Aerosol coagulation and nucleation

Abstract

For aerosol Brownian coagulation in the transition regime of Knudsen number in the presence of an interparticle potential, the Fokker-Planck equation is solved by using the Grad's 13-moment method. The mass and energy accommodation coefficients that are used to describe the results of collisional processes are appropriately defined and interfaced with the Fokker-Planck moment equations. Analytical and numerical solutions of the number and energy flux profiles for the potential-free, power-law potential, van der Waals potential, and Coulombic potential situations are obtained. The results are in good agreement with those predicted by the flux-matching method of Fuchs. The present fundamental approach, therefore, provides theoretical support of the coagulation coefficient expression obtained by the empirical flux-matching method. For coagulation between ultrafine particles, we solved the BGK equation for large but finite Knudsen number situations by taking into account the van der Waals potential and/or the Coulombic/image potential. We present closed form best-fit equations for data calculated from the theory. The conditions where either Coulombic, image, or van der Waals forces predominate are determined. A new expression of the image potential between a charged particle and an uncharged particle is obtained. We calculate the coagulation rate between the particles and are able to determine the enhancement of coagulation rate due to the interparticle potential in all size regimes. An aerosol coagulation process is applied to the formation of aerosol particles in the semiconductor thin film preparation. In the CVD reactor, we consider simultaneous aerosol coagulation, diffusion, and generation of aerosol monomers by chemical reaction. The mass and number concentration of monomers and particles are computed as functions of temperature, pressure, input vapor concentration, and position in the reactor. The thin film growth rate can be subsequently evaluated. It is found that under certain circumstances, aerosol particle generation may significantly suppress the film growth due to monomers. The formulation of the homogeneous nucleation free energy change of aerosol clusters is reexamined. It is shown that the inclusion of the cluster translational and rotational motion in the cluster formation free energy change is appropriate. The classical and statistical thermodynamics are shown to be consistent. The cell model of liquids of statistical mechanics is employed to reevaluate the free energy change of cluster formation in aerosol nucleation. We provide a new molecular level theory that is applicable in the larger cluster size range where liquid-like properties begin to emerge and a cluster surface is present. The microcluster surface tension can be appropriately defined. The cluster rotational contribution to the free energy change, though it must be accounted for, is shown to be insignificant for liquid-like clusters.