Reaction Route Graphs

A graph circle is a final sequence of the edges in which no node except the starting point occurs twice. A graph for the isomerization reaction has one circle, whereas that for vinyl chloride synthesis contains two circles. Every route of a chemical reaction corresponds to a graph s circle and vice versa. The number of independent reaction routes is equal to the number of elements in the basis of circles. It permits us to determine independent reaction routes from the graph type. 

Apart from enzyme kinetics, this new trend had also appeared in the kinetics of heterogeneous catalysis. In the 1950s, Horiuti formulated a theory of steady-state reactions [11, 12], many of the concepts of which correspond to the graph theory. Independent intermediates, a reaction route, an independent reaction route, all these concepts were introduced by Horiuti. 

The subscripts which distinguish the steps honor, respectively, Tafel, Volmer and Heyrovsky. Unlike the MCFC cathodic reaction mechanisms, however, these steps combine pairwise to yield the overall reaction. The reaction mechanism graphs for each of the three reaction mechanisms are shown in Figure 6. Notice that it is not possible to represent the entire mechanism by a single reaction mechanism graph. This is because, unlike in the MCFC case, there are now independent full reaction routes which yield the over all reaction. In both of the MCFC examples, there was only one. Still the three separate graphs do clearly convey the three HER reaction routes. 

The applications of reaction route graphs are in general among the most advance uses of graphs in the study of reaction networks... 

Figure 7. Reaction route graphs for the peroxide and superoxide-peroxide mechanisms reaction steps occur on directed edges nodes n, represent the component potentials, the difference between these potentials for adjacent nodes is the affinity of the associated reaction step and terminal nodes are open, intermediate nodes, closed.

Figure 8. Equivalent component-potential reaction route graph for the peroxide and superoxide-peroxide mechanisms.

The reaction route graphs, however, do have certain limitations. It is not in general possible, for example, to depict the physical location of the various reactions and species. It is not easy to distinguish on reaction route graphs that the peroxide ions, which must move across the electrolyte in the peroxide mechanism, exist only on the phase interfaces (gas-electrolyte and electrolyte-solid) in the superoxide-peroxide mechanism. This depiction is one of the strong points for reaction mechanism graphs. 

Construction of reaction route graphs when there are a number (perhaps many) independent reaction routes can be difficult and is... 

Reaction route graphs as developed above were defined by Fishtik, Callaghan and Datta (2004-2005) 26,31,32 similar graphs in... 

The graph represented in Pig. 1.3 has two independent reaction routes. The reaction rate for routes 0140 and 12341 is given by the equations ... 

In the case of mechanisms whose elementary steps incorporate one intermediate to the left and right of the reaction equality (called by Temkin linear mechanisms ), each edge in the cyclic graph stands for an elementary step of the reaction mechanism, i.e. for a pair of mutually reversed elementary reactions. Each vertex of the kinetic graph corresponds to a certain intermediate while the linearly independent reaction routes are represented by graph cycles. For example, the mechanism of the water vapour methane conversion over Ni incorporates two independent routes, five intermediates, and six steps it is depicted by kinetic graph 1. 

Analysis of the luetic equations of stationary processes reveals that only the mechanism of classes characterized by elementary steps common to two or more reaction routes (Cf,x " code substituent) differ in terms of their equation. Thus, for example, eqns. (4) for the rate for a route do not contain encompassing cydes when applied to dasses A and and. hence, r — 0. More sped-fically, for the 3-l-B >2,2,2 mechanism (graph 7), the catalytic reaction rate for route I is given... 

The use of graphs in electrochemical reaction networks, specifically (1) reaction species graphs, (2) reaction mechanism graphs, and (3) reaction route graphs... 

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