The scaling behaviour of screened polyelectrolytes

TL;DR

This paper uses a field-theoretic RG approach to analyze the scaling behavior of a single screened polyelectrolyte chain in a polar solvent, revealing complex interplay of length scales and calculating key exponents.

Contribution

It introduces a field-theoretic RG framework for the Debye-Hückel chain, connecting it to a generalized Potts model and deriving explicit scaling exponents and chain length.

Findings

Identifies two interplaying length scales in the system.

Calculates critical exponents for the chain's behavior.

Provides explicit mean end-to-end length expression.

Abstract

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.