Topological catenation induced swelling of ring polymers revealed by molecular dynamics simulation

Abstract Equilibrium conformational properties of a ring polymer (named by ‘inner ring’) simultaneously concatenated with a varying number of outer rings in a ‘flower’-shaped polymer catenane are explored by molecular dynamics simulations. Two different cases have been considered. In Case I, the excluded volume interactions between the outer rings are absent in a polymer catenane, while they are present in Case II. Results demonstrate that, compared to an isolated ring polymer, size and shape properties of the same, inner ring in a polymer catenane can be greatly modified by the catenation topology in both Cases. It is concluded that the topological catenation can induce a swelling of the inner ring in a catenane compared to the same ring in isolation. Importantly, scaling relationships between the swelling degree, f sw , of the inner ring and number of the outer rings, n , have been established in both Case I and Case II, f sw = a n α , where the prefactor a and scaling exponent α are all predominantly dependent on molecular-weight ratio of the inner to outer rings in catenane. Besides, swelling of inner ring in a catenane of Case II is more pronounced than the same inner ring in a catenane of Case I. The mean asphericity of the inner ring is slightly increased due to the catenation topology, while its mean prolateness is remarkably modified by the catenation topology. The inner ring in a catenane becomes more oblate, compared to the same ring in isolation, with increasing either number or molecular weight of the outer rings in the catenane. Profiles of the mean prolateness changes of the inner ring from those of the same isolated ring with respect to number of the outer rings are also mainly controlled by the molecular-weight ratio of the inner to outer rings.