Shapes of macromolecules in good solvents: field theoretical renormalization group approach

TL;DR

This paper uses the field theoretical renormalization group to analyze the universal shape properties of long polymer chains in porous environments, extending beyond scaling exponents to include shape observables like asphericity.

Contribution

It introduces a novel application of the renormalization group to study the shape of polymers in porous media, considering the effects of environmental obstacles characterized by a power-law correlation.

Findings

Estimated size ratio <R_e^2>/<R_G^2>

Calculated asphericity ratio 

Extended understanding of polymer shape in porous environments

Abstract

In this paper, we show how the method of field theoretical renormalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solvent in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats'ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) \sim r-a. We apply the field-theoretical renormalization group approach and estimate the size ratio <R_e^2>/<R_G^2 > and the asphericity ratio \hat{A}_d up to the first order of a double \epsilon=4-d, \delta=4-a expansion.