Statistical Mechanics of Polymer Solutions. Parts I and II

Some contributions are made to the refining of the lattice model theory of Flory of chain polymer solutions by introducing the idea used in the recent theory of regular assembly that combinatory factor constructed in terms of multiple site clusters can be properly used to take long-range correlations between a given site and its far distant neighbors into account. In Part I, the combinatory factors of Flory and others in current use are reconstructed to exemplify the pseudo-assembly method which has been presented by Kikuchi and the present authors for an easy construction of combinatory factors of higher-order approximation for regular assembly, and to give a thorough understanding of the succeeding uses in Part II. In Part II, a refined theory of chain polymer solutions is developed. The final expressions for the entropy of dilution and the osmotic pressure depend on the flexibility and the degree of branching of the polymer chain, and give a better agreement with observed data even at high dilution.