Morphology and material stability in polymer solar cells

Polymer solar cells are promising in that they are inexpensive to produce, and due to their mechanical flexibility have the potential for use in applications not possible for more traditional types of solar cells. The performance of polymer solar cells depends strongly on the distribution of electron donor and acceptor material in the active layer. Understanding the connection between morphology and performance as well as how to control the morphology, is therefore of great importance. Furthermore, improving the lifetime of polymer solar cells has become at least as important as improving the efficiency.   In this thesis, the relation between morphology and solar cell performance is studied, and the material stability for blend films of the thiophene-quinoxaline copolymer TQ1 and the fullerene derivatives PCBM and PC70BM. Atomic force microscopy (AFM) and scanning transmission X-ray microscopy (STXM) are used to investigate the lateral morphology, secondary ion mass spectrometry (SIMS) to measure the vertical morphology and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy to determine the surface composition. Lateral phase-separated domains are observed whose size is correlated to the solar cell performance, while the observed TQ1 surface enrichment does not affect the performance. Changes to the unoccupied molecular orbitals as a result of illumination in ambient air are observed by NEXAFS spectroscopy for PCBM, but not for TQ1. The NEXAFS spectrum of PCBM in a blend with TQ1 changes more than that of pristine PCBM. Solar cells in which the active layer has been illuminated in air prior to the deposition of the top electrode exhibit greatly reduced electrical performance. The valence band and absorption spectrum of TQ1 is affected by illumination in air, but the effects are not large enough to account for losses in solar cell performance, which are mainly attributed to PCBM degradation at the active layer surface.

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.