(244c) Dynamic Density Functional Theory for Drying Colloidal Suspensions: Comparison of Free Energy Functionals

Dynamic density functional theory (DDFT) is a promising approach for predicting structural evolution and self-assembly in 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-expansion, and Boublik–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 drying films. We compare the DDFT-predicted volume-fraction profiles to Brownian dynamics (BD) simulations for films with varied initial heights and compositions. In the one-component suspension, FMT accurately predicts the structure of the suspension even at high concentrations and when significant density gradients develop, but the virial-expansion and BMCSL equations of state provide reasonable approximations for smaller concentrations and gradients at a reduced computational cost. In the two-component suspension, FMT and BMCSL are similar to each other but modestly overpredict the extent of self-assembly into stratified layers compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials undergoing nonequilibrium processes such as drying.