Lognormal Size Distributions in Particle Growth Processes without Coagulation

Abstract

A new model is proposed to explain lognormal particle size distributions found in vapor growth processes such as gas evaporation, without invoking coagulation. In the model, particles are moving by diffusion and drift through a finite growth region. The particle size is assumed to be a power function of growth time, and the final size distribution is determined by the first passage times. By computer simulation, lognormal size distributions and scaling laws interrelating the distribution parameters, the size of the growth region, and the drift speed were found. [S0031-9007(98)05606-3] PACS numbers: 81.10. Bk, 61.46. + w, 81.05.Ys, The particle size distribution is a very important property of finely divided systems such as aerosols, emulsions, and powders. Particle growth processes and their influence on the size distribution have been studied for a long time and general theories exist [1][2][3]. In the case of growth from vapor, initial nucleation gives rise to droplets or particles which first grow by vapor absorption and then possibly by coagulation. A vapor growth process studied in great detail is the gas evaporation method for production of ultrafine particles with mean size in the nanometer range [4]. In this method, a metal is evaporated, and the vapor is subsequently cooled in an inert gas such as He. The technique was studied extensively by Granqvist and Buhrman [5]. Since then, intense development has taken place [6-8], and nanostructured materials composed of ultrafine particles have become important in fundamental and applied physics. In several such materials, extraordinary physical and chemical properties have been found [9][10][11][12]. Many of these properties depend critically on a small mean particle size and a narrow size distribution.It was shown in [5] that the particle diameters r after gas evaporation are well described by a lognormal distribution,which is defined by the geometric mean diameter r and the dimensionless geometric standard deviation s. Also in [5], a coalescence model leading to lognormality was derived, and it was argued that growth by absorption of atomic vapor could not give rise to a lognormal particle size distribution. Subsequent work emphasizing the influence of absorption on the size distribution has been done [13,14], but lognormal distributions are usually explained by the Brownian coagulation models [15][16][17][18]. The applicability of these models can be questioned, since they are based on the theory of Smoluchowsky [1], which treats coagulation in a closed system of particles. A modern setup for gas evaporation is an open system, with particles constantly being added and removed. Furthermore, the coagulation models do not explain the origin of the lognormal distribution but rather assume its presence.This Letter takes a different approach, which does not involve coagulation. A new model is proposed by emphasizing the time spent for growth, which has not been properly considered until now. It will be shown that the distribution of particle growth times can be ac...

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