Phase equilibrium studies

Cohen and Ramost describe some phase equilibrium studies of block copolymers of butadiene (B) and isoprene (I). One such polymer is described as having a 2 1 molar ratio of B to I with the following microstructure ... 

Results of phase equilibrium studies are shown in Figures... 

Chai, X.S. and Zhu, J.Y. Indirect headspace gas chromatographic method for vapor-liqtrid phase equilibrium study, J. Chromatogr. A, 799(2) 207-214, 1998. 

Hamilton D. L. and MacKenzie W. S. (1965). Phase equilibrium studies in the system NaAlSi04 (nepheline)-KAlSi04 (kalsilite)-Si02-H20. Min. Mag., 34 214-231. 

During the 1940s, a large amount of solubility data was obtained by Francis (6, 7), who carried out measurements on hundreds of binary and ternary systems with liquid carbon dioxide just below its critical point. Francis (6, 7) found that liquid carbon dioxide is also an excellent solvent for organic materials and that many of the compounds studied were completely miscible. In 1955, Todd and Elgin (8) reported on phase equilibrium studies with supercritical ethylene and a number of... 

Identification of crystals under the microscope. Of the characteristics which are most useful for identification purposes the most readily determined are shape and refractive indices, The determinative method which has proved most valuable for microscopic crystals (such as those in the average experimental or industrial product) is to measure the principal refractive indices (up to three in number, depending on the symmetry of the crystal) and, if possible, to find the orientation of the principal opticafdirections with respect to the geometrical form of the crystal. This information, which can all be obtained by simple and rapid microscopio methods, is usually sufficient to identify any crystalline substances whose properties have previously been recorded. Mixtures of two or more crystalline substances can be identified by the same method in phase equilibrium studies and in industrial research it is not uncommon to encounter mixtures of three or four constituents, all of which can be identified in this way. 

By writing molar component balances for gas and crystallite phases, assuming Henry s law equilibrium between these phases and applying exponential rate decay, the equilibrium model (model a) is obtained (13). All parameters in the model can be measured or estimated, independent of reaction studies, with the exception of Mi and M2y which are obtained from the observed rate decay. The Henry s law constant H was estimated from a liquid-phase equilibrium study. A model involving diffusional limitations within the crystallites has been developed by Tan and Fuller (6) and is not discussed here. 

Relative to our phase equilibrium study in Chapters 4 and 5, the above three techniques are illustrated on the phase diagram of Figure 7.18, as AT = 0, AT = 0, and 10% methanol, for depressurization, thermal stimulation, and inhibitor injection, respectively. Additional explanation is given in the figure caption. 

Tien TY, Petzow G, Gauckler LJ, Weiss J (1983) Phase Equilibrium Studies in Si3N4-Metal Oxides Systems. In Riley FL (ed) Progress in Nitrogen Ceramics. NATO ASI Ser E 65. Kluwer Acad Publ, Dordrecht, p 89... 

The Gibbs phase rule is of use in phase equilibrium studies of multicomponent systems. 

The olivine spinel phase transition Experimental phase equilibrium studies have confirmed deductions from seismic velocity data that below 400 km, olivine and pyroxene, the major constituents of Upper Mantle rocks, are transformed to denser polymorphs with the garnet, y-phase (spinel) and P-phase (wadsleyite) structures (fig. 9.2). In transformations involving olivine to the P- or y-phases, transition pressures... 

From the thermodynamic standpoint, the conclusion that AG is dominated by a very large positive AH term turns entirely on whether the calculation of the endothermicity of random, defective crystals is valid. In so far as direct thermodynamic measurements or phase equilibrium studies are available for oxide systems (and these, as the most truly ionic of allegedly nonstoichiometric compounds, should be the ones for which the Bertaut type of calculation should be least unreliable), it seems clear that the endothermicity of the random, compared with the ordered, structure has been grossly overestimated. 

Several early phase equilibrium studies on systems of calcium silicates or aluminates with alkalis were reported (N9), but their significance needs to be reassessed because they postulated the existence of the compounds NCgAj or KC23Sj2, which in neither case is supported by more recent work. 

Some limestones contain substantial proportions of SrO. Small contents favour alite formation, but phase equilibrium studies show that it increases the range of compositions at which free lime, with SrO in solid solution, is present at the clinkering temperature (B34,G27,G28). This limits the permissible content of SrO in mixes of normal LSFs to about 3%. 

Hashizume, J. Teramoto, A. Fujita, H., "Phase Equilibrium Study of the Ternary System Composed of Two Monodisperse Polystyrenes and Cyclohexane," J. Polym. Sci., Polym. Phys. Ed., 19, 1405 (1981). 

J. B. Ott and J. R. Goates, Temperature Measurement with Application to Phase Equilibrium Studies, in B. W. Rossiter and R. C. Baetzold (eds.). Physical Methods of Chemistry. Vol. VI Determination of Thermodynamic Properties, 2d ed., chap. 6, Wiley-Interscience, New York (1992). 

I, If CO concentrations are to be measured spectroscopically during a chemical process or in chemical equilibrium or phase equilibrium studies, quite different optical path lengths / and thus reactor dimensions may be used. As an example, / is calculated for a system where the CO concentration is 0.15 g cm In order to ensure the good quality of the spectra, the absorbance at the band maxima should not exceed = 1. With this limiting absorbance, the optical path lengths calculated from the values in the band maxima (Fig. 6.2-7) are 0.066 mm, 7.9 mm, and 1120 mm, respectively, in the fundamental, first, and second overtone region. 

Elkins L. T., Fernandes V. A., Delano J. W., and Grove T. L. (2000) Origin of lunar ultramafic green glasses constraints from phase equilibrium studies. Geochim. Cosmochim. Acta 64, 2339-2350. 

The first systematic phase equilibrium study of hydrates was carried out at the US Bureau of Mines by Deaton and Frost for a number of natural gas hydrate systems. Although the separation methods were somewhat crude (e.g., a distinction could not be made between butane isomers), their hydrate formation pressure and temperature data continue to be foundations for prediction comparisons. 

The sol-gel process was first used for the preparation of silicates used in phase equilibrium studies. Often the sol-gel process makes use of a concentrated hydrous sol, a colloidal dispersion of (hydrated) oxide particles produced by controlled precipitation. It is also a precipitation process that makes use of immobilization of ions in a gel or glassy structure. 

T. Y. Tien, G. Petzow, L. J. Gauckler, and J. Weiss, Phase equilibrium studies in Si3N4-metal oxide systems. In Progress in Nitrogen Ceramics (F. L. Riley, ed.), pp. 89-99. Martinus Nijhoff, Boston, 1983. 

Much of the information on hydrate processes has come from macroscopic studies, that is, from the observation of gas consumption, pressure drop, particle size measurements, or crystal morphology observations. However clathrate hydrates in many ways are unique materials that make it imperative that studies on the molecular scale are also carried out. For instance, several structures of hydrate may coexist, and often this is not obvious from phase equilibrium studies ... 

We now have encountered a number of techniques that can be used to determine hydrate structure, either directly or indirectly. In order to study processes we must add some capability of time resolution so that the process can be followed, preferably from nucleation to some level of conversion of the aqueous or ice phase. The usual method by which hydrate has been made is to use a stirred reactor - often the method of choice in phase equilibrium studies.(fig. 3). However, as mentioned previously, it is difficult to obtain kinetic parameters that are system... 

Figure 3 Different methods of hydrate formation (1-5) each can give a distinct perspective on certain aspects of hydrate formation l-ice + gas at T< 273K 2- ice with the temperature ramped above T = 273K 3 - amorphous ice +gas at T < 13 OK 4 and 5, either quiescent or with agitation are usually used for phase equilibrium studies and the effect of inhibitors. Simulation of natural gas hydrate requires the addition of sediment at various levels of water-sediment content.

The interpretation of the viscosity-temperature behavior of these complex systems is difficult since many aspects of the melt conditions must be simultaneously considered. These include the chemical composition of the melt to establish the nature of the polymeric network including the amphoteric behavior of species like AI2O3 and Fe2O3> as well as the acid/base behavior of mixed valence constituents such as iron oxides, and the formation of immiscible liquid phases sometimes associated with the existence of several types of stable anions of significantly different size or charge in the system the nature of the container since some of it may dissolve and affect the composition of the melt the existence of a solid phase to establish the effect on the composition of the residual liquid phase (the solid phase may not be the one expected from related phase equilibrium studies) the relative amount of the liquid and solid phases to establish the composition of the liquid phase (this composition changes as the solid crystallizes out of... 

Next, the MgO content is constrained from the observation that molar Mg/(Mg - - Fe ) (i.e., bulk-rock Mg ) ought not to be affected by modal segregation, since mineral Mg s are nearly the same in olivine and in pyroxenes (as shown by experimental phase equilibrium studies and empirical studies of coexisting phases in peridotites). Hence, (Mg )oi = (Mg )buik, to a very good approximation, in spinel Iherzolites. Extraction of partial melt causes an increase in Mg, so that the most primitive samples should have the lowest Mg. Histograms of olivine compositions in spinel Iherzolites from a wide variety of environments show that the most fertile samples that have not been grossly disturbed by metasomatism have Mg s from 0.888 to —0.896. Since the uncertainty with which olivine Mg s are determined in individual samples is typically —0.001, we interpret this distribution as implying an Mg for the primitive depleted mantle of 0.890, which value we adopt. Hence,... 

Phase equilibrium studies were made on relatively simple systems. Thus, at room temperature when one volume of hexane and one volume of toluene were mixed with two volumes of dicyanobutane, the mixture separated rapidly into two phases on cessation of mixing. The upper phase showed a 40% volume decrease with a corresponding... 

Phase equilibrium studies on the stabilities of the three-phase mineral assemblages listed above and determinations of the chemical composition of aqueous solutions in equilibrium with these assemblages will provide data which can be used for a quantitative assessment of the conditions under which these and other comparable zeolite occurrences have formed. 

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