# Mathematical modelling of semiconductor photocatalysis

• Grant MacDonald

Student thesis: Doctoral Thesis

### Abstract

Semiconductor photocatalysis can be extremely effective in the complete mineralisation of hundreds of organic materials and has been utilised in various different commercial systems, for example, self-cleaning glass, purification of water, the purification of air, sterilisation/disinfection and detecting oxygen in food packaging. The aim of this thesis is to further the understanding of semiconductor photocatalysis using mathematical models. One of the main issues considered is the applicability of assuming that reaction intermediates remain in a steady-state throughout the majority of any reactions taking place. We show that this assumption is not always valid. First, we consider an intelligent ink that is used to test the effectiveness of self-cleaning glass. The system is modelled by a diffusion equation for the transport of dye molecules in the film coupled to an ordinary differential equation describing the photocatalytic reaction taking place at the glass surface. A finite difference method is introduced to solve the equations arising from the model. We are able to show that the proposed model can replicate experimental results well. The model also offers an explanation as to why the initial reaction rate is dependant on film thickness for several different reaction regimes considered. Second, we consider models motivated by systems where photocatalytic reactions take place throughout the domain as opposed to exclusively at domain boundaries. We present a numerical method to solve such systems, and based on informal experimental results, explain the reasons behind the initial reaction rate being dependent on the size of the domain. Third, we consider four previously published models based on the removal of organic pollutants using semiconductor photocatalysis. We introduce more generalmathematical models and demonstrate that by doing so there are a wider rangeof systems that the models can be applied to. One model involves an expanding domain and we present a moving mesh finite difference method that is used to solve such systems.Fourth, we propose a moving mesh finite element method for coupled bulk-surface problems in two-dimensional time-dependant domains. These problems are motivated by a system where semiconductor photocatalysis is used to destroy organic dirt across a domain which is increasing in size. Finally, we show how to determine the colour of a substance based on its absorbance spectrum. By comparing predictions made from experimental data to published photographs we are able to demonstrate that we can accurately predict the colour of a substance.
Date of Award 6 Jun 2016 English University Of Strathclyde University of Strathclyde & EPSRC (Engineering and Physical Sciences Research Council) John MacKenzie (Supervisor) & Tell Tuttle (Supervisor)

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