Entropic Colloidal Crystal Prediction: A Quantum Density Functional Theory Inspired Approach

TL;DR

This paper introduces a novel classical density functional theory inspired by quantum DFT to predict the most stable colloidal crystal structures of convex particles by mapping to an auxiliary system and minimizing free energy.

Contribution

It develops a new classical DFT approach that predicts colloidal crystal stability by mapping particles to an auxiliary system and minimizing free energy, inspired by quantum DFT.

Findings

The auxiliary system's lowest free energy predicts the most probable crystal structure.

Validation against known equations of state confirms the theory's accuracy.

The method successfully identifies stable colloidal crystal arrangements.

Abstract

In pursuit of a colloidal analogue to quantum density functional theory (DFT) predictions of atomic crystal structures, we report a new, classical DFT that predicts the relative thermodynamic stability of colloidal crystals of hard, convex particle shapes. In contrast to standard classical DFT approaches, our theory maps the hard particle system to an auxiliary system in which we treat the particles as fixed "nuclei" embedded in a fictitious, spatially varying density field that distributes throughout the auxiliary system. By minimizing the free energy of the auxiliary system, and through comparison with known equations of state and free energy calculations using thermodynamic integration, we show that the auxiliary system with the lowest free energy corresponds to the most probable crystal of hard shapes in the original system.