The coil-globule transition of confined polymers

TL;DR

This study investigates how confinement between parallel walls affects the coil-globule transition of polymers, revealing an increase in theta temperature with wall separation and unexpected long transient behaviors in scaling properties.

Contribution

It provides new insights into the effects of geometric confinement on polymer phase transitions, challenging previous claims and exploring scaling behaviors in confined environments.

Findings

Theta temperature increases with wall separation D.

Observed long transient scaling behaviors before reaching asymptotic regimes.

Found that R scales less rapidly than N^{1/2} at the theta point, contrary to expectations.

Abstract

We study long polymer chains in a poor solvent, confined to the space between two parallel hard walls. The walls are energetically neutral and pose only a geometric constraint which changes the properties of the coil-globule (or "$\theta$-") transition. We find that the $\theta$ temperature increases monotonically with the width $D$ between the walls, in contrast to recent claims in the literature. Put in a wider context, the problem can be seen as a dimensional cross over in a tricritical point of a $\phi^4$ model. We roughly verify the main scaling properties expected for such a phenomenon, but we find also somewhat unexpected very long transients before the asymptotic scaling regions are reached. In particular, instead of the expected scaling $R\sim N^{4/7}$ exactly at the ($D$-dependent) theta point we found that $R$ increases less fast than $N^{1/2}$, even for extremely long chains.