Chemically homogeneous substrates

Employing the MC simulation technique introduced in the previous section we now turn to a detailed discussion of thermoph3raical properties of confined fluids. In particular, we intend to illustrate the intimate relation between these properties and imique structural features caused by the competition between various length scales pertinent to specific confinement scenarios. These studies arc largely motivated by parallel experimental work employing the SFA. Therefore, we begin with a concise description of some key aspects of SFA experiments. 

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The previously discussed confinement scenario becomes slightly more complex if we allow the substrates to attract molecules in addition to just repelling them. We focus on a chemically homogeneous substrate surface first. 

We now extend the previous discussion of pure confined lattice fluids to binary (A-B) mixtures on a simple cubic lattice oi J f = nz sites, whose lattice constant is again i. We deviate from our previous notation (i.e., M = nx%r ) because we concentrate on chemically homogeneous substrates where n = n riy located in a plane at some fixed distance from the substrate, which are energetically equivalent. Moreover, our subsequent development will benefit notationally by replacing henceforth n by just z. 

In addition to classic fluids with interacting molecules, we shall also consider below the ideal quantum gas of Bosons and Fermions. The ideal quantum gases arc confined by plane parallel, structureless, and chemically homogeneous substrates represented by... 

This equation (1) describes the relationship between macroscopic interfacial quantities such as the surface tension Xab and the wall free energy Xaw - Ibw- At this point, it should be pointed out that this relation only makes sense for purely flat and chemically homogeneous substrates. When the solid surface becomes disordered, we then have to consider advancing and receding angles as defined in fig.2 by considering a drop in which we put or from which we take some quantity of liquid. 

These non-bulk structures also provide a window for the study of surface reconstruction of block copolymers [31]. It has been shown that surface reconstruction of the domains in thin films of cylinder-forming block copolymers on a chemically homogeneous surface can lead to a variety of structures, such as perforated lamellae, undulating cylinders, and spherical nodules [31, 66]. Additionally, separate research demonstrated that cylindrical domains can assume very tortuous, three-dimensional (3D) structures in films on chemically homogeneous substrates as the film thickness is increased beyond a first layer of cylinders adjacent to the substrate [29]. 

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