Cottrellian Behavior Research Articles

Electrocatalytic oxidation of methanol on Ni and NiCu alloy modified glassy carbon electrode

Nickel and nickel–copper alloy modified glassy carbon electrodes (GC/Ni and GC/NiCu) prepared by galvanostatic deposition were examined for their redox process and electrocatalytic activities towards the oxidation of methanol in alkaline solutions. The methods of cyclic voltammetery (CV) and chronoamperometry (CA) were employed. The cyclic voltammogram of NiCu alloy demonstrates the formation of β/β crystallographic forms of the nickel oxyhydroxide under prolonged repetitive potential cycling in alkaline solution. In CV studies, in the presence of methanol NiCu alloy modified electrode shows a significantly higher response for methanol oxidation. The peak current of the oxidation of nickel hydroxide increase is followed by a decrease in the corresponding cathodic current in presence of methanol. The anodic peak currents show linear dependency with the square root of scan rate. This behavior is the characteristic of a diffusion controlled process. Under the CA regime the reaction followed a Cottrellian behavior and the diffusion coefficient of methanol was found to be 2 × 10 −6 cm 2 s −1 in agreement with the values obtained from CV measurements.

Cell-Impedance-Controlled Lithium Transport Through Li1 − δMn2O4 with Fractal Surface by Analyses of Experimental PCT and LSV

Lithium transport through the fractal film electrode with partially inactive surface under the cell-impedance-controlled constraint was investigated by employing ac-impedance spectroscopy, potentiostatic current transient (PCT) technique and linear sweep voltammetry (LSV). For this purpose, the totally active and partially inactive film electrodes were obtained by surface modification of film with polyvinylidene fluoride (PVDF) binder. Based upon the perimeter-area relation, the fractal dimension of the partially inactive surface was determined. From the analysis of the ac-impedance spectra obtained from the totally active and partially inactive fractal electrodes, it was found that the charge-transfer kinetics strongly depends upon the surface coverage by active sites θ. All the potentiostatic current transients did not exhibit the generalized Cottrell behavior even before the characteristic time and all the power dependence of the peak current on the potential scan rate deviated from the generalized Randles-Sevčik behavior even above the characteristic scan rate in the linear sweep voltammograms. In particular, as either θ or falls in value, the value of is prolonged and at the same time the value of is reduced as well. From the analyses of the potentiostatic current transients and the linear sweep voltammograms in terms of and , it was experimentally confirmed that the partial inactivity of the surface plays a significant role in the interfacial charge-transfer reaction and subsequent diffusion reaction during the whole lithium intercalation and deintercalation processes.

Dimensional Analysis of Chronoamperometry: Proof and Verification of Cottrellian Behavior of Systems with Composition-Dependent Diffusion Coefficients

Chronoamperometry with a Dirichlet boundary condition and semi-infinite linear diffusion exhibits Cottrellian behavior, that is, the product it1/2 is constant as a function of time as long as the system is initially homogeneous, a conclusion that can be reached using only dimensional analysis; no detailed mathematical analysis is required. The generality of this result is known to include purely diffusional systems and systems in which transport also involves migration. In the present work, it is shown that Cottrellian behavior obtains, even when the system diffusion coefficients are a function of system composition, regardless of the exact form of that function. These conclusions are confirmed by simulations of examples for purely diffusional systems as well as for systems with migration. Some experimental examples from the literature are cited.

Theoretical approach to cell-impedance-controlled lithium transport through Li 1 − δMn 2O 4 film electrode with partially inactive fractal surface by analyses of potentiostatic current transient and linear sweep voltammogram

Lithium transport through the partially inactive fractal Li 1 − δ Mn 2O 4 film electrode under the cell-impedance-controlled constraint was theoretically investigated by using the kinetic Monte Carlo method based upon random walk approach. Under the cell-impedance-controlled constraint, all the potentiostatic current transients calculated from the totally active and partially inactive fractal electrodes hardly exhibited the generalised Cottrell behaviour and they were significantly affected in shape by the interfacial charge-transfer kinetics. In the case of the linear sweep voltammogram determined from the totally active and partially inactive fractal electrodes, all the power dependence of the peak current on the scan rate above the characteristic scan rate deviated from the generalised Randles–Sevčik behaviour. From the analyses of the current transients and the linear sweep voltammograms simulated with various values of the simulation parameters, it was further recognised that the cell-impedance-controlled lithium transport through the partially inactive fractal Li 1 − δ Mn 2O 4 film electrode strongly deviates from the generalised diffusion-controlled transport behaviour of the electrode with the totally active surface, which is attributed to the impeded interfacial charge-transfer kinetics governed by the surface inhomogeneities including the fractal dimension of the surface and the surface coverage by active sites and by the kinetic parameters including the internal cell resistance.

Spectroelectrochemical Study of N‐Substituted Phenoxazines as Electrochemical Labels of Biomolecules

AbstractThe electrochemical conversion of N‐substituted phenoxazines (NSP's) bearing a CH2CH2X substitute (where XOH, COOH, CH2NH2, CH2SO3H, CH2NHCOR) was investigated using cyclic voltammetry on a bulk gold electrode and a thin‐layer spectroelectrochemical cell. The electrochemical oxidation of NSP's on the gold electrode was quasi‐reversible and proceeded in a diffusion‐controlled regime. The formal redox potential of NSP's covered the range from 0.39 to 0.45 V vs. SCE. The electrochemical oxidation of NSP's in the thin‐layer spectroelectrochemical cell produced radical cations that showed absorbance at 385, 410 and 530 nm. Electrochemical conversion fitted the general voltammetric current‐potential equation of a reversible wave, whereas electrolysis at constant potential showed a typical Cottrell behavior. Combining of NSP's with a biologically‐relevant theophylline molecule did not change electrochemical and spectral properties of the phenoxazine core. Theophylline enlarged with NSP's demonstrated electrochemical and biocatalytic behavior similar to that of NSP's. The investigated NSP's possess electrochemical and spectral properties that are useful as biomolecular labels for electroanalysis.

The cell-impedance-controlled lithium transport through LiMn 2O 4 film electrode with fractal surface by analyses of ac-impedance spectra, potentiostatic current transient and linear sweep voltammogram

Lithium transport through the fractal LiMn 2O 4 film electrode under the cell-impedance-controlled constraint was investigated by employing ac-impedance spectroscopy, potentiostatic current transient technique and linear sweep voltammetry. For this purpose, the flat and fractal LiMn 2O 4 film electrodes were prepared on the as-deposited Pt/polished Al 2O 3 substrate and the surface modified Pt/unpolished Al 2O 3 substrate, respectively. From the analysis of the ac-impedance spectra obtained from the flat and fractal electrodes, it is found that the apparent self-similar fractal dimension reduces the charge-transfer resistance, and the phase angle of the diffusion impedance under the semi-infinite diffusion condition positively deviates in absolute value from 45° with increasing fractal dimension. All the potentiostatic current transients experimentally measured from the flat and fractal LiMn 2O 4 electrodes showed non-generalised Cottrell behaviour which resulted from the cell-impedance-controlled constraint during lithium transport. In the case of linear sweep voltammogram theoretically calculated and experimentally measured from the flat and fractal LiMn 2O 4 electrodes, the power dependence of the peak current on the scan rate hardly exhibited the generalised Randles–Sevčik behaviour. From the analyses of the potentiostatic current transients and the linear sweep voltammograms, furthermore, it is experimentally confirmed that the internal cell resistance mainly determining the cell-impedance-controlled lithium transport strongly depends upon the fractal dimension as well as such external parameters as the applied potential step and the amount of lithium transferred during lithium transport.

Analysis of anodic current transient measured on Pd electrode with fractal surface: Hydrogen diffusion coupled with interfacial charge transfer

Hydrogen transport through Pd electrode with fractally rough surface was investigated in 0.1 M NaOH solution by analysis of the anodic current transient. The Pd electrode surfaces were electrochemically modified to be rough by redox cycling in 1 M H 2SO 4 solution. From the triangulation analysis of the atomic force microscopy images, it was found that the modified electrode surfaces exhibited self-similar scaling properties with different fractal dimensions, depending upon the number of redox cycles. The anodic current transient measured on the surface-modified fractal electrode subjected to the hydrogen discharging potentials of 0.3–0.7 V reversible hydrogen electrode, (RHE) showed the non-generalised Cottrell behaviour, which resulted from the constraint of hydrogen diffusion mixed with interfacial charge transfer during hydrogen transport. Especially, it displayed an inflexion point at the time that corresponds to the temporal outer cut-off of fractality, i.e. the crossover time required for the fractal to flat transition. In addition, the temporal outer cut-off under the constraint of mixed control was observed to be shortened with increasing hydrogen discharging potential, which could be accounted for by the increased growth rate of diffusion layer in the electrode accompanying the facilitated charge transfer kinetics at the electrode/electrolyte interface.

An experimental study on cell-impedance-controlled lithium transport through Li 1− δCoO 2 film electrode with fractal surface by analyses of potentiostatic current transient and linear sweep voltammogram

The effect of the surface roughness on the cell-impedance-controlled lithium transport through the Li 1− δ CoO 2 film electrode was experimentally investigated in a 1 M LiClO 4-PC solution by the analyses of the potentiostatic current transient (PCT) and the linear sweep voltammogram (LSV). The flat and fractal Li 1− δ CoO 2 film electrodes were prepared on the Pt/polished Al 2O 3 substrate and the surface-modified Pt/unpolished Al 2O 3 substrate, respectively. From the ac-impedance spectra obtained from the flat and fractal electrodes, it is found that the apparent self-similar fractal dimension reduces the charge-transfer resistance. All the PCTs did not exhibit the generalised Cottrell behaviour until the characteristic time t ch and all the power dependence of the peak current on the potential scan rate positively deviated from the generalised Randles–Sevcik behaviour above the characteristic scan rate ν ch in the LSVs. From the analyses of the PCTs and the LSVs in terms of t ch and ν ch, furthermore, it is experimentally confirmed that the surface roughness plays a significant role in the kinetic facilitation of the interfacial charge-transfer reaction during the whole lithium intercalation and deintercalation processes.

Theoretical approach to cell-impedance-controlled lithium transport through Li 1− δCoO 2 film electrode with fractal surface: numerical analysis of generalised diffusion equation

In the present work, lithium transport through the Li 1− δ CoO 2 film electrode with a fractal surface was investigated under the cell-impedance-controlled constraint at the electrode/electrolyte interface along with the impermeable constraint at the electrode/current collector interface by using the numerical analysis of the generalised diffusion equation (GDE). Under the cell-impedance-controlled constraint, all the potentiostatic current transients (PCTs) calculated from the flat and fractal electrodes did not exhibit the generalised Cottrell behaviour until the characteristic time t ch and they were significantly affected in shape by the electrode thickness. In the case of the linear sweep voltammograms (LSVs) determined from the flat and fractal electrodes, all the power dependence of the peak current on the potential scan rate above the characteristic scan rate ν ch negatively deviated from the generalised Randles–Sevcik behaviour. From the analyses of the PCTs and the LSVs, furthermore, it is recognised that the cell-impedance-controlled lithium transport through the fractal Li 1− δ CoO 2 film electrode is enhanced by the surface roughness, but it is impeded by the internal cell resistance.

A study on the potentiostatic current transient and linear sweep voltammogram simulated from fractal intercalation electrode: diffusion coupled with interfacial charge transfer

Potentiostatic current transient and linear sweep voltammogram, theoretically calculated from the well-defined fractal profiles were analysed, with particular emphasis on hydrogen transport under the condition where hydrogen diffusion in the electrode is kinetically coupled with the charge-transfer reaction at the electrode/electrolyte interface. Under such a constraint of mixed control, the simulated current transient from the fractal electrode hardly exhibited the generalised Cottrell behaviour, and, especially, it displayed an inflexion point at the time that corresponds to the temporal outer cut-off of fractality (crossover time required for the fractal to flat transition). In the case of the linear sweep voltammogram computed from the fractal electrode, moreover, the power dependence of the peak current on the scan rate deviated negatively from the generalised Randles–Sevčik behaviour, above the slow threshold scan rate (crossover scan rate needed for the fractal to flat transition). From the analyses of the current transients and the linear sweep voltammograms calculated with various values of the simulation parameters, it was further recognised that during the potential jump as well as the potential scan, the temporal cut-off ranges of fractality under the constraint of mixed control are crucially determined by the interfacial charge-transfer kinetics, even though the spatial cut-off range and the hydrogen diffusivity in the electrode are maintained constant.

Electro-oxidation of methanol on copper in alkaline solution

The electro-oxidation of methanol on copper in alkaline solutions has been studied by the methods of cyclic voltammetry, quasi-steady state polarization and chronoamperometry. It has been found that in the course of an anodic potential sweep the electro-oxidation of methanol follows the formation of Cu III and is catalysed by this species through a mediated electron transfer mechanism. The reaction also continues in the early stages of the reversed cycle until it is stopped by the prohibitively negative potentials. The process is diffusion controlled and the current–time responses follow Cottrellian behavior. The rate constants, turnover frequency, anodic transfer coefficient and the apparent activation energy of the electro-oxidation reaction are reported.

A study on lithium transport through fractal Li1−δCoO2 film electrode by analysis of current transient based upon fractal theory

Lithium transport through fractal Li1−δCoO2 film electrode was investigated in a 1M lithium perchlorate (LiClO4)–propylene carbonate (PC) solution by analysis of current transient based upon fractal theory. For this purpose, two kinds of Li1−δCoO2 films were deposited by rf magnetron sputtering method on the substrates with different roughnesses. From the analysis of AFM image by the triangulation method, it was found that two Li1−δCoO2 film electrodes have the self-similar scaling properties with different spatial outer cut-off ranges. From the analysis of the potentiostatic current transient, it was recognised that the cell-impedance-controlled constraint at the electrode surface is changed to the real potentiostatic boundary condition (diffusion-controlled constraint) when the applied potential step exceeds a critical value and simultaneously the internal cell resistance is below a certain value in the region of single-β-phase. In addition, from the comparison between the cathodic current transients obtained from two fractal Li1−δCoO2 film electrodes, it was experimentally confirmed that the current transient shows the generalised Cottrell behaviour before the temporal outer cut-off of fractality, followed by a linear relationship with the slope of −0.5 after the temporal outer cut-off of fractality, when the real potentiostatic boundary condition is maintained at the electrode surface.

Investigation of lithium transport through LiMn 2O 4 film electrode in aqueous LiNO 3 solution

Lithium transport through LiMn 2O 4 film electrode was investigated in aqueous saturated LiNO 3 solution by analyses of the potentiostatic current transient and ac-impedance spectra. It was found that the current transient hardly shows the Cottrell behaviour, and the initial current is linearly proportional to the potential step. This strongly suggests that lithium transport through the film electrode proceeds in aqueous LiNO 3 solution by the same mechanism involving the cell-impedance-controlled constraint, as does lithium transport in non-aqueous organic solution such as LiClO 4 in propylene carbonate (PC). However, the cell-impedance in aqueous LiNO 3 solution was determined to be much smaller by more than one order in value than that cell-impedance in non-aqueous LiClO 4–PC solution over the whole potential range, indicating lithium transport is markedly enhanced in aqueous electrolyte. From the comparison between the ac-impedance spectra obtained in aqueous and non-aqueous electrolytes, the reduced cell-impedance in aqueous electrolyte can be accounted for by the kinetic facility for the interfacial charge-transfer reaction in the absence of the resistive surface film as well as by the high conductivity of the electrolyte itself.

Kinetics of lithium transport through a hard carbon electrode studied by analysis of current transients

The kinetics of lithium transport through a Carbotron-P hard carbon composite electrode was investigated by analysis of the current transients based upon the modified McNabb-Foster equation. The electrode potential curve ran continuously throughout the whole deintercalation of lithium ions, without the appearance of any potential plateau. However, the anodic current transients showed inflexion points, indicating that several kinds of lithium deintercalation sites present within the electrode are kinetically distinguishable among themselves. Moreover, the anodic current transients did not follow Cottrell behaviour but Ohmic behaviour. The anodic current transients experimentally measured coincided well with those transients numerically simulated based upon the modified McNabb-Foster equation as a governing equation and the "cell-impedance-controlled" constraint as a boundary condition. This strongly indicates that lithium transport is governed by "cell impedance" and at the same time the difference in activation energies for lithium deintercalation between the four different lithium deintercalation sites existing within the electrode accounts for the different kinetics of lithium transport between these sites.

Lithium transport through the Li 1− δCoO 2 film electrode prepared by RF magnetron sputtering

Lithium transport through the Li 1− δ CoO 2 film electrode prepared by RF magnetron sputtering was investigated in a 1 M solution of LiClO 4 in propylene carbonate using the galvanostatic intermittent titration technique (GITT), electrochemical impedance spectroscopy (EIS), and the potentiostatic current transient technique. The experimental cathodic and anodic current transients in the presence of a single phase Li 1− δ CoO 2 did not follow Cottrell behaviour, but Ohmic behaviour. This means the relationship between the initial current level and the potential step obeys Ohm's law. In addition, the current transients obtained in the case of coexistence of two phases α and β were characterised by a flatter shape, as compared to those transients in the presence of the respective α and β phases. Also, during phase transformation, the instantaneous current level was proportional to the potential step, in compliance with Ohm's law. From these results, it was suggested that the flux of lithium ion at the electrode ∣ electrolyte interface during lithium transport is limited purely by the ‘cell-impedance’, not only in the presence of a single phase, but also when the two phases coexist. The value of the ‘cell-impedance’ calculated from the current transient was almost equal to the values obtained from the impedance spectra and the galvanostatic discharge curve. The current transients were modelled under the assumption of the ‘cell-impedance-controlled’ lithium intercalation and deintercalation. The current transients calculated theoretically coincided well in value and shape with those measured experimentally.

The kinetics of lithium transport through vanadium pentoxide composite and film electrodes by current transient analysis

The kinetics of lithium transport through vanadium pentoxide composite and film electrodes have been investigated in a 1 M solution of LiClO 4 in propylene carbonate using current transient technique. In the case of the vanadium pentoxide composite electrode, all the cathodic and anodic current transients experimentally measured hardly followed the Cottrell behaviour and the relation between initial current level in current transient and applied potential step held Ohmic law. Lithium transport through the composite electrode was theoretically analysed by means of the numerical simulation of the current transient under the assumption of the ‘cell-impedance controlled’ lithium transport. The current transients theoretically calculated shared quantitatively well those experimentally measured. In contrast, all the cathodic and anodic current transients experimentally obtained from the film electrode, exhibited clearly a linear relationship between logarithmic current and logarithmic time, followed by an exponential decay. From the results, it is suggested that lithium transport through the film electrode proceeds under the ‘diffusion controlled’ lithium transport towards rough (fractal) interface. The difference in the mechanism of lithium transport between through vanadium pentoxide composite electrode and through film electrode was discussed in terms of the chemical diffusivity of lithium ion and ‘cell-impedance’ of the two electrodes.

The kinetics of lithium transport through Li 1− δCoO 2 thin film electrode by theoretical analysis of current transient and cyclic voltammogram

Lithium transport through lithium cobalt dioxide thin film electrode prepared by rf-magnetron sputtering was investigated in a 1 M solution of LiClO 4 in propylene carbonate (PC) by means of analysis of current transient and cyclic voltammogram. All the experimental current transients in shape deviated markedly from the Cottrell behaviour, and the cathodic current transients intersected the corresponding anodic current transients each other. Moreover, the relation between initial current level and applied potential step followed Ohmic law. The current transient was simulated as a function of applied potential by means of the numerical analysis underlain by the ‘cell-impedance controlled’ lithium transport. The numerically simulated current transients coincided quantitatively almost with those current transients experimentally determined. The cyclic voltammograms theoretically obtained at various scan rates under the assumption of the ‘cell-impedance controlled’ lithium transport, were also quantitatively in good agreement with those cyclic voltammograms experimentally measured.

Monitoring Concentration Profiles In Situ with an Ultramicroelectrode Probe

Using an ultramicroelectrode placed inside the diffusion layer of a larger working electrode we demonstrated to which extent amperometric and potentiometric detections allow spatially resolved information at the micrometric scale, so that the composition of a diffusion layer created in the vicinity of a millimetric working electrode can be examined with adequate precision. The validity of both methods was established experimentally in steady state conditions through the investigation of a simple redox reaction as well as for more complex mechanistic situations. The amperometric detection is also used to probe a time-expanding diffusion layer, thus showing the transition from perfect Cottrellian behavior to steady state imposed by spontaneous convection.

The real meaning of Nernst's steady diffusion layer concept under non-forced hydrodynamic conditions. A simple model based on Levich's seminal view of convection

A model accounting for the role of convection in macroscopically immobile solutions (viz., not submitted to any macroscopic flow or any density gradient) is developed to predict the resulting alterations on electrochemical experiments performed at long time durations. The model is based on a seminal idea introduced by Levich, and shows that in macroscopically still solutions microscopic chaotic motion has the same effect as an apparent diffusion coefficient that depends on the distance from the electrode, x. When the electrochemical perturbation affects only the viscous sub-layer adjacent to the electrode, this apparent diffusion coefficient varies as x4. The model remarkably predicts the experimental distortions of chronoamperometric currents from their ideal Cottrellian behavior. The model is thoroughly tested with success by comparing its predictions to experimental results (current and concentration profiles) obtained for the oxidation of Fe(CN)64− in aqueous KCl.

The kinetics of lithium transport through LiNiO 2 by current transient analysis

The kinetics of lithium transport through Li 1− δ NiO 2 have been investigated in a 1 M solution of LiClO 4 in propylene carbonate using current transient technique. All the cathodic and anodic current transients experimentally measured hardly follow the Cottrell behaviour. From the linear relationship between initial current level in current transient and applied potential step, ‘cell-impedance’ was determined as a function of the electrode potential. ‘Cell-impedance’ with the electrode potential calculated from the current transient, is similar in value to that of internal cell resistance composed of solution resistance, contact resistance, and absorption resistance obtained from the Nyquist plot. Taking the variation of ‘cell-impedance’ with the electrode potential into account, the lithium transport through the Li 1− δ NiO 2 electrode was theoretically analysed by means of numerical simulation of the current transient under the assumption of the ‘cell-impedance controlled’ lithium transport. The current transients theoretically calculated quantitatively shared well those experimentally measured. Lithium transport through the Li 1− δ NiO 2 electrode being even degraded by jumping the electrode potential to the value higher than 4.20 V Li/Li + , proceeds under the ‘cell-impedance controlled’ constraint.