A.C. polarography and faradaic impedance of strongly adsorbed electroactive species: Part I. Theoretical and experimental study of a quasi-reversible reaction in the case of a Langmuir isotherm

The expression of the faradaic impedance is calculated in the case of a quasi-reversible system O+ne R under the following conditions: (a) both the oxidized and the reduced forms are strongly adsorbed; (b) the adsorption rate is large, and does not control the kinetics of the system; (c) the adsorption of both O and R obeys a Langmuir isotherm. The results show that the tangent of the phase angle is proportional to κ_s/ω (κ_s=rate constant of the electrochemical reaction). When ω→o, the phase angle tends towards 90°: the faradaic impedance becomes purely capacitive. The equation of the a.c. polarogram has been derived; whatever κ_s/ω, the peak height is proportional to the bulk concentration of the reactant, to τ^7/6 (τ=drop time), and to h^?1/2 (h=height of the mercury reservoir). When κ_s/ω→∞, the shape of the a.c. wave is identical to that of a “diffusion-controlled” a.c. wave. The experimental results obtained by a.c. polarography for the three systems azo-hydrazobenzene, benzo(c)cinnoline-dihydrobenzo(c)cinnoline and phenazine-dihydrophenazine are in excellent agreement with the theoretical predictions.     

Theory of electrode reactions of redox couples confined to electrode surfaces at monolayer levels: Part II. Cyclic voltammetry and ac impedance measurements

The expression of the current-potential relationship derived in Part I for simple one-step surface redox-electrode reactions of the species confined to electrode surfaces is applied to cyclic voltammetry and the method of faradaic impedance measurements. A method to obtain cyclic voltammograms is presented for a quasi-reversible or general case and equations for reversible and irreversible cyclic voltammograms are derived. The effect of the interaction parameters, W/RT and ΔW^≠/RT, kinetic parameters, Λ and α, and coordination number z on the waveform of the cyclic voltammograms is discussed. An interesting feature in the voltammograms, i.e. the appearance of two peaks, is predicted when W/RT < −2.19 for z = 6 in spite of the simple one-step redox process. Furthermore, equations for the faradaic resistance and capacitance are derived and it is shown that the faradaic impedance is independent of the frequency of ac perturbation.     

Faradaic admittance with reactant adsorption: Adsorption detection limits for redox systems with finite charge transfer rate

On basis of equations for the faradaic admittance given by Moreira and De Levie [8] the numerical data are presented which show the frequency dependence for cases with the finite charge transfer rate and various degrees of adsorption contribution. The reliability of diagnostic criteria for the adsorption detection is discussed and in some cases the resulting error in the k⁰ value (if the diagnostic test failed) is given.     

A.C. Cyclic voltammetry: A digital simulation study of the slow scan limit condition for a reversible electrode process

Rate laws presented to date for analysis of a.c. cyclic voltammetric data have invoked the so-called “slow scan limit approximation” which requires that ΔEω ? v, where Δ E and ω are the applied a.c. potential amplitude and angular frequency, respectively, and v is the d.c. potential scan rate. To provide a more useful guideline for the experimentalist than this qualitative condition, a pure digital simulation approach has been used to compute the a.c. cyclic time domain waveform for a reversible process under small amplitude conditions. The a.c. content of this waveform is extracted by the digital FFT alogirthm. Results of this study are presented here. Among the conclusions reached are more quantitative limitations for the slow scan limit rate laws describing the fundamental and second harmonic responses (approximately 128 a.c. cycles/d.c. cyclic sweep and 512 a.c. cycles/d.c. cyclic sweep, respectively) and an interesting prediction that the latter limitations can be relaxed further by a current waveform subtraction strategy, to as low as about 16 a.c. cycles/d.c. cyclic sweep for the fundamental and second harmonics. The cycles/sweep values assume one triangular wave potential scan of ±200 mV is encompassed.     

Ac voltammetry studies of electron transfer kinetics for a redox couple attached via short alkanethiols to a gold electrode

Ac voltammetry (ACV) is used to determine the chain length dependence of electron transfer kinetics between gold bead electrodes and ruthenium redox centers attached to the electrode surface via short alkanethiols. The pentaamminepyridine ruthenium redox centers are attached to pre-assembled monolayers of mercaptoalkanecarboxylic acids (HS(CH₂)_mCOOH, m=5, 7, 10). Equations for faradaic admittance of strongly adsorbed, non-interacting electroactive species are fitted to the experimental faradaic admittance data. Kinetic heterogeneity is suggested to be a probable reason for the apparent increase in the standard rate constant (k_s) and decrease in the total coverage of redox centers (θ_total) as the perturbation frequency increases. Because of the frequency dependence of k_s and because of limitations in the correction for uncompensated resistance, faradaic admittance at a fixed phase angle of 70° is chosen to compare k_s for different chain lengths. The plot of ln(k_s) versus m (the number of methylene units) is linear with a slope of −1.2±0.1 per CH₂.     

Ac polarography and faradaic impedance of strongly adsorbed electroactive species: Part IV. Experimental study of the faradaic impedance of the redox systems benzo(c)cinnoline-dihydrobenzo(c) cinnoline

The faradaic impedance of the surface redox system benzo(c)cinnoline-dihydrobenzo(c)-cinnoline is studied experimentally in aqueous medium between pH 5 and 13. The variations of the impedance components are in good accord with the theoretical predictions. A V-shaped curve is found for log k_s=f(pH) (k_s=rate constant of the surface electrochemical reaction). It is estimated that the determination of rate constant values up to 2×10⁴ s^?1 on a mercury electrode is possible by this method.     

Electrochemical capacitors with KCl electrolyte

Potassium manganese dioxide K_xMnO_{2 + δ}·nH₂O and amorphous MnO₂ in a mild 2 M KCl aqueous electrolyte prove to be excellent electrodes for faradaic electrochemical capacitors. The K_xMnO_{2 + δ}·nH₂O materials were prepared by direct thermal decomposition of KMnO₄ and contained a large amorphous/crystalline ratio. A sample decomposed at 550 °C gave a specific cyclic capacitance between −0.2 and +1.0 V/SCE of 240 F·g⁻¹, which corresponds to nearly one-third of the Mn(IV) ions participating in the faradaic reaction. Excellent cyclability at 12 mA·cm⁻² was found for 100 cycles. On short-circuit, K_0,31MnO_2,12·0,63 H₂O in 2 M KCl and pH 10.6 aqueous solution gave an initial current density of 0.58 A·cm⁻² and a total released charge of 4.6 C·cm⁻² compared with 0.32 A·cm⁻² and 11.1 C·cm⁻² for RuOOH·nH₂O in 5.3 M H₂SO₄. Similar results obtained with amorphous MnO₂ demonstrate that alkali ions can be used as the working ion in a faradaic supercapacitor, which frees the search for new materials from the constraint of working in a strong-acid aqueous medium.     

Application of convolution procedures to chronopotentiometry

Convolution procedures are used to extract the faradaic information from chronopotentiometric data, in conditions where significant distortion by double layer charging occurs. The faradaic component of the imposed current is obtained, after measurement of the double layer capacitance, by differentiation of the initial chronopotentiogram. Convolution of this current with the function (πt)^?1/2 leads to a potential-convoluted current relationship freed from the effect of double layer charging. The kinetic characterization of the system using a combined analysis of this relationship and that relating the faradaic current to the electrode potential is discussed for the various types of reaction mechanism. The efficiency of the proposed procedure is tested on the galvanostatic reduction of fluorenone in DMF.     

The influence of uncompensated solution resistance on the determination of standard electrochemical rate constants by cyclic voltammetry,and some comparisons with a.c. voltammetry

a digital simulation analysis is presented of the deleterious effects of uncompensated solution resistance, R_us, on the evaluation of standard rate constant, k^s_ob, by cyclic voltammetry. The results are expressed in terms of systematic deviations of “apparent measured” rate constants, k^s_ob(app), evaluated in the conventional manner without regard for R_us, from the corresponding actual values, k^s_ob(true), as a function of R_us and other experimental parameters. Attention is focused on the effects of altering the electrode area and the double-layer capacitance on the extent of the deviations between k^s_ob(app) and k^s_ob(true), and on comparisons with corresponding simulated results obtained from phase-selective a.c. impedance data. The extent to which k^s_ob(app) <k^s_ob(true) for small R_us values was found to be similar for the cyclic and a.c. voltammetric techniques. The latter method is, however, regarded as being preferable under most circumstances in view of the greater ease of minimising, as well as evaluating, R_us for a.c. impedance measurements. The influence of solution resistance on k^s_ob measurements with microelectrodes and without iR compensation is also considered.     

Kinetics of the Hg(II)/Hg electrode reaction in DMSO solutions of chloride ions

The electrode reaction Hg(II)/Hg in complex chloride solutions with dimethyl sulfoxide as solvent has been investigated at the equilibrium potential by the faradaic impedance method and a cyclic current-step method. The ionic strength was 1 M with ammonium perchlorate as supporting electrolyte, and the temperature was 25°C. Double-layer data have been determined by electrocapillary measurements. From the results of the kinetic measurements at ligand numbers ≤1.1 or ≥2.3 it is concluded that the overall charge transfer proceeds step-wise. The solvated Hg²⁺ and Hg₂²⁺ as well as the complexes HgCl_j^2?j and the dinuclear Hg₂Cl³⁺ contribute to the exchange current density. The rate constant of the step HgCl_j^2?j/ Hg(I) is found to increase with the number of Cl^? coordinated. This increase can be correlated to a decrease in solvation and a lengthening of the Hg?Cl distance. For 1.1 << 2.3, impedance measurements indicate a rate-controlling adsorption step. It is suggested that the uncharged HgCl₂ then forms an adsorbed network on the mercury surface.     

The investigation of the adsorptive behaviour of electroactive species by means of admittance analysis: Part II. Anion-induced adsorption of cadmium(II) from bromide and iodide solutions at the dropping mercury electrode

The adsorption of Cd(II) has been studied by measuring the interfacial admittance spectra at different dc potentials of the dropping mercury electrode (DME) in solutions of: (a) 1 M KBr+0.48 mM Cd(NO₃)₂,(b) 1 M KI+0.105 mM CdI₂ and (c) 0.1 M NaI+0.9 M NaClO₄ +0.116 mM CdI₂ The experimental data were analysed using the procedures described in Part I of this series. The frequency dependence of the admittance corresponds to that of a reversible electrode reaction with reactant adsorption. The potential dependence of the resulting adsorption parameters can be mathematically described by a Langmuir isotherm for adsorption of Cd(II) with the adsorption energy being at least a quadratic function of potential. Detailed checks on the consistency of this model have been applied and were found to be satisfactory.     

Redox capacitance of poly-3,4-ethylenedioxythiophene studied by cyclic voltammetry and faradaic impedance spectroscopy

The paper presents results of studying the electrochemical properties of poly-3,4-ethylenedioxythiophene films using the methods of cyclic voltammetry and faradaic impedance spectroscopy in acetonitrile and propylene carbonate solutions of different electrolytes: LiClO₄, Bu₄NBF₄, Bu₄NPF₆. The effect of the film synthesis conditions, the nature of anion and solvent, and the supporting electrolyte concentration on the film redox capacitance is discussed. Main attention is paid to the comparison of values characterizing the redox capacitance of a poly-3,4-ethylenedioxythiophene film C _lf (determined using the faradaic impedance method) and C _cv (determined using the cyclic voltammetry method) and the studies of their dependence on the varied experimental factors. The experimental C _lf vs. E curves are analyzed using the relationships of a model of a uniform film.     

Limitations in the analysis of ac impedance data with poorly separated faradaic and diffusional processes

The kinetics of charge transfer across liquid-liquid interfaces is frequently analysed in terms of the Randles equivalent circuit. For this circuit, two time constants, t_f and t_d, can be defined for the faradaic and diffusional components respectively. Conventional methods of analysing impedance/admittance data will give valid estimates for the kinetic parameters only when t_f < t_d. Non-linear regression is capable of extracting valid estimates of the kinetic parameters for t_f 30t_d. Liquid-liquid systems appear to have t_f t_d. The difficulties in extracting kinetic parameters from such data will also apply to other transient techniques.     

Chronopotentiometry of systems involving follow-up chemical reactions: Application of convolution and finite difference procedures

Distortion of polarization curves by double layer charging severely limits the standard application of chronopotentiometry to mechanism and rate constant analysis of systems involving fast follow-up chemical reactions. A procedure is proposed to overcome these difficulties in the case of irreversible electrochemical-chemical processes (pure kinetic conditions). It starts with the extraction of the faradaic component, i_f, of the imposed current and the computation of its convolution integral, I, with the function (πt)^?1/2. The i_f-E and I-E are then simultaneously treated by a logarithmic analysis the form of which depends upon the expected mechanism. The efficiency of the method in mechanism and rate determination is illustrated experimentally on the example of the electrohydrodimerization of p-methylbenzylidene malononitrile for which discrimination between 32 possible limiting mechanisms has to be carried out. The same reaction is also used to test another type of analysis to be applied to partially reversible systems. Data processing then combines finite difference approach and convolution. It amounts to fitting the formal kinetics with the experimental data automatically in a small size computer avoiding tedious manual fitting with a priori calculated working curves. It is shown that the rate constants can be thus determined with a good accuracy even from single-step experiments.     

Solid-state NMR studies of methyl celluloses. Part 2: Determination of degree of substitution and O-6 vs. O-2/O-3 substituent distribution in commercial methyl cellulose samples

Solid state NMR spectroscopy was applied to determine the overall degree of substitution (DS) and the degrees of substitution at C-6 (DS_C-6) and C-2/3 (DS_C-2/3). Four commercial methyl cellulose samples were used, having a DS between 0.51 and 1.96 as determined by wet-chemical analysis. The strategy and optimization of the NMR data acquisition as well as the data evaluation procedures are explained in detail. Optimization of the approach mainly comprised (a) maximizing the signal by choice of NMR probe, MAS spinning frequency and B ₀ field, (b) minimizing the measurement time by a Torchia-type experiment and (c) suppressing probe background by rotor-synchronized echo detection. Data evaluation used simply the integration of three different spectral ranges in the ¹³C NMR spectrum. The results of the experiments were in good agreement with the wet-chemical data. The NMR approach takes about the same analysis time as the conventional hydrolysis/chromatography analysis. However, it is a generally applicable and simple alternative without need for an extended sample preparation which is most useful if wet-chemical/chromatographic analyses are undesired or unavailable. Further studies have to concentrate on the validation of the analytical method and application to a larger sample array.     

Evaluation of electrochemical charge-transfer rates by using (real) laplace space analysis: Single potential-step chronoamperometry of hexacyanoferrate(III)/(II) and Europium(III)/(II) couples

The one-electron hexacyanoferrate(III)/(II) and europium(III)/(II) redox couples were evaluated by using single-pulse chronoamperometry at a planar glassy carbon electrode (and also a mercury-pool electrode for europium) to test Wijnen's method for calculating heterogeneous electron-transfer rate constants by using (real-axis) Laplace space analysis. The k⁰ values obtained for the former couple in potassium or lithium chloride supporting electrolytes agreed well with published constants obtained by diverse real-time techniques. Transfer coefficients (α⁰) obtained from (? in k^a/?η)_η=0 for LiCl electrolyte were 0.4–0.5, rather than 0.22 previously reported. The cathodic rate values calculated for europium(III) reduciton (in NaClO₄/HClO₄) on both glassy carbon and mercury agreed very well with each other and with published values obtained by d.c. polarography and faradaic impedance measurements. Owing to several factors, including its ability to utilize virtually any set of recorded i(t) data points, Wijnen's Laplace technique offers an attractive alternative to conventional single-pulse analysis in real-time.     

Stable and Highly Efficient Electrochemical Production of Formic Acid from Carbon Dioxide Using Diamond Electrodes

High faradaic efficiencies can be achieved in the production of formic acid (HCOOH) by metal electrodes, such as Sn or Pb, in the electrochemical reduction of carbon dioxide (CO₂). However, the stability and environmental load in using them are problematic. The electrochemical reduction of CO₂ to HCOOH was investigated in a flow cell using boron‐doped diamond (BDD) electrodes. BDD electrodes have superior electrochemical properties to metal electrodes, and, moreover, are highly durable. The faradaic efficiency for the production of HCOOH was as high as 94.7 %. Furthermore, the selectivity for the production of HCOOH was more than 99 %. The rate of the production was increased to 473 μmol m^?2 s^?1 at a current density of 15 mA cm^?2 with a faradaic efficiency of 61 %. The faradaic efficiency and the production rate are almost the same as or larger than those achieved using Sn and Pb electrodes. Furthermore, the stability of the BDD electrodes was confirmed by 24 h operation.     

Cu/Cu2O Electrodes and CO2 Reduction to Formic Acid: Effects of Organic Additives on Surface Morphology and Activity

Copper/copper oxide (Cu/Cu₂O) electrodes are known to display interesting electrocatalytic performances for the reduction of CO₂, and thus, deserve further investigation for optimization. Here, we show that the addition of nitrogen‐based organic additives greatly improves the activity of these electrodes (higher current densities, greater selectivity, and higher faradaic yields). The best effector is found to be tetramethyl cyclam. For example, electrolysis at ?2.0 V versus Fc⁺/Fc in CO₂‐saturated DMF/H₂O (99:1, v/v) in the presence of this effector results in formic acid with almost 90 % faradaic yield. SEM and XPS analysis of the electrode surface reveals that the organic additive promotes the formation of active Cu⁰ nanoparticles from Cu₂O during electrolysis. This simple approach provides a straightforward strategy toward the optimization of Cu/Cu₂O electrodes.     

The admittance of an electrochemical cell with adsorption of electroactive species at the DME

Equations for the electrode admittance in, the case of adsorption of electroactive species have been derived, considering both a.c. and d.c. aspects of adsorption. It was shown that due to the d.c. aspects the function also contains a drop-time dependent term f(t_m): =c_OD_O^1/2+c_RD_R^1/2 +f(t_m)?s Under normal polarographic conditions the value of is constant, so c_O and c_R are drop-time dependent and consequently also the value of the Warburg coefficient σ, as well as the adsorption parameters C_LF and C_HF.     

Enzyme-free impedimetric glucose sensor based on gold nanoparticles/polyaniline composite film

A non-enzymatic impedimetric glucose sensor was fabricated based on the adsorption of gold nanoparticles (GNPs) onto conductive polyaniline (PANI)-modified glassy carbon electrode (GCE). The modified electrode (GCE/PANI/GNPs) was characterized by using cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and scanning electron microscopy (SEM). The determination of glucose concentration was based on the measurement of EIS with the mediation of electron transfer by ferricyanide ([Fe(CN)₆]^3?). The [Fe(CN)₆]^3? is reduced to ferrocyanide ([Fe(CN)₆]^4?), which in turn is oxidized at GCE/PANI/GNPs. An increase in the glucose concentration results in an increase in the diffusion current density of the [Fe(CN)₆]^4? oxidation, which corresponds to a decrease in the faradaic charge transfer resistance (R _ct). A wide linear concentration range from 0.3 to 10 mM with a lower detection limit of 0.1 mM for glucose was obtained. The proposed sensor shows high sensitivity, good reproducibility, and stability. In addition, the sensor exhibits no interference from common interfering substances such as ascorbic acid, acetaminophen, and uric acid.