Phase stability, definition

There are two issues central to this proposal, namely is there an inversion of phase stability at atmospheric pressure and does the hexagonal phase then crystallize before the orthorhombic As will become clear, the available data do not allow a definite answer to the first but probably not, to the second the answer is certainly no. We consider these matters in turn, first testing the inequality 5 against measured parameters. 

Physical-chemistry offers a different approach to the definition of nanoparticles based on the fact that several properties - typically melting point, phase stability, electronic states and defects (usually resulting in peculiar colours) - change from those typical of larger particles when approaching nanodimensions ... 

Quantitative thermodynamic criteria of stability in the gas phase 58 Definitions and experimental techniques 58 The specific case of carbocations 61 Theoretical calculations 64 Uncertainties 65... 

But this is only necessary for one-phase stability it is not sufficient. This means if a mixture violates (8.4.5), then it is definitely not stable however, a mixture can obey (8.4.5) but still split into two phases. An additional requirement is (8.3.14), which can be expressed in terms of as... 

The one-phase stability criteria are posed in terms of g " in (8.4.5) and (8.4.6), but before we use those criteria to test for stability, it will prove more convenient to repose them in terms of the fugacity. We can rewrite (8.4.5) and (8.4.6) in terms of fugacities by combining the definition otg (3.7.38) with the integrated definition of the fugacity in (4.3.12). Then (8.4.5) requires that stable phases have... 

Phase stability diagrams refer to a specific temperature. In order to determine them, it is necessary to know the equilibrium constants for the reactions at that temperature. Table 9.33 presents the different equilibria represented in Figure 9.32 using the definition pK = -log K. 

The mesomorphic properties and physical properties of nematic (and smectic) materials and nltimately their suitability for applications are all fundamentally dictated by the chemical stracture of the constituent molecules. Before progressing further, several terms and their definitions need to be clarified this will be done by using the nematic phase. The term nematic phase stability refers to the upper-temperature limit (T j) to... 

Amorphous solid dispersions are leveraged at varying stages in development for a number of reasons. For extruded dispersions, a limited number of polymer systems summarized in Table 6.3 form the backbone of the compositional definition. In early development, they are most commonly used to support elevated exposures necessary for preclinical assessment and/or assure phase stability when a crystalline form is not readily isolated. At this stage of development, the amount of material available for development will be restricted. As discussed previously, this constraint can challenge the utility of extruded systems where minimum batch sizes are significantly larger than for development of spray-dried dispersions or coprecipitated material. 

One of the most useful pieces of information that can be provided by a standard mass spectrometer is the molecular mass of a compound with an accuracy of 1 dalton (Da) (1 Da= 1 unified atomic mass unit (u)= 1.660538921(73) x 10 kg). Even better, high-resolution mass spectrometry can provide us with accurate molecular masses, which are accurate to about 10 Da, depending on the total resolution of the spectrometer. At this level the atomic masses deviate substantially from multiples of 1 Da, e.g. is 12.0000 Da by definition, but the mass of isotope is 15.9949 Da (not 16), and that of is 14.0031 Da (not 14). This sensitivity can be used to work out the elemental composition or, more critically, the isotopic distribution of atoms in a molecule, which can help to identify unknown compounds. And since the basic experimental procedure involves supplying a particular quantity of energy to a molecule or ion to cause it to fragment, we can use it to deduce compound gas-phase stabilization energies, which can be further substantiated by computational modeling. This last application is rather specialized, so discussion is provided in the on-line supplementary section for Chapter 11 on stabilization. 

The traditional view of emulsion stability (1,2) was concerned with systems of two isotropic, Newtonian Hquids of which one is dispersed in the other in the form of spherical droplets. The stabilization of such a system was achieved by adsorbed amphiphiles, which modify interfacial properties and to some extent the colloidal forces across a thin Hquid film, after the hydrodynamic conditions of the latter had been taken into consideration. However, a large number of emulsions, in fact, contain more than two phases. The importance of the third phase was recognized early (3) and the lUPAC definition of an emulsion included a third phase (4). With this relation in mind, this article deals with two-phase emulsions as an introduction. These systems are useful in discussing the details of formation and destabilization, because of their relative simplicity. The subsequent treatment focuses on three-phase emulsions, outlining three special cases. The presence of the third phase is shown in order to monitor the properties of the emulsion in a significant manner. 

In some cases there also occur semistable limit cycles (in this discussion the single term cycle is used wherever it is unambiguous or if no confusion is to be feared) characterized by stability on one side and instability on the other side. Figure 6-5(a), (b), and (c) illustrate these definitions. Physically, only stable cycles are of interest the unstable cycles play the role of separating the zones of attraction of stable cycles in the case when there are several cycles. It is seen from this definition that, instead of an infinity of closed trajectories, we have now only one such trajectory determined by the differential equation itself and the initial conditions do not play any part. In fact, the term initial conditions means just one point (x0,y0) of the phase plane as a spiral trajectory O passes through that point and ultimately winds itself onto the cycle 0, it is clear that the initial conditions have nothing to do with this ultimate closed trajectory C—the stable [Pg.329]

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

In this statement, we have used "polar plot of G0l" to replace a mouthful of words. We have added G0L-plane in the wording to emphasize that we are using an analysis based on Eq. (7-2a). The real question lies in what safety margin we should impose on a given system. This question leads to the definitions of gain and phase margins, which constitute the basis of the general relative stability criteria for closed-loop systems. 

As Skinner has pointed out [7], there is no evidence for the existence of BFyH20 in the gas phase at ordinary temperatures, and the solid monohydrate of BF3 owes its stability to the lattice energy thus D(BF3 - OH2) must be very small. The calculation of AH2 shows that even if BFyH20 could exist in solution as isolated molecules at low temperatures, reaction (3) would not take place. We conclude therefore that proton transfer to the complex anion cannot occur in this system and that there is probably no true termination except by impurities. The only termination reactions which have been definitely established in cationic polymerisations have been described before [2, 8], and cannot at present be discussed profitably in terms of their energetics. It should be noted, however, that in systems such as styrene-S C/4 the smaller proton affinity of the dead (unsaturated or cyclised) polymer, coupled, with the greater size of the anion and smaller size of the cation may make AHX much less positive so that reaction (2) may then be possible because AG° 0. This would mean that the equilibrium between initiation and termination is in an intermediate position. 

As discussed above, the activation barrier of solvated complexes (type b) is larger, since the starting complex is more stabilized than the TS. Notwithstanding this barrier increase, solvated TSs reside at much lower (absolute) energies than their unsolvated counterparts. However, hydrated TSs are entropically disfavored (by 9 kcal/mol in the gas phase) with respect to the corresponding water-free TSs. These observations prevent a definitive decision whether 5 or 5b is the active epoxidant species in solution. 

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