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  • 1Nuclear Department, Defence Academy, HMS Sultan, Military Road, Gosport PO12 3BY, United Kingdom.

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Summary

This study estimates fluid free energy using mean-field density functional theory. It refines pair correlation functions and modifies nucleation rates for spherical droplets, revealing a dependence on droplet radius.

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Area of Science:

  • Physical Chemistry
  • Statistical Mechanics
  • Computational Fluid Dynamics

Background:

  • Mean-field density functional theory (DFT) is a tool for estimating free energy in non-uniform fluids.
  • The direct correlation function is mathematically linked to the free energy's second functional derivative.

Purpose of the Study:

  • To develop an improved approximation for the pair correlation function and free energy using DFT.
  • To investigate the relationship between DFT and field-theoretic approaches for vapor-liquid interfaces.
  • To analyze free energy corrections for spherical droplets and their impact on nucleation rates.

Main Methods:

  • Utilizing mean-field density functional theory.
  • Approximating repulsive interactions with the local density approximation and attractive interactions with the Yukawa form.
  • Solving Schrödinger-like equations to find eigenvalues, analytically for the planar case of the Φ4 model.
  • Analyzing correction terms (cluster translational invariance, droplet growth mode, capillary waves) for spherical droplets.

Main Results:

  • The random phase approximation is derived for improved pair correlation and free energy calculations.
  • Analytical solutions are obtained for planar systems within specific models.
  • Ultraviolet divergences are managed by term separation.
  • Correction terms proportional to lnR are identified for spherical droplets.
  • The classical nucleation rate is modified by a factor dependent on the droplet radius R.

Conclusions:

  • The DFT approach, combined with specific interaction models, provides a framework for calculating fluid free energy and correlation functions.
  • The study elucidates the connection between DFT and field theory for interface phenomena.
  • Free energy calculations for spherical droplets reveal size-dependent corrections affecting nucleation rates, with a modification factor proportional to R^(4/3).