We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many-body effects of topological origin in dense systems. We predict that although the compact statistics with the Flory exponent $\nu =1/3$ is realized for very long chains, most practical cases fall into the crossover regime with the apparent exponent $\nu \simeq 2/5$ during which the system evolves toward a topological dense-packed limit.

• Received 8 October 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.167802