Aerosol dynamics modeling of silicon nanoparticle formation during silane pyrolysis: a comparison of three solution methods

A numerical model has been developed to predict gas-phase nucleation, growth, and coagulation of silicon nanoparticles formed during thermal decomposition of silane. A detailed chemical kinetic model of particle nucleation was coupled to an aerosol dynamics model that includes particle growth by surface reactions, coagulation with instantaneous coalescence, and convective transport. Solution of the aerosol general dynamic equation was handled by three approaches: (1) the efficient and reasonably accurate method of moments; (2) the quadrature method of moments, which requires no prior assumption of the shape of the particle size distribution; and (3) a computationally more expensive sectional method (SM). The SM includes a conceptually simple and computationally efficient algorithm for treating coagulation that is found to be superior to widely used methods from the literature. All three approaches gave similar results for the evolution of the first few moments of the particle size distribution. The SM was able to capture the bimodal distribution that appears briefly at short residence times due to simultaneous nucleation and coagulation. At longer residence time, only coagulation remains important and both the sectional and moment methods give very similar results as they approach the self-preserving size distribution.