Seminar – 1. Letnik, II. stopnja

Nematic elastomer actuators

Author: Matic Pirc

Mentor: prof. Martin Čopič

Co-mentor: Andrej Petelin

Ljubljana, April 2012

Abstract In this seminar, the liquid crystal elastomers (LCEs) and their building blocks – liquid crystals and polymers are presented. The specific rod-like molecular shape of liquid crystals forces LCEs to form a special molecular distribution of the underlying polymer network. This allows them expand up to 400 % with temperature, which could be used in applications. The physics of this spontaneous distortion is explained, and applications of LCEs are presented.

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Contents Abstract ................................................................................................................................................... 1

1. Introduction ......................................................................................................................................... 3

2. Liquid crystals ...................................................................................................................................... 3

2.1. Nematic order .............................................................................................................................. 4

2.2. Free energy and phase transitions of nematics ........................................................................... 4

3. Polymers .............................................................................................................................................. 5

3.1. Configurations of polymers .......................................................................................................... 6

3.2. Classical rubber elasticity ............................................................................................................. 6

4. Liquid crystal elastomers ..................................................................................................................... 8

4.1. LCEs main properties .................................................................................................................... 8

4.2. Shape of liquid crystalline polymers............................................................................................. 9

4.3. Nematic rubber elasticity ........................................................................................................... 10

4.4. Applications ................................................................................................................................ 12

5. Conclusion ......................................................................................................................................... 14

6. Bibliography ....................................................................................................................................... 15

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1. Introduction Liquid crystal elastomers (LCEs) (1) define a special type of material that combines properties of liquid crystals and polymers. Cross-linking of polymers is of great importance, since cross-links are bonds that link one polymer chain to another to form a classical rubber, without cross-linking we get nothing more than “polymer liquid”. Moreover, the same method is used to create rubbery LCEs, and will be explained in the coming paragraph. Liquid crystal elastomers combine thermal and orientational properties of liquid crystals and at the same time the elasticity of polymers. These properties, acting together, give a lot of new physical phenomena – shape change with a change of temperature, extreme opto-mechanical effect and rotatory-mechanical coupling. Consequently, LCEs have been a field of interest for many physicists in the past twenty years. A french physicist Pierre-Gilles de Gennes was the first who predicted the properties of LCEs but the great break through was made by Küpfer and Finkelmann in 1991, when they discovered a method of obtaining large, perfect monodomain nematic elastomers, which is required to observe the mentioned thermomechanical effects. On the other hand, the first polydomain samples were obtained a decade before.

To obtain LCEs the polymer chains need to be linked together into a gel network to fix their topology. In this way the melt becomes an elastic solid – a rubber. In order to create a well aligned monodomain sample a special process, known as the two-step crosslinking method has to be used. To obtain a monodomain sample, usually, the liquid crystal polymer is first lightly crosslinked, then stretched so that the director orients in the stretching direction, and finally crosslinked again. The second crosslinking locks the director and strain is applied during fabrication so that it acts as an internal orienting field, which keeps the director oriented.

In next chapters of this paper we will first describe the properties of liquid crystals followed by the description of polymers. Later on, we will pay the most attention to the properties of LCEs and physics connected with them. Finally, we are going to take a peek into an application field of LCEs.

2. Liquid crystals Liquid crystals are typically relatively stiff rod molecules with long range orientational order (1). Liquid crystals can be found in few different mesophases, which are defined by the local molecule orientation type. The simplest phase is known as the nematic phase, which will be discussed below. Let us also mention smectic phase in which molecules are arranged in layers, and cholesterics, where the molecules are chiral and the director forms a pitch. From now on we are going to focus on nematic phase only. In nematics the average molecule orientation is along some preferred direction called the director, but there is no positional ordering. Shape and conjugated chemical bonds of unit molecule constructing nematic liquid crystals render it more polarizable along its long axis. Molecules that are most likely to form such liquids are so-called para-azoxyanizole (PAA). There are two types of effects which cause molecules to be parallel. First are so-called steric effects: rod-like shape encourages molecules to be parallel when in dense solution or in melt, since they can translate more freely without overlapping. They thereby maximize the disorder of translation, increase the entropy and thus lower the free energy. Nematics which undergo the entropic effect of anisotropic excluded volume are known as lyotropics. Second are so-called thermotropic effects: the van der Waals attraction between two rods is greater when they are parallel and not perpendicular; consequently this leads to a lower energy of the pair of molecules. When long-range van der Waals forces of anisotropic attraction are the dominant ordering influence, a reduction in temperature will lead to nematic ordering. Moreover, nematics that undergo such effects are known as thernotropic. Rod-like or disk-like molecules similar to PAA, continue to order when incorporated into polymer chains and thereby create the essential alignment required to obtain nematic elastomers (1).

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2.1. Nematic order Director is a unit vector that describes the main axis of alignment and is labeled with n. Since director’s “up” orientation cannot be distinguished from “down” orientation, the director is a double headed vector. Let us now define the nematic order parameter, Q, via the average of second Legendre polynomial:

Q = ⟨ ⟩ = ⟨

⟩ (2.1.1)

where ⟨ ⟩ represents an average over rod directions . We can look at some important values of Q. When Q = 1, must be either 0 or , which are equivalent values and as we have mentioned before, direction up cannot be distinguished from down - looking at the Figure 1, one can see that Q = 1 represents perfect nematic order. Q = 0 is when rods are randomly oriented and ⟨ ⟩ = 1/3. Compering values Q = 1/2 and Q = -1/2, we deduce that first value represents moderate nematic order, which sees rods with an average angle of 35°, while the second value represents physically very implausible orientation in conventional nematics, having all rods perpendicular to preferred direction ( = ). In more general discussion, when director also varies in space, it is better to introduce the tensor order parameter (Q)

Qij = ⟨

⟩ = ⟨

⟩ (2.1.2)

where ui is a unit vector representing direction of considered molecule (see Figure 1). We can see that Qzz is indeed the average ⟨ ⟩, if n is along the z axis.

Figure 1: We can see the coordinates of a molecule used to define the order parameter tensor. There is also seen double headed director n. Vector u is also a unit vector representing direction of considered molecule. Orientation of liquid crystal molecules fluctuate around the director.

2.2. Free energy and phase transitions of nematics The nematic order parameter is a function of temperature; at high temperatures Q 0, while at low temperatures Q 1. A phase transition to the isotropic phase is normally spotted above some Tni. Landau – de Gennes phenomenological theory of phase transitions is typically used to describe these phenomena. As mentioned in the previous paragraph there is a big difference between Q = 1/2 and Q = -1/2, which leads us to the following conclusion; since a system free energy depends on the equilibrium order parameter Q, it must distinguish between states Q. This enables us to express free energy as a function of the scalar order parameter, Q, as following:

Fnem =

AQ2 -

BQ3 +

CQ4 + … - fQ. (2.2.2)

We must be aware that equation is valid only if no director variations are present, otherwise one needs to expend a free energy in terms of the tensor order parameter and its gradients that are allowed by the symmetry of nematic state. The Landau expansion of the nematic free energy density contains odd powers of Q, which is an important consequence of nematic symmetry. The linear part

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of the equation, - fQ, represents the effect of an external field – electric or magnetic. On the other

hand, the term -

BQ3 corresponds to the difference between Q and –Q, and at the same time it is

responsible for the weak first-order transition observed in liquid crystals. If we look at the Figure 2 (left), we can see that at low enough temperatures a metastable minimum with Q > 0 appears. The most sensitive temperature dependence can be encapsulated by writing A = A0 (T – T*). Most physical properties of nematic to isotropic phase transition of liquid crystals are explained with this model, including the first-order nature of the phase transition and the supercritical behavior under applied fields.

Figure 2: On the left side there is a dependence of free energy and the nematic order parameter for some temperatures. TC (green curve) represents the transition point (Tni), red curve represents temperature below Tni and aqua curve represents supercooling point. On the right side we have the order parameter as a function of temperature. We can see that above the critical value of external field, fc, the transition becomes supercritical.

In Figure 2 (right), we can see a discontinuous jump (typical in nematics is a jump of Q 0.4) to Q = 0 without external field f = 0, but at sufficient external fields fc transition to isotropic phase becomes continuous. The values of three phenomenological parameters describing the transition from equation (2.2.2) A, B and C differ slightly from material to material. To determine their values three independent measurement must be made – the jump of order parameter, the width of temperature hysteresis and the enthalpy of transition.

3. Polymers A polymer is a large molecule (macromolecule) composed of repeating structural units. These sub-units are typically connected by covalent chemical bonds. Although the term polymer is sometimes taken to refer to plastics, it actually encompasses a large class of compounds comprising both natural and synthetic materials with a wide variety of properties. The great breakthrough in term of polymer industry was made in 1844 by Goodyear, since they had discovered procedures for vulcanizing rubber with sulphur and heat. The name worth mentioning is Hermann Staudinger, who was one of the founders of polymer chemistry. The actual industrialized synthesis of polyester and polyamides began in the beginning of 20th century. To discuss physics of nematic polymers, which are the building blocks of liquid crystal elastomers, we must first describe some properties of classical, isotropic polymers. Most commonly, the continuously linked backbone of a polymer consists mainly of carbon atoms.

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3.1. Configurations of polymers The most illustrating approach describing elastomer behavior is to present polymers as a chain composed of N rods (monomers) of length a freely jointed together. Consequently, a also represents the effective step length over which the chain can essentially bend, meaning the whole chain conformation retraces a path of random walk with a fixed step length. The mean square end-

to-end vector for such a random walk of N steps is ⟨ ⟩ = ⟨

⟩ = ⟨ ⟩ =

⟨ ⟩ =

a2N

aL, where L

= aN is the actual chain length (see Figure 3).

Figure 3: A random walk composed of freely jointed segments with N such monomers or »steps«. R represents end-to-end vector, which is the sum of the steps or the joint vectors u of the component rods. Length of vector ui is a.

For a long chain we can write the probability that a given conformation will have an end-to-end vector R, pN (R). When central limit theorem can be applied the chain distribution is always Gaussian:

pN (R) =

⁄ , (3.1.1)

where R02 = aL = a2N represents its variance. Since we are discussing an idealized chain, the R0 is the

only significant quantity. Let us as look at the free energy of a polymer chain with end-to-end vector R, which can be simply written as

F (R) = F0 + kBT (3R2/2 R02). (3.1.2)

F0 represents free energy of an unconstrained chain and is an additive constant. It can be left out in the further discussion. One can see that the free energy as written in equation (3.1.2) represents Hooke’s law for the extension of a single chain, with 3kBTR0

2 being Hooke’s constant. We must be aware that quite few approximations were made in the discussion of polymers. We have neglected internal energy, interactions between chains, self-avoidance, etc. A fact that enables us to do so is that all contribute very little to elastic properties of LCEs in comparison with the dramatic effect of nematic ordering leading, for instance, to spontaneous shape changes of 10-400 % in LCEs.

3.2. Classical rubber elasticity Now we discuss an elasticity of a network constructed with crosslinked chains of polymers. Without crosslinks rubber would be a polymer melt – a fluid which would eventually flow under stress. The degree of polymerization, N, may be quite large (N = 102 – 104), but the number of monomers that are locally constrained by crosslinking is very low so that chains continue to be fluid like but now they are unable to flow.

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Figure 4: Represents an extension of a rubber block with underlying polymer network. λii are extension factors for the three principal directions. The right scheme shows the extended test network span, R=λ Rf.

Let us continue our discussion by focusing on a selected strand at rubber network formation. This strand has been given an end-to-end distance Rf which will be deformed to a new value R given by:

R = λ ∙ Rf, (3.2.1) where λ represents the deformation (see Figure 1). The free energy of the considered strand can be expressed with the equation (3.1.2) from previous section. Considering the term (3.2.1), free energy is

FS (R) =

(Rf ∙ λ

T ∙ λ ∙ Rf). (3.2.2)

We have neglected few constants, which is completely acceptable as we have explained in the previous section. We must be aware that equation (3.2.2) represents a free energy of only one selected network strand. To obtain an overall elastic free energy of the block of rubber, contributions like equation (3.2.2) for all other network strand must be added together. The end-to-end distance, Rf, differs from a strand to strand but fortunately we know the proportion of chains, which is the probability distribution of chains having this end-to-end distance before crosslinking. It is written as in equation (3.1.1) except that a substitution R Rf has to be made:

pN (Rf) =

⁄

. (3.2.3)

Now we can write down the average energy per strand:

F(R) =

⟨ ⟩ . (3.2.4)

The integration obtained in the latter equation is of the form ∫ , and yields the

appropriate averages:

⟨

⟩

. (3.2.5)

Applying these averages into equation (3.2.4), the free energy density, f, becomes

f =

( )

. (3.2.6)

ns is the average number of strands per unit volume The latter term applies for a case where λ is diagonal, without shear deformation. We can see that there is no dependence of the structure of the component chains; of course they must be long enough to satisfy laws of Gaussian statistics. For a further discussion it is more appropriate to introduce the characteristic rubber modulus, μ = nskBT, which takes values between 104 – 106 Pa. Considering the constancy of volume we must satisfy the following condition:

λxxλyyλzz det [λ] = 1. (3.2.7)

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While extending the sample, say in direction z (λ = λzz), the other two directions must satisfy the term

(3.2.7), which gives us λxx = λyy = 1/√ . Considering the latter finding, the free energy density (3.2.6) becomes:

f =

μ

. (3.2.8)

In relaxed, undeformed state deformation λ = 1. When λ < 1 we speak of compression, and of elongation when λ > 1.

4. Liquid crystal elastomers We have described both building block of liquid crystal elastomer, which was necessary to continue our discussion of liquid crystal elastomers (LCEs). In connection with types of liquid crystals there are three types of conventional LCEs; nematic, cholesteric and smectic elastomers. We will focus on nematic liquid crystal elastomers. Let us first concentrate on polymer liquid crystals (PLCs), which are later cross-linked to create LCEs as described in introduction.

Figure 5: Illustrates all types of PLCs. The darkest links represent crosslinkers, which connect PLCs into elastic rubber.

We must note the sensitivity of creating a proper mixture of both building blocks to sustain a suitable stiffness. There are two strategies of synthesis. The first one gives us a so called main chain (MC) polymer, where rigid rod-like elements are linked in a head-to-tail fashion. On the other hand the second one leads us to side-chain (SC) polymers, where rods are pendant to a flexible backbone giving polymers the comb-like topology. SC polymers can be seen in two different forms; end-on and side-on form. For a better understanding see Figure 5.

4.1. LCEs main properties What makes polymers (rubbers) very extensible is a highly mobile and liquid-like nature of monomers constructing rubber. Thermal fluctuations move the chains as rapidly as in the melt, although only as far as their topological crosslinking constraints allow them to. But we must still be aware that rubber is a solid and as such would normally require an energy input to change its macroscopic shape. This is where the great difference between LCEs and conventional rubber occurs. Nematic polymers suffer spontaneous shape changes as a response to changes at the molecular level. This means we do not need to apply special force to obtain macroscopic change, since nematic state can be achieved by cooling the LCE. Polymers are on average spherical in the isotropic state and elongate when they are cooled to the nematic state (see Figure 6, left). The director n points along the principal axis of extension. If we consider a unit cube of rubber in the isotropic state it elongates by a factor λm > 1 on cooling, on the other head it shrinks by a 1/λm < 1 by heating from nematic to isotropic state. This process is completely reversible.

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Figure 6: Left scheme shows reversible transition between isotropic (I) and nematic (N) state. We can see that polymers elongate when they are cooled to nematic state, since they are on average spherical in isotropic state. While right scheme illustrates factor λm by which the block of rubber elongates. (1)

The fact we described above enables nematic rubber to achieve large deformations, see Figure 7. Starting from the nematic state, LCEs can lift weight by shrinking.

Figure 7: Looking at a scale behind a strip of nematic rubber, we can see large deformation. At the same time we can notice that by heating a nematic state the strip can lift weight. (1)

Another property of the monodomain nematic rubber is its complete transparency and high birefringence. This property enables to easily differ between monodomain and polydomain nematic form, since polydomain rubber is completely transparent in isotropic phase but opaque in nematic phase.

The third property is so-called rotatory-mechanical coupling. It presents a rotation of director without the rubber matrix costs energy. Local rotations are central to nematic elastomers and yield a subtle and spectacular new elastic phenomenon which we call “soft elasticity” (1).

4.2. Shape of liquid crystalline polymers The equilibrium elastic response of LCEs is generated by the nematic polymer backbone, which makes the average shape of the backbone very important. Unlike ordinary polymers, nematic polymers, whether side- or main-chain, have backbones with an average shape distorted by the nematic ordering of the associated rods. Therefore, more than one dimension is needed to describe their anisotropic shape, while R0 was enough to describe ordinary polymers. Let us now write the mean square quantity in general:

⟨ ⟩

(4.2.1)

where is a tensor representing the effective step lengths and L the arc length. Let us also define

the ratio ( ) = (R||/ )2 = r representing the anisotropy (see Figure 8), and is proportional to (Q +

1). Moreover, and are the effective lengths of steps in the directions parallel and perpendicular

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to n and both depend on Q. We can also look at the sign of the difference , that tells us

whether chains naturally extend or flatten. The Gaussian distribution of chain conformations, p(R), must be generalized for the anisotropic case:

p(R) = [(

)

[ ]]

(

). (4.2.2)

Since uniaxial polymers are of special interest we can focus on them. In such polymers mean square

sizes are: ⟨ ⟩

and ⟨

⟩ = ⟨ ⟩ =

L. The effective step tensor in such case is:

l0 = δ + ( )nn. (4.2.3)

While the inverse step length tensor is:

l-1 = δ + (

)nn. (4.2.4)

Figure 8: The arrow indicates the nematic director. As expected distribution of polymers in nematic phase is no longer spherical, we can see the distribution can be either prolate (r > 1) or oblate (r < 1). Very rarely the coupling between the aligning rods and the backbone may be so weak that the chain remains spherical.

4.3. Nematic rubber elasticity

In this section we will finally discuss the elasticity of LCEs. Throughout the discussion of nematic rubber elasticity we will consider and use many conclusions and equations from previous section and section about classical rubber elasticity (3.2.), since principally the only difference between nematic and classical elastomers is that of molecular shape anisotropy induced by the liquid crystalline order. We will use the subscript 0 to denote formation before deformation, while the subscript t

denotes total deformation, since there might be several deformation steps. In this spirit we rewrite the term (3.2.1) into R = λt ∙ Rf. The free energy Fs of a strand is

Fs =

kBT Tr(l0 ∙ λt

T∙ l-1 ∙λt). (4.2.5)

l0 represents the initial step-length tensor, while l is the step-length tensor after deformation. Equation (4.2.5) represents so-called neo-classical free energy of an average network strand since it is a simple generalization of classical, Gaussian elasticity described in section 3.2. We must simply count the number of such network strand per unit volume, ns, to convert free energy into a free energy density; f = ns Fs. Considering the characteristic rubber modulus we have defined in section 3.2, the free energy density can be written as:

f =

μ Tr(l0 ∙ λt

T∙ l-1 ∙λt). (4.2.6)

This is the fundamental equation and will be used in the description of most of the nematic phenomena. We should mention that it records the initial (n0) and current (n) directors of the elastomer, furthermore the initial and current magnitudes of the local nematic order parameter are also contained in f through the anisotropy of l0 and l. For a better understanding we will calculate the free energy density for specific example - spontaneous distortion in the fallowing section.

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By going through this example it will also help us to describe the equilibrium shape of nematic elastomers. We consider an elastomer formed in the isotropic state with l0 = aδ, we cool it to its current, relaxed, monodomain nematic state in which natural shape of chains is represented by the tensor lr. Spontaneous distortion is labeled as λm and since the sample has been cooled we know it must be uniaxial deformation along n. We take the director to be along the z axis. This means the deformation tensor must have its principal extension element, λ, along z. This gives us the diagonal

matrix for the deformation: λ = diag(1/√ , 1/√ , λ) λT. From equation (4.2.6.) we can see that we also need the inverse step length tensor lr

-1 which is also a diagonal matrix: lr

-1 = diag(1/

, 1/ , 1/

).

We must calculate the product of four diagonal matrices, [(aδ)∙λT∙lr

-1∙λ], since we need its trace:

(

) (4.2.7)

All together gives us a free energy density for our example:

f =

μ(

). (4.2.8)

In the latter equation we can see separate factors

and

. The first one represents a shape change

for a parallel direction, while the second one for the two perpendicular directions. By minimizing the

free energy density from (4.2.8),

, we get a spontaneous uniaxial elongation:

λm = (

)

. (4.2.9)

Now we can look at another possible example in which the formation and current state both are

nematic. In such case l0 is no longer aδ, but it is characterized by principal values and

: l0 = diag

( ,

, ) while the other three matrices (λ, λT and.lr

-1) are the same as in previous example.

Multiplying them together we get a different trace than the trace (4.2.7):

(

) (4.2.10)

Consequently, this gives us a different free energy density than in previous example:

f =

μ(

). (4.2.11)

Minimizing,

, yields optimal spontaneous elongation:

λm = (

)

. (4.2.12)

Considering both examples we can see that the ratio between the sample length L and the length in the isotropic state Liso gives us information about the chain anisotropy parameter:

L/Liso = r1/3. (4.2.13)

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Figure 9: Shows the temperature dependence of the anisotropy and the nematic order parameter, Q.

4.4. Applications All of the properties we have described in previous sections make liquid crystal elastomers appropriate for many different applications. In this section we will describe some of them. Normally we all think of optical applications when we hear about liquid crystals. But liquid crystal elastomers alone are not very applicable in display technology, since they cannot be manipulated with electric field. Assuming the electric field E interacts with a dielectrically anisotropic nematic medium, causing the director to rotate, the characteristic energy density could be estimated as

. For a field E 106 V/m3 and typical dielectric parameters of nematic liquid crystals, this gives a densety of 103 J/m3. The rubbery elastic network resists any such rotation with a characteristic energy density of the order of rubber modulus μ 105 J/m3 or higher; clearly no effect could be expected. Consequently, scientists came up with an idea to incorporate carbon nanotubes into the rubber, which makes it controllable by electric field (2).

The control or better the manipulation of optical birefringence of LCEs makes them suitable for opto-mechanical sensors and other similar devices (3). Spontaneously shape-changing thermo-mechanical systems or rubbers with selective shape-memory are adequate for another wide field of usage - temperature sensors and temperature-controlled actuators. There are also so-called photo-elastomers which can be used as a light-driven actuation. Furthermore, rubbers with piezoelectric and non-linear optical properties represent a highly prospective area, since they allow large deformations and manipulation of polarization by mechanical means. Another property making LCEs highly applicable is the optical clarity when in monodomain state as mentioned in section 4.1. The fact that they are rather soft mechanically in contrast to solids, but they still retain their shape as solids, makes them highly suitable for bifocal contact and intra-ocular lenses. But the most important field where LCEs could be applied is the manufacture and development of artificial muscles. Muscles are anisotropic, because they are stretching in only one direction along muscle fiber. That is the same as for LCEs, which are stretching only in direction of director n. Other properties describing muscles are maximal contraction and maximal mechanical strength. The maximal frequency of contraction can be obtained by incorporating materials with high thermal conductivity, since liquid crystal elastomers have quite slow response to thermal changes. Researchers find LCEs mixed with appropriate materials with exactly same value of these properties as natural muscles. We have mentioned the most often usage of LCEs, in further discussion of this section we will take a closer look into some of application.

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Since the use of LCEs in the development of artificial muscles is of great importance we must discuss this field more closely. As we have mention before the uniqueness of LCEs lies in their responsiveness to various external stimuli, such as temperature, light, etc. Therefore, in principle, different stimuli-responsive artificial muscles could be prepared with LCEs. Moreover, thermo-responsive, photo-responsive and electro-responsive muscle-like materials have been reported. More generally, any polymer chain shape change induced by the disorganization or reorganization of LC mesogens, in response to external stimulation, can be used to produce muscle-like contraction in a monodomain sample. Since thermo-responsive muscle-like material is the most frequently use, it is fair to describe how it works. The operating cycle of such a muscle involves four steps: heating from low temperature T- to high temperature T+ (above Tni), producing a nearly isothermal work, cooling back to T- and releasing work, again at nearly constant temperature.

Figure 10: A striated artificial muscle (b) based on a triblock copolymer RNR (a) in a lamellar phase with suitable crosslinking of the elastomer part R.

De Gennes was the first who proposed a composite structure based on the lamellar phase of a triblock copolymer RNR (R - classical elastomer; N - nematic polymer; see Figure 10). In the RNR the crosslinking is present only in the R parts (see Figure 10 (b)). Consequently this striated structure is more robust mechanically and the monodomain nematic ordering is better preserved during the contraction/elongation cycles. Another fact making this structure interesting is that this triblock composite structure mimics not only muscle function (contraction/elongation), but also, to a certain extent, the hierarchical and striated structure of real muscle cells. In the (4), a bottom-up strategy is showed to make artificial muscles, or more generally stimuli-responsive materials, using nematic side-on LC polymer as building block. A series of thermo- or photo-responsive self-assembled LC elastomers were prepared. The overall material response in these artificial muscles reflected the individual macromolecular response. This approach is particularly interesting for the development of micro- or nano-sized artificial muscles, since it opens the way to a broad range of micro- or nano-level devices and active surfaces. (4), (5) LCEs with highly crosslinked network and with incorporated azobenzene moieties can be used in a way which makes them equivalent to a bimetallic or birubber strip, but on a much smaller scale; micro- or nano-scale.

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Figure 11: Shematic depiction of nematic (left) to isotropic (right) phase transformation in liquid-crystal containing photoisomerizable mesogenic molecules, which turn from a rodlike trans to a kinked cis conformation under uv irradiation.

On irradiation with light, the crosslinker undergoes trans–cis isomerization, contracting the network in the horizontal direction on top, and dilating it on the bottom, causing a strip to bend (see Figure 12). To get a better feeling, let us write down the speed of trans-cis transition at 600 mW, which is 20 ms for rise time and 75 ms for relaxation time. Consequently, this provides an effective way of transferring energy to the working element without the need for compliant electrodes and wires, as in the case of electrically driven systems. (6), (7)

Figure 12: Blue ovals are mesogenic units while yellow ovals represent azo-crosslinker. Left side (a) represent the strip before irradiation while (b) shows the strip deformed in a flap, after it has been irradiated.

As one of the latest application of LCEs we can expose haptic displays. Haptic refers to technology that interfaces to the user via the sense of touch by applying forces and/or motions. LCEs’s response to stimuli is quite slow (minutes). To make their response speed appropriate (few ms) for haptic technology carbon nanotubes (CNT) segments must be incorporate into a monodomain (uniaxial) nematic LCEs. Furthermore, this mixture is called CNT-LCE composite. CNTs absorb all light and convert it to heat fast and efficiently at the same time this allows making LCE actuators triggered remotely and individually. On the other hand, LCEs alone would need UV which is quite expensive. A problem occurs with heat removal, since it is slow because the LCEs are isolators. To accelerate heat removal, a commonly used technique is to include conducting particles to the polymer. Unfortunately, the presence of carbon particles in the prepolymerization mixture inhibits the formation of an elastomer network with liquid crystalline properties. Scientists have developed several prototype displays so-called dynamic Braille display, but the actual one is not yet on the market. (8) As we can see there are severe different fields where LCEs can find their place. Since LCEs represent quite new material we can without a doubt say that we will hear more of this “liquid-like” rubber in coming years.

5. Conclusion In this seminar we have first described liquid crystals and their main properties, since they are one of the building blocks of liquid crystal elastomers. We have focused on nematic liquid crystals in which the average molecule orientation is along some preferred direction called the director. Then we have defined the free energy and described phase transitions of nematics. Later on we have continued with description of polymers and phenomena connected with them. Moreover, we have taken a closer look at configurations of polymers and we have described the main physical properties of classical rubber elasticity. At that point we have described both building blocks of LCEs, so we have had everything we have needed to start explaining phenomena connected with LCEs.

The most important property of liquid crystal elastomers is their ability to achieve high extension along the director. Moreover, the shape change can be achieved with a temperature

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change or uv irradiation, since nematic phase can be achieved by cooling a strip of liquid crystal elastomers. Scientists have used these properties of LCEs to create artificial muscles. It turned out that mixture of LCEs and some other appropriate materials enables the manufacture of artificial muscles with properties extremely similar to those of natural muscles. To sum up we can say that this paper shows us how two at first sight incompatible structures work perfectly together. Moreover mixing together liquid crystals and polymers have opened new doors and ways in many different fields of modern technology.

6. Bibliography 1. Terentjev, M. Warner and E. M. Liquid Crystal Elastomers. Oxford : s.n., 2003. 2. S. Courty, J. Mine, A. R. Tajbakhsh and E. M. Terentjev. Nematic elastomers with aligned carbon nanotubes: New electromechanical actuators. [Online] December 1, 2003. http://iopscience.iop.org/0295-5075/64/5/654. 3. A New Opto-Mechanical Effect in Solids. Nishikawa, H. Finkelmann & E. 2001, Vol. 87. 4. Keller, Min-Hui Li and Patrick. Artificial muscles based on liquid crystal elastomers. Philosophical transactions of royal society. [Online] 2006. http://rsta.royalsocietypublishing.org/content/364/1847/2763.full. 5. MICRO-ACTUATORS: WHEN ARTIFICIAL MUSCLES MADE OF NEMATIC LIQUID CRYSTAL ELASTOMERS MEET SOFT LITHOGRAPHY. Buguin A., Li M.H., Silberzan, P., Ladoux B., Keller P. s.l. : JACS communications , 2006. 6. Printed actuators in a flap. Palffy-Muhoray, Peter. s.l. : Macmillan Publishers Limited, 2009, Vol. 8. 7. Fast liquid-crystal elastomer swims into the dark. M. Camacho-Lopez, H. Finkelmann, P. Ralffy-Muhoray and M. Shelley. s.l. : Nature Publishing Group, 2004. 8. Applications of Liquid Crystal Elastomers in HapticDisplaysBiological and. Laboratory, Cavendish. Lisbon : s.n., 2011. 9. Spontaneous thermal expansion of nematic elastomers. Terentjev, A.R. Tajbakhsh & E.M. Cambridge : The European physical journal E, 2001. 10. McGowan, Dr Maggie. Liquid Crystal Elastomer Beads. The University of York - Working with university. [Online] June 20, 2010. file:///D:/Documents/fax/2.%20stopnja/seminar%201/ang/Liquid%20Crystal%20Elastomer%20Beads%20-%20Working%20with%20the%20University,%20The%20University%20of%20York-vir.htm. 11. [Online] http://lizika.pfmb.uni-mb.si/projekti/kako_deluje_narava/ftk4.htm. 12. Kutnjak, Zdravko. Kaj imajo razvoj hladilnikov nove generacije, umetnih mišic in izboljšanih virov ultrazvoka skupnegas faznim diagramom vode? [Online] http://videolectures.net/kolokviji_ijs/. 13. Liquid Crystal Elastomers. [Online] http://www.lcelastomer.org.uk/.