Multiroute mechanism

Among two-route mechanisms, those illustrated in Fig. 5(c) (those having one common intermediate) and in Fig. 5(e) (mechanisms having a common step) are widespread. The graph in Fig. 5(d) accounts for the mechanism in which two cycles are connected by a bridge "arch . It can easily be seen that the steady-state rate corresponding to the "arch will be zero, i.e. this step is in equilibrium. These typical schemes are present as fragments for multiroute mechanisms. 

Studies on the mechanisms of catalytic and non catalytic reac tions undertaken over the past 15-20 years have led to significant progress in the theory of reaction mechanisms. Most of the reactions involving homogeneous, metal-complex, and enzymatic catalyses were shown to be no less complex in terms of their mechanism compared with the mechanisms of radical chain processes. Infact, they appear to be much more complicated. Numerous examples of complicated mechanisms can be found in the literature. At present, multiroute mechanisms (with 2 to 4 reaction routes), involving as many as 8 intermediates and up to 12 elementary steps, are widely known to exist even in heterogeneous catalysis by metals and nonmetals where the simplest two-step schemes have hitherto been very popular. The existence of many routes and elementary steps is the most important general feature of the mechanisms of catalytic and also many noncatalytic reactions. 

Contemporary chemical kinetics and the theory of reaction mechanisms are characterized not only by increased complexity of the mechanisms (hypotheses of mechanisms) but also by the considerable number of hypotheses (the possible mechanisms describing each reaction). Cases are known where the mechanism of formation of a certain product in a complicated multiroute mechanism incorporates completely different sequences of elementary steps and intermediates" even in the case of reactions that have one linearly independent stoichiometric equation The greater mechanistic complexity and high number of hypotheses raise the issue of the formalization and automation of the procedure adopted for the generation of hypotheses. 

The topological approach proved to be of g reat importance in generating hypothetical multiroute mechanisms by combining one-route mechanisms. ... 

Derivation of Steady-State Kinetic Equations for Multiroute Mechanisms Kinetic Coupling... 

Equation (3.146) reflects two nontrivial kinetic features of cycle coupling that are characteristic for multiroute mechanisms ... 

In cycles of type (ii), a step of one cycle is also part of other cycles and the reaction rate of this step is a linear combination of multiple reaction route rates. As a result, this reaction rate cannot be represented by the difference between a forward and reverse reaction rate. Other cycles influence the reaction rate of the selected step not only quantitatively but qualitatively as well. Indeed, other cycles can change the direction of the overall reaction corresponding to the selected cycle. This is the main difference between multiroute mechanisms of types (i) and (ii). Many examples of deriving such equations using graph theory can be found in the books by Yablonskii et al. (1991) and Marin and Yablonsky (2011). 

Often in heterogeneous catalysis, the reaction mechanism is rather complex and cannot be represented by a one-route multistep reaction sequence, as there are several routes leading to a variety of products. An example of the rate derivation for a multiroute mechanism of butadiene hydrogenation was presented in Chapter 4. Often for the derivation of kinetic equations in such a case, it is assumed that the adsorption/desorption steps are in quasi-equdibria. The rate of formation of a certain component in the reaction mixture is then defined as... 

We now Ulustrate what has been said so far with an example of a complex multiroute reaction (the isomerization of butenes over C0-M0/AI2O3 (22)) with a linear mechanism ... 

The application of graph theory methods for deriving kinetic equations of heterogeneous catalytic reactions is based upon the so-called Rule of Mason this is also known in American literature as the Shannon-Mason Rule of Cycles. Although established by Shannon in 1941 (23), the rule acquired great popularity after its rediscovery by Mason in 1955 (24.25). A strict proof for the validity of the Rule of Mason for multiroute linear mechanisms was presented only recently by Evstigneev and Yablonskii (26), where both an inductive proof and a proof based on the Rule of Krammer are set forth. 

In formulating hypotheses for the mechanism of a given complex reaction, and in using different procedures for the selection of one out of many hypotheses (discrimination of hypotheses), the question arises as to the hierarchy of the hypotheses. The intuitive principle of simplicity cannot play the role of a tool for the selection of hypotheses in the case of multiroute reactions because the number of vertices and cycles and the ways of linking cycles in the kinetic graph are already variables. Proceeding from linear mechanisms, we examine here possible approaches to the construction of a quantitative scale for mechanistic complexity or to the selection of a complexity index". 

We have proposed the complexity index, K, based on the fractional rational form of the rate laws for reaction routes. This index is deHned as the total number of weights (rate constants) for the elementary steps included in the numerator and denominator of the kinetic laws for all routes of a multiroute reaction. In calculating K it is convenient to use the Vorkenstein-Gordstein algorithm which is applicable to the derivation of the rate laws for the routes of all catdytic and noncatal3d ic reactions having linear mechanisms. 

In accordance with the theory developed by Yablonskii et al. (1991) for the analysis of multiroute linear mechanisms, the steady-state rate of step s is written as follows ... 

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