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Title: Mathematical problems relating to the fabrication of organic photovoltaic devices
Author: Hennessy, Matthew Gregory
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2014
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The photoactive component of a polymeric organic solar cell can be produced by drying a mixture consisting of a volatile solvent and non-volatile polymers. As the solvent evaporates, the polymers demix and self-assemble into microscale structures, the morphology of which plays a pivotal role in determining the efficiency of the resulting device. Thus, a detailed understanding of the physical mechanisms that drive and influence structure formation in evaporating solvent-polymer mixtures is of high scientific and industrial value. This thesis explores several problems that aim to produce novel insights into the dynamics of evaporating solvent-polymer mixtures. First, the role of compositional Marangoni instabilities in slowly evaporating binary mixtures is studied using the framework of linear stability theory. The analysis is non-trivial because evaporative mass loss naturally leads to a time-dependent base state. In the limit of slow evaporation compared to diffusion, a separation of time scales emerges in the linear stability problem, allowing asymptotic methods to be applied. In particular, an asymptotic solution to linear stability problems that have slowly evolving base states is derived. Using this solution, regions of parameter space where an oscillatory instability occurs are identified and used to formulate appropriate conditions for observing this phenomenon in future experiments. The second topic of this thesis is the use of multiphase fluid models to study the dynamics of evaporating solvent-polymer mixtures. A two-phase model is used to assess the role of compositional buoyancy and to examine the formation of a polymer-rich skin at the free surface. Then, a three-phase model is used to conduct a preliminary investigation of the link between evaporation and phase separation. Finally, this thesis explores the dynamics of a binary mixture that is confined between two horizontal walls using a diffusive phase-field model and its sharp-interface and thin-film approximations. We first determine the conditions under which a homogeneous mixture undergoes phase separation to form a metastable bilayer. We then present a novel mechanism for generating a repeating lateral sequence of alternating A-rich and B-rich domains from this bilayer.
Supervisor: Muench, Andreas; Breward, Christopher J.; Please, Colin P. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Fluid mechanics (mathematics) ; Approximations and expansions ; evaporating films ; multiple scales ; Marangoni instability ; WKB approximation ; confined phase separation ; sharp-interface asymptotics ; topological transformation ; multiphase flow