Density-functional theory of hard-sphere condensation under gravity

Area of Science:

• Physics
• Statistical Mechanics
• Materials Science

Background:

• Understanding phase transitions like condensation is crucial in statistical mechanics.
• Hard sphere models provide a fundamental basis for studying fluid-olid transitions.
• Gravitational effects can significantly influence condensation phenomena.

Purpose of the Study:

• To investigate the onset of condensation for hard spheres in a gravitational field.
• To compare results from different density-functional theory (DFT) approaches.
• To analyze the influence of gravitational field on particle layering.

Main Methods:

• Utilizing density-functional theory (DFT) to model hard sphere systems.
• Comparing the local density approximation (LDA) with weighted density-functional theory (WDFT).
• Analyzing density profiles under varying gravitational conditions and temperatures.

Main Results:

• Local density approximation (LDA) results align with prior kinetic theory findings.
• Weighted density-functional theory (WDFT) shows condensation temperature scales linearly with particle weight, diameter, and layer number.
• Quantitative differences observed between DFT methods for low-temperature density profiles.
• WDFT reveals distinct layering of hard spheres in the solid regime.

Conclusions:

• DFT provides a robust framework for studying gravitational condensation of hard spheres.
• WDFT offers a more detailed view of particle arrangement, revealing layering in solid phases.
• The choice of DFT approximation impacts quantitative predictions of density profiles.