Charged current reactions

Fig. 17.16. Quark and antiquark distributions determined from low energy charged current reactions. (Prom Cabibbo, 1976.)...

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

Normal-pulse voltammetry consists of a series of pulses of increasing amplitude applied to successive drops at a preselected time near the end of each drop lifetime (4). Such a normal-pulse train is shown in Figure 3-4. Between the pidses, the electrode is kept at a constant (base) potential at which no reaction of the analyte occurs. The amplitude of the pulse increases linearly with each drop. The current is measured about 40 ms after the pulse is applied, at which time the contribution of the charging current is nearly zero. In addition, because of the short pulse duration, the diffusion layer is thinner than that in DC polarography (i.e., there is larger flux of... 

The detection of the AC component allows one to separate the contributions of the faradaic and charging currents. The former is phase shifted 45° relative to the applied sinusoidal potential, while the background component is 90° out of phase. The charging current is thus rejected using a phase-sensitive lock-in amplifier (able to separate the in-phase and out-of-phase current components). As a result, reversible electrode reactions yield a detection limit around 5 x 10 7m. 

The experimental setup is depicted schematically in Figure 1.2. Upon varying the potential of the catalyst/working electrode the cell current, I, is also varied. The latter is related to the electrocatalytic (net-charge transfer) reaction rate re via re=I/nF, as well known from Faraday s law. The electrocatalytic reactions taking place at the catalyst/solid electrolyte/gas three-phase-boundaries (tpb), are ... 

In the latter case one would like to know the length Apb of the metal-solid electrolyte-gas three-phase-boundaries (tpb) (in m or in metal mols, for which we use the symbol Ntpb throughout this book) and the value of the exchange current I0, where (W2F) expresses the value of the (equal and opposite under open-circuit conditions) forward and reverse rates of the charge-transfer reaction 4.1. 

The activation overpotential Tiac,w is due to slow charge transfer reactions at the electrode-electrolyte interface and is related to current via the Butler-Volmer equation (4.7). A slow chemical reaction (e.g. adsorption, desorption, spillover) preceding or following the charge-transfer step can also contribute to the development of activation overpotential. 

Due to the small amplitude of the superimposed voltage or current, the current-voltage relationship is linear and thus even charge-transfer reactions, which normally give rise to an exponential current-potential dependence (Chapter 4), appear as resistances, usually coupled with a capacitance. Thus any real ohmic resistance associated with the electrode will appear as a single point, while a charge transfer reaction (e.g. taking place at the tpb) will appear ideally as a semicircle, i.e. a combination of a resistor and capacitor connected in parallel (Fig. 5.29). 

When a positive current I is applied between the catalyst-electrode and the Pt counter-electrode, then the catalyst potential Urhe changes to more positive values (Fig. 10.1) and the following electrochemical (net charge-transfer) reactions take place at the Pt catalyst-electrode surface ... 

It is particularly difficult to study charge transfer reactions by the usual internal ionization method since the secondary ions produced will always coincide with ions produced in primary ionization processes. Indeed these primary ions frequently constitute the major fraction of the total ion current, and the small intensity changes originating from charge transfer reactions are difficult to detect. For example, Field and Franklin (5) were unable to detect any charge transfer between Xe + and CH4 by the internal ionization method although such reactions have been observed using other techniques (3, 9,22). 

From a kinetic point of view a describes the influence of a change of the electrode potential on the energy of activation for the charge transfer reaction which in turn influences the partial current density. The transfer coefficients % for the anodic charge transfer reaction and for the cathodic reaction add up according to... 

The educt/reacting species for the charge transfer reaction to which y o is referring to is stated only if it is not already given by the composition of the electrolyte solntion. If the concentration of the educt is given in addition the exchange current densityy o wiU be stated. 

In all cases the electrode reaction secures continuity of current flow across the interface, a relay type of transfer of charges (current) from the carriers in one phase to the carriers in the other phase. In the reaction, the interface as a rule is crossed by species of one type electrons [e.g., in reaction (1.22)] or ions [e.g., in reaction (1.21)]. 

The net current crossing the electrode at any time is the algebraic sum of the faradaic and various nonfaradaic currents. During the transition time, part of the net current is consumed for surface-layer charging and is not available for the primary electrode reaction. This part of the current is called the charging current It is highest at the start of the transition period, but toward the end of this period it falls to zero. The transition time of charging, depends on the value of current and on the system, and may vary within wide limits (between 0.1 ms and 1 s). 

FIGURE 12.9 Anodic (1,2) and cathodic (l, 2 ) potentiodynamic i vs. E curves for a reversible (1,1 ) and an irreversible (2,2 ) reaction (horizontal lines above and below the axis of E refer to the charging current in the absence of reactants). 

A particular constant current density is applied to the electrode, and the potential variation is followed as a function of time. When there is no electrode reaction, the entire current is a nonfaradaic charging current According to Eq. (12.13), the slope of the E vs. t curve (Fig. 12.10, curve 1) is determined by the EDL capacitance. 

FIGURE 12.10 Galvanostatic curves (1) without a reaction (2) with a reaction (3) corrected for the charging current. 

The relation between E and t is S-shaped (curve 2 in Fig. 12.10). In the initial part we see the nonfaradaic charging current. The faradaic process starts when certain values of potential are attained, and a typical potential arrest arises in the curve. When zero reactant concentration is approached, the potential again moves strongly in the negative direction (toward potentials where a new electrode reaction will start, e.g., cathodic hydrogen evolution). It thus becomes possible to determine the transition time fiinj precisely. Knowing this time, we can use Eq. (11.9) to find the reactant s bulk concentration or, when the concentration is known, its diffusion coefficient. 

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