Kinetics dimensionless

Here ia is the exchange current density of the electrode reaction based on the bulk concentration aa and ac are the anodic and cathodic charge transfer coefficients, respectively and y is a dimensionless kinetic parameter. 

The simplest scenario to simulate is a homopolymerization during which the monomer concentration is held constant. We assume a constant reaction volume in order to simplify the system of equations. Conversion of monomer to polymer, Xp defined as the mass ratio of polymer to free monomer, is used as an independent variable. Use of this variable simplifies the model by combining several variables, such as catalyst load, turnover frequency, and degradation rate, into a single value. Also, by using conversion instead of time as an independent variable, the model only requires three dimensionless kinetics parameters. 

BATCHD - Dimensionless Kinetics in a Batch Reactor System... 

Dynamics of an Equalisation Basin 560 Dimensionless Kinetics in a Batch Reactor 235 Batch Reactor with Complex Reaction Sequence 240 Single Solute Batch Extraction 442 Mixing and Segregation 394... 

We start with the case where the initial electron transfer reaction is fast enough not to interfere kinetically in the electrochemical response.1 Under these conditions, the follow-up reaction is the only possible rate-limiting factor other than diffusion. The electrochemical response is a function of two parameters, the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic parameter, 2, that measures the competition between chemical reaction and diffusion. In cyclic voltammetry,... 

FIGURE 2.1. EC reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and follow-up reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X. The boundaries between the zones are based on an uncertainty of 3 mV at 25°C on the peak potential. The dimensionless equations of the cyclic voltammetric responses in each zone are given in Table 6.4. 

FIGURE 2.7. Double potential step chronoamperometry for an EC mechanism with an irreversible follow-up reaction, a Potential program with a cyclic voltammogram showing the location of the starting and inversion potentials to avoid interference of the charge transfer kinetics, b Example of chronoamperometric response, c Variation of the normalized anodic-to-cathodic current ratio, R, with the dimensionless kinetic parameter X. 

Eor the case of spherical pendulum, it is relevant to ask how the frequency of vertical oscillations changes as the initial horizontal velocity V increases from zero, in terms of the dimensionless kinetic energy K defined by... 

Figure 6 shows the approximate frequency of the spherical pendulum relative to the ideal value for the simple pendulum, plotted as a function of the dimensionless kinetic energy. 

If the reaction (1.1) is controlled by the electrode kinetics, i.e., when the electrode reaction is not electrochemically reversible, the response depends on the dimensionless kinetic parameter k = and the transfer coefficient a [15-17],... 

Fig. 2.13 The dependence of peak potentials on the logarithm of dimensionless kinetic parameter, a = 0.1, sw = 50 mV and A = —2 mV. The crosses denote the potentials of maxima of the peak II...

The overall effect of the preceding chemical reaction on the voltammetric response of a reversible electrode reaction is determined by the thermodynamic parameter K and the dimensionless kinetic parameter . The equilibrium constant K controls mainly the amonnt of the electroactive reactant R produced prior to the voltammetric experiment. K also controls the prodnction of R during the experiment when the preceding chemical reaction is sufficiently fast to permit the chemical equilibrium to be achieved on a time scale of the potential pulses. The dimensionless kinetic parameter is a measure for the production of R in the course of the voltammetric experiment. The dimensionless chemical kinetic parameter can be also understood as a quantitative measure for the rate of reestablishing the chemical equilibrium (2.29) that is misbalanced by proceeding of the electrode reaction. From the definition of follows that the kinetic affect of the preceding chemical reaction depends on the rate of the chemical reaction and duration of the potential pulses. 

The real power of digital simulation techniques lies in their ability to predict current-potential-time relationships when the reactants or products of an electrode reaction participate in some intervening chemical reaction. These kinetic complications often result in a fairly difficult differential equation (when combined with the conditions for diffusion or convection encountered in electrochemical problems) that resists solution by ordinary means. Through simulation, however, the effect of any number of chemical steps may be predicted. In practice, it is best to limit these predictions to cases where the reactants and products participate in one or two rate-determining steps each independent step adds another dimensionless kinetics parameter that must be varied over the range of... 

Table 23.2 Relationship of the Dimensionless Kinetic Parameter T to CV Peak Potential Separations3...

Dimensionless kinetic parameters for the acetylcholinesterase catalyzed reaction ... 

In Fig. 7.36, the SWV curves of a first-order catalytic mechanism for different values of the dimensionless kinetic constant /sw (= (k + k2)z) at disc electrodes are shown. For jsw > 1.5, a time-independent current is reached whatever the shape and size of the electrode. In order to determine the transient or stationary nature of the SWV current, the forward (y/f) and reverse (i/q) components of the response must be analyzed, since the net current is bell shaped in all the cases. 

When both redox reactions are sluggish, both SWV and SWVC responses become very complex because they are influenced by both the kinetic and thermodynamic parameters of the electrode reactions and those associated with the square wave waveform (i.e., Sw> / and A s). Basically, when two peaks are observed, their peak heights are determined mainly by the magnitude of the dimensionless kinetic... 

With the substrate biased at a potential slightly more positive than E° of A/B couple, B is oxidized to form A for both DISP1 and ECE mechanisms. However, in the latter case the reduction of C also occurs at the substrate. The numerical solution of corresponding diffusion problems (see Ref. [85] for problem formulations) yielded several families of working curves shown in Fig. 12 (DISP1 pathway) and Fig. 13 (ECE pathway). In both cases, the tip and the substrate currents are functions of the dimensionless kinetic parameter, K = ka2/D. 

Kinetic parameter — Also known as a dimensionless kinetic parameter . Any dimensionless combination of... 

For the sequential case (Aris, 1989), let a(x) be the (dimensionless) kinetic constant for the second step. One obtains... 

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