Dynamic scaling of the submonolayer island size distribution during self-assembled monolayer growth

Abstract

In situ atomic force microscope observations of the formation of octadecylphosphonic acid monolayers, deposited from solution onto mica, indicate that growth proceeds via the nucleation, growth, and coalescence of densely packed submonolayer islands of adsorbate molecules. Three regimes are observed: (1) an initial growth regime where nucleation of new islands is significant, (2) an aggregation regime where nucleation essentially stops and existing islands grow, and (3) a coalescence regime where individual islands merge, resulting in fewer islands. In analogy with vapor phase thin-film deposition (such as molecular-beam epitaxy) the island size distribution in the aggregation regime is predicted to show dynamic scaling behavior, indicating that at a given time, only one length scale is present. We explicitly verify this dynamic scaling assumption, showing that the island size distributions, over a range of surface coverage from 0.06--0.17, can be collapsed into a single dimensionless distribution function by the theoretically predicted scaling relationships. The shape of this distribution function implies that Ostwald ripening is not a significant factor and that the critical nucleus is \ensuremath{\leqslant}2 molecules.