Autocatalysis, nonlinear chemical

As for theoretical research on the chiral symmetry breaking, Frank was the first to show that a linear autocatalysis with an antagonistic nonlinear chemical reaction can lead to homochirality [16]. His formulation with rate equations corresponds to the mean-field analysis of the phase transition in a nonequilibrium situation [17], and other variants have been proposed [6, 18-23]. All these analyses have been carried out only for open systems where... 

Note the use of activities, as well as of an equilibrium constant based on activities. The kinetic constants for autocatalyzed and catalyzed reactions, k and k, were determined from initial reaction rates with liquid activity coefficients calculated by UNIQUAC. Near chemical equilibrium the fCT is about 6, while Kx is about 5. Table 8.7 gives activation energies and pre-exponential factors obtained by nonlinear regression. The simulation shows tbat the autocatalysis effect is neghgible below 150 °C, but it might increase to 20% at 180 °C. 

The oscillatory chemical reactions can only be realized in some nonlinear system having feedback in the form of autocatalysis or autoinhibition [7,23-29]. 

Generally, the nonlinearity is further relates with autocatalysis, self-inhibition, or a delayed feedback loop etc., which cooperatively acted to play role in chemical oscillations [1, 3]. 

The kinetics of oscillatory chemical reaction must have nonlinearity and their rate equations be supposed to quadrant function of concentration of reactants. The kinetically control reaction steps have two values, (+ve) is associated with autocatalysis and (—ve) value is associated with auto-inhibition feedback loops [1]. 

The known mechanisms that produce oscillatory behavior have two characteristics in common. The first is autocatalysis. The product of a step must catalyze that step, as in steps 1 and 2 of the Lotka-Volterra mechanism. The second is that nonlinear differential equations occur. That is, the variables must occur with powers greater than unity or as products. A mechanism has been proposed for the BZ reaction that has 18 steps and involves 21 different chemical species. A computer simulation of the 18 simultaneous rate differential equations for the mechanism has been carried out and does produce oscillatory behavior. It also exhibits the interesting behavior that all curves in phase space corresponding to different initial states eventually approach... 

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