On the location of the surface-attached globule phase in collapsing polymers

TL;DR

This paper explores the existence and precise location of the Surface-Attached Globule (SAG) phase in lattice models of collapsing polymers attached to a wall, providing Monte Carlo evidence and discussing boundary scenarios.

Contribution

It offers the first Monte Carlo evidence supporting the existence of the SAG phase and analyzes potential boundary locations for this surface phase in polymer models.

Findings

Monte Carlo simulations up to length 256 support SAG phase existence

The surface phase boundary may lie along the zero wall interaction line

No new phase boundary curve is necessary for the SAG phase

Abstract

We investigate the existence and location of the surface phase known as the "Surface-Attached Globule" (SAG) conjectured previously to exist in lattice models of three-dimensional polymers when they are attached to a wall that has a short range potential. The bulk phase, where the attractive intra-polymer interactions are strong enough to cause a collapse of the polymer into a liquid-like globule and the wall either has weak attractive or repulsive interactions, is usually denoted Desorbed-Collapsed or DC. Recently this DC phase was conjectured to harbour two surface phases separated by a boundary where the bulk free energy is analytic while the surface free energy is singular. The surface phase for more attractive values of the wall interaction is the SAG phase. We discuss more fully the properties of this proposed surface phase and provide Monte Carlo evidence for self-avoiding walks up to length 256 that this surface phase most likely does exist. Importantly, we discuss alternatives for the surface phase boundary. In particular, we conclude that this boundary may lie along the zero wall interaction line and the bulk phase boundaries rather than any new phase boundary curve.