Critical solution pressure

Case III. As the pressure increases still further, the solubility curve intersects larger liquid-liquid regions until the critical solution pressure of the system has been reached. Above this critical pressure, no vapor phase exists, and the phase diagram consists of only the coexistence curve, as shown in Fig. 28c. In Fig. 28, L, and L2 stand for the two liquid phases and F stands for a fluid phase. 

According to theory and simulation studies by Johnston [7] and coworkers, colloidal suspensions will be stable above the upper critical solution pressure (UCSP) if the graft... 

Experimental results are presented for high pressure phase equilibria in the binary systems carbon dioxide - acetone and carbon dioxide - ethanol and the ternary system carbon dioxide - acetone - water at 313 and 333 K and pressures between 20 and 150 bar. A high pressure optical cell with external recirculation and sampling of all phases was used for the experimental measurements. The ternary system exhibits an extensive three-phase equilibrium region with an upper and lower critical solution pressure at both temperatures. A modified cubic equation of a state with a non-quadratic mixing rule was successfully used to model the experimental data. The phase equilibrium behavior of the system is favorable for extraction of acetone from dilute aqueous solutions using supercritical carbon dioxide. 

The physical picture that underlies this behavior, as pointed out first by Elgin and Weinstock (1), is the salting out effect by a supercritical fluid on an aqueous solution of an organic compound. As pressure is increased, the tendency of the supercritical fluid to solubilize in the organic liquid results in a phase split in the aqueous phase at a lower critical solution pressure (which varies with temperature). As pressure is further increased, the second liquid phase and the supercritical phase become more and more similar to each other and merge at an upper critical solution pressure. Above this pressure only two phases can coexist at equilibrium. This pattern of behavior was also observed by Elgin and Weinstock for the system ethylene - acetone - water at 288 K. In addition, the same type of... 

An interesting feature of the phase equilibrium behavior is the relative insensitivity of the phase envelope and positions of the tielines to variations in pressure in the two-phase region, as evidenced by comparison of the diagrams at 100 and 150 bar in Figure 4. This would seem to imply that similar separations can be achieved by operation at a range of pressures above the upper critical solution pressure of -95 bar. 

Figure 1. Three-dimensional phase model for polyethylene + ethylene mixtures with constant temperature cuts at 120, 160 and 200 °C (showing upper critical solution pressures) and a constant pressure cut (showing lower critical solution temperature). [ Adapted from ref 6].

In closing, we would like to mention some applications of the GEMC/CBMC approach and very much related combination of CBMC and the grand canonical Monte Carlo technique to other complex systems prediction of structure and transfer free energies into dry and water-saturated 1-octanol [72], prediction of the solubility of polymers in supercritical carbon dioxide [73], prediction of the upper critical solution pressure for gas-expanded liquids [74], investigation of the formation of multiple hydrates for a pharmaceutical compound [75], exploration of multicomponent vapor-to-particle nucleation pathways [76], and investigations of the adsorption of articulated molecules in zeolites and metal organic frameworks [77, 78]. 

Figure 8 shows the plots of the Flory-Huggins interaction p>arameters against temperature at fixed PS concentration (( )p5 = 0.5) under different pressures. It is shown that y is almost linear with the temperature and decreases with the increasing of temperature, and the inserted figure shows that y increases with pressure at fixed temperature and composition, which is consistent with the experimental measured results that TD/PS system shows low critical solution pressure (LCSP) behavior. 

Kennis et al. [40] reported on the influence the addition of nitrogen exerts on the location of the miscibility gap for linear polyethylene in -hexane at pressures up to 7.5 MPa in the temperature range 393-453 K for small concentrations of nitrogen. Liquid-liquid phase boundaries (cloud points) were determined with the aid of a Cailletet-like apparatus in which the phase separation was observed visually. Experimental cloud-point isopleths (/ vs r at constant composition) for linear polyethylene in -hexane were reported to be nearly parallel values for dpjdT are positive which indicates upper critical solution pressures (at constant T) and lower critical solution temperatures (at constant p) (Fig. 5). The addition of small amounts of nitrogen shifts these isopleths to higher pressures and lower temperatures. 

The monomeric aqueous solubility of surfactants also depends on pressure, and decreases with increasing pressure. This effect is opposite to that of temperature. In other words, with decreasing pressure the monomeric solubility increases up to the CMC, at which micellization is accompanied by a rapid solubility increase (Fig. 4.19). The pressure at which a solubility-pressure cruve intercepts the CMC-pressure curve is the critical solution pressure Pc for micelle formation, which corresponds to the conventional Krafft point for temperature (see Chapter 6). The presence of Pc is observed... 

Figure 4.19. Effect of pressure on the CMC and solubility of sodium dodecyl sulfate at 20°C. M, micellar solution S, monomer solution C, hydrated solid critical solution pressure. (Reproduced with permission of Academic Press.)...

Figure 4.20. Three>dimensional phase diagram of ionic surfactant/water system. T, Krafft point Pc critical solution pressure K—Pg, critical solubility curve.

All points on the critical loci of Fig. 2 satisfy the criteria of 6-points (7f and like the 6-point of polymer solutions under more familiar conditions they represent concentrations low in polymer. The more familar 6-point, usually observed closer to room temperature and at atmospheric pressure represents, of course, an upper critical solution temperature (UCST). This UCST becomes, however, merely the end point of a critical locus representing a liquid-liquid mixture, if pressure is introduced as additional variable (77), just as the LCST noted in hydrocarbon polymers by Freeman and Rowlinson merely becomes the critical end point of the critical locus of a fluid-liquid mixture. F. 2 shows the critical locus for polyethylene-pentane, which is of the latter type. Turning our attention to the stem polyethylene-ethane, a fluid-liquid mixture whose critical locus will be seen to lie closest to that of the system polyethylene-ethylene, inspection of Fig. 2 indicates that it as quite appropriate to state that polyethylene dissolves in ethane above an upper critical solution pressure (UCSP) which varies somewhat with... 

Interestingly, CH4 modifies the MDPE stracture but is easily removed from the modified polymer. Since the upper critical solution pressure of the MDPE-CH4 system is rather high (>250 MPa [57]), CH4 can be a plasticizer of MDPE up to elevated pressures. Experimentally, an MDPE sample (density 938 kg m degree of... 

Ikawa et al. [136] determined the critical solution temperature (Krafft point) and the critical solution pressure (Tanaka pressure) of sodium perfluorodecanoate in water. A phase diagram of sodium perfluorodecanoate versus pressure at 55°C is shown in Fig. 6.29. The curves of solubility versus pressure (aQb) and of cmc versus pressure (dQe) intersect at point Q, representing the Tanaka pressure. The phase diagram is divided into three regions solution of monomolecular species (S), the micellar solution (M), and the hydrated solid (C). The rapid decrease of solubility with increasing pressure (curve aQ) was attributed to the transfer of surfactant from micelles to the hydrated solid phase, which is accompanied by a large decrease in partial molar volume. 

Fig. 6.29 The phase diagram of sodium perfluorodecanoate concentration versus pressure at 55°C. M, S, and C denote the micellar, singly dispersed, and hydrated solid states, respectively Q, a triple point CSP, critical solution pressure. (From Ref. 136. Reproduced by permission of Plenum Publishing.)...

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