The Swelling of Olympic Gels

The swelling equilibrium of Olympic gels is studied by Monte Carlo Simulations. We observe that gels consisting of flexible cyclic molecules of a higher degree of polymerization $N$ show a smaller equilibrium swelling degree $Q\propto N^{-0.28}\phi_{0}^{-0.72}$ for the same monomer volume fraction $\phi_{0}$ at network preparation. This observation is explained by a disinterpenetration process of overlapping non-concatenated polymers upon swelling. In the limit of a sufficiently large number of concatenations per cyclic molecule we expect that the equilibrium degree of swelling becomes proportional to $\phi_{0}^{-1/2}$ independent of $N$. Our results challenge current textbook models for the equilibrium degree of swelling of entangled polymer networks.