Mechanical expression slit-pore

The simplest case that we shall be discussing hen in some detail is that of a fluid confined to a nanoscopic. slit-pore with homogeneous (infinitesimally) smooth substrate surfaces. For this prototypical model, it was shown in Section 1.6.1 that a mechanical expression for the grand potential exists. However, in what follows, it is more convenient to focus on the grand-potential density rather than on il itself. The former is defined through the relation... 

We now turn to a microscopic treatment of the. Toule-Thomson effect and begin with the limit of vanishing density. Th(j treatment below is very sinrilar to the one presented in Section 3.2.2 where we derived molecular expressions for the first few virial coefficients of the one-dimensional hard-rod fluid. Here it is important to realize that a mechanical expression for the grand potential exists for a fluid confined to a slit-pore with chemically structured substrate surfaces as we demonstrated in Section 1.6.1 [see Eq. (1.65)]. Combining this cxpres.sion with the tnolocular expression given in Eq. (2.81) we may write... 

The computational procedures now used in the application of density functional theory and molecular simulation for the prediction and analysis of physisorption isotherms are based on the statistical mechanics of confined fluids [14]. These important advances are described in several chapters of this book and therefore the present introductory remarks are confined to a few general comments. Whichever computational procedure is adopted [39, 40], it is first necessary to define a 3-D model of the pore structure within a sohd of known and uniform composition [14]. It has been customary to assume that the pores of different width are aU of the same shape (e.g., slits in activated carbons). Further assumptions made by many investigators are that the filling or emptying of each group of pores can occur independently and reversibly, that the internal surface is uniform and that the solid-fluid and fluid-fluid interactions can be expressed in terms of standard potential functions [14],... 

---