Point, critical solution triple

Fig. 12. Partial phase diagrams for the dilute region of aqueous solutions of the disodium salts of sulfated monohydroxy bile salts glycolithocholate sulfate (GLCS at pH 10.0) and taurolithocholate sulfate (TLCS at pH 7.0, inset). The solid solubility curves and the interrupted CMC curves demarcate areas where crystals (and monomers), micelles (and monomers), and monomers alone are found. The critical micellar temperature (CMT) represents an equilibrium between micelles and hydrated crystals connected via the monomer concentration at the CMC. The Krafft point is a triple point and only represents the CMT at the CMC. (After ref. 6 with permission.)...

Polymer solutions display a typical phase diagram as illustrated in Fig. 8.1a, which exhibits a highest critical phase separation temperature, called upper critical solution temperature (UCST). Within the same temperature window, polymer solutions may also crystallize below the solution-crystal coexistence line, as illustrated in Fig. 8.1b. Two kinds of phase transitions will interplay with each other, so that an interception point is observed in the corresponding phase diagrams. The interception point is a three-phase-coexisting point, as illustrated in Fig. 8.1c, called the monotectic triple point. At this point, a dilute solution, a concentrated solution and a crystalline phase can coexist. 

In Fig. 11, we draw schematically the case of fluid-solid phase behavior for the Type-I fluid mixture water-NaCl. For critical temperatures this far apart, the three-phase line Sb-L-V from the low-temperature quadruple point (where four three-phase lines meet) to the solutes triple point develops a high maximum that reaches above water s critical pressure and temperature. If a salt solution is heated at a pressure above the critical pressure of water, the vapor-liquid critical line is crossed first, and a two-phase L-V region entered. At high enough temperature the three-phase line Sb-L-V may be crossed, and solid salt will form. Thus supercritical water, fully miscible with air constituents and hydrocarbons, becomes a poor solvent for salts. 

In polymer solutions, liquid-liquid (L-L) demixing is another common phase transition besides crystallization. The thermodynamic boundary conditions for both of them behave as the functions of polymer concentrations and temperatures, demonstrated as phase diagrams. The schematic L-L binodal and liquid-solid (L-S) coexistence curves in polymer solutions and their interception are shown in Figure 13.2. The illustrated L-L binodal contains an upper critical solution temperature. Some other solutions also contain binodals with a lower critical solution temperature. When the L-S curve intersects with the L-L curve in the overlapping temperature windows, both curves are terminated at the intersection point, which is referred to as the monotectic triple point. 

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.)...

White monoclinic crystals density 5.09 g/cm melts at 64°C (triple point) sublimes at 56.6°C critical temperature 232.65°C critical pressure 46 atm critical volume 250 cm /mol reacts with water forming UO2F2 and HF soluble in chloroform, carbon tetrachloride and fluorocarbon solvents soluble in liquid chlorine and bromine dissolves in nitrobenzene to form a dark red solution that fumes in air. 

Type II (Solid-Fluid) System. In type II systems (when the solid and the SCF component are very dissimilar in molecular size, structure, and polarity), the S-L-V line is no longer continuous, and the critical (L = V) mixture curve also is not continuous. The branch of the three-phase S-L-V line starting with the triple point of the solid solute does not bend as much toward lower temperature with increasing pressure as it does in the case of type I system. This is because the SCF component is not very soluble in the heavy molten solute. The S-L-V line rises sharply with pressure and intersects the upper branch of the critical mixture (L = V) curve at the upper critical end point (LfCEP), and the lower temperature branch of the S-L-V line intersects the critical mixture curve at the lower critical end point (LCEP). Between the two branches of the S-L-V line there exists S-V equilibrium only (13). 

As described in Figure 4b the phase behavior of a type II binary system is depicted by the vapor pressure (L-V boundary) curves for the pure components, sublimation (S-V boundary) and melting (S-L boundary) curves for the solid component, and especially the S-L-V line on the P-T space. For an organic solid drug solute, the triple-point temperature is sufficiently higher than the critical temperature of the SCF solvent. The (L = V) critical locus has two branches and is intersected by two S-L-V lines at LfCEP and LCEP, respectively, in the presence of the solid phase. The S-L-V line indicates that the melting of the solid is lowered in the presence of the SCF solvent component as it is dissolved in the molten (liquid) phase. The S-L-V line... 

Fig. 1. The fatty acid soap-water phase diagram of McBain (58) modified (1) to show the molecular arrangement in relation to aqueous concentration (abscissa) and temperature (ordinate). Ideal solution, i.e., true molecular solution, is to the left of the vertical dashed line, indicating the critical micellar concentration (CMC), which varies little with temperature. At concentrations above the CMC, provided that the temperature is above the critical micellar temperature (CMT), a micellar phase is present. At high concentrations, the soap exists in a liquid crystalline arrangement, provided that the solution is above the transition temperature of the system, i.e., the temperature at which a crystalline phase becomes liquid crystalline. The Krafft point is best defined (D. M. Small, personal communication) as the triple point, i.e., the concentration and temperature at which the three phases (true solution, micelles, and solid crystals) coexist, but in the past the Krafft point has been equated with the CMT. The diagram emphasizes the requirement for micelle formation (a) a concentration above the CMC, (b) temperature above the CMT, and (c) a concentration below that at which the transition from micelles to liquid crystals occurs. Modified from Hofmann and Small (1).

Supercritical extraction often involves separation of relatively non-volatile components, often in the solid phase, through selective solubility in the supercritical gasses. Thus, the critical temperatures of the pure components are likely to be significantly different and the critical temperature of the solvent is likely to be lower than the triple point temperature of the solute. The implication is that there is no common temperature range where both... 

There is a critical temperature of amphiphilic compounds for formation of a micellar solution. Below this temperature the amphiphile forms crystals coexisting with water or a gel phase and above this temperature the micellar solution is formed. This temperature varies with amphiphile concentration. The Krafft point has been defined as the knee in the melting curve of the amphiphile in the presence of water, which corresponds to a kind of triple point... 

Returning now to the phase diagram of polymer solutions, we emphasize also that much more complicated phenomena than envisaged in Figure 2a can occur. For example, considering the solution of short alkane chains (eg hexadecane) in carbondioxide, one encounters a competition between gas-liquid transitions of both polymer (Cie H34) and solvent (CO2) and liquid-liquid phase separation (99,100). Thus the phase diagram not only contains (in the space of three variables p,T, and ) various lines of critical points, but special points such as critical end points, triple points, and tricritical points may also occur. Each system then... 

The narrow biphasic gap in the diagram is essentially unaffected by interactions for negative values of x. On the other hand, if the interaction between solute segments is attractive then the biphasic region is abruptly broadened when x exceeds a small positive value. A critical point emerges at xi = 0.055. For xi values immediately above this critical value, the shallow concave curve delineates the loci of co-existing anisotropic phases, in addition to the isotropic and nematic phases at lower concentration within the narrow biphasic gap. At xi = 0.070 these phases co-exist at this triple point. 

For the exact solution of A -electron atoms at the large dimension limit, the symmetry breaking is shown to be a first-order phase transition. For the special case of two-electron atoms, the first-order transition shows a triple point where three phases with different symmetry exist. Treatment of the Hartree-Fock solution reveals a different kind of symmetry breaking where a second-order phase transition exists for N — 2. The Hartree-Fock two-electron atoms in weak external electric field exhibit a critical point with mean-field critical exponents ( = j, a = Odis, 5 = 3, and y — 1). ... 

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