Understanding dynamics of looping of a long chain polymer in solution: Wilemski-Fixman Approach

TL;DR

This paper presents a theoretical analysis of the looping time of long polymer chains in solution using the Wilemski-Fixman approach, highlighting how various parameters influence the looping dynamics.

Contribution

It applies the Wilemski-Fixman method to derive the dependence of looping time on polymer length, bond length, and relaxation time for long chains in solution.

Findings

Looping time depends on polymer length, bond length, and relaxation time.

Theoretical framework models end-to-end dynamics with a Smoluchowski-like equation.

Results provide insights into how parameters affect polymer looping in solvents.

Abstract

We investigate theoretically the end-to-end looping time of a long chain polymer molecule immersed in a solvent. The dynamics of the end-to-end distance is governed by a Smoluchowski-like equation of a particle moving under the influence of a parabolic potential in presence of a Dirac delta sink of arbitrary strength and location. Using Wilemski-Fixman [ G. Wilemski and M. Fixman, J. Chem. Phys. {\bf 60}, {\it 866} (1974)] approach we calculate the looping time for a long chain molecule immersed in a solvent. We find that looping time varies with several parameters such as length of the polymer (N), bond length (b) and the relaxation time ${\tau_R}$.