# Postponing the dynamical transition density using competing interactions

## TL;DR

This study investigates whether adding a longer-ranged repulsive interaction to short-ranged attractive spheres delays the dynamical arrest, testing a mean-field prediction through numerical simulations.

## Contribution

The paper provides a comprehensive numerical test of mean-field predictions on delaying dynamical arrest with competing interactions in three-dimensional systems.

## Key findings

- No significant delay observed beyond short-range attraction effects
- Simulations do not confirm the mean-field prediction of delayed arrest with added long-range repulsion
- Discussion of possible reasons for the discrepancy between theory and simulation

## Abstract

Systems of dense spheres interacting through very short-ranged attraction are known from theory, simulations and colloidal experiments to exhibit dynamical reentrance. The liquid state can thus be fluidized to higher densities than otherwise possible with interactions that are purely repulsive or long-ranged attractive. A recent mean-field, infinite-dimensional calculation predicts that the dynamical arrest of the fluid can be further delayed by adding a longer-ranged repulsive contribution to the short-ranged attraction. We examine this proposal by performing extensive numerical simulations in a three-dimensional system. We first find the short-ranged attraction parameters necessary to achieve the densest liquid state, and then explore the parameters space for an additional longer-ranged repulsion that could enhance the effect. In the family of systems studied, no significant (within numerical accuracy) delay of the dynamical arrest is observed beyond what is already achieved by the short-ranged attraction. Possible explanations are discussed.