On the size and shape of excluded volume polymers confined between parallel plates

TL;DR

This paper investigates the size and shape of excluded volume polymers confined between parallel plates, using scaling arguments and a mean-field approach, and compares predictions with simulations and recent experimental observations.

Contribution

It introduces a mean-field model that predicts the polymer's size behavior in confined geometries, bridging different scaling regimes and aligning with simulation results.

Findings

Non-monotonic size behavior with plate separation predicted by scaling arguments.

Size in the plane parallel to plates is predicted to be monotonic, contrasting with experiments.

Good agreement between the mean-field theory and Langevin dynamics simulations.

Abstract

A number of recent experiments have provided detailed observations of the configurations of long DNA strands under nano-to-micrometer sized confinement. We therefore revisit the problem of an excluded volume polymer chain confined between two parallel plates with varying plate separation. We show that the non-monotonic behavior of the overall size of the chain as a function of plate-separation, seen in computer simulations and reproduced by earlier theories, can already be predicted on the basis of scaling arguments. However, the behavior of the size in a plane parallel to the plates, a quantity observed in recent experiments, is predicted to be monotonic, in contrast to the experimental findings. We analyze this problem in depth with a mean-field approach that maps the confined polymer onto an anisotropic Gaussian chain, which allows the size of the polymer to be determined separately in the confined and unconfined directions. The theory allows the analytical construction of a smooth cross-over between the small plate-separation de Gennes regime and the large plate-separation Flory regime. The results show good agreement with Langevin dynamics simulations, and confirm the scaling predictions.