Investigation of the structure and thermodynamics of star-polymers in semi-dilute solution

TL;DR

This paper models the interactions, structure, and thermodynamics of semi-dilute solutions of star-polymers, revealing a logarithmic effective potential and deriving key physical properties from the structure factor.

Contribution

It introduces a new effective pair-potential for star-polymers and applies integral equation methods to analyze their structure and thermodynamics.

Findings

Effective pair-potential is logarithmic below a characteristic distance.

Structure factor computed for various densities.

Derived thermodynamic quantities like pressure and internal energy.

Abstract

In this work, we consider a semi-dilute solution of identical star-polymers, made of attached flexible long polymer chains of the same polymerization degree N. We first compute the effective pair-potential between star-polymers. Such a potential results from the excluded volume forces between monomers. We show that this potential is logarithmic, below some known characteristic distance, σ, depending on the number of attached chains per star-polymer, f, and volume fraction of polymers, φ0 . Beyond σ, the potential fails exponentially. Second, we investigate the structure and thermodynamics of these star-polymers. To this end, we use the integral equation method with the hybridized-mean spherical approximation. The numerical resolution of this equation gives the structure factor of the star-polymers, for various particle densities. Finally, the standard relationships between thermodynamics and structure enable us to deduce three physical quantities, namely the isotherm compressibility, pressure and internal energy, as functions of density.