Construction of phase diagrams

Partial pressure as a variable. As mentioned in 2.1, many types of thermodynamic variables may be used in the construction of phase diagrams. The various rules of construction, based on the laws of chemical thermodynamics, which apply to the different types of phase diagrams have been discussed in several books and papers (for instance, Pelton and Schmalzried 1973, Okamoto 1991, Pelton 1991). Following a classification proposed by Pelton, the various, bidimensional, phase diagrams may be subdivided into three types as follows ... 

The study of phase equilibria and the construction of phase diagrams is a complex and difficult undertaking. This review has only been offered as a means to introduce concepts and situations that aid in the study of condensed materials systems. Nonetheless, it does provide the foundation for understanding practical problems in materials synthesis. For those who wish to study further, Phase Diagrams for Ceramists (1) has an excellent introductory explanation of phase equilibria which includes an extensive bibliography. 

Construction of phase diagrams can be tedious. They require preparation and equilibration of possibly hundreds of samples spanning all proportions of the components. These are thoroughly mixed and equilibrated under controlled temperatures, typicaH 3iii mimicin vivo conditions. 

Figure 5. A possible construction of phase diagram W03-NaxW03 to x — 0.70...

A—B—A block copolymers assessment of samples, 23—24 construction of phase diagrams, 24 light-scattering measurements, 24—25 preparation of samples, 23 Adsorbed polymer layer around a sphere, self-similar picture, 32132 323 Ammonia—ammonium thiocyanate mixtures, solvents for cellulose, 157 Amphiphilic lipopeptides advantages, 117... 

CONSTRUCTION OF PHASE DIAGRAMS FROM PROJECTIONS AND EXPERIMENTAL OBSERVATIONS... 

It is clear from Figure 1.2 that the technique may easily and rapidly detect the temperature at which a particular thermal event is occurring. Indeed, current uses of the technique are based largely on the ability of the method to detect the initial temperatures of thermal processes and to qualitatively characterize them as endothermic or exothermic, reversible or irreversible, first order or higher order, etc. (2). The ability to run experiments in a range of atmospheres has also rendered the approach particularly useful for the construction of phase diagrams. 

The Margules equations such as those in Table 15.1 can be fitted by standard least-squares regression analysis to data for real solutions. For example, if data for the total free energy of a binary asymmetric solution is available over a range of compositions at different T and P, you could fit equation (15.41) for Greai (or the equation for in Table 15.1) and obtain Wq, and ITcj as regression parameters. The same could be done with the equations for excess enthalpy, entropy, and so on. This permits construction of phase diagrams and determination of thermodynamic properties based... 

A change in slope of a cooling curve is an indication that the system is passing across a phase boundary, irrespective of the complexity of the system. Cooling curves are therefore usefiil in mapping out the presence of phase boundaries and in the construction of phase diagrams. 

Microemulsions are prepared by the spontaneous anulsilication method (phase titration method) and can be depicted with the help of phase diagrams. Construction of phase diagram is a useful approach to study the complex series of interactions that can occur when different components are mixed. Microemulsions are formed along with varions association structures (including emulsion, micelles, lamellar, hexagonal, cubic, and varions gels and oily dispersion), depending on the chemical composition and concentration of each component. 

The proposed approach leads directly to practical results such as the prediction—based upon the chemical potential—of whether or not a reaction runs spontaneously. Moreover, the chemical potential is key in dealing with physicochemical problems. Based upon this central concept, it is possible to explore many other fields. The dependence of the chemical potential upon temperature, pressure, and concentration is the gateway to the deduction of the mass action law, the calculation of equilibrium constants, solubilities, and many other data, the construction of phase diagrams, and so on. It is simple to expand the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc. Furthermore, the same tools allow us to solve problems even at the atomic and molecular level, which are usually treated by quantum statistical methods. This approach allows us to eliminate many thermodynamic quantities that are traditionally used such as enthalpy H, Gibbs energy G, activity a, etc. The usage of these quantities is not excluded but superfluous in most cases. An optimized calculus results in short calculations, which are intuitively predictable and can be easily verified. 

The interaction parameters can be calculated from the PVT data of polymer blends (Jain et al. 1982 Privalko et al. 1985) however, due to the need for subtraction of two large numbers, the resulting values were often erratic, with errors up to 6 %. Such errors may be acceptable for some applications, but not for the construction of phase diagrams. A more straightforward experimental route is the computation of the reducing parameters, P, V, and 7, by, e.g., two possible approaches ... 

The construction of phase diagrams of poly(oxyethylene) materials e.g., compound 7) in water reveals the generation of lyotropic liquid crystal phases. Compound 7 is a non-ionic surfactant where the polar head group comprises the oxyetltylene units and, as usual, the hydrophobic alkyl chain is the non-polar unit. At high concentrations (70-90%) of compound 7 in water the lamellar (L ) phase is generated up to moderate temperatures... 

In this chapter, the phase relations of those oxide components will be discussed that most commonly occur in ceramics, namely silica, alumina, calcia, magnesia, potassia, and iron oxide. The chapter is introduced by a cursory analysis of the anatomy and construction of phase diagrams based on Gibbs phase rule, progressing from one component to two components, and from three components to multicomponent systems. The thermodynamics of these phase assemblies will be described, some important phase diagrams discussed, and conclusions drawn. 

In order to simplify the construction of phase diagrams the following limitations for the main types of binary complete phase diagrams are accepted ... 

Information on maximal solubilization of the dispersed phase is acquired upon construction of phase diagrams. When dealing with microemulsions, (pseudo)temary diagrams are very usefiil to represent the phase behavior established when varying the composition of a chemical system that comprises a certain number of components. 

We shall in section 4.2 deal with regular solutions of small-molecule substances. The construction of phase diagrams from the derived equations is demonstrated. The Flory—Huggins mean-field theory derived for mixtures of polymers and small-molecule solvents is dealt with in section 4.3. It turns out that the simple Flory—Huggins theory is inadequate in many cases. The scaling laws for dilute and semi-dilute solutions are briefly presented. The inadequacy of the Flory-Huggins approach has led to the development of the equation-of-state theories which is the fourth topic (section 4.6) Polymer-polymer mixtures are particularly complex and they are dealt with in section 4.7. 

Seifert Hans-Joachim (1930-), Ger, chem.., expert in construction of phase diagrams Sestdk Jaroslav (1938-), Czech, phys.chem., expert on thermodynamics (of glasses), known for application of fractal kinetics (Sestak-Berggren equation), propagator of interdisciplinarity, books on thermophysical propertis of solids, glass... 

The construction of phase diagrams—as well as some of the principles governing the conditions for phase equilibria—are dictated by laws of thermodynamics. One of these is the Gibbs phase rule, proposed by the nineteenth-century physicist J. Willard Gibbs. This rule represents a criterion for the number of phases that coexist within a system at equilibrium and is expressed by the simple equation... 

Example 15-6. Construction of Phase Diagram (Fig. 16-13). A 28 API catalytic cycle stock has the following distillation curve ... 

The above four terms define the key differences between a polymer and PAB.The specific tests developed for the characterization of polymer blends focus on the detection of miscibility, construction of phase diagrams, evaluation of compatibUization and the characterization of interphase. 

Nine ternary phases are accepted for the construction of phase diagrams. These are labeled as T1/T9 to Tiq-Among these, [1940Tak] reported six ternary phases (ti/tq to Tg), four of which (T2, T4, and Tg) could be identified without much difficulty. Their investigation was mainly based on thermal analysis and micro-stmctural examination, supplemented by limited X-ray diffraction. The details of the crystal sfructures and lattice parameters of stable solid phases are listed in Table 3. The composition ranges of the equihbrium... 

The conditions of temperature and concentration that produce the various solution phases in surfactant-solvent systems can be determined (with a great deal of laboratory work) by the construction of phase diagrams. The construction-interpretation of such diagrams is a complex undertaking that is beyond the scope of this work. However, sufficient literature exists to permit certain generalizations that will help in understanding the activity of most reasonably simple surfactant systems. 

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