Limiting-current measurement overpotential

The conceptual development of limiting-current measurement was advanced substantially by Agar and Bowden (A2), who investigated the current-overpotential relationship for oxygen evolution at nickel electrodes in fused sodium hydroxide. Here water transport is the limiting step ... 

The total overpotential in limiting-current measurements is therefore represented as the sum of these three components ... 

The ohmic contribution to the overpotential can be minimized by suitable placement of the reference electrode, but the surface overpotential cannot be reduced similarly. In making limiting-current measurements, the surface overpotential, or rather its rate of increase with current density, should be low enough to permit observation of a long, clearly defined limiting-current plateau. 

In limiting-current measurements, the counterelectrode is sometimes used as a reference electrode. In that case, the surface overpotential of the counterelectrode contributes to the recorded overpotential that is, the potential of the reference electrode is now current dependent. Unless precautions are taken (e.g., the area of the counterelectrode is much larger than that of the working electrode), a properly defined limiting-current plateau may not be obtained. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

For most of the reactions frequently employed in limiting-current studies, the surface overpotential is not negligible. A criterion for assessing its magnitude is the exchange-current density i0, which is a measure of the reaction rate at the equilibrium potential of the electrode (i.e., when anodic and cathodic rates are equal). 

The second bracket contains the aspect ratio. The group in the first bracket is a measure of the approach to the limiting current modified by a total overpotential. The authors describe this group as a ratio of mass-transfer resistance to kinetic resistance. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Typical potentiostatic transients are shown in Fig. 14K. Such data can be employed in two ways to evaluate the activation-controlled rate as a function of overpotential. We have already seen that the measured current density is related to the diffusion-limited current density by the equation... 

We have already seen by way of Equation (26.77) that the electrode surface concentration of a reacting species is related to its bulk solution concentration, the applied current density, and the diffusion limiting current density. Substimtion of Equation (26.77) (which is applicable to an electro-active species that is consumed at the electrode) into Equation (26.95) gives a more useful form of the concentration overpotential, since it does not contain the surface concentration, which is often difQcult to measure ... 

The rate of reaction was too slow to produce measurable current (ij ) for arsenic and selenium species within the stability range of water at platinum. For those two elements an upper limit was estimated for the value of the rate constant by solving the current overpotential equation (Equation 3) for k with the assumption of a = 0.5 and ij = 4x10" amps cm . This value of ij was chosen empirically from examination of the data it represents the lowest current that could clearly be distinguished from background currents with the instruments used. The true value of k must therefore be equal to or less than the value that is calculated from the minimum limiting current. 

When a voltammetric sensor operates with a small overpotential, the faradaic reaction rate is also small consequently, a high-precision instrument for the measurement is needed. An amperometric sensor is usually operated under limiting current or relatively small overpotential conditions. Amperometric sensors operate under an imposed fixed electrode potential. Under this condition, the cell current can be correlated with the bulk concentration of the detecting species (the solute). This operating mode is commonly classified as amperometric in most sensor work, but it is also referred to as the chronosupero-metric method, since time is involved. 

In certain biosensors an irreversible heterogeneous reaction is transformed into a homogeneous redox reaction via a very reversible redox system. The latter can be transformed back at the working electrode by a much lower overpotential, thereby reducing the chance of co-oxidation or co-reduction of interfering compounds. Since the limiting current is strictly proportional to the analyte concentration and also to the concentrations of interfering compounds, chemometric data treatment and/or differential measurements may be used to correct for errors. 

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