Mean-field nematic–smectic-Atransition in a random polymer network

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-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 of 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 TNA, a suppression of the Halperin-Lubensky-Ma effect (thus recovering the mean-field continuous transition to the smectic state), and a new tricritical 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 the phenomenological long-wavelength coupling between smectic phase and elastic strain. {} 1996 The American Physical Society.