Evidence of structural equilibration

A larger energy barrier obviously requires a higher temperature to achieve equilibrium in a fixed time. The formation energy U and the barrier energy are often of very different magnitudes. The equilibrium state and its kinetics are discussed separately in Sections 

Any defect reaction which has an energy barrier of the form shown in Fig. 6.1 exhibits a high temperature equilibrium and a low temperature frozen state. The temperature, T, at which freezing occurs is calculated from Eq. (6.2) by equating the cooling rate with dr/dx,  

The equilibration of the structure is manifested in reversible changes of the material properties as the temperature is changed. Most of the evidence for bulk thermal equilibration of defect and dopant states in doped a-Si H comes from electronic transport measurements. Fig. 6.3 shows that the temperature dependence of the dc conductivity 

slowly decays to a steady state, with the decay taking more than a year at room temperature, but only a few minutes at 125 °C. The temperature dependence of the relaxation time is plotted in Fig. 6.5 and 

When no structural changes take place, both and Nj are 

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Evidence for the equilibration of light olefins within SAPO-34 prior to diffusion out of the crystalline structure has been obtained by comparing the ethylene/propylene ratio in the MTO product with that calculated from thermodynamic equilibrium. Figure 12.7 shows the thermodynamic ratios of the C2-C5 olefins at 0 psig as a function of temperature. The concentration of ethylene increases at higher temperatures. The influence of equilibrium on the ethylene/propylene product ratio obtained with the MTO-100 catalyst over a range... 

For many years, a lively controversy centered over the actual existence of nonclassical carbocalions. " The focus of argument was whether nonclassical cations, such as the norbornyl cation, are bona fide delocalized bridged intermediates or merely transition states of rapidly equilibrating carbenium ions. Considerable experimental and theoretical effort has been directed toward resolving this problem. Finally, unequivocal experimental evidence, notably from solution and solid-state C NMR spectroscopy and electron spectroscopy for chemical analysis (ESCA), and even X-ray crystallography, has been obtained supporting the nonclassical carbocation structures that are now recognized as hypercoordinate ions. In the context of hypercarbon compounds, these ions will be reviewed. 

Licjuid-liquid phase transition phenomena in polymer-polymer systems were studied. Evidence is presented which suggests that spinodal decomposition occurs in this system. It was not possible to prove that nucleation and growth also occurred for the dispersed-phase structure because of the rapid rate of phase equilibration. 

Perhaps the "classic" example of a nonclassical carbocation is the 2-norbornyl cation, which was at the center of what has been called "the most heated chemical controversy in our time." In Chapter 8 we will review the experimental evidence, largely based on solvolysis reactions, that led to the proposal of the nonclassical carbonium ion structure shown in Figure 5.48. However, this description was not accepted by all researchers, and an alternative model for the 2-norbomyl cation was a pair of rapidly equilibrating classical (carbenium) ions, as shown in Figure 5.49. Many papers relating to the development of contrasting ideas in this area were published in a reprint and commentary volume by Bartlett. ... 

DMSO form an isomeric semidione which is also quite stable but is converted by additional oxygen into The hfsc for this species suggest structures 25 or possibly a rapidly equilibration mixture of 2 and 24. There is no evidence for any equilibration between this species and 22 although such an interconversion... 

Labelling studies with (525) clearly establish that either ion (526) is stable at -115 °C or equilibration between less symmetric structures must be rapid at that temperature. Now, in accordance with earlier predictions, evidence for a square-pyramidal ion is obtained from the n.m.r. spectrum of (527) in superacid media. Although solvolytic studies with the benzoate of (527) suggested that (528) was not an intermediate, the speetrum from (527) is best interpreted on the basis of strueture (528) or a set of rapidly equilibrating ions. 

Therefore, thermodynamic equilibrium of a macroscopic system is an effect of local equilibration processes at a subsystem level (structural hierarchies). In other words, concentration equilibrium in a system (molecular composition equilibrium) doesn t correspond to the equilibrium number and size and especially inner structure (topological) distributions of supramolecular structures and completion of the phase separation process with stationary concentrations in contacting phases doesn t characterize phase solution layering because of possible further coalescence and morphology system changes. All these aspects are evidently stipulated by thermodynamical equilibration kinetics. Further information on equilibration kinetics at various structural organization levels is presented in Parts II and III of this book. 

There is little doubt that Shallenberger s AH,B hypothesis is the most plausible concept in the explanation of the initial stimulation of the sweet-taste receptor. However, it was unfortunate that the evidence was accrued largely with the aid of reducing sugars, which, in solution, equilibrate between many isomers, so that it is not possible to relate total gustatory response to any one particular stereochemical structure It is also not... 

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