Three-phase point

Figure 1.1. Derivation of Equation (1.12). When this equation is satisfied an infinitesimal change of position of the three-phase point, dx, will not change the total surface energy of the system and thus it is in equilibrium.

Air diffusion electrodes In fuel cells and in air-breathing batteries, a mesoporous carbon electrode is made up of two layers an outer layer composed of carbon powder and a hydrophobic (nonwettable) binder, typically PTFE. This enables the access of gas to the inner layer, where the binder is selected to be both a hydrophilic (wettable) and an ion-conducting ionomer, to support (rather than impair if the binder was nonconducting) the ionic conductivity of the porous electrode. The catalyst particles are dispersed in-between the carbon particles. Thus, a very tortuous interface between the two layers is formed. The reacting gas approaches this interface, forming three phase points of contact providing a high active surface area. See also - air electrode. 

Figure 4.3 shows three isotherms where the hydrogen sulfide can condense. The dashed plateaus on this figure are three-phase points. The leftmost point on the plateau is the water content of the gas and the rightmost is that of the F S-rich liquid. The water content of the F S-rich liquid is greater than the water content of the vapor. For example,... 

Vf)]. Here p, P2, and are the densities of polymer 1, polymer 2, and monomer 2. respectively W, is the weight ratio of total monomer 2 to polymer 1 X is the polymerization conversion, /t], Rz, and R are the radii of polymer phase-1, polymer phase-2, and the overall composite particles, respectively 0 and 9 (see Figure 9,2) are the angles between the line that connects the two centres of the hemispheres and the line that coimects the centres and the three-phase point Yvi, Xiw. X2w are the interfacial tensions between the two polymer phases, polymer phase-1 and water (containing siirfactant, if present), and polymer phase-2 and water (containing surfactant, if present) respectively. A polymer phase is defined as polymer 1 or polymer 2 dissolved in MMA monomer V, is the volume ratio of polymer phase-2 to polymer phase-1 (from ref. 39)... 

Fig. 3.4 illustrates the surface tension vectors at the three-phase point of contact of solid, liquid and vapour. The Young equation relating these tensions to 0 is... 

Figure 3.95. Schematic of the CP( location with a three-phase point 7 . GTHDTF arc the CPC s branches, GTF is the stable part, TBDT is the mctastable part G"B iyF is tlie SL G"T" and T F are the stable parts, T"B D T is the inetastable part C is the metastable critical point (Sole, 1974) [Reprinted from K.Solc. J. Polym. Sci. Polym. Phys. Kd. 12 (1974) 555-562. Copyright 1974 by Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

Figure 4.1 Illustration of the canonical ensemble. Each phase point of the ensemble moves along a constant energy (isoenergetic) surface. (Only three phase points are shown.) The average kinetic energy of the molecules over the ensemble is fixed at a prespecified value in the canonical ensemble.

While, in principle, a tricritical point is one where three phases simultaneously coalesce into one, that is not what would be observed in the laboratory if the temperature of a closed system is increased along a path that passes exactly tlirough a tricritical point. Although such a difficult experiment is yet to be perfomied, it is clear from theory (Kaufman and Griffiths 1982, Pegg et al 1990) and from experiments in the vicinity of tricritical points that below the tricritical temperature only two phases coexist and that the volume of one slirinks precipitously to zero at T. ... 

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Figure C3.6.7(a) shows tire u= 0 and i )= 0 nullclines of tliis system along witli trajectories corresponding to sub-and super-tlireshold excitations. The trajectory arising from tire sub-tlireshold perturbation quickly relaxes back to tire stable fixed point. Three stages can be identified in tire trajectory resulting from tire super-tlireshold perturbation an excited stage where tire phase point quickly evolves far from tire fixed point, a refractory stage where tire system relaxes back to tire stable state and is not susceptible to additional perturbation and tire resting state where tire system again resides at tire stable fixed point.

Fig. 7. The concept of contact angle with a captive bubble in an aqueous medium, adhering to a hydrophobic sofld P is the three-phase contact point. Here, the vector passes through P and forms a tangent to the curved surface of the air bubble. The contact angle 0 is drawn into the Hquid.

For sodium palmitate, 5-phase is the thermodynamically preferred, or equiUbrium state, at room temperature and up to - 60° C P-phase contains a higher level of hydration and forms at higher temperatures and CO-phase is an anhydrous crystal that forms at temperatures comparable to P-phase. Most soap in the soHd state exists in one or a combination of these three phases. The phase diagram refers to equiUbrium states. In practice, the drying routes and other mechanical manipulation utilized in the formation of soHd soap can result in the formation of nonequilibrium phase stmcture. This point is important when dealing with the manufacturing of soap bars and their performance. 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Phenomena at Liquid Interfaces. The area of contact between two phases is called the interface three phases can have only aline of contact, and only a point of mutual contact is possible between four or more phases. Combinations of phases encountered in surfactant systems are L—G, L—L—G, L—S—G, L—S—S—G, L—L, L—L—L, L—S—S, L—L—S—S—G, L—S, L—L—S, and L—L—S—G, where G = gas, L = liquid, and S = solid. An example of an L—L—S—G system is an aqueous surfactant solution containing an emulsified oil, suspended soHd, and entrained air (see Emulsions Foams). This embodies several conditions common to practical surfactant systems. First, because the surface area of a phase iacreases as particle size decreases, the emulsion, suspension, and entrained gas each have large areas of contact with the surfactant solution. Next, because iaterfaces can only exist between two phases, analysis of phenomena ia the L—L—S—G system breaks down iato a series of analyses, ie, surfactant solution to the emulsion, soHd, and gas. It is also apparent that the surfactant must be stabilizing the system by preventing contact between the emulsified oil and dispersed soHd. FiaaHy, the dispersed phases are ia equiUbrium with each other through their common equiUbrium with the surfactant solution. 

The KTTS depends upon an absolute 2ero and one fixed point through which a straight line is projected. Because they are not ideally linear, practicable interpolation thermometers require additional fixed points to describe their individual characteristics. Thus a suitable number of fixed points, ie, temperatures at which pure substances in nature can exist in two- or three-phase equiUbrium, together with specification of an interpolation instmment and appropriate algorithms, define a temperature scale. The temperature values of the fixed points are assigned values based on adjustments of data obtained by thermodynamic measurements such as gas thermometry. 

Properties. Thallium is grayish white, heavy, and soft. When freshly cut, it has a metallic luster that quickly dulls to a bluish gray tinge like that of lead. A heavy oxide cmst forms on the metal surface when in contact with air for several days. The metal has a close-packed hexagonal lattice below 230°C, at which point it is transformed to a body-centered cubic lattice. At high pressures, thallium transforms to a face-centered cubic form. The triple point between the three phases is at 110°C and 3000 MPa (30 kbar). The physical properties of thallium are summarized in Table 1. 

The final factor influencing the stabiHty of these three-phase emulsions is probably the most important one. Small changes in emulsifier concentration lead to drastic changes in the amounts of the three phases. As an example, consider the points A to C in Figure 16. At point A, with 2% emulsifier, 49% water, and 49% aqueous phase, 50% oil and 50% aqueous phase are the only phases present. At point B the emulsifier concentration has been increased to 4%. Now the oil phase constitutes 47% of the total and the aqueous phase is reduced to 29% the remaining 24% is a Hquid crystalline phase. The importance of these numbers is best perceived by a calculation of thickness of the protective layer of the emulsifier (point A) and of the Hquid crystal (point B). The added surfactant, which at 2% would add a protective film of only 0.07 p.m to emulsion droplets of 5 p.m if all of it were adsorbed, has now been transformed to 24% of a viscous phase. This phase would form a very viscous film 0.85 p.m thick. The protective coating is more than 10 times thicker than one from the surfactant alone because the thick viscous film contains only 7% emulsifier the rest is 75% water and 18% oil. At point C, the aqueous phase has now disappeared, and the entire emulsion consists of 42.3% oil and 57.5% Hquid crystalline phase. The stabilizing phase is now the principal part of the emulsion. 

The six secondary phases are obtained by shorting the centre points of each of the three-phase windings of a 3p transformer secondary. 

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