Pinning and unbinding of (ideal) polymers from a wedge corner

TL;DR

This paper investigates how ideal polymers can become pinned or unbound from wedge corners, revealing that the unbinding transition exhibits angle-dependent singular behavior, supported by analytical and numerical methods.

Contribution

It introduces a detailed analysis of polymer unbinding from wedge corners, highlighting the continuous variation of critical exponents with the wedge angle.

Findings

Localization length diverges with angle-dependent exponent

Numerical results confirm analytical predictions

Unbinding transition behavior varies continuously with wedge angle

Abstract

A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.