Force-induced desorption of $3$-star polymers: a self-avoiding walk model

TL;DR

This paper rigorously analyzes a lattice model of 3-star polymers under force, revealing a complex phase diagram with four distinct phases, including a novel mixed phase not seen in simpler models, relevant for AFM experiments.

Contribution

It provides a rigorous determination of the free energy and phase diagram of 3-star polymers under force, identifying a new mixed phase with unique properties.

Findings

Four phases identified: adsorbed, ballistic, mixed, free.

Mixed phase involves two arms adsorbed and one ballistic.

Phase boundaries are first order transitions.

Abstract

We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied force. We determine rigorously the free energy of the model in terms of properties of a self-avoiding walk, and show that the phase diagram includes 4 phases, namely a ballistic phase where the extension normal to the surface is linear in the length, an adsorbed phase and a mixed phase, in addition to the free phase where the model is neither adsorbed nor ballistic. In the adsorbed phase all three branches or arms of the star are adsorbed at the surface. In the ballistic phase two arms of the star are pulled into a ballistic phase, while the remaining arm is in a free phase. In the mixed phase two arms in the star are adsorbed while the third arm is ballistic. The phase boundaries separating the ballistic and mixed phases, and the adsorbed and mixed phases, are both first order phase transitions. The presence of the mixed phase is interesting because it doesn't occur for pulled, adsorbed self-avoiding walks. In an atomic force microscopy experiment it would appear as an additional phase transition as a function of force.