Loop formation in polymers in crowded environment

TL;DR

This paper investigates how structural defects in a disordered environment affect the probability of loop formation in long flexible polymers, revealing that defects decrease loop formation likelihood.

Contribution

It provides a theoretical analysis of loop formation probabilities in polymers within correlated disordered environments using renormalization techniques.

Findings

Structural defects reduce loop formation probability.

Critical exponents depend on defect correlation and loop position.

Quantitative scaling relations for loop formation probabilities.

Abstract

We analyze the probability of a single loop formation in a long flexible polymer chain in disordered environment in $d$ dimensions. The structural defects are considered to be correlated on large distances $r$ according to a power law $\sim r^{-a}$. Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities of loop formation with various positions along the chain as function of loops length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.