Monte-Carlo and Fundamental Measure Theory Insights into Structure of Ultra-Multicomponent Hard-Sphere Fluid Mixtures in Highly Confined Environments and Effective Interaction

Abstract

Study of multi-component hard-sphere fluid behaviour in confined environments represents a fundamental problem in statistical mechanics and condensed matter physics, where accurately describing particle distributions near solid surfaces and effective interactions between surfaces are crucial for understanding phenomena such as wetting, adsorption, and programmable assembly. This study employs Grand Canonical Monte Carlo simulations to re-examine accuracy of Fundamental Measure Theory in ultra-multicomponent (up to seven components) hard-sphere fluid mixtures, circumventing the limitations of softened potential approximation and ensemble mismatch inherent in prior molecular dynamics studies. We systematically investigated density distributions of three- to seven-component hard-sphere fluid mixtures confined between hard and soft walls, and calculated effective interactions between parallel hard plates. Results demonstrate that the White Bear approximation of the FMT consistently outperforms the Oleksy-Hansen dimensional crossover approximation across a wide range of packing fractions, with the agreement between theoretical predictions and simulation results validating the reliability of the FMT White Bear functional in ultra-multicomponent hard sphere fluids, while the Oleksy-Hansen functional shows unexpectedly diminished precision in low effective dimensionality scenarios—particularly at lower packing fractions where the crossover correction becomes dominated by smaller species rather than reflecting the true confinement experienced by large particles. Force curve analysis reveals the correspondence between oscillation characteristics and the diameter of the larger components, as well as the distortion effect of smaller particles on oscillation patterns. Solvation force studies reveal multiple repulsive potential barriers and wells (depending on the number of larger-sized components) when slit width becomes smaller than the maximum particle diameter, with barrier heights and well depths closely correlated with total packing fraction and mole fractions of the larger-sized components involved. These findings provide a theoretical foundation for designing smart colloidal systems with specific functionalities and suggest directions for improving fluid-state crossover functionals through additional constraints such as extra sum rules, tensorial contributions, or species-sensitive crossover diagnostics—offering significant application prospects in microfluidics, soft matter science, and advanced materials design.