# Microrheological study on the entanglement dynamics of salt-free polyelectrolyte solutions in the semidilute entangled regime

## TL;DR

This study explores how salt-free polyelectrolyte solutions behave when polymer strands become entangled, revealing a transition to neutral polymer behavior at specific concentrations and chain lengths.

## Contribution

The study identifies a crossover in behavior of salt-free polyelectrolytes at a critical concentration and polymer length, supported by experimental validation of the Dobrynin model.

## Key findings

- A crossover from polyelectrolyte-like to neutral polymer-like behavior occurs at cD ~ 0.3 M and N* ~ 6000.
- Scaling relationships of entanglement parameters align with the Dobrynin model predictions.
- DWS microrheology effectively probes complex rheological behavior in polyelectrolyte systems.

## Abstract

We investigate the entanglement dynamics of salt-free aqueous solutions of poly(sodium styrenesulfonate) (NaPSS) across a range of molecular weights, focusing on the semidilute entangled regime. By combining conventional bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we characterize key parameters, including the entanglement concentration, plateau modulus, reptation time, and Rouse time of entanglement strands. A clear crossover from polyelectrolyte-like to neutral polymer-like behavior is identified as the degree of polymerization decreases, corresponding to a critical monomer concentration cD ~ 0.3 M and a critical degree of polymerization N* ~ 6000. The experimental scaling relationships closely agree with the predictions from the Dobrynin model. Our findings provide new insights into the long-standing debate on the entanglement dynamics of polyelectrolytes and establish a framework for analyzing and controlling the solution properties of salt-free polyelectrolytes in the semidilute entangled regime. Moreover, they demonstrate the power of DWS microrheology for probing complex rheological behavior in polyelectrolyte systems.

The entanglement dynamics of salt-free aqueous solutions of poly(sodium styrenesulfonate) was investigated using conventional bulk shear rheometry and diffusing wave spectroscopy microrheometry. Our scaling analysis of the entanglement concentration, plateau modulus, and relaxation time revealed a clear crossover from polyelectrolyte-like to neutral polymer-like behavior at a critical monomer concentration cD ~ 0.3 M and a critical degree of polymerization N* ~ 6000. We also found that the polymer concentration and molecular weight dependence of the tested entanglement parameters showed good agreement with the Dobrynin model.