Mapping a Homopolymer onto a Model Fluid

TL;DR

This paper models a linear homopolymer using a grand canonical formalism and demonstrates its equivalence to simple fluid models, providing insights into polymer-fluid mappings and perturbative interactions.

Contribution

It introduces a formalism mapping a homopolymer onto a simple fluid model and explores the implications of this equivalence using diagrammatic and perturbative methods.

Findings

Polymer properties are equivalent to fluid equations like Ornstein-Zernike.

Perturbative pair interactions can be incorporated via Mayer expansion.

Mapping provides a new perspective on polymer-fluid analogies.

Abstract

We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and an external, confining, field are present, and then show how a general pair interaction can be introduced perturbatively, making use of a Mayer expansion. Through a diagrammatic analysis, we shall show how constitutive equations derived for the polymeric system are equivalent to the Ornstein-Zernike and P.Y. equations for a simple fluid, and find the implications of such a mapping for the simple situation of Van der Waals mean field model for the fluid.