Chain Stiffness and the Lattice Theory of Polymer Phases

General formulas for the thermodynamic properties of amorphous polymer phases are obtained from statistical mechanics, with the aid of the lattice model, in a manner which avoids the use of restrictive assumptions concerning the nature of the individual polymer chains. Certain results, such as prediction of a second-order transition for systems of semiflexible chains and the Flory-Huggins formula for the entropy of mixing with monomeric solvent, are thus shown to be independent of the precise nature of the model assumed for the polymer chains. More complete information may be obtained by application of the general formulas to models descriptive of the molecular chains in question. As an example, the results of Flory for semiflexible linear chains whose stiffness arises exclusively from intramolecular nearest neighbors are obtained as a special case. (The conventional thermodynamic properties of polydisperse systems of chains of this type are shown to depend on the number average molecular weight.)