Homogenization of Nonlinear Drift-diffusion Systems for Charge Transport through Bicontinuous Media

We study the periodic homogenization of strongly coupled reaction-diffusion systems with nonlinear drifts posed in bicontinuous media, with interwoven and connected microstructures.

The target system of equations arises in the modeling of charge transport through heterogeneous morphologies of organic solar cells (OSC).

The efficiency and long-time stability of OSC is not only a modern technological problem with clear societal relevance, but it also raises interesting and challenging mathematical questions in the field of asymptotic analysis for partial differential equations.

Starting off from detailed descriptions of polymer-polymer morphologies of OSC, we plan to derive upscaled equations for the transport of excitons, electrons, holes, and polarons, coupled together via an electrostatic potential.

New mathematical homogenization techniques need to be developed to cope with the strong nonlinear drifts present in the system.

We will use the obtained upscaled objects to forecast numerically how well the OSC fonctions given a certain morphology.

At the end of the project, we will be able to evaluate quantitatively to which extent defects and traps can affect the overall motion of electrons.

Any scientific progress in theoretical understanding of the multiscale details of the physics of photoelectronics is likely to lead to significant technological improvements of the OSC as energy-harvesting device, strengthening also the importance of homogenization as investigation tool.