Phase field methods, parameter identification and process optimisation

该项目旨在a)通过旋涂和印刷工艺推导出有机太阳能电池生产过程中形态形成的精确数学模型，b)开发高效的数值方案，允许在二维和三维空间对这些模型进行快速和准确的数值模拟，以及c)使用参数识别技术来使用研究单位内其他项目获得的实验数据来校准模型。建模方法将基于二元聚合物-NFA体系的相场描述，其动力学由基于Flory-Huggins理论的自由能泛函控制。通过引入额外的序参数来考虑溶剂的蒸发，允许灵活地处理几何效应，但也与流体动力学自然耦合。此外，适当的迁移率将考虑到当大部分溶剂蒸发时发生的尺寸排斥效应。我们将在本方案中开发的有效数值格式对于评估复杂的相场模型是必不可少的。为了达到期望的精度，离散化需要足够细粒度，需要求解许多大规模(非线性)方程组。算法的效率取决于开发合适的需要结构化预条件的迭代解方案，依赖于这些算法，通过数值求解适当的非线性最小二乘问题来进行参数辨识。由于特定的形貌对初始条件和参数的选择非常敏感，而所得到的有机太阳能电池的效率主要取决于平均数量，因此为了进行参数识别，开发合适的损耗泛函是最重要的。此外，还将进行敏感性分析，以确定与这些感兴趣的数量相关的最重要的参数。

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.