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Book	M. Kröger, H.S. Sellers A molecular theory for spatially inhomogeneous, concentrated solutions of rod-like liquid crystal polymers in Complex Fluids, Ed. L. Garrido, from the series: Lecture notes in physics 415 Springer, NY (1992) 295-301
Polymer liquid crystals assume a variety of spatially varying structures in equilibrium, common examples being defects in alignment. In order to model such textures, an adequate theory needs to incorporate spatially inhomogeneous systems. We present here an extension of the Doi molecular theory for concentrated solutions of rigid, rod-like polymers to spatially inhomogeneous systems. The procedure is based upon a mesoscopic description using a Smoluchowski equation for the orientational distribution function and a Maier-Saupe mean-field potential for particle-particle interactions. This takes into account the effects of translational and rotational fluctuations. The second moment of the Smoluchowski equation with the microscopic alignment yields a relaxation equation for the second-order alignment tensor. Since higher-order terms also appear, we assume a simple decoupling relation in order to obtain a closed equation in terms of the second moments. For the case of uniaxial alignment in equilibrium, we compare the alignment tensor equation to the Euler-Lagrange equations obtained by minimizing a macroscopic, phenomenological expression for the free energy. This comparison allows us to relate the phenomenological coefficients in the free energy to parameters in the Doi theory. @book{MKröger1992, author = {M. Kröger, H.S. Sellers }, title = {A molecular theory for spatially inhomogeneous, concentrated solutions of rod-like liquid crystal polymers in Complex Fluids, Ed. L. Garrido, from the series: Lecture notes in physics }, volume = {415 }, year = {1992}, publisher = {Springer, NY }