Correlation functions in mixtures with energetically favoured nearest-neighbours of different kind: a size-asymmetric case

TL;DR

This study combines theory and simulations to analyze correlation functions in size-asymmetric binary mixtures with energetic preferences for different neighbors, revealing how size disparity influences structure and fluctuations.

Contribution

It introduces a mesoscopic theory that accounts for local volume fraction fluctuations and compares it with Monte Carlo simulations for size-asymmetric mixtures.

Findings

Correlation functions show exponentially damped oscillations influenced by interaction potential.

Size asymmetry increases correlation length and amplitude, affecting particle distribution.

Particles are more uniformly distributed when energetic preferences favor different neighbors, especially at high size asymmetry.

Abstract

Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the two components are taken into account. Semi-quantitative agreement between the simulation and theoretical results is obtained, except from very small distances. The correlation functions exhibit exponentially damped oscillations, with the period determined by the interaction potential, and both the amplitude and the correlation length increasing significantly with increasing diameter ratio. Increasing size asymmetry leads also to decreasing fluctuations of the number of the smaller particles in the attractive shell of the bigger ones. For small size asymmetry, the strongest correlations occur for comparable volume fraction of the two components. When the size ratio increases, the maximum of the structure factor moves to a larger volume fraction of the bigger particles, and for the size ratio as large as 4, the maximum goes beyond the accessible range of volume fractions. Our results show that when the neighbourhood of different particles is energetically favoured, the particles are much more uniformly distributed than in the random distribution even at relatively high temperature, especially for large size asymmetry.