Isochoric path

Besides shear-induced phase transitions, Uquid-gas equilibria in confined phases have been extensively studied in recent years, both experimentally [149-155] and theoretically [156-163]. For example, using a volumetric technique, Thommes et al. [149,150] have measured the excess coverage T of SF in controlled pore glasses (CPG) as a function of T along subcritical isochoric paths in bulk SF. The experimental apparatus, fully described in Ref. 149, consists of a reference cell filled with pure SF and a sorption cell containing the adsorbent in thermodynamic equilibrium with bulk SF gas at a given initial temperature T,- of the fluid in both cells. The pressure P in the reference cell and the pressure difference AP between sorption and reference cell are measured. The density of (pure) SF at T, is calculated from P via an equation of state. 

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... 

Equation (4.42) can now be solved under experimentally relevant conditions [31], that is, for bulk isochoric paths (pb = const) and T —> T. Again wc defer a detailed description of the numerical procedure to Appendix D.1.3. Once the numerical solution has been found, we are in a position to calculate the excess coverage for the thermodynamically stable pore phase via... 

If, on the other hand, the substrates are sufficiently attractive, one notices from the plots in Fig. 4.7 that F (T, pb) may either vary continuously or discontinuously depending on whether the (bulk) isochoric path is super-or subcritical, respectively, with regard to the critical point of the confined fluid. Hence, discontinuities in the plots in Fig. 4.7 indicate capillary condensation (evaporation) in the model pore prior to condensation in the bulk, which would, of course, occur at bulk gas-liquid coexistence, i.e., at T - Tzb) /Tzb = 0. 

We have chosen a set of state conditions to cover three densities along the isotherm l.OSTc and three temperatures along the isochore 1.5pc, where subscript c denotes the solvent s critical condition. By critical conditions we mean the critical conditions for the SPC water, = 587 K and pc = 0.27 g mL rather than the critical constant for water, Tc = 647 K and pc = 0.322 g mL. The simulated dielectric constant of the SPC water determined according to Neumann s prescription, along the isothermal and isochoric paths, is presented in Figures 23 and 24 in comparison with those from the correlation of Haar et al. for real water. The main... 

Similar behavior is observed for the equilibrium constant Kc along either the isothermal or the isochoric path (Table 7) in that the CIP population changes (decreases) only by 10% when the solvent density is changed by a factor of 2 along an isothermal path, while this change is 25% (increase) when the temperature is increased by a factor of 1.4 along the isochoric path. In fact, at T, = 1.4 and p, = 1.5, 95% of all ion pairs are in the CIP configuration. Note that the near-critical speciation contrasts dramatically with that at ambient conditions, in that the dissociation is essentially complete, i.e., a > 0.999, even at a salt concentration of 10" M. 

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