Pressure dependence of phase

Temperature and Pressure Dependence of Phase Equilibria for Pure Phases... 

JIA Jiang, S., An, L., Jiatrg, B., and Wolf, B. A., Tenrperature and pressure dependence of phase separation of rrans-decahydrorraphthalene/polystyrene solutiorr, Chem. Phys., 298,37,2004. 

Fig. 1. Pressure dependence of phase transition temperature for TD/PS polymer solution at the indicated compositions (In SI units Ibar = 10 N m-2).

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

Fig. 5.10. The pressure dependence of saturation magnetization for iron-nickel alloys shows a strong pressure dependence in the neighborhood of the Invar alloys (28.5 to 40-at. % nickel in the fee phase). The shock data shown are in excellent agreement with the static high pressure data (after Wayne [69W01]).

This paper presents the results of ab initio calculation investigating the pressure dependence of properties of rutile, anatase and brookite, as well as of columbite and hypothetical fluorite phases. The main emphasis is on lattice properties since it was possible to locate transitions and investigate transformation precursors by using constant-pressure optimization algorithm. 

The most notable theoretical analysis of the instability problem has been presented by McClure and Hart (M5). These investigators postulated a generalized combustion zone that includes a temperature-dependent and pressure-independent solid-phase reaction zone, and a temperature- and pressure-dependent gas-phase reaction zone. From this general model, Hart... 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

While the Gibbs phase rule provides for a qualitative explanation, we can apply the Clapeyron equation, derived earlier [equation (5.71)], in conjunction with studying the temperature and pressure dependences of the chemical potential, to explain quantitatively some of the features of the one-component phase diagram. 

In order to properly account for the effect of pressure on liquid phase reaction rates one should eliminate the pressure dependence of the concentration terms by expressing the latter in terms of mole ratios. It is then customary to express the general dependence of the rate... 

The behavior of a-quartz PON under pressure has been studied, in particular the pressure dependence of the cell parameters (200, 202). A displacive phase transition to an a-quartz II structure occurs at close to 20 GPa. Progressive and irreversible amorphization is observed above 30 GPa and, above 42 GPa, the product becomes com-... 

ArV is not necessarily positive, and to compare the relative stability of the different modifications of a ternary compound like AGSiOs the volume of formation of the ternary oxide from the binary constituent oxides is considered for convenience. The pressure dependence of the Gibbs energies of formation from the binary constituent oxides of kyanite, sillimanite and andalusite polymorphs of A SiOs are shown in Figure 1.10. Whereas sillimanite and andalusite have positive volumes of formation and are destabilized by pressure relative to the binary oxides, kyanite has a negative volume of formation and becomes the stable high-pressure phase. The thermodynamic data used in the calculations are given in Table 1.7 [3].1... 

An interesting example of a one-component systems is SiOa, which can exist in five different crystalline forms or as a liquid or a vapor. As C = 1, the maximum number of phases that can coexist at equilibrium is three. Each phase occupies an area on the T P diagram the two-phase equilibria are represented by curves and the three-phase equilibria by points. Figure 13.1 (2, p. 123), which displays the equUi-brium relationships among the sohd forms of Si02, was obtained from calculations of the temperature and pressure dependence of AG (as described in Section 7.3) and from experimental determination of equUibrium temperature as a function of equilibrium pressure. 

The heat flux transferred back from the gas phase to the burning surface is dependent on the temperature gradient in the gas phase, which is inversely proportional to the thickness of the reaction zone in the gas phase. Since the reaction in the gas phase is complete at the upper end of the bluish flame, the heat flux defined by Am conforms to the proportionality relationship Am l/6g p0- . The observed pressure dependence of the burning rate, is caused by the pressure depend-... 

Size and Yield as a Function of Flow Rate and Gas Pressure. The effect of gas pressure on the size of particles prepared by the gas evaporation method was noticed at an early period of the development of this method (17). It was reported that to obtain the same size, the pressure of helium had to be about 10 times as large as that of argon, and the size was larger under high-pressure gas. More quantitative work was done by Yatsuya et a). (18) on the pressure dependence of the size of the Al fine particle. In these studies, particles were sampled in the gas phase. 

The surface decomposition process of AP propellants is net exothermic, with heat absorbed at the AP and fuel surfaces by endothermic pyrolysis but with more heat liberated in the gas phase close to the AP crystals. In detail, decomposition at the AP surface consists of endothermic pressure-independent solid-to-gas phase dissociative sublimation, followed by exothermic pressure-dependent gas-phase oxidation. The over-all reaction for the AP decomposition is pressure dependent. 

Fig. 35. Effect of phase behavior on palladium-catalyzed oxidation of benzyl alcohol to benzaldehyde in supercritical CO2 characterized by transmission- and ATR-IR spectroscopy combined with video monitoring of the reaction mixture (102). The figure at the top shows the pressure dependence of the reaction rate. Note the strong increase of the oxidation rate between 140 and 150 bar. The in situ ATR spectra (middle) taken at 145 and 150 bar, respectively, indicate that a change from a biphasic (region A) to a monophasic (B) reaction mixture occurred in the catalyst surface region in this pressure range. This change in the phase behavior was corroborated by the simultaneous video monitoring, as shown at the bottom of the figure.

F. Yoshida and S.I. Arakawa, Pressure dependence of liquid phase mass transfer coefficients, AIChE Journal, 14 (1968) 962-963. 

EOS models were derived for polymer blends that gave the first evidence of the severe pressure - dependence of the phase behaviour of such blends [41,42], First, experimental data under pressure were presented for the mixture of poly(ethyl acetate) and polyfvinylidene fluoride) [9], and later for in several other systems [27,43,44,45], However, the direction of the shift in cloud-point temperature with pressure proved to be system-dependent. In addition, the phase behaviour of mixtures containing random copolymers strongly depends on the exact chemical composition of both copolymers. In the production of reactor blends or copolymers a small variation of the reactor feed or process variables, such as temperature and pressure, may lead to demixing of the copolymer solution (or the blend) in the reactor. Fig. 9.7-1 shows some data collected in a laser-light-scattering autoclave on the blend PMMA/SAN [46],... 

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