Diffusion coefficient chronopotentiometry

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). 

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. 

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)] ... 

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). 

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". ... 

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... 

The electrochemical properties of Np, dissolved in LiCl-KCl eutectic, were investigated using cyclic voltammetry and chronopotentiometry. At 400 to 550C, the diffusion coefficients of Np3+ and Np + were of similar magnitude and were described by ... 

Before attempting to measure diffusion coefficients, some basic information regarding the electrochemical behavior of the redox species must be known. This is particularly important for newly prepared compounds. First, one should evaluate the reversibility of the electron transfer reaction. Certain techniques, such as LSV, can only be applied to measure diffusion coefficients for nemstian systems. Second, the presence of any coupled homogeneous reactions should be established. The current for each technique is often dependent on such reactions, thus making measurements of the diffusion coefficient unreliable. Finally, the adsorption of reactants or products can produce faiadaic current that can greatly affect the measurement of the diffusion coefficient. For example, measuronent of the critical time in chronopotentiometry is less reliable when adsorption is present For these reasons, the electrochemical behavior of the compound must be factored into the selection of a technique. 

During chronopotentiometry, the concentration of U at the surface of the liquid Cd electrode (Cy) decreases continuously. After Cy reaches zero, the electrode potential steeply shifts positively towards the liquid Cd dissolution potential. When the transition time (t) is defined as the time taken for Cy to drop to zero, the diffusion coefficient of U in the liquid Cd (Dy) is calculated according to Equation 6.12.2 [12] ... 

Fung and Mamantov studied the electrochemical oxidation of Ti + [added as Ti(AlCl4)2] in AlCl3-NaCl (50-65 mole % AICI3) melts by linear sweep voltammetry, voltammetry, and chronopotentiometry at solid electrodes. TF" is oxidized stepwise to Ti " and TF " both processes are electro-chemically reversible at a platinum electrode. The lower oxidation states were found to be more stable at lower temperatures and in more acidic melts. The diffusion coefficient for Ti + was reported. 

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