Transfer-matrix theory of the crystal–columnar transition in polymeric liquid crystals

The statistical–mechanical problem of the transition between crystalline and columnar phases in a main-chain liquid–crystalline polymer is treated in a simple model in which only longitudinal motions of the polymer chains are permitted. A mean-field approximation for the interchain potential is used to obtain a self-consistent equation for the crystalcolumnar transition temperature. When applied to typical homopolymers this theory correctly predicts transition temperatures above the degradation temperature; when applied to a crude model of a random copolymer a temperature in the observed range is predicted.