Confined fluid critical-point, shift

Zhang, X., and Wang, W. 2006. Phys. Rev. E. Square-well fluids in confined space with discretely attractive wall-fluid potentials Critical point shift. 74 062601. 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

As indicated before the locus of the phase diagram of a confined fluid compared to the coexistence curve of the bulk fluid is of importance for the occurence of pore condensation and hysteresis, i.e. for the shape of the sorption isotherm. It is expected that the critical temperature and the triple point temperature will be shifted to lower values for a confined fluid compared to a bulk fluid, i.e. the smaller the pore width the lower the critical temperature and triple point temperature of the pore fluid [8,9,20]. Pore condensation occurs whenever the pore... 

More subtle effects are observed if the lattice fluid is confin by solid substrates as plots in Fig. 4.12(a) show. For sufficiently large ri, chemical decoration of the substrate does not matter but eonfiuement effects prevail. For example, for Ux = 15, the critical point is shifted to lower 7 and pf compared with bulk Tcb = and peb = —3. Moreover, pf (T) is no longer parallel with the temperature axis as in the bulk. 

The coexistence curves and properties of confined fluid were extensively studied by computer simulations. Shift of the parameters of the liquid-vapor critical point of fluids in pores was seen in many simulation studies. The most accurate results were obtained by simulations of LJ fluid in the Gibbs ensemble [10, 28-30, 32, 127, 141, 186, 187, 205, 249,250,262,274,325,326], but this method is restricted to the pores of simple geometry only. In the narrow slit pore with weakly attractive walls and widths of 6,7.5, and 10 a, the liquid-vapor critical point of LJ fluid decreases to 0.8897] , 0.9197] , and 0.9577] , respectively [325, 326]. For comparable fluid-wall interaction, the liquid-vapor critical temperature is about 0.9647] and 0.9817] in the pores with a width Hp= 12 a and 77p = 40(7, respectively [29]. The dependence of the pore critical temperature on the pore width is shown in Fig. 53. This dependence may be satisfactorily described by equation (15) (solid line) when we take into account that centers of molecules do not enter an interval of about 0.5 <7 near each wall. The critical temperatures of U fluid in the pores with strongly attractive walls are noticeably lower than in pores with weakly attractive walls (compare circles and squares in Fig. 53) [325,326]. This should be attributed to the effective decrease in the pore width due to the appearance of adsorbed film on the pore walls, which is almost identical in both phases. In this case, dependence of Tc p on Hp may be satisfactorily described by equation (15) (dashed line) if we take into account that... 

The earliest applications of the replica integral equation approach date back to the beginning of the 1990s. They focused on quite simple QA systems such as hard-sphere (HS) and LJ (12,6) fluids in HS matrices (see, for example. Refs. 4, 286, 290, 298, 303, 312, and 313 for reviews). Fiom a technical point of view, these studies have shown that the replica integral equations yield accurate correlation functions compared with parallel computer simulation results [292, 303, 314, 315]. Moreover, concerning phase behavior, it turned out that the simple LJ (12,6) fluid in HS matrices already displays features also observed in experiments of fluids confined to aerogels [131, 132]. These features concern shifts of the vapor liquid critical temperature toward values... 

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