Thommes-Findenegg experiment

Theoretically, several aspects of the Thommes-Findenegg experiment can be analyzed at the mean-field level [157]. A key quantity of a mean-field theory of confined fluids is the (Helmholtz) free energy, given by... 

If one is interested only in properties of the pore phase as a whole, such as the excess adsorption and the phase behavior, and not in properties that depend explicitly on local density, or on intermolecular correlations, then it may be sufficient to neglect entirely variations in the local density. It is in this spirit that we present a simple model for the adsorbed phase that yields closed expressions for the free energy and for the equation of state. Tlie model is a direct extension of van der Waals model for the bulk fluid. For simplicity we adopt the slit-pore geomet ry, although the significant conclusions of the study are not altered for pores of other shapes. As we shall demonstrate below, some features of the Thommes Findenegg experiment [31] can indeed be understood in terms of a simple van der Waals equation of state. 

Howrever, the reader should note that the latter feature is not correct with respect to corresponding experimental observations w here the critical density is usually shifted to higher values and the coexistence curve of the confined fluid turns out to be narrower with respect to its bulk counterpart [31]. This reflects the fact that, with regard to mean densities, gas- and liquid-like confined phases aic more alike than in the bulk. The absence of a shift in critical density in the theoretical curves is caused by the fact that within the context, of the current perturbational approach the density dependence of the free energy remains the same in both confined and bulk fluids [see, for example, Eq. (4.26)], which shows that confinement effects are solely restricted to the density-independent van der Waals parameter ap(0- How cvor, on the positive side, we are now- equipped with equations of state for both the confined fluid [sckj Eq. (4.28)] and its bulk counterpart [see Eq. (4.29)]. Together these equations of state enable us to revisit the Thommes Findenegg experiment at mean-field level. 

Prom a theoretical perspective, the Thommes Findenegg experiment [31] can be represented by the equation... 

A key result of the sorption experiments conducted 1 Thommes and Findenegg concerns the pore condensation line T p (pb) > T b (Pb) at which pore condensation occurs along a subcritical isochoric path Pb/Pch < 1 in the bulk (/ b and peb arc the density of tliis isochore and the bulk critical density, respectively). Experimentally, Txp (pb) is directly inferred from the temperature dependence of F (T), which changes discontinuously at n, (Pb) (see Ref. 31 for detaiLs). The pore condensation line ends at the pore critical temperature Tep (rigorously defined only in the ideal single slit-pore case) [31]. Because of confinement Tep is shifted to lower values with decreasing pore size. If, on the other hand, the pore becomes large, Tep — (the bulk... 

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