Nonlinear Elasticity of Single Linear Polycatenane: Emergence of Stress-Softening

Single-chain elasticity is one of the most fundamentally important topics in polymer physics, which underlies many processes and properties and functions of synthetic and biological polymer systems. Following our recently computational study on the linear elasticity of linear polycatenane (or named [n]catenane with n being the number of concatenated rings) [Chen, Y. X. Topological Catenation Enhances Elastic Modulus of Single Linear Polycatenane. Chin. J. Polym. Sci. 2023, 41, 1486–1496], its nonlinear elasticity was further investigated by extensive molecular dynamics simulations based on the Kremer–Grest model, endeavoring to unravel and understand unique features, if existing, of the elastic response of the linear polycatenane in the nonlinear regime. To this end, the single-chain elasticity of [n]bonded-ring polymers was studied as well for comparison. It is concluded from our simulation results that there are three characteristic regimes of the nonlinear elasticity of the catenane polymer, where two of them exhibit stress-stiffening behavior (i.e., the elastic modulus increases with increasing stretching force). Specifically, we found that elastic modulus, E, of [20]catenane with a total chain length N = 480 seems to vary with the stretching force, Fx, following a scaling law E ∼ Fxα with α ≈ 1.0 at relatively low forces and α ≈ 1.5 at high forces. These stress-stiffening behaviors have also been seen in the case of its stretched [20]bonded-ring polymer counterparts. Molecular origin of these two stress-stiffening responses could be ultimately attributed to the orientational correlation of the largest principal axes of the two neighboring rings’ gyration ellipsoids, which makes the polycatenane semiflexible. More interestingly, topological catenation leads to the emergence of the stress-softening behavior in the stretched linear polycatenane, which is absent in the single-chain entropic elasticity not only of traditional linear polymers but also in the case of its bonded-ring counterpart. It turns out that the emergence of stress-softening is attributed to the ring’s rotational sliding around its concatenated one, which occurs if (a) the catenated ring is of a noticeably oblate (i.e., disk-like) shape and (b) the ring chain length is large enough so that sliding of a ring on its concatenated one can be possible.