Scaling and Exponent Equalities in Island Nucleation: Novel Results and Application to Organic Films.

It is known in thin-film deposition that the density of nucleated clusters varies with the deposition rate as a power law, . The exponent α is a function of the critical nucleus size in a way that changes with the aggregation limiting process. We extend here the derivation of the analytical capture-zone distribution function () = · ·exp(-) of Pimpinelli and Einstein to generic aggregation-limiting processes. We show that the parameter β is generally related to the critical nucleus size and to the exponent α by the equality α·β = , in the case of compact islands. This remarkable result allows one to measure with no knowledge of the actual aggregation mechanism. We apply this equality to measuring the critical nucleus size for pentacene deposition on mica. This system shows a crossover from diffusion-limited to attachment-limited aggregation with increasing deposition rates.