Completely unstable

Tl(III) < Pb(IV), and this conclusion has been confirmed recently with reference to the oxythallation of olefins 124) and the cleavage of cyclopropanes 127). It is also predictable that oxidations of unsaturated systems by Tl(III) will exhibit characteristics commonly associated with analogous oxidations by Hg(II) and Pb(IV). There is, however, one important difference between Pb(IV) and Tl(III) redox reactions, namely that in the latter case reduction of the metal ion is believed to proceed only by a direct two-electron transfer mechanism (70). Thallium(II) has been detected by y-irradiation 10), pulse radiolysis 17, 107), and flash photolysis 144a) studies, butis completely unstable with respect to Tl(III) and T1(I) the rate constant for the process 2T1(II) Tl(III) + T1(I), 2.3 x 10 liter mole sec , is in fact close to diffusion control of the reaction 17). 

Experimental measurements in each lake included particle concentration and size measurements in the water column, sedimentation fluxes in sediment traps, and chemical and size characteristics of materials recovered from sediment traps. The colloidal stability of the particles in the lake waters was determined with laboratory coagulation tests. Colloidal stability was described by the stability ratio (a). For a perfectly stable suspension, a = 0 for a complete unstable one, a = 1.)... 

Under these conditions there is a theoretical equilibrium vapor pressure of monomer above solid polymer which varies with temperature. This pressure is substantial at ambient temperature for poly (olefin sulfone)s and will increase exponentially with temperature. Thus, there will be a critical temperature above which the depropagation equilibrium vapor pressure will be higher than the condensation pressure and the polymer will be thermodynamically completely unstable. 

Fig. 4. Stability of carbon on different sites (A-D) on a pure nickel(l 11) surface (below) and a gold-alloyed nickel(l 11) surface (above). The probability of nucleation of graphite is determined by the stability of the adsorbed carbon atoms. The less stable the adsorbed carbon, the larger the tendency to react with adsorbed oxygen to form CO and the lower the coverage. On the pure nickel) 111) surface, the most stable adsorption configuration of carbon is in the threefold (hep) site (lower curve). The upper graph shows that carbon adsorption in threefold sites next to a gold atom is completely unstable (sites B and C), and even the threefold sites that are next-nearest neighbors (sites A and D) to the gold atoms are led to a substantial destabilization of the carbon. From Reference (79).

An illustration of the effect is shown in Figure 14 where the change in stability of a polystyrene latex with a diameter of 52.7 nm is shown as a function of the ratio N-/ (N+ + N ) where N = the number of negatively charged particles per unit volume and N+ = the number of positively charged particles per unit volume. As can be seen, the system becomes completely unstable when this ratio reaches ca. 0.25. 

In summary, many foams are completely unstable in the presence of oil, many others are moderately unstable in the presence of oil, and some foams are very stable in the presence of oil. Much is known about the factors contributing to foam-oil sensitivity, but attempts at correlation with independent physical parameters have met with mixed success. 

In their model, Clyne and McDermid [37] assumed a five level system the initially excited state J, a higher energy state J 4- K, and three lower energy states J — K, J — 2K, J — 3K. R—T transitions could occur between consecutive levels with AJ = K, whilst upward transfer from J + K gave a completely unstable (non-fluorescing) state. Rate coefficients for upward and downward R—T transfer (kR) were assumed to be the same and not to vary with J over the range modelled. On the basis of this simple model, the fluorescence intensity, I, is given by... 

The weight percent of bulk phases which separated after heating the styrene (dispersed phase)-acrylamide (continuous phase) gel at 40 °C for 22 h is plotted in Fig. 31 vs the weight percent of acrylamide in water. It increased as the concentration of acrylamide increased the gel became completely unstable when the amount of acrylamide in the continuous phase reached about 50 wt%. Gels did not form even at room temperature when the amount of acrylamide was greater than this value. The loss of hydrophilidty caused by the increase in the amount of acrylamide accounts for the destabilization of the gel. 

H For this value the classical method i.e. the method produced from (73)-(75) and (82) and (83) for w 0 is completely unstable since the characteristic equation has no roots. 

S2.7nm) with sulfete-groups on the surfoce the cationic latex was also polys ene (diameter 43.4 nm) with surface amidine groups. It can be seen from Fig. 24 that the system becomes completely unstable when the ratio N / N+ + W ) reaches 0.25. 

The redox activity of these molecules is a function of the number of heteroatoms. In fact, the MCo2 cores display at least one reversible one-electron reduction, whereas the FeCoM species exhibit only irreversible reduction steps. This means that the MCo2 monoanions are relatively stable, even more long-lived than the similar carbon-capped species. In contrast, the FeCoM monoanions are completely unstable [50,51]. The relevant redox potentials are summarized in Table 8. The FeCoM complexes are significantly more difficult... 

Cohan (1965a) plotted in fig. 2.5 does not show this. The two neighbouring ion states are thus at best metastable and may even be completely unstable towards recombination. There is, however, a finite possibility that, while the neighbouring dissociated state is in existence, a further proton jmnp may take place along another bond of one of the partners as in fig. 7. i b, so that the two ion states become separated. Once this has happened, the two defects are stable in the sense that, though there is an attractive electrostatic... 

In summary, many foams are completely unstable in the presence of oil, many others are moderately most unstable in the presence of oil and some foams are... 

Another possibility is the use of substituted TTF derivatives ethylenedithio-dialkylthio-TTF (EDT-TTF, Fig. Ic). This is a qualitative step in building conducting films, because new specific properties can be expected from the no longer ID character of the conductivity, especially the dependence on lattice concentration defects. An example of such a strategy is given in Refs. [21,23]. The neutral molecule (EDT-TTF) is entirely hydrophobic, and yields completely unstable films at any surface pressure value. In contrast, the complex obtained by mixing with TCNQF4, in the molecular ratio 1 1, yields very stable monolayers, which can be readily transferred as thick films, with only a very small amount of defects. At this step, the... 

In electron-impact or photon-impact studies, this is not the case. As an illustration, a case will be discussed where the molecular ion that is formed at 15.8 eV is completely unstable and therefore dissociates immediately. If this process is studied by use of charge exchange with Ar, no parent ions will be seen, but if the process is studied by use of 15.8-eV electrons, the parent ion peak is probably strong. The explanation is that part of these electrons give up a smaller energy than 15.8 eV to the molecule and therefore the molecular ions are created in several different electronic states. Some of these may be stable and give rise to the parent peak, and therefore only part of the states dissociate. Use of photon impact gives the same result. 

The fact that this limit law can be obtained numerically by making a = 0 in expression [4.82] does not mean that it must be attributed to an approximation in which the ions are assimilated to single-point charges. This approximation, which is sometimes presented, is totally erroneous, because it is easy to show that a collection of electrically-charged points is completely unstable indeed, it is the existence of a non-null radius a which lends stability, because two ions can never come together completely, as is demonstrated by the second form [4.34] of the potential function. 

When a liquid is forced to cover a substrate, which it does not like to wet, the film is either metastable or completely unstable (de Gennes 1985 Brochard-Wyart and de Gennes 1992 Leger and Joanny 1992). Initiated by a defect or some other perturbation, a hole may be nucleated and grow in diameter. The liquid removed from the dry circular spot (the hole in the liquid film) is collected in a liquid ridge (the rim ) (see Fig. 5.1). The shape of this rim may be described approximately as a portion of a cylinder that is characterized by two contact angles fidyn and (p (see Fig. 5.6). 

A topological type (m, p) is assigned to each equilibrium state, where m is the number of the characteristic exponents in the open left half-plane and p is that in the open right half-plane. Therefore, m -hp = n. If m = n (m = 0), the equilibrium state is stable (completely unstable). An equilibrimn state is of saddle type when m 0,n. ... 

Let us suppose next that system (7.5.1) has a periodic trajectory L x = d t), of period r. The periodic orbit L is structurally stable if none of its (n — 1) multipliers lies on the unit circle. Recall that the multipliers of L are the eigenvalues of the (n — 1) x (n — 1) matrix A of the linearized Poincare map at the fixed point which is the point of intersection of L with the cross-section. The orbit L is stable (completely unstable) if all of its multipliers lie inside (outside of) the unit circle. Here, the stability of the periodic orbit may be understood in the sense of Lyapunov as well as in the sense of exponential orbital stability. In the case where some multipliers lie inside and the others lie outside of the unit circle, the periodic orbit is of saddle type. 

Recall that a fixed point 0 x = xq) is called structurally stable if none of its characteristic multipliers, i.e. the roots of the characteristic equation (7.5.2), lies on the unit circle, A topological type (m,p) is assigned to it, where m is the number of roots inside the unit circle and p is that outside of the unit circle. If m = n (m = 0), the fixed point is stable (completely unstable). The fixed point is of saddle type when m 0,n. The set of all points whose trajectories converge to xq when iterated positively (negatively) is called the stable (unstable) manifold of the fixed point and denoted by Wq Wq). In the case where m = n, the attraction basin of O is Wq. If the fixed point is a saddle, the manifolds Wq and Wq are C -smooth embeddings of and MP in respectively. 

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