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

Abstract

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., ⟨Rg2⟩~N2ν with ν≈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, ⟨λ1⟩/⟨λ3⟩, ⟨λ1⟩/⟨λ2⟩ and the mean asphericity, ⟨A⟩, and the mean prolateness, ⟨P⟩ of polycatenanes are smaller than those of bonded-ring polymers. In regime of n~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.