Phase field methods, parameter identification and process optimisation

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This project aims at a) the derivation of accurate mathematical models for the morphology formation during organic solar cell production, both via spin coating and printing processes, b) to develop efficient numerical schemes that allow for the fast and accurate numerical simulation of these models in two and three spatial dimensions, and c) the use of parameter identification techniques to calibrate the models using experimental data obtained by other projects within the research unit.The modelling methodology will be based on phase field descriptions of binary polymer-NFA systems whose dynamics is governed by a free energy functional based on the Flory-Huggins theory. Evaporation of the solvent will be taken into account by introducing an additional order parameter, allowing for a flexible treatment of geometric effects but also a natural coupling to hydrodynamics. In addition, appropriate mobilities will take care of size exclusion effects that occur when most of the solvent is evaporated.The efficient numerical schemes we will develop in this proposal are essential for evaluating the complex phase-field models. In order to achieve the desirable accuracy, the discretization needs to be sufficiently fine-grained requiring the solution of many large-scale (non)linear systems of equations. The efficiency will rely on developing suitable iterative solution schemes requiring structured preconditioners.Relying on these algorithms, parameter identification is carried out by numerically solving appropriate non-linear least squares problems. As the specific morphology is very sensitive to the initial conditions and the choice of parameters, yet the efficiency of the resulting organic solar cells mostly depends on averaged quantities, it is most important to develop appropriate loss functionals for the purpose of parameter identification. In addition, a sensitivity analysis will be carried out to identify the most important parameters in terms of these quantities of interest.