Application of the Smoluchowski equation to the formation kinetics of cluster ions

Abstract

Cluster ions with various sizes and compositions have been generated from direct laser vaporization. The Smoluchowski rate equation is extended to describe the formation kinetics of the cluster ions, which have been assumed to be produced from ion-molecule reactions with same-rate constants. By solving the kinetic equation analytically we obtained the distribution function of the cluster ions. Analysis of the distribution function showed that the function can characterize the statistical size distribution of the cluster ions and can be reduced to the asymptotic solution suggested by Jullien [1]

Extended Smoluchowski Model for the Formation of Size-Selected Silver Nanoclusters Generated via Modulated Pulsed Power Magnetron Sputtering

“…The Smoluchowski rate equation has been shown to describe the irreversible condensation of NCs. , Huang and co-workers further considered NC ion-neutral interactions in the vapor phase, and obtained good agreement with the results of a laser vaporization experiment . However, sputtered materials in the plasma plume of a pulsed magnetron sputtering system comprise high-density neutral, cationic, and anionic species (up to 10 20 m –3 ) owing to their high peak power.…”

“…13,14 Huang and coworkers further considered NC ion-neutral interactions in the vapor phase, and obtained good agreement with the results of a laser vaporization experiment. 15 However, sputtered materials in the plasma plume of a pulsed magnetron sputtering system comprise high-density neutral, cationic, and anionic species (up to 10 20 m −3 ) 16 owing to their high peak power. While the peak power density on the target of a conventional direct current (DC) MSP is less than 50 W/cm 2 , that of an MPP-MSP can approach several kW/cm 2 .…”