Orientation-Dependent Interactions in Polymer Systems. 4. Chain-Length Dependence of the Nematic-Isotropic Transition Behavior of Thermotropic Semiflexible Polymers

The nematic-isotropic transition behavior of semiflexible polymers in the bulk was studied on the basis of three typical models of orientation-dependent interactions (the Onsager-Kimura-type mean-field model, the lattice version of the Onsager model, and the Maier-Saupe-type soft interaction model) and two polymer models (the wormlike chain and the freely jointed chain with randomly distributed joints). The critical value of x = q/D required to stabilize the nematic phase was evaluated as a function of m = L/q for various combinations of the models, where L, q, and D are the contour length, the persistence length, and the diameter, respectively, of the chain. Even though x and x_∞, the value of x at L → ∞, strongly depended on the models, the predicted ln(x/x_∞) vs m relations were reasonably model-insensitive, offering a hopefully quantitative interpretation for the known dependence of the transition temperature T_i on chain length. (Note that q and hence x is a function of temperature.) Like T_i, the enthalpy change of transition was predicted to increase with L, approaching a constant value for large L. This behavior originates in the conformational change of semiflexible polymers and is not a characteristic of rigid rodlike molecules.