# Effects of non-pairwise repulsion on nanoparticle assembly

## TL;DR

This study uses Brownian dynamics simulations to explore how non-pairwise electrostatic interactions influence nanoparticle assembly, revealing differences from pairwise models and identifying conditions for ordered crystal formation.

## Contribution

It demonstrates the impact of non-pairwise electrostatic effects on nanoparticle assembly, highlighting differences from traditional pairwise models and identifying phases and stability conditions.

## Key findings

- Non-pairwise interactions lead to an amorphous phase in strongly charged particles.
- Ordered crystal formation occurs within a narrow parameter range.
- Many-body electrostatic interactions limit maximum density in assemblies.

## Abstract

Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures, or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous phase for strongly charged particles. This phase appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.