Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions

TL;DR

This paper develops a quantitative theory for dilute salt-free polyelectrolyte solutions, revealing conditions for chain stretching or collapse and identifying a first-order phase transition caused by counterion condensation.

Contribution

It introduces a new theoretical framework describing chain behavior and phase transitions in dilute polyelectrolyte solutions based on electrostatic interactions.

Findings

Polyelectrolytes can undergo strong stretching or compression depending on electrostatic strength.

A first-order phase transition occurs with polymer collapse due to counterion condensation.

The theory predicts specific scaling laws for polymer size in different regimes.

Abstract

A new quantitative theory for polyelectrolytes in salt free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension R_g\sim l_B^{1/3}N, where l_B is the Bjerrum length and N is the number of the chain segments) or strong compression (with R_g\sim l_B^{-1/2}N^{1/3}). A strong polymer collapse occurs as a first-order phase transition due to accompanying counterion condensation.