Nanopatterned model substrate

Precisely this latter situatiun aris if the cuiifining solid surface is endowed with a chemical pattern that is both nanoscopic in size and finite in extent. Such chemical patterns may be created by lithographic methods (1791. Atomic beams have b n employed to produce hexagonal nanostructures [180]. Other methods capable of creating cliemically nanostructured substrate surfaces involve microphase separation in diblock copolymer films [181] or the use of force micTOscopy to locally oxidize silicon surfaces [182]. 

If one aims at understanding this rather peculiar phase behavior from a microscopic perspective, one again needs to know the relevant thermodynamic potential. However, one is immediately confronted with a complication because a mechanical expression for thermodynamic potentials cannot be derived due to the low symmetry of the confined fluid (see also discussion in Section 1.6.2). Therefore, a different means of calculating these potentials must be devised. This alternative computational technique will be based on a perturbational approach to which the current section is devoted. 

Specifically, we consider the situation depicted schematically in Fig. 5.12 a simple fluid confined between two planar substrate surfaces composed of like atoms wdiere the fluid fluid interaction is described by Eq. (5.39) for 

Efg sets the energy scale of fluid substrate interactions. For simplicity we take 

To model substrate surfaces with imprinted chemical iiaiiopatterns (see Fig. 5.12), we modify Eq. (5.82) according to 

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Combinations of the very simple spin-coated reactive polymer films discussed in Sect. 2.1.4 with the micro- and nanopatterning approaches studied and refined in model studies on weU-defined macromolecular (dendrimer) systems are ciu rently being investigated with substantial success. Thus, the lessons learned in these model studies can be applied to practical formats in order to provide reactive micro- and nanopatterned platforms for the development of biosensors, biochips (DNA, proteins, saccharides, and so on) and studies of cell-cell and ceU-substrate interactions. 

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