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The adsorption of molecules and their assemblies to substrates through non-covalent bonds can lead to very well ordered structures and the use of surface science techniques reveals the often crystalline character. These systems formed at close to equilibrium conditions reveal fascinating structures and properties. Under ultrahigh vacuum conditions, the self-assembly of discrete clusters and one-dimensional structures occurs on a variety of molecules that interact in specific ways through non-covalent interactions. The chapter plots the advances taken from the study of full monolayers of simple molecules with minimal supramolecular design, to complex multicomponent monolayers where all the hallmarks of self-assembly are expressed, meaning a spontaneous process at equilibrium leading selectively to aggregates whose structure is determined by non-covalent interactions. The dominant interactions tend to be between adsorbate molecules, although the surface can influence in the nature of the aggregates, particularly when weaker interactions between molecules determine the long range order. The control over the relative orientation of aromatic molecules in particular leads to systems that are of interest in the area of molecular electronics. The rapid developments in surface-based structures with void spaces in the plane—that are of great interest for the preparation of defined spaces for molecular recognition—are described, for purely organic and coordination systems.

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