  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.
