The orientational structure of a model patchy particle fluid: Simulations, integral equations, density functional theory, and machine learning.

We investigate the orientational properties of a homogeneous and inhomogeneous tetrahedral four-patch fluid (Bol-Kern-Frenkel model). Using integral equations, either (i) HNC or (ii) a modified HNC scheme with a simulation input, the full orientational dependence of pair and direct correlation functions is determined. Density functionals for the inhomogeneous problem are constructed via two different methods.

Machine Learning of a Density Functional for Anisotropic Patchy Particles.

Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here, we formulate an approach to the Kern-Frenkel model via the classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation.