Statistical mechanical theory of polymers. II. Thermodynamic functions of a single ring polymer

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Abstract
Statistical thermodynamics of a single ring polymer with an intersegmental interaction is developed. Volume in this system is defined in terms of the mean‐square radius of gyration. The concept of compressed and expanded states of the polymer is developed by introducing a coefficient‐of‐expansion σ. In this way, the volume of the single polymer can be varied and change of free energy with this variation in volume can be studied. Tension is now defined as the infinitesimal change in free energy due to an infinitesimal change of volume, i.e., infinitesimal expansion of the system. The chemical potential is the change in free energy due to charging (or severing of) one of the segments of the polymer chain. Using these definitions and methods analogous to statistical mechanical theory of fluids, explicit expressions are derived for the equation of state as well as other thermodynamic properties in terms of the binary intersegmental correlation function g(2)(R) and the intersegmental interaction u (R). The techniques developed here are applicable to the study of gas–liquid type phase transitions observed in polymer solutions and Monte Carlo simulation experiments.

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