Scaling and Exponent Equalities in Island Nucleation: Novel Results and Application to Organic Films Alberto Pimpinelli, Levent Tumbek, and Adolf Winkler

As discussed in the first talk, the scaling of the island density with the flux $F$ and/or the capture zone distribution (CZD) can be used to determine the size of the critical nucleus $i$, but so far an analytic function for CZD exists only for diffusion-limited aggregation (DLA). For CZD the scaling function is $P_\beta(s) = a_{\beta} s^{\beta}\exp(-b_{\beta} s^2)$, with $\beta = i+2$. We have extended the analytic description of the CZD in terms of $P_\beta$ also to attachment-limited aggregation (ALA); in this case we obtain $\beta = (i+3)/2$. Furthermore, we could demonstrate that the general relationship $\alpha \beta = i$ holds, independent of the aggregation mechanism.\footnote{A. Pimpinelli, L. Tumbek, \& A. Winkler, J. Phys. Chem. Lett. 5, 995 (2014)} This important exponent equality should help to better characterize nucleation and growth of thin films.