A Review of Lattice Theory for Lyotropic Liquid Crystalline Polymers, Spinodal Decomposition, and Gel Formation

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Abstract
Polymer chain conformations can be described by many models. Some of the main ones are shown in Fig. 1. The rod-like model describes polymer molecules as rigid cylinders with high axis ratio. The axis ratio, X, is equal to the length of the polymer divided by the diameter. X = L/d for molecules in any conformation. Linear polymer chains that are not completely rod-like can be described by Kuhn chains, worm-like chains, or segmented rod-like and random coil chains. Kuhn chains are characterized by rigid segments connected by universal joints. The rod-like segment, known as the Kuhn segment, has a characteristic length, 2q. Worm-like chains have continuous deviation from rod-like behavior but are not necessarily completely flexible. The worm-like chains are characterized by a persistence length, q. Polymers of types a-d in Fig. 1 can all form liquid crystalline solutions under appropriate conditions. The final type of chain, the random coil, is not expected to form liquid crystalline solutions.