Phase equilibrium solids

The data for the phase equilibrium solid-liquid for the binary system cocoa butter-CC>2 and for the equilibrium solubility data of CO2 in the liquid phase of cocoa butter have been presented [70],... 

Weidner E, Wiesmet V, Knez Z et al (1997) Phase equilibrium (solid-liquid-gas) in polyethylene glycol-carbon dioxide systems. J Supercrit Fluids 10(3) 139-147... 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

The rate at which a solid-fluid system can reach equilibrium is significant in the design of systems for these applications. Compared to vapor-liquid or liquid-liquid systems approaching phase equilibrium, solid-related equilibria require additional considerations. 

Figure 5.1 presents the behaviour of a pure species that can exist as solid, liquid or vapour in a pressure-temperature diagram. We may have three types of two-phase equilibrium solid/liquid, vapour/liquid and solid/vapour. There is a point where all three phases coexist, designated by the triple point. Here the phase rule gives F=C+2-P= +2-3=Q degrees of freedom. Neither pressure nor temperature can be used to modify the equilibrium. If only two phases can be found at equilibrium F=l+2-2=l, and either pressure or temperature can vary. The most important equilibrium in process engineering is vapour-liquid equilibrium, abbreviate as VLE. It may be observed that the two phases will coexist up to a point where it is difficult to make a distinction between vapour and liquid. This is the critical point, a fundamental physical property characterised by critical parameters and. Above the critical point the state... 

WEI Weidner, E., Wiesmet, V., Knez, Z., and Skerget, M., Phase equilibrium (solid-liquid-gas) in polyethyleneglycol-caibon dioxide systems, J. Supercrit. Fluids, 10, 139, 1997. 

Water in the cathode catalyst layer may exist in multiple states such as absorbed in the ionomer, as vapor, and as sohd phases at sub-freezing conditions. Assuming phase equilibrium, solid water can emerge when the vapor pressure reaches the saturated level. Before that, most water produced from the ORR can be absorbed in the ionomer, which hereby can be defined as the first stage. The second stage is characterized by solid production and ice volume growth within the catalyst layer. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

High mass-transfer rates in both vapor and hquid phases. Close approach to eqiiilihriiim. Adiabatic contact assures phase eqiiilihriiim, Only moderate mass-transfer rate in liquid phase, zero in sohd. Slow approach to equilibrium achieved in brief contact time. Included impurities cannot diffuse out of solid. Sohd phase must be remelted and refrozen to allow phase equilibrium. 

I rcdici.s properties and lompuics ihcmical and solid-liquid phase equilibrium for aqueous mixtures. Up to 20 composition data sets may be handled in memory at once. Requires 512K memory. 

Point A on a phase diagram is the only one at which all three phases, liquid, solid, and vapor, are in equilibrium with each other. It is called the triple point. For water, the triplepoint temperature is 0.01°C. At this temperature, liquid water and ice have the same vapor pressure, 4.56 mm Hg. 

In Chapter 10 we used the principles of equilibrium to help us understand solubility in liquids. In such a system constituents in solution reach the dynamic balance of equilibrium with another phase, a solid or a gas. Equilibrium can also exist among two or more constituents present in the same solution. One of the examples already encountered (in Chapter 9 and in Experiment IS) is... 

Let us first consider the three-phase equilibrium ( -clathrate-gas, for which the values of P and x = 3/( +3) were determined at 25°C. When the temperature is raised the argon content in the clathrate diminishes according to Eq. 27, while the pressure can be calculated from Eq. 38 by taking yA values following from Eq. 27 and the same force constants as used in the calculation of Table III. It is seen that the experimental results at 60°C and 120°C fall on the line so calculated. At a certain temperature and pressure, solid Qa will also be able to coexist with a solution of argon in liquid hydroquinone at this point (R) the three-phase line -clathrate-gas is intersected by the three-phase line -liquid-gas. At the quadruple point R solid a-hydroquinone (Qa), a hydroquinone-rich liquid (L), the clathrate (C), and a gas phase are in equilibrium the composition of the latter lies outside the part of the F-x projection drawn in Fig. 3. The slope of the three-phase line AR must be very steep, because of the low solubility of argon in liquid hydroquinone. 

The equilibria between clathrate and gas, and Qa, clathrate, and gas could be determined by using w-propanol as the auxiliary solvent.53 In the latter equilibrium, the composition of the clathrate is found from the amount of gas required for the conversion of a given amount of solid a-hydroquinone suspended in the propanol solution into clathrate at constant temperature and pressure. The dissociation pressure of the clathrate is given by the total pressure of the four-phase equilibrium -clathrate-solution-gas, corrected for the vapor pressure of w-propanol saturated with a-hydroquinone. Using this technique it was found that the equilibrium clathrates of hydroquinone and argon have yA = 0.34 at 25°C63 and 0.28 at 60°C.28... 

If we look at the mechanistic and crystallographic aspects of the operation of polycomponent electrodes, we see that the incorporation of electroactive species such as lithium into a crystalline electrode can occur in two basic ways. In the examples discussed above, and in which complete equilibrium is assumed, the introduction of the guest species can either involve a simple change in the composition of an existing phase by solid solution, or it can result in the formation of new phases with different crystal structures from that of the initial host material. When the identity and/or amounts of phases present in the electrode change, the process is described as a reconstitution reaction. That is, the microstructure is reconstituted. 

The major differences between polymer and liquid electrolytes result from the physical stiffness of the PE. PEs are either hard-to-soft solids, or a combination of solid and molten in phases equilibrium. As a result, wetting and contact problems are to be expected at the Li/PE interface. In addition, the replacement of the native oxide layer covering the lithium, under the... 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

In Fig. 8.8, we see that sulfur can exist in any of four phases two solid phases (rhombic and monoclinic sulfur), one liquid phase, and one vapor phase. There are three triple points in the diagram, where various combinations of these phases, such as monoclinic solid, liquid, and vapor or monoclinic solid, rhombic solid, and liquid, coexist. However, four phases in mutual equilibrium (such as the vapor, liquid, and rhombic and monoclinic solid forms of sulfur, all in mutual equilibrium) in a one-component system has never been observed, and thermodynamics can be used to prove that such a quadruple point cannot exist. 

Two situations are found in leaching. In the first, the solvent available is more than sufficient to solubilize all the solute, and, at equilibrium, all the solute is in solution. There are, then, two phases, the solid and the solution. The number of components is 3, and F = 3. The variables are temperature, pressure, and concentration of the solution. All are independently variable. In the second case, the solvent available is insufficient to solubilize all the solute, and the excess solute remains as a solid phase at equilibrium. Then the number of phases is 3, and F = 2. The variables are pressure, temperature and concentration of the saturated solution. If the pressure is fixed, the concentration depends on the temperature. This relationship is the ordinary solubility curve. 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

Fig. 42. The unfolded baseline and the Cyt c burst phase. The solid curves show the equilibrium behavior of Cyt c. The equilibrium fluorescence and CD of the (unfolded) fragments (A and <>) match the unfolded holo Cyt c baseline at high GdmCl and define the continuation of the unfolded baseline to lower GdmCl concentrations. The horizontal dashed line shows the initial fluorescence and CD in the stopped-flow experiments (4.3 M GdmCl). The solid symbols indicate the fluorescence (A) and the ellipticity at 222 nm (B) reached by holo Cyt c in the burst phase on dilution into lower (or higher) GdmCl, as suggested by the arrows (starting from either pH 2 ( ) or pH 4.9 ( )). These comparisons are made on an absolute, per-molecule basis. Forster-averaged distance (Trp-59 to heme) is at the right of A. (From Sosnick et al., 1997, with permission. 1997, National Academy of Sciences, USA.)...

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