Page - 16 - in Advanced Chemical Kinetics

speciesnear theequilibriumpointmeasured insecondreactionroutemechanism,whoseNkc= 3.Note that it’s invariant regionandequilibriumpoint exactly lie over the invariant regionof the first route, i.e.,Figures8,9. Now, the overall reaction mechanism involves no intermediate, and the variations of the concentrationof involvedchemical speciesaregiven inFigure10. 7.Summary In this chapter, both the physicochemical conceptual assumptions (used for species behavior and activated complex) and a set of mathematical tools (for their dynamical behavior and simplification) are presented. Mathematically, simplification can be done by “model reduc- tion,” that is, the rigorouswayofapproximatingandrepresentingacomplexmodel insimpli- fied form. Here,wehaveconsideredacomplexproblemhavingacommonstep:conferredtheiravailable routes then allied graphically. Although we have not applied any numerical or analytical technique tomeasure the SIMbut one can easily examine (byapplying such techniques) that their solution trajectorieswill also lie in the same invariant regions that canalsobe correlated witheachotherandevenwith thewhole reactionmechanism. Thus, the idea initiatedherecaneasilybecorrelatedwith themethodusedfor theconstruction of slowmanifold in a complex chemical reaction based on the decomposition techniques of entropymaximum alongwith certain constraints (lies on themanifold or given by slowest eigenvectors) at the equilibriumpoint. Thiswill allowus tobring togetherdifferent available mathematical ideas andmethods, commonly used to transform the complex chemical prob- lems fromonewayto theother, toenhanceprogress inunderstanding. Figure10. Variationof chemical species concentrationofoverall reactionmechanismwithrespect to time,whileNkc=1. Advanced Chemical Kinetics16