Verification of numerical simulation of the self-assembly of polymer-polymer-solvent ternary blends on a heterogeneously functionalized substrate

Phase-Field Simulation of Liquid-Vapor Equilibrium and Evaporation of Fluid Mixtures

In solution processing of thin films, the material layer is deposited from a solution composed of several solutes and solvents. The final morphology and hence the properties of the film often depend on the time needed for the evaporation of the solvents. This is typically the case for organic photoactive or electronic layers. Therefore, it is important to be able to predict the evaporation kinetics of such mixtures. We propose here a new phase-field model for the simulation of evaporating fluid mixtures and simulate their evaporation kinetics. Similar to the Hertz-Knudsen theory, the local liquid-vapor (LV) equilibrium is assumed to be reached at the film surface and evaporation is driven by diffusion away from this gas layer. In the situation where the evaporation is purely driven by the LV equilibrium, the simulations match the behavior expected theoretically from the free energy: for evaporation of pure solvents, the evaporation rate is constant and proportional to the vapor pressure. For mixtures, the evaporation rate is in general strongly time-dependent because of the changing composition of the film. Nevertheless, for highly nonideal mixtures, such as poorly compatible fluids or polymer solutions, the evaporation rate becomes almost constant in the limit of low Biot numbers. The results of the simulation have been successfully compared to experiments on a polystyrene-toluene mixture. The model allows to take into account deformations of the liquid-vapor interface and, therefore, to simulate film roughness or dewetting.

A phase-field model for the evaporation of thin film mixtures

The performance of solution-processed solar cells strongly depends on the geometrical structure and roughness of the photovoltaic layers formed during film drying. During the drying process, the interplay of crystallization and liquid-liquid demixing leads to structure formation on the nano- and microscale and to the final rough film. In order to better understand how the film structure can be improved by process engineering, we aim at theoretically investigating these systems by means of phase-field simulations. We introduce an evaporation model based on the Cahn-Hilliard equation for the evolution of the fluid concentrations coupled to the Allen-Cahn equation for the liquid-vapour phase transformation. We demonstrate its ability to match the experimentally measured drying kinetics and study the impact of the parameters of our model. Furthermore, the evaporation of solvent blends and solvent-vapour annealing are investigated. The dry film roughness emerges naturally from our set of equations, as illustrated through preliminary simulations of spinodal decomposition and film drying on structured substrates.