Dimensional and shape properties of a single linear polycatenane: Effect of catenation topology

Effect of topological catenation on dimensional and shape properties of a single linear polycatenane (or [n] catenane), a polymer composed entirely of interlocking rings (macrocycles) arranged in a linear architecture, have been investigated by molecular dynamics simulation. The specific role of topological catenation in a polycatenane is revealed through comparing conformational properties of polycatenane to those obtained in a linear bonded-ring polymer, in which the same number of rings with the same ring size are connected via covalent bonds instead. We find that the mean-square radii of gyration of a polycatenane and a bonded-ring polymer obey the same scaling laws with a linear chain with respect to chain length, i.e., < R-g(2)> similar to N-2v with v approximate to 3/5, but topological catenation makes dimension of a polycatenane smaller than the corresponding bonded-ring polymer. On properties of ring dimensions, it is found that dimensions of the middle rings along a linear polycatenane are larger than those of the two edge rings located at two chain ends. Furthermore, the dimensional ratio of the middle to the edge rings remains a constant, i.e., independent of the number of rings along the chain, n, and the ring length. In contrast, rings along a bonded-ring polymer have the same dimensions, and their values remain approximately unchanged from the dimensions of the rings in isolation. Shape properties of the whole polycatenane and bonded-ring polymer are solely determined by their chain topologies and the number of rings along the chain, while the ring length doesn't play a role. Conclusion is that topological catenation makes shape of polycatenane chains more isotropic than their bonded-ring polymer counterparts. For instance, in the regime of n being small (e.g. n < 10), ratios of the average eigenvalues of gyration tensors, / , / and the mean asphericity, < A >, and the mean prolateness, < P > of polycatenanes are smaller than those of bonded-ring polymers. In regime of n similar to 10 or larger, these quantities approximately recover corresponding values of linear polymers. On shape properties of rings along a polycatenane, it is concluded that all the middle rings become more prolate than those edge rings, which isn't seen in the case of bonded-ring polymer.

Automated summary

The impact of topological catenation on the dimensional and shape properties of a single linear polycatenane has been investigated through molecular dynamics simulation. Topological catenation results in smaller dimensions and increased prolateness of middle rings compared to edge rings in the polycatenane structure. Furthermore, the shape properties of the polycatenane chains are found to be more isotropic compared to their bonded-ring polymer counterparts.