Statistical-Mechanical Theory of Polymers. I. An Integral Equation for the Excluded-Volume Effect

Abstract

Statistical mechanics of a single polymer in a continuous medium is considered. Partition function, the reduced distribution functions, and related statistical concepts are defined. Thermodynamic functions of the system are calculated in terms of the distribution functions. Finally, a Kirkwood‐Born‐Green integrodifferential equation is derived for the excluded‐volume effect, and its approximate solution for the case of a ringpolymer is given. The results show that the zeroth‐order approximate solution of the integral equation is equivalent to the self‐consistent approximation of Edwards and of Reiss. The mean‐square radius of gyration in this approximation varies as 4 3 power of the molecular weight.