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Abstracts and Talk Materials:

Modeling the Dynamics of Liquid Crystal Elastomers

May 24-25, 2005

Mark Warner & Eugene Terentjev (Remote lecture from Cambridge)

Nematic elastomers can elongate or contract by as much as factors of x4 or x5 in response to small changes of temperature in response to illumination. Such deformations can be rapid and are reversible.

In nematic polymers, changes in liquid crystal ordering gives a molecular shape change. When such polymers are crosslinked to form a network, as in a rubber or elastomer, then the molecular shape changes induce macroscopic shape change. Nematic order is lowered by heating, or by bending rods on the absorption of a photon, hence giving rise to the thermal or optical effects above.

Actuation is a possibility in nematic elastomers. Experiments show thermo-actuation where 400+ % strains can lift weights. Artificial muscles have been speculated upon, but actuation at the micro and nano-scale, where motors are relatively less efficient, is more likely. The photo-analogue seems much richer. We discuss the photo-bending of beams and the writing of structures in thin photo-rubber films stuck to substrates (a possible route to the control of micro-fluidics). We discuss the dynamics of lightinduced strains and in particular the character of the photo-stationary state.

Polydomain rubbers have been shown to be sensitive to the polarisation of light. Their curling follows the polarisation direction which can then be changed. Problems for the future include explaining the strange, and seemingly as yet unremarked, observation that sheets continue curling after they have eclipsed the light source and are in effect illuminated from the reverse side. A non-equilibrium effect is evidently at work. Experiments determining the photo-stationary shape of a sheet or beam are clearly needed.

Patricia Cladis (Advanced Liquid Crystal Technologies)

Liquid crystalline elastomers as artificial muscles

To reduce the very large electric field needed to elicit an electromechanical response from "pure" liquid crystalline elastomers (LCE), our idea was to apply electric fields to LCEs that had been swollen with low molecular weight liquid crystals.

In the past three decades, swelling properties of isotropic polymer gels in isotropic solvents have attracted much attention and their physical mechanisms are now well understood [1]. On the other hand, a liquid crystal elastomer (LCE), an anisotropic gel, has been recently synthesized, for which swelling properties in an anisotropic solvent such as low molecular weight liquid crystals (LMWLCs) are different from the well-known isotropic case [2]. In particular, we found that the swelling properties and temperature behavior (thermomechanical property) of volume changes were also anisotropic.

Understanding the physical mechanisms responsible for thermomechanical effects in LCEs is important to make functional materials that can work as, e.g., temperature-driven actuators or artificial muscles [3]. Another useful property for them would be as devices that changed their shape in applied electric fields rather than temperature, i.e. their electromechanical effect. In current dry LCEs, however, fields of about 1V/micron are required to induce electromechanical effects.

In contrast to this, the electric field response of LMWLCs in the parallel plate geometry is a well-known cooperative phenomena, i.e. is a voltage effect, not a field effect as it is for nematic elastomers. As a result, LCEs swollen with nematic LMWLCs could be a good candidate to observe measurable shape changes at low voltages. Indeed, only a small voltage (about 1V) is required to change the orientation of nematic LMWLCs. Should there be a strong enough coupling between the mesogenic side-chains of the LCE and LMWLC molecules, the question is, can the low voltage response of LMWLCs be harnessed to induce reorientation effects in the tethered LCE side chains to obtain measurable shape changes at low voltages? Our brief answer is yes. However, while the voltages are small, comparable to that of LMWLCs, the reorientation effect is also small [4].

In this talk, I will give some snapshots of our experimental results to date [2,4].

1. A. Onuki, Adv. Poly. Sci., 109, 63 (1993).

2. Y. Yusuf, Y. Ono, Y. Sumisaki, P. E. Cladis, H. R. Brand, H. Finkelmann, and S. Kai, Phys. Rev. E, 69, 021710 (2004).

3. P. G. de Gennes, M. Hubert, and R. Kant, Macromol. Symp., 113, 39 (1997); M. Hubert, R. Kant, and P. G. de Gennes, J. Phy. I France, 7, 909 (1997).

4. Y. Yusuf, J-H. Huh, P.E. Cladis, H.R. Brand, H. Finkelmann, S. Kai, Phys. Rev. E. (in press).

Tom C. Lubensky (University of Pennsylvania)

Elasticity and dynamics of LC elastomers

presentation slides only

Patrick T. Mather (Case Western Reserve University)

Real liquid crystalline elastomers pose really tough problems

In this talk, I will overview experimental aspects of liquid crystalline elastomer (LCE) materials and thermomechanical behavior. An emphasis will be placed on materials synthesized in our own laboratory. We have separately designed and synthesized rigid nematic networks and compliant smectic-C networks, each existing with polydomain textures at equilibrium and accessible isotropization temperatures. The materials share molecular similarity by use of identical mesogens, but in the nematic case these mesogens are linked directly together by ADMET polymerization, leaving residual unsaturation for crosslinking, while in the smectic-C case the mesogens are bridged by short siloxane spacers that afford the macroscopic compliance. In this presentation I show that despite dramatically different stiffnesses and phase symmetries for these materials, they share in common reversible elongation/contraction on cooling and heating through liquid crystallization/isotropization, respectively. It is argued that this common feature derives from a polydomain-monodomain transition possible in both types of material due to their existence as highly textured materials. I will show further that large strain "fixing" is possible in both types of materials, such fixing being possible by vitrification of the entire material in the nematic case or of the mesogen-rich layers only in the smectic case. In light of this phenomenology, I will pose broad and specific challenges for the modeling community that are both relevant and necessary for advances in this exciting field.

Robert B. Meyer (Brandeis University)

Buckling instabilities in nematic elastomers

Buckling instabilities are well known in the mechanics of elastic beams under compressive stress. Intuitively, for ordinary elastic materials, it is clear that tall thin beams buckle easily, while short thick ones do not buckle at all. For nematic elastomer materials, these intuitive ideas break down, because of the extreme anisotropy of these materials. For nematic elastomers, certain shear deformation modes exhibit "soft elasticity," meaning that these modes are characterized by a vanishing shear modulus. This has the consequence that nematic elastomers are often subject to buckling instabilities, even for sample geometries that would only allow simple linear elastic response, were the sample composed of an ordinary elastic medium. Examples of these instabilities in several sample geometries will be discussed, along with some experimental results.

Peter Palffy-Muhoray (Kent State University) http://ppm2002.lci.kent.edu/

A non-local model for liquid crystal elastomers

We have developed a fully non-local model to describe the dynamic response of nematic liquid crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these is taken into account through non-local interactions rather than through the use of gradient expansions. The equations of motion, for displacement and orientational order, are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We outline potential advantages of this formalism, and present preliminary numerical results.

Harald Pleiner (Max Planck Institute for Polymer Research)

Elasticity of Nematic Side-Chain Elastomers

We review the linear and nonlinear elasticity theory of isotropic and anisotropic solids in the absence or presence of external fields. This is used to deal with the elastic properties of nematic side chain elastomers that are isotropically and/or anisotropically crosslinked. The notion of soft elasticity or spontaneous elastic shape anisotropy is discussed and compared with experimental results in the literature.

Michael J. Shelley (New York University)

Locomotion in fluids of active shape-changing materials

A fascinating question is how an active material like an LCE interacts with a surrounding fluidic environment. I will discuss methods and difficulties in simulating such problems, and then discuss some simulation and modeling work of fluid/active-structure interactions stimulated by experiments of LCE samples locomoting through a fluid, and by organismal locomotion.