Metastability stability states

FIGURE 14.4 Stabilization of a nonisothermal CSTR near a metastable steady state. 

The noble gases (Table 2.6) are uniform in their inability to bind a positron. The stability of the system of a positron and an excited helium atom in its metastable 23S state is interesting. This state has an optical lifetime of about 20 ns. The excited electron in a 2s-orbital is far enough from the nucleus to attract and bind a positron. Similar states of other atoms must be common. 

Stable A term describing a system in a state of equilibrium corresponding to a local minimum of the appropriate thermodynamic potential for the specified constraints on the system. Stability cannot be defined in an absolute sense, but if several states are in principle accessible to the system under given conditions, that with the lowest potential is called the stable state, while the other states are described as metastable. Unstable states are not at a local minimum. Transitions between metastable and stable states occur at rates that depend on the magnitude of the appropriate activation energy barriers that separate them. 

Let Tstep be the temperature above Tn at which inclusion no 31-7 is stabilized in the metastable liquid state. Let to be the time at which the temperature step begins (to is taken as 0). Let t be the timelength elapsed between to and the vapour nucleation event (t > 0). The variable t is continuous and characterized by a density probability function f(t) such that ... 

If one attempts to study metastable anion states without carrying out such a stabilization study, one is doomed to failure, even if one employs an extremely large and flexible set of diffuse basis functions. In such a calculation, one will certainly obtain a large number of anion states with energies lying above that of the neutral, but one will not be able to select from these states the one that is the true resonance state because the true state will be buried in the myriad of states representing the N2 + e continuum. 

If the pressure is reduced to 30 bar, below the mechanical critical point, the loop in the fugacity becomes more pronounced. Here violates the diffusional stability criterion dfildxi > 0 for stability) over only a small range of Xj but the mechanical stability criterion (k > 0) is also violated at states between the extrema in fp Finally, at the lowest pressure (10 bar), the loop in has completely closed, dividing into two parts a vapor part that is linear and obeys the ideal-gas law, and a fluid part that includes stable and metastable liquid states at small x values plus mechanically unstable fluid states at higher x values. The broken horizontal lines in Figure 10.1 are vapor-liquid tie lines, computed by solving the phi-phi equations (10.1.3) simultaneously for both components. 

Metastable liquids can spontaneously and rapidly change phase under adiabatic conditions. Metastable liquid states (shown in Fig. 1) can be experimentally reached from equilibrium states through processes of adiabatic depressurization and/or isobaric heating. The region of metastable liquid states is bounded by the equilibrium or saturation boundary on one side and the superheat limit on the other. The superheat limit is the temperature at which phase change is initiated by homogeneous nucleation this temperature lies close to but below the absolute limit of thermodynamic stability, (dp/dv)j< = 0, known as the spinodal. 

Wilhelm Ostwald was the first to recognise this state of affairs clearly. Indeed, he went further, and made an important distinction. In the second edition of his Lehrbuch der Allgenieinen Chemie, published in 1893, he introduced the concept of metastability, which he himself named. The simplest situation is just instability, which Ostwald likened to an inverted pyramid standing on its point. Once it begins to topple, it becomes ever more unstable until it has fallen on one of its sides, the new condition of stability. If, now, the tip is shaved off the pyramid, leaving a small flat... 

If 5v //v /coex is not small, the simple description Eq. (14) in terms of bulk and surface terms no longer holds. But one can find AF from Eq. (5) by looking for a marginally stable non-uniform spherically symmetric solution v /(p) which leads to an extremum of Eq. (5) and satisfies the boundary condition v /(p oo) = v(/ . Near the spinodal curve i = v /sp = Vcoex /a/3 (at this stability limit of the metastable states both and S(0) diverge) one finds "... 

When determining the solubility and dissolution rate of amorphous or partially crystalline solids, the metastability of these phases with respect to the highly crystalline solid must be considered. While the low diffusivity of the molecules in the solid state can kinetically stabilize these metastable forms, contact with the solution, for example during measurements of solubility and dissolution rate, or with the vapor, if the solid has an appreciable vapor pressure, may provide a mechanism for mass transfer and crystallization. Less crystalline material dissolves or sublimes whereas more crystalline material crystallizes out. The equilibrium solubility measured will therefore approach that of the highly crystalline solid. The initial dissolution rate of the metastable form tends to reflect its higher... 

Glass, a supercooled liquid, is in a metastable state, that is, an apparently stable condition that may be perturbed by external conditions and undergo unpredictable changes, so that the supercooled liquid may be converted to a solid. When glass is made from a well-balanced mixture of former, modifier, and stabilizer, it is remarkably stable. Environmental changes may,... 

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

The monolayer stability limit is defined as the maximum pressure attainable in a film spread from solution before the monolayer collapses (Gaines, 1966). This limit may in some cases correspond directly to the ESP, suggesting that the mechanism of film collapse is a return to the bulk crystalline state, or may be at surface pressures higher than the ESP if the film is metastable with respect to the bulk phase. In either case, the monolayer stability limit must be known before such properties as work of compression, isothermal compressibility, or monolayer viscosity can be determined. 

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