Instability phase

In the previous sections, we indicated how, under certain conditions, pressure may be used to induce immiscibility in liquid and gaseous binary mixtures which at normal pressures are completely miscible. We now want to consider how the introduction of a third component can bring about immiscibility in a binary liquid that is completely miscible in the absence of the third component. Specifically, we are concerned with the case where the added component is a gas in this case, elevated pressures are required in order to dissolve an appreciable amount of the added component in the binary liquid solvent. For the situation to be discussed, it should be clear that phase instability is not a consequence of the effect of pressure on the chemical potentials, as was the case in the previous sections, but results instead from the presence of an additional component which affects the chemical potentials of the components to be separated. High pressure enters into our discussion only indirectly, because we want to use a highly volatile substance for the additional component. 

The nOe difference spectrum is highly demanding, since even the slightest variation in the spectra recorded with and without preirradiations will show up as artifacts in the difference spectrum (Fig. 4.8). The errors can be random, due to phase instability caused by temperature effects on the Rf circuits, variations in spinner speed, etc. The problem of phase instability is reduced in the latest generation of instruments with digital... 

Expressions for the medium modifications of the cluster distribution functions can be derived in a quantum statistical approach to the few-body states, starting from a Hamiltonian describing the nucleon-nucleon interaction by the potential V"(12, l/2/) (1 denoting momentum, spin and isospin). We first discuss the two-particle correlations which have been considered extensively in the literature [5,7], Results for different quantities such as the spectral function, the deuteron binding energy and wave function as well as the two-nucleon scattering phase shifts in the isospin singlet and triplet channel have been evaluated for different temperatures and densities. The composition as well as the phase instability was calculated. 

We conclude that not only the a-particle but also the other fight clusters contribute significantly to the composition. Furthermore they also contribute to the baryon chemical potential and this way the modification of the phase instability region with respect to the temperature, baryon density and asymmetry can be obtained. As an example, for symmetric matter the baryon chemical potential as a function of density for T = 10 MeV is shown in Fig.3... 

In certain regions of the density-temperature plane, a significant fraction of nuclear matter is bound into clusters. The EOS and the region of phase instability are modified. In the case of /3 equilibrium, the proton fraction and the occurrence of inhomogeneous density distribution are influenced in an essential way. Important consequences are also expected for nonequilibrium processes. 

Defects in the transmitter path may cause total signal loss, increased I, noise or diamond patterns. Problems with the frequency control unit or the synthesizer will lead to no signal or amplitude or phase instabilities. Random variations in amplitude or phase will increase q noise. A more subtle point arises when the phase presetting time is too short such that the... 

Experimentally, the third-phase limit is determined by a stepwise increase of solute in the aqueous phase until phase instability occurs, then the concentration of the solute just before the third-phase formation is taken as the two- to three-phase sample (third phase or LOC). 

Figure 9. Diagram of the antiferromagnetism vector L (left-hand) and the magnetization M (right-hand) turn at sublattice flipping in tilted field (ip < ipc)- The arrows show the turn directions in the I and II phases. The dashed line encloses the angles, corresponding to the regions of phase instability and realization of domain boundaries [1,2].

Hence, both UCST and LCST shift to higher temperatures with increasing pressure. However, if AVM > 0 in the gap between UCST and LCST then the gap diminishes with increasing pressure. As a rule, taken from the theory, positive volumes of mixing are likely when the gap between LCST and UCST is sufficiently small. In other words, an increasingly positive volume of mixing is unfavorable for miscibility of polymers and leads ultimately to phase instability. 

One interesting feature of the HC formulae is that phase separation is predicted when there is a small concentration of large spheres [21]. There is some earlier numerical data from integral equations [52-54] indicating that phase separation occurs in asymmetric hard sphere mixtures. This may shed light on recent experimental results [55-65] who have observed evidence of phase instability in colloidal suspensions. 

Further, data of Nishi and Kwei (68) show that the LCST for the polystyrene-poly(vinyl methyl ether) system is constant to within 10°C when the polystyrene Mw lies between 50,000 and 1,000,000. This result again suggests that entropic contributions to the phase transition are of secondary importance when the component molecular weights are high and that the phase instability at LCST is governed by enthalpic consider-... 

These two methods of synthesis have led to the discovery that at compositions around x = 2, a monophase, polycrystalline NASION is very difficult to produce, even though it can be sintered to reasonable mass density ( >3.20 g/cm ) at relatively low temperatures (1100-1375°C). Unfortunately these materials contain a ZtOz second phase, possess poor mechanical strength with a low fracture toughness, have an anomalous thermal expansion behaviour, and are subject to chemical and phase instability during densification . 

Another class of DFTs, which are close in spirit to the original Kirkwood-Monroe theory, are the bifurcation theories. It is usually stated that these are theories of solid phase instability. However, Bagchi et al. argue that the bifurcation analysis, if carried through exactly, predicts the equilibrium melting point [136]. We will not attempt to review these theories here, but simply refer the reader to the recent work... 

Tlusty, T., Safran, S.A. and Strey, R. (2000) Topology, phase instabilities, and wetting of microemulsion networks. Phys. Rev. Lett., 84, 1244-1247. 

Looking at the curve in the problem statement, we see that at points B and C this derivative is zero, and between points B and C it is negative. This implies phase instability or phase separation, with points B and C being the limits of stability. 

Vapor pressures at 25°C are Pf = 2.452 psia (16.9 kPa) and P = 1.886 psia (13.0 kPa). Activity coefficients can be computed from the van Laar equation in Table 5.3. The resulting equilibrium plot is shown in Fig. 5.9, where it is observed that over much of the liquid-phase region three values of y] exist. This indicates phase instability. Experimentally, single liquid phases can exist only for cyclohexane-rich mixtures of X) = 0.8248 to 1.0 and for methanol-rich mixtures of X) =0.0 to 0.1291. Because a coexisting vapor phase exhibits only a single composition, two coexisting liquid phases prevail at opposite ends of the dashed line in Fig. 5.9. The liquid phases represent solubility limits of methanol in cyclohexane and cyclohexane in methanol. 

Because of the isomorphous structures of the four compounds and their phase instabilities, they are an interesting set of compounds for detailed lattice-dynamic calculations. However, despite their relative simplicity with respect to other metal azides, their structure, with eight atoms per primitive unit cell, presents a formidable calculational problem. With compounds of this complexity it is imperative that dispersion-curve data be available to test lattice-dynamic models, and, thus far, this has been possible only for KN3. 

In addition, there are also appreciable individual distinctions between different objects of this type. Recent measurements of circular polarization paint a complex picture of its evolution with phase of the light curve and with wavelength. Many polars possess strong phase instability in both brightness and polarization. Characteristic values observed circular polarization are limited from small percentage up to 20 30 %, with frequent sign changes. To... 

One of the reasons of defective plastics with low anticorrosion properties (especially films) is phase instability and thermal destruction of Cl and other low-molecular-weight components under elevated temperatures. In this regard, the thermal stability values of LDPE, PI and their blends with PE and some VCI of the PHC series are also cited in Table 1.6 for comparison [50,51]. Above considered low-molecular-weight components have Tdi at or above the LDPE processing temperatures and will not undergo thermal destruction during combination with the polymer binder melt. High thermal stability of VCI of PHC series is one of the merits of inhibited plastics. 

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