Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals

TL;DR

This study compares different free-energy functionals within dynamic density functional theory to predict the structure of drying colloidal suspensions, validating results against particle-based simulations and providing guidance for modeling soft materials.

Contribution

It evaluates the accuracy of various free-energy functionals, including FMT and equations of state, for modeling drying colloidal suspensions in DDFT.

Findings

FMT accurately predicts high-concentration structures

Virial and BMCSL are computationally cheaper with reasonable accuracy at lower concentrations

Fidelity varies with suspension composition and concentration

Abstract

Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions including local-density approximations based on the ideal-gas, virial, and Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume-fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes such as solvent drying, solvent freezing, and sedimentation.