Topological distribution functions and the second virial coefficients of ring polymers

A new method (a topological moment method) is presented for treating statistical problems of ring polymer chains of which the topological state (Gauss linking coefficient) is prescribed. It is shown that the topological interaction among ring polymers formally resembles the excluded volume effect among linear polymers. A ’’topological parameter γ’’ which corresponds to the binary cluster integral β in the excluded volume problem is newly introduced for representing the strength of the topological interaction among submolecules. The parameter γ is given as a function of bond length, bond angle, internal-rotational potential, and of interaction potentials among chain elements. Analytical expressions for the distribution function of the intermolecular distance and the second virial coefficient are derived and they are computed numerically.