Epitaxy and molecular organization on solid substrates

The recent emergence of molecular films as candidates for functional electronic materials has prompted numerous investigations of the underlying mechanisms responsible for their structure and formation. This review describes the role of epitaxy in molecular organization on crystalline substrates. A much-needed grammar of epitaxy is presented that classifies the various modes of epitaxy according to transformation matrices that relate the overlayer lattice to the substrate lattice. The different modes of epitaxy can be organized hierarchically to reflect the balance of overlayer-substrate and molecule-molecule energies. In the case of molecular overlayers, the mismatch of overlayer and substrate symmetries commonly leads to coincident epitaxy in which some of the overlayer lattice points do not reside on substrate lattice points. Analyses of numerous reported epitaxial molecular films reveal that coincidence is quite common even though, based on overlayer-substrate interface energies alone, not as energetically favorable as commensurism. The prevalence of coincidence can be attributed to overlayer elastic constants, associated with molecule-molecule interactions within the overlayer, that are larger than the elastic constants of the overlayer-substrate interface. This condition facilitates prediction of the epitaxial configuration and overlayer structure through simple and comparatively efficient geometric modeling that does not require the input of potential energies, while revealing the role of phase coherence between the overlayer and substrate lattices.