Ring polymers in crowded environment: conformational properties

TL;DR

This paper investigates how structural obstacles in disordered environments affect the size and shape of flexible ring polymers, providing quantitative estimates of their conformational properties using renormalization techniques.

Contribution

It introduces a theoretical analysis of ring polymer conformations in disordered environments with correlated impurities, extending understanding of their size characteristics.

Findings

Size ratio of ring to linear polymers increases with disorder strength.

Quantitative estimates of gyration and spanning radii in disordered environments.

Effective size and anisotropy of ring polymers are significantly influenced by environmental disorder.

Abstract

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law \sim r^{-a} is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius $\langle R_{g\,{\rm ring}} \rangle$ and spanning radius $\langle R_{1/2\,{\rm ring}} \rangle$ of typical ring polymer conformation up to the first order of double \varepsilon=4-d, \delta=4-a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to $\langle R^2_{g\,{\rm ring}} \rangle / \langle R^2_{g\,{\rm chain}} \rangle =\frac{1}{2} \left(1+\frac{13}{48}\delta \right)$.