Heterogeneous rate constants

The electrocatalytic activity of novel redox films in regeneration of NAD/NADH has been investigated by means of chronoamperometry, hydrodynamic and potentiodynamic methods. In order to achieve the most efficient electrocatalytic properties indicated as both the highest heterogeneous rate constant and maximum sensitivity, the further optimization of electropolymerisation conditions has been made. 

Heterogeneous rate constants, 12, 113 Hofmeister sequence, 153 Hybridization, 183, 185 Hydrodynamic boundary layer, 10 Hydrodynamic modulation, 113 Hydrodynamic voltammetry, 90 Hydrodynamic voltammogram, 88 Hydrogen evolution, 117 Hydrogen overvoltage, 110, 117 Hydrogen peroxide, 123, 176... 

Glassy carbon electrodes polished with alumina and sonicated under clean conditions show activation for the ferrl-/ ferro-cyanlde couple and the oxidation of ascorbic acid. Heterogeneous rate constants for the ferrl-/ ferro-cyanlde couple are dependent on the quality of the water used to prepare the electrolyte solutions. For the highest purity solutions, the rate constants approach those measured on platinum. The linear scan voltammetrlc peak potential for ascorbic acid shifts 390 mV when electrodes are activated. 

The cyclic voltammograms of ferrlcyanlde (1.0 mM In 1.0 M KCl) In Fig. 2 are Illustrative of the results obtained for scan rates below 100 mV/s. The peak separation is 60 mV and the peak potentials are Independent of scan rate. A plot of peak current versus the square-root of the scan rate yields a straight line with a slope consistent with a seml-lnflnlte linear diffusion controlled electrode reaction. The heterogeneous rate constant for the reduction of ferrlcyanlde was calculated from CV data (scan rate of 20 Vs using the method described by Nicholson (19) with the following parameter values D 7.63 X 10 cm s , D, = 6.32 X 10 cm s, a 0.5, and n =1. The rate constants were found to be... 

Although there are differences in the approach curves with the constant-composition model, it would be extremely difficult to distinguish between any of the K cases practically, unless K was below 10. Even for K = 10, an uncertainty in the tip position from the interface of 0. d/a would not allow the experimental behavior for this rate constant to be distinguished from the diffusion-controlled case. For a typical value of Z)Red, = 10 cm s and electrode radius, a= 12.5/rm, this corresponds to an effective first-order heterogeneous rate constant of just 0.08 cm s. Assuming K,. > 20 is necessary... 

Since the mass-transfer coefficient at a micropipette is inversely proportional to its radius, the smaller the pipette the faster heterogeneous rate constants can be measured. Micrometer-sized pipettes are too large to probe rapid CT reactions at the ITIES. Such measurements require smaller (nm-sized) pipettes. Nanopipettes are also potentially useful as SECM tips (see Section IV.D) because they can greatly improve spatial resolution of that technique. The fabrication of nanopipettes was made possible by the use of a micro-processor-controlled laser pipette puller capable of puling quartz capillaries [26]. Using this technique, Wei et al. produced nanopipettes as small as 20 nm tip radius and employed them in amperometric experiments [9]. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

In electrochemical literature the standard rate constant fe is often designated as fes h or fe9, called the specific heterogeneous rate constant or the intrinsic rate constant. According to eqns. 3.5 and 3.6, we have... 

Note that the term with E° still changes with the analyte concentration, the transfer coefficient a and the specific heterogeneous rate constant ks h (cf., eqn. 3.7). 

Secondly, Fig. 5 shows that the polymeric rate constants parallel values of heterogeneous rate constants that have been observed for the electrochemical reactions of solutions of the corresponding dissolved porphyrin monomers. (The slope of the line is 0.5). This re-emphasizes what was said above, that measurements of electron hopping in polymers can give rate constants that are meaningful in the context of the metalloporphyrin s intrinsic electron transfer chemistry. 

For a totally irreversible electrochemical process, the heterogeneous rate constant ke for electron transfer at the CV peak potential Ep is given by... 

We deemed it necessary to confirm the CV results by the alternate method using convolutive potential sweep voltammetry, which requires no assumptions as to the form of the free energy relationship and is ideally suited for an independent analysis of curvature revealed in Figure 7. In convolutive linear sweep voltammetry, the heterogeneous rate constant ke is obtained from the cur-... 

Figure 6. Variation of the heterogeneous rate constant (log kj with the applied potential for some representative organometals.

The striking correlation of the homogeneous and heterogeneous rate constants, when both processes are measured under conditions of equivalent thermodynamic driving force, is presented in Figure 8 (left) (9). Note the slope of 0.76. We now turn to the quadratic... 

It should be noted here that the ultra thin-layer cells (UTLC) which result from the close approach of an STM tip to a conducting substrate may have important electroanalytical applications in studies other than STM imaging (64). This is because extremely large current densities should be attainable in such cells, and also because of the fast transit times (e.g., 50 nsec for d - 10 nm) for reactants across the cell. Thus, such UTLC s might facilitate the determination of fast heterogeneous rate constants or the study of reactive electrochemical intermediates (64). 

Definition of symbols AEp = peak potential difference, Epa = peak potential at cathodic peak current, Epc = peak potential at anodic peak current, tpa = anodic peak current, ipc = cathodic peak current, s = scan rate, t = time after peak (the Cottrell region), n = number of electrons involved in redox reaction. Rate parameters (acn ) and heterogeneous rate constant can be found from irreversible wave. 

---