Energy interpretation

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

This relationship identifies the surface energy as the increment of the Gibbs free energy per unit change in area at constant temperature, pressure, and number of moles. The path-dependent variable dWs in Eq. (2.60) has been replaced by a state variable, namely, the Gibbs free energy. The energy interpretation of y has been carried to the point where it has been identified with a specific thermodynamic function. As a result, many of the relationships that apply to G also apply to y ... 

Equation (42) provides a thermodynamically valid way to determine y for an interface involving a solid. The thermodynamic approach makes it clear that curvature has an effect on activity for any curved surface. The surface free energy interpretation of y is more plausible for solids than the surface tension interpretation, which is so useful for liquid surfaces. Either interpretation is valid in both cases, and there are situations in which both are useful. From solubility studies on a particle of known size, y5 can be determined by the method of Example 6.2. 

More relevant for our purposes are models for oxides in which, in some way, the affinity of charge-determining ions is related to the surface electric fleld For example, in the theoiy of Hiemstra et al. proton affinities are computed in terms of bond distances, coordinations and charge distribution in the solid surface, i.e. it is essentially an energy Interpretation. For several oxides there are arguments that this is an acceptable approximation. This model also showed that not all potentially available sites are titrated in the usual pH range. 

A similar model was analyzed by Pikios and Luss (283). They analyzed the same set of reaction steps with the coverage-dependent activation energy interpreted in terms of surface heterogeneity. They derived criteria for the occurrence of oscillations as did Belyaev et al. (154,162). They also found a singular steady state, which became a limit cycle for values of the surface heterogeneity lying above a certain threshold value, and they performed numerical analyses of these oscillatory states. 

This energy interpretation is corroborated by the acceleration, already referred to, of the autoxidation by light. For, as shown by Backstrom (I), it is the absorption of this radiant energy which initiates the reaction chains. According to this author, however, the absorption of light by the autoxidizable molecule transforms it into an unstable body, a radical. 

Second, in thermodynamics it is more common to define surface tension in terms of work or the amount of energy needed to increase the surface with one unit area (i.e., the energy needed to bring a certain amount of molecules from the bulk to the surface). In this context the surface tension has a character of a surface free energy per unit area. The latter definition is in fact equivalent to the unit force per unit length (i.e. Nmjvr = NIm). The energy interpretation is by many researchers in thermodynamics considered the more fundamental one, and thus this interpretation is usually adopted for theoretical derivations. The surface tension is then defined as [1] [166] ... 

The theory of luminescence transitions is best described by using a molecular-energy interpretation for a molecular-orbital interpretation, the reader is referred to specialized monographs [1,2]. The transitions of an aromatic hydrocarbon, anthracene, will be used to illustrate the molecular-energy interpretation given below. 

Binding Energy interpretation of Different Forms of Alumina... 

Contradictory results have been published on the photoluminescence of porous InP. Some authors reported blue-shifted photoluminescence peaks lying above the band gap energy interpreted in terms of quantum confinement [230]. Hamamatsu and coworkers reported that contrary to expectation of blue-shifted emission caused by quantum confinement at pore walls, porous (001) InP samples exhibited an intense red-shifted photoluminescence peak [231]. This was explained by the formation of a set of well-defined new surface state levels on anodized pore wall surfaces. 

This assumption is not necessary in proving the energy interpretation of the J integral, but it considerably simplifies the proof. 

During the derivation, we used the fact that the result is independent of how we obtained the final state of the system (i. e., body B) from the initial state. Strictly speaking, this is valid only for elastic bodies. If plastic deformations occur, the energy interpretation has to be handled with care. It is still valid if the so-called theory of deformation plasticity is used, which assumes that there is no unloading within the material. This condition is frequently met so that the J integral can used even in plasticity in many cases. 

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