Escape transition of a polymer chain from a nanotube: how to avoid spurious results by use of the force-biased pruned-enriched Rosenbluth algorithm

TL;DR

This paper introduces a force-biased PERM algorithm to accurately study the escape transition of a polymer chain from a nanotube, overcoming sampling issues of standard methods and enabling analysis of large systems.

Contribution

A novel force-biased PERM algorithm is proposed to improve sampling of polymer escape states in confined geometries, addressing limitations of traditional Monte Carlo methods.

Findings

Successfully simulated chains up to N=18000 monomers

Accurately estimated free energy, end-to-end distance, and order parameters

Demonstrated the algorithm's potential for other polymer phase transition problems

Abstract

A polymer chain containing $N$ monomers confined in a finite cylindrical tube of diameter $D$ grafted at a distance $L$ from the open end of the tube may undergo a rather abrupt transition, where part of the chain escapes from the tube to form a "crown-like" coil outside of the tube. When this problem is studied by Monte Carlo simulation of self-avoiding walks on the simple cubic lattice applying a cylindrical confinement and using the standard pruned-enriched Rosenbluth method (PERM), one obtains spurious results, however: with increasing chain length the transition gets weaker and weaker, due to insufficient sampling of the "escaped" states, as a detailed analysis shows. In order to solve this problem, a new variant of a biased sequential sampling algorithm with re-sampling is proposed, force-biased PERM: the difficulty of sampling both phases in the region of the first order transition with the correct weights is treated by applying a force at the free end pulling it out of the tube. Different strengths of this force need to be used and reweighting techniques are applied. Using rather long chains (up to N=18000) and wide tubes (up to D=29 lattice spacings), the free energy of the chain, its end-to-end distance, the number of "imprisoned" monomers can be estimated, as well as the order parameter and its distribution. It is suggested that this new algorithm should be useful for other problems involving state changes of polymers, where the different states belong to rather disjunct "valleys" in the phase space of the system.