Search

Electrochemical impedance spectroscopy was used to study electrochemical lithium insertion into the electrodes based on germanium nanowires in a temperature range of +20 to −40 °C. Since such electrodes have a regular structure and do not contain binders and conductive additives, they are described by a relatively simple equivalent circuit including the electrolyte resistance (Rs), the resistance of the solid electrolyte film (RSEI) on the surface of germanium nanowires, the capacitance of the solid electrolyte film (CSEI), the charge transfer resistance (Rct), a constant phase element (CPE), reflecting the capacitance of the double layer, and the Warburg impedance (W), reflecting the diffusion of lithium in germanium. It is characteristic of the RSEI and Rct values to grow with an increase in the lithiation degree from 0.3 to 0.9, respectively, by 28% and 16%. A decrease in temperature leads to an increase in the values of Rs, RSEI, and Rct in accordance with the Arrhenius law with activation energies of 21.8, 24.1, and 36.5 kJ/mol, respectively. At the same time, the SEI capacity is independent of temperature.

After exploring in Part I the redox behaviour of CaCl2 melts at 900 °C in presence of residual moisture impurity and those containing CaCl2.2H2O and Ca(OH)2, which resulted in enhancement of effect of moisture in voltammetric features, present work was focussed on extending the experimental work to analyze the impedance response in pre-electrolysed CaCl2 melt at tungsten electrode in potential range −0.20 to −2.10 V (vs. Ni | NiO as reference) at 900 °C using electrochemical impedance spectroscopy. Two equivalent circuit models were selected for fitting of experimental complex impedance data; one being applicable to potential range −0.20 to −1.60 V and the other one to −1.70 to −2.10 V. Effective capacitance was calculated from values of constant phase element to confirm the strong adsorption effects at specific potentials. Impedance data were also validated by Kramers–Kronig transforms where they showed good compliance fit with pseudo- χ 2 being in range 10 - 6 to 10 - 4 . Impedance response in CaCl2 melts containing CaCl2.2H2O and Ca(OH)2 was expected to be similar as mechanism of cathodic reduction of [ ( CaOH ) 2 2 + ] adsorbed in those melts was exactly same, which was established in Part I of work.

The success of fractional-order fractance (FOF) as a modeling tool in (photo)bio(electro)chemical systems can be readily gauged by the large body of research work that has been conducted over the past few years in terms of materials fabrication, building integer-order emulators of their behavior, as well as applications in filter design, controller design, modeling of energy storage devices and biomaterials. The impedance of FOF has the general form Z α ( s ) = k α s α where k α and α are real constant and s = j ω is the complex Laplace number. In this work, we investigate the possibility of decoupling the magnitude and phase properties of a FOF, and the application of this modified circuit element in the modeling of spectral electrochemical data. The proposed modification relies on the complex parametric function j β ω α = j β - α s α which can been viewed as a phase-shifted version of s α = ( j ω ) α by a β -dependent constant angle. This extra degree of freedom is expected to be useful in facilitating the modeling of more complex systems in which the classical FOF fails, and is here verified on the low-frequency response of a lithium-ion battery showing unstationary and/or nonlinear behavior.

This report reviews the time-dependence of the double layer (DL) capacitors in the polarized potentials domains and the related subjects, which have been observed as the behavior of the constant phase element (CPE). The DL capacitance decreases with an increase in the ac-frequency of the applied voltage, obeying a power law of the frequency. This variation necessarily yields an electric resistance component at the interfaces. The DL resistance does not really exist but is involved inevitably in the measured current as a result of the time-dependent capacitance. It cannot be discriminated against the heterogeneous kinetics with the Butler-Volmer type. The frequency-dependence agrees with the behavior of the CPE. The DL capacitance is brought about by orientation of solvent molecules, independent of concentrations of salts, kinds of salts, and applied dc-potential. The orientation is modeled by combination of the external electric field, the image force of polarized charge of solvent on the electrode, and the interaction of nearest neighboring solvent molecules. The combination belongs to cooperative phenomena because the orientation is competitive with the molecular interactions energetically. The competition generates two-dimensional local phases, prolonging the orientation much larger than flip rates of solvent dipoles.

The electric double layer capacitances for a series of titanium dioxide based composite nanotube-arrays (TNTAs, Pt/TNTAs, CdS/TNTAs, CdS/Pt/TNTAs) in aqueous solutions were examined at the polarized potential. As a result, the capacitance increases with a decrease in the ac-frequency, obeying the inverse of the power law of the frequency. The power law is demonstrated to be equivalent to the constant phase element. The intensity of frequency dispersion varies with nanoarrays as to different nano architectonics and materials. The CdS coated TNTAs yield the largest specific capacitance of 2.33 mF cm − 2 at a frequency of 1 Hz, which is about 9 times higher than the capacitance obtained from bare TNTAs at the same condition. The coating of Pt, however, shows less capacitive behavior with more obvious frequency-dispersion.

We present the theoretical underpinnings for the use of a constant phase element (CPE), along with the potential-step test method (PSM), to determine the parameter values of a CPE-RP Randles-type circuit model from the transient-current response. Specifically, we analyze the potential-step hold time covering the fractional-order dynamic transition between the sufficiently short times, in which the current measured is practically due to the non-ideal interfacial capacitance, and the longer times corresponding to a current practically faradaic. An interface of biomedical interest consisting of a gold electrode immersed in a 0.9% NaCl physiological saline solution was analyzed using both PSM and impedance measurements.

In this work conductive polymeric polyaniline (PANI) nanofibers are prepared by a fast chemical method and in-situ assembled with electrostatic double-layer (multi-wall carbon nanotubes, MWNTs) and pseudocapacitive materials (metal oxides) to construct MWCNT/PANI, NiCo2O4/PANI and NiCo2O4/MWCNT/PANI coral-like nanostructured composites for electrochemical energy storage electrodes. X-ray diffraction, Raman spectroscopy, nitrogen adsorption isotherms, and scanning electron microscopy (SEM) are used to analyze the structure of the resulting composite materials. Afterwards, electrochemical energy storage electrodes are prepared using the obtained nanostructured composites on glassy carbon (GC), and electrochemical tests are performed. The specific capacitance of PANI nanofibers, MWCNT/PANI, NiCo2O4/PANI and NiCo2O4/MWCNT/PANI coral-like nanostructured composites are 402, 645, 617 and 725 F/g, respectively, at the current density of 1 A/g. The analysis of electrochemical impedance spectroscopy (EIS) data in this work reported perfectly by constant phase element (CPE) and provided trustable method to compare nanostructured composites.

The double layer capacitance per weight of graphene (GN) flakes in aqueous solution at the polarized potential increases with a decrease in the ac-frequency, obeying the inverse of the power law of the frequency. The power law is demonstrated to be equivalent to the constant phase element. The frequency-dependence increases with the thickness of the GN films. Thus, the lower the frequency and the thinner the film is, the larger is the capacitance density per weight. This is confirmed by cyclic voltammetry for several thickness of GN films and several scan rates. Resistance-like voltammograms at thick films are caused by frequency-dispersion. The overall capacitive properties of the GN films are as follows: the thickness of one GN flake is estimated to be 2 nm in average from the comparison of the thickness with the capacitances at the HOPG, which is consistent with values by the STM and AFM images.

An analytical formula for the impedance of a disk electrode for general local interfacial impedances has been derived. The formula indicates that the current and potential distributions will affect the impedance data when the measurement frequency is close to or higher than certain critical value. For capacitive or Warburg-like local interfacial impedances, both relevant for porous and intercalation electrode films, the criterion is the same as that previously obtained by Orazem, Tribollet and co-workers through numerical simulation (Huang et al., 2007). Numerical simulation performed here for square and rectangular electrodes show that the criterion will be similar to that for the disk but with the shorter edge length of the electrode playing the role of the disk radius. The local impedances calculated for the square and rectangular electrodes are qualitatively similar to those of the disk. However, for square or rectangular electrodes the current-distribution effects lead to a different appearance in the various plots of the global impedance (impedance-plane plots, Bode plots, etc.) than those for the disk. This is suggested to be due to the “edge-like” and “center-like” local admittances receiving different weight when summed up to the global impedance of the electrode.

A phenomenological theory of electric double layer (EDL) polarization of an electrode (in the absence and presence of electroactive species) is obtained using the Debye–Falkenhagen equation for the potential. The influence of surface heterogeneities on the compact layer causes the distribution in relaxation time, resulting in constant phase element (CPE) response. This contribution of the compact layer is included through the current balance boundary constraint at the outer Helmholtz plane. The results for the impedance and the capacitance are obtained in terms Debye screening length and dynamic polarization length which is dependent on the surface heterogeneity parameter. At frequencies less than the characteristic compact layer relaxation frequency, the EDL is controlled by the compact layer dynamics and shows CPE response. The intermediate frequencies show the emergence of pseudo-Gerischer and pseudo-Warburg like behavior for systems with lower concentration and lower diffusion coefficients of ions. EDL behaves like a resistor at larger frequencies. Theoretical results capture various observations in the experimental capacitance dispersion data.

The behavior of electric double layers at polarized interfaces in KCl solutions is revisited in order to examine properties of the constant phase element (CPE). We pay attention specifically to frequency-dependence of both the capacitance and the resistance. Two parallel platinum wires immersed in solution are used as insulator-free electrodes. They avoid stray capacitance or irreproducibility of impedance caused by incompleteness of electric shield of electrodes. The Nyquist plot takes approximately a straight line because the in-phase component, Z 1 is inversely proportional to ac-frequency, similar to the capacitance. Since Z 1 extrapolated to zero separation of the electrodes is non-zero, a resistance is present at the double layer in parallel form. It is not a Faradaic resistance because of absence of any electroactive species. The parallel resistance is inversely proportional to the frequency, whereas the capacitance decreases with a linear relation to logarithm of the frequency. The latter is responsible for the frequency-dependence of the former. The parallel resistance is the apparent one involved inevitably in ac-measurements of the capacitance. Values of the capacitance are independent of concentration of KCl in the domain from 0.1 mM to 3 M.

This article deals with the influence of interfacial CPE (constant phase element) behaviour on linear scan voltammograms (LSV) and cyclic voltammograms (CV). Theoretical investigation is carried out using the generalised Mittag–Leffler function which arises naturally in the solution of fractional order integral or differential equations. First, ohmic drop and CPE effects are analysed in the absence of electrochemical reaction through the closed-form expression of current vs. time. Next, the combined effects of ohmic drop, CPE and faradaic processes are modelled using the integral equation approach. Finally, the example of one-step electrochemical reaction, investigated under semi-infinite linear diffusion conditions, is dealt with for illustration of the calculation procedure.

Semiconducting lead sulfide film was deposited on Stainless Steel (SS) electrode by cyclic voltammetry (CV) at room temperature. Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry were used to investigate the electrochemical properties of PbS film in Na 2 SO 4 solution. The voltammetric results showed that oxidative dissolution of PbS film occurred at about 0.21 V vs. Ag/AgCl and total film detachment from the surface occurs with increasing potential. It is concluded that the electrode surface was not passivated by sulfur produced from oxidative dissolution of PbS film. Also, cathodic reduction of the film continued to beyond the hydrogen evolution at −1.35 V vs. Ag/AgCl. Capacitive parts of impedance spectra showed frequency dispersion and constant phase element (CPE) was used instead of capacitor to simulate the interfacial capacitance in the corresponding equivalent circuit. The flat band potential and carrier concentration were determined from Mott–Schottky plot and are estimated to be −0.32 V and 1.6 × 10 23 m −3 respectively. The film was p-type semiconductor.

This paper reports an amplification procedure application of multi-functionalized gold nanoparticles (MFAuNPs) which was used for electrochemical impedance immunosensor. The modified electrode which was utilized for the affinity adsorption of protein A, was fabricated by stepwise immobilization of 1, 6-hexanedithiol, AuNPs, and IgG on the gold electrode via self-assembling technique. The interfacial properties of the modified electrodes were evaluated in the presence of Fe(CN) 6 4 - / 3 - couple redox as a probe by cyclic voltammetry and electrochemical impedance spectroscopy. An equivalent circuit model with a constant phase element was used to interpret the obtained impedance spectra. The electrochemical behavior of the redox probe was affected by the accumulation of treated substances on the electrode surface. There is no significant increase in the electron transfer resistance after the binding of protein A to IgG on the electrode surface without amplification. The changes in the electron transfer resistance on the IgG-modified electrodes became more sensitive after the MFAuNPs were introduced for signal amplification. The increments of amplified impedance showed good correlation of the detection of protein A in the range of 5–1000 pg/mL with a detection limit of 1 pg/mL. The development of a rapid, facile, and sensitive amplification method capable to detect biomolecules in the picogram range, utilizing EIS measurement, may be achieved in this study.

Alloy 22 in acidified, NaCl brines over wide ranges in temperature and composition is characterized by high interfacial impedance, thereby illustrating its high corrosion resistance. The impedance data are shown to transform correctly in the complex plane, via the Kramers–Kronig (K–K) relations, thereby demonstrating that the system conforms to the constraints of Linear Systems Theory (LST). The interfacial impedance (and the polarization resistance, R p ) initially increased with applied potential, within the passive range, due to the growth of the passive oxide layer. At a sufficiently high potential ( V > 0.4 V SHE ), within the transpassive dissolution region, the interfacial impedance (polarization resistance) is observed to decrease with increasing voltage, due to layer thinning and/or oxidative ejection of cations from the barrier layer. The interfacial impedance data for Alloy 22 as a function of voltage can be accurately modeled using an electrical analog comprising two R//C sub-circuits in series, which in turn are in series with a R//constant phase element sub-circuit. Because this analog is in a minimum phase, passive circuit, it must satisfy the K–K transforms a priori, which confirms the compliance of the system with the constraints of LST. The rate of corrosion of the alloy was found not to depend significantly on pH (1 − ] −1 (H 2 O)), and was generally found to compare well with corrosion rates reported by other workers.

A study on the etching of monocrystalline silicon p(1 0 0) was carried out in 2 M KOH solution at 50 °C in the dark using electrochemical and surface analysis techniques such as cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS) and atomic force microscopy (AFM). Two different surface pre-treatments were used. The study was carried out at three different potentials: negative to the open circuit potential (ocp): −1.8 V saturated calomel reference electrode (SCE); near-ocp: −1.42 V (SCE); positive to the ocp: −1.18 V (SCE). From electrochemical experiments it was clear that a fundamental feature in the study of silicon etching was a time dependence. The surface of the silicon working-electrode, which is smooth at the beginning of the etching becomes rough due to the formation of pyramidal hillocks. After about 20 min the CVs remain constant, indicating that a steady state has been reached on the surface. The Nyquist plots change in dimension and shape with time and as well show a steady state after about 20 min of etching. The EIS experimental data have been fitted using an equivalent circuit containing a constant phase element and a Warburg element (W). A diffusion coefficient for electro-active species was found to be of the order of 10 −12 cm 2 s −1 . This low value is indicative of hindrance to the diffusion process due to the possible presence of polymeric species such as silicate reaction products on the silicon surface.

Composite electrodes of graphite, paraffin and potassium nickel(II) hexacyanoferrate(II) (Ni hcf) were studied by cyclic voltammetry and impedance spectroscopy at the formal potentials for the electrolytes LiCl, NaCl and KNO 3 . All Nyquist impedance plots exhibit depressed semicircles in the high frequency range changing over into straight lines with slopes smaller than 45° at lower frequencies. The experimental Nyquist plots can be well described theoretically with a new model based on the well known Randles model. In the new model, the double layer capacity as well as the Warburg impedance for semi-infinite diffusion are replaced by constant-phase elements taking into consideration an inhomogeneous electrode surface and diffusion of the cations in an electrode with inhomogeneities. The model enables the determination of the rate constants of the ion transfer (of the order of 10 −6 m s −1 ) between the solution and the solid, the double layer capacities (of the order of 0.3 μF) of Ni hcf particles, the diffusion coefficients of the cations in the Ni hcf (of the order of 10 −8 cm 2 s −1 ) as well as the distribution coefficients referring to the inhomogeneities at the electrode surface and in the bulk of the electrode.

Electrochemical capacitors made of activated carbon fabrics containing different compositions of surface oxides are analyzed using ac impedance spectroscopy. The oxides are introduced and controlled via HNO 3 treatment followed by thermal treatment at different temperatures within 150–900 °C. The impedance spectra showed that the overall resistance mainly came from the fiber contact resistance, which was an increasing function of oxide number, while the overall capacitance was contributed by the interface inside micropores. Oxidation enhanced the specific capacitance of the electrodes, but it was found that a thermal treatment temperature of 450 °C gave the highest capacitance. Constant phase element (CPE) analysis of the capacitive behavior showed insignificant deviation from ideality, indicating the low resistance in the carbon micropores as well as the domination of the double layer mechanism in energy storage. Thus, the capacitance increase from oxidation resulted mainly from the double layer mechanism as well. The deviation from ideality was more obvious for lower temperature treated electrodes, indicating that the surface oxides that desorb as CO 2 upon heat treatment may enhance formation of aggregates to retard the charge process, while the surface oxides that desorb as CO are responsible for the promotion of the double layer capacitance.

Differential capacitance versus frequency curves simulated for different equivalent circuits representing different cases of anion adsorption have been analyzed. The analysis showed that in all cases with an ideal, homogeneous electrode surface, the real value of the differential capacitance, representing the sum of the double layer and adsorption capacitances (independent of frequency) could be obtained only at frequencies lower than about 2 Hz. In the case of real surfaces, presented by introduction of a constant phase element instead of a double layer capacitance, differential capacitance versus frequency curves were found to be more complex, with no possibility to obtain values of the double layer capacitance at high and adsorption capacitance at low frequencies, since the differential capacitance was found to depend on frequency in the whole range of frequencies (10 −4 –10 5 Hz). Chloride adsorption onto the Ag(111) face in 0.01 M NaCl solution was found to follow the approach initiated in this work by introducing a constant phase element instead of the double layer capacitance. It is shown that impedance diagrams deviate from the ‘ideal double layer behavior’ and that differential capacitance versus potential curves depend on frequency. It is confirmed by the analysis of differential capacitance versus frequency curves that this is the consequence of adsorption of chloride anions presented by adsorption resistance and capacitance connected in series, as well as of inhomogeneity of the real single crystal face.

The impedance spectra of NiAlCl LDH-modified electrodes after oxidation at different dc potentials were recorded. The data were fitted to a simple Randles type cell by replacing the Warburg impedance with a mass transfer resistance in parallel with a constant phase element. The film charge transfer resistance decreased dramatically at the onset of nickel oxidation, from more than 10 6 Ω for the unoxidized films, to a minimum of about 60 Ω in a film oxidized to Ni 2.5+ , before increasing slightly for more extensively oxidized films. For the partially oxidized films, the Nyquist plots consisted of depressed semicircles at high frequency, followed by larger capacitive loops at lower frequency where the impedance was dominated by mass transport. Effective diffusion coefficients estimated from the low frequency impedance varied between 1 and 5×10 −9 cm 2 s −1 , in agreement with previous reports for proton diffusion in nickel hydroxide films. The resistive component of the mass transport impedance decreased with increase in the nickel oxidation state. The addition of [Mo(CN) 8 ] 4− caused an increase of 140 mV in the dc potential required to affect the changes in the NiAlCl film impedance spectra associated with oxidation of the nickel sites. The impedance of a redox inactive ZnAlCl film was unaffected by the use of dc conditioning potentials.

Electrochemical measurements were performed on 00Cr18Ni10 (AISI 304L) stainless steel before and after plasma nitriding in a 80% N 2 +20% H 2 gas mixture at 400 or 425 °C, resulting in the formation of a supersaturated solid solution of nitrogen in austenite (S-phase), and at 550 °C giving nitride precipitates in the diffusion zone. Polarisation curves and impedance measurements showed that in a solution of 0.1 M Na 2 SO 4 acidified to pH 3.0, the anodic reactivity of the materials increased in the sequence: unnitrided R 0 ( Q 1 [ R 1 ( Q 2 R 2 )] in which Q 1 and R 1 were assigned to the constant phase element (CPE) and the electrolyte resistance in the pores of the surface film, respectively. The latter parameters suggested that the porosity of the film on nitrided steel was higher than that on the untreated steel. The anodic behaviour of the nitrided material was explained by structural factors, such as distortion of the S-phase or chromium depletion, and also by a possible formation of NH 4 + , NO 2 − or NO 3 − from the nitrogen introduced.

Constant phase elements (CPEs) with impedance Z CPE =1/( Qs α f ) are widely used to explain electrochemical impedance spectroscopy (EIS) data. It has long been known that different circuits can explain EIS data in an equivalent manner because they exhibit identical impedance for all frequencies (two-terminal non-distinguishable (TTND) circuit). Equivalent circuits containing two CPEs are considered here. TTND circuits containing two CPEs become distinguishable, at least theoretically, if the CPE exponents are different. The experimental distinguishability of these circuits is discussed. The 12 transformation formulae between the four circuits containing two CPEs and two resistors are given for CPEs with equal exponents.

The impedance response of polymers derived from aryl amines and ring-substituted aryl amines shows a CPE behavior at low frequencies with α between 0.5 and unity. In this work, the dependence of the CPE behavior of a poly- o -toluidine film on its thickness, on the applied potential and on the electrolyte concentration is reported. The α dependence on the thickness is explained through the correlation between the film thickness and the film morphology. The α dependence on the applied potential is explained by a change in the mechanism of charge transport in the polymer, with the potential.

The relevance of the concept of ideal polarisability to solid electrodes displaying constant phase angle behaviour (constant phase element (cpe)) is reconsidered in the context of the recent dispute in this Journal [Zoltowski, 443 (1998) 149; Lang and Heusler, 457 (1998) 257]. It is shown that the cpe as a model of the electrochemical interface is ‘unphysical’ due, first of all to unattainability of the steady state after potential or current perturbation. It is also concluded that the thermodynamic equations governing the equilibria of an ideally polarisable electrode cannot be applied to an electrode modelled by cpe because the notions of the charge and double layer capacitance (Cd) are irrelevant in the framework of the cpe model. As a consequence, procedures of calculation of Cd from impedance data modelled by cpe are unjustified.

This paper is concerned with frequency dispersion in the low frequency range of electrochemical impedance measurements in thin layer cells such as electrochromic devices, conducting polymer-coated electrodes, ion exchange membranes, and in general any type of diffusion layer which exerts some hindrance to mass transport at the boundaries. New theoretical models are developed for diagnostic applications and treatment of cases in which systematic deviations from the standard models for spatially restricted diffusion impedances are found. This is done by using a generalized boundary condition in the solution of Fick’s law for a small ac perturbation. The resulting model has several satisfactory properties: (a) it generalizes in effect classical boundary conditions related to absorbing and reflecting boundaries, (b) it provides exact analytical solutions which can be tested experimentally, and (c) it provides a very simple physical picture of the origin of low frequency dispersion in film electrodes in terms of interfacial transfer functions. The properties of the generalized diffusion impedance imply that boundary effects cannot influence the impedance for frequencies in excess of the characteristic diffusion frequency ωd=D/L2. On the other hand, at low frequencies the response is a mixture of ‘volume’ and ‘boundary’ properties of the layer. Several particularized examples of blocking and non-blocking dispersive boundary conditions are studied in detail. An extended discussion is focused on a blocking interface that presents a capacitive dispersion describable as a constant phase element (CPE). Approximating expressions are derived which allow separation of boundary and volume contributions in the extreme low frequency range. This is expected to provide a powerful analytical tool for analysis in those instances where a sloped line is found in the low frequency region of the measured impedance.

Simultaneous electrochemical impedance (EI) and electroreflectance (ER) measurements were performed on ‘bare’ gold, N-acetyl-l-cysteine(NAC) modified gold, and cytochrome c (cyt c) adsorbed on a NAC modified gold electrode. The electrical impedance of the electrode interface was modeled by a series connection of a constant phase element (CPE), a capacitor, and a resistor. The analysis of the combined EI and ER data yielded the heterogeneous electron transfer (ET) rate constant at each frequency of the modulating potential. This is in contrast to previous techniques which used the frequency dependence of the EI or ER response to obtain a value of the rate constant. Assuming that the Faradaic potential was equal to the potential at the nodes of the three element impedance model yielded frequency dependent rate constants. A small modification of the three element impedance model was needed to obtain a frequency independent rate constant of 850±80 s−1. This suggests that the distribution of the potential at the electrode interface (reflected in the choice of the electrical impedance model) is an important factor in the determination of the ET rate constant.

Self-assembly of octadecyl mercaptan on gold has been investigated by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). CV experiments show that well-assembled thiol monolayers on gold are essentially free of pinhole defects. Support for the existence of ‘collapsed’ sites in thiol monolayers is obtained by comparing the apparent electron transfer rate constant, which is obtained from CV experiments at a film covered Au electrode, with the theoretical one, which is calculated by assuming electrons tunnel across the collapsed-site-free monolayer. The empirical relationship Z Rs 1:[s(jv) a ] is used to describe the film coated Au in inert electrolyte and the degree of disorder of the monolayer structure is estimated from the a value. It is demonstrated that the admittance plane plot of an ideally polarizable electrode with constant phase element behavior is a circular arc which can be used to determine a. Results of EIS experiments show that a increases sharply after the initial adsorption time and approaches its final value slowly. This is attributed to the rapid adsorption step followed by a slow crystallization process in the kinetics of alkanethiol adsorption onto the Au electrode. For a well-assembled thiol monolayer on gold, a can approach 0.99, which means that the number of collapsed sites is not large and the surface of the monolayer Au electrode is rather smooth. © 1999 Elsevier Science S.A. All rights reserved.

The energetics of electrified interfaces exhibiting constant phase element (CPE) behaviour is discussed. In the double layer region energy can be dissipated in various ways other than by charge transfer. Therefore, contrary to the statement in Zoltowski, J. Electroanal. Chem. 443 (1998) 149, an electrode with a double layer of CPE character can be an ideally polarisable electrode.

Gold single crystals oriented to expose the (111) and (210) faces were investigated using electrochemical immittance spectroscopy (EIS) in aqueous solutions of HClO 4 and KF in the double layer region with the aim of identifying and explaining the frequency dispersion of interfacial capacitance known as constant phase angle (CPA) dispersion. Au(111) and Au(210) were chosen as representing the whole range of variance of electrochemical properties of Au( hkl ) electrodes. Au(111) as the most uniform, microscopically smooth surface behaved with almost ideal capacitance in HClO 4 solutions in the whole potential range and also in KF solutions, in that case with the exception of potentials well positive to the potential of zero charge (pzc). Au(210) being microscopically the most corrugated surface displayed significant CPA dispersion in both electrolytes. In HClO 4 , dispersion on Au(210) occurred mostly in the potential region slightly positive to the potential of zero charge where the capacitance hump of the Helmholtz layer appeared. Analogous dispersion occurred on Au(210) in KF solutions only at high concentrations. The behaviour closest to ideal, dispersionless behaviour was always observed at sufficiently negative potentials. In KF solutions at positive potentials dispersion on both electrodes may be attributed to the adsorption (OH − , HF). In the intermediate potential range, close to the Helmholtz capacitance hump it can be attributed to solvent-metal interactions. Dispersion was lower in well conducting (concentrated) electrolytes and this suggests its geometrical nature is related possibly to the fractal pattern of the structured solvent.

We construct a model of ac impedance response to blocked linear diffusion that has a sloped low frequency region in the impedance plot. The approach is based on the transmission line analogy to linear diffusion, and it is equivalent to solving Fick’s law with a boundary condition that allows us to set an arbitrary impedance response at low frequencies. We argue that roughness at the blocking interface gives rise to constant phase element (CPE) response at low frequencies, and we give an impedance model function that can fit data along the whole frequency range when such a CPE is found. This is tested in an experiment of Li + insertion in Nb 2 O 5 . The model should be of significance for metal oxide thin film electrodes and modified polymer electrodes.

It is stressed that any attempt to characterise the interfacial double layer exhibiting a constant phase element (CPE) behaviour by electrical capacitance is misleading. The only possibility to obtain the value of the interfacial double layer capacitance is to ascribe to the double layer a capacitive character. Such a simplifying assumption causes a modelling error and influences all parameters of the system. The problem is analysed for several characteristic examples of an electrode system, where a simple electrode reaction takes place. The two most frequently used definitions of CPE are applied. One of them should be rejected, as intrinsically erroneous. An electrode with a double layer of CPE character can never be an `ideally polarizable electrode'. The conclusions can be qualitatively applied to all systems with an interface revealing CPE behaviour.

Two methods were used to investigate the adsorption of a human protein onto glassy carbon under well-defined conditions, i.e. in 0.1 M phosphate buffer (pH = 7.4), at T = 25°C, in the presence of equimolar (5 × 10−4 M) ferricyanide + ferrocyanide ions as steady-state indicator, with a three-electrode potentiostatic system at a bias potential of −0.67 V (SCE), under the laminar shear flow obtained by a carbon disc electrode rotated at 700 rev min−1. The protein concentration was 1 g dm−3. With the long-time method, the behaviour of the interface in its entirely was studied through the time-evolution of the impedance diagrams over a wide frequency range (sine-wave perturbation from 40 mHz to 10 kHz). With the short-time method, the time-evolution of the double-layer capacitance was determined at only one frequency, starting from the imaginary part of the impedance, on the basis of the well-known interface equivalent circuit without diffusion. However, investigation of the whole interface shoed that diffusion was actually indicated and the double-layer capacitance exhibited a fractional power-law (constant phase element) and was therefore frequency-dependent. The contribution of the characteristic electrical parameters of the interface in the overall impedance was determined. Use of the two methods justified the choice of the frequency value in the second method and showed the necessity of performing complete investigations of the interface over a wide frequency range before any capacitance measurements.

Time-resolved in situ electrochemical impedance spectroscopy measurements were performed in HF-electrolyte during the initial stages of nano- and mesoporous layer formation on p-Si and p + -Si electrodes respectively. A simple electrical equivalent circuit which involves a constant phase element to account for the distributed nature of the interfacial capacitance was chosen to model the impedance behaviour of the Si electrode. The experimental impedance spectra obtained were subjected to data validation and were then used to estimate the circuit parameters. Their time dependence is discussed in terms of the porous silicon growth mechanism.

Analysis of the frequency dependence of the impedance of boron-doped diamond thin film electrodes resulted in elucidation of their equivalent circuit. The latter generally comprises a frequency-independent capacitance (or a constant phase element) and a resistance, connected in parallel, with a series-connected “bulk” resistance. For electrodes whose impedance contains a constant phase element, a frequency-dependent Mott-Schottky plot enabled us to determine the flat-band potential. The constant phase element was shown to describe properties of the space charge region in diamond, rather than those of surface states. The behaviour of diamond electrodes is often affected by a series (“Helmholtz”) capacitance, which may be compared with the space charge capacitance of a semiconductor.

In order to explore the origins of the capacitance dispersion observed for single crystal electrodes, voltammetric and impedance measurements on Au(l 11) and Au(100), in the absence and the presence of specifically adsorbed anions, mostly Br−, have been carried out. Interfacial capacitances and rate coefficients characterizing the kinetics of adsorption have been evaluated from the impedance spectra. We present evidence that the double layer behaves as an ideal capacitance in the absence of specific adsorption. The approximation with a constant phase element yields an exponent larger than 0.99. The “capacitance dispersion” observed in the presence of specific adsorption is either assigned to a slow diffusion or adsorption process, or to transformations within the adlayer or the substrate surface.

Impedance spectroscopy was used to measure the properties of the gold electrode in 0.5 M H 2 SO 4 solution in the double-layer region (−0.25 to 1.05 V vs. sodium chloride saturated calomel electrode (SSCE)) and the region of oxide monolayer formation (1.05–1.4 V vs. SSCE). The dependence of the capacitance on potential was analysed. In both regions equivalent circuits composed of a resistor corresponding to the resistivity of the solution and a capacitor were proposed. It was found that in the double-layer region the capacitance reflected the properties of the pure gold electrode, whereas in the oxide region it depended on the coverage of the surface, corresponding partially to pure gold, MOH dipoles, oxide or a reconstructed gold surface. The improvements made by introducing a constant phase element instead of the capacitor and adding a parallel resistor in the oxide region were analysed. The roughness of the gold electrode was also estimated. The results obtained by impedance measurements were complemented by voltammetric studies to clarify the process, to confirm the measured values and to explain the meanings of the calculated parameters.