Normalization dimensionless

As was pointed out by Spalding [15], some aspects of the analysis of combustion waves in which kinetic energy is of importance can be simplified by using the stagnation enthalpy (CpT + v /2) as a variable. A normalized dimensionless measure of the stagnation enthalpy is... 

Fig. 17.2 Tafel plots for the (normalized, dimensionless) current, yjy, that accompanies hydrogen evolution in a solution containing 3.4 mM HCl + 1.0 M KCl, corrected for diffuse-double-layer effects, mass transport controlled kinetics and ohmic potential drop, measured at three temperatures (5, 45, 75°C all results fall on the same line of this reduced plot) at a dropping mercury electrode. The slope obtained from this plot is 0.52, independent of temperature. (Based on data from E. Kirowa-Eisner, M. Schwarz, M. Rosenblum, and E. Gileadi, J. Electroanal. Chem. 381, 29 (1995) and reproduced by the authors.)...

The variable 6a in equation 8 is the product of the fractional surface coverage and the catalyst number, ou The catalyst number is the ratio of the total number of moles of active centers and the number of moles of gas A in the inlet pulse, or the number of active centers per molecule of gas A in the inlet pulse. In a typical TAP-2 pulse response experiment, the amount of catalyst sample, such as a metal or metal oxide, is =10 g, the total number of active sites is usually between 10 " to 10, and the number of molecules in a pulse is a 10. Thus, in a typical TAP-2 pulse response experiment, the catalyst number is = 10 to 105. 6a is called the pulse-normalized dimensionless surface concentration, and is described by... 

Here s = cotr is a normalized frequency variable, and h is the normalized, dimensionless form of Zzarc- Notice that it is exactly the same as the similarly normalized Cole-Cole dielectric response function of Eq. (1) when we set y/zc= 1 - a. We can also alternatively write the ZARC impedance as the combination of the resistance Rr in parallel with the CPE impedance Zcpe (see Section 2.2.22). The CPE admittance is (Macdonald [1984])... 

For solid electrolytes one usually is concerned with intrinsically condncting systems rather than with intrinsically nonconducting (dielectric) ones. It is then appropriate and usual to consider basic systan response at the impedance rather than the complex dielectric constant level. Then if one assumes that the overall impedance of the system, Z, approaches Ro at sufficiently low frequencies and at sufficiently high ones, one can form the normalized dimensionless quantity... 

A useful tool for easier evaluation is the transformation of experimental variables and kinetic parameters into normalized dimensionless quantities that are related to suitable reference states. For example, the kinetic peak current. Ip in the linear-sweep voltammetric response can... 

Processes with reversible chemical steps The cyclic voltam-mograms characteristic for the C evE mechanisms in the diffusion- and kinetic-limited zones are shown in Figs 12A and B. In these figures the normalized (dimensionless) current functions are used, defined by the relationship... 

On the other hand, in dimensionless simulations, all parameters values are normalized. Dimensionless results are particularly valuable... 

The kinetic analysis of a complicated electrochemical process involves two crucial steps the validation of the proposed mechanism and the extraction of the kinetic parameter values from experimental data. In cyclic voltammetry, the variable factor, which determines the mass transfer rate, is the potential sweep rate v. Therefore, the kinetic analysis relies on investigation of the dependences of some characteristic features of experimental voltammograms (e.g., peak potentials and currents) on v. Because of the large number of factors affecting the overall process rate (concentrations, diffusion coefficients, rate constants, etc.), such an analysis may be overwhelming unless those factors are combined to form a few dimensionless kinetic parameters. The set of such parameters is specific for every mechanism. Also, the expression of the potential and current as normalized (dimensionless) quantities allows one to generalize the theory in the form of dimensionless working curves valid for different values of kinetic, thermodynamic, and mass transport parameters. 

---