On the uniaxial-biaxial nematic phase transition in liquid-crystalline polymers and elastomers

We study how the uniaxial-biaxial nematic phase transition changes its nature when going from a low molecular-weight liquid crystal to a liquid-crystalline or polymer (the latter above the Maxwell frequency) and find a qualitative change due to the presence of a coupling to the strain field in these materials. While this phase transition can be of second-order in low-molecular weight materials, as is also experimentally observed, we, show. here that the order of this phase transition is changed generically to no phase transition at all or to a first-order phase transition in mean-field approximation. We analyze the influence of an external mechanical stress;field above the uniaxial-biaxial nematic phase transition and find that either biaxial nematic order is induced, which, is linear or quadratic in the stress intensity, or no response to an external stress results at all, depending on the relative orientation of the applied shear with respect to the director of the uniaxial nematic phase.