Mathematical simulation of gas-phase synthesis of metal nanoparticles in a chamber with an arc discharge

Numerical simulation of the metallic nanoparticles synthesis in a chamber with an arc discharge were elaborated. The efficiency of the vapor phase condensation of metallic nanoclusters and nanopowders was determined by setting optimum process parameters, the possibilities of experimental estimation of which is limited. Mathematical and physical models were developed to perform computer analysis of the vapor phase condensation to describe the macroscopic characteristics of the process (temperature regime, gas mixture dynamics, diffusion and convective transport of clusters) with allowance for the properties of the components on a microscopic level. The classical Becker–Döring–Folmer–Weber thermodynamic nucleation theory was used for the description of the probability of atom-cluster aggregation. The distributions of macroscopic (temperature, pressure, velocity field) and microscopic (cluster size distribution) values in the chamber were obtained. It is found that the size distribution function of clusters deposited on the chamber walls has two peaks, the first — in the region of small clusters ($1$–$50$ atoms) and the second — for the clusters containing more than $10^4$ atoms. Based on the results of numerical calculations the assumptions are made about the relationship between the type of size distribution function and characteristics of the process.