Cross linkage problems of polymers II. Dilute cross linked systems of polymers

Abstract

For pt. I, see ibid., vol. 3, no. 4, (1970) 739. The problem of the equation of state of n polymer chains each of length L, monomer length l, with m cross links between them, is studied. It is shown that this problem depends on two dimensionless coupling constants p=m/n and q=V/(n(Ll)³2/), i.e. the number of cross links per polymer, and the ratio of the specific volume per polymer to its 'natural' volume i.e. the cube of its mean square radius. The equation of state is derived. Polymer- polymer correlation functions which are of interest in light scattering experiments are discussed in the appendix.