Polymer escape from a confining potential

TL;DR

This study investigates how polymers escape from a confining potential well, revealing a non-monotonic escape rate for self-avoiding polymers and highlighting the importance of polymer shape in transition state definition.

Contribution

It introduces a detailed analysis of polymer escape rates using path integral hyperdynamics and emphasizes the significance of polymer shape in accurately modeling escape processes.

Findings

Escape rate has a minimum at intermediate polymer length for self-avoiding chains.

Longer self-avoiding polymers exhibit increased escape rates due to crowding effects.

Simple centroid-based models overestimate escape rates, especially for longer polymers.

Abstract

The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were calculated using the path integral hyperdynamics method to evaluate the escape rate. A minimum is found in the rate for self-avoiding polymers of intermediate length while the escape rate decreases monotonically with polymer length for ideal polymers. The increase in the rate for long, self-avoiding polymers is ascribed to crowding in the potential well which reduces the free energy escape barrier. An effective potential curve obtained using the centroid as an independent variable was evaluated by thermodynamic averaging and Kramers rate theory then applied to estimate the escape rate. While the qualitative features are well reproduced by this approach, it significantly overestimates the rate, especially for the longer polymers. The reason for this is illustrated by constructing a two-dimensional effective energy surface using the radius of gyration as well as the centroid as controlled variables. This shows that the description of a transition state dividing surface using only the centroid fails to confine the system to the region corresponding to the free energy barrier and this problem becomes more pronounced the longer the polymer is. A proper definition of a transition state for polymer escape needs to take into account the shape as well as the location of the polymer.