# Heterogeneous morphology and dynamics of polyelectrolyte brush condensates in trivalent counterion solution

## TL;DR

This study uses simulations and theory to reveal how trivalent ions induce heterogeneous, micelle-like structures in polyelectrolyte brushes, with morphology and dynamics strongly dependent on ion concentration and system parameters.

## Contribution

It demonstrates the heterogenous collapse and slow dynamics of polyelectrolyte brushes induced by trivalent counterions, highlighting the role of ion concentration in morphology and relaxation behavior.

## Key findings

- Polymer collapse into micelle-like structures at specific ion concentrations.
- Maximum heterogeneity and slowest dynamics at 1:3 ion-to-charge ratio.
- Charge inversion leads to reswelling and more uniform brush morphology.

## Abstract

Recent experiments have shown that trivalent ion, spermidine$^{3+}$, can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of trivalent ions to polyelectrolyte charge. A further increase of trivalent ion concentration conducive to a charge inversion elicits modest reswelling and homogenizes the morphology of brush condensate. Our study provides a new insight into the origin of the diversity in DNA organization in cell nuclei as well as the ion-dependent morphological variation in polyelectrolyte brush layer of biological membranes.