Olympic Gels: Concatenation and Swelling

Concatenation and equilibrium swelling of Olympic gels, which are composed of entangled cyclic polymers, is studied by Monte Carlo Simulations. The average number of concatenated molecules per cyclic polymers, $f_n$, is found to depend on the degree of polymerization, $N$, and polymer volume fraction at network preparation, ${\phi}_0$, as $f_n ~ {\phi}_0^{{\nu}/(3{\nu}-1)}N$ with scaling exponent ${\nu} = 0.588$. In contrast to chemically cross-linked polymer networks, we observe that Olympic gels made of longer cyclic chains exhibit a smaller equilibrium swelling degree, $Q ~ N^{-0.28} {\phi}_0^{-0.72}$, at the same polymer volume fraction ${\phi}_0$. This observation is explained by a desinterspersion process of overlapping non-concatenated rings upon swelling, which is tested directly by analyzing the change in overlap of the molecules upon swelling.