Extreme Intermediate States

Currently the authors are developing three classes of models of extreme intermediate states (MEIS) (1) with variable parameters (2) with variable flows, and (3) those describing spatially inhomogeneous systems. All these classes of the models are formulated and analyzed in terms of MP, which, in the authors opinion, can be defined as a mathematical theory of equilibrium states. It is natural to start the analysis of the created modifications with the MEIS with variable parameters, which is the closest in character to the traditional equilibrium thermodynamics models. 

Figure 5 A graphical interpretation of the model of extreme intermediate states.

Though in formulations of MEIS of type (7)-(12) or the particular form (53)-(57) the possibility of projecting the space of thermodynamic variables to a tree is not shown, the knowledge of principal possibility to reduce the set Dt(y) to the tree makes the analysis of capabilities and comparative merits of the model of extreme intermediate states essentially easier, clearer, and more convincing. 

The main idea of the research being described is the refusal to use an equation of trajectory and construction of stepwise methods to analyse processes on the basis of the model of extreme intermediate states (MEIS) that was created by B.M.Kaganovich, S.P.Filippov and E.G. Antsiferov (Antsiferov et al., 1988 Kaganovich, 1991 Kaganovich et al., 1989). The features that make MEIS different from the traditional thermodynamic models are 1) statement of the problem to be solved (instead of search for a sole point of final equilibrium the entire set of thermodynamic attainability Dj(y) from the given initial state y is considered and the states with extreme values of modeled system characteristics of interest to a researcher are found) 2) dual interpretation of the equilibrium notion, i.e. both as a state of rest and as an instant of motion in which the equality of action and counteraction is observed and 3) dual interpretation of dynamic quantities (work t, heat q, rate w, flow of substance x, etc.) both... 

Models of extreme intermediate states and construction of trajectories... 

Relations between the theories of states and trajectories and capabilities of equilibrium thermodynamic analysis to study reversible and irreversible kinetics can be more fully revealed by considering another type of models of extreme intermediate states, namely MEIS of hydraulic circuits (Gorban et al., 2001, 2006 Kaganovich et al., 1997, 2007, 2010). Convenience and clearness of using these models to describe the considered problems are determined by the fact that they are intended to study an essentially irreversible process, i.e. motion of a viscous fluid. Besides, they can be treated as models of the mechanism of fluid transportation from the specified source nodes of a hydraulic system to the specified consumption nodes. The major variable of the hydraulic circuit theory (Khasilev, 1957,1964 Merenkov and Khasilev, 1985), i.e. continuous medium flow, has an obvious kinetic sense. 

However, the made groundwork in studying physical-mathematical properties of the models of extreme intermediate states and in their ap>plication enables one to highly estimate the forthcoming achievements in solution of discussed ptroblems and to prove the necessity for continuation and expansion of the scope of kinetic-thermodynamic studies. 

In the process of passivation, metals usually are found only in one of the two extreme states, active or passive. The transition between these states occurs suddenly and discontinuously. The intermediate state in region BC can only be realized with special experimental precautions. It is in this sense that passivation differs from the inhibition of electrochemical reactions observed during adsorption of a number of surface-active substances, where the degree of inhibition varies smoothly with the concentration of added material. 

He suggested that the ionic formulas, like the nonionic formulas, "represent formulations of extremes" and that no bond across the ring is required. Using the hypothesis of the motions of valence electrons, as developed by Stark and Kossel, Arndt suggested the possibility of intermediate valence states (Zwitterstufen) as well.32 Independently, Robinson proposed possible electronic shifts in pyrones and similar systems, but he did not state the idea of a definite "intermediate state" of the molecule between the ionic and uncharged formulas.33... 

The ab initio calculation of the transition rate between two electronic states with the emission of p phonons involves a very complicated sum over phonon modes and intermediate states. Due to this complexity, these sums are extremely difficult to compute however, it is just this complexity, which permits a very simple phenomenological theory to be used. There are an extremely large number of ways in which p phonons can be emitted and the sums over phonon modes and intermediate states are essentially a statistical average of matrix elements. In the phenomenological approach it is assumed that the ratio of thep-th and (p - l)-th processes will be given by a couphng constant characteristic of the matrix in which the rare earth is situated and not depending... 

The detonation wave is a combination of a shock and combustion front, and has a constant width on the time-distance plot. Passage thru the intermediate state would require the attainment of extremely high peak pressure, and of wave-front velocities above the CJ value. Oppenheim quotes (Ref 3, p 476) some exptl evidence of these phenomena... 

As A4> can amount to several volts, the electron deformation of the adsorbed molecules can be expected to influence their chemical behavior substantially. Therefore, when reactions are catalyzed via the intermediate formation of boundary layers on a catalyst, we may assume that the activation of the reacting molecules is frequently correlated to their polarization on the catalyst surface. There are two effects of polarization either it causes a strong but reversible adsorption, or the deformation of the electron shell of the adsorbed molecule is so thorough that the system—provided that it possesses sufficient activation energy— switches over irreversibly into a new quantized equilibrium position, forming a chemical bond (1) under liberation of energy. Intermediate states exist between these two extremes. 

Fig. 7.2 Energy levels of the H n = 15, m = 0 Stark levels. The broadening of the levels corresponds to an ionization rate of 106 s-1. The extreme red and blue state ionization rates are taken from the calculations of Bailey et al. (ref. 5), and those of the intermediate states...

It is worthwhile, however, pointing out that the existence of a long-lived intermediate state and the absence of a barrier in the exit channel do not necessarily imply statistical product state distributions. The fragment distributions in the dissociation of weakly bound van der Waals molecules are usually neither thermal nor statistical, despite the extremely long lifetime of the complex. We will come back to this in Chapter 12. 

Shown in Fig. 7.2 are the relevant structural parameters, schematic representations of the extreme, intermediate and transition state conformations of the chelate ring, and the calculated energy profile. Heavy equipotential lines are spaced by... 

Figure 7.2 Conformational interconversion of the five-membered diamine chelate ring of [Co(en)(NH3)4]3+. (a) Nomenclature of the torsional angeles. (b) Representation of the extreme, intermediate and transition state conformations, (c) Graphical representation of the potential energy surface (see text). Taken from [180]. John Wiley and Sons, Inc, 1987.

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