Formation of Crystalline Bulk Heterojunctions in Organic Solar Cells: Insights from Phase-Field Simulations.

The performance of organic solar cells strongly depends on the bulk-heterojunction (BHJ) morphology of the photoactive layer. This BHJ forms during the drying of the wet-deposited solution, because of physical processes such as crystallization and/or liquid-liquid phase separation (LLPS). However, the process-structure relationship remains insufficiently understood. In this work, a recently developed, coupled phase-field-fluid mechanics framework is used to simulate the BHJ formation upon drying. For the first time, this allows to investigate the interplay between all the relevant physical processes (evaporation, crystal nucleation and growth, liquid demixing, composition-dependent kinetic properties), within a single coherent theoretical framework. Simulations for the model system P3HT-PCBM are presented. The comparison with previously reported in situ characterization of the drying structure is very convincing: The morphology formation pathways, crystallization kinetics, and final morphology are in line with experimental results. The final BHJ morphology is a subtle mixture of pure crystalline donor and acceptor phases, pure and mixed amorphous domains, which depends on the process parameters and material properties. The expected benefit of such an approach is to identify physical design rules for ink formulation and processing conditions to optimize the cell's performance. It could be applied to recent organic material systems in the future.

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.

Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures.

The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale L ∼ Ctα. To understand the structure-property relationship, the knowledge of the coarsening exponent α and the coarsening rate constant C is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory-Huggins free energy and a constant composition-independent mobility term and show that the coarsening for off-critical mixtures is slower than the expected t1/3-growth. Instead, we find α to be dependent on the mixture composition and associate this with the observed morphologies. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant C.

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.