# Definitions of local density in density-dependent potentials for mixtures

## TL;DR

This paper explores how different definitions of local density in density-dependent potentials affect the modeling of multi-component systems, proposing a combined density approach that yields physically meaningful results and enables simulation of phase coexistence.

## Contribution

It introduces a new combined local density definition for multi-component systems in density-dependent potentials, overcoming previous limitations and enabling accurate phase behavior simulations.

## Key findings

- Only combined local densities produce meaningful results across compositions.
- Redefinition of local density accommodates different inter-type interactions.
- Simulations demonstrate liquid-liquid and liquid-solid coexistence by tuning parameters.

## Abstract

Density-dependent potentials are frequently used in materials simulations due to their approximate description of many-body effects at minimal computational cost. However, in order to apply such models to multi-component systems, an appropriate definition of total local particle density is required. Here, we discuss two definitions of local density in the context of many-body dissipative particle dynamics. We show that only a potential which combines local densities from all particle types in its argument gives physically meaningful results for all composition ratios. Drawing on the ideas from metal potentials, we redefine local density such that it can accommodate different inter-type interactions despite the constraint to keep the main interaction parameter constant, known as Warren's no-go theorem, and generalise the many-body potential to heterogeneous systems. We then show via simulation how liquid-liquid and liquid-solid coexistence can arise just by tuning the interaction parameters.