Expanding Plane Electrode Research Articles

Application of the superposition principle to the study of multistep electrode processes and systems with several components in chronopotentiometry with programmed current. Part I

In this paper we present the solution to the differential equations system corresponding to the problem of multistep processes and systems with several components when a programmed current-time function is applied to planar and spherical electrodes. The analytical solutions have been obtained in both cases, by a recurrent procedure, which facilitates the numerical determination of results. This solution has been found for an expanding spherical electrode, since by using simple substitutions it is transformed into that corresponding to a stationary spherical electrode, to an expanding plane electrode or to a stationary plane electrode.

Reverse pulse voltammetry and polarography: a general analytical solution

A rigorous analytical solution to reverse pulse techniques for a plane electrode expanding with an arbitrary power of time is presented. Our results include the plane approximation for SMDE as well as the expanding plane electrode model for DME. In the case of SMDE, our results have been contrasted with those obtained by numerical solution of the problem, obtaining identical results. Finally, we have compared our treatment with previous solutions in literature.

Chronopotentiometry with several types of programmed current at most usual electrodes: General study of systems with coupled first-order chemical reactions

The general equations corresponding to CEC and catalytic processes when current-time functions of the forms I ( t) = I 0 t u ewt and I( t) = I 0( t 1 + t) v are applied to a DME were deduced taking into account the electrode sphericity and using a blank period t 1. From these expressions we deduce as particular cases those corresponding to other types of electrodes (for example expanding plane electrode, static mercury dropping electrode and stationary plane electrode), other well-known current-time functions (power current, exponential current and step current), other reaction schemes (CE, EC and E mechanisms) and those cases in which the blank period is zero. Moreover, methods for determining heterogeneous and homogeneous kinetic parameters are proposed in each reaction scheme.

Potential-time response for several types of programmed current at most usual electrodes. Theoretical study of CE and EC mechanisms

The theoretical study of the potential-time response corresponding to the CE and EC mechanisms at the DME by using non linear perturbation functions with the general form I(t) = I0tuewt and I(t) = I0(t1 + t)v is presented. Equations for the potential-time curves and for the transition times have been derived by taking into account the sphericity of the electrode. Methods for determining heterogeneous and homogeneous kinetic parameters are proposed. The expressions corresponding to an null blank period, to an expanding plane electrode and to spherical and plane stationary electrodes, can be deduced as particular cases of the equations obtained in this work.

Study of Higher Order Electrochemical Reactions Involving an Insoluble Product with Several Chronopotentiometric Techniques

AbstractThe general theory for higher order electrochemical reactions involving an insoluble product at the DME, by using different chronopotentiometric techniques, is presented. The expressions corresponding to a null blank period, to an expanding plane electrode and to spherical and plane stationary electrodes, can be deduced as particular cases of the equations obtained in this work. The particular features of the potential‐time curves are discussed and methods for determining kinetic parameters and the conditional (formal) potential are proposed.

Chronopotentiometry with a potential-exponential current-time function at the DME with a preceding blank period: Application to the study of higher order electrochemical reactions

The general theory for higher order electrochemical reactions with a current-time function of the form I( t) = I o t u e wt applied to a DME after a blank period t 1, is presented. The existence intervals for the transition times, depending on the relative sign of the exponents u and w, are discussed. Methods for determining the forward reaction order and the kinetic parameters for irreversible processes are proposed. The expressions corresponding to the expanding plane electrode, the static mercury dropping electrode and the stationary plane electrode can also be deduced as particular cases of the equations obtained here.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I( t) = I 0( t− t 0) q for t ⩾ t 0, I( t) = 0 for t < t 0; and (ii) I( t) = I 0 t q for t ⩾ t 0, I( t) = 0 for t < t 0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

Potentiostatic response when reactant and product are adsorbed at an electrode expanding with any power law or at a DME (expanding sphere electrode model)

Equations for a potentiostatic reversible reaction with an adsorption process following Henry's isotherm have been derived for an electrode expanding according to the law A( t) = A 0 t z , where A( t) is the area of the electrode. Hence, these equations can be applied both for a stationary plane electrode and for a DME (expanding plane electrode model) by making z = 0 and z = 2 3 , respectively. In addition, we have also derived the corresponding equations when we adopt for the DME the more rigorous expanding sphere electrode model, which allows us to carry out a comparison with the results obtained with the simplified model (expanding plane). Finally, our equations can also be readily converted to the corresponding equations for the adsorption controlled by diffusion only of surface-active species when they are not involved in a charge transfer reaction.

Theory of the chronoamperometric and polarographic response of the catalytic-deactivation mechanism

Equations which describe the chronoamperometric and polarographic response of the catalytic deactivation mechanism at a plane electrode expanding according to the law A(t) = A ot z , where A(t) is the area of the electrode, have been derived. Hence these equations are valid both for a stationary plane electrode and for a dropping mercury electrode (expanding plane electrode model) by making z = 0 and z = 2 3 respectively. In addition, this response at spherical electrodes, namely in a DME when the more rigorous expanding sphere electrode model is considered, and in a static mercury dropping electrode (SMDE), has also been obtained by deriving the corresponding equations for these types of electrodes. Procedures to determine the rate constant values of the chemical reactions involved in this mechanism are discussed.

Theory of the ee mechanism with adsorption of the intermediate at an electrode expanding with any power law or at a DME (expanding sphere electrode model)

The theory for the EE mechanism with adsorption of the intermediate species following Henry's isotherm has been developed for an electrode expanding according to the law A( t) = A 0 t 2, where A( t) is the area of the electrode. Hence, the corresponding equations can be applied both for a stationary plane electrode and for a dropping mercury electrode (expanding plane electrode model) by making z = 0 and z = 2 3 , respectively. In addition, we have also derived the corresponding equations when we adopt for the DME the more rigorous expanding sphere electrode model so that we may consider the influence exerted by the sphericity of the electrode on the current-potential ( I- E) curves. Characteristics of the I - E curves are discussed.

Theoretical study of the chronopotentiometric response with programmed current of electrode processes with regeneration mechanisms

A theoretical study of the chronopotentiometric response for regeneration mechanisms at an electrode expanding with any power law by using a programmed current of the form I(t) = I 0 t q is presented. These equations are valid both for a stationary electrode and for a dropping mercury electrode if the expanding plane electrode model is adopted. In addition, the sphericity of the DME has also been taken into account by adopting the more rigorous expanding sphere electrode model. Characteristics of the potential-time curves and procedures to determine the rate constant of the chemical reaction are shown. If the regeneration fraction, p, is <1, a transition time, τ, is always obtained. However, for p ⩾ 1 transition times are not always observed. Conditions for this case are discussed.

Pulse polarography: current-potential curves in normal pulse polarography, reverse pulse polarography, differential normal pulse polarography and differential pulse polarography for a slow charge-transfer step

Explicit equations for normal pulse polarography (NPP), reverse pulse polarography (RPP), differential normal pulse polarography (DNPP) and differential pulse polarography (DPP) for a slow chargetransfer reaction have been derived in a rigorous way. These equations are valid for an expanding plane electrode (DME) and for a stationary plane electrode. The characteristics of the I/ E curves are shown.

Current-potential curves with an EE mechanism

The dc polarographic response for the EE mechanism both in the expanding plane electrode and in the expanding sphere electrode is examined. Explicit equations for the current-potential curves when all species are initially added to the solution and without using the steady-state approximation have been derived. The situation obtained in some particular cases (reversible steps, one reversible and the other irreversible, totally irreversible steps and well-separated steps) is also discussed.

Pulse polarography Part VII. Theory for electrode processes with first-order regeneration mechanisms

A theoretical study of the limiting current in pulse polarography is given for first-order regeneration mechanisms: fractional regeneration and catalytic regeneration (regeneration ≥1). Rigorous equations for the current have been derived, taking into account both the expanding plane electrode and the expanding sphere electrode models. In addition, the corresponding asymptotic solutions which show the behavior of the current when the rate constant values are large, have been derived by using the steady-state approximation.

Pulse polarography: Part VIII. Theory for electrode processes with first-order regeneration mechanisms

A theoretical study of the limiting current in pulse polarography is given for first-order regeneration mechanisms: fractional regeneration and catalytic regeneration (regeneration ≥1). Rigorous equations for the current have been derived, taking into account both the expanding plane electrode and the expanding sphere electrode models. In addition, the corresponding asymptotic solutions which show the behavior of the current when the rate constant values are large, have been derived by using the steady-state approximation.

Pulse polarography Part VII. Theoretical relationships for electrode processes with an ECE mechanism

A theoretical study of the pulse polarographic response for the instantaneous limiting current with an ECE mechanism is presented. Thus, equations for the current have been derived under the following conditions: (a) Both the expanding plane electrode and the expanding sphere electrode models have been accounted. (b) The steady-state approximation was not used. (c) All species are initially present in the solution. With these conditions we have: (a) proposed a method for the calculation of the rate constant values through measurements of instantaneous limiting currents; (b) shown that the interval of the rate constant values that can be determined is about 103 times larger than in dc polarography; (c) checked the validity of the steady-state approximation.

A Contribution to the Theory of Pulse Polarography. I. Theory of Current-Potential Curves

Abstract A general theory of pulse polarographic current-potential curves is developed for a simple electrode reaction proceeding at the expanding plane electrode. It is shown that when the ratio of the sampling time to the pre-electrolysis time is smaller than 1/30, this condition being satisfied in usual pulse polarographic practice, the equation of current-potential curves can be greatly simplified. The theory developed is applied to the three modes of pulse polarography nowadays practically employed, i.e., normal pulse, scan-reversal pulse and differential pulse polarography. For each mode, the dependence of current-potential curves on the kinetic parameters of electrode reaction as well as on the experimental variables is discussed.

Pulse polarography: Part VII. Theoretical relationships for electrode processes with an ECE mechanism

A theoretical study of the pulse polarographic response for the instantaneous limiting current with an ECE mechanism is presented. Thus, equations for the current have been derived under the following conditions: (a) Both the expanding plane electrode and the expanding sphere electrode models have been accounted. (b) The steady-state approximation was not used. (c) All species are initially present in the solution. With these conditions we have: (a) proposed a method for the calculation of the rate constant values through measurements of instantaneous limiting currents; (b) shown that the interval of the rate constant values that can be determined is about 10 3 times larger than in dc polarography; (c) checked the validity of the steady-state approximation.

DC Polarography: current–potential curves with an ece mechanism

A theoretical study of the dc polarographic response with the ECE mechanism is presented. Explicit equations for the current-potential curves with Nernstian behavior and without using the steady-state approximation have been derived. These equations are valid in the context of the expanding sphere electrode and of the expanding plane electrode models. In addition, our solution is also applied when all species are initially added to the solution. Under these conditions if K, k1 and k2 are, respectively, the equilibrium constant and the rate constants of the chemical reaction, we show a method of determining these parameters from the limiting current values.

Dc polarography: Current-potential curves with an ECE mechanism

A theoretical study of the dc polarographic response with the ECE mechanism is presented. Explicit equations for the current-potential curves with Nernstian behavior and without using the steady-state approximation have been derived. These equations are valid in the context of the expanding sphere electrode and of the expanding plane electrode models. In addition, our solution is also applied when all species are initially added to the solution. Under these conditions if K, k 1 and k 2 are, respectively, the equilibrium constant and the rate constants of the chemical reaction, we show a method of determining these parameters from the limiting current values.