The entropy of high polymer solutions. Generalization of formulae

Abstract The theory of Huggins is extended so as to include application to molecules containing rings and crosslinks. At the same time the definition of Guggenheim's parameter q is slightly revised in such a way that also back bending of flexible and particularly of branched molecules is accounted for as ring formation. It is shown that Huggins' and Guggenheim's equations are not applicable to molecules containing rings, as they lead to inconsistencies when q differs from its maximum value for a ring‐free molecule. The inconsistency is removed by an improved calculation of the number of configurations of the molecules on the lattice. The number of factors accounting for the fact that a newly placed submolecule is known to be a neighbour of an already placed submolecule is increased. Instead of taking this number equal to the number of submolecules to be placed, viz. r‐1, it must be taken equal to the number of neighbours already placed, viz. 1/2 z(r ‐ q ). In this way an equation is obtained which is applicable to molecules of any degree of ring formation or back bending, and which can be easily generalized to mixtures of any kind of molecules. The formula for the entropy of the solvent derived from this theory contains two parameters even in the athermal case. From a qualitative consideration of these parameters it is seen that flexibility and particularly branching will reduce the deviations from Raoult's law markedly, and thus the ununderstandable insensitivity of the older formulae with respect to these structural factors is removed.