Critical island size, scaling, and ordering in colloidal nanoparticle self-assembly

In order to obtain a better understanding of short-range (SR) and long-range (LR) nanoparticle (NP) interactions during the self-assembly of dodecanethiol-coated Au NPs in toluene via drop drying, we have investigated the dependence of the island density, scaled island-size distribution (ISD), and scaled capture-zone distribution (CZD) on coverage, deposition flux, and NP size. Our results indicate that, while the critical island size is larger than 1 for all NP sizes studied, due to the increase in the strength of the SR attraction between NPs with increasing NP size, both the exponent describing the dependence of the island density on deposition flux and the critical island-size decrease with increasing NP size. We also find that, despite the existence of significant cluster diffusion and coalescence, the ISD is sharply peaked as in epitaxial growth. In particular, for large NP size, we find good agreement between the scaled ISD and epitaxial growth models as well as good agreement between the scaled CZD and scaled ISD. However, for smaller NPs the scaled ISD is less sharply peaked despite the fact that the critical island size is larger. This latter result suggests that in this case additional effects such as enhanced island coalescence or NP detachment from large islands may play an important role. Results for the ordering of NP islands are also presented which indicate the existence of LR repulsive interactions. One possible mechanism for such an interaction is the existence of a small dipole moment on each NP which arises as a result of an asymmetry, driven by surface tension, in the thiol distribution for NPs adsorbed at the toluene-air interface. Consistent with this mechanism, we find good agreement between experimental results for the nearest-neighbor island-distance distribution and simulations which include dipole repulsion.