Modeling of SiO_2 deposition in porous Vycor: Effects of pore network connectivity

Abstract

A mathematical model developed for SiO_2 deposition in porous Vycor glass using SiCl_4 hydrolysis describes reaction, diffusion and evolution of the pore structure due to accumulation of the solid product. The deposition reaction is described by transient heterogeneous kinetics in terms of the concentrations of silanol and chloride groups in the product layer as well as those of the gaseous reactants. For typical deposition conditions the pseudo steady-state approximation for surface species could lead to erroneous predictions. Pore structure evolution is modeled by incorporating results of percolation theory. For this purpose the porous glass is represented by a Bethe lattice with coordination number 3 and alternatively by a decorated Bethe lattice in which each bond is replaced by a composite bond consisting of two bonds in series. The second network can capture the effect of pore radius variation along a single pore. For the decorated lattice, pore connectivity interruption at a higher void fraction leads to thinner deposits and shorter deposition times for pore plugging compared to the corresponding ones for the simple lattice.

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