The mean square radius of gyration for ring polymers in dilute solution

Abstract

We review some recent theoretical studies on the mean square radius of gyration for ring polymers in dilute solution at a temperature close to the 8 temperature of the corresponding linear polymers. Near the 8 temperature, the topological effect becomes enhanced so that the mean square radius of gyration is much larger than that of phantom ring chains. We call the phenomenon topological swelling. For ring polymers in good solvents near the 8 temperature we give a phenomenological explanation for the topological swelling. For ring polymers in the 8 solvent we suggest that the scaling behavior of ring polymers shows novel criticality. Here, we recall that the topological constraint plays a central role in the theoretical random models of real ring polymers. ©2011, The Society of Polymer Science, Japan.