Pure-fluid metastable states

Figure 5.1. Schematic representation of stable, metastable, and unstable states in a pure fluid.

Actually, when water separates as pure ice, as is the case for diluted solutions, there might be a considerable degree of supercooling in the remaining interstitial fluids. It is, then, compulsory to go to much lower temperatures to rupture these metastable states and provoke their separation as solid phases. This, indeed, has a great significance because it is precisely within those hypertonic concentrated fluids that the active substances lie whether they are virus particles, bac-... 

Abstract A synthetic pure water fluid inclusion showing a wide temperature range of metastability (Th - Tn 50°C temperature of homogenization Th = 144°C and nucleation temperature of Tn = 89°C) was selected to make a kinetic study of the lifetime of an isolated microvolume of superheated water. The occluded liquid was placed in the metastable field by isochoric cooling and the duration of the metastable state was measured repetitively for 7 fixed temperatures above Tn. Statistically, metastability lifetimes for the 7 data sets follow the exponential reliability distribution, i.e., the probability of non nucleation within time t equals. This enabled us to calculate the half-life periods of metastability r for each of the selected temperature, and then to predict i at any temperature T > Tn for the considered inclusion, according to the equation i(s) = 22.1x j Hence we conclude that... 

We now use the stability criteria from 8.1.2 to help judge the observability of pure-fluid states and to help describe phase behavior of pure fluids. Issues of observability constitute the theme of this chapter, and so it may be helpful to clarify how an observable state differs from one that is observed. We use observable to mean a state that can be realized in a laboratory. To realize an observable state, it is necessary to adjust certain measurables, such as T, f) and [x], to particular values however, such adjustments may not be sufficient to create an observable state. Some observable states can only be observed when measimables are manipulated in certain ways. In general, stable equilibrixun states are always observable, but they are not always observed sometimes a metastable state will be observed instead of a stable state. In contrast, an unstable state is neither observable nor observed (see Figure 8.1). 

Figure 8.4 Four isotherms of a pure fluid computed from the Redlich-Kwong equation of state. Parameters a and b were computed from and using the relations in Table 4.4. The critical point (filled square) was taken to be = 304.2 K and = 73.8 bar, which is that for carbon dioxide. However, with these values the Redlich-Kwong equation gives = 114 cc/mol, which is not a good approximation to the experimental value of 94 cc/mol for CO2. Note that the two isotherms below P contain metastable and unstable states.

Along any pure-fluid, subcritical isotherm, the spinodal separates unstable states from metastable states. At the other end of an isotherm s metastable range, metastable states are separated from stable states by the points at which vapor-Uquid, phase-equilibrium criteria are satisfied. Those criteria were stated in 7.3.5 the two-phase situation must exhibit thermal equilibrium, mechanical equilibrium, and diffusional equilibrium. Since we are on an isotherm, the temperatures in the two phases must be the same, and the thermal equilibrium criterion is satisfied. 

However, the full instability criteria (8.5.1)-(8.5.3) still cannot distinguish stable states from metastable states but then, no differential test can make this distinction. To distinguish stable states from metastable states, we must apply an appropriate equilibrium criteria. For example, if T and P have been specified for a proposed state, then the stable state is the one that minimizes the Gibbs energy. Using this as a basis, we showed how to identify the stable state for pure fluids and for binary mixtures. 

A second theme of this chapter is that phase transitions decouple from unstable states. Unstable fluids may or may not split into two phases, depending on where the state lies on the phase diagram and on what external constraints are imposed. If T and V are fixed, then unstable pure fluids will undergo phase splits. But if T and P are fixed, then an unstable pure fluid will not necessarily separate into two phases it may relax to another one-phase situation. In addition, unstable binary fluids at fixed T and P above the mechanical critical line always split into two phases, but below the mechanical critical line they do not necessarily split. Moreover, phase separations do not necessarily originate from unstable states metastable fluids may also separate into two phases. These comments mean that, at fixed (T, P, x ), differential stability criteria alone may not be enough to help us decide whether a phase split will occur. 

Figure 9.3 Along subcritical isotherms for pure fluids, the fugacity passes through stable, metastable, and unstable regions just as does the pressure. Here we have plotted the subcritical isotherm TlT = 0.863 for a van der Waals fluid. Each point (a-f) on the fugacity plot corresponds to the point of the same label on the Pv diagram. Points b and e have the same fugacity and pressure (P /= 0.539) and therefore locate the vapor-liquid equUibrium state. Points c and d are on the spinodal. Line segment be locates metastable liquid states segment de locates metastable vapor states segment cd locates unstable states.

The first step in quantitative description of pure polyamorphic fluid is a selection of the model that can qualitatively describe a possible multiplicity of critical points in wide range of temperatures and pressures. A great many of explanations of multicriticality in monocomponent fluids (perturbation theory models semiempirical models lattice models, two-state models, field theoretic models, two-order-parameter models, and parametric crossover model has been disseminated after the pioneering work by Hemmer and Stell Here we test more extensively the modified van der Waals equation of state (MVDW) proposed in work and refine this model by introducing instead of the classical van der Waals repulsive term a very accurate hard sphere equation of state over the entire stable and metastable regions... 

The differential stability criteria were derived by finding conditions that maximize the total entropy in an isolated system. Those conditions constrain how the system responds to thermal, mechanical, and diffusional fluctuations. In the derivations, those constraints are conveniently posed as stability criteria they show us that a stable substance must always obey the thermal criterion (8.1.23), the mechanical criterion (8.1.31), and the diffusional criterion (8.3.14). But the converses of those statements are not always true for example, a mechanically stable fluid always has Kj > 0, but a fluid having Kj > 0 is not necessarily stable— it might be metastable. Therefore, in using these differential criteria (as opposed to merely deriving them), many ambiguities can be avoided if we repose each constraint in the form of an instability criterion such criteria identify those thermodynamic states at which a pure substance or mixture is differentially unstable. 

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