# Grand-canonical Monte-Carlo simulation of solutions of salt mixtures: theory and implementation

## TL;DR

This paper introduces a Grand-canonical Monte-Carlo simulation method for electrolyte salt mixtures, addressing charge neutrality constraints, and demonstrates its application to various salt solutions, revealing linear osmotic pressure dependence and ion insertion effects.

## Contribution

It extends Grand-canonical Monte-Carlo methods to simulate electrolyte mixtures with charge neutrality constraints, providing a practical recipe and implementation details.

## Key findings

- Osmotic pressure depends linearly on salt concentration.
- Divalent cations facilitate monovalent cation insertion.
- Simulation results align with experimental observations.

## Abstract

A Grand-canonical Monte-Carlo simulation method extended to simulate a mixture of salts is presented. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. This leads to some complications compared to regular Grand Canonical simulation. Here, a recipe for simulation of electrolyte solution of salt mixture is presented. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts or their mixtures at different concentrations using the primitive ion model. The osmotic pressures of the electrolyte solutions are calculated and shown to depend linearly on the salt concentrations within the concentration range simulated. We also show that at the same concentration of divalent anions, the presence of divalent cations make it easier to insert monovalent cations into the system. This can explain some quantitative differences observed in experiments of the MgCl$_2$ salt mixture and MgSO$_4$ salt mixture.