Kinetic equations generalized

Generalized first-order kinetics have been extensively reviewed in relation to teclmical chemical applications [59] and have been discussed in the context of copolymerization [53]. From a theoretical point of view, the general class of coupled kinetic equation (A3.4.138) and equation (A3.4.139) is important, because it allows for a general closed-fomi solution (in matrix fomi) [49]. Important applications include the Pauli master equation for statistical mechanical systems (in particular gas-phase statistical mechanical kinetics) [48] and the investigation of certain simple reaction systems [49, ]. It is the basis of the many-level treatment of... 

The fimdamental kinetic master equations for collisional energy redistribution follow the rules of the kinetic equations for all elementary reactions. Indeed an energy transfer process by inelastic collision, equation (A3.13.5). can be considered as a somewhat special reaction . The kinetic differential equations for these processes have been discussed in the general context of chapter A3.4 on gas kmetics. We discuss here some special aspects related to collisional energy transfer in reactive systems. The general master equation for relaxation and reaction is of the type [H, 12 and 13, 15, 25, 40, 4T ] ... 

For a closed chemical system witli a mass action rate law satisfying detailed balance tliese kinetic equations have a unique stable (tliennodynamic) equilibrium, In general, however, we shall be concerned witli... 

T. Burkhardt, H. Muller-Krumbhaar, D. Kroll. A generalized kinetic equation of crystal growth. J Cryst Growth 5S 13, 1973. 

Although the literature contains a very large number of research articles concerned with the kinetics and mechanisms of reactions involving solids, there are comparatively few authoritative, critical and comprehensive reviews of the formidable quantity of information which is available. Probably the most important general account of the field is the book Chemistry of the Solid State, edited by Gamer [63]. Chapters 7—9 are particularly relevant in the present context as they provide a systematic exposition of the kinetic equations applicable to the decomposition of single solids (Jacobs and Tompkins [28]) and their application to endothermic [64] and exothermic [65] reactions. 

In deducing from the resulting kinetic equation the nature of the electrophile and how it is produced it is important to represent all the reagents present in terms of the species which they may produce. In this way it is possible to eliminate many negative or fractional orders in reagent and generally obtain a simpler kinetic equation. For example, the observed rate law in the uncatalyzed iodination of aniline can be written21,22 as... 

In the present section the general kinetic equation (3.26) will be solved within the Keilson-Storer model for an arbitrary angular momentum correlation [163], We consider here the case of spherical molecules (for linear molecules see Appendix 5). The corresponding initial condition is the equilibrium distribution... 

The necessary generalization of the description is achieved by using instead of Eq. (4.3) the integral kinetic equation... 

Time evolution of this component, as is proven in Appendix 7, is described by the kinetic equation of impact theory, which is a generalization of Eq. (3.26) ... 

The present appendix represents a detailed derivation of the kinetic equations of the fluctuating liquid cage model in the classical formalism. A natural generalization is done for the case of partially ordered media, e.g. nematic liquid crystals. One of the simplest ways to take into account the back reaction is demonstrated, namely to introduce friction. 

Keilson-Storer kernel 17-19 Fourier transform 18 Gaussian distribution 18 impact theory 102. /-diffusion model 199 non-adiabatic relaxation 19-23 parameter T 22, 48 Q-branch band shape 116-22 Keilson-Storer model definition of kernel 201 general kinetic equation 118 one-dimensional 15 weak collision limit 108 kinetic equations 128 appendix 273-4 Markovian simplification 96 Kubo, spectral narrowing 152... 

It is natural that a general kinetic equation for every case is different ... 

The first part of the equation is the general kinetic equation, from which it is... 

The specific rate of an electrode reaction depends not only on electrode polarization but also on tfie reactant concentrations. Changes in reactant concentrations affect not only reaction rates but also the values of equilibrium potentials. To differentiate both these influences, kinetic equations are generally used (especially at high values of polarization), relating the current density not with the value of polarization AE but with the potential of the electrode E ... 

When the laws of the partial reactions are preserved throughout the entire range of potentials (Butler, 1924), a general kinetic equation that is valid for both the anodic and cathodic currents can be written... 

The principle of independent electrochemical reactions applies when several reactions occur simultaneously. It says that each reaction follows its own quantitative laws, irrespective of other reactions. At a given potential, the rates of the different reactions are not at all interrelated, and at a given CD they are merely tied together by relation (13.53). This does not mean that the reactions have no influence on each other at all. One of the reactions may produce changes in the external conditions for other reactions (e.g., in the temperature or solution pH, the amount of impurities adsorbed on the electrode). However, the form of the kinetic equation of each reaction is not affected by these changes. The principle of independent electrochemical reactions is quite general, and rarely violated (we discuss an instance of such a departure in Section 22.2). 

Matheson, I. B. C. The method of successive integration a general technique for recasting kinetic equations in a readily soluble form which is linear in the coefficients and sufficiently rapid for real time instrumental use. Anal Instrum. 1987, 16, 345-373. 

---