Molecular-statistical theory for curvature elasticity of thermotropic main-chain-polymer liquid crystals

We develop a microscopic molecular-statistical theory for thermotropic nematic polymers, composed of semiflexible chains of bonded nematogenic monomers. In the framework of a mean-field approximation we account for pair-interaction forces between monomers, including long-range attraction, steric repulsion, and effective rigidity of the bonds between subsequent monomers on the same chain. The functional correction to the probability distribution in a nonuniform orienting field is obtained for the case of very-long-wavelength deformations. We then derive a curvature-elastic free energy for this system, in which the Frank elastic constants are expressed in terms of definite molecular and thermodynamic parameters. It is shown that for a very long semiflexible chain the splay elastic constant is exponentially large and is proportional to the average distance between sharp bends on the chain.