# 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.

## Key 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 ${\tau_R}$.