Multi-blob coarse graining for ring polymer solutions.

We present a multi-scale molecular modeling of concentrated solutions of unknotted and non-concatenated ring polymers under good solvent conditions. The approach is based on a multi-blob representation of each ring polymer, which is capable of overcoming the shortcomings of single-blob approaches that lose their validity at concentrations exceeding the overlap density of the solution [A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter, 2010, 6, 2435]. By means of a first principles coarse-graining strategy based on analytically determined effective pair potentials between the blobs, computed at zero density, we quantitatively reproduce the single molecule and solution properties of a system with well-defined topological constraints. Detailed comparisons with the underlying, monomer-resolved model demonstrate the validity of our approach, which employs fully transferable pair potentials between connected and unconnected blobs. We demonstrate that the pair structure between the centers of mass of the rings is accurately reproduced by the multi-blob approach, thus opening the way for simulation of arbitrarily long polymers. Finally, we show the importance of the topological constraint of non-concatenation on the structure of the concentrated solution and in particular on the size of the correlation hole and the shrinkage of the rings as melt concentrations are approached.

Effective interactions of knotted ring polymers.

In the present article, we review recent computational investigations on the properties of ring polymers in solution. In particular, we focus on effective interactions obtained by means of coarse-graining techniques. We discuss the relative importance of the self-avoidance and the topological contributions in the qualitative features of the effective potential. We extend our previous results on identical rings and determine the effective potential between dissimilar ring polymers of distinct topology and size. The results obtained reveal the dramatic effects of the specific topology on the effective interactions, and hence in the structural correlations, of polymeric systems.

Cluster Glasses of Semiflexible Ring Polymers.

We present computer simulations of concentrated solutions of unknotted nonconcatenated semiflexible ring polymers. Unlike in their flexible counterparts, shrinking involves a strong energetic penalty, favoring interpenetration and clustering of the rings. We investigate the slow dynamics of the centers-of-mass of the rings in the amorphous cluster phase, consisting of disordered columns of oblate rings penetrated by bundles of prolate ones. Scattering functions reveal a striking decoupling of self- and collective motions. Correlations between centers-of-mass exhibit slow relaxation, as expected for an incipient glass transition, indicating the dynamic arrest of the cluster positions. However, self-correlations decay at much shorter time scales. This feature is a manifestation of the fast, continuous exchange and diffusion of the individual rings over the matrix of clusters. Our results reveal a novel scenario of glass formation in a simple monodisperse system, characterized by self-collective decoupling, soft caging, and mild dynamic heterogeneity.

Architecture-Induced Size Asymmetry and Effective Interactions of Ring Polymers: Simulation and Theory.

We investigate, by means of Monte Carlo simulations, the role of ring architecture and topology on the relative sizes of two interacting polymers as a function of the distance between their centers-of-mass. As a general rule, polymers swell as they approach each other, irrespectively of their topologies. For each mutual separation, two identical linear polymers adopt the same average size. However, unknotted rings at close separations adopt different sizes, with the small one being "nested" within the large one over long time intervals, exchanging their roles in the course of the simulation. For two rings of different architectures and identical polymerization degree, the knotted one is always smaller, penetrating the unknotted one. On the basis of these observations, we propose a phenomenological theory for the effective interactions between rings, modeling them as unequal-sized penetrable spheres. This simple approximation provides a good description of the simulation results. In particular, it rationalizes the non-Gaussian shape and the short-distance plateau observed in the effective potential between unknotted ring polymers and pairs of unequal-sized unknotted/knotted ones. Our results demonstrate the crucial role of the architecture on both the effective interactions and the molecular size for strongly interpenetrating polymers.

Effects of Knots on Ring Polymers in Solvents of Varying Quality.

We employ extensive computer simulations to investigate the conformations and the interactions of ring polymers under conditions of worsening solvent quality, in comparison with those for linear polymers. We determine the dependence of the Θ-temperature on knotedness by considering ring polymers of different topologies. We establish a clear decrease of the former upon changing the topology of the polymer from linear to an unknotted ring and a further decrease of the same upon introducing trefoil- or 5-fold knots but we find no difference in the Θ-point between the two knotted molecules. Our results are based on two independent methods: one considering the scaling of the gyration radius with molecular weight and one based on the dependence of the effective interaction on solvent quality. In addition, we calculate several shape-parameters of the polymers to characterize linear, unknotted, and knotted topologies in good solvents and in the proximity of the Θ-point. The shape parameters of the knotted molecules show an interesting crossover at a degree of polymerization that depends on the degree of knottedness of the molecule.