Inversion temperature at low density

Confinement causes B2 (T) to be shifted with respect to the bulk curve. If the substrate potential is wettable [model A, see Fig. 5.27(a)], B2 (T) is 

on the other hand, the degree of confinement decreases (i.e., with increasing 8 0)1 (T) for a confined fluid is expected to approach its bulk 

For the cmwes plotted in Figs. 5.27(a), Tj v (0) is calculated from differential equation Eq. (5.155). Results are compiled in Table 5.7 for models A and B and s o = 10. They show that Tj v (0) is higher for a hydrophobic 

From the mean-field expressions Eqs. (4.24) and (5.185) one expects the difference 

The plot in Fig. 5.28. shows that data compiled in Table 5.7 are consistent with this scaling relation except for. s o = 5.0 where the assumption of homogeneity of the confined fluid, on which the mean-field theory is based (see Section 4.2.2), can hardly be expected to be valid. The results in this section therefore confirm our expectation that the inversion temperature should depend on the substrate separation and that it becomes higher the more severely confined is the fluid (i.e., the smaller s o bec omes). 

However, it seems worthwhile stressing that the relation between Boyle and inversion temperatures is only approximately described by the mean-field theorj. For example, the mean-field Ekjs. (5.185) and (5.188) predict TBoyie/Tinv (0) = 2 irrespective of s, but entries in Table 5.7 show that this ratio is lower and depends on s o as well as on the chemical nature of the substrate. This clearly indicates that the mean-field treatment developed in Sections 4.2.2 and 5.7.5 is not fully adequate as one would have expected. However, the deviation from the limiting value TBoyie/Tlnv (0) = 2 does not exceed 6.5% for. s o = 100, where the mean-field treatment is expected to work best. This, on the other hand, shows that mean-field theory is quite useful to understand the behavior of confined fluids at least from a qualitative point of view. 

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