# Free-energy cost of localizing a single monomer of a confined polymer

## TL;DR

This paper introduces a Monte Carlo simulation method to compute the free-energy cost of localizing a single monomer in a confined polymer, analyzing how it varies with geometry, position, and polymer length.

## Contribution

The paper presents a simple, adaptable Monte Carlo approach for calculating localization free energies in confined polymers, with detailed analysis across different geometries and positions.

## Key findings

- Free energy depends on cavity size and shape.
- Localization position influences free-energy cost.
- Results align with scaling theories and simple models.

## Abstract

We describe a simple Monte Carlo simulation method to calculate the free-energy cost of localizing a single monomer of a polymer confined to a cavity. The localization position is chosen to be on the inside surface of the confining cavity. The method is applied to a freely-jointed hard-sphere polymer chain confined to cavities of spherical and cubic geometries. In the latter case we consider localization at a corner and at the center of a face of the confining cube. We consider cases of end-monomer localization both with and without tethering of the other end monomer to a point on the surface. We also examine localization of monomers at arbitrary position along the contour of the polymer. We characterize the dependence of the free energy on the cavity size and shape, the localization position, and the polymer length. The quantitative trends can be understood using standard scaling arguments and use of a simple theoretical model. The results are relevant to those theories of polymer translocation that focus on the importance of the free-energy barrier as the translocation process requires an initial localization of a monomer to the position of a nanopore.