MEAN-FIELD NEMATIC-SMECTIC-A TRANSITION IN A RANDOM POLYMER NETWORK

Liquid-crystal elastomers present a rich combination of effects associ ated with orientational symmetry breaking and the underlying rubber el asticity. In this work we focus on the effect of the network on the ne matic-smectic-A transition, exploring the additional translational sym metry 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 b e 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 t emperature T-NA, a suppression of the Halperin-Lubensky-Ma effect (thu s 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 ph onons in the network. We also discuss the microscopic origin of the ph enomenological long-wavelength coupling between smectic phase and elas tic strain.