Two Solid Phases

Rice and G. L. Haller, Proceedings of the 5th International Congress on Catalysis , North-Holland, Amsterdam, 1973, Vol. 1, p. 317. 

The addition of iridium to platinum on ij-AlaOa causes a marked increase in the H/M ratio of hydrogen uptake assuming that H/Ms = 1.69.70 value of two was not taken to be conclusive proof of spillover so the authors turned to the chemisorption of carbon monoxide and compared the ratios H/CO for uptake at saturation on the supported and unsupported bimetallic catalysts. The following results were obtained for the quotient of the two H/CO ratios at various catalyst compositions — 

The influence of the support is undoubted and spillover was further confirmed by the excess of hydrogen chemisorbed by a mechanical mixture of unsupported alloy and TJ-A1203 above that calculated from the known values for the separate components. It was also observed that the chemisorption was slower on the supported than on the unsupported metal and that the greater part of the adsorbate was held reversibly no comment could be made on the possible mediation by traces of water. On the other hand, spillover from platinum-rhenium onto alumina appears to be inhibited for ratios Re/(Pt Re) 0.6. In an infrared investigation of isocyanate complexes formed between nitric oxide and carbon monoxide, on the surface of rhodium-titania and rhodium-silica catalysts, it seems that the number of complexes exceeded the number of rhodium surface atoms.The supports have a pronounced effect on the location of the isocyanate bond and on the stability of the complexes, with some suggestion of spillover. 

Sermon and G. C. Bond, Reaction Kinetics and Catalysis Letters, 1974, 1, 3. 

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The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

From 160°C to room temperature. The lead-rich phase becomes unstable when the phase boundary at 160°C is crossed. It breaks down into two solid phases, with compositions given by the ends of the tie line through point 4. On further cooling the composition of the two solid phases changes as shown by the arrows each dissolves less of the other. A phase reaction takes place. The proportion of each phase is given by the lever rule. The compositions of each are read directly from the diagram (the ends of the tie lines). 

At 183°C. The liquid composition has reached the eutectic point (the bottom of the V). This is the lowest temperature at which liquid is stable. At this temperature all the remaining liquid transforms to two solid phases a tin-rich a phase, composition Xpb= 1.45% and a lead-rich (3 phase, composition Xpi, = 71%. This reaction ... 

DEF. A eutectic reaction is a three-phase reaction, by which, on cooling, a liquid transforms into two solid phases at the same time. It is a phase reaction, of course, but a special one. If the bottom of a liquid-phase field closes with a V, the bottom of the V is a eutectic point. 

From 183°C to room temperature. In this two-phase region the compositions and proportions of the two solid phases are given by constructing the tie line and applying the lever rule, as illustrated. The compositions of the two phases change, following the phase boundaries, as the temperature decreases, that is, a further phase reaction takes place. 

DEF. A peritectoid is a three-phase reaction by which, on cooling, two solid phases react to give a single new solid phase. 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

The phase-diagram (temperature vs concentration) for a eutectic two-component alloy shows at low temperatures a central two-phase region and two solid one-phase regions at low and high relative concentrations. At the eutectic temperature the liquid phase at an intermediate concentration can all of a sudden coexist with the two solid phases. Upon further increase of temperature, the liquidus lines open up a V-shaped liquid... 

Fig. 4.14 Poiemial/pH diagram for (he Pb-H20 system. The area between and corresponds to the thermodynamic stability of water. Light lines represent equilibrium conditions between a solid phase and an ion al activities 1, 10 , 10" and 10 . Heavy lines represent equilibrium conditions between two solid phases. Broken lines represent equilibrium conditions between two ions for a ratio of these ions equal to unity (after Delahay, Pourbaix and van...

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

FIGURE 8.8 The phase diagram for sulfur. Notice that there are two solid phases and three triple points. The pressure scale, which is logarithmic, covers a very wide range of values. 

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. 

To differentiate and to be able to determine the differences between the phases that may arise when two compounds are present (or are made to react together), we use what are termed "phase-diagrams" to Illustrate the nature of the interactions between two solid phase compositions. 

Up to this point, we have considered only one solid at a time. However, when two (2) or more solids are present, they can form quite complicated systems which depend upon the nature of each of the solids involved. To differentiate and to be able to determine the differences between the phases that may arise when two compounds are present (or are made to react together), we use what are termed "phase-diagrams to illustrate the nature of the interactions between two solid phase compositions. You will note that some of this material weis presented earlier in Chapter 1. It is presented here again to further emphasize the importance of phase diagrams. 

In topochemical reactions all steps, including that of nucleation of the new phase, occur exclusively at the interface between two solid phases, one being the reactant and the other the product. As the reaction proceeds, this interface gradually advances in the direction of the reactant. In electrochemical systems, topochemical reactions are possible only when the reactant or product is porous enough to enable access of reacting species from the solution to each reaction site. The number of examples electrochemical reactions known to follow a truly topochemical mechanism is very limited. One of these examples are the reactions occurring at the silver (positive) electrode of silver-zinc storage batteries (with alkaline electrolyte) ... 

Fig. 23 Tie lines associated with different systems (1) a solid phase D (pure enantiomer) in the presence of mother liquor of variable composition, (2) a solid phase L, (solvated enantiomer) in mother liquor of variable composition, (3) a solid phase R (pure racemic compound) in mother liquor of variable composition, (4) a solid phase Rs (solvated racemic compound) in mother liquor of variable composition, (5) two solid phases, one enantiomer and the racemic compound (or two enantiomers if E is on SR, i.e., for a conglomerate) in mother liquor of fixed composition E (eutectic), and (6) the tie lines do not converge one solid phase is present (solid solution of D and L) in mother liquor of variable composition. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., New York, from Ref. 141, p. 177.)...

In Fig. 24 points A and A represent the equal solubilities at the temperature T0 of the pure enantiomers, while E represents the solubility of the eutectic mixture. AEA is the solubility-composition curve, above which undersaturated solutions exist and below which a saturated solution is in equilibrium with the two solid phases, D and L. Figure 21 shows that, with an increase in temperature, A and A move toward the pure enantiomers D and L, while E moves toward the pure eutectic. All of these trends indicate an increase in solubility upon increasing the temperature. 

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

For the alloy marked 1 , on cooling, the liquidus curve was intercepted at a relatively high temperature and there was a fair temperature interval during which for the Mg crystals it was possible to grow within the remaining part of liquid. The solidification finally ended at the eutectic temperature. At this temperature the eutectic crystallization occurs (L (Mg) + Cu2Mg) in isothermal conditions, where the simultaneous separation of the two solid phases results in a fine mixture... 

CNT can markedly reinforce polystyrene rod and epoxy thin film by forming CNT/polystyrene (PS) and CNT/epoxy composites (Wong et al., 2003). Molecular mechanics simulations and elasticity calculations clearly showed that, in the absence of chemical bonding between CNT and the matrix, the non-covalent bond interactions including electrostatic and van der Waals forces result in CNT-polymer interfacial shear stress (at OK) of about 138 and 186MPa, respectively, for CNT/ epoxy and CNT/PS, which are about an order of magnitude higher than microfiber-reinforced composites, the reason should attribute to intimate contact between the two solid phases at the molecular scale. Local non-uniformity of CNTs and mismatch of the coefficients of thermal expansions between CNT and polymer matrix may also promote the stress transfer between CNTs and polymer matrix. 

If the transport process is rate-determining, the rate is controlled by the diffusion coefficient of the migrating species. There are several models that describe diffusion-controlled processes. A useful model has been proposed for a reaction occurring at the interface between two solid phases A and B [290]. This model can work for both solids and compressed liquids because it doesn t take into account the crystalline environment but only the diffusion coefficient. This model was initially developed for planar interface reactions, and then it was applied by lander [291] to powdered compacts. The starting point is the so-called parabolic law, describing the bulk-diffusion-controlled growth of a product layer in a unidirectional process, occurring on a planar interface where the reaction surface remains constant ... 

In a SOFC, there is no liquid electrolyte present that is susceptible to movement in the porous electrode structure, and electrode flooding is not a problem. Consequently, the three-phase interface that is necessary for efficient electrochemical reaction involves two solid phases (solid electrolyte/electrode) and a gas phase. A critical requirement of porous electrodes for SOFC is that they are sufficiently thin and porous to provide an extensive electrode/electrolyte interfacial region for electrochemical reaction. 

A favorable combination of valence forces of both components seems to be the basic principle of the nickel-molybdenum ammonia catalyst. It has been found (50) that an effective catalyst of this type requires the presence of two solid phases consisting of molybdenum and nickel on the one hand and an excess of metallic molybdenum on the other. Similar conditions prevail for molybdenum-cobalt and for molybdenum-iron catalysts their effectiveness depends on an excess of free metal, molybdenum for the molybdenum-cobalt combination and iron for the molybdenum-iron combination, beyond the amounts of the two components which combine with each other. A simple explanation for the working mechanism of such catalysts is that at the boundary lines between the two phases, an activation takes place. In the case of the nickel-molybdenum catalyst, the nickel-molybdenum phase will probably act preferentially on the hydrogen and the molybdenum phase on the nitrogen. 

Then the water is removed in a rotational evaporator resulting in two solid phases.The lower, yellowish phase is very compact and adheres to the flask it contains only sodium acetate.The upper phase is a light powder and contains only poly(ethyleneimine). 

This reactor contains at least two solid phases, two Hquid phases, and a gas phase. The flows are largely driven by gravity caused by the density differences of the soHd and Hquid phases. Taconite and coke are admitted at the top of the reactor and O2 at the bottom. Liquid Fe and slag are withdrawn at the bottom of the reactor. The Hquid iron is either cast into ingots in molds or directly passed from the reactor through rolling mills to process it into sheets. 

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