Thermodynamic stability 324 INDEX

As thermodynamic stability indexes for the hydrocarbon ions, pA R+ and pA a values [(4) and (5)] have been widely applied for the carbocation and carbanion, respectively, in solution. Here K + stands for the equilibrium constant for the reaction (6) of a carbocation and a water molecule stands for the equilibrium constant for the reaction (7) of a hydrocarbon with a water molecule to give the conjugate carbanion. The equilibrium constants are given by (8) and (9) for dilute aqueous solutions. Obviously, the reference system for the pKn+ scale is the corresponding alcohol, and... 

Sufficient stability of the hydrocarbon ions, as the salt or in the solution, is an obvious prerequisite for these procedures, and, in practice, selecting or designing the stable ions and choosing a proper solvent are tasks of primary importance. As an ordinary stability index for the ions, thermodynamic scales referred to the water molecule, i.e. p CR+ and pKa values, are chosen for the carbocation and carbanion, respectively. 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

The Davison SOx Index of a catalyst decreases with increasing regenerator temperature. We have observed this for all the materials we have tested. These materials covered a variety of chemical compositions. This effect of temperature is believed to be due to the thermodynamic stability of the sulfate-type complex on the surface of the catalyst. Data are shown in Figure 4 for DA-250 + 10% Additive R. 

The slice through a bulk crystal can differ from both the 111 plane and the 100 plane by small angles. This produces a kink in the face of the step. By an extension of the analysis that leads to step characterization, these kinks can also be characterized. For example, a plane with Miller indices 10,8,7 has 111 terraces seven atoms wide, 110 steps one atom high, and kinks of 100 orientation every two atoms. Because of the greater thermodynamic stability of the planes of low Miller index, these surfaces of ordered roughness are stable and can be prepared and studied. Since it is sensitive to periodicity over a domain about 20 nm in diameter, LEED sees the pattern associated with terraces of various widths and may be used to characterize these surfaces. Satisfactory LEED patterns do not require absolute uniformity of terrace width but may be obtained with experimental surfaces that display a distribution of widths. 

The IR spectrum of the unsubstituted cydopropenylium ion exhibits only four bands at 3105, 1276, 908 and 736 cm , as expected from the Djij-symmetry. The band at 1276 cm is due to an E ring deformation vibration of the central three-membered ring, which is generally observed as a strong band in the range of 1400 to 1490 cm for the aryl- and alkyl-substituted derivatives (Table 2). The frequency of this band for the trimethyl-, tri-zc-rt-butyl, triphcnyl, and unsubstituted cydopropenylium ions exhibits a linear correlation with the index of the cation s thermodynamic stability such as For heteroatom-substituted derivatives... 

It may be tempting to assimilate molecular complexity (complexity of structure) with synthetic complexity (complexity of the synthetic process). However, indices of molecular complexity, even ones such as that described by Bertz, are not equally good as indices of synthetic difficulty. For one thing, there are features such as thermodynamic stability that cannot easily be incorporated into such an index. Also, because each individual feature of structure places constraints on the specific chemical reactions and conditions that may be applied during the time it is present in the synthetic sequence, and because synthetic difficulties may arise through the synergy of certain structural elements, complexity increases nonlinearly with the accumulation of structural elements. In other words, specific combinations of the same structural features can... 

Langelier indices measure thermodynamic tendencies of water and contain no kinetic information about rates of deposition. To get around this difficulty, Ryznar developed the stability index. This is defined as follows ... 

The studied triblock copolymer PS-PVP-PEO was purchased from Polymer Source (Dorval, Canada). The number-average molar masses of PS, PVP, and PEO blocks were 2.1 x 10 , 1.2 x 10 , and 3.5 x 10 g mol , respectively, and the poly-dispersity index of the sample was 1.10. The copolymer is insoluble in aqueous media, but the micelles can be prepared indirectly both in acidic and alkaline aqueous solutions by dialysis from 1,4-dioxane-methanol mixtures [88]. The micelles can be transferred from acidic to alkaline alkaline solutions and vice versa, but the addition of a base together with intense stirring promotes aggregation. Two factors contribute to the destabilization of micelles after the pH increase (a) In alkaline media, the PVP blocks become insoluble, collapse and form an upper layer of the core. Since the cores of micelles are kinetically frozen, the association number does not change. The mass of insoluble cores increases, while the length of soluble shellforming chains decreases, which results in a deteriorated thermodynamic stability of micellar solutions, (b) The PVP middle layer shrinks and PEO chains come close to each other, which worsens the solubility due to insufficient solvation of PEO blocks. 

In cases in which direct equilibration is impossible, it is sometimes possible to use readily measured physical properties which correlate with thermodynamic stability. According to Allinger s conformational rule, the more stable of two isomers not differing appreciably in dipole moment is usually the one with the lower density, refractive index, J and boiling point. There is some indication that the first two of these correlate more reliably than the last. ... 

The number of Kekule stmctures (Kekule structure count, KSC) of a conjugated hydrocarbon gives information on the thermodynamic stability and chemical reactivity and is used for the computation of various structural indices for ben-zenoid hydrocarbons " the Pauling bond order, PBO the stability index SI, SI = KSC the r-electron energy, Kekul6 structures are considered in valence-bond resonance-theoretical models such as the Pauling-Wheland model, the... 

A theoretical study at a HF/3-21G level of stationary structures in view of modeling the kinetic and thermodynamic controls by solvent effects was carried out by Andres and coworkers [294], The reaction mechanism for the addition of azide anion to methyl 2,3-dideaoxy-2,3-epimino-oeL-eiythrofuranoside, methyl 2,3-anhydro-a-L-ciythrofuranoside and methyl 2,3-anhydro-P-L-eiythrofuranoside were investigated. The reaction mechanism presents alternative pathways (with two saddle points of index 1) which act in a kinetically competitive way. The results indicate that the inclusion of solvent effects changes the order of stability of products and saddle points. From the structural point of view, the solvent affects the energy of the saddles but not their geometric parameters. Other stationary points geometries are also stable. 

Thermodynamic parameters have greater utility than equilibrium constants (Kc). The majority of workers use AHd, the enthalpy of dissociation, as the index for complex stability, which can be derived from the variation of Kc with temperature T ... 

Physical and thermodynamic properties density and refractive index, thermal and electrical conductivity, hygroscopicity, melting points, free energy and chemical potential, heat capacity, vapor pressure, solubility, thermal stability... 

In this paper, we advance a thermodynamic interpretation of the effect of chloride on copper surfaces in plating solutions. We have pursued this interpretation experimentally by observation of faceting on the sub-micron scale on low-index surfaces of copper single crystals. In the two sections that follow, relevant portions of the theory of equilibrium roughness and its relation to macroscopic faceting are presented. We consider how adsorbed chloride may stabilize the Cu(100) surface at equilibrium and relate this mechanism to simple models of thermal roughening. AFM experiments on copper plating on low-index copper crystal electrodes are then described and related to the theory. 

ZnO surfaces are more complex than those of the rock-salt type oxides Uke MgO and NiO. ZnO crystalhzes in the wurtzite structure in which each Zn cation is tetrahedrally coordinated to four O anions and vice versa [105]. This crystal structure has no inversion center. The most important low-index surface planes are two polar planes, the Zn-terminated ZnO(OOOl) and 0-termi-nated ZnO(OOO-l) plane, and two neutral planes, ZnO(lO-lO) and ZnO(l 1-20). According to Nosker et al. [106] and Tasker [107], the two polar surfaces are thermodynamically unstable, however, they can be easily prepared and characterized experimentally, and do even show rather regular (1x1) LEED patterns [108]. This indicates that they are not stabilized by major reconstructions or other modifications. Therefore, it was believed for a long time that both polar surfaces exist in an unreconstructed bulk-Hke trimcation. Several contradicting proposals have been made to explain how the stability of the polar un-... 

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