Back
to the Home page 
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.
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.
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.
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.
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.
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.
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.
Back
to the Home page