Effects of topological constraints on linked ring polymers in solvents of varying quality

We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their theta-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that R-g similar to m(mu)n(nu) and we find that mu = 0.65 +/- 0.02 and nu = 0.60 +/- 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of mu = 16/25 and nu = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of N-L topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its theta-temperature in comparison to isolated linear and ring chains with the following ordering: T theta catenane > T theta linear > T theta ring. Finally, we show that the presence of links similarly raises the theta-temperature of a single linked ring in comparison to an unlinked one, bringing its theta-temperature close to the one of a poly[n]catenane.