## Effects of Random Disorder...

(check out the classical l.c.elastomers)

• S.V. Fridrikh and E. M. Terentjev,

• Polydomain-Monodomain Transition in Nematic Elastomers

Director textures and alignment of polydomain nematic elastomers under uniaxial extension are described theoretically applying the concept of randomly quenched disorder introduced by network crosslinks. Within this model, treated with the replica trick and Gaussian variational approximation, the polydomain-monodomain transition occurs in a critical fashion with a small jump and rapid increase of the macroscopic order parameter. The transition is characterised by a plateau on the stress-strain curve. The critical stress value at which the transition takes place is estimated as the product of  rubber modulus of the elastomer and the degree of backbone chain anisotropy. The aligning of polydomain texture occurs via rotation of domains rather than their growth, with domain size almost unchanged through and above the transition. Experimental data obtained by several groups for various nematic elastomers are analysed, showing a qualitative agreement with model predictions.

• S.M. Clarke and E.M. Terentjev,

• Slow stress relaxation in randomly disordered nematic elastomers and gels,

Randomly disordered (polydomain) liquid crystalline elastomers align under stress. We study the dynamics of stress relaxation before, during and after the Polydomain-Monodomain (P-M) transition. The results for different materials show the universal ultra-slow logarithmic behaviour, especially pronounced in the region of the transition. The data is approximated very well by an equation Sigma(t) ~ (1+ a Log[t])^{-1}. We propose a theoretical model based on the concept of cooperative mechanical resistance for the re-orientation of each domain, attempting to follow the soft-deformation pathway. The exact model solution can be approximated by compact analytical expressions valid at short and at long times of relaxation, with two model parameters determined from the data.

• S.M. Clarke, E.M. Terentjev, I. Kundler and H. Finkelmann,

• Texture Evolution during the Polydomain-Monodomain Transition in Nematic Elastomers,

We study the behaviour of a liquid crystalline elastomer undergoing a Polydomain-Monodomain transition. The textures emerging under increasing extensional load have been examined with a combination of optical microscopy, X-ray and small angle polarised light scattering. The experimental data are interpreted in terms of reorientation of the local director with increasing extension. The results of this combination of techniques at low extensions are consistent with a two-dimensionally periodic director texture. The amplitude of this modulation decreases continuously as the mesogens are pulled into the extensional direction at high loads. In this manner the samples which are polydomain under no load become essentially monodomain with increasing extension.

• S.V. Fridrikh and E.M. Terentjev,

• Order-Disorder Transition in External Field in Random Ferromagnets and Nematic Elastomers,

We study the effect of external homogeneous field on random anisotropy ferromagnets and nematic elastomers, using replica and Gaussian variational methods. The system evolves on increasing field, from the correlated spin glass state with zero average magnetization and characteristic domain size $\xi_0$, to the ferromagnetic state with the long-range order. We find that this evolution takes place in a critical fashion, via the phase transition at a threshold field, which is manifested by appearance of stable replica-symmetric solution. The transition is of the first order with a significant jump of the average magnetization. The second important conclusion is that the characteristic size of spin-correlated regions (domains) does not change significantly through the transition, and at the further increasing of field: the increase of mean magnetization is achieved by reorientation, rather than growth, of individual domains. We discuss the additional hardening mechanisms in nematic elastomers that increase the threshold of the transition, which has been observed experimentally.

• S.M. Clarke, E. Nishikawa, H. Finkelmann and E.M. Terentjev,

• Light-scattering study of random disorder in liquid crystalline elastomers,
Macromol. Chem. Phys. v.198, 3485 (1997).

We perform a structural study of non-uniform (polydomain) director texture in nematic and smectic liquid crystalline elastomers. Polarised light scattering is used to probe the equilibrium director correlations in the region of transition under stress between the opaque polydomain material and the transparent, macroscopically monodomain elastomer. A characteristic four-peak scattering image is obtained in this transient region. The lobes of intensity are oriented along and perpendicular to the axes of crossed polars, with anisotropy along the direction of principal extension. We propose a theoretical model, based on the competition between the random disordering field due to the network crosslinks and of the external aligning field (mechanical stress) to explain the observations.

• E.M. Terentjev,

• Thermodynamic order and random disorder in liquid crystal elastomers,
Macromol. Symp. v.117, 79, 1997.

This short review article focuses on the continuum aspects of liquid crystal elastomer structure. There are two opposing tendencies, the lack of thermal fluctuations that enhances the order in the system, and the random quenched disorder that leads to a highly frustrated polydomain state in equilibrium. Imposing an external field (mechanical stress) changes the balance between order and disorder, this process being monitored by a polarised light scattering.

• P.D. Olmsted and E.M. Terentjev,

• Mean-Field Nematic--Smectic-A Transition in a Random Polymer Network,
Phys. Rev. E53, 2444, 1996.

Liquid crystal elastomers present a rich combination of effects associated with orientational symmetry breaking and the underlying rubber elasticity. In this work we focus on the effect of the network on the nematic--smectic-{\sl A} transition, exploring the additional translational symmetry breaking in these elastomers. We incorporate the crosslinks as a random field in a microscopic picture, thus expressing the degree to which the smectic order is locally frozen with respect to the network. We predict a modification in the NA transition, notably that it can be treated at the mean-field level (type-I system), due to the coupling with elastic degrees of freedom. There is a shift in the transition temperature $T_{NA}$, a suppression of the Halperin-Lubensky-Ma (HLM) effect (thus recovering the mean-field continuous transition to the smectic state), and a new tri-critical point, depending on the conditions of network formation. When the nematic phase possesses `soft elasticity', the NA transition becomes of first order due to the coupling with soft phonons in the network. We also discuss the microscopic origin of phenomenological long-wavelength coupling between smectic phase and elastic strain.