Uniform distributions in nonuniform systems: Wall potentials generating constant density profiles in classical...

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Soft Matter Physics

Background:

• Classical density functional theory (DFT) describes inhomogeneous fluids.
• Understanding fluid behavior near surfaces is crucial for various applications.
• Inverse problems in DFT, like finding potentials for specific density profiles, are challenging.

Purpose of the Study:

• To solve the inverse problem of finding wall potentials that yield constant equilibrium density profiles for inhomogeneous fluids.
• To develop analytical and numerical methods for constructing these potentials across different geometries.
• To provide a microscopic realization of structure-cancelling wall fields.

Main Methods:

• Utilizing Rosenfeld's fundamental measure theory (FMT).
• Solving the inverse problem for one-component fluids in planar, spherical, and cylindrical geometries.
• Considering hard-sphere fluids and fluids with truncated Lennard-Jones attractions (mean-field).
• Obtaining explicit analytical expressions for planar and spherical geometries, and numerical solutions for cylindrical geometry.

Main Results:

• Derived explicit analytical expressions for wall potentials producing flat density profiles in planar and spherical geometries.
• Developed numerical methods for the cylindrical case.
• Provided formulas for weighted densities and one-body direct correlation functions.
• Validated the constructed analytic wall potentials through independent DFT calculations, confirming accurate recovery of flat profiles.

Conclusions:

• Successfully determined wall potentials that enforce constant equilibrium density profiles in inhomogeneous fluids.
• The developed methods and derived formulas offer valuable reference expressions for DFT implementations.
• The study establishes a microscopic basis for structure-cancelling wall fields relevant to interfacial phenomena.