The force distribution probability function for simple fluids by density functional theory.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Physical Chemistry

Background:

• Understanding particle interactions and net forces is crucial in fluid dynamics.
• Classical density functional theory (DFT) offers a framework for studying these properties.
• Previous models often struggled with accurate force distribution predictions.

Purpose of the Study:

• To derive a probability distribution function for the net force on a particle in simple fluids using DFT.
• To validate the derived theoretical model against computational simulations.
• To assess the applicability of the model across different fluid densities and potentials.

Main Methods:

• Applied classical density functional theory (DFT) to derive force distribution functions P(F) and W(F).
• Utilized the hypernetted chain (HNC) closure for the Ornstein-Zernike equation.
• Compared theoretical predictions with molecular dynamics (MD) simulations for Gaussian and bounded soft sphere potentials.

Main Results:

• Derived a formula P(F) ∝ exp(-AF(2)), where A is dependent on fluid properties and pair potential.
• DFT predictions for W(F) showed agreement with MD simulations for Gaussian and bounded soft spheres at high densities.
• The Gaussian form for P(F) remained accurate at moderate densities, though with a modified constant A.

Conclusions:

• The derived DFT-based formula provides a robust method for predicting particle net force distributions in simple fluids.
• The model demonstrates good agreement with simulations, particularly at higher densities.
• The Gaussian approximation offers a useful, albeit slightly adjusted, representation of force distributions across a range of densities.