Bodenstein-principle

In almost every case differential equations for the quantitative description of the time dependence of particular species resulting from a catalytic cycle cannot be solved directly. This requires approximate solutions to be made, such as the equilibrium approximation [15], the Bodenstein principle [16], or the more generally valid steady-state approach [17]. A discussion of differences and similarities of different approximations can be found in [18]. 

The Bodenstein principle which states that the radical concentrations are constant, is assumed valid (7). 

Equipped with the Bodenstein principle, let us now continue the derivation of the rate law for SN reactions that take place according to Figure 2.11. The completely inadequate approximation [carbenium ion] = 0 must be replaced by Equation 2.6. Let us now set the left-hand side of Equation 2.6, the change of the carbenium ion concentration with time, equal to the difference between the rate of formation of the carbenium ion and its consumption. Because the formation and consumption of the carbenium ion are elementary reactions, Equation 2.7 can immediately be set up. If we now set the right-hand sides of Equations 2.6 and 2.7 equal and solve for the concentration of the carbenium ion, we get Equation 2.8. With this equation, it is possible to rewrite the previously unusable Equation 2.5 as Equation 2.9. The only concentration term that appears in this equation is the concentration of the alkylating agent. In contrast to the carbenium ion concentration, it can be readily measured. 

The quasi-steady-state approximation (QSSA) is also called the Bodenstein principle, after one of its first users (Bodenstein 1913). As a first step, species are selected that will be called quasi-steady-state (or QSS) species. The QSS-species are usually highly reactive and low-concentration intermediates, like radicals. The production rates of these species are set to zero in the kinetic system of ODEs. The corresponding right-hand sides form a system of algebraic equations. These... 

Intermediate B in Scheme 11.15 can be observed in principle but, if it undergoes rapid decay, it is usually expressed in concentrations very small compared with those of reactants and products, and it may be too dilute to be observed by instrumental techniques it is then usually called a transient intermediate. Under these conditions, the Bodenstein steady-state hypothesis applies and the rate equation for Scheme 11.15 can be solved to give Equation 11.10 (see Chapter 4) ... 

This term was introduced to the normal chemical language in the 20th century due to the efforts of Bodenstein. In Semenov s view, the understanding that, no matter how complicated is a reaction s process the law of the elementary act is sufficiently simple, is exclusively the credit "of Van t Hoff s genius prediction, though he himself did not understand it quite clearly [5, p. 6]. Though the epithet "genius with respect to Jacob Henri Van t Hoff is still valid, the situation, however, defies its complete reconstruction. On the one hand, it is likely that Van t Hoff renounced in principle the analysis of complex reactions that do not obey the laws of "normal conversions . Apparently, it is for this reason that in the "Etudes he did not examine etherification reactions practically [19]. Van t Hoff studied such simple reactions as the decomposition of dibromosuccinic acid and the reaction of... 

The first who used this principle was Chapman (6), and half a year later Bodenstein in his paper on the hydrogen-chlorine reaction (5) also used it. Since the latter defended its use so ardently, it is not unjustly often connected with his name. 

The application of Bodenstein s principle (a quasi-steady state with respect to radicals) to nonisothermal processes is shown not always to be correct. 

The steady-state approximation was first enunciated by Bodenstein.> It states that in a reaction in which transient species, such as atoms or radicals, are involved, a steady state sets in, characterized by an equal rate of formation and disappearance of the species. This principle, applied to the case of a polymerization reaction, means that at a certain reaction stage the amount of active centers formed is equal to the amount of growing chains terminated ... 

Conclusion (a) Photochemical steps of reaction include many thermal degradation processes, which do not need to be considered in the rate law, if the Bodenstein hypothesis is valid, (b) The mechanism has to be reduced as far as possible to avoid linear dependencies, (c) Thermal and photochemical reactions can be treated in principle by the same formalism. Rate constants times concentrations have to be substituted by the product of the partial photochemical quantum yield times the amount of light absorbed, which contains the concentration of the reactant which starts the photoreaction. 

The concentration of the primary radical cr is characterized by the fast establishment of a steady-state value. Applying Bodenstein s quasi-steady-state principle to this concentration yields the following description of the initiating reaction ... 

The polymer radical concentration cp , which is part of the propagation rate, can be obtained by applying the Bodenstein quasi-steady state principle. 

Fri>ni time to time a paper emerges in the literature aimed at emphasising the net essity of the foundation of the principle of quasistationarity, pseudo-steady state hypothesis, or Bodenstein(-Semenov) method. The essence of the method seems to be an absolutely crazy idea — from the mathematical point ofview. In a system of differential equations let us consider the variables that late on small values to be constant. So if a function is small, so is its derivative It turns out that among the conditions that occur in chemical reaction kinetics it does work well. 

Any textbook on chemical kinetics makes use of the Bodenstein stationary principle if in a system of consecutive reaction steps A B C the concentration of... 

Based on the ideas of Bodenstein, many attempts have been made to develop simplified descriptions of chemical reaction systems, e.g., for the simulation of complex combustion processes, and a variety of different approaches can be found in the literature (see, e.g., [6-8] for references considering combustion processes). In principle two ways of simplifying the chemical kinetics can be distinguished. One is to use the knowledge about the reaction system, i.e. the information on which species are in quasi-steady state or which reactions are in partial equilibrium (see [6,7] for references). The other is to extract exactly... 

By assuming the Bodenstein steady state principles for all intermediates and that all rate constants are independent of the degree of polymerization, Bohm has deduced the following equation. 

Max Bodenstein (1871-1942) a German physic-chemist and one of the founders of chemical kinetics. He introduced the principle of quasi-stationarity, which was named after him. He worked intensively on the reaction of hydrogen with chloride. 

In order to calculate the conversion of a reaction the axial mixing coefficient has to be known. There are ample experimental data available. In principle, the axial mixing coefficient of a component A is determined by flow conditions and by the diffusivity of A, Generally speaking, the Bodenstein number for axial mixing is a function of the Reynolds and Schmidt numbers (for definitions see eq. 4.23) ... 

For each reacting species, a differential equation of the concentration change may be written. The Bodenstein-Semenov steady-state principle can be applied only for short-lived active species therefore, either the obtaining system is analytically nonsolved or its complex solution is impracticable. 

The kinetics of stationary (quazistationary after radicalconcentration in accordance with the Bodenstein—Semenov principle) photoinitiated copol5mierization of bifimctional (meth)acrylates was studied by laser interferometry [11, 20]. The experimental kinetic curves were obtained for the systems 1.6-hexanedioldiacrylate - trielhylene glycol dimethacrylate (HDDA - TGM-3) at molar ratios of components HDD A TGM-3 4 1, 2 1, 1 1, 1 2 and 1 4 in thin layers till high conversion depending on photoinitiator (2,2-dimethoxy-l,2-diphenylethane-l-on (IRGACURE... 

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