Forcing Adsorption of a Tethered Polymer by Pulling

TL;DR

This paper analyzes a tethered polymer under pulling force using a directed walk model, deriving phase diagrams and revealing how force angle influences adsorption, including reentrance transitions in three dimensions.

Contribution

It provides an exact solution for the phase behavior of a tethered polymer under angled pulling forces, extending previous models to include non-vertical forces and three-dimensional analysis.

Findings

Force induces adsorption at angles below a critical value.

Transition shifts from second-order to first-order with vertical force component.

Reentrance transition occurs in three dimensions at small temperatures.

Abstract

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled.