Mean-field nematic-smectic-A transition 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 T-NA, 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 become's 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.