Abstract
We derive and introduce anisotropic effective pair potentials to coarse-grain solutions of semiflexible ring polymers of various lengths. The system has been recently investigated by means of full monomer-resolved computer simulations, revealing a host of unusual features and structure formation, which, however, cannot be captured by a rotationally averaged effective pair potential between the rings’ centers of mass [BernabeiM.; Soft Matter2013, 9, 1287]. Our new coarse-graining strategy is to picture each ring as a soft, penetrable disk. We demonstrate that for the short- and intermediate-length rings the new model is quite capable of capturing the physics in a quantitative fashion, whereas for the largest rings, which resemble flexible ones, it fails at high densities. Our work opens the way for the physical justification of general, anisotropic penetrable interaction potentials.
Highlights
By the simple process of joining the ends of a linear polymer chain, one obtains a ring polymer (RP).1 While the architecture of ring polymers is very simple, they differ in many interesting ways from their linear counterparts and are the subject of active research in physics, biology, chemistry, and even pure mathematics
We have introduced a minimal anisotropic model to coarsegrain ring polymers with a finite bending rigidity as soft, penetrable disks
Whereas this is valid more for N = 20 and N = 50, which have a contour length to persistence length ratio of N/sp ∼ 2.7 and 6.7, respectively, some important features, such as the penetration of elongated rings in columns formed by oblate rings, are suppressed or even lost in the effective description, as genuine many-body effects come into play
Summary
By the simple process of joining the ends of a linear polymer chain, one obtains a ring polymer (RP). While the architecture of ring polymers is very simple, they differ in many interesting ways from their linear counterparts and are the subject of active research in physics, biology, chemistry, and even pure mathematics. For the large intermediate density domain between dilute solutions and melts, there are relatively few theoretical results despite the practical relevance of this regime for instance in the field of biophysics, where the topological interactions between chromatin loops plays a crucial role in the creation of chromosome territories.− A fruitful and modern approach for the economic description and simulation of macromolecules in this regime is the method of coarse-graining The idea behind this method is to bridge the time and length scales in the system by describing the macromolecules via an effective model with a reduced set of suitably chosen effective degrees of freedom (dof). Anisotropy is strong for rings with high bending stiffness or few monomers, as they have a strong tendency to orient with respect to other rings in their proximity This motivates us to introduce an anisotropic effective model for the description of semiflexible ring polymers in this article. In the Appendix, we explain the expansion of the anisotropic pair-correlation function of a system of two RPs, which contains all the information for calculating the effective potential, as a sum of suitably chosen basis functions
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