Statistical mechanical theory of polymers. III. Equation of state for the hard sphere model of a single ring polymer

Thermodynamic functions for a single ring polymer with hard-sphere binary intersegmental interactions are studied. The integral equation of the binary intersegmental correlation function g(2)(R) developed earlier is expressed in terms of a parameter λ in a manner analogous to Kirkwood, Maun, and Alder for the case of fluids. The parameter λ is related to the coefficient of expansion σ (and therefore density) by a thermodynamic identity. The binary intersegmental correlation function g(2)(R) is now computed numerically by an iterative procedure. Numerical values of various thermodynamic functions are computed. The data are in qualitative agreement with Monte Carlo calculations of Mazur and McCrackin at high temperatures.