Amplitude second order reactions

We proceed with the consideration of a linear chain of coupled first- and second-order reactions (fig. 5.7). If species Xi is pulsed, then the relaxation of the various species is shown in fig. 5.8. There are interesting approximate relations for such systems among the amplitudes of changes of relative concentrations. Consider the variation of X2 upon a pulse of Xi administered to the system the deterministic rate equations are... 

A1.6.3.2 SECOND-ORDER AMPLITUDE CLOCKING CHEMICAL REACTIONS... 

Garbutt (5) showed that the decay of surface stabilized CH radicals was complex and appeared to follow second order kinetics more closely than first order. A typical detailed decay curve for CH on PVG at 152 K (0 = 0.05 for CHjI) is shown in Fig. 5. A plot of - log Rate vs log C (where C is the concentration of CH as determined by peak-to-peak amplitude) gave a slope of about 10 (7 to 12) for the order of the reaction. 

First derivative spectra of levomepromazine (LV) and its sulphoxide were employed for investigation of LV photodegradation [11]. The degradation process of biapenem was monitored by measurement of first-derivative amplitude at 312 nm [12]. The determined rate constants for studied process were in good agreement with those obtained by HPLC method [12]. The second-order derivative spectrophotometric method was used for investigation of solvolytic reaction 2-phenoxypropionate ester of fluocinolone acetonide [45]. The run of process was observed by measurement the second-order amplitude at 274.96 nm corresponded to fluocinolone acetonide. The solvolysis rate constant was calculated using derivative method and compare with those obtained by HPLC methods [45]. 

Because neuro-stimulation occurs at a relatively fast time scale, the reactions do not have time to equilibrate. To simulate the condition of many reactions occurring concurrently, one just needs the average impedance during the entire pulse duration. Typically, good simulation can be obtained using a second-order model similar to Fig. 1. The drawback is that because the electrode behavior is dependent on the stimulation conditions, this model may lose accuracy when applied to different pulse width and amplitude settings. 

Figure 12. Reduced Nx amplitude near the second-order transition to homogeneous oscillations in the trimolecular reaction, as a function of the system size, N. The order parameter value at each experimental point is an average over 10 simulations, the error bars for N< = 100 indicating the dispersion about the mean. Same macroscopic parameters as Figure 11 (22).

In all cases of second- or higher-order coupled homogeneous reactions, it is a severe problem that products of concentrations are present in the rigorous mass transfer equations. Consequently, straightforward Laplace transformation is not feasible. However, already in 1951 Gerischer (146] pointed to the fact that linearization of such terms is permitted if one confines the treatment to apply only to small amplitude perturbations. For example, a product cAcB will be written as... 

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