Chronopotentiometry

Theory for chronopotentiometry of reversible channel electrode reactions under the Levich approximation has been presented by Aoki and Matsuda [73]. The transition time in flowing solution, tc, was found to be related to that in stationary solution, t0, via the approximations 

Switching on a current larger than the limiting current, the diffusion profile is described by the following boundary conditions 

The meaning of the last condition is that the diffusion can freely expand into the electrolyte (semi-infinite condition). The solution of Eq. (5.13) gives the Sand equation. If formulated for a decrease of concentration on the surface the equation is 

The concentration on the electrode surface decreases with the square root of time. For metal deposition, the corresponding potential is given by the equation 

Ward [119] has discussed in some detail the determination of phenolic and amine types of antioxidant and antiozonant in polymers by the chronopotentiometric techniqne, using a paraffin wax impregnated graphite indicating electrode and solntions of lithinm chloride and lithium perchlorate and acetonitrile in 95% ethanol as snpporting electrolytes. The precision obtainable for repeated chronopotentiometric runs in acetonitrile was fonnd to be better than 1.0% in cases in which electrode fouling did not occnr, and 1.7% when the electrode was fouled by electrolysis products. 

Although irWC always increased as antioxidant concentration (C) was decreased, plots of ir% versus (C) gave a nearly straight line suitable for use as an analytical working curve (Table 2.16). 

At a given concentration of electroactive species, the product irVi was constant as i, and thus r were varied over a 2- to 3-fold range. 

The range of transition times measured was limited to not less than 5 or not more than 30 seconds. The lower limit was imposed by the accuracy with which it was possible to measure r with the recorder used. The upper limit results from disturbance of the diffnsion layer by such effects as vibration, convection, etc. Within these limits, the precision with which transition times could be reproduced was 1.0%, even when the electrode was removed from the solution between runs and dried before being replaced. This increase in reproducibility appears to rise from the ability of the solvent to wet the electrode and suggests an important advantage to be gained by the use of non-aqueous solvents with carbon electrodes. 

I Santowhite powder refined 4,4 -butylidene-bis-(3-methyl-6-t-butylphenol)  

we simulate a system where a chemical reaction takes place in solution. An electroactive species is produced in solution, homogeneously distributed at bulk concentration Cj, by a radiation flash. The species decays with a first order chemical reaction. A potential is applied to the electrode such that the diffusion limited current is measured this corresponds to the Cottrell experiment on a decaying species. Reinert and Berg (1962) have solved this system analytically and found the ratio r of current at time t to the (diffusion) current i, in the absence of the chemical reaction  

Choosing a moderate value K = 1 then gives us a system in which diffusion and the chemical reaction play comparable roles. The diffusion equation is 

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The method, as so far developed, is limited by the condition that the hydration-dehydration reaction must proceed at a rate that is slow compared with the time needed to obtain a polarogram. In principle, the method is capable of much wider application to covalent-hydration studies if use is made of oscillographic polarographic techniques or of chronopotentiometry. These refinements are currently being investigated. 

Cyclic voltammetry (adsorption, monolayers) Potentiodynamic polarisation (passivation, activation) Cathodic reduction (thickness) Frequency response analysis (electrical properties, heterogeneity) Chronopotentiometry (kinetics)... 

Impedance spectroscopy is best suited for the measurement of electronic conductivities in the range 10 -7to 10 2S cm 1.145 In principle, it is perhaps the best method for this range, but it is often difficult to interpret impedance data for conducting polymer films. The charge-transfer resistance can make measurements of bulk film resistances inaccurate,145 and it is often difficult to distinguish between the film s ionic and electronic resistances.144 This is even more of a problem with chronoamperometry146 and chronopotentiometry,147 so that these methods are best avoided. 

For the tetrabutylammonium salts of substituted acetate the quarter wave potentials have been determined by chronopotentiometry in acetonitrile. The ease of oxidation, as reflected in the Ej -values, decreases with increasing strength of the acid [88]. 

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. 

Verbrugge MW, Tobias CW (1985) Triangular current-sweep chronopotentiometry at rotating disk and stationary, planar electrodes. J Electroanal Chem 196 243-259... 

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. 

The ionic potentials can be experimentally determined either with the use of galvanic cells containing interfaces of the type in Scheme 7 or electroanalytically, using for instance, polarography, voltammetry, or chronopotentiometry. The values of and Aj f, obtained with the use of electrochemical methods for the water-1,2-dichloroethane, water-dichloromethane, water-acetophenone, water-methyl-isobutyl ketone, o-nitrotol-uene, and chloroform systems, and recently for 2-heptanone and 2-octanone [43] systems, have been published. These data are listed in many papers [1-10,14,37]. The most probable values for a few ions in water-nitrobenzene and water-1,2-dichloroethane systems are presented in Table 1. 

For controlled-current DC polarography, especially its current density mode, see under Chronopotentiometry at a dme (p. 172). For charge-step polarography, i.e., a controlled charge of coulostatic technique, see ref. 9, pp. 424-429, and ref. 3, pp. 270-276. 

Fig. 3.53 shows the effect of an electroactive species such as an acid or a more active depolarizer that undergoes cathodic reduction in one ac half-period and anodic oxidation in the next ac half-period (see also Fig. 3.54) x is the so-called transition time, well known from chronopotentiometry (see later), i.e., in Fig. 3.53 the transition time of reduction. 

In contrast to the previous voltammetric methods at stationary electrodes, chronopotentiometry, which is based on interpretation of E-t curves, represents a controlled current method. 

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... 

A more usual procedure for overcoming the disturbances from contaminants is current reversal chronopotentiometry here the current is reversed at the initial transition time tf of the forward reaction and the next transition time xb of the backward reaction is measured as a rule the reversal wave will not be influenced by the contaminant because it will react either before the forward or after the backward reaction of the analyte (see Fig. 3.60a) the entire procedure can be even repeated as cyclic chronopotentiometry (see Fig. 3.60b), which may provide a further check on the reliability. The reversal technique can be applied to initial reduction followed by re-oxidation and also to initial oxidation followed by re-reduction79. 

Chronopotentiometry at a dme appeared to be impossible until Kies828 recently developed polarography with controlled current density, i.e., with a current density sweep. He explained the method as follows. The high current density during the first stage of the drop life results in the initiation of a secondary electrolysis process at a more negative electrode potential followed by a reverse reaction with rapid (reversible) systems because of the increase in the electrode potential. 

Analogously to eqn. 3.72 for stationary electrodes and a reversible redox couple of soluble ox and red, Kies derived for chronopotentiometry at a dme via insertion in the Nernst equation... 

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. 

An early study on C02 reduction in non-aqueous solvents was carried out by Haynes and Sawyer (1967) who employed chronopotentiometry, controlled potential coulometry and galvanostatic methods to study the reduction of C02 at Au and Hg in dimethylsulphoxide (DMSO). 

E. Katz, L. Alfonta, and I. Willner, Chronopotentiometry and Faradaic impedance spectroscopy as methods for signal transduction in immunosensors. Sens. Actuators B 76, 134-141 (2001). 

T. Gueshi, K. Tokudam, and H. Matsuda, Voltammetry at partially covered electrodes Part I. Chronopotentiometry and chronoamperometry at model electrodes. J. Electroanal. Chem. 89, 247-260 (1978). 

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