For a semi-flexible, nematic polymer, the Landau-de Gennes expansion for the free energy of the homogeneous melt is derived. The theory contains three parameters : the degree of polymerization, the inherent elasticity of the polymer chain, and the quadrupolar mean field between monomers. The dependence on chain length and chain flexibility of the transition temperature, the order parameter and the latent heat of the nematic-isotropic transition is discussed
A theory for the nematic-isotropic phase transition in semirigid polymer/liquid crystal solutions is proposed. The polymer is described by an elastic chain and van der Waals and steric intermolecular interactions are included in a mean field approximation. It is shown that these interactions orient the liquid crystal molecules and the polymer chains in the solution. The order parameter of the liquid crystal molecules and of the polymer are calculated as a function of temperature and concentration and the phase diagram for the first order phase transition is given. The effects of chain length and chain flexibility are discussed.
SUMMARY:In liquid-crystal elastomers, the simultaneous presence of rubber elasticity due to the crosslinked backbone chains and of optical birefringence due to the mesogens in the side chains lead to exceptional physical properties. An elastic deformation of the network influences the order of the mesogens and, therefore, the optical properties. A theory based on a Landau-de Gennes expansion of the free energy is proposed. In the opaque polydomain phase, the local orientation is given by a compromise between the external mechanical field and a local anchoring interaction. As the field is increased, it becomes energetically favorable for the mesogens to align parallel to the mechanical field, and a transition to a transparent monodomain structure occurs. Results for the average orientation, the stress and the chain conformation are given.
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