Reversible Electrode Reaction Research Articles

Staircase voltammetry with varied current sampling times: Theory for diffusion controlled, rate controlled, and mixed rate and diffusion controlled electrode reactions

Summary The theory for staircase voltammetry with a varied current sampling time has been derived for the cases of reversible, irreversible, and quasireversible electrode reactions. The equations derived have been used to calculate theoretical voltammograms employing several different values of the electrode reaction parameters k s and α n a and several values of the experimentally controllable step time, step size and current sampling time. The current sampling time is shown to be an important parameter in the application of staircase voltammetry to analytical and kinetic studies.

Electrochemical noise of reversible electrode reactions

Electrochemical noise of reversible electrode reactions

The dependence of the dropping mercury electrode potential at constant current on the concentration of an electroactive constituent involved in reversible or irreversible electrode reactions

A new method is described in which the potential of the d.m.e. is measured as a function of the concentration of an electroactive constituent when a constant current is maintained by adjusting the voltage applied to the polarographic cell. Equations are derived describing the expected potential change caused by changing the concentration of a constituent involved in a reversible or an irreversible electrode reaction. Graphical interpretations of the derived equation are made, indicating the most suitable conditions for performing potential measurements, yielding potential differences that greatly exceed those obtained by conventional potentiometry, especially when the method is applied to irreversible electrode reactions at the d.m.e. Experimental evidence is presented, which not only verifies all expectations, but also indicates that the method offers a new approach to the investigation of some fundamental problems.

On the theory of Kalousek commutator, square-wave and related techniques: I. Equations for current-potential curves

Starting from Koutecky's general relations for alternating current polarography, equations of Kalousek curves (types I, II, III, IV), square-wave, Fournier's, and radio-frequency polarograms have been formulated for the case of the reversible electrode reaction. The possibility of analyzing various polarograms by means of these equations is discussed. Some disadvantages of the techniques mentioned are presented. The equation for the square-wave polarogram presented is compared with similar expressions given by Breyer and Matsuda.

On the theory of kalousek commutator, square-wave and related techniques I. Equations for current-potential curves

Starting from Koutecky's general relations for alternating current polarography, equations of Kalousek curves (types I, II, III, IV), square-wave, Fournier's, and radio-frequency polarograms have been formulated for the case of the reversible electrode reaction. The possibility of analyzing various polarograms by means of these equations is discussed. Some disadvantages of the techniques mentioned are presented. The equation for the square-wave polarogram presented is compared with similar expressions given by Breyer and Matsuda.

Unified theory of reversible diffusion-limited electrode reactions with adsorption under potentiostatic conditions

Summary It is shown that equations arising in the theoretical treatment of diffusion-limited reversible electrode reactions with adsorption of reactants under potentiostatic conditions are the same as those arising in the simpler cases of diffusion-limited adsorption without reaction in a broad class of cases. Thus, previously published treatments of the latter case for linear, Langmuir, and Frumkin adsorption at stationary planar and spherical and expanding planar electrodes can be transposed readily to the former case. Simple limiting approximations which can be applied with any adsorption isotherm are also given.

Reversible electrode reactions: Reduction of Cd-oxalate-succinate complex at D.M.E.

The reduction of Cd-oxalate-succinate system has been studied at D.M.E. It has been found to be reversible and diffusion-controlled involving two electrons as indicated by slope of straight line curve of E de vs. log ( i i d − i ) and direct proportionality of diffusion current to the effective height of mercury column. The stability constants β 12 β 11 and β 21 for complexes Cd(ox.)(succ.) 2, Cd(ox.)(succ.) and Cd(ox.) 2(succ.) have been evaluated by Schaap and McMasters' method; log β 12 = 4017, log β 21 = 4·982 ± 0·020 and a negative value for β 11. Cd(ox.)(succ.) probably does not exist in solution.

Unified theory of reversible diffusion-limited electrode reactions with adsorption under potentiostatic conditions

Unified theory of reversible diffusion-limited electrode reactions with adsorption under potentiostatic conditions

Effects of langmuirian adsorption on potentiostatic relaxation of diffusion-limited reversible electrode reactions

A theoretical treatment is given of the effect of Langmuirian adsorption on Nernstian, diffusion-limited electrode reactions at a plane electrode under potentiostatic conditions. Relaxation currents generally consist of three components, an instantaneous initial conversion of adsorbed reactant to product, the same diffusional component that would be observed in the absence of adsorption, and a time-distributed adsorptive component due to interconversion between adsorbed and diffusing species. The magnitude, sign, and time-constant associated with the time-distributed adsorptive component vary widely with experimental conditions. In favorable situations the magnitudes of both adsorptive components can be determined conveniently by extrapolation of two separate linear segments of a chronocoulometric plot of charge vs. square root of time to time zero. This feature and other prominent effects of adsorption are shown to be qualitatively independent of the detailed form of the adsorption isotherms.

Effects of Langmuirian adsorption on potentiostatic relaxation of diffusion-limited reversible electrode reactions

A theoretical treatment is given of the effect of Langmuirian adsorption on Nernstian, diffusion-limited electrode reactions at a plane electrode under potentiostatic conditions. Relaxation currents generally consist of three components, an instantaneous initial conversion of adsorbed reactant to product, the same diffusional component that would be observed in the absence of adsorption, and a time-distributed adsorptive component due to interconversion between adsorbed and diffusing species. The magnitude, sign, and time-constant associated with the time-distributed adsorptive component vary widely with experimental conditions. In favorable situations the magnitudes of both adsorptive components can be determined conveniently by extrapolation of two separate linear segments of a chronocoulometric plot of charge vs . square root of time to time zero. This feature and other prominent effects of adsorption are shown to be qualitatively independent of the detailed form of the adsorption isotherms.

Theory of ohmic loss in d.c. polarography

A theoretical analysis is presented of the effect of ohmic potential loss on results obtained with reversible electrode reactions in d.c. polarography. Simple correction of observed half-wave potentials by subtracting iR is reasonably accurate but not exact for small corrections (up to 5–10 mV). More accurate corrections for small values can be obtained by multiplying iR by a potential-dependent coefficient. For large ohmic losses higher order corrective terms are required.

Theory of ohmic loss in d.c. polarography

Summary A theoretical analysis is presented of the effect of ohmic potential loss on results obtained with reversible electrode reactions in d.c. polarography. Simple correction of observed half-wave potentials by subtracting iR is reasonably accurate but not exact for small corrections (up to 5–10 mV). More accurate corrections for small values can be obtained by multiplying iR by a potential-dependent coefficient. For large ohmic losses higher order corrective terms are required.

On the pH-dependence of polarographic half-wave potentials II. Protonation of an electro-inactive group

The pH-dependence of half-wave potentials of reversible and irreversible electrode reactions has been studied for a depolarizer bearing, besides the electroactive, an electroinactive acidic/basic group. Solution of two theoretical cases of an irreversible two-electron reduction indicates that the break which may occur on the E 1/2 vs . pH plot does not denote the dissociation constant p K A of the acidic form of the electroinactive group. The qualitative conclusions from the solution have been discussed for some examples of the reduction of nitrobenzene derivatives.

On the pH-dependence of polarographic half-wave potentials: II. Protonation of an electro-inactive group

Summary The pH-dependence of half-wave potentials of reversible and irreversible electrode reactions has been studied for a depolarizer bearing, besides the electroactive, an electroinactive acidic/basic group. Solution of two theoretical cases of an irreversible two-electron reduction indicates that the break which may occur on the E1/2 vs. pH plot does not denote the dissociation constant pKA of the acidic form of the electroinactive group. The qualitative conclusions from the solution have been discussed for some examples of the reduction of nitrobenzene derivatives.

Reversible oxygen electrode systems in molten salts

The nature of the “oxygen electrode”, one of the most controversial topics in fused salts, has been investigated in the molten (Na, K) NO3 eutectic at 10−3–10−1 m oxide concentration levels, by combining potentiometric and voltammetric techniques. Experimental evidence is produced to show that two well-defined kinds of reversible electrode can exist under extreme experimental conditions. In the complete absence of water the oxygen electrode behaves as a superoxide electrode, characterized by the reversible electrode reaction O2+e=O2−; EO2/O2−0=−0.645±0.005 V vs. Ag/Ag+ (0.07 m), while in the presence of an excess of water the oxygen electrode is actually an hydroxide electrode, characterized by the reversible process: O2+2 H2O+4e=4 OH−; EO2,H2O/OH−0=−0.495±0.005 V vs. Ag/Ag+ (0.07 m). From the experimental data the following equilibrium constants have been calculated at 503 K: 2O2−+H2O=1.5O2+2OH−K=103mol−12kg122O22−+H2O=2OH−+0.5O2K=2×1010mol12kg−12O2−+H2O=2OH−K≃1018 The conclusions of the study offer a completely new point of view on the problems related to the oxygen electrode systems in fused media. Several “uninterpreted” literature findings, relevant to different solvents over a large temperature range, seem reasonably explicable on the basis of the models proposed here.

Influence of non-specific adsorption of reactants on the electrode impedance

Summary The influence of non-specific adsorption of reactants on the electrode impedance is discussed. A method is proposed for calculating the double layer parameters, starting from experimental values of q and C d . Substitution of the double layer parameters in the expressions for the electrode impedance, derived by Delahay, makes it possible to predict the importance of non-specific adsorption. It appears that only for rather reversible electrode reactions (rate constant, k sh >0.1 cm s −1 ) adsorption effects can be expected. Theoretical predictions have been verified on the system Ba 2+ /Ba(Hg) in 0.1 and 1 M LiCl solutions. For both solutions no abnormal behaviour was found in the a.c. peak potential region, because the reaction is too irreversible ( k sh =(91)×10 −3 cm s −1 and (1.6±0.3)×10 −2 cm s −1 for resp. 1 M and 0.1 M LiCl solutions). The double layer capacity increases with Ba 2+ concentration at potentials anodic of the a.c. peak, because of the non-specific Ba 2+ adsorption.

Potential-step electrolysis followed by linear-sweep voltammetry

The method of potential-step electrolysis followed by linear potential-sweep voltammetry is considered theoretically. It is shown that, for a reversible electrode reaction without kinetic complications, the current—potential curve obtained during the linear potential-sweep is closely connected with the Ševčik—Randies P-function of normal linear-sweep voltammetry. Analytical implications are pointed out, while the presence of kinetic complications and the effect of finite electrode volume are briefly discussed.

Theory of staircase voltammetry

The theoretical relationships for voltammetry with a staircase potential function are developed for a reversible electrode reaction and are shown to be in accord with experiment. Current-potential curves are calculated and tabulated.

The Influence of Ionic Strength on Polarographic Half-Wave Potentials. I. Aqueous Systems Involving Reversible Electrode Reactions and Amalgamation of the Reduced Species in Uni-univalent Inert Electrolytes

The Influence of Ionic Strength on Polarographic Half-Wave Potentials. I. Aqueous Systems Involving Reversible Electrode Reactions and Amalgamation of the Reduced Species in Uni-univalent Inert Electrolytes

Theoretical Considerations on Reversible Electrode Reaction in Oscillographic Square Wave Polarography

Theoretical Considerations on Reversible Electrode Reaction in Oscillographic Square Wave Polarography