Qualitative stability

Table 1. Demetallation reaction conditions for metalloporphyrins based on the qualitative stability constant...

Using the qualitative stability analysis from the flow diagram as outlined in 1.7.3 and 6.1.5, we find the following pattern. For conditions where there is a single stationary state, it is always stable to perturbations in regions of multiple solutions, the uppermost and lowest are stable whilst the middle... 

The situation becomes more complicated if a given ionization reaction is studied in solvents that differ both in their EPD and EPA properties. This may be illustrated for the complex formation between Co and Cl ions. Qualitatively, stabilities of cobalt-chloro complexes usually decrease with increasing EPD strength of the solvent (25, 26). Quantitative measurements reveal, however, a number of irregularities which cannot be understood by considering the differences in solvent donicities. Accurate thermodynamic data have recently been determined for the reaction... 

For reaction 20-1 mentioned above, carried out hypothetically in the vapor phase, the enthalpies have been estimated from thermodynamic data for the metals, M, in the series Mn2+, Fe2+,..., Cu2+, Zn2+. At the same time, from the spectra of the [M(H20)6]2 + and [MC14]2 " ions the values of A0 and A, have been evaluated and the differences between the two LFSE s calcu-J ated. Fig. 20-33 shows a comparison-between- these Two sets-of quantities — It is evident that the qualitative relationship is very close even though some quantitative discrepancies exist. The latter may well be due to inaccuracies in the AH values since these are obtained as net algebraic sums of the independently measured enthalpies of several processes. The qualitatively close agreement between the variation in the enthalpies and the LFSE difference justifies the conclusion that it is the variations in LFSE s that account for gross qualitative stability relations such as the fact that tetrahedral complexes of Co11 are relatively stable while those of Ni11 are not. 

Chatter Prediction, Fig. 9 Qualitative stability lobe diagram of a milling process (Week and Brecher 2006)... 

The first resulted in several pavement failures associated to the quality of bitumen, whereas the second one resulted in an increase of the total construction cost. As a consequence, the need to improve bitumen quality emerged in order to ensure the qualitative stability and improvement of the construction quality. 

TLC has been often employed for qualitative stability testing. Thus, preparations containing nicotinate esters have been tested for... 

Figure 1. Shows a qualitative stability diagram of the protein, Zn-cytochrome c, in a buffer/glycerol mixture obtained from pressure experiments. The y-axis represents the pressure in MPa and the x-axis is temperature in Celsius. Inside the ellipse the protein is in its native state, outside in the denatured state. The AS=0 (S being entropy) line cuts vertically at T=30, dividing the ellipse into two sections. The left part being AS<0 and the right hand side AS>0. The figure is...

Part II Qualitative control and long term stability of imaging devices... 

Part II Qualitative Control and Long Term Stability of Imaging Devices... 

It is helpful to consider qualitatively the numerical magnitude of the surface tensional stabilization of a particle at a liquid-liquid interface. For simplicity, we will assume 6 = 90°, or that 7sa = 7SB- Also, with respect to the interfacial areas, J sA = SB, since the particle will lie so as to be bisected by the plane of the liquid-liquid interface, and. AB = rcr - The free energy to displace the particle from its stable position will then be just trr 7AB- For a particle of l-mm radius, this would amount to about 1 erg, for Tab = 40 ergs/cm. This corresponds roughly to a restoring force of 10 dyn, since this work must be expended in moving the particle out of the interface, and this amounts to a displacement equal to the radius of the particle. 

If an ionic surfactant is present, the potentials should vary as shown in Fig. XIV-5c, or similarly to the case with nonsurfactant electrolytes. In addition, however, surfactant adsorption decreases the interfacial tension and thus contributes to the stability of the emulsion. As discussed in connection with charged monolayers (see Section XV-6), the mutual repulsion of the charged polar groups tends to make such films expanded and hence of relatively low rr value. Added electrolyte reduces such repulsion by increasing the counterion concentration the film becomes more condensed and its film pressure increases. It thus is possible to explain qualitatively the role of added electrolyte in reducing the interfacial tension and thereby stabilizing emulsions. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

We might be hard pressed to estimate the individual resonance stabilization energies in Eqs. (7.23) and (7.24), but the qualitative apphcation of these ideas is not difficult. Consider once again the styrene-vinyl acetate system ... 

The pyrazole ring is particularly difficult to cleave and, amongst the azoles, pyrazoles together with the 1,2,4-triazoles are the most stable and easiest to work with. This qualitative description of pyrazole stability covers the neutral, anionic and cationic aromatic species. On the other hand, the saturated or partially saturated derivatives can be considered as hydrazine derivatives their ring opening reactions usually involve cleavage of the N—C bond and seldom cleavage of the N—N bond. It should be noted, however, that upon irradiation or electron impact the N—N bond of pyrazoles can be broken. 

Aromatic character in isoxazoles has been studied from a number of viewpoints, and these studies indicate that although isoxazole may be formally considered an aromatic system, the disposition of the ring heteroatoms modifies this character to an appreciable extent. From a qualitative viewpoint, thermal stability and electrophilic attack at the 4-position may be considered consistent with an aromatic character. Furthermore, NMR chemical shifts of the ring protons are consistent with those of an aromatic compound. References related to these studies may be found in Section 4.16.2.3.4. 

The central role of the concept of polarity in chemistry arises from the electrical nature of matter. In the context of solution chemistry, solvent polarity is the ability of a solvent to stabilize (by solvation) charges or dipoles. " We have already seen that the physical quantities e (dielectric constant) and p (dipole moment) are quantitative measures of properties that must be related to the qualitative concept of... 

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