Statistical Mechanics of Sterically Interacting Ring Polymers

Abstract

This paper derives a new model describing sterically interacting polymers in a solution, a finite fraction of which forms closed rings. The model is closely related to a magnetic partition function for classical spin model, but vanishing limit (n→0) for the internal degrees of freedom is not assumed. For given average molecular weights and amounts of ring and chain fractions, the number of spin components is uniquely determined. The osmotic pressure and the single chain end-to-end distance are obtained in the case of an athermal solvent. The effect of ring formation is discussed.