelescu et al., 2009; Manaila, Martin, Craciun et al., 2009; Stelescu et al., 2008; Manaila, Stelescu, Ighigeanu et al., 2011; Manaila, Stelescu et al., 2011) on elastomer crosslinking by irradiation with accelerated electrons, a much more ecologic method that does not need to add crosslinking agents into the blend.

In addition, the main advantages that the new technique brings are: (a) almost 100% efficiency in converting raw material into finished materials; (b) reduction from tens to hundreds of times of the production length; (c) achieving unique properties of materials which cannot be obtained by conventional methods; (d) perfect adaptability to the highest demands on the environment because no reaction by-products are released into the atmosphere; (e) adaptability to any degree of automation (allows technological lines with speeds of over 500 m/min) and strict control of technological processes; (f) in many cases, reduction of energy consumption by 20 to 30 times compared to "classic heating" or conventional processes; (g) the process is simple and can be controlled by only one single parameter, i.e. absorbed dose, the quantity that varies with the application; (h) radiation crosslinking is technically and economically feasible as a pure physical process, i.e. without

the addition of sensitizers, there are no residues of alien substance needed for the chemical processes, or of their decomposition products.

At the interaction of ionizing radiation with (co)polymers, breaking of covalent bonds occurs, as well as the emergence of free radicals (transitional chemical species) on the main chain (if the lateral groups break) or in the main chain (if it breaks itself). The final effect is either crosslinking of macromolecular assembly or cutting the main chain of macromolecules and decreasing average molecular weight. In fact, the two effects, crosslinking and degradation, coexist and we need to point out the predominance of one of them.

In our study we used five polyfunctional monomers: TAC (triallylcyanurate) and TAIC (triallylisocyanurate) of type II, and TMPT (trimethylopropane trimethacrylate), EDMA (ethylene glycol dimethacrylate) and ZDA (zinc diacrylate) of type I.

Table 1 presents the chemical structure, type, functionality, and characteristics of polyfunctional monomers (co-agents) PFMs used.


**Table 1.** Characteristics of polyfunctional monomers (co-agents) PFMs used

### **4. Experimental installations, sample irradiation and laboratory tests**

8 Advanced Elastomers – Technology, Properties and Applications

processes, or of their decomposition products.

polyfunctional monomers (co-agents) PFMs used.

Luvomaxx TAC DL 70 (TAC) II

Trimethylolpropanetrimethacrylate Luvomaxx TMPT DL 75 (TMPT) <sup>I</sup>

Ethylene glycol dimethacrylate

Luvomaxx EDMA DL 75 (EDMA) <sup>I</sup>

Zinc-diacrylate ZDA GR 75 (ZDA) I

**Table 1.** Characteristics of polyfunctional monomers (co-agents) PFMs used

**PFMs Type** Chemical

them.

Triallylcyanurate

Triallylisocyanurate Luvomaxx TAIC DL

70C (TAIC)

the addition of sensitizers, there are no residues of alien substance needed for the chemical

At the interaction of ionizing radiation with (co)polymers, breaking of covalent bonds occurs, as well as the emergence of free radicals (transitional chemical species) on the main chain (if the lateral groups break) or in the main chain (if it breaks itself). The final effect is either crosslinking of macromolecular assembly or cutting the main chain of macromolecules and decreasing average molecular weight. In fact, the two effects, crosslinking and degradation, coexist and we need to point out the predominance of one of

In our study we used five polyfunctional monomers: TAC (triallylcyanurate) and TAIC (triallylisocyanurate) of type II, and TMPT (trimethylopropane trimethacrylate), EDMA

Table 1 presents the chemical structure, type, functionality, and characteristics of

II

structure

N N N O

O

O O

O

O-O-Zn++

O O

O

O

O

O

O N N O N O **Characteristics** 

Melting point: 26–28 0C; Boiling point: 149–152 0C; Density: 1.34 g/cm3; 26% percentage of ash, 30% active synthetic silica.

Melting point: 26–28 0C; Boiling point: 119–120 0C; Density: 1.34 g/cm3; 30% active synthetic silica.

Melting point: -25 0C; Boiling point: >200 0C; Density: 1.36 g/cm3; 22% percentage of ash, 75 ± 3% active ingredient.

Melting point: -40 0C; Boiling point: 85 0C; Density: 1.25 g/cm3; 23% percentage of ash, 75 ± 3% active ingredient.

Melting point: 240-244 0C; Boiling point: 141 0C; Density: 1.23 g/cm3; 75 ± 3% active ingredient.

(ethylene glycol dimethacrylate) and ZDA (zinc diacrylate) of type I.

The experimental installation consists mainly of the following units: an accelerated electron beam source, a microwave source of 2.45 GHz and a multimode rectangular cavity used as reaction chamber. As accelerated electron beam source is used the electron accelerator ILU-6M and electron linear accelerator ALIN-10. Two experimental installations for the separate EB irradiation and combined irradiation with EB and MW are carried out: *experimental installation A* and *experimental installation B*.

Each experimental installations consists mainly of the following units: an electron beam source, a microwave source of 2.45 GHz, a multimode rectangular cavity in which are injected both, EB and MW. Experimental installation A uses as electron beam source the electron linear accelerator ALIN-10 of 6.23 MeV and 70 Gy s-1 maximum dose rate (built in the NILPR Institute, Bucharest, Romania). Experimental installation B uses as electron beam source the industrial electron accelerator ILU-6M of 1.8 MeV and 10.8 kW maximum output power, built in Russia, Institute of Nuclear Physics-Novosibirsk. It is placed at Electrical Project and Research Institute from Bucharest, Romania.

The ALIN-10 electron accelerator was built in Romania, National Institute for Lasers, Plasma and Radiation Physics, Electron Accelerator Laboratory-Bucharest, is of the travelling-wave type, driven by 2-MW peak power tunable EEV M5125-type magnetrons operating in Sband The optimum values of the EB peak current IEB and EB energy EEB to produce maximum output power PEB for a fixed pulse duration EB and repetition frequency fEB are as follows: EEB = 6.23 MeV; IEB = 75 mA; PEB = 164 W (fEB = 100 Hz, EB = 3.5 s). The main characteristics of the ALIN-10 electron accelerator are presented in Table 2.


**Table 2.** The main characteristics of electron accelerator ALIN-10

The ILU-6M accelerated electron beam source is placed at Electrical Project and Research Institute from Bucharest, Romania. The ILU-6M is a resonator-type accelerator, operating at 1155 MHz. This accelerator generates electron beam pulses of 0.375 ms duration, up to 0.32 A current peak intensity and up to 6 mA mean current intensity. The cross-sectional size of the scanned EB at the ILU-6M vacuum window exit is 1100 mm x 65 mm. The EB effects are related to the absorbed dose (D), expressed in Gray or J kg-1. The single pass dose with conveyor under the ILU-6M scanner is adjustable from 12.5 kGy to 50 kGy. The main characteristics of the ILU-6M electron accelerator are presented in Table 3.


**Table 3.** The main characteristics of cavity electron accelerator ILU-6M

The Experimental installation A uses the multimode rectangular cavity of a mechanical and electrical proper modified MW oven (MEM-MWO) of 2.45 GHz and 710 W output power. The conventional operation of the 2.45 GHz oven magnetron was properly modified in order to permit the use of an electronic regulator that ensures variable magnetron output power (Martin et al., 2001). Microwaves are generated as 10 ms pulses at 50 Hz repetition rate. For MW irradiation was used the SAR values which prevents during MW+EB irradiation the rise of the samples final temperature above 60-70oC.

The rubber samples were obtained from raw rubber mixtures, as compressed sheets of 2 mm in the polyethylene foils to minimize oxidation. For radiation treatments the sheets were cut in rectangular shape of two different sizes: *type 1* of 0.1 m x 0.03 m2 and *type 2* of 0.15 x 0.15 m2. The treatment was performed with layers of 10 sandwiched *type 1* sheets irradiated using ALIN-10 accelerator and three sandwiched *type 2* sheets using the ILU-6M accelerator.

The EB effects are related to the absorbed dose (D) expressed in Gray or J kg-1 and absorbed dose rate (D\*) expressed in Gy s-1 or J kg-1 s-1. The MW effects are related to SAR (Specific Absorption Rate, expressed in W. kg-1) which is equivalent to D\* and SA (Specific Absorption, expressed in J. kg-1) which is equivalent to D.

According to the Technical Report Series No. 277 (Andreo et al., 1997), the absorbed dose is the major parameter in the accelerated electron radiation. The vulcanizing and grafting process performances are provided by the severe control of this parameter. The relation defining the absorbed dose is:

$$\mathbf{D} = \mathbf{d}\boldsymbol{\omega} / \text{ dm} \tag{1}$$

where:

10 Advanced Elastomers – Technology, Properties and Applications

EA energy 1.8 MeV EA power in impulse 0–1 A EA impulse duration τ= 500 μs

Mean power 0–6 mA Maximum mean power 10.8 kW

**Table 3.** The main characteristics of cavity electron accelerator ILU-6M

irradiation the rise of the samples final temperature above 60-70oC.

Absorption, expressed in J. kg-1) which is equivalent to D.

defining the absorbed dose is:

Useful section of EA field at scanning device

Conveyor belt for samples to be irradiated

with the following characteristics:

output

EA impulse repeat frequency 2, 3, 5 10, 15, 25, 50 Hz

Electron scattering method Electromagnetic scanning device

The Experimental installation A uses the multimode rectangular cavity of a mechanical and electrical proper modified MW oven (MEM-MWO) of 2.45 GHz and 710 W output power. The conventional operation of the 2.45 GHz oven magnetron was properly modified in order to permit the use of an electronic regulator that ensures variable magnetron output power (Martin et al., 2001). Microwaves are generated as 10 ms pulses at 50 Hz repetition rate. For MW irradiation was used the SAR values which prevents during MW+EB

The rubber samples were obtained from raw rubber mixtures, as compressed sheets of 2 mm in the polyethylene foils to minimize oxidation. For radiation treatments the sheets were cut in rectangular shape of two different sizes: *type 1* of 0.1 m x 0.03 m2 and *type 2* of 0.15 x 0.15 m2. The treatment was performed with layers of 10 sandwiched *type 1* sheets irradiated using ALIN-10 accelerator and three sandwiched *type 2* sheets using the ILU-6M accelerator. The EB effects are related to the absorbed dose (D) expressed in Gray or J kg-1 and absorbed dose rate (D\*) expressed in Gy s-1 or J kg-1 s-1. The MW effects are related to SAR (Specific Absorption Rate, expressed in W. kg-1) which is equivalent to D\* and SA (Specific

According to the Technical Report Series No. 277 (Andreo et al., 1997), the absorbed dose is the major parameter in the accelerated electron radiation. The vulcanizing and grafting process performances are provided by the severe control of this parameter. The relation

100 cm x 6.5 cm

Moving speed, Vbelt=1.56-12.8 cm/s;

Distance between terminals: 1282 mm Distance from the scanning device output

Dimensions of sample holder: 500 mm x 300 mm (with possibility of extension

mm; thickness = 160 mm;

Window: H = 100–500 mm;

up to 1500 mm x 600 mm)

Dimensions: length = 125 mm; width = 290

*Characteristic Value* 

**d** is the mean energy given up by the ionizing radiation to the mass amounts **dm** of the substance interacting with this ionizing radiation.

**dm** is emphasized to be very low but not so low that the mean energy **d** given up by the radiation would undergo a significant fluctuation.

**Absorbed dose** is measured in **J/kg**. The SI unit measure for the absorbed dose is the **gray**  (Gy): **1 Gy** = 1 Joule/kg. The **rad** unit is also used, with the following relation between the **Gy** and **rad**: **1 Gy = 100 rad.** A relevant example: a material irradiated by 2 Mrad (20 kGy) means that AE (accelerated electron beam) have deposited 2.108 ergs or about 1019 eV per gram substance.

After irradiation the samples are analyzed by mechanical testing. Tensile strength and tear strength tests were carried out with a Schoppler strength tester with testing speed 460 mm/min, using dumb-bell shaped specimens according to ISO 37/1997, respectively angular test pieces (type II) in according to ISO 34-1/2000. Hardness was measured by using a hardener tester according to ISO 7619/2001. Elasticity was evaluated with a test machine of type Schob. The cure characteristics of the compounds were measured at 160°C using an oscillating disk rheometer (Monsanto), according to the SR ISO 3417/1997.

## **5. Electron beam and microwaves processing of elastomers/rubbers with polyfunctional monomers**

### **5.1. Aspects regarding crosslinking of a natural rubber (NR) blend**

Natural rubber is a heavily researched material. The outstanding strength of natural rubber has maintained its position as the preferred material in many engineering applications. It has a long fatigue life and high strength even without reinforcing fillers. Other than for thin sections it can be used to approximately 100 oC, and sometimes above. It can maintain flexibility down to -60 oC if compounded for the purpose. It has good creep and stress relaxation resistance and is low cost. Its chief disadvantage is its poor oil resistance and its lack of resistance to oxygen and ozone, although these latter disadvantages can be ameliorated by chemical protection. An natural rubber structure is illustrated in Figure 1.

**Figure 1.** Chemical structure of natural rubber (NR)

The vulcanisation of natural rubber (NR) by sulphur in presence of organic accelerator is a complicated process. The mechanism of vulcanisation and its acceleration depends on the structure of the rubber, type and concentration of accelerators and activators (zinc oxide and fatty acid) and on the thermodynamics of each particular reaction. The chemistry of vulcanisation is complex and the resulting crosslinks may be mono-, di-, tri- or higher polysulphides, with a proportion which is among others largely determined by the vulcanisation system, the cure time and the temperature.(Stelescu et al., 2010).

This section presents the influence of the vulcanization method – of the crosslinking mechanism – on the characteristics of a natural rubber blend (Stelescu et al., 2010) .

The following raw materials have been used: Crep natural rubber, Ultrasil VN3 precipitated silica (50 phr), zinc oxide quality I (5 phr), stearic acid (0.5 phr), polyethylene glycol coupling agent (3 phr), Irganox 1010 antioxidant (1 phr). For crosslinking blends, the following were used: Perkadox 40 benzoyl peroxide (8 phr) – for peroxide vulcanization; sulphur (1.5 phr) and vulcanization accelerators (tetramethyl thiuram disulfide TMTD (1 phr) and mercaptobenzothiazol MBT (0.5 phr) – for sulphur vulcanization; accelerated electrons (EB) and polyfunctional monomer – trimethylopropane trimethacrylate TMPT DL 75 C (6 phr) for electron beam vulcanization.

Blends have been made by means of blending technique, on a laboratory roll with electric heating at 65-70°C, total blend time of 12'. Plates for physical-mechanical determinations have been made by means of hydraulic press. Blends crosslinked with *peroxide* or with *sulphur and accelerators* have been reticulated at 160°C and vulcanization time was chosen depending on curves obtained on the Monsando rheometer (rheologic characteristics) of blends in order to obtain the following blend samples: subvulcanized (T50), vulcanized (T90) and supravulcanized (T140). Thus, the time needed to obtain T50 and T90 blends was determined from rheograms and corresponds to T50 and T90 in Table 1, and the time needed to obtain T140 supravulcanized blends was 22' for both types of blends. Plates for irradiation were modeled by pressing at low temperatures of maximum 100°C for 3'.

The EB vulcanization rubber processing is performed with the accelerator ILU-6M of 1.8 MeV and 10.8 kW. For EB treatment the rubber sheets were cut in rectangular shape of 0.15 x 0.15 m2. The layers of three sandwiched sheets were irradiated by repeatedly passing on a conveyor under the ILU-6M scanner. Samples were irradiated with 5, 10, 15 and 20 Mrad respectively (1 Mrad = 10 kGy).

Rheologic characteristics of blends crosslinked with peroxide (symbol NRI-P) and with sulphur (symbol NPI-S) respectively, obtained by means of Monsanto rheometer (Table 4), show that the minimum moment and the maximum moment have high values because the charge and the other ingredients introduced in the blend have led to an increase of blend viscosity, and as a result, the blend opposes a high resistance force to the rotation of the oscillating disk of Monsanto rheometer. Physical-mechanical properties of obtained blends are presented in Table 5, Table 6 and Table 7.


**Table 4.** Rheologic characteristics of blends

12 Advanced Elastomers – Technology, Properties and Applications

75 C (6 phr) for electron beam vulcanization.

respectively (1 Mrad = 10 kGy).

are presented in Table 5, Table 6 and Table 7.

system, the cure time and the temperature.(Stelescu et al., 2010).

The vulcanisation of natural rubber (NR) by sulphur in presence of organic accelerator is a complicated process. The mechanism of vulcanisation and its acceleration depends on the structure of the rubber, type and concentration of accelerators and activators (zinc oxide and fatty acid) and on the thermodynamics of each particular reaction. The chemistry of vulcanisation is complex and the resulting crosslinks may be mono-, di-, tri- or higher polysulphides, with a proportion which is among others largely determined by the vulcanisation

This section presents the influence of the vulcanization method – of the crosslinking

The following raw materials have been used: Crep natural rubber, Ultrasil VN3 precipitated silica (50 phr), zinc oxide quality I (5 phr), stearic acid (0.5 phr), polyethylene glycol coupling agent (3 phr), Irganox 1010 antioxidant (1 phr). For crosslinking blends, the following were used: Perkadox 40 benzoyl peroxide (8 phr) – for peroxide vulcanization; sulphur (1.5 phr) and vulcanization accelerators (tetramethyl thiuram disulfide TMTD (1 phr) and mercaptobenzothiazol MBT (0.5 phr) – for sulphur vulcanization; accelerated electrons (EB) and polyfunctional monomer – trimethylopropane trimethacrylate TMPT DL

Blends have been made by means of blending technique, on a laboratory roll with electric heating at 65-70°C, total blend time of 12'. Plates for physical-mechanical determinations have been made by means of hydraulic press. Blends crosslinked with *peroxide* or with *sulphur and accelerators* have been reticulated at 160°C and vulcanization time was chosen depending on curves obtained on the Monsando rheometer (rheologic characteristics) of blends in order to obtain the following blend samples: subvulcanized (T50), vulcanized (T90) and supravulcanized (T140). Thus, the time needed to obtain T50 and T90 blends was determined from rheograms and corresponds to T50 and T90 in Table 1, and the time needed to obtain T140 supravulcanized blends was 22' for both types of blends. Plates for irradiation

The EB vulcanization rubber processing is performed with the accelerator ILU-6M of 1.8 MeV and 10.8 kW. For EB treatment the rubber sheets were cut in rectangular shape of 0.15 x 0.15 m2. The layers of three sandwiched sheets were irradiated by repeatedly passing on a conveyor under the ILU-6M scanner. Samples were irradiated with 5, 10, 15 and 20 Mrad

Rheologic characteristics of blends crosslinked with peroxide (symbol NRI-P) and with sulphur (symbol NPI-S) respectively, obtained by means of Monsanto rheometer (Table 4), show that the minimum moment and the maximum moment have high values because the charge and the other ingredients introduced in the blend have led to an increase of blend viscosity, and as a result, the blend opposes a high resistance force to the rotation of the oscillating disk of Monsanto rheometer. Physical-mechanical properties of obtained blends

were modeled by pressing at low temperatures of maximum 100°C for 3'.

mechanism – on the characteristics of a natural rubber blend (Stelescu et al., 2010) .


**Table 5.** Physical-mechanical properties of NR rubber blends vulcanized with peroxide (NRI-P), and sulphur and accelerators (NRI-S)


**Table 6.** Physical-mechanical properties of NR rubber blends vulcanized with EA (NRI)


**Table 7.** Physical-mechanical properties of NR rubber blends vulcanized with EA in the presence of TMPT (NRI-TMPT)

Comparing physical-mechanical properties of subvulcanized (T50), vulcanized (T90) and supravulcanized (T140) samples from each type of NRI-S and NRI-P blend (table 5), it is noticed that: (a) in the case of blends crosslinked with peroxides, as the vulcanization time increases, hardness, elasticity and tensile stress at 100% elongation increase and tensile strength, elongation at break, permanent set and tear strength decrease; (b) for blends crosslinked with sulphur and accelerators, as the vulcanization time increases, a slight decrease of hardness, elasticity, tensile stress at 100% elongation, tensile strength, permanent set and tear strength, and a slight increase of elongation at break take place; (c) hardness, elasticity and tensile stress at 100% elongation of blends with ingredients vulcanized with sulphur are lower than those vulcanized with peroxide, instead, tensile strength, tear strength, elongation at break and permanent set have higher values; (d) characteristics of blends crosslinked with peroxide decrease significantly when increasing vulcanization time compared to samples obtained through other vulcanization methods, indicating degradation of polymer chain in the presence of peroxide; (e) physical-mechanical properties of subvulcanized, vulcanized and supravulcanized samples of NR blend depend on the crosslinking technique and mechanism.

Comparing blends cross-linked with peroxide to NRI and NRI-TMPT type (table 6 and table 7), irradiated with EA (in both cases crosslinking is done by radicalic mechanism), it can be noticed that: (a) the optimal dose needed can be 20 Mrad and 10-15 Mrad respectively in the case of blends containing 6 phr TMPT; (b) upon increasing the irradiation dose, hardness, elasticity, tensile stress at 100% elongation, tensile strength and tear strength increase and permanent set decreases; (c) blends crosslinked with EA in the presence of TMPT exhibit superior values of tear strength, have good values of permanent set – similar to those obtained through other methods – indicating an efficient crosslinking, and tensile strength, elongation at break, hardness, elasticity and tensile stress at 100% elongation have values ranging between those obtained in vulcanization with peroxide and those made by vulcanization with sulphur and accelerators; (d) natural rubber blends containing 6 phr TMPT irradiated at 15 Mrad and 20 Mrad respectively, exhibit superior physical-mechanical properties compared to control blend NRI-P tip T90 (obtained by vulcanization with peroxide). Based on results obtained and existing literature studies, reaction mechanisms are suggested for crosslinking natural rubber using the crosslinking systems presented above.

Vulcanization with sulphur and accelerators of NR (Figure 2) is done in general by ionic mechanism and leads to the formation of sulphur bridges between (C-Sx-C) macromolecules or cyclic combination of sulphur. At high temperatures, desulphuration takes place, determining the formation of shorter sulphur bridges. As a consequence of thermal instability of sulphurs, NR vulcanized with sulphur can be devulcanized in the presence of disulphur diaryls or amines, at temperatures of over 300ºC (Stelescu et al., 2010).

Vulcanization with peroxides (Figure 3) is done by radicalic mechanism when bonds form between C-C macromolecules; crosslinking is initiated by thermal decomposition of peroxide, which is considered the determining stage of crosslinking speed. Then free radicals formed extract hydrogen atoms from natural rubber chains in order to form macroradicals (Stelescu et al., 2010; Hofmann, 1967). Macroradicals recombine forming crosslinked structure.

14 Advanced Elastomers – Technology, Properties and Applications

on the crosslinking technique and mechanism.

Comparing physical-mechanical properties of subvulcanized (T50), vulcanized (T90) and supravulcanized (T140) samples from each type of NRI-S and NRI-P blend (table 5), it is noticed that: (a) in the case of blends crosslinked with peroxides, as the vulcanization time increases, hardness, elasticity and tensile stress at 100% elongation increase and tensile strength, elongation at break, permanent set and tear strength decrease; (b) for blends crosslinked with sulphur and accelerators, as the vulcanization time increases, a slight decrease of hardness, elasticity, tensile stress at 100% elongation, tensile strength, permanent set and tear strength, and a slight increase of elongation at break take place; (c) hardness, elasticity and tensile stress at 100% elongation of blends with ingredients vulcanized with sulphur are lower than those vulcanized with peroxide, instead, tensile strength, tear strength, elongation at break and permanent set have higher values; (d) characteristics of blends crosslinked with peroxide decrease significantly when increasing vulcanization time compared to samples obtained through other vulcanization methods, indicating degradation of polymer chain in the presence of peroxide; (e) physical-mechanical properties of subvulcanized, vulcanized and supravulcanized samples of NR blend depend

Comparing blends cross-linked with peroxide to NRI and NRI-TMPT type (table 6 and table 7), irradiated with EA (in both cases crosslinking is done by radicalic mechanism), it can be noticed that: (a) the optimal dose needed can be 20 Mrad and 10-15 Mrad respectively in the case of blends containing 6 phr TMPT; (b) upon increasing the irradiation dose, hardness, elasticity, tensile stress at 100% elongation, tensile strength and tear strength increase and permanent set decreases; (c) blends crosslinked with EA in the presence of TMPT exhibit superior values of tear strength, have good values of permanent set – similar to those obtained through other methods – indicating an efficient crosslinking, and tensile strength, elongation at break, hardness, elasticity and tensile stress at 100% elongation have values ranging between those obtained in vulcanization with peroxide and those made by vulcanization with sulphur and accelerators; (d) natural rubber blends containing 6 phr TMPT irradiated at 15 Mrad and 20 Mrad respectively, exhibit superior physical-mechanical properties compared to control blend NRI-P tip T90 (obtained by vulcanization with peroxide). Based on results obtained and existing literature studies, reaction mechanisms are suggested for crosslinking natural rubber using the crosslinking systems presented above.

Vulcanization with sulphur and accelerators of NR (Figure 2) is done in general by ionic mechanism and leads to the formation of sulphur bridges between (C-Sx-C) macromolecules or cyclic combination of sulphur. At high temperatures, desulphuration takes place, determining the formation of shorter sulphur bridges. As a consequence of thermal instability of sulphurs, NR vulcanized with sulphur can be devulcanized in the presence of

Vulcanization with peroxides (Figure 3) is done by radicalic mechanism when bonds form between C-C macromolecules; crosslinking is initiated by thermal decomposition of peroxide, which is considered the determining stage of crosslinking speed. Then free radicals formed extract hydrogen atoms from natural rubber chains in order to form

disulphur diaryls or amines, at temperatures of over 300ºC (Stelescu et al., 2010).

**Figure 2.** Reaction scheme – Mechanism of crosslinking natural rubber with sulphur and accelerators (Stelescu et al., 2010).

**Figure 3.** Reaction scheme – Mechanism of crosslinking natural rubber with peroxides (Stelescu et al., 2010) .

**Figure 4.** Reaction scheme – Mechanism of crosslinking natural rubber with EB

Elastomer crosslinking by means of EB (Figure 4) is done without heating and in the absence of vulcanization agents. The chemistry of the process is based on macroradical formation from elastomer chains, which recombine, causing structuring. Isomerisations, double bond migrations, cyclizations, destructions etc. take place simultaneously with vulcanization. The reaction mechanism is similar to that presented in crosslinking with peroxides, but in this case, reaction initiation is due to the action of EB (Boye, 2008).

### **5.2. The influence of trimethylol-propane trimethacrylate (TMPT) co-agent on the mechanical properties of the natural rubber (NR) cross-linked by EB irradiation**

In the following experiment (Stelescu & Manaila, 2007) the natural rubber blends were grafted and crosslinked by means of the accelerated electrons in the presence of a multifunctional monomer - trimethylol-propane trimethacrylate (TMPT), and the influences of the trimethylol-propane trimethacrylate (TMPT) percentage and accelerated electron irradiation dose on the physical-mechanical characteristics of the natural rubber (NR) blends were investigated.

The used materials were: natural rubber Crep 1X (NR), trimethylol-propane trimethacrylate TMPT DL 75 (TMPT), Ultrasil VN3 precipitated silica (50 phr), zinc oxide quality I (5 phr), stearic acid (0.5 phr), polyethylene glycol coupling agent (3 phr), Irganox 1010 antioxidant (1 phr) and benzoyl peroxide Perkadox 14-40B-GR (8 phr) as curing agent for the control blend.Natural rubber blends containing 0, 3, 6 and 9 phr of TMPT were prepared by blending on a laboratory roller mill. From these samples in a shape of plates were obtained by means of hydraulic press at 150 MPa and 100oC. The resulted plates were treated by irradiation, using the accelerator ALIN-10. The accelerated electrons dose rate was established to 2.4 kGy/min in order to accumulate 5 Mrad, 10 Mrad, 15 Mrad and 20 Mrad respectively (1 Mrad = 10 kGy). The control blend was obtained with benzoyl peroxide as curing agent. The blend was prepared on a laboratory roller mill and the control sample curing was accomplished on hydraulic press at 160oC. The best curing time (12'30'') was determined by means of a Monsanto Rheometer.

Figures 5-10 illustrate the changes in physical-mechanical characteristics depending on the TMPT percentage in the blend and irradiation dose. Hardness (figure 5) increases as the irradiation dose and TMPT percentage increase; the hardness values for the blends with 6 and 9 phr of TMPT each irradiated at 15 and 20 Mrad are similar to those of the control blend (83oShA). Tensile stress at 100 % elongation (figure 6) for the blends with 6 and 9 phr TMPT at an irradiation dose of 20 Mrad shows a higher value than tensile stress at 100 % elongation for the control sample (4,6 N/mm2). Tensile strength (figure 7) for the samples from blends with 6 and 9 phr TMPT, irradiated by means of accelerated electrons shows higher values than for the control sample (10,3 N/mm2), even at an irradiation dose of 10 Mrad. Values of the elongation at break (figure 8) for the samples irradiated with accelerated electrons are higher than those for the control sample (246 %). This aspect decreases as the irradiation dose and TMPT percentage increase. Permanent set (figure 9) decreases as the irradiation dose and TMPT percentage increase; for the blends with 6 and 9 phr of TMPT irradiated with 15 and 20 Mrad, the permanent set values are lower than those for the control sample (14,6 %), revealing a high crosslinking level. Tear strength (figure 10) for the samples from the blends irradiated with accelerated electrons shows higher values than those for the control sample (14,6 N/mm).

16 Advanced Elastomers – Technology, Properties and Applications

**Figure 4.** Reaction scheme – Mechanism of crosslinking natural rubber with EB

case, reaction initiation is due to the action of EB (Boye, 2008).

determined by means of a Monsanto Rheometer.

**irradiation** 

were investigated.

Elastomer crosslinking by means of EB (Figure 4) is done without heating and in the absence of vulcanization agents. The chemistry of the process is based on macroradical formation from elastomer chains, which recombine, causing structuring. Isomerisations, double bond migrations, cyclizations, destructions etc. take place simultaneously with vulcanization. The reaction mechanism is similar to that presented in crosslinking with peroxides, but in this

**5.2. The influence of trimethylol-propane trimethacrylate (TMPT) co-agent on the mechanical properties of the natural rubber (NR) cross-linked by EB** 

In the following experiment (Stelescu & Manaila, 2007) the natural rubber blends were grafted and crosslinked by means of the accelerated electrons in the presence of a multifunctional monomer - trimethylol-propane trimethacrylate (TMPT), and the influences of the trimethylol-propane trimethacrylate (TMPT) percentage and accelerated electron irradiation dose on the physical-mechanical characteristics of the natural rubber (NR) blends

The used materials were: natural rubber Crep 1X (NR), trimethylol-propane trimethacrylate TMPT DL 75 (TMPT), Ultrasil VN3 precipitated silica (50 phr), zinc oxide quality I (5 phr), stearic acid (0.5 phr), polyethylene glycol coupling agent (3 phr), Irganox 1010 antioxidant (1 phr) and benzoyl peroxide Perkadox 14-40B-GR (8 phr) as curing agent for the control blend.Natural rubber blends containing 0, 3, 6 and 9 phr of TMPT were prepared by blending on a laboratory roller mill. From these samples in a shape of plates were obtained by means of hydraulic press at 150 MPa and 100oC. The resulted plates were treated by irradiation, using the accelerator ALIN-10. The accelerated electrons dose rate was established to 2.4 kGy/min in order to accumulate 5 Mrad, 10 Mrad, 15 Mrad and 20 Mrad respectively (1 Mrad = 10 kGy). The control blend was obtained with benzoyl peroxide as curing agent. The blend was prepared on a laboratory roller mill and the control sample curing was accomplished on hydraulic press at 160oC. The best curing time (12'30'') was

**Figure 5.** Changes in hardness versus the irrad iation dose and TMPT percentage

**Figure 6.** Changes in tensile stress at 100% elongation versus the irradiation dose and TMPT percentage

**Figure 7.** Changes in tensile strength versus the irradiation dose and TMPT percentage

**Figure 8.** Changes in elongation at break versus the irradiation dose and TMPT percentage

**Figure 9.** Changes in permanent set versus the irradiation dose and TMPT percentage

**Figure 10.** Changes in tear strength versus the irradiation dose and TMPT percentage

**Figure 7.** Changes in tensile strength versus the irradiation dose and TMPT percentage

**Figure 8.** Changes in elongation at break versus the irradiation dose and TMPT percentage

**Figure 9.** Changes in permanent set versus the irradiation dose and TMPT percentage

As a conclusion, the natural rubber blends containing 6 and 9 phr of TMPT irradiated each of them at 20 Mrad have shown higher physical-mechanical characteristics than those for the control sample (obtained by curing with peroxide at 160oC). This proves the advantages of a new processing technique for the NR blends resulting in 10 times shorter curing time, removing the curing agents, and lack of wastes.

### **5.3. Characteristics of natural rubber (NR) blends cross-linked by electron beam and microwave irradiation**

Crosslinking of elastomers or rubbers by electron beam (EB) and microwave (MW) radiations could be a new method for improve their mechanical properties. Interaction of each of the two physical systems, EB and MW, with a substance has revealed their ability for changing physical and chemical proprieties of the treated substance. Therefore, the physical and chemical effects of the EB and MW radiation have drawn high interest, resulting in a large industrial application range of the new materials with improved characteristics. In the following we present the effect of the polyfunctional monomers (PFMs) on the mechanical properties of the NR (natural) rubber crosslinked by electron beam (EB) and microwave processing (Manaila, Stelescu et al., 2011).

The following materials were used in the study: natural rubber Crep 1X; triallylcyanurate TAC DL 70 (3 phr); triallylisocyanurate TAIC DL 70C (3 phr); trimethylopropanetrimethacrylate TMPT DL 75 (3 phr) and zinc-diacrylate ZDA GR 75 (3 phr). Blends were prepared on an electrically heated laboratory roller mill. For preparation of NR with polyfunctional monomers, the blend constituents were added in the following sequence and amounts: 100 phr NR and 3 phr polyfunctional monomers (TAC, TAIC, TMPT and ZDA respectively). Process variables: temperature 25-50oC, friction 1:1.1, and total blending time 5 min. Plates required for physico-mechanical tests were obtained by pressing in a hydraulic press at 110 ±5oC and 150 MPa. Dibenzoyl peroxide vulcanized samples were prepared similarly to the experimental ones with the following specifications: 8 phr of dibenzoyl

peroxide as vulcanizing agent was added and the blend vulcanization was achieved in a hydraulic press at 160oC; the vulcanization time was measured by means of Monsanto Rheometer. The resulted plates were treated by irradiation, using the accelerator ILU - 6M. For EB and EB+MW treatments the rubber samples were cut as compressed sheets of 2 mm thick in the polyethylene foils to minimize oxidation. The layers of three sandwiched sheets were irradiated by repeatedly passing on a conveyor under the ILU-6M scanner.


The mechanical properties of samples are summarized in Tables 8-11.

**Table 8.** Physical-mechanical characteristics of blends: NR+TAC


**Table 9.** Physical-mechanical characteristics of blends: NR+TAIC


**Table 10.** Physical-mechanical characteristics of blends: NR+TMPT


**Table 11.** Physical-mechanical characteristics of blends: NR+ZDA

20 Advanced Elastomers – Technology, Properties and Applications

*Mechanical characteristics* 

*Mechanical characteristics* 

*Mechanical characteristics* 

*Tensile stress at 100%elongation,* 

peroxide as vulcanizing agent was added and the blend vulcanization was achieved in a hydraulic press at 160oC; the vulcanization time was measured by means of Monsanto Rheometer. The resulted plates were treated by irradiation, using the accelerator ILU - 6M. For EB and EB+MW treatments the rubber samples were cut as compressed sheets of 2 mm thick in the polyethylene foils to minimize oxidation. The layers of three sandwiched sheets

*BP* 

*BP* 

*BP* 

*Elasticity, %* 68 48 53 48 *Tensile stress at 100%elongation, N/mm2* - 0.4 0.4 0.29 *Tensile strength, N/mm2* 0.82 3.6 8.3 8.7 *Elongation at break, %* 60 673 727 785 *Permanent set, %* 3 9 7 14 *Tear strength, N/mm* 1.39 13.5 21 13

*Elasticity, %* 68 42 42 50 *Tensile stress at 100%elongation, N/mm2* - 0.4 0.4 0.21 *Tensile strength, N/mm2* 0.96 0.7 2.2 4.8 *Elongation at break, %* 87 387 647 850 *Permanent set, %* 9 11 13 15 *Tear strength, N/mm* 2.5 7 13 13

*Elasticity, %* 50 44 44 42

*N/mm2* - 0.3 0.4 0.19 *Tensile strength, N/mm2* 0.9 0.8 0.9 4.6 *Elongation at break, %* 87 487 300 935 *Permanent set, %* 5 15 8 19 *Tear strength, N/mm* 2 9.5 14.5 11

*vulcanization EB vulcanization EB+MW* 

*vulcanization EB vulcanization EB+MW* 

*vulcanization EB vulcanization EB+MW* 

**NR - P 5 Mrad 10 Mrad 5 Mrad + 55'** 

**NR - P 5 Mrad 10 Mrad 5 Mrad + 55'** 

**NR - P 5 Mrad 10 Mrad 5 Mrad + 55'** 

*vulcanization* 

*vulcanization* 

*vulcanization* 

were irradiated by repeatedly passing on a conveyor under the ILU-6M scanner.

The mechanical properties of samples are summarized in Tables 8-11.

**Table 8.** Physical-mechanical characteristics of blends: NR+TAC

**Table 9.** Physical-mechanical characteristics of blends: NR+TAIC

**Table 10.** Physical-mechanical characteristics of blends: NR+TMPT

Analyzing the mechanical characteristics obtained from the EB cross-linked samples compared with those of cross-linked with peroxide mixtures in the presence of the same types of PFMs can be observed: (1) significant improvements in tensile strength (between 130% for NR+TAIC and NR+ZDA at 10 Mrad, and 912% for NR+TMPT at 5 Mrad; (2) elongation at break increases, for all polyfunctional monomers type, the smallest increase being 142% for NR+ZDA at 5 Mrad and highest 1112% for NR+TMPT at 10 Mrad; (3) tear strenght increases with radiation dose, (between 180% for NR+TAIC at 5 Mrad, and 1410% for NR+TMPT at 10 Mrad; (4) for all samples was noticed a decrease in elasticity.

Relatively low permanent set values indicate a good return to its original shape after applying a force, so an efficient curing for all samples. In conclusion, even at a dose of 5 Mrad was achieved an efficient crosslinking of NR. The polyfunctional monomer influence on these parameters for the samples vulcanized with EB is the following: TMPT > ZDA > TAC > TAIC.

Comparing the mechanical characteristics obtained from the EA+MW cross-linked samples with those of cross-linked with peroxide mixtures in the presence of the same types of MP can be observed a significant improvement in tensile strength (up to 411% for NR+TAC, 400% for NR+TAIC, 960% for NR+TMPT and 184% for NR+ZDA), in elongation at break (up to 974% for NR+TAC, 877% for NR+TAIC, 1208% for NR+TMPT and 382% for NR+ZDA) and tear strenght (up to 450% for NR+TAC, 420% for NR+TAIC, 835% for TMPT and 300% for NR+ZDA). The order of influence of polyfunctional monomers on the studied parameters for EA+MW is identical to that in the case of irradiation with EA (TMPT > ZDA > TAC > TAIC).

Improved characteristics of hardened mixtures with EA and EA + MW from the hardened peroxide is due on the one hand the advantages of accelerated electrons (the process is very fast, and due to high penetration power of radiation there is an effective and uniform curing), and on the other hand, the advantages of microwave (promote a narrow distribution of the molecular masses, as the crosslinking occurs simultaneously in the bulk of material because of the microwave interaction with all material under irradiation; promote fast crosslinking processes) (MGM Rubber Company-Research and Development, 2007; Martin, 2002). Also, due to reduced processing time, it is removed the degradation due to thermal degradation at high temperature elastomer maintenance of about 1600C for 10-30 min.

Analyzing the characteristics influence of polyfunctional monomers type, can be seen that the best results were obtained by using TMPT followed by ZDA (coagents curing Type I). Type I polyfunctional monomers are highly reactive and increase the rate and state of cure. Type II (TAC and TAIC) polyfunctional monomers increase the state of cure only. Also, the influence of polyfunctional monomers to increasing the mechanical characteristics is determined by the reactivity, the number of reactive groups (functionality): TMPT has functionality three and ZDA has functionality two (Boye, 2008; Henning, 2008).

### **5.4. Characteristics of materials based on chlorinated polyethylene (CPE) obtained by cross-linked by electron beam in the presence of triallylcyanurate (TAC).**

Chlorinated polyethylene (CPE) is a synthetic elastomer produced by the means of controlled chlorination of polyethylene and has been commercially produced since the late 1960s (Stelescu et al., 2011; Stelescu et al., 2008; U.S. Patent, 1969). A generalized chemical structure for CPE is shown in Figure 11.

**Figure 11.** Chemical structure of chlorinated polyethylene (CPE).

Chlorinated Polyethylene Elastomers (CPE) are produced from HDPE that is randomly chlorinated in an aqueous slurry. Polymers are differentiated by chlorine content, molecular weight and crystallinity. Chlorine contents generally range from 25 to 42%. Advantages in using CPE, include very good resistance to ozone, oxidation, abrasion and flex cracking. CPE also has good resistance to alcohols, alkalis and acids. Limitations for CPE include moderate resistance to aromatic oxygenated solvents (Hallstar, 2009) Cure agents for CPE compounds are typically based on (1) peroxide cure systems with coagents; (2) thiadiazolebased chemistries; or (3) irradiation crosslinking techniques (Stelescu et al., 2011; Stelescu et al., 2008). The choice of cure system depends upon a number of factors such as compound cost, processing equipment and curing equipment. Peroxide cures are preferred when extra scorch safety, shelf life, bin stability, low permanent set and high-temperature performance are desired. Irradiation-curable compounds are usually formulated in a manner similar to the peroxide-curable compounds, except that no peroxide is necessary (Stelescu et al., 2011; Flynn et al., 1985). About 70% of CPE is used in wire and cable applications with trimellitates the plasticizer of choice. The remaining applications, each at 15%, are hydraulic hose and molded/extruded automotive parts (Hallstar, 2009).

In our experiments (Stelescu et al., 2008), we chose an efficient coagent for crosslinking of CPE by electron beam irradiation: triallyl cyanurate (TAC), to increase the rate and degree of cure. Materials used in the study**:** CPE TX10 chlorinated polyethylene (35 % chlorine), barium sulphate, titanium dioxide, calcium silicate, chlorinated paraffin, Uvinul 5050 antioxidant and TAC DL 70 trialylcyanided polyfunctional monomer; in the control blends the vulcanizing agent di(tert-buthylperoxiisopropyl) benzene (Perkadox 14-40B-GR) was used. Blends were prepared by mixing on a laboratory roller mill electrically heated up to 100-110oC for 10'. Ingredients were added in the following sequence: CPE, titanium dioxide after CPE was adhered to the roller, calcium silicate and the antioxidant, barium sulphate and chlorinated paraffin, and finally the polyfunctional TAC monomer. To the control blends 8 phr Perkadox was added after the blend preparation. Blends were homogenized on the laboratory roller mill, and from these plates were obtained by pressing in an hydraulic press. The resulting plates were packed in a polyethylene film and subjected to 5, 10 15 and 20 Mrad irradiation in the ILU-6M electron bem accelerator.

22 Advanced Elastomers – Technology, Properties and Applications

structure for CPE is shown in Figure 11.

**Figure 11.** Chemical structure of chlorinated polyethylene (CPE).

hose and molded/extruded automotive parts (Hallstar, 2009).

**(TAC).** 

Analyzing the characteristics influence of polyfunctional monomers type, can be seen that the best results were obtained by using TMPT followed by ZDA (coagents curing Type I). Type I polyfunctional monomers are highly reactive and increase the rate and state of cure. Type II (TAC and TAIC) polyfunctional monomers increase the state of cure only. Also, the influence of polyfunctional monomers to increasing the mechanical characteristics is determined by the reactivity, the number of reactive groups (functionality): TMPT has

functionality three and ZDA has functionality two (Boye, 2008; Henning, 2008).

**5.4. Characteristics of materials based on chlorinated polyethylene (CPE) obtained by cross-linked by electron beam in the presence of triallylcyanurate** 

Chlorinated polyethylene (CPE) is a synthetic elastomer produced by the means of controlled chlorination of polyethylene and has been commercially produced since the late 1960s (Stelescu et al., 2011; Stelescu et al., 2008; U.S. Patent, 1969). A generalized chemical

Chlorinated Polyethylene Elastomers (CPE) are produced from HDPE that is randomly chlorinated in an aqueous slurry. Polymers are differentiated by chlorine content, molecular weight and crystallinity. Chlorine contents generally range from 25 to 42%. Advantages in using CPE, include very good resistance to ozone, oxidation, abrasion and flex cracking. CPE also has good resistance to alcohols, alkalis and acids. Limitations for CPE include moderate resistance to aromatic oxygenated solvents (Hallstar, 2009) Cure agents for CPE compounds are typically based on (1) peroxide cure systems with coagents; (2) thiadiazolebased chemistries; or (3) irradiation crosslinking techniques (Stelescu et al., 2011; Stelescu et al., 2008). The choice of cure system depends upon a number of factors such as compound cost, processing equipment and curing equipment. Peroxide cures are preferred when extra scorch safety, shelf life, bin stability, low permanent set and high-temperature performance are desired. Irradiation-curable compounds are usually formulated in a manner similar to the peroxide-curable compounds, except that no peroxide is necessary (Stelescu et al., 2011; Flynn et al., 1985). About 70% of CPE is used in wire and cable applications with trimellitates the plasticizer of choice. The remaining applications, each at 15%, are hydraulic

In our experiments (Stelescu et al., 2008), we chose an efficient coagent for crosslinking of CPE by electron beam irradiation: triallyl cyanurate (TAC), to increase the rate and degree of The crosslinking and grafting of CPE blends by accelerated electron radiation was proved by comparing physical-mechanical characteristics of the irradiated blends with those of the control blends with the same composition but crosslinked by classical method with peroxides. Physical-mechanical characteristics for the blends of CPE TX10 chlorinated polyethylene containing barium sulphate, titanium dioxide, calcium silicate, chlorinated paraffin, Uvinul 5050 and TAC, irradiated with different doses of accelerated electrons are shown in Figures 12-17. Hardness has shown higher values than that of the non-irradiated blend (63ºShA), and a slight decrease with the increase in the TAC amount (Figure 12); increasing further the EB dose above 5 Mrad has resulted in no improvement of this characteristic. The control blends have shown an increase of the hardness from 69 ºShA up to 76 ºShA with the increase in the TAC amount. The resulting values for these are comparable with the values obtained by irradiation.

**Figure 12.** Changes in hardness versus the irradiation dose and TAC percentage.

**Figure 13.** Changes elasticity versus the irradiation dose and TMPT percentage

**Figure 14.** Changes in tensile stress at 100% elongation versus the irradiation dose and TMPT percentage

**Figure 15.** Changes in tensile strength versus the irradiation dose and TMPT percentage

**Figure 16.** Changes in elongation at break versus the irradiation dose and TMPT percentage

**Figure 13.** Changes elasticity versus the irradiation dose and TMPT percentage

**Figure 14.** Changes in tensile stress at 100% elongation versus the irradiation dose and TMPT

**Figure 15.** Changes in tensile strength versus the irradiation dose and TMPT percentage

percentage

**Figure 17.** Changes in tear strength versus the irradiation dose and TMPT percentage

Elasticity (Figure 13) has shown a decrease when irradiating the sample with 5 Mrad and thereafter has increased with the in increase in the AE dose. Elasticity has increased as the TAC amount was increased. The elasticity in controls (crosslinked with Percadox) has decreased (from 18 % down to 15%) as the TAC amount was increased. Tensile stress at 100% elongation has shown a decrease as the TAC amount was increased and has shown higher values than those for the non-irradiated blend for all irradiation doses (Figure 14); in controls the tensile stress at 100% elongation has shown increased values (from 1.6 N/mm2 up to 3 N/mm2) as the TAC amount was increased. Tensile strength (figure 15) has shown a decrease as the as the irradiation dose was increased from 5 Mrad up to 15 Mrad, and thereafter a slight increase revealed for all the TAC amounts; it has shown values comparable with those for the samples crosslinked with peroxides; Elongation at break have decreased as the irradiation dose and the TAC amount were increased, the resulting values being lower than those for the non-irradiated blend (Figures 16); the variation of this characteristic has revealed the CPE crosslinking with an irradiation dose as low as 5 Mrad.

The control blends have shown a decrease in the elongation at break (from 50 % down to 260 %) as the TAC amount was increased. Tear strength (Figure 17) has increased at irradiation doses of 5 Mrad, and thereafter has decreased as the EB irradiation dose was increased. Tear strength has shown a non-uniform variation as the TAC amount was increased. In controls the tear strength has increased as the TAC amount was increased from 29.5 N/mm up to 38 N/mm.

The rheological characteristics of the controls obtained measured by the Monsanto rheometer are shown in table 12.


**Table 12.** Rheological characteristics of CPE blends cross-linked with peroxides

The above data have revealed the following features with the increase in the amount of polyfunctional TAC monomer: the minimum moment of shearing has decreased, and the maximum moment of shearing has increased up to a TAC amount of 6 phr; the best vulcanization time has shown a minimum at 6 phr TAC and thereafter has increased. The index of vulcanization rate has increased by 59 % at 3 phr TAC, then has decreased slightly (by 10 %) when the amount of TAC was increased up to 6 phr, and has decreased significantly when the amount of TAC was increased further up to 9 phr. The highest value (by 4.5 % higher than that for a blend free TAC) of the vulcanization factor was found for 6 phr TAC, and it has decreased (by 0.5 %) as the TAC amount was increased up to 9 phr.

The best physical-mechanical characteristics were obtained by adding 0 – 6 phr TAC to the blends and applying an irradiation dose of 5 Mrad. When comparing the best vulcanization time (T90) with the time required with an irradiation of 5 Mrad, it has shown a decrease of 2.8 times in crosslinking by irradiation that has resulted in a shorter time required to obtain CPE-based finished products. In addition, the irradiation process is in continuous flow.

### **5.5. Characteristics of ethylene-propylene rubber (EPDM) obtained by crosslinked with electron beam and microwave in the presence of trimethylopropane trimethacrylate (TMPT)**

Ethylene-propylene rubbers use the same chemical building blocks or monomers as polyethylene (PE) and polypropylene (PP) thermoplastic polymers. These ethylene (C2) and propylene (C3) monomers are combined in a random manner to produce rubbery and stable polymers. A wide family of ethylene-propylene elastomers can be produced ranging from amorphous, non-crystalline to semi-crystalline structures depending on polymer composition and how the monomers are combined (Karpeles & Grossi, 2001). These polymers are also produced in an exceptionally wide range of Mooney viscosities (or molecular weights). The ethylene and propylene monomers combine to form a chemically saturated, stable polymer backbone providing excellent heat, oxidation, ozone and weather aging. A third, non-conjugated diene monomer can be terpolymerized in a controlled manner to maintain a saturated backbone and place the reactive unsaturation in a side chain available for vulcanization or polymer modification chemistry. The terpolymers are referred to as EPDM (or ethylene-propylene-diene with "M" referring to the saturated backbone structure). An EPDM polymer structure is illustrated in Figure 18. The ethylene-propylene copolymers are called EPM.

**Figure 18.** Chemical structure of ethylene-propylene terpolymer (EPDM)

26 Advanced Elastomers – Technology, Properties and Applications

N/mm.

rheometer are shown in table 12.

**trimethacrylate (TMPT)** 

The control blends have shown a decrease in the elongation at break (from 50 % down to 260 %) as the TAC amount was increased. Tear strength (Figure 17) has increased at irradiation doses of 5 Mrad, and thereafter has decreased as the EB irradiation dose was increased. Tear strength has shown a non-uniform variation as the TAC amount was increased. In controls the tear strength has increased as the TAC amount was increased from 29.5 N/mm up to 38

The rheological characteristics of the controls obtained measured by the Monsanto

*Characteristic 0 phr TAC 3 phr TAC 6 phr TAC 9 phr TAC*  Tmin 1'30 1'30 1'15 1'15 T2 2'30 3' 2'15 2'15 Mmin (dN/m) 10 7.5 6.4 7.5 Mmax (dN/m) 33.2 36.2 47 45 M90 30.88 33.33 42.94 41.25 T90, min 9'15" 7'15" 7' 10' Ivv 14.81 23.53 21.05 12.9 V2c 0.814 0.830 0.851 0.847

The above data have revealed the following features with the increase in the amount of polyfunctional TAC monomer: the minimum moment of shearing has decreased, and the maximum moment of shearing has increased up to a TAC amount of 6 phr; the best vulcanization time has shown a minimum at 6 phr TAC and thereafter has increased. The index of vulcanization rate has increased by 59 % at 3 phr TAC, then has decreased slightly (by 10 %) when the amount of TAC was increased up to 6 phr, and has decreased significantly when the amount of TAC was increased further up to 9 phr. The highest value (by 4.5 % higher than that for a blend free TAC) of the vulcanization factor was found for 6 phr TAC, and it has decreased (by 0.5 %) as the TAC amount was increased up to 9 phr.

The best physical-mechanical characteristics were obtained by adding 0 – 6 phr TAC to the blends and applying an irradiation dose of 5 Mrad. When comparing the best vulcanization time (T90) with the time required with an irradiation of 5 Mrad, it has shown a decrease of 2.8 times in crosslinking by irradiation that has resulted in a shorter time required to obtain CPE-based finished products. In addition, the irradiation process is in continuous flow.

**5.5. Characteristics of ethylene-propylene rubber (EPDM) obtained by crosslinked with electron beam and microwave in the presence of trimethylopropane** 

Ethylene-propylene rubbers use the same chemical building blocks or monomers as polyethylene (PE) and polypropylene (PP) thermoplastic polymers. These ethylene (C2) and propylene (C3) monomers are combined in a random manner to produce rubbery and stable

**Table 12.** Rheological characteristics of CPE blends cross-linked with peroxides

The most important stage in the EPDM rubber processing technology is vulcanization / crosslinking by sulphur and accelerator or by peroxides. Radiation vulcanization is applicable, but the dose required for EPDM vulcanization is very high (Odian, 1964). To reduce the dose for vulcanization of EPDM, some researches have worked on the introduction of coagents/polyfunctional monomers such as ethylene glycol dimethacrylate, triallyl cyanurate, triallyl isocyanurate, trimethylolpropane trimethacrylate etc (Manaila, Stelescu, Ighigeanu et al., 2011)

The following materials were used in the study: EPDM rubber (Nordel 4760); trimethylopropane-trimethacrylate Luvomaxx TMPT DL 75; dibenzoyl peroxide Perkadox 14-40B for he control blends (Manaila, Stelescu, Ighigeanu et al., 2011).

Blends were prepared on an electrically heated laboratory roller mill. For preparation of EPDM with polyfunctional monomer TMPT, the blend constituents were added in the following sequence and amounts: 100 phr EPDM and 3 phr TMPT. Process variables: temperature 75±5oC, friction 1:1.1, and total blending time 5 min. Plates required for physical-mechanical tests were obtained by pressing in a hydraulic press at 120 ±5oC and 150 MPa. Dibenzoyl peroxide vulcanized samples were prepared similarly to the experimental ones with the following specifications: 8 phr of dibenzoyl peroxide as vulcanizing agent was added and the blend vulcanization was achieved in a hydraulic press at 160oC; the optimum vulcanization time was measured by means of Monsanto Rheometer. The resulted plates were treated by irradiation, using the accelerator ALIN-10.

In Table 13 are presented characteristics of the mixtures cross-linked with dibenzoyl peroxide. These, along with non-irradiated and non-crosslinked samples are considered control samples for mixtures cross-linked by irradiation with EA or EA and microwave.


**Table 13.** Rheological characteristics of EPDM/TMPT blends cross-linked with peroxides

The mechanical properties of samples are summarized in Figures 19-26. The hardness (Figure 19) increases with 7 ºShA by EB irradiation at a dose of 120 kGy and with 5 ºShA by EB + MW irradiation at 30 kGy+83 s and 60 kGy+176 s. For the other treatments, hardness change insignificantly - with 1-2 ºShA; also, there is no big difference between the EB and EB + MW crosslinking. Analyzing the irradiated samples (with EB or EB+MW) and the control sample crosslinked with peroxide (see Table 13), can be noticed that there are no significant differences. The hardness increasing of samples crosslinked by irradiation or by curing with peroxide comparing with non-crosslinked sample is due to the reinforcing effect that occurs as a result of the formation of crosslinking bridges. The elasticity (Figure 20) does not change significantly by irradiation with EB or EB + MW (an increase of only 2%). There is a growing of elasticity with maximum 1% for EB + MW compared with EB only, for the treatment of 30 kGy + 88 s. The same increase in elasticity was observed in the case of crosslinked with peroxide. The tensile stress at 100% elongation (Figure 21) and tensile stress at 300% elongation (Figure 22) increase by irradiation, but the obtained values are small because the material is not with filler.

There are little differences between values obtained by peroxide, EB and EB + MW crosslinking. Considering the fact that the tensile stress at 100% elongation is a measure of the crosslinking degree, the values obtained show that by samples irradiation takes place the increasing of the crosslinking degree (Yasin et al., 2005).

**Figure 19.** The EB and EB+MW effects on the hardness of the EPDM samples

*Physical-mechanical characteristics* 

because the material is not with filler.

the increasing of the crosslinking degree (Yasin et al., 2005).

In Table 13 are presented characteristics of the mixtures cross-linked with dibenzoyl peroxide. These, along with non-irradiated and non-crosslinked samples are considered control samples for mixtures cross-linked by irradiation with EA or EA and microwave.

*Rheologic characteristics EPDM+TMPT+ dibenzoyl peroxide* 

T90 (minutes) 23'30" M min (dNm) 1 M max (dNm) 46.8 Δ M (dNm) 31.6 M90 (dNm) 42.64 T90 (minutes) 6'45"

Hardness, °ShA 64 Elasticity, % 60 Tensile strength, N/mm2 2.1 Elongation at break, % 127 Permanent set, % 5 Tear strength, N/mm 13.5

**Table 13.** Rheological characteristics of EPDM/TMPT blends cross-linked with peroxides

The mechanical properties of samples are summarized in Figures 19-26. The hardness (Figure 19) increases with 7 ºShA by EB irradiation at a dose of 120 kGy and with 5 ºShA by EB + MW irradiation at 30 kGy+83 s and 60 kGy+176 s. For the other treatments, hardness change insignificantly - with 1-2 ºShA; also, there is no big difference between the EB and EB + MW crosslinking. Analyzing the irradiated samples (with EB or EB+MW) and the control sample crosslinked with peroxide (see Table 13), can be noticed that there are no significant differences. The hardness increasing of samples crosslinked by irradiation or by curing with peroxide comparing with non-crosslinked sample is due to the reinforcing effect that occurs as a result of the formation of crosslinking bridges. The elasticity (Figure 20) does not change significantly by irradiation with EB or EB + MW (an increase of only 2%). There is a growing of elasticity with maximum 1% for EB + MW compared with EB only, for the treatment of 30 kGy + 88 s. The same increase in elasticity was observed in the case of crosslinked with peroxide. The tensile stress at 100% elongation (Figure 21) and tensile stress at 300% elongation (Figure 22) increase by irradiation, but the obtained values are small

There are little differences between values obtained by peroxide, EB and EB + MW crosslinking. Considering the fact that the tensile stress at 100% elongation is a measure of the crosslinking degree, the values obtained show that by samples irradiation takes place

**Figure 20.** The EB and EB+MW effects on the elasticity of the EPDM samples

**Figure 21.** The EB and EB+MW effects on the tensile stress at 100% elongation of the EPDM samples

**Figure 22.** The EB and EB+MW effects on the tensile stress at 300% elongation of the EPDM samples

**Figure 23.** The EB and EB+MW effects on the tensile strength of the EPDM samples

**Figure 24.** The EB and EB+MW effects on the elongation at break of the EPDM samples

**Figure 25.** The EB and EB+MW effects on the permanent set of the EPDM samples

**Figure 26.** The EB and EB+MW effects on the tear strength of the EPDM samples

Tensile strength (Figure 23), elongation at break (Figure 24), permanent set (Figure 25) and tear strength (Figure 26) decrease with the irradiation dose increasing for both EB and EB + MW irradiation, (comparing with non-irradiated control sample), but the characteristics from crosslinking by irradiation are better compared with crosslinking with peroxide. For all these mechanical features the best results are obtained for a dose of 150 kGy (crosslinking with EB) and 150 kGy + 466 s (crosslinking wit EB + MW). Following the obtained results it can be stated that a dose of maximum 150 kGy + 466s. leads to a good degree of crosslinking, for which there is a return to its original shape after a very good stretching (29%).

#### **6. Conclusion**

30 Advanced Elastomers – Technology, Properties and Applications

**Figure 22.** The EB and EB+MW effects on the tensile stress at 300% elongation of the EPDM samples

**Figure 23.** The EB and EB+MW effects on the tensile strength of the EPDM samples

**Figure 24.** The EB and EB+MW effects on the elongation at break of the EPDM samples

This review gives an overview about our research on elastomer crosslinking by irradiation with accelerated electrons, a much more ecologic method that does not need to add crosslinking agents into the blend. Crosslinking by EB and EB+MW also shows a series of

advantages, like as: reduced crosslinking time, no polymer degradation due to high temperature (as in the classic peroxide curing) because EB and EB+MW crosslinking is performed at room temperature, the process is very fast and can be controlled precisely. At the interaction of ionizing radiation with (co)polymers, breaking of covalent bonds occurs, as well as the emergence of free radicals (transitional chemical species) on the main chain (if the lateral groups break) or in the main chain (if it breaks itself). The final effect is either crosslinking of macromolecular assembly or cutting the main chain of macromolecules and decreasing average molecular weight. In fact, the two effects, crosslinking and degradation, coexist and we need to point out the predominance of one of them. In addition, through appropriate surface treatments, some features of the feet such as appearance, adhesion to different materials or slip resistance can be significantly improved (Zaharescu, 2000).

### **Author details**

Elena Manaila, Maria Daniela Stelescu\* and Gabriela Craciun *National Research and Development Institute for Laser, Plasma and Radiation Physics, Magurele, Bucharest, Romania* 

Maria Daniela Stelescu *National Research and Development Institute for Textiles and Leather – Leather and Footwear Research Institute, Bucharest, Romania* 

### **7. References**


<sup>\*</sup> Corresponding Author

Endstra, W.C. (1990). Application of coagents for peroxide crosslinking, *Kautschuk und Gummi Kunststoffe,* Vol.43, No.9, pp.790-793

32 Advanced Elastomers – Technology, Properties and Applications

**Author details** 

Maria Daniela Stelescu

**7. References** 

\* Corresponding Author

Elena Manaila, Maria Daniela Stelescu\*

3, Enschede, Netherlands

*National Research and Development Institute for Laser, Plasma and Radiation Physics, Magurele, Bucharest, Romania* 

*National Research and Development Institute for Textiles and* 

*Chemistry and Technology,* Vol.79, No.3, pp. 402-428

*Technology,* Vol.74, No.3, pp. 451-492

*Leather – Leather and Footwear Research Institute, Bucharest, Romania* 

advantages, like as: reduced crosslinking time, no polymer degradation due to high temperature (as in the classic peroxide curing) because EB and EB+MW crosslinking is performed at room temperature, the process is very fast and can be controlled precisely. At the interaction of ionizing radiation with (co)polymers, breaking of covalent bonds occurs, as well as the emergence of free radicals (transitional chemical species) on the main chain (if the lateral groups break) or in the main chain (if it breaks itself). The final effect is either crosslinking of macromolecular assembly or cutting the main chain of macromolecules and decreasing average molecular weight. In fact, the two effects, crosslinking and degradation, coexist and we need to point out the predominance of one of them. In addition, through appropriate surface treatments, some features of the feet such as appearance, adhesion to

different materials or slip resistance can be significantly improved (Zaharescu, 2000).

and Gabriela Craciun

Alvarez Grima, M.M. (2007). *Novel Co-agents for Improved Properties in Peroxide Cure of Saturated Elastomers*, PhD Thesis, Printed by Print Partners Ipskamp, ISBN: 90-365-2456-

Andreo, P., Cunningham, J.F., Hohlfeld, K., &. Svensson, H. (1997). Absorbed dose determination in photon and electron beams : An International code of practice, *Technical Reports Series No.277*, 2nd edition, International Atomic Energy Agency, Vienna Bhowmick, A. K. & Vijayabaskar, V. (2006). Electron beam curing of elastomer, *Rubber* 

Boye, W.M. (2008). Utilizing Coagents in the Electron Beam Cure of Elastomers, Proceedings

Chowdhury, R. & Banerji, M.S. (2005). Electron Beam Irradiation of Ethylene-propylene Terpolymer: Evaluation of Trimethylol Propane Trimethacrylate as a Crosslink

Dikland, H. G., Ruardy, T., Van der Does, L. & Bantjes, A. (1993). New coagents in peroxide vulcanization of EPM, *Rubber Chemistry and Technology*, Vol.66, No.5, pp.693-711 Dluzneski, P.R. (2001). Peroxide vulcanization of elastomers, *Rubber Chemistry and* 

of the 57th International Wire & Cable Symposium IWCS, pp.335- 341

Promoter, *Journal of Applied Polymer Science, Vol.97, No.3, pp.* 968–975 Chlorinated polyethylene; CM (CPE). (2009). pp. 23-25, www.hallstar.com;

	- Odian, G. (1964). Radiation crosslinking of polyethylene–polyfunctional monomer mixtures, *Journal of Polymer Science*, Vol.2, No.6, pp.2835-2848
	- Stelescu, M.D, Manaila, E. & Zuga, N. (2011). The use of polyfunctional monomers in the radical cure of chlorinated polyethylene, *Polymer Journal*, Vol.43, No.9, pp.792–800
	- Stelescu, M.D., Manaila, E., Craciun, G. & Zuga, N. (2012). Crosslinking and grafting ethylene vinyl acetate copolymer with accelerated electrons in the presence of polyfunctional monomers, *Polymer Bulletin*, Vol. 68, No.1, pp.263-285.
	- Stelescu, M.D. & Manaila, E. (2007), Crosslinking and grafting the natural rubber by means of accelerated electrons in the presence of trimethylol-propane trimethacrylate (TMPT), *Scientific Bulletin, B Series: Chemistry and Materials Science*, Vol.69, No.4, pp.33-38
	- Stelescu, M.D., Georgescu, M. & Manaila, E. (2010). Aspects regarding crosslinking of a natural rubber blend, *Proceedings of the 3rd International Conference Advanced Materials and Systems, ICAMS 2010*, pp. 313-318, Bucharest, Romania, 16-18 September 2010
	- Stelescu, M.D., Niculescu-Aron, I.G. & Manaila, E. (2009). Processing and statistical analysis of the experimental data resulted from EPDM rubber grafting and crosslinking with accelerated electrons in the presence of TMPT, *Materiale plastice*, Vol.46, No.1, pp.48-52
	- Stelescu, M.D., Vaslan, M. & Manaila, E. (2008). Materials based on chlorinates polyethylene obtained by crosslinking and grafting by accelerated electrons in the presence of trialylcyanurated, *Proceedings of the 2rd International Conference Advanced Materials and Systems, ICAMS 2008*, pp. 96-101, Bucharest, Romania, 23-24 October 2008
	- U.S. Patent 3 454 544, Process for the Chlorination of Polyolefins, Issued 8 July 1969 to Dow Chemical USA.
	- Van Duin, M. (2002). Chemistry of EPDM Crosslinking, *Kautschuk und Gummi, Kunststoffe*,Vol.55, No.4, pp.150-156
	- Vijayabaskar, V. & Bhowmick, A. K. (2005). Electron beam modification of nitrile rubber in the presence of polyfunctional monomer, *Journal of Applied Polymer Science*, Vol. 95, No.2, pp. 435-447
	- Yasin, T., Ahmed, S., Ahmed, M. & Yoshii, F. (2005). Effect of concentration of polyfunctional monomers on physical properties of acrylonitrile-butadiene rubber under-electron beam irradiation, *Radiation Physics and Chemistry,* Vol.73, No.3, pp. 155- 158
	- Zaharescu, T., Setnescu, R., Jipa, S. & Setnescu, T. (2000). Radiation processing of polyolefin blends. I. Crosslinking of EPDM–PP blends, *Journal of Applied Polymer Science,* Vol. 77, No.5, pp. 982-987
	- Zuga, M.D., Iovu, H., Trandafir, V., Manaila, E., Martin., D. & Stelescu, M.M. (2007). Study on the preparation of some biocomposites based on silicone elastomers and collagen, *Jurnal of Optoelectronics and Advenced Materials (JOAM)*, Vol.9, No.11, pp.3325-3329
	- Zuga, M.D., Miu., L., Crudu, M., Bratulescu, V., Iovu, H. & Manaila, E. (2007). Products of ethylene-propylene-terpolymer rubber (EPDM) obtained by an environmentally friendly process, *Advanced Materials Research – Materials and Technologies*, Vol.23, pp. 333-336

**Section 2** 

**Liquid Crystal Elastomers** 

34 Advanced Elastomers – Technology, Properties and Applications

Chemical USA.

No.2, pp. 435-447

No.5, pp. 982-987

158

333-336

*Kunststoffe*,Vol.55, No.4, pp.150-156

*Journal of Polymer Science*, Vol.2, No.6, pp.2835-2848

Odian, G. (1964). Radiation crosslinking of polyethylene–polyfunctional monomer mixtures,

Stelescu, M.D, Manaila, E. & Zuga, N. (2011). The use of polyfunctional monomers in the radical cure of chlorinated polyethylene, *Polymer Journal*, Vol.43, No.9, pp.792–800 Stelescu, M.D., Manaila, E., Craciun, G. & Zuga, N. (2012). Crosslinking and grafting ethylene vinyl acetate copolymer with accelerated electrons in the presence of

Stelescu, M.D. & Manaila, E. (2007), Crosslinking and grafting the natural rubber by means of accelerated electrons in the presence of trimethylol-propane trimethacrylate (TMPT),

*Scientific Bulletin, B Series: Chemistry and Materials Science*, Vol.69, No.4, pp.33-38 Stelescu, M.D., Georgescu, M. & Manaila, E. (2010). Aspects regarding crosslinking of a natural rubber blend, *Proceedings of the 3rd International Conference Advanced Materials and* 

*Systems, ICAMS 2010*, pp. 313-318, Bucharest, Romania, 16-18 September 2010 Stelescu, M.D., Niculescu-Aron, I.G. & Manaila, E. (2009). Processing and statistical analysis of the experimental data resulted from EPDM rubber grafting and crosslinking with accelerated electrons in the presence of TMPT, *Materiale plastice*, Vol.46, No.1, pp.48-52 Stelescu, M.D., Vaslan, M. & Manaila, E. (2008). Materials based on chlorinates polyethylene obtained by crosslinking and grafting by accelerated electrons in the presence of trialylcyanurated, *Proceedings of the 2rd International Conference Advanced Materials and* 

*Systems, ICAMS 2008*, pp. 96-101, Bucharest, Romania, 23-24 October 2008

U.S. Patent 3 454 544, Process for the Chlorination of Polyolefins, Issued 8 July 1969 to Dow

Van Duin, M. (2002). Chemistry of EPDM Crosslinking, *Kautschuk und Gummi,* 

Vijayabaskar, V. & Bhowmick, A. K. (2005). Electron beam modification of nitrile rubber in the presence of polyfunctional monomer, *Journal of Applied Polymer Science*, Vol. 95,

Yasin, T., Ahmed, S., Ahmed, M. & Yoshii, F. (2005). Effect of concentration of polyfunctional monomers on physical properties of acrylonitrile-butadiene rubber under-electron beam irradiation, *Radiation Physics and Chemistry,* Vol.73, No.3, pp. 155-

Zaharescu, T., Setnescu, R., Jipa, S. & Setnescu, T. (2000). Radiation processing of polyolefin blends. I. Crosslinking of EPDM–PP blends, *Journal of Applied Polymer Science,* Vol. 77,

Zuga, M.D., Iovu, H., Trandafir, V., Manaila, E., Martin., D. & Stelescu, M.M. (2007). Study on the preparation of some biocomposites based on silicone elastomers and collagen, *Jurnal of Optoelectronics and Advenced Materials (JOAM)*, Vol.9, No.11, pp.3325-3329 Zuga, M.D., Miu., L., Crudu, M., Bratulescu, V., Iovu, H. & Manaila, E. (2007). Products of ethylene-propylene-terpolymer rubber (EPDM) obtained by an environmentally friendly process, *Advanced Materials Research – Materials and Technologies*, Vol.23, pp.

polyfunctional monomers, *Polymer Bulletin*, Vol. 68, No.1, pp.263-285.

## **Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers**

Kokou D. (Honorat) Dorkenoo, Emel Sungur, Hervé Bulou, Grégory Taupier and Alex Boeglin

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50496

### **1. Introduction**

Liquid crystal materials offer many opportunities for applications such as data storage [1], image processing [2], or optical modulators [3] calling for media that are sensitive to external stimuli . Today, they are considered to have great potential for the realization of so called "smart materials" through micro- to nano-scale patterning techniques. One interesting material in the flourishing group of smart materials is the Liquid Crystal Elastomer (LCE) which combines the properties of liquid crystals and polymers. An elastomer is formed by a weakly crosslinked network of polymers, which confers it a high elasticity. The polymer network has maximum entropy in his undistorted state, and as a result, it resists deformation [4]. As for liquid crystals, these are materials which present phases intermediate between crystalline and isotropic called mesophases, the molecules responsible for this property are named mesogens.

In this chapter, we will present our results on the optical microstructuring of a LCE and the monitoring of its elastic properties. The liquid crystal based elastomer can be considered as an artificial muscle material. The designation of artificial muscle is attributed to soft actuators which can have muscle like behavior. A muscle is in reality an energy converter which converts chemical energy to mechanical motion. The actuators are converters which accept different types of energy and deliver a mechanical quantity like a displacement, a tension, *etc.*. The LCEs can be considered as artificial muscles in the sense that they may present a distortion, for example a contraction/extension generated by the crystalline-isotropic phase transition. The possibility of using liquid crystal elastomers (LCE) as external stimuli driven size changing materials was predicted by de Gennes in 1997 [5]. Since then, different LCE materials showing reversible macroscopic shape changes under thermal [6][7] or optical [8] stimulations have been produced. Here, we explore the use of this contraction/extension property to create stimulable microsystems.

©2012 Dorkenoo et al., licensee InTech. This is an open access chapter 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. © 2012 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.

#### 2 Will-be-set-by-IN-TECH 38 Advanced Elastomers – Technology, Properties and Applications

The LCE used in this study is a nematic thermotropic (sensitive to thermal stimuli) elastomer. A nematic elastomer can be described as crosslinked polymer chains with incorporated mesogens corresponding to rigid rod-like units which can order nematically. The average shape of the material is coupled to the molecular orientation order [4][9]: the nematic-isotropic phase transition results in the change of shape of the macroscopic sample. When the elastomer is judiciously prepared to obtain a monodomain sample [10], meaning that all the mesogens are oriented uniformly, the sample is elongated in the nematic phase where all the mesogens are parallel to each other, and has a contracted shape in the isotropic phase where the nematic order is lost.

First, we will show that advantage can be taken of the crosslinking properties of the material to inscribe refractive index modulations by optical means as in a common photoresist [11]. We present two approaches based respectively on one- and two-photon photopolymerization, that can be implemented using an optical microscopy setup. Such a method provides an accurate way to locally modify the properties of the material. Compared to its one-photon relative, the two-photon excitation mode will yield finer patterns because of its higher intrinsic spatial resolution. This technique relies on the fact that the simultaneous absorption of two low energy photons is equivalent to the absorption of a high energy photon with an energy equal to the sum of these two photons energy. The two-photon absorption (TPA) process is a quadratic phenomenon: the probability of the simultaneous absorption of two photon is not proportional to the photon flux as in the case for the linear absorption, but to the square of the flux. TPA is then significant only for high incident fluences. Thus, the use of ultra-short pulse lasers combined with microscopy techniques allows light-matter interaction to be confined within a micrometric volume around the focal point.

After the presentation of the microstructuring process, we will describe how the contractile properties of the material can be measured by detecting the thermally induced step size changes of an inscribed grating. Finally, these results will be interpreted with the help of Molecular Dynamics (MD) simulations. MD is a powerful tool to elucidate the structure and the behavior of the molecules. It has been used to simulate the behavior of polymers [12] and has proved its efficiency to describe the liquid crystalline phases [13], thus it also allows the description of elastomer behavior [14]. MD consists of a computational method which calculates time dependent atomic motions by applying the laws of classical mechanics. We have used a combination of Lennard-Jones and Gay-Berne potentials to represent the anisotropic mesogens and the calculations have been carried out in the Parrinello-Rahman-Nosé-Hoover ensemble.

### **2. Materials**

#### **2.1. Photopolymerizable liquid crystals**

LCE are materials combining the elastic properties of the elastomers and the anisotropic properties of liquid crystals. They are formed by reticulated liquid crystalline polymers, which, in general, at low reticulation degrees, conserve the mesomorphic properties of the polymer before reticulation as well as the nature of the phases and the transition temperatures. These elastomers, when subjected to external stimuli like temperature or electromagnetic fields, can mimic the actions of muscles (contraction/extension). They are, thereby, considered as artificial muscle materials. Different types of actuators have been developed using polymers as parent material, like for example polymer gels [15] [16] [17], conductive polymers [18] [19] [20], carbon nanotubes [21] [22] [23] [24] or dielectric elastomers [25]. Soft and highly flexible, the polymers are well adapted to be used as artificial muscle materials due to their high strength, deformation capabilities, and their capacity to keep intact their properties after several operating cycles. Recently, LCE took over the field of artificial muscles. They are robust and don't need any solvent to operate (unlike the gels or conductive polymers). The concept of LCE was proposed by P. G. de Gennes in 1975 [9]. In his studies on reticulated liquid crystal polymers, he mentioned the possibility of the material deformation without constraint. In 1981 Frinkelmann *et al.* have realized the first mesomorphic oriented side-chain LCE [26] and afterwards the first main-chain LCE was synthesized by Bergmann *et al.* [27]. Indeed, according to the insertion topology of the mesogen (liquid crystal phase-forming unit)

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The LCE used in this study is a nematic thermotropic (sensitive to thermal stimuli) elastomer. A nematic elastomer can be described as crosslinked polymer chains with incorporated mesogens corresponding to rigid rod-like units which can order nematically. The average shape of the material is coupled to the molecular orientation order [4][9]: the nematic-isotropic phase transition results in the change of shape of the macroscopic sample. When the elastomer is judiciously prepared to obtain a monodomain sample [10], meaning that all the mesogens are oriented uniformly, the sample is elongated in the nematic phase where all the mesogens are parallel to each other, and has a contracted shape in the isotropic phase where the nematic

First, we will show that advantage can be taken of the crosslinking properties of the material to inscribe refractive index modulations by optical means as in a common photoresist [11]. We present two approaches based respectively on one- and two-photon photopolymerization, that can be implemented using an optical microscopy setup. Such a method provides an accurate way to locally modify the properties of the material. Compared to its one-photon relative, the two-photon excitation mode will yield finer patterns because of its higher intrinsic spatial resolution. This technique relies on the fact that the simultaneous absorption of two low energy photons is equivalent to the absorption of a high energy photon with an energy equal to the sum of these two photons energy. The two-photon absorption (TPA) process is a quadratic phenomenon: the probability of the simultaneous absorption of two photon is not proportional to the photon flux as in the case for the linear absorption, but to the square of the flux. TPA is then significant only for high incident fluences. Thus, the use of ultra-short pulse lasers combined with microscopy techniques allows light-matter interaction to be confined

After the presentation of the microstructuring process, we will describe how the contractile properties of the material can be measured by detecting the thermally induced step size changes of an inscribed grating. Finally, these results will be interpreted with the help of Molecular Dynamics (MD) simulations. MD is a powerful tool to elucidate the structure and the behavior of the molecules. It has been used to simulate the behavior of polymers [12] and has proved its efficiency to describe the liquid crystalline phases [13], thus it also allows the description of elastomer behavior [14]. MD consists of a computational method which calculates time dependent atomic motions by applying the laws of classical mechanics. We have used a combination of Lennard-Jones and Gay-Berne potentials to represent the anisotropic mesogens and the calculations have been carried out in the

LCE are materials combining the elastic properties of the elastomers and the anisotropic properties of liquid crystals. They are formed by reticulated liquid crystalline polymers, which, in general, at low reticulation degrees, conserve the mesomorphic properties of the polymer before reticulation as well as the nature of the phases and the transition temperatures. These elastomers, when subjected to external stimuli like temperature or electromagnetic fields, can mimic the actions of muscles (contraction/extension). They are, thereby, considered

within a micrometric volume around the focal point.

Parrinello-Rahman-Nosé-Hoover ensemble.

**2.1. Photopolymerizable liquid crystals**

**2. Materials**

order is lost.

**Figure 1.** Schematic representation of different types of liquid crystal polymers: (a) main-chain, (b) side-chain side-on, (c) side-chain end-on.

in the elastomer, there exist two main families of LCEs: side-chain and main-chain elastomers. In the case of main-chain elastomers, the mesogens are directly integrated in the polymer chain, while in the case of side-chain elastomers, they are laterally attached to the polymer chain, either orthogonal to the chain, attached by one end (end on), or parallel to the chain, attached by the side (side on), as shown in figure 1.

Since the monomer used in this study is thermotropic, we will study the contraction properties of the resulting elastomer as a function of temperature. The studied elastomer is a nematic elastomer. The nematic phase is favored by the side-chain conformation. In nematic crystals, the mesogens have a random position but an orientational order: they are, on average, parallel to each other. This behavior is encouraged by the elongated form of these units. For a nematic crystal, the amount of order can be characterized by the order parameter *P*<sup>2</sup> defined as the average value of a second-order Legendre polynomial [28]:

$$P\_2 = \frac{1}{2} < 3\cos^2(\theta) - 1 > \tag{1}$$

**Figure 2.** Schematic representation of a liquid crystal in the nematic phase (left) and in the isotropic phase (right). The average orientation is represented by the nematic director **n**.

where *θ* corresponds to the angle between the long axis of the molecule and the nematic director. For a completely ordered phase *P*2=1, while *P*2=0 corresponds to a completely disordered phase (isotropic). The mesogens interact *via* long range dipolar or Van der Walls interactions. Below a given temperature, the interactions are sufficiently strong to orient the director axis and organize the system. Beyond this temperature, the preferential orientation of the mesogens is destroyed by the effect of entropy and an isotropic phase appears.

**Figure 3.** Contraction of a nematic thermotropic elastomer. Microscopic point of view (top), macroscopic point of view (bottom).

In the case of the elastomer, the mesomorphic properties (as the nature of phases of the initial monomers) are conserved. The mesogens attached to the sides of the main chain are free to move. During the nematic-isotropic phase transition the mesogens are disoriented and the main chain drag behind them. These microscopic form changes are transferred to the macroscopic sample. The destruction of the nematic order thus generates a contraction of the system along the mesogens alignment direction and an extension in the orthogonal directions as schematized in figure 3.

#### **2.2. Elastomer thin film preparation**

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**Figure 2.** Schematic representation of a liquid crystal in the nematic phase (left) and in the isotropic

of the mesogens is destroyed by the effect of entropy and an isotropic phase appears.

where *θ* corresponds to the angle between the long axis of the molecule and the nematic director. For a completely ordered phase *P*2=1, while *P*2=0 corresponds to a completely disordered phase (isotropic). The mesogens interact *via* long range dipolar or Van der Walls interactions. Below a given temperature, the interactions are sufficiently strong to orient the director axis and organize the system. Beyond this temperature, the preferential orientation

**Figure 3.** Contraction of a nematic thermotropic elastomer. Microscopic point of view (top), macroscopic

In the case of the elastomer, the mesomorphic properties (as the nature of phases of the initial monomers) are conserved. The mesogens attached to the sides of the main chain are free to move. During the nematic-isotropic phase transition the mesogens are disoriented and the main chain drag behind them. These microscopic form changes are transferred to the macroscopic sample. The destruction of the nematic order thus generates a contraction of the system along the mesogens alignment direction and an extension in the orthogonal directions

point of view (bottom).

as schematized in figure 3.

phase (right). The average orientation is represented by the nematic director **n**.

The precursor of the LCE used in this study is a mixture of three compounds: a liquid crystalline acrylate monomer, a crosslinker and an ultraviolet (UV) photoinitiator. The monomer whose structure is represented in figure 4 is the 4'-acryloyloxybutyl 2,5-(4'-butyloxybenzoyloxy)benzoate [29]. The part containing the aromatic chains is the rigid part of the monomer and the attached carbon chains correspond to soft parts. The photoinitiator is the 2-benzyl-2-(dimethylamine)-4' morpholinobutyrophenone (Irgacure 369) added at a concentration of 1 mol %, the crosslinker is the 1,6-hexanediol diacrylate at a concentration of 10 mol %. The elastomer is obtained by the photopolymerization of the monomers and the crosslinking of the polymeric chains. Let us recall that in the case

**Figure 4.** Chemical structure of the acrylate monomer. Inbox: schematics representation.

of a thermotropic nematic elastomer, the destruction of the nematic order by an increase in temperature will cause the contraction of the material along the nematic director. For the contraction to be maximum, the initial order parameter of the sample should be high. The samples were prepared in several micrometer thick glass cells filled by capillarity with the material in its isotropic phase (above 81.5 ◦C, the nematic-isotropic phase transition temperature). The cell surfaces were coated with rubbed poly-vinyl alcohol to insure the alignment of the liquid crystal moieties by guiding them during the filling process and allowing the production of a fully monodomain aligned sample. Thus the contraction can be unidirectional and along the original mesogens' alignment. To produce the elastomer the filled cell was slowly cooled down (1 ◦C/min) to the nematic phase (63 *<sup>o</sup>*C) conserving the alignment of the liquid crystal moieties. The elastomer film was then obtained by radical photopolymerization and photocrosslinking under UV light, fixing in this way the nematic alignment of the mesogens. The resulting monodomain elastomer film is named "Liquid Single Crystal Elastomer" (LSCE). The radical photopolymerization starts with the excitation of the photoinitiator Irgacure 369 which is a benzoyl type chromophore with a large absorbance and a high initiation efficiency in the range of 300-400 nm. The initiator generates a radical (a chemical species possessing one or several unpaired electrons in the outer shell) which can react with the monomer and form the macroradical which is also able to react with other monomers. The propagation of the polymerization proceeds by successive addition of monomers to this macro-radical. The monomers are bound to each other by the CH=CH2 groups located at the extremities of the molecules. It is the breaking of the double bond that

#### 6 Will-be-set-by-IN-TECH 42 Advanced Elastomers – Technology, Properties and Applications

allows the bonding between monomers. The polymerization takes place in such a way as to produce a form of "sheathing" of mesogen around the principal chain, thus avoiding steric hindrance (see figure 5). The crosslinker present in the mixture helps to create a crosslinked network and the elastomer so obtained can be extracted from the cell.

**Figure 5.** Elastomer formation by photopolymerization and photocrosslinking a) the initial mixture, b) the elastomer: the radical generated by the photoinitiator will activate the monomer which can then make a C-C bond with the following monomer; hence, the pôlymerization is accompanied by the formation of a sheathing around a main chain.

#### **3. Experimental setup**

Two different light sources were used to photo-structure the elastomers. We have used 365 nm UV light from an Argon Ion (Ar+) laser to polymerize the mixture by one-photon photopolymerization or 780 nm infrared (IR) femtosecond laser pulse for two-photon photopolymerization. The advantage of two-photon absorption is the possibility to spatially confine the process by limiting the light-matter interaction to volumes which can be smaller than 1 *μm*3. The probability of TPA is very low, its cross section is about 31 orders of magnitude lower than a one-photon absorption cross section. To be efficient TPA therefore necessitates a high density of photons. Thus, we have to spatially and temporally confine the photons. This can be achieved by combining the use of high numerical aperture objectives and ultra-short pulsed lasers such as titanium-sapphire lasers emitting in the near-IR region. When approaching the focal point of the objective, the photon density will sharply increase. The low probability TPA process will thus be automatically confined around this focal point in a volume called "voxel". If the sample is transparent to the IR radiation of the laser, but absorptive for the UV light, only the confined volume around the focal point will be excited, while the rest of the sample will remain transparent to the incident radiation. This microscopy technique is named "two-photon microscopy". Figure 6 presents a comparison between the excitation volumes in the case of conventional microscopy and two-photon microscopy. From the Rayleigh criterion, in optimal conditions, the radial resolution of a conventional microscope is given by the radius of the Airy disc:

$$r\_{\mathbf{x},y} = \frac{0.61\lambda}{NA} \tag{2}$$

In the case of two-photon microscopy, Webb *et al.* have proposed an estimation of the *ωxy* and axial *ωz* dimensions of the voxel [30]:

**Figure 6.** Comparison of the excitation volumes for the linear absorption (left) and two-photon absorption (right): in the linear case all the volume of the sample crossed by the beam is excited, in the case of two-photon absorption the excitation is confined to the voxel around the focal point. The photographies show the fluorescence signal emitted by the excited part of the sample.

$$\omega\_{xy} = \begin{cases} \frac{0.32\lambda}{\sqrt{2}\text{ON}} & \text{if } \text{ON} \le 0.7\\\\ \frac{1}{\sqrt{2}\text{ON}} & \text{and} \quad \omega\_z = \frac{0.532\lambda}{\sqrt{2}} \left(\frac{1}{n - \sqrt{n^2 - \text{ON}^2}}\right) \\\\ \frac{0.325\lambda}{\sqrt{2}\text{ON}\sqrt{\text{ON}}} & \text{if } \text{ON} > 0.7 \end{cases} \tag{3}$$

The excitation is given by:

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allows the bonding between monomers. The polymerization takes place in such a way as to produce a form of "sheathing" of mesogen around the principal chain, thus avoiding steric hindrance (see figure 5). The crosslinker present in the mixture helps to create a crosslinked

**Figure 5.** Elastomer formation by photopolymerization and photocrosslinking a) the initial mixture, b) the elastomer: the radical generated by the photoinitiator will activate the monomer which can then make a C-C bond with the following monomer; hence, the pôlymerization is accompanied by the

Two different light sources were used to photo-structure the elastomers. We have used 365 nm UV light from an Argon Ion (Ar+) laser to polymerize the mixture by one-photon photopolymerization or 780 nm infrared (IR) femtosecond laser pulse for two-photon photopolymerization. The advantage of two-photon absorption is the possibility to spatially confine the process by limiting the light-matter interaction to volumes which can be smaller than 1 *μm*3. The probability of TPA is very low, its cross section is about 31 orders of magnitude lower than a one-photon absorption cross section. To be efficient TPA therefore necessitates a high density of photons. Thus, we have to spatially and temporally confine the photons. This can be achieved by combining the use of high numerical aperture objectives and ultra-short pulsed lasers such as titanium-sapphire lasers emitting in the near-IR region. When approaching the focal point of the objective, the photon density will sharply increase. The low probability TPA process will thus be automatically confined around this focal point in a volume called "voxel". If the sample is transparent to the IR radiation of the laser, but absorptive for the UV light, only the confined volume around the focal point will be excited, while the rest of the sample will remain transparent to the incident radiation. This microscopy technique is named "two-photon microscopy". Figure 6 presents a comparison between the excitation volumes in the case of conventional microscopy and two-photon microscopy. From the Rayleigh criterion, in optimal conditions, the radial resolution of a conventional

*rx*,*<sup>y</sup>* <sup>=</sup> 0.61*<sup>λ</sup>*

In the case of two-photon microscopy, Webb *et al.* have proposed an estimation of the *ωxy* and

*NA* (2)

network and the elastomer so obtained can be extracted from the cell.

formation of a sheathing around a main chain.

microscope is given by the radius of the Airy disc:

axial *ωz* dimensions of the voxel [30]:

**3. Experimental setup**

$$V\_{2\text{photon}} = \pi^{3/2} \omega\_{xy}^2 \omega\_z \tag{4}$$

The experimental setup used for the microstructurating and the realization of the elastomers is based on a confocal microscope. The cell containing the elastomer precursor mixture is placed on a heating plate mounted on a motorized stage that can execute computer-controlled 3D translations along the X, Y, and Z axes. The observation is done by reflection with a CCD camera. The sample is illuminated in transmission with a white light lamp; a filter is used to stop any UV photons. The sample is also placed between polarizers allowing the monitoring of isotropic and nematic zones through the polarization of transmitted light induced by the mesogen alignment. The photo-patterning of the desired structures is realized in the nematic phase by moving the sample under the focus of the objective with the translation stage.

#### **4. Experimental results**

#### **4.1. Photostructuration of the material**

We have first studied the creation of a patterned elastomer by photopolymerization initiated by linear or two-photon absorption. Different sets of experiments have been performed depending on the sample alignment state (using treated or untreated glass cells) and the excitation source (UV or IR light). The first set of experiments was made using UV excitation (Argon laser, *λ*= 365 nm, power = 8 *μW*, objective N.A = 0.45) and a non-aligned nematic monomer sample. In a first step the photopolymerizable mixture was introduced in an untreated cell. Then the cell was heated beyond the isotropic-nematic

8 Will-be-set-by-IN-TECH 44 Advanced Elastomers – Technology, Properties and Applications

**Figure 7.** Experimental setup.

phase transition temperature (> 81.5 ◦C) for the mixture initially in the form of a powder to liquefy and penetrate by capillarity. The mixture was then cooled down until the nematic phase could form (63 ◦C). A shape representing the capital letter E has been patterned by photopolymerization with the focused UV beam using the translation stage with a displacement velocity of 200 *μm*/s. The resulting polymerized and crosslinked part draws the letter "E" as can be seen in figure 8(a). The second set of experiments was performed under the same conditions as described above, except that an aligned nematic monomer sample was used figure 3(b). This polymerization was also successful. The polymerized letter "E" presents thinner (30 *μm*) and smoother lines than those obtained for the non-aligned sample (50-60 *μm*). The patterned lines are undistorted in the aligned sample. Therefore, using aligned nematic samples results in considerably improved micro-pattern formation. In the third set of experiments performed again on aligned samples, the IR source (Ti:Sa laser, pulses duration = 100 fs, repetition rate = 80 MHz , *λ*= 780 nm, power = 500 mW, objective N.A = 0.45) was used instead of the Argon laser. The results presented in figure 3(c) show that such two-photon excitation processes produce a smooth pattern with even thinner lines measuring 5 to 10 *μm* across. The high resolution achieved in this case is indeed better than UV illumination.

**Figure 8.** Letter "E" patterns (a) by one-photon photopolymerization (UV irradiation) in a nonaligned sample, (b) by one-photon photopolymerization (UV irradiation) in an aligned sample, (c) by two-photon photopolymerization (IR irradiation) in an aligned sample. The nematic director orientation is indicated by the arrow.

#### **4.2. Obtaining the thermo-active elastomer**

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phase transition temperature (> 81.5 ◦C) for the mixture initially in the form of a powder to liquefy and penetrate by capillarity. The mixture was then cooled down until the nematic phase could form (63 ◦C). A shape representing the capital letter E has been patterned by photopolymerization with the focused UV beam using the translation stage with a displacement velocity of 200 *μm*/s. The resulting polymerized and crosslinked part draws the letter "E" as can be seen in figure 8(a). The second set of experiments was performed under the same conditions as described above, except that an aligned nematic monomer sample was used figure 3(b). This polymerization was also successful. The polymerized letter "E" presents thinner (30 *μm*) and smoother lines than those obtained for the non-aligned sample (50-60 *μm*). The patterned lines are undistorted in the aligned sample. Therefore, using aligned nematic samples results in considerably improved micro-pattern formation. In the third set of experiments performed again on aligned samples, the IR source (Ti:Sa laser, pulses duration = 100 fs, repetition rate = 80 MHz , *λ*= 780 nm, power = 500 mW, objective N.A = 0.45) was used instead of the Argon laser. The results presented in figure 3(c) show that such two-photon excitation processes produce a smooth pattern with even thinner lines measuring 5 to 10 *μm* across. The high resolution achieved in this case is indeed better than UV illumination.

**Figure 8.** Letter "E" patterns (a) by one-photon photopolymerization (UV irradiation) in a nonaligned sample, (b) by one-photon photopolymerization (UV irradiation) in an aligned sample, (c) by

two-photon photopolymerization (IR irradiation) in an aligned sample. The nematic director orientation

**Figure 7.** Experimental setup.

is indicated by the arrow.

In order to stabilize the patterns, a post-photopolymerization of the whole sample can be performed using UV light of weak intensity. Under these conditions, the pattern written by photopolymerization using a high intensity beam is preserved as it can be seen on figure 9. The resulting rubber-like film is then removed from the cell and placed on a heating plate to observe the shape changes as a function of temperature. Figure 10 represents the heating of an elastomer with an inscribed grating of 170 *μm* step size. The elastomer lies on a film of glycerol oil to minimize the constraints during the contraction. By heating this sample up from room temperature to 120 ◦C, a clear deformation of the film is observed in the direction of the mesogen alignment. An elastomer with a circular pattern was also produced to highlight the

**Figure 9.** Concentric figure inscribed by photopolymerization before postpolymerization of the whole sample (left), after postpolymerization (right), the zone surrounding the pattern has a weaker polymerization degree.

**Figure 10.** Contraction of a 20 *μm* thick elastomer as a function of temperature (from 60 ◦C to 120 ◦C).

uniaxial contraction and the reversible aspect of the phenomenon as can be seen in figure 11.

### **5. Discussion**

#### **5.1. Contraction properties**

Direct observation of the micropatterned elastomer's contraction can be readily achieved by optical microscopy. Figure 12 shows the temperature dependent deformation of the concentric pattern inscribed in a 13 *μm* thick film of elastomer. The value of the width perpendicular to the nematic director (denoted a) shows a small variation (less than 2% of extension) whereas the perpendicular direction (denoted b) experiences about 17% of contraction. This demonstrates that the shape change consists mostly in a contraction along the nematic director and proves that a well aligned monodomain sample was achieved. This contraction factor varies with the sample thickness. About 50% contraction is observed in 30 *μm* thick samples

**Figure 11.** Deformation of concentric cercle patterned in the elastomer as a function of temperature. "a" and "b" correspond to the resulting ellipse axis, "b" is in the mesogen alignment direction.

but as the thickness decreases, the contraction drops to about 30% for 20 *μm* thick samples and to about 17 % for 13 *μm* thick samples. This behavior can be attributed to mechanical stress. Indeed, the size of the artificial muscle with respect to the surface of adhesion is larger for a thick film than for a thin film. The contraction forces thus become prevalent (as the samples become thicker) over the constrains resulting from the friction of the film on its substrate. It is noteworthy that no dependency of the rate of contraction on the pattern structure has been observed, suggesting that any diffraction element can be inscribed without altering the physical properties of the material. The contraction of the elastomer starts around 90 ◦C. It stops when the phase becomes isotropic, towards 100 ◦C. Both of these temperatures are higher than the phase transition temperatures of the initial liquid crystal which is 81.5 ◦C. The mesogens being free to move within the elastomer, the thermal characteristics of the mesophases should be preserved. This is, however, only partially true since the mesogens are not completely decoupled from the main chain. However it is reasonable to assume that the longer the spacer, the higher the degree of this decoupling. This aspect may thus bear on the phase transition temperature but there is no doubt that the primary cause behind the observed contraction temperatures lies with the fact that the response of the material to the drop in nematic order is not immediate. Contraction will only occur once the degree of disorientation of the mesogens reaches levels that are enough to overcome the frictional forces between the elastomer and its substrate. In addition, with the monitoring technique that is being put to use, the contraction becomes only apparent beyond a certain level. All this may be the origin of the gap between the phase transition temperature and the temperature at which contraction is being observed.

#### **5.2. Diffraction properties**

The contraction of the material can be monitored indirectly by the observation of the diffraction pattern proceeding from a grating inscribed in the elastomer. Temperature induced contraction of the material will result in a change in the grating period which will modify the diffraction pattern. We present the study of the diffraction pattern obtained for a 13

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**Figure 11.** Deformation of concentric cercle patterned in the elastomer as a function of temperature. "a"

but as the thickness decreases, the contraction drops to about 30% for 20 *μm* thick samples and to about 17 % for 13 *μm* thick samples. This behavior can be attributed to mechanical stress. Indeed, the size of the artificial muscle with respect to the surface of adhesion is larger for a thick film than for a thin film. The contraction forces thus become prevalent (as the samples become thicker) over the constrains resulting from the friction of the film on its substrate. It is noteworthy that no dependency of the rate of contraction on the pattern structure has been observed, suggesting that any diffraction element can be inscribed without altering the physical properties of the material. The contraction of the elastomer starts around 90 ◦C. It stops when the phase becomes isotropic, towards 100 ◦C. Both of these temperatures are higher than the phase transition temperatures of the initial liquid crystal which is 81.5 ◦C. The mesogens being free to move within the elastomer, the thermal characteristics of the mesophases should be preserved. This is, however, only partially true since the mesogens are not completely decoupled from the main chain. However it is reasonable to assume that the longer the spacer, the higher the degree of this decoupling. This aspect may thus bear on the phase transition temperature but there is no doubt that the primary cause behind the observed contraction temperatures lies with the fact that the response of the material to the drop in nematic order is not immediate. Contraction will only occur once the degree of disorientation of the mesogens reaches levels that are enough to overcome the frictional forces between the elastomer and its substrate. In addition, with the monitoring technique that is being put to use, the contraction becomes only apparent beyond a certain level. All this may be the origin of the gap between the phase transition temperature and the temperature at which contraction

The contraction of the material can be monitored indirectly by the observation of the diffraction pattern proceeding from a grating inscribed in the elastomer. Temperature induced contraction of the material will result in a change in the grating period which will modify the diffraction pattern. We present the study of the diffraction pattern obtained for a 13

and "b" correspond to the resulting ellipse axis, "b" is in the mesogen alignment direction.

is being observed.

**5.2. Diffraction properties**

**Figure 12.** Deformation of concentric circles separated by 25 *μ*m as a function of temperature; "a" and "b" correspond to the axes of the resulting ellipse. The insets show the samples at the temperatures indicated by the arrows.

*μm* thick sample with a 30 *μm* period linear grating using a linearly polarized He-Ne laser beam at 633nm. Before testing the properties of the obtained gratings, we have examined

**Figure 13.** Grating step as a function of temperature, in the case of a 13 *m* thick sample. The internal figures represent the grating at the corresponding temperatures.

the surface of the elastomer with a profilometer. In some cases when the sample is removed from the cell, its surface exhibits ridges corresponding to the grating. Such observations are commonly made in photopolymerization experiments [31]. The surface corrugation comes from the relaxation of the mechanical stresses introduced by the cross-linking process and which have been maintained by the glass plates. These ondulations are not observed in two-photon photopolymerized samples where the patterns are much thinner and inscribed inside the volume of the elastomer. In the cases where inscribed gratings led to surface ridges, we have checked that the addition of a compensating liquid did not modify the diffraction properties. Thus we may pretend that we are dealing with refractive index gratings. Index

#### 12 Will-be-set-by-IN-TECH 48 Advanced Elastomers – Technology, Properties and Applications

inhomogeneity stems from spatial variations in material density between parts that have been strongly polimerized and the remainder of the sample which has only been subjected to a light post-polymerization. The diffraction regime is indicated by the Klein-Cook parameter *Q* = 2*πλ*0*L*/Λ2*n*0, where L is the grating thickness, *λ*<sup>0</sup> is the vacuum wavelength of light, Λ is the grating step size, and *n*<sup>0</sup> is the mean refractive index. High values of Q (Q>10) correspond to the Brag regime while low values (Q<1) correspond to the Raman-Nath regime. One usually ascribes the Bragg regime, with essentialy only one diffracted wave being produced, to gratings that are thick with respect to step size and the Raman-Nath regime, with several diffracted waves being produced, to thin gratings. In the case of a grating with a step size of 30 *μm* and a thickness of 13 *μm* yielding the diffraction pattern shown in figure 14, the Q parameter is about 0.4, placing the diffraction in the Raman-Nath regime as demonstrated by the multiple order diffraction pattern. Figure 15 shows the variation of the angle of diffraction for the +1 order as a function of temperature. It clearly demonstrates the decrease

**Figure 14.** Diffraction figure of 30*m* step gratings inscribed into the elastomer.

of the grating step with the temperature rise stemming from the unidirectional contraction accompanying the nematic/isotropic transition. In figure 15, the black dots correspond to measurements of the diffraction angle, while the red dots represent values calculated following the diffraction grating formula from the data shown in figure 13 for the 13 *μm* thick sample. The agreement between both sets of data shows the consistency between the grating period and the diffraction angle measurements (discrepancies between data points may come from the fact that they have been gathered over several heating cycles). In conclusion, the contraction induced by the temperature is easily monitored by the widening of the diffraction figure. This allows a feedback on the deformation of the material through direct monitoring of the resulting diffraction.

Since we work with a cross-linked polymer, the contraction/extension process will affect all three directions in space. The initial homogeneous nematic order makes the film behave as a biaxial material with an optical axis oriented along the nematic director. Thus, the material may change the polarization state of the light upon diffraction. To illustrate the birefringence properties of the gratings, we have measured the diffraction efficiency dependence on the orientation of the incident linear polarization. The resulting angular distribution for the polarization of the diffracted light is presented in figure 16b. Here, the simplest configuration is adopted: the incident beam is normal to the surface and its polarization is linear. As one can see in figure 16a, the diffraction efficiency is higher when the direction of the polarization of the incident beam and the grating vector are parallel. The diffracted light intensity has been fitted by :

$$I = \eta\_{\parallel} \cos^2 \phi + \eta\_{\perp} \sin^2 \phi \tag{5}$$

where the angle *φ* corresponds to the rotation of the polarisation and *I* is the light intensity of the first diffracted order. Thus we can determine the parallel and the perpendicular diffraction

**Figure 15.** Variation of the first order diffraction angle of a 30 *μ*m period grating as a function of temperature: black dots are the measured diffraction angles, red dots are calculated from the data on figure 13.

efficiencies which amount respectively to *<sup>η</sup>*� <sup>=</sup> 1 and *<sup>η</sup>*<sup>⊥</sup> <sup>=</sup> 0.53.

12 Will-be-set-by-IN-TECH

inhomogeneity stems from spatial variations in material density between parts that have been strongly polimerized and the remainder of the sample which has only been subjected to a light post-polymerization. The diffraction regime is indicated by the Klein-Cook parameter *Q* = 2*πλ*0*L*/Λ2*n*0, where L is the grating thickness, *λ*<sup>0</sup> is the vacuum wavelength of light, Λ is the grating step size, and *n*<sup>0</sup> is the mean refractive index. High values of Q (Q>10) correspond to the Brag regime while low values (Q<1) correspond to the Raman-Nath regime. One usually ascribes the Bragg regime, with essentialy only one diffracted wave being produced, to gratings that are thick with respect to step size and the Raman-Nath regime, with several diffracted waves being produced, to thin gratings. In the case of a grating with a step size of 30 *μm* and a thickness of 13 *μm* yielding the diffraction pattern shown in figure 14, the Q parameter is about 0.4, placing the diffraction in the Raman-Nath regime as demonstrated by the multiple order diffraction pattern. Figure 15 shows the variation of the angle of diffraction for the +1 order as a function of temperature. It clearly demonstrates the decrease

of the grating step with the temperature rise stemming from the unidirectional contraction accompanying the nematic/isotropic transition. In figure 15, the black dots correspond to measurements of the diffraction angle, while the red dots represent values calculated following the diffraction grating formula from the data shown in figure 13 for the 13 *μm* thick sample. The agreement between both sets of data shows the consistency between the grating period and the diffraction angle measurements (discrepancies between data points may come from the fact that they have been gathered over several heating cycles). In conclusion, the contraction induced by the temperature is easily monitored by the widening of the diffraction figure. This allows a feedback on the deformation of the material through direct monitoring

Since we work with a cross-linked polymer, the contraction/extension process will affect all three directions in space. The initial homogeneous nematic order makes the film behave as a biaxial material with an optical axis oriented along the nematic director. Thus, the material may change the polarization state of the light upon diffraction. To illustrate the birefringence properties of the gratings, we have measured the diffraction efficiency dependence on the orientation of the incident linear polarization. The resulting angular distribution for the polarization of the diffracted light is presented in figure 16b. Here, the simplest configuration is adopted: the incident beam is normal to the surface and its polarization is linear. As one can see in figure 16a, the diffraction efficiency is higher when the direction of the polarization of the incident beam and the grating vector are parallel. The diffracted light intensity has been

where the angle *φ* corresponds to the rotation of the polarisation and *I* is the light intensity of the first diffracted order. Thus we can determine the parallel and the perpendicular diffraction

*<sup>I</sup>* <sup>=</sup> *<sup>η</sup>*� cos2 *<sup>φ</sup>* <sup>+</sup> *<sup>η</sup>*<sup>⊥</sup> sin2 *<sup>φ</sup>* (5)

**Figure 14.** Diffraction figure of 30*m* step gratings inscribed into the elastomer.

of the resulting diffraction.

fitted by :

In the case of figure 16b the incident beam polarization is at 45*<sup>o</sup>* of the grating vector. This time a light intensity dependence on the rotation of an analyzer placed after the sample is observed. Equation (6) represents the theoretical function which will fit the intensity of light measured after the analyser.

$$I = \left| \sqrt{\eta\_{\parallel}} \cos \phi \, \frac{\sqrt{2}}{2} e^{(i \, \psi/2)} + \sqrt{\eta\_{\perp}} \sin \phi \, \frac{\sqrt{2}}{2} e^{(-i \, \psi/2)} \right|^2 \tag{6}$$

For *<sup>η</sup>*� and *<sup>η</sup>*<sup>⊥</sup> we take the diffraction efficiencies determined in figure 16a. The phase difference *ψ* is introduced by the birefringence and *φ* is the analyser angle. Figure 16b represents experimental data and the fits for the zero and the first diffraction orders. We observe the slight depolarization of the zero order due to the intrinsic material birefringence when comparing it to the polarization of the incident beam added as a reference. Diffraction order +1 shows a more elliptic polarization and a rotation of the major axis. Calculations give a rotation of 29.7*o*. We have been able to make these observations on various samples and are led to consider that this behavior finds its origin in two simultaneous effects. The first is obviously the birefringence of the material which introduces a phase difference between the parallel and the perpendicular components of the field and causes the depolarization of the diffracted beam. The other effect originates in the diffraction grating: the refractive index modulation seen by the beam is different for the direction along the grating vector and for the perpendicular to it. Therefore, the diffraction efficiencies for polarizations along these two directions are not identical. Hence, the decomposition of the polarization of the diffracted beam along these directions will be different with respect to that of the incoming light. As temperature increases, the material tends to the isotropic configuration and the observed birefringence tends to get attenuated.

**Figure 16.** Polarization of diffracted light. (a) zero- and first-order diffraction intensities versus incident beam linear polarization orientation. (b) Incident beam, zero-, and first-order diffraction intensities versus analyzer angle. The direction of the grating vector corresponds to the angle zero.

#### **5.3. Molecular dynamics simulations**

Molecular dynamics (MD) simulations are a powerful tool for understanding the properties of a sample in terms of molecular collective phenomena. We used classical MD method to simulate the contraction of the elastomer. First, the monomer molecules composed of 95 atoms was fully optimized by the density functional theory (DFT). The chosen functional was B3LYP, a hybrid functional obtained by linear combination of exchange-correlation energy functionals (Local-density approximations LDA, Generalized gradient approximations GGA) and the Hatree-Fock exchange [32]. The orbital basis set was the contracted Gaussian 6-311\*\* set. All calculations were carried out with NWChem [33], executed on the IBM Power 6 at the "Institut du Développement et des Ressources en Informatique Scientifique" of Orsay. The obtained minimum energy configuration is represented in figure 17. This model presents a dipole localized on the mesogen corresponding to the aromatic core. This will allow

**Figure 17.** Model of the monomer: minimum energy configuration. Inbox: schematical representation; a dipole is localized on the rigid mesogenic site corresponding to the aromatic core.

dipole-dipole interactions between the monomers. Then to simulate the contraction of the elastomer resulting from the collective behavior of the monomers the interaction between pairs of anisotropic rigid mesogenic sites was modeled using Gay-Berne (GB) potential. The Gay-Berne potential corresponds to a modified form of Lennard-Jones potential which can be easily adjusted to modify the shape of the studied system [34]. In that sense it has proven its efficiency to model mesogenic systems [35][36][37].

14 Will-be-set-by-IN-TECH

**Figure 16.** Polarization of diffracted light. (a) zero- and first-order diffraction intensities versus incident beam linear polarization orientation. (b) Incident beam, zero-, and first-order diffraction intensities

Molecular dynamics (MD) simulations are a powerful tool for understanding the properties of a sample in terms of molecular collective phenomena. We used classical MD method to simulate the contraction of the elastomer. First, the monomer molecules composed of 95 atoms was fully optimized by the density functional theory (DFT). The chosen functional was B3LYP, a hybrid functional obtained by linear combination of exchange-correlation energy functionals (Local-density approximations LDA, Generalized gradient approximations GGA) and the Hatree-Fock exchange [32]. The orbital basis set was the contracted Gaussian 6-311\*\* set. All calculations were carried out with NWChem [33], executed on the IBM Power 6 at the "Institut du Développement et des Ressources en Informatique Scientifique" of Orsay. The obtained minimum energy configuration is represented in figure 17. This model presents a dipole localized on the mesogen corresponding to the aromatic core. This will allow

**Figure 17.** Model of the monomer: minimum energy configuration. Inbox: schematical representation; a

dipole is localized on the rigid mesogenic site corresponding to the aromatic core.

versus analyzer angle. The direction of the grating vector corresponds to the angle zero.

**5.3. Molecular dynamics simulations**

The force field modeling intra and inter-molecular contribution to the interaction energy is given by the following expression:

$$\begin{aligned} \mathcal{U} &= \sum\_{i=1}^{N\_{\text{Magic}}} \frac{k\_i^{\text{Rg}}}{2} \left(\theta\_i - \theta\_i^0\right)^2 \\ &+ \sum\_{i=1}^{N\_{\text{GIF}}} \frac{k\_i^{\text{GIF}}}{2} \left(\boldsymbol{\nu}\_i - \boldsymbol{\nu}\_i^0\right)^2 + \\ &+ \sum\_{i=1}^{N\_{\text{Magic}}} \left(a\_{i,1} \left(1 + \cos\phi\_i\right) + a\_{i,2} \left(1 - \cos 2\phi\_i\right) + a\_{i,3} \left(1 + \cos 3\phi\_i\right)\right) \\ &+ \sum\_{i=1}^{N\_{\text{L}}} \sum\_{j>i}^{N\_{\text{L}}} \mathcal{U}\_{\text{L}J} \\ &+ \sum\_{i=1}^{N\_{\text{L}}} \sum\_{j=1}^{N\_{\text{GIF}}} \mathcal{U}\_{\text{L}J/GB} \\ &+ \sum\_{i=1}^{N\_{\text{GIF}}} \sum\_{j>i}^{N\_{\text{GIF}}} \mathcal{U}\_{\text{G}B} \end{aligned}$$

where *Nangles*, *Ndihedrals*, *NGB*, *NLJ*, are respectively the angles number of the dihedral angles of the numbers, and the number of GB and LJ sites numbers. The variations in dihedral angles *φ*, which represent torsions, are modeled by a truncated Fourier series (*ai*,1,2,3 coefficients). The alkyne groups of the chain are condensed into single atom sites and represented as spheres. All the chain segment parameters are modeled by resorting to universal force field [38]. *ULJ*, *UGB* et *ULJ*/*GB* are respectively Lennard-Jones, Gay-Berne and the mixte Lennard-Jones/Gay-Berne potentials. Bond lengths between the mesogen and the flexible chains were set from *ab initio* results. They are 1.495 Å for the C-mesogen bond and 1.353 Å for the O-mesogen bond. The bond lengths between chain segments and GB unit were constrained by using the SHAKE procedure [39] during molecular dynamics calculations. *ν<sup>i</sup>* corresponds to the angle between the long axis of the GB site and the bond between this site and the adjacent one. *ν*<sup>0</sup> *<sup>i</sup>* is the equilibrium value and *<sup>k</sup>GB <sup>i</sup>* corresponds to the force constant given by DFT calculations (*ν*<sup>0</sup> *GBC* <sup>=</sup>112.62 ◦C and *<sup>k</sup>*<sup>0</sup> *GBC*=6.521 eV/rad2).

For a separation distance of *rij* between two particles, the standard LJ potential is written as:

$$\mathcal{U}\_{LJ} = \sum\_{i} \sum\_{j>i} 4\varepsilon\_{ij} \left( \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} + \sigma\_{ij}^{(0)}} \right)^{12} - \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} + \sigma\_{ij}^{(0)}} \right)^{6} \right) \tag{8}$$

**Figure 18.** Representation of different bonding angles.

where *�ij* corresponds to the energy well depth, *σij* is the contact parameter, it corresponds to the separation distance at which the inter-particle potential is zero.

*UGB* represents the orientation dependent interaction energy for two GB particles:

$$\begin{split} \mathcal{U}\_{GB} &= \sum\_{i} \sum\_{j>i} 4\epsilon\_{ij} \left( \hat{\mu}\_{i\cdot} \hat{\mu}\_{j\cdot} r\_{ij}^{\cdot} \right) \left( \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} \left( \hat{\mu}\_{i\cdot} \hat{\mu}\_{j\cdot} r\_{ij}^{\cdot} \right) + \sigma\_{ij}^{(0)}} \right)^{12} \\ &- \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} \left( \hat{\mu}\_{i\cdot} \hat{\mu}\_{j\cdot} r\_{ij}^{\cdot} \right) + \sigma\_{ij}^{(0)}} \right)^{6} \end{split} \tag{9}$$

where *μ*ˆ*<sup>i</sup>* and *μ*ˆ*<sup>j</sup>* are unitary vectors along the molecular axis of GB particles, *�ij* and *σij* correspond respectively to the energy well depth and the contact parameter depending on the relative orientation of the particles. These terms are defined as [36] [40]:

$$
\sigma\_{\rm ij} \left( \mathfrak{h}\_{i\prime} \mathfrak{h}\_{\rm j}, r\_{\rm ij}^\* \right) = \frac{\sigma\_{\rm ij}^{(0)}}{\sqrt{1 - \frac{\chi}{2} \left[ \frac{\left( \mathfrak{h}\_i \cdot \mathfrak{h}\_{\rm ij} + \mathfrak{h}\_j \cdot \mathfrak{h}\_{\rm ij} \right)^2}{1 + \chi \left( \mathfrak{h}\_i \cdot \mathfrak{h}\_{\rm j} \right)} + \frac{\left( \mathfrak{h}\_i \cdot \mathfrak{h}\_{\rm ij} - \mathfrak{h}\_j \cdot \mathfrak{h}\_{\rm ij} \right)^2}{1 - \chi \left( \mathfrak{h}\_i \cdot \mathfrak{h}\_{\rm j} \right)} \right]}} \tag{10}
$$

$$
\varepsilon\_{\vec{\imath}\vec{\jmath}} \left( \hat{\mu}\_{\dot{\imath}\nu} \hat{\mu}\_{\dot{\jmath}\nu} r\_{\vec{\imath}\vec{\jmath}}^{\gamma} \right) = \epsilon\_0 \varepsilon\_1^{\gamma} \left( \hat{\mu}\_{\dot{\imath}\nu} \hat{\mu}\_{\dot{\jmath}\nu} r\_{\vec{\imath}\vec{\jmath}} \right) \epsilon\_2^{\nu} \left( \hat{\mu}\_{\dot{\imath}\nu} \hat{\mu}\_{\dot{\jmath}} \right) \tag{11}
$$

$$\left(\boldsymbol{\varepsilon}\_{1}\left(\boldsymbol{\hat{\mu}}\_{i\prime}\boldsymbol{\hat{\mu}}\_{j\prime}\boldsymbol{r}\_{ij}\right) = 1 - \frac{\boldsymbol{\chi}^{\prime}}{2} \left[ \frac{\left(\boldsymbol{\hat{\mu}}\_{i}\cdot\boldsymbol{\hat{\sigma}}\_{ij} + \boldsymbol{\hat{\mu}}\_{j}\cdot\boldsymbol{\hat{\sigma}}\_{ij}\right)^{2}}{1 + \boldsymbol{\chi}^{\prime}\left(\boldsymbol{\hat{\mu}}\_{i}\cdot\boldsymbol{\hat{\mu}}\_{j}\right)} + \frac{\left(\boldsymbol{\hat{\mu}}\_{i}\cdot\boldsymbol{\hat{\sigma}}\_{ij} - \boldsymbol{\hat{\mu}}\_{j}\cdot\boldsymbol{\hat{\sigma}}\_{ij}\right)^{2}}{1 - \boldsymbol{\chi}^{\prime}\left(\boldsymbol{\hat{\mu}}\_{i}\cdot\boldsymbol{\hat{\mu}}\_{j}\right)} \right] \tag{12}$$

52 Advanced Elastomers – Technology, Properties and Applications Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers <sup>17</sup> Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 53

$$\begin{aligned} \epsilon\_2 \left( \hat{\mu}\_i, \hat{\mu}\_j \right) &= \frac{1}{\sqrt{1 - \chi^2 \left( \hat{\mu}\_i \cdot \hat{\mu}\_j \right)^2}} \\ \chi &= \frac{(\sigma\_E / \sigma\_s)^2 - 1}{(\sigma\_E / \sigma\_s)^2 + 1} \end{aligned} \tag{13}$$

$$\chi' = \frac{1 - (\varepsilon\_E/\varepsilon\_s)^{1/\gamma}}{1 + (\varepsilon\_E/\varepsilon\_s)^{1/\gamma}} \tag{14}$$

with *σ<sup>E</sup>* and *σ<sup>S</sup>* corresponding to the contact parameter along the GB particle length and width and *�<sup>E</sup>* and *�<sup>S</sup>* corresponding to the energy well depth for two GB particles with an "end to end" and a "side by side". *rij* is the distance between the two particles i and j, *r*ˆ*ij* corresponds to the unitary vector along *rij*, *μ*ˆ*<sup>i</sup>* and *μ*ˆ*<sup>j</sup>* are unitary vectors along the molecular axis of the particles i and j. *γ* and *ν* are adjustable parameters which were set to their canonical values of 1.0 and 2.0, respectively. The ratio was *σE*/*σs*=3.46 and *�*0=21.2 meV.

*ULJ*/*GB* corresponds to the potential representing the mixte interaction between LJ and GB sites [40]:

$$\begin{split} \mathcal{U}\_{\text{GB}/\text{LI}} &= \sum\_{i} \sum\_{j} 4\epsilon\_{ij} \left( \hat{\mu}\_{i}, r\_{ij}^{\circ} \right) \left( \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} \left( \hat{\mu}\_{i}, r\_{ij}^{\circ} \right) + \sigma\_{ij}^{(0)}} \right)^{12} \\ &- \left( \frac{\sigma\_{ij}^{(0)}}{r\_{ij} - \sigma\_{ij} \left( \hat{\mu}\_{i}, r\_{ij}^{\circ} \right) + \sigma\_{ij}^{(0)}} \right)^{6} \end{split} \tag{15}$$

We have considered the molecular dynamics in a modified isothermal-isobaric (NPT) ensemble to allow an anisotropic deformation of the simulation cell. The ensemble used is the Parrinello-Rahman-Nosé-Hoover ensemble based on the *HPRNH* Hamiltonian [41] [42] [43]. Thanks to the introduction of a thermostat and a barostat, this ensemble allows to control the temperature and the constraints acting on the simulation cell. It allows the study of anisotropic deformation of a system as a function of temperature. It is in that sense well adapted to the study of systems containing liquid crystal molecules. The *HPRNH* Hamiltonian is given by:

$$\begin{split} H\_{PRNH} &= \frac{1}{2} \sum\_{i=1}^{N} \frac{1}{m\_i} \vec{P}\_i^T \tilde{G} \vec{P}\_i + \mathcal{U} \\ &\quad + \frac{1}{2Q} P\_\eta^2 + \mathcal{g}k\_B T \eta \\ &\quad + \frac{1}{2W} Tr\left( \vec{P}\_h^T \bar{P}\_h \right) + P\_{ext} \Delta \bar{h} \\ &\quad + \frac{1}{2} \sum\_{i=1}^{N\_{\mathcal{G}}} \frac{1}{m\_{\tilde{\rho}\_i}} \vec{P}\_{\tilde{\rho}\_i}^T \vec{P}\_{\tilde{\rho}\_i} \\ \end{split} \tag{17}$$

with *G* ¯¯ = ¯¯ *h<sup>T</sup>* ¯¯ *<sup>h</sup>*. ¯¯

16 Will-be-set-by-IN-TECH

θ 0 CCC θ 0 CCO

> θ 0 CCO

> > GBC ν θCOC <sup>0</sup> <sup>0</sup>

> > > *<sup>σ</sup>*(0) *ij*

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

� + *<sup>σ</sup>*(0) *ij*

⎞ ⎠

2

�

�2

⎤ ⎥

<sup>1</sup>−*χ*(*μ*ˆ*i*·*μ*ˆ*j*)

*μ*ˆ*<sup>i</sup>* · *r*ˆ*ij* − *μ*ˆ*<sup>j</sup>* · *r*ˆ*ij*

1 − *χ*� � *μ*ˆ*<sup>i</sup>* · *μ*ˆ*<sup>j</sup>* �

12

(9)

(10)

(11)

<sup>⎦</sup> (12)

�

θ 0 CCO <sup>0</sup>

GBC ν <sup>0</sup>

where *�ij* corresponds to the energy well depth, *σij* is the contact parameter, it corresponds to

� � <sup>⎛</sup> ⎝

> � + *<sup>σ</sup>*(0) *ij*

where *μ*ˆ*<sup>i</sup>* and *μ*ˆ*<sup>j</sup>* are unitary vectors along the molecular axis of GB particles, *�ij* and *σij* correspond respectively to the energy well depth and the contact parameter depending on

<sup>=</sup> *<sup>σ</sup>*(0)

*rij* − *σij*

⎞ ⎠

*ij*

2 <sup>1</sup>+*χ*(*μ*ˆ*i*·*μ*ˆ*j*) <sup>+</sup> (*μ*ˆ*i*·*r*ˆ*ij*−*μ*ˆ*j*·*r*ˆ*ij*)

> � *�ν* 2 � *μ*ˆ*i*, *μ*ˆ*<sup>j</sup>* �

�2

� <sup>+</sup>

�

(*μ*ˆ*i*·*r*ˆ*ij*+*μ*ˆ*j*·*r*ˆ*ij*)

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

*μ*ˆ*<sup>i</sup>* · *r*ˆ*ij* + *μ*ˆ*<sup>j</sup>* · *r*ˆ*ij*

1 + *χ*� � *μ*ˆ*<sup>i</sup>* · *μ*ˆ*<sup>j</sup>* 6 �

*UGB* represents the orientation dependent interaction energy for two GB particles:

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

�

the relative orientation of the particles. These terms are defined as [36] [40]:

�

� = *�*0*� γ* 1 �

⎡ ⎢ ⎣

�

<sup>1</sup> <sup>−</sup> *<sup>χ</sup>* 2 �

*<sup>σ</sup>*(0) *ij*

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

θ 0 CCC

θ 0 CCC

θCOC 0

θ 0 CCC

θCOC 0

**Figure 18.** Representation of different bonding angles.

*UGB* = ∑ *i* ∑ *j>i* 4*�ij* �

> *σij* �

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

*�*1 � −

⎛ ⎝

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

*�ij* �

�

*rij* − *σij*

�

*μ*ˆ*i*, *μ*ˆ*j*,*r*ˆ*ij*

<sup>=</sup> <sup>1</sup> <sup>−</sup> *<sup>χ</sup>*� 2

GBC ν

the separation distance at which the inter-particle potential is zero.

θCOC 0 θ 0 CCO θ 0 CCO

θ 0 CCC

θ 0 CCO

θ 0 CCC

θ 0 CCC

θ 0 CCO

> *h* is the matrix containing the dimensions of the unit cell *Lx*, *Ly* and *Lz*, *P* ¯¯ *<sup>h</sup>* is the conjugated moment and together they form the dynamical variables of the system relating to the control of

the constraints acting on the simulation cell. *W* is a fictive mass which allows the adjustments of the barostat's reactions to the constraints' changes. *mi* is the *i* particle mass. *Pi* is its momentum:

$$
\vec{P}\_{\bar{l}} = m\_{\bar{l}} \frac{d\vec{S}\_{\bar{l}}}{dt} \tag{18}
$$

where *Si* is the reduced position of the particle in the simulation cell

$$
\vec{S}\_{\dot{i}} = \vec{h}^{-1} \vec{q}\_{\dot{i}} \tag{19}
$$

and *qi* corresponds to the absolute position. *η* and *P<sup>η</sup>* are dynamical variables relating to the control of the temperature. *Q* is a fictive mass which allows to adjust the thermostat reactions to temperature changes in the system. *ρ* and *P<sup>ρ</sup>* are dynamical variables relating to the long range interactions between GB sites. *m<sup>ρ</sup>* is the mass relating to this type of interactions and controlling its dynamics.

The forces acting on the system are obtained by deriving the field U. The system's deformations are obtained by integrating the equations of motion using Beeman's algorithme [44]:

$$\vec{S}\_{l}\left(t+\delta t\right) = \vec{S}\_{l}\left(t\right) + \frac{\delta t}{m\_{l}}\vec{P}\_{l}\left(t\right) + \frac{\delta^{2}}{6m\_{l}}\left(4\frac{d\vec{P}\_{l}\left(t\right)}{dt} - \frac{d\vec{P}\_{l}\left(t-\delta t\right)}{dt}\right) \tag{20}$$

$$
\vec{P}\_i(t+\delta t) = \vec{P}\_i(t) + \frac{\delta t}{6} \left( 5\frac{d\vec{P}\_i(t)}{dt} + 2\frac{d\vec{P}\_i(t+\delta t)}{dt} - \frac{d\vec{P}\_i(t-\delta t)}{dt} \right) \tag{21}
$$

$$\bar{\tilde{h}}\left(t+\delta t\right) = \bar{\tilde{h}}\left(t\right) + \frac{\delta t}{\mathcal{W}}\bar{\tilde{P}}\_{\mathcal{h}}\left(t\right) + \frac{\delta^2}{6\mathcal{W}}\left(4\frac{d\bar{P}\_{\mathcal{h}}\left(t\right)}{dt} - \frac{d\bar{P}\_{\mathcal{h}}\left(t-\delta t\right)}{dt}\right) \tag{22}$$

$$
\tilde{P}\_h(t+\delta t) = \tilde{P}\_h(t) + \frac{\delta t}{6} \left( 5 \frac{d\tilde{P}\_h(t)}{dt} + 2 \frac{d\tilde{P}\_h(t+\delta t)}{dt} - \frac{d\tilde{P}\_h(t-\delta t)}{dt} \right) \tag{23}
$$

$$\eta\left(t+\delta t\right) = \eta\left(t\right) + \frac{\delta t}{Q}P\_{\eta}\left(t\right) + \frac{\delta^2}{6Q}\left(4\frac{dP\_{\eta}\left(t\right)}{dt} - \frac{dP\_{\eta}\left(t-\delta t\right)}{dt}\right) \tag{24}$$

$$P\_{\eta} \left( t + \delta t \right) = P\_{\eta} \left( t \right) + \frac{\delta t}{6} \left( 5 \frac{dP\_{\eta} \left( t \right)}{dt} + 2 \frac{dP\_{\eta} \left( t + \delta t \right)}{dt} - \frac{dP\_{\eta} \left( t - \delta t \right)}{dt} \right) \tag{25}$$

$$\vec{\rho}\_{i}\left(t+\delta t\right) = \vec{\rho}\_{i}\left(t\right) + \frac{\delta t}{m\_{\vec{\rho}\_{i}}}\vec{P}\_{\vec{\rho}\_{i}}\left(t\right) + \frac{\delta t^{2}}{6m\_{\vec{\rho}\_{i}}}\left(4\frac{d\vec{P}\_{\vec{\rho}\_{i}}\left(t\right)}{dt} - \frac{d\vec{P}\_{\vec{\rho}\_{i}}\left(t-\delta t\right)}{dt}\right) \tag{26}$$

$$
\vec{P}\_{\vec{\rho}\_i}(t+\delta t) = \vec{P}\_{\vec{\rho}\_i}(t) + \frac{\delta t}{6} \left( 5 \frac{d \vec{P}\_{\vec{\rho}\_i}(t)}{dt} + 2 \frac{d \vec{P}\_{\vec{\rho}\_i}(t+\delta t)}{dt} - \frac{d \vec{P}\_{\vec{\rho}\_i}(t-\delta t)}{dt} \right) \tag{27}
$$

An autocoherent process is necessary to calculate the conjugated moments. The time derivatives of the moments are calculated with the Parrinello-Rahman-Nosé-Hoover Hamiltonian.

*Pi* is its

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

*dt* (18)

*qi* (19)

*P<sup>ρ</sup>* are dynamical variables relating to the long

*Pi* (*t* − *δt*) *dt*

*<sup>h</sup>* (*t* − *δt*) *dt*

¯¯

*dt* <sup>−</sup> *dP<sup>η</sup>* (*<sup>t</sup>* <sup>−</sup> *<sup>δ</sup>t*)

¯¯

*dt* <sup>−</sup> *dP<sup>η</sup>* (*<sup>t</sup>* <sup>−</sup> *<sup>δ</sup>t*) *dt*

*Pi* (*t* − *δt*) *dt*

*<sup>h</sup>* (*t* − *δt*) *dt*

*dt*

*P<sup>ρ</sup><sup>i</sup>* (*t* − *δt*) *dt*

> *P<sup>ρ</sup><sup>i</sup>* (*t* − *δt*) *dt*

18 Will-be-set-by-IN-TECH

the constraints acting on the simulation cell. *W* is a fictive mass which allows the adjustments of the barostat's reactions to the constraints' changes. *mi* is the *i* particle mass.

and *qi* corresponds to the absolute position. *η* and *P<sup>η</sup>* are dynamical variables relating to the control of the temperature. *Q* is a fictive mass which allows to adjust the thermostat reactions

range interactions between GB sites. *m<sup>ρ</sup>* is the mass relating to this type of interactions and

The forces acting on the system are obtained by deriving the field U. The system's deformations are obtained by integrating the equations of motion using Beeman's algorithme

> *δ*2 6*mi*

*δ*2 6*W*

*δ*2 6*Q* 4 *dP<sup>η</sup>* (*t*)

> *δt* 2 6*m<sup>ρ</sup><sup>i</sup>*

An autocoherent process is necessary to calculate the conjugated moments. The time derivatives of the moments are calculated with the Parrinello-Rahman-Nosé-Hoover

 4 *d P<sup>ρ</sup><sup>i</sup>* (*t*) *dt* <sup>−</sup> *<sup>d</sup>*

*d*

*P<sup>ρ</sup><sup>i</sup>* (*t* + *δt*)

*dt* <sup>−</sup> *<sup>d</sup>*

 4 *dP* ¯¯ *<sup>h</sup>* (*t*) *dt* <sup>−</sup> *dP*

 4 *d Pi* (*t*) *dt* <sup>−</sup> *<sup>d</sup>*

*d*

*dP* ¯¯

*Pi* (*t* + *δt*) *dt* <sup>−</sup> *<sup>d</sup>*

> *<sup>h</sup>* (*t* + *δt*) *dt* <sup>−</sup> *dP*

*dP<sup>η</sup>* (*t* + *δt*)

*d Si*

 *Pi* = *mi*

 *Si* <sup>=</sup> ¯¯ *h*−<sup>1</sup>

*Si* is the reduced position of the particle in the simulation cell

to temperature changes in the system. *ρ* and

controlling its dynamics.

¯¯

*P* ¯¯

*Si* (*t* + *δt*) =

*Pi* (*t* + *δt*) =

*h* (*t* + *δt*) = ¯¯

*<sup>h</sup>* (*t* + *δt*) = *P*

*η* (*t* + *δt*) = *η* (*t*) +

*P<sup>η</sup>* (*t* + *δt*) = *P<sup>η</sup>* (*t*) +

*ρ<sup>i</sup>* (*t* + *δt*) = *ρ<sup>i</sup>* (*t*) +

*<sup>P</sup><sup>ρ</sup><sup>i</sup>* (*<sup>t</sup>* <sup>+</sup> *<sup>δ</sup>t*) <sup>=</sup>

*Si* (*t*) +

*Pi* (*t*) +

*h* (*t*) +

¯¯ *<sup>h</sup>* (*t*) +

*δt mi Pi* (*t*) +

*δt* 6

*δt <sup>W</sup> <sup>P</sup>* ¯¯ *<sup>h</sup>* (*t*) +

> *δt* 6

*δt <sup>Q</sup> <sup>P</sup><sup>η</sup>* (*t*) <sup>+</sup>

> *δt* 6 5 *dP<sup>η</sup>* (*t*) *dt* <sup>+</sup> <sup>2</sup>

*δt m<sup>ρ</sup><sup>i</sup> P<sup>ρ</sup><sup>i</sup>* (*t*) +

*δt* 6

 5 *d P<sup>ρ</sup><sup>i</sup>* (*t*) *dt* <sup>+</sup> <sup>2</sup>

*P<sup>ρ</sup><sup>i</sup>* (*t*) +

 5 *dP* ¯¯ *<sup>h</sup>* (*t*) *dt* <sup>+</sup> <sup>2</sup>

 5 *d Pi* (*t*) *dt* <sup>+</sup> <sup>2</sup>

momentum:

where

[44]:

$$\frac{d\vec{P}\_i}{dt} = -\frac{1}{Q} P\_\eta \vec{P}\_i - \vec{G}^{-1} \frac{d\vec{\bar{G}}}{dt} \vec{P}\_i - \vec{h}^{-1} . \vec{\nabla}\_{\vec{q}\_i} \mathsf{U} \tag{28}$$

$$\frac{d\vec{P}\_{\vec{\rho}\_{i}}}{dt} = -\vec{\nabla}\_{\vec{\rho}\_{i}}\mathcal{U} \tag{29}$$

$$\frac{dP\_{\eta}}{dt} = \sum\_{i=1}^{N} \frac{1}{m\_{i}} \vec{P}\_{i}^{T} \vec{\bar{G}} \vec{P}\_{i} + \frac{1}{W} \text{Tr} \left( \vec{\bar{P}}\_{h}^{T} \vec{\bar{P}}\_{h} \right) - gk\_{B}T \tag{30}$$

$$\begin{split} \frac{dP\_{\hbar,a\emptyset}}{dt} &= -\frac{1}{\bigotimes} P\_{\eta} P\_{\hbar,a\emptyset} + \frac{1}{2} \sum\_{i=1}^{N} \frac{1}{m\_{i}} \vec{P}\_{i}^{T} \frac{d\bar{\tilde{G}}}{d\hbar\_{a\emptyset}} \vec{P}\_{i} - \frac{\partial \mathcal{U}}{\partial \hbar\_{a\emptyset}} - P\_{\text{ext}} \frac{\partial \Delta \tilde{h}}{\partial \hbar\_{a\emptyset}} \\ \alpha, \beta &= \propto, y, z \end{split} \tag{31}$$

*∂U ∂μk*,*<sup>α</sup>* <sup>=</sup> <sup>1</sup> *μk NGB* ∑ *i*�=*k* (*μ*ˆ*i*,*<sup>α</sup>* − *μ*ˆ *<sup>k</sup>*,*αμ*ˆ *<sup>k</sup>* · *μ*ˆ*i*) · *νχ*2*ϕki*Ω<sup>2</sup> *kiμ*ˆ*<sup>i</sup>* · *μ*ˆ *<sup>k</sup>* + *μχ*� <sup>2</sup> *ϕki* Θ*ki* (*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>+</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki*)<sup>2</sup> (<sup>1</sup> <sup>+</sup> *<sup>χ</sup>*�*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>μ</sup>*ˆ*i*)<sup>2</sup> <sup>−</sup> (*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>−</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki*)<sup>2</sup> (<sup>1</sup> − *<sup>χ</sup>*�*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>μ</sup>*ˆ*i*)<sup>2</sup> <sup>−</sup> *<sup>χ</sup>*<sup>2</sup> *<sup>σ</sup>*(0) *ki* <sup>3</sup> *�kiσ*<sup>3</sup> *ki* 12*ρ*<sup>13</sup> *ki* <sup>−</sup> <sup>6</sup>*ρ*<sup>7</sup> *ki* (*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>+</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki*)<sup>2</sup> (<sup>1</sup> <sup>+</sup> *χμ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>μ</sup>*ˆ*i*)<sup>2</sup> <sup>−</sup> (*μ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>−</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki*)<sup>2</sup> (<sup>1</sup> − *χμ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>μ</sup>*ˆ*i*)<sup>2</sup> + 2 *<sup>r</sup>*ˆ*ki*,*<sup>α</sup>* <sup>−</sup> *<sup>μ</sup>*<sup>ˆ</sup> *<sup>k</sup>*,*αμ*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki χ <sup>σ</sup>*(0) *ki* <sup>3</sup> *�kiσ*<sup>3</sup> *ki* 12*ρ*<sup>13</sup> *ki* <sup>−</sup> <sup>6</sup>*ρ*<sup>7</sup> *ki* · *μ*ˆ *<sup>k</sup>* · *r*ˆ*ki* + *μ*ˆ*<sup>i</sup>* · *r*ˆ*ki* 1 + *χμ*ˆ *<sup>k</sup>* · *μ*ˆ*<sup>i</sup>* <sup>+</sup> *<sup>μ</sup>*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>−</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki* 1 − *χμ*ˆ *<sup>k</sup>* · *μ*ˆ*<sup>i</sup>* − *μχ*� *ϕki* Θ*ki μ*ˆ *<sup>k</sup>* · *r*ˆ*ki* + *μ*ˆ*<sup>i</sup>* · *r*ˆ*ki* 1 + *χ*�*μ*ˆ *<sup>k</sup>* · *μ*ˆ*<sup>i</sup>* <sup>+</sup> *<sup>μ</sup>*<sup>ˆ</sup> *<sup>k</sup>* · *<sup>r</sup>*ˆ*ki* <sup>−</sup> *<sup>μ</sup>*ˆ*<sup>i</sup>* · *<sup>r</sup>*ˆ*ki* 1 − *χ*�*μ*ˆ *<sup>k</sup>* · *μ*ˆ*<sup>i</sup>* (32)

Calculations have been carried out for 100 molecules and for simulation times up to *δt* =1 fs. We considered that the molecules are bonded by the CH=CH2 groups located at their extremity as represented in figure 19. The bonding of the molecules (the polymerization) takes

**Figure 19.** Schematical representation of the modeled elastomer.

place in such a way to produce a form of sheathing around the principal chain. Crosslinking between principal chains was modeled by resorting to alkyne chains.

To measure the contraction of the simulated system we have monitored the obtained dimensions of the simulation cell vectors *Lx* and *Ly*. In figure 20 and 21 we have represented the results of the simulation and the measured contraction. We can notice a difference between the curvature of the two curves. Figure 22 represents the behavior of the order parameter

**Figure 20.** Contraction of the elastomer: fractional change in length (*L* − *L*0)/*L*<sup>0</sup> as a function of temperature.

**Figure 21.** Simulation result. The curve is a guide to the eye.

obtained by polarized Fourier transform spectroscopy (FTIR) in the case of the same elastomer [45]. If we compare the simulation curve with figure 22 we can see that they have the same apparence. This similarity was to be expected, in fact it is the decrease of the order parameter which generates the contraction of the material. But differences between the behavior of the order parameter and the contraction can be identified: the contraction is not immediate, it

**Figure 22.** Order parameter as a function of reduced temperature *T*/*TN I*, *TN I* is the phase transition temperature [45].

starts above a given temperature which is higher than the phase transition temperature. In reality a sufficient contraction force should be achieved before observing the phenomena and these contraction forces should also exceed the friction forces with the glass plate. The fact that the simulation curve looks like the order parameter curve more than the contraction curve encourages us to consider external mechanical forces acting on the elastomer in the future.

#### **6. Conclusion**

20 Will-be-set-by-IN-TECH

To measure the contraction of the simulated system we have monitored the obtained dimensions of the simulation cell vectors *Lx* and *Ly*. In figure 20 and 21 we have represented the results of the simulation and the measured contraction. We can notice a difference between the curvature of the two curves. Figure 22 represents the behavior of the order parameter

**Figure 20.** Contraction of the elastomer: fractional change in length (*L* − *L*0)/*L*<sup>0</sup> as a function of

obtained by polarized Fourier transform spectroscopy (FTIR) in the case of the same elastomer [45]. If we compare the simulation curve with figure 22 we can see that they have the same apparence. This similarity was to be expected, in fact it is the decrease of the order parameter which generates the contraction of the material. But differences between the behavior of the order parameter and the contraction can be identified: the contraction is not immediate, it

**Figure 21.** Simulation result. The curve is a guide to the eye.

temperature.

We have demonstrated that one photon "UV" photopolymerization as well as two-photon "IR" photopolymerization can be used to microstructure artificial muscle materials made of nematic liquid crystalline elastomers without losing the contraction/extension properties. We have shown that the use of two-photon absorption allows to achieve 65 % greater spatial resolutions. A major advantage of the TPA consists in creating shape-changing volume objects, a property particularly interesting for the domain of microfluidics. We have established the possibility of generating a grating design in the sample which can be used as a step changing grating when subject to a temperature increase. We have shown that the contraction induced by the temperature is easily monitored by the widening of the diffraction figure. We can then consider the use of this kind of grating for temperature adjusted feedback devices. In addition, the birefringence properties of the gratings can open the path for polarization dependent diffractive elements.

Molecular dynamics simulations have been used to describe the contraction of the elastomer as a function of temperature. The proposed model allows the simulation of anisotropic molecules made from a combination of Gay-Berne potentials, representing the rigid mesogenic parts, and Lennard-Jones sites representing the alkyne groups of the flexible chains. Even if experimental and numerical contractions behave somewhat differently as functions of the temperature, a fact that may be attributed in part to the neglect of external

#### 22 Will-be-set-by-IN-TECH 58 Advanced Elastomers – Technology, Properties and Applications

mechanical forces, a rather good agreement between the behavior of the simulation curve and the order parameter has been achieved and a reasonable agreement with the contraction curve has been obtained.

### **Author details**

Kokou D. (Honorat) Dorkenoo, Hervé Bulou, Grégory Taupier, and Alex Boeglin *IPCMS, UMR 7504, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France*

Emel Sungur

*Bilkent University, Department of Physics, Advanced Research Laboratories, 06800, Ankara, Turkey*

### **7. References**


22 Will-be-set-by-IN-TECH

mechanical forces, a rather good agreement between the behavior of the simulation curve and the order parameter has been achieved and a reasonable agreement with the contraction curve

*Bilkent University, Department of Physics, Advanced Research Laboratories, 06800, Ankara, Turkey*

[1] Ikeda, T. and Tsutsumi, O. (1995) Optical switching and image storage by means of

[2] Lagerwall, S. T. (1999) Ferroelectric and Antiferroelectric Liquid Crystals. Wiley-VCH.

[4] Warner, M. and Terentjev, E.M. (2003) Liquid crystal elastomers. Oxford University

[5] de Gennes, P.G. (1997) A semi-fast artificial muscle. CR Acad. Sci. Ser. II B 324: 343-348. [6] Yu, Y. and Ikeda, T. (2006) Two-Photon Excitation in CaF2Eu2+. Phys. Rev. Lett. 45:

[7] Naciri, J. and Srinivasan, A. and Jeon, H. and Nikolov, N. and Keller, P. and Ratna, B.R.

[8] Ikeda Y. Yu T., and Mamiya J.(2007) Soft actuators based on liquid-crystalline elastomers.

[9] De Gennes, P.G(1975) Réflexions sur un type de polymères nématiques. ACR Acad. Sci.

[10] Kupfer, J. and Finkelmann, H. (1991) Nematic liquid single crystal elastomers.

[11] Lessard, R. A. Gurusamy, M. (1995) Photoreactive Polymers in Advance Applications.

[12] McCammon, J.A. and Gelin, B.R. and Karplus, M. (1977) Dynamics of folded proteins.

[13] Allen, M.P. and Warren, M.A. and Wilson, M.R. and Sauron, A. and Smith, W. (1996) Molecular dynamics calculation of elastic constants in Gay-Berne nematic liquid

[14] Darinskii, A.A. and Zarembo, A. and Balabaev, N.K. (2007) Molecular Dynamic Simulation of Side-Chain Liquid Crystalline Elastomer Under Load. Macromolecular

[15] Osada, Y. and Okuzaki, H. and Hori, H.(1992) A polymer gel with electrically driven

[16] Osada, Y. and De Rossi, D.E.(2000)Polymer sensors and actuators. Springer Berlin. [17] Osada, Y. and Khokhlov, A.R. (2002)Polymer Gels and Networks. Marcel Dekker, Inc,

270 Madison Avenue, New York, NY 10016, USA, 1-381.

(2003) Nematic elastomer fiber actuator. Macromolecules 36: 8499-8505.

Kokou D. (Honorat) Dorkenoo, Hervé Bulou, Grégory Taupier, and Alex Boeglin *IPCMS, UMR 7504, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France*

azobenzene liquid-crystal films. Science 268: 1873–1875.

[3] Drzaic, P. S. (1999) Liquid Crystal Dispersions. World Scientific.

has been obtained.

**Author details**

Emel Sungur

**7. References**

Press, USA.

5416-5418.

Angaw. Chem. Int. Ed, 46: 506.

Chapman and Hall, New York.

crystals. J. Chem. Phys. 105: 2850-2858.

Makromol Chem., Rapid Commun. 12: 717-726.

Paris, Ser. B, 46: 101-103.

Nature. 267: 585–590.

Symposia. 252: 101-109.

motility. Nature 355: 242-244.

	- [36] Luckhurst, G.R. and Stephens, R.A. and Phippen, R.W.(1990) Computer simulation studies of anisotropic systems. XIX. Mesophases formed by the Gay-Berne model mesogen. Liq. Cryst. 8: 451.
	- [37] Allen M. P., M. A. Warren, M. R. Wilson, A. Sauraon, and w. Smith(1996) molecular dynamics calculation of elastic constants in Gay-Berne nematic crystals. J. Chem. Phys. 105: 2850-2858.
	- [38] Rappe, AK and Casewit, CJ and Colwell, KS and Goddard Iii, WA and Skiff, WM (1999) UFF, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. JOSA 114: 10024-10035.
	- [39] Allen M. P., M. A. Warren, M. R. Wilson, A. Sauraon, and w. Smith(1985) molecular dynamics calculation of elastic constants in Gay-Berne nematic crystals. Mol. Phys. 55: 549.
	- [40] Cleaver, D.J. and Care, C.M. and Allen, M.P. and Neal, M.P.(1996) Extension and generalization of the Gay-Berne potential. Phys. Rev. E 54: 559-567.
	- [41] Parrinello, M. and Rahman, A.(1981) Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52: 7182.
	- [42] Nose, S.(1984) A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81: 511.
	- [43] Hoover, W.G.(1985) Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31: 1695-1697.
	- [44] Beeman, D.(1976) Some multistep methods for use in molecular dynamics calculations. J. Comput. Phys. 20: 130.
	- [45] Li, M.H. and Keller, P. and Li, B. and Wang, X. and Brunet, M.(2003) Light-driven side-on nematic elastomer actuators. Adv. Mater. E 15: 5569-572.
