Diffusion chronopotentiometry

The possibility that adsorption reactions play an important role in the reduction of telluryl ions has been discussed in several works (Chap. 3 CdTe). By using various electrochemical techniques in stationary and non-stationary diffusion regimes, such as voltammetry, chronopotentiometry, and pulsed current electrolysis, Montiel-Santillan et al. [52] have shown that the electrochemical reduction of HTeOj in acid sulfate medium (pH 2) on solid tellurium electrodes, generated in situ at 25 °C, must be considered as a four-electron process preceded by a slow adsorption step of the telluryl ions the reduction mechanism was observed to depend on the applied potential, so that at high overpotentials the adsorption step was not significant for the overall process. 

Chronopotentiometry has been widely used to determine diffusion coefficients in molten salts. Chronopotentiometry is an experimental procedure in which the potential of an electrode is observed as a function of time during the passage of a constant current sufficiently large to produce concentration polarization with respect to the species undergoing electrochemical reaction. 

This equation applies to all reversible electrode reactions with soluble ox and red, so it includes cathodic chronopotentiometry of ions of amalgamating metals such as Cd2+, Cu2+, Pb2+ and Zn2+ at stationary Hg electrodes. For a redox couple such as Fe3+/Fe2+ the diffusion coefficients DTeA and Dox will not differ much, so that Etl4 is approximately equal to E° (770 V). 

A complicated situation arises when ox or red is insoluble, for instance in the reductive chronopotentiometry of an ion of a non-amalgamating metal then the metal precipitates on the stationary Hg electrode surface without further diffusion, so that... 

Table 2.4 Diffusion coefficients D x 106 (cm2 s 1) determined by means of polar-ography or chronopotentiometry at various indifferent electrolyte concentrations c (mol dm-3) at 25°C. The composition of the indifferent electrolyte is indicated for each ion. (According to J. Heyrovsky and J. Kuta)...

Experimental methods for determining diffusion coefficients are described in the following section. The diffusion coefficients of the individual ions at infinite dilution can be calculated from the ionic conductivities by using Eqs (2.3.22), (2.4.2) and (2.4.3). The individual diffusion coefficients of the ions in the presence of an excess of indifferent electrolyte are usually found by electrochemical methods such as polarography or chronopotentiometry (see Section 5.4). Examples of diffusion coefficients determined in this way are listed in Table 2.4. Table 2.5 gives examples of the diffusion coefficients of various salts in aqueous solutions in dependence on the concentration. 

Fig. 8.7. A chronopotentiometry diagram. The electrode potential turns up sharply when the diffusion layer is exhausted of material for the electrode reaction. The electrode attempts to seek another source of electrons.

A very important feature of chronopotentiometry is the characteristic variation in ix1/2 that occurs for certain electrode reactions when i is varied over a wide range by varying i. The behavior of ix1/2 can be effectively used to diagnose certain mechanisms of electrode reactions. Diagnostic curves for ix1/2 versus i are shown in Figure 4.4 for several mechanistic situations. A constant value of ix1/2 over a wide range of x (Fig. 4.4A) is characteristic of an uncomplicated, diffusion-controlled electrode reaction with no kinetic or adsorption phenomena at a planar electrode. 

Current-reversal chronopotentiometry is also useful for detecting adsorption of the product generated during the forward electrolysis time. Complete adsorption of the product on the electrode surface causes tr to equal tf since no product is lost by diffusion from the electrode. This approach has been used to determine the amount of adsorbed material formed during the reduction of riboflavin and the oxidation of iodide [10]. 

In practice two methods are used for stationary planar electrodes in quiescent solution chronoamperometry and chronopotentiometry. By use of an electroactive species whose concentration, diffusion coefficient, and n value are known, the electrode area can be calculated from the experimental data. In chronoamperometry, the potential is stepped from a value where no reaction takes place to a value that ensures that the concentration of reactant species will be maintained at essentially zero concentration at the electrode surface. Under conditions of linear diffusion to a planar electrode the current is given by the Cottrell equation [Chapter 3, Eq. (3.6)] ... 

The mercury-pool electrode. Mercury pools of sufficient diameter to approach a planar configuration obey the equations derived for linear diffusion to a planar electrode. This has certain theoretical advantages because of the large number of equations that have been derived for the planar electrode geometry, especially in terms of constant-current chronopotentiometry and linear-potential sweep chronoamperometry. 

Viscosity. In many applications a low viscosity is desirable so that mass transport by diffusion or convection will extend the time range for mass transport by pure diffusional control to periods as long as 40-50 s, which can be advantageous to electroanalytical techniques such as chronopotentiometry.34 At low temperatures the solvent may not appear to crystallize, but may form a rigid glass whose viscosity is so high that mass transport practically ceases the experimentalist must be alert to this possibility. 

This would suggest that chronopotentiometry could be a sensitive electroanalytical technique. It is rarely used in this context, however, since it is often difficult to determine the transition time accurately, because of double-layer charging at short times and competing reactions at long times. The same limitations apply when one attempts to use Eq. 49K to measure the diffusion coefficient. On the other hand this equation can be used as a quick method of obtaining n,... 

X 10 cm /s ) is correctly chosen, because for the determination of concentration by different methods use is made of different dependences relating the concentration to the diffusion coefficient Cg for chronopotentiometry Cg rotating disc electrode... 

For example, for the special case tiiOf Cf = n Oy Cf, = 3ti. Thus, while in controlled-potential voltammetric methods two substances at equal concentration with equal diffusion coefficients show two waves of equal height, in chronopotentiometry unequal transition times arise. The long second transition results from the continued diffusion of Oi to the electrode after ti, so that only a fraction of the applied current is available for reduction of O2 (Figure 8.5.1). 

For current reversal chronopotentiometry involving the forward reduction of a species O under conditions of semi-infinite linear diffusion, the reverse transition time can be made equal to forward... 

This equation applies to the totally mass-transfer-limited condition at the RDE and predicts that //c is proportional to Cq and One can define the Levich constant as which is the RDE analog of the diffusion current constant or current function in voltammetry or the transition time constant in chronopotentiometry. 

Reversal results are usually very sensitive to perturbing chemical reactions. For example, in the Ej-Ci case for cyclic voltammetry, would be 1 in the absence of the perturbation (or in chronopotentiometry r lrf would be 1/3). In the presence of the following reaction, /pa//pc 1 (or Tf/Tf < 1/3) because R is removed from near the electrode surface by reaction, as well as by diffusion. A similar effect will be found for a catalytic (EC ) reaction, where not only is the reverse contribution decreased, but the forward parameter is increased. 

The theoretical treatments for the different voltammetric methods (e.g., polarography, linear sweep voltammetry, and chronopotentiometry) and the various kinetic cases generally follow the procedures described previously. The appropriate partial differential equations (usually the diffusion equations modified to take account of the coupled reactions producing or consuming the species of interest) are solved with the requisite initial and boundary conditions. For example, consider the EfCi reaction scheme ... 

Figure 12.2.1 Variation of Ej/4 with log( t) for chronopotentiometry with the ErCj reaction scheme. Zone KD is a transition region between the pure diffusion and pure kinetic situations.

For simple reversal chronopotentiometry, the ratio of reversal transition time T2 to the forward time t is 1/3, just as in the diffusion-controlled case, independent of the rate constants. However, for cyclic chronopotentiometry the transition times for the third (73) and subsequent reversals differ from those of the diffusion-controlled case (31). 

Elimination of diffusion contribution to the overpotential in chronoamperometry and chronopotentiometry... 

Let us imagine an electrolyte with two monovalent ions, A X , such that the couple at the anode is identical to that at the cathode, and only is an electroactive species. A" is produced at the anode and consumed at the cathode. Remember that in this case it is possible to attain steady states different from equilibrium states . For example in a chronopotentiometry, after a while the concentration profile ceases to change. Remember also that electroneutrality requires the anion and cation concentrations to be equal at all points throughout the electrolyte. In systems with unidirectional geometry, linear concentration profiles emerge in the zones where there is no convection, and the slopes depend solely on the current and the diffusion coefficient of the electroactive species A". ... 

Chronopotentiometry with semi-infinite unidirectional diffusion... 

Chronopotentiometry with steady-state unidirectional diffusion. 310... 

Chronopotentiometry with diffusion-convection according to the Nernst model 311 Chronoamperometry with steady-state unidirectional diffusion. 312... 

Similar situation arose in the system of HfCl4-NaCl-KCl. Two steps were recorded at higher concentrations of HfCl4. The plot of /r( ) had a positive slope for the first step, and negative for the second step. Only at high current densities (chronopotentiometry) and at high scan rates (LSV) did the plot indicate an uncomplicated diffusion process. It was concluded that the adsorption of either Hf(II) or Hf(I) species caused the inactivation of the intermediates. 

The same authors also studied the polarization behavior of a rotating-disc electrode and the chronopotentiometry of a graphite disc electrode. Figure 15.11 illustrates the situation in the vicinity of the cathode. A cupric chloride ion, CUCI3, moves to the cathode through its diffusion layer (Step 1) and is electrochemically reduced to CuClg (Step 2). 

Electroanalytical techniques, essentially similar to those employed in aqueous solutions, can be adapted for use in melts to provide data on solution equilibria by way of stability constant determinations, ion transport through diffusion coefficient measurements, as well as mechanistic analysis and product identification from mathematical data treatment. Indeed, techniques such as linear sweep voltammetry and chronopotentiometry may often be applied rapidly to assess or confirm general characteristics or overall stoichiometry of electrode processes in melts, prior to more detailed kinetic or mechanistic investigations requiring more elaborate instrumentation and equipment, e.g., as demanded by impedance studies. Thus, answers to such preliminary questions as... 

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