Non-formal Kinetics

Moore, J. W. Pearson, R. G. Kinetics and Mechanism, 3rd Ed. John Wiley Sons New York, 1981. Schmid, R. Sapunov, V. N. Non-Formal Kinetics In Search for Chemical Reaction Pathways Verlag Chemie Weinheim, 1982. 

R. Schmid and Y. N. Sapunov, Non-Formal Kinetics, Verlag-Chemie,Weinheim, 1982, pp 123-156. 

Schmid, R., Sapunov, V. N. (1982). Non-formal Kinetics, Verlag Chemie, Weinheim. A marvelous book showing how applied mathematics can be used to describe many complex reaction schemes. 

Schmid, R., and Sapunov, V.N. (1982). Non-Formal Kinetics. Monographs in Modern Chemistry, Vol. 14. Deerfield Beach, Fla., and Basel Verlag Chemie Weinheim. 

Shmidt, R Sapunov, VN. Non-formal kinetics, Verlag Chemie, Weinheim-Dearfield Beach-Florida-Basel, 1982. 

The examples to be presented illustrate the diversity of fields of applications, but they are mentioned in outline form only. Many biological phenomena used to be modelled by real or formal kinetic models. A biochemical control theory that is partially based on non-mass-action-type enzyme kinetics seems to be under elaboration, and certain aspects will be illustrated. A few specific models of fluctuation and oscillation phenomena in neurochemical systems will be presented. The formal structure of population dynamics is quite similar to that of chemical kinetics, and models referring to different hierarchical levels from elementary genetics to ecology are well-known examples. Polymerisation, cluster formation and recombination kinetics from the physical literature will be mentioned briefly. Another question to be discussed is how electric-circuit-like elements can be constructed in terms of chemical kinetics. Finally, kinetic theories of selection will be mentioned. 

Formal Kinetics of Multicentered Non-Branching Chain Reactions... 

Let us pass to a brief description of the formal kinetics of multicentered chain reactions. A multicentered non-branching chain reaction with linear steps of transformation of the active reactive centers (chain carriers) may be represented in the form of a formal scheme [9], as some kind of a flow graph for the dynamic process (see Section 4.5). 

In this appendix we evaluate the functional derivative of the non interacting kinetic energy functional which is simple occupied-orbital dependent functional and thus can be treated with the chain-rule formalism developed... 

Furthermore, during the cracking process there is an increase in the number of moles of products being formed from the gas oil. In a riser, which is normally modeled as a plug flow reactor, this results in a decrease in the massic vapour density. If the concentration of the reactants is defined at a constant volumetric flow, the apparent order also increases because the actual concentration decreases much faster than expected as the conversion increases. A pseudo-second-order reaction has been normally used to account for these non-linear effects (Weekman, 1968). However, the reaction order should be independent of the reaction system used and an additional term to account for the increased vapour velocity in a flow unit should be used to define the formal kinetics (Shaikh and Carberry, 1984). 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

The pentacoordinate molecules of trigonal bipyramidal form, like PF5, are a very nice example for the study of the formal properties of stereoisomerizations. They are characterized by an appreciable nonrigidity and they permit the description of kinetics among a reasonable number of isomers, at least in particular cases (see below). Therefore the physical and chemical properties of these molecules have been thoroughly investigated in relation to stereoisomerization. Recent reviews may be found in the literature on some aspects of this problem. Mislow has described the role of Berry pseudorotation on nucleophilic addition-elimination reactions and Muetterties has reviewed the stereochemical consequences of non-rigidity, especially for five- and six-atom families as far as their nmr spectra are concerned. 

Kinetic studies of the hydride cluster [W3S4H3(dmpe)3] with acids in a non-coordinating solvent, i.e., dichloromethane, under the pseudo-first-order condition of acid excess, show a completely different mechanism with three kineti-cally distinguishable steps associated to the successive formal substitution of the coordinated hydrides by the anion of the acid, i.e., Ch in HCl [37]. The first two kinetic steps show a second-order dependence with the acid concentration. 

The positional selectivity on formation of the cydoadducts from 221 is less pronounced than that of the isobenzene 162, but it is the conjugated double of the allene moiety as well that predominantly undergoes the reaction. As demonstrated by the thermolysis of several products, these are formed from 221 under kinetic control. For example, on heating, the styrene adduct 240 and the furan adduct 231 rearranged virtually completely to 241 and 232, which are formally the cycloadducts to the non-conjugated double bond of the allene subunit of 221 [92, 137]. The cause of the selectivity may be the spin-density distribution in the phenylallyl radical entity of the diradical intermediates. 

Although their conceptual basis is now firmly established, non-adiabatic electron transfer processes are still the subject of intensive theoretical studies. Nevertheless, the framework provided by the standard formalism presented in this section seems sufficiently general to be used for the interpretation of kinetic data obtained in biological systems. Owing to the great number of parameters involved in the theoretical expressions, attainment of useful information requires obtaining numerous data by elaborate experiments. The next section is devoted to a review of the different approaches that have been developed over the last few years. 

It was shown in Sect. 2 that the standard formalism appropriate for non-adiabatic electron transfer processes leads to the definition of an electronic and a nuclear factor in the rate expression. This separation into factors of quite different physical origin is conceptually very useful. As a matter of fact, it is systematically emphasized throughout this presentation to clarify the nature of the different parameters involved in biological electron transfers. It happens also to be very useful when the relation between the kinetics and the biochemical function of these processes is considered. This is illustrated below by a few examples. 

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