Open circuit theory

PART I Open Circuit Theory and Parabolic Tarnishing Kinetics Historical Background... 

Capstone Comments on the Open Circuit Theory of Parabolic Oxidation... 

F. Zhang, X. Guo, and H. Zhang, Advances of Clar s aromatic sextet theory and Randic s conjugated circuit model. Open Org. Chem. J. (Suppl. 1-M6) (2006) 87-111. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

The piezoelectric constant of polymer films is usually a function of the frequency of the applied strain, and the constant is expressed by a complex quantity. In other words, the open-circuit voltage across the film surfaces is not in phase with the applied strain and the short-circuit current is not in phase with the strain rate. This effect, first pointed out by Fukada, Date and Emura (1968) and designated piezoelectric relaxation or dispersion, will be discussed in this review in terms of irreversible thermodynamics and composite-system theory. 

Why is the open circuit potential more positive when the rotation rate is increased (Hint use mixed potential theory to prove that it should be )... 

An alternative technique for the measurement of sc is to study the photopotential. The theory of this is discussed in some detail in Sect. 7, but the essential features of the measurement are shown in Fig. 16. After equilibration in the dark, when the potential of the electrode at open circuit becomes equal to the redox potential Vredox, the light is turned on and the electrode potential changes at open circuit in such a way that the bands become flat. There are many problems with this technique and it is considerably less reliable than a properly conducted a.c. experiment, but it may give a reasonably accurate picture if surface recombination is small (vide infra). Some results for p-GaAs in aqueous solution are shown in Fig. 17 and the S values derived are of the order 0.7, though the dispersion apparent in Fig. 17 makes a quantitative interpretation difficult. 

According to the fundamental theory of overpotential for aqueous electrochemical systems, the electrochemical cell overpotential is defined as the potential difference deviahon from the open-circuit value. The electrochemical cell overpotential is then defined as ... 

The subject of multiplicative fluctuations (in linear and especially nonlinear systems) is still deeply fraught with ambiguity. The authors of Chapter X set up an experiment that simulates the corresponding nonlinear stochastic equations by means of electric circuits. This allows them to shed light on several aspects of external multiplicative fluctuation. The results of Chapter X clearly illustrate the advantages resulting from the introduction of auxiliary variables, as recommended by the reduced model theory. It is shown that external multiplicative fluctuations keep the system in a stationary state distinct from canonical equilibrium, thereby opening new perspectives for the interpretation of phenomena that can be identified as due to the influence of multiplicative fluctuations. 

Despite the fact that open-system behavior in mineral-isotopic systems is governed by a combination of volume and short-circuit diffusional processes, most thermochronologists make the simplifying assumption that volume diffusion alone controls the open- to closed-system transition that is so important to thermochronologic theory. There are a variety of reasons to believe that this assumption is reasonable. First, the stmcture of short-circuit pathways is such that they should be characterized by much faster diffusion than the intact crystal structure that surrounds them if so, then the rate of daughter isotope loss should be limited by the rate of diffusion out of intact domains and into short-circuit pathways. Second, the volumetric proportion of short-circuit pathways to intact domains is small in all but the most strongly deformed natural crystals, implying that their contribution to bulk... 

The isotopic labeling of the source molecules should lead to the ratio H/D = 1 (D2 mol% = 50) in the evolved gas under open-circuit conditions at equal rates of reactions (19.11) and (19.12) (equal partial currents in and /12). Furthermore, as it follows from the mixed potential theory, the isotopic composition of the evolving gas could be varied by changing the electrode potential due to the change in the partial reaction rates. 

Online mass spectrometry data presented and discussed in the previous sections suggest that catalytic hypophosphite oxidation on nickel in D2O solutions proceeds via the coupling of anodic (19.11) and cathodic (19.12) half-reactions at the catalyst surface. The classical mixed-potential theory for simultaneously occurring electrochemical partial reactions [14] presupposes the catalyst surface to be equally accessible for both anodic (19.11) and cathodic (19.12) half-reactions. Equilibrium mixtures of H2, HD, and D2 should be formed in this case due to the statistical recombination of Hahalf-reactions (19.11) and (19.12) for example, the catalytic oxidation of hypophosphite on nickel in D20 solution under open-circuit conditions should result in the formation of gas containing equal amounts of hydrogen and deuterium (H/D=l) with the distribution H2 HD D2= 1 2 1 (the probability of HD molecule formation is twice as high as for either H2 or D2 formation [75]). Therefore, to get further mechanistic insight, the distribution of H2, HD, and D2 species in the evolved gas was compared to the equilibrium values at the respective deuterium content [54]. 

However, according to the mixed potential theory, the value of the open-circuit potential varies when changing the rate of reaction (19.18) or reaction (19.19) due to H/D substitution in formaldehyde or water (for corresponding Em values see Figure 19.8A(b) and B(b)). Therefore, the effect of H/D substitution on the rates of individual partial reactions must be studied under electrode potential control. 

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