APPLICATION OF FRACTALS AND KINETIC-EQUATIONS TO CLUSTER FORMATION

We describe a rigorous connection between a coalescence growth model employing the Smoluchowski equation and the log-normal distribution which has been used for decades to classify empirically small particle distributions. The model assumes that only binary collisional events occur, there is conservation of monomers over the lifetime of the process, the clusters can be represented using a mass fractal approach and there are no ''magic numbers''. Numerically, it is easy to account for the effects of evaporation, magic numbers, other inhomogeneities and possibly a non-conservative process. The model correctly incorporates the existence of multiple kinetic pathways for producing almost all cluster sizes. The properties of elemental cluster size distributions can apparently be related to the nature of the monomers as represented by the Periodic Table. The model classifies cluster size distributions on the basis of a single scaling parameter which itself is a function of the dimensionality of the space in which the coalescence process occurs, the fractal dimensionality of the clusters, the fractal dimensionality of the trajectories of the agglomerating species between collisions and the scaling of the cluster velocities with increasing cluster size.