Renormalized Field Theory of Polyelectrolyte Solutions

TL;DR

This paper develops a field-theoretic renormalization group approach to analyze dilute solutions of flexible, screened polyelectrolyte chains, deriving scaling laws for osmotic pressure considering chain size and screening effects.

Contribution

It introduces a novel RG formalism for polyelectrolyte solutions, explicitly accounting for two length-scales and providing scaling functions for various chain distributions.

Findings

Derived scaling dependence of osmotic pressure on chain density and screening length.

Mapped Debye-Hückel chains to a local field theory with two length-scales.

Provided explicit forms for monodisperse chain size distributions.

Abstract

We present a field-theoretic renormalization group (RG) analysis of a dilute solution of flexible, screened polyelectrolyte chains (Debye-Hueckel chains) in a polar solvent. We perform a virial expansion to calculate the scaling dependence of the Osmotic pressure on the chain density, chain size and screening length. The formalism is developed for general chain distributions and we give explicit forms for a monodisperse chain size distribution. We utilize the fact that a Debye-Hueckel chain may be mapped to a local field theory with TWO length-scales requiring the calculation of scaling functions as well as exponents to fully describe its scaling behaviour.