Stochastic modelling of silicon nanoparticle synthesis
Menz, William Jefferson
University of Cambridge
Department of Chemical Engineering and Biotechnology
Sidney Sussex College
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Menz, W. J. (2014). Stochastic modelling of silicon nanoparticle synthesis (doctoral thesis). https://doi.org/10.17863/CAM.16077
This thesis presents new methods to study the aerosol synthesis of nano-particles and a new model to simulate the formation of silicon nanoparticles. Population balance modelling is used to model nanoparticle synthesis and a stochastic numerical method is used to solve the governing equations. The population balance models are coupled to chemical kinetic models and offer insight into the fundamental physiochemical processes leading to particle formation. The first method developed in this work is a new mathematical expression for calculating the rate of Brownian coagulation with stochastic weighted algorithms (SWAs). The new expression permits the solution of the population balance equations with SWAs using a computationally-efficient technique of majorant rates and fictitious jumps. Convergence properties and efficiency of the expression are evaluated using a detailed silica particle model. A sequential-modular algorithm is subsequently presented which solves networks of perfectly stirred reactors with a population balance model using the stochastic method. The algorithm is tested in some simple network configurations, which are used to identify methods through which error in the stochastic solution may be reduced. It is observed that SWAs are useful in preventing accumulation of error in reactor networks. A new model for silicon nanoparticle synthesis is developed. The model includes gas-phase reactions describing silane decomposition, and a detailed multivariate particle model which tracks particle structure and composition. Systematic parameter estimation is used to fit the model to experimental cases. Results indicated that the key challenge in modelling silicon systems is obtaining a correct description of the particle nucleation process. Finally, the silicon model is used in conjunction with the reactor network algorithm to simulate the start-up of a plug-flow reactor. The power of stochastic methods in resolving characteristics of a particle ensemble is highlighted by investigating the number, size, degree of sintering and polydispersity along the length of the reactor.
silicon, nanoparticles, population balance equations, stochastic weighted algorithms, reactor networks
This work was supported by the Cambridge Australia Trust.
This record's DOI: https://doi.org/10.17863/CAM.16077
CC0 1.0 Universal
Licence URL: http://creativecommons.org/publicdomain/zero/1.0/
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