Theory of nematic networks

Abstract

Using classical elasticity theory, the rise in free energy upon crosslinking nematogenic polymers into a network is calculated for the isotropic and nematic phases. Spontaneous strains are allowed for in the network. The consequence of network formation upon nematic–isotropic equilibria is calculated by adding these elastic contributions to a conventional Landau theory. Memory of the crosslinking conditions yields quartic and quadratic additions to the standard Landau theory. We find that crosslinking in the isotropic state lowers the nematic–isotropic phase transition temperature compared with the unlinked case and the application of suitable stress raises it again. Crosslinking in the nematic state raises the transition temperature. We recover the mechanical critical point proposed long ago by de Gennes. Our Gaussian theory encompasses both main- and side-chain polymers. The hairpin limit for main chain networks yields a modulus varying exponentially with temperature. The Landau–de Gennes free energy for comb polymers is presented for the first time.