Depletion potential in hard-sphere mixtures: theory and applications

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Computational Chemistry

Background:

• Calculating depletion potentials is crucial for understanding fluid mixtures and colloidal systems.
• Traditional methods can be computationally intensive, especially for complex geometries and size ratios.

Purpose of the Study:

• To present a versatile density functional theory (DFT) for calculating depletion potentials in general fluid mixtures.
• To simplify calculations by considering the system as an inhomogeneous binary mixture in the limit of vanishing big particle density.
• To provide accurate predictions for hard-sphere mixtures and assess the validity of approximations.

Main Methods:

• Developed a DFT approach that relies on equilibrium density profiles of a one-component fluid and density-independent weight functions.
• Implemented the approach for additive hard-sphere mixtures.
• Compared results with computer simulations for depletion potentials near planar walls and other large spheres.

Main Results:

• The DFT approach accurately predicts depletion potentials for hard-sphere mixtures, even for small size ratios (s=0.1) and high packing fractions (eta(s)=0.3).
• The method correctly captures damped oscillatory decay at large separations.
• The study assesses the limitations of the Derjaguin approximation for hard-sphere mixtures.

Conclusions:

• The presented DFT approach offers an accurate and computationally efficient method for calculating depletion potentials.
• Provides an accurate parametrization of depletion potentials in hard-sphere fluids for effective Hamiltonian studies.
• The findings offer insights into colloid-colloid mixtures and validate against experimental data.