Application of fractals and kinetic equations to cluster formation

Abstract

The log normal distribution is shown to be useful for characterizing cluster distributions produced by coalescence growth mechanisms. The Smoluchowski equation and variations thereof produce cluster size distributions very similar to those produced using nozzle beam expansions and laser chemistry of organometallics. The model provides a statistically unbiased basis for interpreting cluster size distributions produced using a wide variety of synthetic methods. It also provides a unified chemical and physical basis for discussing and rationalizing the results of a wide range of gas phase cluster experiments. Under certain conditions, size distributions can be produced in which there is an alteration in the number of odd and even clusters produced. In addition to some inferences regarding fullerene chemistry, data gleaned from the literature are rationalized on the basis of the kinematics of cluster formation, the fractal dimension of clusters composed of different atoms, the Periodic Table, and the degree to which the translational motion of the coalescing species is diffusional or ballistic.