Abstract
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.
Highlights
Ring polymers are the most characteristic prototype of topologically constrained molecules.[1]
Interest in ring polymers dates from many decades ago, as is witnessed, e.g., in three pioneering papers on the subject: in the work of Frank-Kamenetskii et al.,[2] the notion of the topological interaction between two rings has been introduced and analyzed quantitatively, which arises from the non-concatenation condition of the same; in the work of Grosberg et al.,[3] the crumpled globule model of rings in the melt has been put forward, making a strong distinction between the structures of linear- and ring-polymer melts; and nally, Obukhov et al.[4] have put forward an annealed lattice-animal picture of a ring polymer in a melt, deriving thereby novel scaling laws for the diffusion coefficient and the longest relaxation time of a ring, and thereby revising previous predictions.[5,6]
In 1993, Grosberg et al.[3] demonstrated that molecules that have a topological constraint appear to be able to survive longer in an out-of-equilibrium state that allows for more compact structures, hypothesizing that the long-lasting problem of packing of e.g., chromosomes in eukaryotes that could not be explained by packing of linear biopolymers could be solved by adding a topological constraint
Summary
A great deal of interest in ring polymers is motivated by their biological relevance. On the other hand, feature a particular form of self-organization in semidilute solutions, forming a disordered state of columnar clusters penetrated by other rings,[31] and displaying an unusual dynamic scenario in which the coherent and the incoherent correlation functions are decoupled from one another, resulting in a state that has been termed cluster glass.[32] It is evident, that the properties of topologically constrained molecules in the semi-dilute regime are extremely difficult to access, both via theoretical approaches and computational studies.
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