Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

TL;DR

This paper models star copolymers with chemically distinct arms using self-avoiding walks, analyzing their adsorption-desorption behavior under force, and provides rigorous results on free energy and phase transitions.

Contribution

It introduces a rigorous self-avoiding walk model for star copolymers with diverse monomers and analyzes their phase diagrams and transition orders.

Findings

Derived the free energy of the system.

Established the general phase diagram structure.

Identified the nature of phase transitions.

Abstract

We consider a model of star copolymers, based on self-avoiding walks, where the arms of the star can be chemically distinct. The copolymeric star is attached to an impenetrable surface at a vertex of unit degree and the different monomers constituting the star have different interaction strengths with the surface. When the star is adsorbed at the surface it can be desorbed by applying a force, either at a vertex of degree 1 or at the central vertex of the star. We give some rigorous results about the free energy of the system and use these to establish the general form of the phase diagrams, and the orders of certain phase transitions in the system. We also consider the special case of spiders, ie stars constrained to have all degree 1 vertices in the surface.