Current -potential reversible couple

The potential at which the current is one-half of its limiting value is called the half-wave potential, El/1. The half-wave potential (for electrochemically reversible couples) is related to the formal potential, E°, of the electroactive species according to... 

Figure 2.91 Schematic representation of the rotating disc electrode response Tor the reduction and oxidation of a reversible couple. / = F/RT, /, is the limiting current, / is the current, E is the potential of the electrode and ° is the standard reduction potential of the couple.

Only one reactant behaves reversibly. If the titrant alone behaves reversibly, no current can flow until it is in excess (Figure 6.16(b)). This is the case if is titrated with I2 at an applied potential of 0.1 V. After the equivalence point the current is linearly related to the concentration of excess I2, that of I being constant. In cases where only the analyte forms a reversible couple, e g. I2 titrated with Na2S203, the current before the equivalence point follows a similar path to that in the Fe(II)/Ce(IV) system, but afterwards remains at zero (Figure 6.15(c)). 

Cyclic voltammetry provides a very convenient method for determining the redox potentials of couples as the peak potentials for the cathodic, E, and anodic, pa, processes of a reversible couple are related, at 25 °C, to the redox potential by pa = E /2 = E° + 0.285/n volts and E. = pa/2 = E° — 0.285/n volts. pc/2 and EpJ2 are the potentials at a point half-way up the wave at these points the current is half the maximum value, i.e. ipc for the cathodic wave or ipa for the anodic wave. Again, this technique will yield redox potentials only if the couple is reversible in the electrochemical sense, but this is now very readily established through the above relationship that pa — -Epc = A p = 57/n mV and by the requirement that ipjip3 = 1. In addition it should be established that Ep is independent of the scan rate, v, and that the process is diffusion controlled by showing ip/v h to be constant. 

Data were obtained in acetonitrile solution containing 0.1 mol dm-3 Bu"NBF4 as supporting electrolyte. Solutions were 3 x 10"3 mol dm-3 in compound and potentials were determined with reference to SCE at 21 1°C at 50 mV s"1 scan rate. The CVs of [28], [29] and [31] consisted of a main current wave (reversible for [30] and [32] and EC mechanism for [28], [29] and [31]) corresponding to the Fc+/Fc couple and minor current waves (irreversible or quasi-reversible) from the oxidation of the amino groups. p, represents the anodic current peak potential of the Fc+/Fc couple. "Anodic shifts of the anodic peak potential of the Fc+/Fc couple produced by the presence of metal cations (1 or 2 equiv added as their perchlorate salts). For [28], [29] and [31], after addition of cations, the current waves from the respective amino groups disappeared and that of the Fc+/Fc couple became reversible. Obtained in methanol, instant oxidation by silver cations. 

Half-wave potentials, E1/2, can be obtained from current-potential curves measured using a variety of voltammetric techniques. E1/2 is a good approximation of E° when the redox couple is reversible and the diffusion coefficients of O and R are equal (119), and a few of the standard potentials in Table 16.6 were obtained in this way. When the redox couple is... 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

Fig. 21. Schematic current-potential curves for various categories of mixed couples, (a) Two irreversible couples (b) two reversible couples (c) two couples whose Em value lies within the plateau region of one of them.

Linear sweep voltammetry (LSV), also known as linear sweep chronoamperometry, is a potential sweep method where the applied potential (E) is ramped in a linear fashion while measming cnrrent (i). LSV is the simplest technique that uses this waveform. The potential range that is scanned begins at an initial or start potential and ends at a final potential. It is best to start the scan at rest potential, the potential of zero current. For a reversible couple, the peak potential can be calcnlated nsing equation (6). ... 

One typical example of this behavior is the voltammogram of the ferro/ferricyanide couple (test reaction) that at carbon electrodes is less reversible than at noble metal electrodes. The kinetics of the test reaction in 1 M aqueous KCl was used as the reference to compare its electrochemical behavior on different carbon electrodes [20]. This electrochemical reaction occurs via an outer sphere mechanism and its rate depends on the electrolyte composition and can be increased by appropriate treatment of carbon electrodes, for instance, by application of a high current potential routine to electrodes of carbon fibers. Similar results have been obtained with glassy carbon surfaces that had been pretreated at 500°C under reduced pressure. An alternative activation method is based on careful electrode surface polishing [6]. 

A detailed discussion of the foregoing electrokinetic model as well as simplified versions of Eqs. (5.8) and (5.9) pertaining to the case of mass transfer controlled as well as irreversible electrode reactions are given in a recent paper by McLendon et al.I94) Suffice it here to evoke some general features concerning the tuning of the potential of the microparticle by the two redox couples. In the case where both redox couples are reversible on the microelectrode in question (k - < , k °°) the particle potential will lie approximately in the middle between the Nernst potentials E and E . If E and E are sufficiently separated, the reaction current will be high and approach the diffusion controlled limit. If, on the other hand, one couple is reversible while the other is not, the particle potential will remain near to the Nernst potential of the reversible couple. 

The strength of the technique in this application is demonstrated by Fig. 51, which depicts the current-potential behaviour (calculated from the experimental data in Fig. 50) with reference to that of a reversible process. It is clear that the kinetic parameters of the ferrocyanide/ferricyanide couple, a typical reversible electrode reaction [163], can be measured. Vielstich and co-workers have suggested [99] that, with the condition I/IKV < 0.95 (over a reasonable potential range), the technique can be used to measure ks values up to 5 cm s"1 with an accuracy of around 10%. This... 

Now we see that for a reversible couple, every current-time curve has the same shape but its magnitude is scaled by 1/(1 + 6) according to the potential to which the step is made. For very positive potentials (relative to ), this scale factor is zero thus i t) has a value between zero and depending on E, as sketched in Figure 5.1.3. 

In sampled-current voltammetry, our goal is to obtain an /(t)-E curve by (a) performing several step experiments with different final potentials E, (b) sampling the current response at a fixed time r after the step, and (c) plotting i r) V5. E. Here we consider the shape of this curve for a reversible couple and the kinds of information one can obtain from it. 

Numerous excellent texts exist on the fundamentals of cyclic voltammetry. The reader is referred especially to the recent text by Bond, which provides an excellent treatment of fundamentals as well as applications. The important aspects of cyclic voltammetry are illustrated by the diagram shown in Figure 1 of a typical voltammogram of a soluble, reversible couple subjected to a linear potential sweep (and return scan) between applied voltages E and E2- The characteristic curve shown in Figure 1 provides peak potentials ( p and E° ) as well as peak currents 1° and Note that... 

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