Fast electrode processes

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

The mass transport rate coefficient, kd, for a RDE at the maximum practical rotation speed of 10000 per min"1 is approximately 2 x 10-2 cms-1 [28], which sets a limit of about 10 3 cms 1 for the electrode reaction kinetics. For the study of very fast electrode processes, such as some outer sphere redox reactions on noble metal electrodes under stationary conditions, higher mass transport rates in the solution adjacent to the electrode must be employed. 

The most important feature of fast electrode processes is that they usually involve the discharge of an adsorbed layer of the electroactive ions. These adsorption processes are complicated by the fact that in molten salts the electroactive ions are usually complex ions. In this case it is possible to presume [126] that the rates of charge transfer for different electrode processes are determined by... 

Refs. [i] Delahay P (1961) Fast electrode processes by relaxation methods. In Delahay P (ed) Advances in electrochemistry and electrochemical engineering, vol. 1. Interscience, New York, Chap. 5 [ii] Reinmuth WH (1964) Anal Chem 36 211R [Hi] Bond AM (1980) Modernpolarographic methods in analytical chemistry. Marcel Dekker, New York, pp 296,298, 361 [iv] Agarwal HP (1974) Faradaic rectification method and its applications in the study of electrode processes. In Bard A (ed) Electroanalyt-ical chemistry, vol. 7. Marcel Dekker, New York, pp 161... 

P. Delahay, The study of fast electrode processes by relaxation methods, in Advances in Electrochemistry and Electrochemical Engineering. Vol. 1, P. Delahay, editor, Wiley-Interscience, New York, 1961, pp. 233-318. 

The above results make it apparent that in order to measure faradaic current, a recording instrument capable of detecting fast electrodic process will improve the separation of faradaic from capacitive current. 

Kinetics may be neglected this is observed for very fast electrode processes, i.e., very small R t-... 

Bernstein C, Heindrichs A, fielstich W (1978) Investigations of fast electrode processes by means of a micro-ring electrode in turbulent pipe flow. J Electroantil Chem 87 81-90... 

After having described one equilibrium method for the measurement of kinetics of rather fast electrode processes and two steady state methods for measurement of slow electrode processes, let us turn now to consider the so called transient or, sometimes, relaxation techniques, where time is a very important factor in the equations. 

Another transient method which may be used to study fast electrode processes is the coulostatic method. Here a known amount of electricity is injected into the electrode in a very short time. The electrode, Initially at... 

From Fig. 103(a) and (c), we see that the power of the cell is high if the current potential curves of the separate electrodes are steep. A steep current potential curve implies a small overpotential, i.e. a fast electrode process. If the electrode process is not naturally fast, its rate can be increased by one of two ways a catalyst may be added to the electrode, or the temperature of operation may be raised. The catalyst used is chosen according to the reaction to be catalysed, i.e. a different one will be used for the decomposition of... 

The layer width is taken from the relation d > 1,5 dg, where dg - thickness of a gas discharge gap. The employment of a resistive layer instead of electrode profiling can significantly simplify the device manufacture. The UV radiation is efficiently converted into a visible one by a number of photo-luminophors, e.g. Zn2Si04 Mn. For stroboscopic registration of fast-proceeding processes the luminophors with short period of luminescence are used, e.g anthracene etc. 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Case (a) If the chemical reaction preceding the electrode reaction, C(a), and the electrode reaction itself, E(a), are sufficiently fast compared to the transport processes, then both of these reactions can be considered as equilibrium processes and the overall electrode process is reversible (see page 290). If reaction C(a) is sufficiently fast and E(a) is slow, then C(a) affects the electrode reaction as an equilibrium process. If C(a) is slow, then it becomes the rate-controlling step (a detailed discussion is given in Section 5.6.3). 

A chemical reaction subsequent to a fast (reversible) electrode reaction (Eq. 5.6.1, case b) can consume the product of the electrode reaction, whose concentration in solution thus decreases. This decreases the overpotential of the overall electrode process. This mechanism was proposed by R. Brdicka and D. H. M. Kern for the oxidation of ascorbic acid, converted by a fast electrode reaction at the mercury electrode to form dehydro-ascorbic acid. An equilibrium described by the Nernst equation is established at the electrode between the initial substance and this intermediate product. Dehydroascorbic acid is then deactivated by a fast chemical reaction with water to form diketogulonic acid, which is electroinactive. 

Sonovoltametric measurement of the rates of electrode processes with fast coupled homogeneous kinetics making macroelectrodes behave like microelectrodes Compton RG, Marken F, Rebbitt TO (1996) Chem Commun 1017-1018... 

There are many possible reaction pathways between acrylonitrile and adiponitrile and, in each, there are several possible rate-determining steps. None of the reaction intermediates has yet been detected electrochemically or spectroscopically thus indicating very fast chemical processes with intermediates of half-lives of < 10-5 s. Bard and Feiming Zhou [104a] have recently detected the CH2 = CHCNT radical by Scanning Electrochemical Microscopy (SCEM) using a 2.5 fim radius Au electrode (1.5 mol CH2 = CHCN in MeCN/TBAPF6). The dimerization rate has been determined to 6.107 M-1 S l. 

Fig. 1.6 Two different immersion cell designs optimized for special applications, (a) Set-up for fast removal and rinsing of a strip-shaped electrode by fast rotation of the shaft (solid arrow). This set-up is useful for measurements of transient electrode processes like...

In addition, one must choose the most appropriate geometrical form for such an electrode. The most common forms for fast voltammetric techniques are the planar geometry and the spherical (or hemispherical) geometry. In this regard, we have seen (Chapter 1, Section 4.2.2) that the simplest theoretical relationships describing the kinetics of electrode processes are valid under conditions of linear diffusion (even if we have briefly discussed also radial diffusion). 

UMEs decrease the effects of non-Earadaic currents and of the iR drop. At usual timescales, diffusional transport becomes stationary after short settling times, and the enhanced mass transport leads to a decrease of reaction effects. On the other hand, in voltammetry very high scan rates (i up to 10 Vs ) become accessible, which is important for the study of very fast chemical steps. For organic reactions, minimization of the iR drop is of practical value and highly nonpolar solvents (e.g. benzene or hexane [8]) have been used with low or vanishing concentrations of supporting electrolyte. In scanning electrochemical microscopy (SECM [70]), the small size of UMEs is exploited to locahze electrode processes in the gm scale. 

CH3CN V = 0.2 V s ) indicated that the electrode process was not a Nernstian two-electron transfer but involved two successive one-electron steps, with the second thermodynamically more favorable than the first one [32]. Therefore, the reversible, overall two-electron process in Sch. 11 is better represented by two successive, reversible, one-electron steps involving a thermodynamically unstable and undetected cation intermediate (see Sch. 13 EE process, or ECE process, where the chemical step C is a fast, reversible deformation of the M2S2 core). In agreement with this, it should be noted that the oxidation of ds-[Mo2(cp )2(/x-SMe)2(CO)4] ds-13 also... 

The mechanism of the reduction of cadmium ions at DME in NaCl04 solutions with varied water activity was also studied [26]. In these solutions, the electrode process of the Cd(II)/Cd(Hg) system was described by the mechanism that includes (1) fast loss of 12.5 water molecules in a preceding equihbrium, (2) a slow chemical step, which is not a desolvation, (3) slow transfer of the first electron. 

For complex mechanisms such as ECE or other schemes involving at least two electron transfer steps with interposed chemical reactions, double electrodes offer a unique probe for the determination of kinetic parameters. Convection from upstream to downstream electrodes allows the study of fast homogeneous processes. The general reaction scheme for an ECE mechanism can be written... 

Thin film electrodes have made feasible thermal jump kinetic measurements of extremely fast electrode reactions [26], by illuminating a thin electrode film by a very rapid laser pulse and monitoring the relaxation process on a nanosecond time scale. Thin films of silver have also been deposited on electrode materials such as carbon to enable surface-enhanced Raman spectroscopic investigation of surface-bound species [27]. 

Because the potential is more positive than E i, the formation of only one wave is observed. In acidic and alkaline media where the rate of the acid-base catalysed reaction (35 b) is fast and during the reaction all the phenylhydroxylamine derivative is transformed to quinoneimine, the height of the single wave corresponds to a transfer of six electrons [(35 a) plus (35 c)]. Because the life-time of the quinoneimine intermediate is short, its hydrolysis to form quinone does not affect the electrode process. In the medium pH range where the rate of dehydration is slow, the wave-height corresponds to a four-electron process. A theoretical... 

When dehydration occurs as a consecutive reaction, its effect on polarographic curves can be observed only, if the electrode process is reversible. In such cases, the consecutive reaction affects neither the wave-height nor the wave-shape, but causes a shift in the half-wave potentials. Such systems, apart from the oxidation of -aminophenol mentioned above, probably play a role in the oxidation of enediols, e.g. of ascorbic acid. It is assumed that the oxidation of ascorbic acid gives in a reversible step an unstable electroactive product, which is then transformed to electroinactive dehydroascorbic acid in a fast chemical reaction. Theoretical treatment predicted a dependence of the half-wave potential on drop-time, and this was confirmed, but the rate constant of the deactivation reaction cannot be determined from the shift of the half-wave potential, because the value of the true standard potential (at t — 0) is not accessible to measurement. 

The measurement of polarographic half-wave potentials is usually a simple, fast procedure, often considerably faster and less tedious than determination of rate or equilibrium constants. Elucidation of the mechanism of an electrode process (or better that part of it which must be understood for quantitative treatment of the potentials) and the choice of the most suitable conditions for measurement of comparable values of half-wave potentials is usually simpler and less time-consuming than the elucidation of the mechanism of a chemical reaction. This is largely due to the fact that in electrode processes the reactant (electron or electrode) is always the same. 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

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