Transition equilibrium phase

The basic features of folding can be understood in tenns of two fundamental equilibrium temperatures that detennine tire phases of tire system [7]. At sufficiently high temperatures (JcT greater tlian all tire attractive interactions) tire shape of tire polypeptide chain can be described as a random coil and hence its behaviour is tire same as a self-avoiding walk. As tire temperature is lowered one expects a transition at7 = Tq to a compact phase. This transition is very much in tire spirit of tire collapse transition familiar in tire theory of homopolymers [10]. The number of compact... 

All relaxation curves exhibited more than one phase at various degrees of conversion and at different temperatures. This clearly rules out the all-or-none mechanism (AON) although the AON model is able to fit easily to the measured equilibrium transition curve. However, a mechanism has been proposed which allows the existence of side... 

An example for a partially known ternary phase diagram is the sodium octane 1 -sulfonate/ 1-decanol/water system [61]. Figure 34 shows the isotropic areas L, and L2 for the water-rich surfactant phase with solubilized alcohol and for the solvent-rich surfactant phase with solubilized water, respectively. Furthermore, the lamellar neat phase D and the anisotropic hexagonal middle phase E are indicated (for systematics, cf. Ref. 62). For the quaternary sodium octane 1-sulfonate (A)/l-butanol (B)/n-tetradecane (0)/water (W) system, the tricritical point which characterizes the transition of three coexisting phases into one liquid phase is at 40.1°C A, 0.042 (mass parts) B, 0.958 (A + B = 56 wt %) O, 0.54 W, 0.46 [63]. For both the binary phase equilibrium dodecane... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

Phase equilibrium requires that A2 = Al and hence that the integral vanish. All conditions are satisfied if the points 1 and 2 are located such that the areas A = B. This geometry defines the Maxwell construction. It shows that stable liquid and vapour states correspond to minima in free energy and that AL = Ay when the external pressure line cuts off equal areas in the loops of the Van der Waals isotherm. At this pressure that corresponds to the saturated vapour pressure, a first-order phase transition occurs. 

Thermodynamic representation of transitions often represents a challenge. First-order phase transitions are more easily handled numerically than second-order transitions. The enthalpy and entropy of first-order phase transitions can be calculated at any temperature using the heat capacity of the two phases and the enthalpy and entropy of transition at the equilibrium transition temperature. Small pre-tran-sitional contributions to the heat capacity, often observed experimentally, are most often not included in the polynomial representations since the contribution to the... 

Pressure-induced amorphization of solids has received considerable attention recently in physical and material sciences, although the first reports of the phenomenon appeared in 1963 in the geophysical literature (actually amorphization on reducing the pressure [18]). During isothermal or near isothermal compression, some solids, instead of undergoing an equilibrium transition to a more stable high-pressure polymorph, become amorphous. This is known as pressure-induced amorphization. In some systems the transition is sharp and mimics a first-order phase transition, and a discontinuous drop in the volume of the substance is observed. Occasionally it is strictly not an amorphous phase that is formed, but rather a highly disordered denser nano-crystalline solid. Here we are concerned with the situation where a true amorphous solid is formed. 

In bulk matter the quark-hadron mixed phase begins at the static transition point defined according to the Gibbs criterion for phase equilibrium... 

Figure 1. Chemical potentials of the three phases of matter (H, Q, and Q ), as defined by Eq. (2) as a function of the total pressure (left panel) and energy density of the H- and Q-phase as a function of the baryon number density (right panel). The hadronic phase is described with the GM3 model whereas for the Q and Q phases is employed the MIT-like bag model with ms = 150 MeV, B = 152.45 MeV/fm3 and as = 0. The vertical lines arrows on the right panel indicate the beginning and the end of the mixed hadron-quark phase defined according to the Gibbs criterion for phase equilibrium. On the left panel P0 denotes the static transition point.

In the developed process it is important to know the influence of the pressure on the melting point of the substance in the presence of the gas s-l-transition and the phase-equilibrium 1-v-data of the system. 

We note here that gel is a coherent solid because its structure is characterized by a polymer network, and hence, the above theoretical considerations on crystalline alloys should be applicable to gels without essential alteration. It is expected that the curious features of the first-order transition of NIPA gels will be explained within the concept of the coherent phase equilibrium if the proper calculation of the coherent energy and the elastic energy of the gel network is made. This may be one of the most interesting unsolved problems related to the phase transitions of gels. 

From the various possible closures, the mean spherical approximation (MSA) [189] has found particularly wide attention in phase equilibrium calculations of ionic fluids. The Percus-Yevick (PY) closure is unsatisfactory for long-range potentials [173, 187, 190]. The hypemetted chain approximation (HNC), widely used in electrolyte thermodynamics [168, 173], leads to an increasing instability of the numerical algorithm as the phase boundary is approached [191]. There seems to be no decisive relation between the location of this numerical instability and phase transition lines [192-194]. Attempts were made to extrapolate phase transition lines from results far away, where the HNC is soluble [81, 194]. 

The repulsive frequency shift, Av0, is expressed explicitly in terms of the first and second derivatives of the excess chemical potential (equation 2) along with the vapor phase vibrational transition frequency, vvib, equilibrium bond length, re, and harmonic and anharmonic vibrational force constants, f and g (232528). 

Lamivudine is an example of the effect of hydrates in nonaqueous solvents (Jozwiakowski et al., 1996). In distilled water at 25D, the anhydrate free base (form II) is 1.2 times as soluble as the 0.2 hydrate (form I). In ethanol at 26, the hydrate is 1.6 times as soluble as the anhydrate. The maximum solubility in ethanol-water mixtures was found to be at 40-60% water in ethanol, when form I is the most stable solid phase. The transition composition was with 18-20% water in ethanol in binary mixtures with more than 20% water, only the hydrate was found at equilibrium, and with less than 18% water, only the anhydrate was found at equilibrium. 

In the first discussion of equilibrium (Ch. 5) we recognized that there may be states of a system that are actually metastable with respect to other states of the system but which appear to be stable and in equilibrium over a time period. Let us consider, then, a pure substance that can exist in two crystalline states, a and p, and let the a phase be metastable with respect to the p phase at normal temperatures and pressures. We assume that, on cooling the a. phase to the lowest experimental temperature, equilibrium can be maintained within the sample, so that on extrapolation the value of the entropy function becomes zero. If, now, it is possible to cool the p phase under the conditions of maintaining equilibrium with no conversion to the a phase, such that all molecules of the phase attain the same quantum state excluding the lattice vibrations, then the value of the entropy function of the p phase also becomes zero on the extrapolation. The molar absolute entropy of the a phase and of the p phase at the equilibrium transition temperature, Tlr, for the chosen... 

The lines represent phase equilibrium boundaries. Crossing one of these lines by changing pressure or temperature results in a phase transition (or a change of state). Temperature and pressure combinations that lie on one of these lines allow for two phases to coexist in equilibrium with each other. The triple point of the substance is the single temperature and pressure combination where all three... 

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... 

Measurements of kinetic parameters of liquid-phase reactions can be performed in apparata without phase transition (rapid-mixing method [66], stopped-flow method [67], etc.) or in apparata with phase transition of the gaseous components (laminar jet absorber [68], stirred cell reactor [69], etc.). In experiments without phase transition, the studied gas is dissolved physically in a liquid and subsequently mixed with the liquid absorbent to be examined, in a way that ensures a perfect mixing. Afterwards, the reaction conversion is determined via the temperature evolution in the reactor (rapid mixing) or with an indicator (stopped flow). The reaction kinetics can then be deduced from the conversion. In experiments with phase transition, additionally, the phase equilibrium and mass transport must be taken into account as the gaseous component must penetrate into the liquid phase before it reacts. In the laminar jet absorber, a liquid jet of a very small diameter passes continuously through a chamber filled with the gas to be examined. In order to determine the reaction rate constant at a certain temperature, the jet length and diameter as well as the amount of gas absorbed per time unit must be known. 

Abstract. A phase equilibriums in intermetallic compounds hydrides in the area of disordered a-, (3-phase in the framework of the model of non-ideal lattice gas are description. LaNi5 hydride was chosen as the subject for the model verification. Position of the critical point of the P—w.-transition in the LaNi5-hydrogen system was definite. 

One of new methods of magnesium, transition and rare-earth metals hydrides and their compounds obtaining is mechanical-chemical method. Numerous quantity of works are devoted to the improving kinetic, sorption properties of hydrides which were treated mechanically or were obtained by this method in hydrogen medium under pressure [1-7]. Great consideration is given to the influence of dispersity on phase equilibrium. At the same time the investigation of mechanical... 

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