Effect of Ring Rigidity on the Statics and Dynamics of Linear Catenanes

Abstract

We used molecular dynamics simulations to investigate the statics and dynamics of poly­[n]­catenanes for different bending rigidities of the constituent rings. We show that stiffer rings yield catenanes with more extended and, at the same time, more flexible backbones. The softening of the backbone reflects the decreasing steric interactions of catenated rings as their shape becomes more oblate due to increased rigidity. The internal dynamics of catenanes is affected too. Going from flexible to rigid rings causes a several-fold slowing of different processes, from segmental rotations and size fluctuations to Rouse modes. Finally, by considering the statics and dynamics of crowded solutions of catenanes, we isolate another emergent property controlled by the rigidity of the rings. Specifically, we show that catenanes with rigid rings hinder each other’s motion more than those with flexible rings. Thus, in equally crowded solutions, the diffusion coefficient is smaller for catenanes with stiffer rings.

Linear Catenanes in Channel Confinement

“…We also note that a similarly short correlation range was previously reported for the influence of mechanical bonding on the statics and dynamics of free catenanes. 15,24,25 The data of Figure 6 thus show that the nematic ordering of rings with even and odd indices persists in channels and is largest at the onset of strong confinement (D ∼ 9σ). At these channel widths, concatenated rings themselves start to elongate, their shape changing from quasi-planar to uniaxially anisotropic, and the principal direction of the gyration tensor is increasingly aligned to the channel axis (Supporting Information).…”

“…In addition, different models have shown that, at small scales, the Rouse-like relaxation modes seen in linear polymers are replaced by slower ones in mechanically bonded chains of rings. 11,15,23,24 These ongoing efforts have significantly advanced our understanding of isolated and interacting catenanes in bulk. 15,16,22−27 However, except for Hopf links, 28,29 no characterization exists yet of catenanes in spatial confinement, despite it being a natural avenue considering the body of knowledge available for conventional polymers in channels and slits.…”

“…The comparisons helped establish how the size and number of constitutive rings differently contribute to the scaling of the gyration radius, , often introducing significant corrections to the asymptotic scaling expected for equivalent self-avoiding chains. In addition, different models have shown that, at small scales, the Rouse-like relaxation modes seen in linear polymers are replaced by slower ones in mechanically bonded chains of rings. ,,, …”

“…These ongoing efforts have significantly advanced our understanding of isolated and interacting catenanes in bulk. ,,− However, except for Hopf links, , no characterization exists yet of catenanes in spatial confinement, despite it being a natural avenue considering the body of knowledge available for conventional polymers in channels and slits. These systems present different metric scaling regimes depending on how the confining region width compares with the polymer length scales, such as thickness, contour length, and persistence length. − Examining catenanes in confinement thus provides a unique opportunity to study the impact of additional degrees of freedom, such as changes in ring size and mechanical bonds, on the overall metric and dynamic properties.…”

To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers

“…Varying the stiffness also affects properties of rings in films, 70,71 melts 56 or catenanes. 72 To understand such complex, many-body effects, we have to at first understand the simpler two-body problem.…”