The role of total pressure in gas-phase nucleation: A diffusion effect

Abstract

A numerical modeling study is presented concerning the role of total pressure in gas-phase nucleation. We consider a generic self-clustering mechanism for particle production in which the cluster transport properties are assumed to scale with monomer properties. A steady-state isothermal plug flow reactor model is considered in which axial diffusion of gas species is allowed. Species conservation equations with appropriate boundary conditions are solved in the one-dimensional reactor space. A steady-state nucleation current is shown to be achievable when the monomer concentration is fixed, regardless of the total pressure. In the case when the monomer concentration is varied, we demonstrate that diffusion can play a critical role at low pressures, where the nucleation rate is found to be highly pressure-sensitive. In this regime steady-state nucleation is not possible. As pressure increases, the nucleation rate becomes gradually pressure-insensitive and approaches the high-pressure limit. A dimensionless analysis is performed for a series of irreversible clustering reactions, and the effects of dimensionless system parameters on the nucleation rate are presented as a function of pressure. The results indicate that to minimize particle formation in chemical vapor deposition reactors while maintaining high deposition rates one should operate in the pressure-dependent regime, with low total reactor pressures and high partial pressures of reactants.