Christiansen sequences

In Figure 6.36 K[ is the dissociation constant for the El complex. An equation for the linear Christiansen sequence with an extra cycle was presented before (equation 5.109) and scheme 5.110 for a similar case... 

If there are more than two steps and the mechanism of a heterogeneous catalytic reaction follows the linear Christiansen sequences, then the general kinetic expressions are given by eq. (5.94-5.95). Some particular cases of Christiansen sequences with 3, 4, 6 and 8 steps were presented for homogeneous catalysis by metal complexes, e.g., equations (5.72, 5.76, 5.84) and (5.88) respectively. It should be stressed that in the case of heterogeneous catalysis equations for the reaction rates are exactly the same, which is not surprising as similar kinetic steps describe the reaction mechanisms. 

Although all reactions showing a closed sequence could be considered to be catalytic, there is a difference between those in which the entity of the active site is preserved by a catalyst and those in which it survives for only a limited number of cycles. In the first category are the truly catalytic reactions, whereas the second comprises the chain reactions. Both types can be considered by means of the steady-state approximation, as in Christiansen s treatment. This important development dates to 1919 (reaction between hydrogen and bromine reported earlier by Bodenstein and Lind. 

In treating catalytic sequences of elementary steps, Christiansen adopted the simplification that each elementary step is first order in both directions with respect to concentration of a single active species. The resulting rates... 

Christiansen also noticed that some closed sequences would not yield an overall reaction and appropriately called such sequences cyclic. He was among the first to advance the viewpoint that the only possible stationary value for flow in such a sequence is zero and identified this with the principle of microscopic reversibility. 

Pallesen L, Poulsen LK, Christiansen G, Klemm P, Chimeric. FimH. Adhesion, of type 1 fimbriae A bacterial surface display system for heterologous sequences, Microbiology, 141 2839-2848, 1995. 

However as mentioned in a paper by Christiansen and Kramers (13) and shown experimentally, notably by Hinshelwood (14) and Semenoff (15), cases are known in which the number of intermediates is increased by one revolution of the closed sequence. In that case it is impossible to fulfil the stationarity conditions, which means that the reaction goes on with ever increasing speed, i.e., we get an explosion. Only by adding inhibitors which remove one or more of the intermediates can the reaction be turned into an ordinary smooth reaction. 

B8. Bonde, M., Garnero, P., Fledelius, C., Qvist, P., Delmas, P. D., and Christiansen, C., Measurement of bone degradation products in serum using antibodies reactive with an isomerized form of an 8 aminoacid sequence of the C-telopeptide of type collagen I. J. Bone Miner. Res. 12,1028—1034 (1997). 

As first clarified by Christiansen, chain and catalytic reactions consist of a closed sequence of elementary steps involving stable reactants, intermediates, and products reacting with reactive intermediates. The first such reactive intermediate in the first step of the sequence is regenerated in the last step of the sequence, closing the chain or catalytic cycle. ... 

Since chain reactions are so common, it would be unreasonable to expect all mechanisms to fit neatly into the four examples of Table 1.3. Illustration 1.5 has already given some further information on thermal decomposition reactions following Rice-Herzfeld mechanisms. Before going on to additional reaction systems, we should add a few comments on the two-active-center reaction illustrated by the combination of hydrogen and bromine in the gas phase. This is probably the first reaction for which a suitable chain sequence was identified. The kinetics of the reaction were carefully studied and reported as early as 1907 [M. Bodenstein and S.C. Lind, Z. Physik. Chem., 57, 168 (1907)] and the chain reaction interpretation of the reported kinetics, as shown in the tabulation of Table 1.3, was given over a decade later [J.A. Christiansen, Kgl. Danske Videnskab. Selskab., 1, 14 (1919) K.F. Herzfeld, Ann. Physik. Chem., 59, 635 (1919) M. Polanyi, Z. Elektrochem., 26, 50 (1920)]. A through discussion of this is given in the text by Frost and Pearson. 

The kinetic treatment of sequences has been systematized by Christiansen, from whose review in Adnan. Catalysis, 5, 311 (1953), much of this section is borrowed. 

Human H, Hagen CM, de Jong G, Harris T, Lombard D, Christiansen M, Bardien S. Investigation of mitochondrial sequence variants associated with aminoglycoside-induced ototoxicity in South African TB patients on aminoglycosides. Biochem Biophys Res Commun 2010 393(4) 751-6. 

As the above example shows, catalysis implies consecutive reactions. One of the historically most useful ideas in the treatment of such processes has been the steady state assumption—i.e., that the intermediates in such a reaction sequence might rapidly reach a given stationary concentration, which then, in the steady state, remains invariant. This concept was first used by Bodenstein and by Michaelis and Menten, and was generalized by Christiansen and Kramers " to reactions involving possible chain mechanisms in the gas phase. It is of some importance, since it illustrates early concepts in the collision theory of reactions. 

In Fig. 6.13a h- c, the number of components at the exit from each section is smaller by one than at the entrance. It was shown in the work (Christiansen, Scogestad, Lien, 1997b), that the complete separation of four-component mixtures into pure components in such sequences requires energy expenditures bigger only by 10% 15% than the separation of two-component mixture. 

The result defied interpretation for a number of years. Independently Christiansen, Herzfeld, and Polanyi< > considered the following reaction sequence ... 

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