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Motivated by recent observations that non-concatenated ring polymers in theirdense solution exhibit a glass-like dynamics, we propose a free volumedescription of the motion of such rings based on the notion of topologicalvolume. We first construct a phenomenological free energy which enables one toqnaitify the degree of topological crowding measured by the coordinationnumber. Then we pinpoint a key role of the cooperative dynamics of neighboringrings, which is responsible for an anomalous dependence of the globalstructural relaxation (diffusion) time on ring length. Predictions on molecularweight dependence of both static (ring size, coordination number) and dynamic(relaxation time, diffusion coefficient) quantities are in very good agreementwith reported numerical simulations. Throughout the discussion, theentanglement length $N_e$ is assumed to be a unique characteristic length forthe topological constraint, hence, all the physical quantities are universallydescribed in terms of the rescaled chain length $N/N_e$. Finally, we discusshow the dense solution of rings is analogous yet different from ordinary glassysystems.

Topological free volume and quasi-glassy dynamics in melt of ring polymers