Excess energy definition

When an excited molecule also consists of a definite vibrational level as shown in Fig. 5.1(a), there shall be no direct dissociation of molecule and a fine structure in the electronic band spectra of the molecule will be observed. The excess energy, in usual course may be dissipated as heat or may give rise to fluorescence. But the molecule may retain its energy until it has not reacted with another molecule or transfer its energy to another molecule, e.g. decomposition of NOC1 as follows ... 

Fig. 2.13. Definition of Eoi and origin of KER. The excess energy of the decomposing ion in the transition state refative to the sum of the heats of formation of the ionic and neutral product is partitioned into vibrational excitation of the products plus KER.

Since the scope of this article is purely theoretical, we just outline below the state of the experimental situation. The ideal experiment in Chemical Dynamics would be that in which starting with reactants in definite intramolecular quantum-states and running towards each other in a definite way (relative velocity and orbital angular momentum) the distribution of the products over the various intramolecular quantum-states and the state of the relative motion (direction and velocity) would be measured. Such an experiment would show whether there is a preferential molecular orientation at the heart of the collision, what the lifetime of the intermediate complex is, how the excess energy is distributed over the various degrees of freedom of... 

The PPg aoion has been observed in the negative ion mass spectra of PF (1 ) and PF CN (2). Both studies included thermochemical calculations on plausible ion formation processes, showing that the measured appearance potentials contained large excess energy contributions. At present, definite values cannot be assigned to these contributions thus, their studies are of little value in defining. ... 

The relaxation In Figure 3 Is clearly nonstatlstlcal. It does not occur with a single exponential and It happens on Coo long a time scale. Furthermore, this nonstatlstlcal behavior has definite Implications If It persists above dissociation (and It does, as will be shown later) since It Implies mode specificity of unlmolecular dissociation. This Is due Co the fact Chat energy tends to stay Crapped In the mode of Initial excitation, but dissociation occurs only when excess energy piles up In the weakest bond (the CS bond). 

On the basis of the translational energy releases in the collision-induced decompositions relative to those in the unimolecular decompositions, it appeared [216] that, in the losses of H2 from (CH3OH2), (CHsOH) and (CH20H), the energy releases became smaller at the higher excess energies. This somewhat surprising conclusion appears not to be supported by the results of a PIPECO study of methanol [18, 658] however, the PIPE CO results are not sufficiently precise to constitute definite proof that the conclusion is incorrect. 

Excess Gibbs Energy definition (for a liquid phase)... 

Surface energies, y, are not easily assessed for the models of the fibers. The excess energy associated with the surface is easily evaluated, but there is an amhiguity in the definition of the surface area. For the free-standing thin films, the surface area for that portion of the film in the periodic box is ILxLy, which is well defined. In contrast, the... 

In most cases of interest, the surface excess mass E is small, so that the acceleration and body force terms may be neglected. Then Equation 1.40 simplifies to two conditions. One of them, V y = 0, requires that interfacial tension be uniform. The other is the Young-Laplace equation (Equation 1.22), which was obtained previously from thermodynamics for situations where body force and acceleration terms were unimportant. That the same equation (Equation 1.22) results from independent thermodynamic and mechanical derivations implies that interfacial tension must have the same value whether it is defined as in Equation 1.9 from energy considerations or as in Equation 1.39 from force considraations. Simply put, the force and energy definitions of interfacial tension are eqnivalrait, a conclusion emphasized in the work of Buff (1956). 

It is meaningful to redefine the interface energy as the energy density per unit cell in the interface region, in place of the conventionally defined excessive energy per unit area. To be in line with the conventional definition, the interface free energy density will equal to the energy per unit cell divided by the cross-sectional area of the cell. 

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