Topological distribution functions of ring polymers II. Theory and computer simulation

Reliability of the methods used in constructing a topological rubber-elasticity theory [K. Iwata, J. Chem. Phys. 76, 6363, 6375 (1982)] is examined in two-ring-polymer systems. This system has been studied in part I [K. Iwata and T. Kimura, J. Chem. Phys. 74, 2039 (1981)], where the ‘‘topological moment (or the first) method’’ has been presented. In this paper, (i) another new method called ‘‘contact series expansion (or the second) method’’ is proposed, (ii) computer simulations for 6-choice-simple-cubic-lattice-model polymers are performed, and (iii) it is found that the first method leads to a good agreement in topological distribution functions, while the second one leads to a good agreement in topological moments with the simulations.