Electrochemical frequency factor

Experiments aimed at probing solvent dynamical effects in electrochemical kinetics, as in homogeneous electron transfer, are only of very recent origin, fueled in part by a renaissance of theoretical activity in condensed-phase reaction dynamics [47] (Sect. 3.3.1). It has been noted that solvent-dependent rate constants can sometimes be correlated with the medium viscosity, t] [101]. While such behavior may also signal the onset of diffusion-rather than electron-transfer control, if the latter circumstances prevail this finding suggests that the frequency factor is controlled by solvent dynamics since td and hence rL [eqn. (23), Sect. 3.3.1] is often roughly proportional to... 

However, this model is employed only rarely to estimate the frequency factor for outer-sphere reactions . Instead, a collisional model is chiefly used . This can be expressed for electrochemical reactions as ... 

Fundamental frequency of the resonator Correlation function for surface roughness Root mean square height of a roughness Wave vector of shear waves in quartz, (Uy pq//rq Correlation length of surface roughness Thickness of the liquid film Thickness of interfacial layer Molecular dynamics Pressure in a liquid Quartz crystal microbalance Hydrodynamic roughness factor Electrochemical roughness factor Coordinates (normal and lateral)... 

As a consequence, the electron surface concentration is drastically reduced for larger band bendings. The electrochemical current from the semiconductor to the solution is usually described by a tunneling process from the semiconductor surface to the oxidized species of the redox couple. This current is hence dependent on the tunneling probability for outer sphere charge transfer to fully solvated ions that form the outer Helmholtz layer, on the surface concentration of electrons and on vibrational frequency factors that are related to nuclear coordinates. In the Marcus-Gerischer approximation, the current is written as... 

Curtiss et al. [44] have carried out measurements for reaction rates of the electrochemical oxidation of Fe(OH2)6 to Fe(OH2)g at a gold electrode in a 0.5 M HCIO4 aqueous solution. The experimental design of a pressurised flow-system allowed electrochemical studies over a vast range of temperatures, from 25 to 250 °C. A good Arrhenius behaviour was found with = 56.8 1.5 kJ mol", a frequency factor of Z = 6 X 10 cm sec and a Tafel coefficient t] = 0.425 0.01, independent of the temperature. The measured standard rate constant at 25 °C is = 6 x 10 cm sec T... 

Filters have a time constant r = R x C which increases the damping of the measuring instrument. The time constant depends on the required attenuation and the interfering frequency, but not on the internal resistance of the measuring instrument. The time constants of the shielding filter are in the same range as those of the electrochemical polarization, so that errors in the off potential are increased. Since the time constants of attenuation filters connected in tandem are added, but the attenuation factors are multiplied, it is better to have several small filters connected in series rather than one large filter. 

Fretting in air-saturated aqueous electrolytes, such as seawater or body fluids , produces enhanced removal of material by stimulation of electrochemical reactions, increasing the reaction rates by factors of 10 to 200 compared with air, depending on the frequency. The importance of the chemical... 

When all these factors contribute, the situation becomes almost hopelessly complicated. The simplest realistic case is that in which the photocarriers are generated in the space-charge region and migrate to the surface, where they are immediately consumed by an electrochemical reaction. We consider this case in greater detail. Suppose that light of frequency i/, with hu > Eg, is incident on a semiconducting electrode with unit surface area under depletion conditions (see Fig. 8.8). Let Iq be the incident photon flux, and a the absorption coefficient of the semiconductor at frequency v. At a distance x from the surface, the photon flux has decreased to Iq exp(—ax), of which a fraction a is... 

The time-dependent formation of cyclohexanone according to Fig. 9 is shown in Fig. 10. We obtained a turnover frequency of 28 turnovers per h. This is larger by a factor of 14 than that reported for the indirect electrochemical oxidation using only the free ligand as mediator [41]. 

Several parameters in Equation 29.19 can be adjusted to optimize the sensitivity of the spectrometer. For example, the incident power can be increased provided that the absorption is not saturated, and the extent of RC filtering can be increased (i.e., the Af decreased). For small samples it is sometimes feasible to use a higher frequency (higher field) spectrometer and thus increase the population difference between the two energy levels (cf. Eq. 29.11). But it can be shown that if the same geometry is maintained, the minimum detectable concentration is theoretically proportional to Vq1/2, so for electrochemical experiments the sensitivity actually decreases at higher frequencies, all other factors being equal. 

The nature of the frequency dependence of Mott-Schottky plots for semiconductor electrodes has been discussed in the electrochemical literature for more than three decades (see e.g. reviews [6, 84]). It has been speculated that it can be caused by the following factors (1) frequency dependence of dielectric relaxation of the space charge region [85], (2) roughness of the electrode surface [84], (3) slow ionization of deep donors (acceptors) in the space charge region in the semiconductor [86], and (4) effect of surface states. 

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