Computation of the grand potential

As a test of Eq. (5.92) we apply the procedure outlined in Section 5.5.2 to a fluid confined to a slit-pore with infinitesimally smooth, chemically homogeneous substrate surfaces. These can be realized by replacing in Eq. (5.83) s x,y R,K) = 1 so that (/ [ (-Zi) in Eq. (5.87) is replaced by (zj). According to the di.scussion in Section 5.5.2 we maj then also replace Eq. (5.92) by 

Consider now the chemically decorated substrates where the fluid substrate interaction potential is given by Eqs. (5.81)-(5.84). Over the temperature range 0.60 T 0.75 to which this study is restricted, the confined fluid may form three distinctly different morphologies characterized by the local density defined here as 

This packing effect is due solely to the geometry of the diemical decoration of the substrate and has not been observed for other geometries, which is for, say, alternating strip-like domains composed of different solid materials (see Figs. 5.8). 

For intermediate chemical potentials, the confined fluid may condense only partly in a subvolume V (r, 2) jO r / , —s j z Szj2 controlled approximately by the circulai attractive area with which the substrates are decorated. This is illustrated by the plot of p r, z) in Fig. 5.15(b) where high(er)-density fluid is spanning the gap between the circular attractive regions on the opposite substrates. Therefore, this morphologj will be referred to as bridge. Notice that in the contact layers the fluid is stratified in radial directions similar to the liquid (see Fig. 5.15(c)]. However, here the radial ordering of fluid molecules is less pronounced compared with the liquid 

For a corresponding liquid state one begins with A = 0 and a sufficiently high pi = —7.15 such that a liquid morphology is stable even though the substrates are not wet (because they are purely repulsive) [see Eq. (5.87)]. Once A = 1 the chemical potential is now lowered and lj is again calculated by 

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