Aggregation Dynamics of Rigid Polyelectrolytes

TL;DR

This study uses large-scale molecular dynamics simulations to analyze how rigid polyelectrolytes aggregate, revealing that aggregate morphology depends on charge density and that the aggregation process follows a universal power-law decay independent of various parameters.

Contribution

It provides a detailed simulation-based analysis of aggregation dynamics, modeling the process with Smoluchowski coagulation equations and identifying universal behavior.

Findings

Aggregate morphology varies with charge density.

Number of aggregates decreases as a power law over time.

Aggregation is diffusion-limited and independent of certain parameters.

Abstract

Similarly-charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of such rigid polyelectrolytes are studied using large scale molecular dynamics simulations. We find that the morphology of the aggregates depends on the value of the charge density of the polymers. For values close to the critical value, the shape of the aggregates is cylindrical with height equal to the length of a single polyelectrolyte chain. However, for larger values of charge, the linear extent of the aggregates increases as more and more polymers aggregate.In both the cases, we show that the number of aggregates decrease with time as power laws with exponents that are not numerically distinguishable from each other, and are independent of charge density of the polymers, valency of the counterions, density, and length of the polyelectrolyte chain. We model the aggregation dynamics using the Smoluchowski coagulation equation with kernels determined from the molecular dynamics simulations, and justify the numerically obtained value of the exponent. Our results suggest that, once counterions condense, effective interactions between polyelectrolyte chains short-ranged and the aggregation of polyelectrolytes is diffusion-limited.