Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

Median Chebyshev spectroscopy of electrochemical noise

Journal of Solid State Electrochemistry - An algorithm for analyzing electrochemical noise based on Chebyshev spectroscopy using the sample median is presented. Chebyshev spectroscopy with the...     

Analysis of discrete spectra of electrochemical noise of lithium power sources

Journal of Solid State Electrochemistry - The Fourier, Daubechies, and Chebyshev transforms are used to analyze discrete spectra of electrochemical noise of lithium power sources under the...     

Discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise

A discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise is developed. Based on the discrete version of Wiener-Khinchin theorem, the theoretical discrete Chebyshev spectrum for the Markov random process is calculated. It is characterized by two parameters: the dispersion and the relaxation frequency (or relaxation time). The noise of corrosion process and the noise of recording equipment are measured. Using the theoretical Chebyshev spectrum, the Markov parameters were found both for the noise of the corrosion process and for the noise of the measuring equipment.     

The discrete Chebyshev algorithm for nonparametric estimation of autocorrelation function of electrochemical random time series

Journal of Solid State Electrochemistry - The discrete Chebyshev algorithm for nonparametric estimation of autocorrelation function of electrochemical random time series is presented. The algorithm...     

Electrochemical noise spectroscopy: Method of secondary Chebyshev spectrum

A new method of electrochemical noise diagnostics is presented: the method of the secondary Chebyshev spectrum based on the splitting of an individual spectral line in the primary Chebyshev spectrum with formation of a system of spectral lines of the secondary Chebyshev spectrum. Algorithm for calculation of the secondary Chebyshev spectrum is developed. The suggested method based on analysis of noises measured in a specific electrochemical system is tested. It is shown that the new method allows determining the differences in the state of the electrochemical system more reliably, than the method of primary Chebyshev noise spectra.     

Time-resolved electrochemical detection of discrete adsorption events

Individual binding events are observed using amperometric detection. Discrete steps in the microelectrode amperometric response correspond to the adsorption of single microspheres on the electrode surface.     

Wavelet transform-based analysis for electrochemical noise

Wavelet transforms are presented as a useful tool to analyse electrochemical noise data. Various concepts developed in the framework of wavelet transforms have been adapted to study electrochemical noise measurements. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients, which contain information about corrosion events occurring at a determined time-scale. Thus, this mathematical approach could become an alternative tool which solves the limitations of other more established procedures for the analysis of electrochemical noise data, such as statistical or Fourier transform-based methods.     

Sources of electrochemical noise in corroding systems

The electrochemical noise method is reasonably well established as a technique that can estimate corrosion rate through the electrochemical noise resistance or impedance. A more interesting potential application is the identification of the nature of the corrosion process. In this paper, a number of corrosion types are examined, and it is concluded that the majority constitute a form of shot noise, possibly with a superimposed baseline current. Methods by which parameters describing the shot noise process can be estimated from the measured data are presented. It appears to be feasible to extract the charge in the shot noise events, and their frequency, providing all of the anodic or cathodic current, is associated with these events. However, the analysis requires a number of assumptions that are not always valid, and these are discussed. Finally, some alternative methods that have been used to identify the type of corrosion are briefly discussed. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 5, pp. 557–566. The text was submitted by the author in English.     

Correction of chaotic distortions in electrochemical impedance spectra

The work is dedicated to the problem of minimization of the effect of industrial noise on electrochemical impedance. A method of moving chaotic points on the impedance curve into new positions on the complex plane is developed. Coordinates of these positions were determined using reproducible impedance measurements at two close frequencies (ω₁ and ω₂). A physically validated sample model representing a resistor–capacitor bipole was used as the basis for approximation of impedance for frequency (ω₃), where chaos is observed. It is shown that this equivalent circuit in the absence of the inductive impedance component adequately describes electric properties of the sample in the frequency range of at least half a decade. Detailed derivation of all relationships required for calculation of impedance at frequency ω₃ is provided. The developed algorithm can be used for implementation of a digital filter that allows correcting the impedance spectrum in the automatic mode. The suggested method is used to correct the impedance spectrum of Bi_1.6Cu_0.8Ti₂O_7.2 solid solution distorted by electromagnetic interference.     

Mid-infrared vibrational spectra of discrete acetone-ligated cerium hydroxide cations

Cerium(iii) hydroxy reactive sites are responsible for several important heterogeneous catalysis processes, and understanding the reaction chemistry of substrate molecules like CO, H(2)O, and CH(3)OH as they occur in heterogeneous media is a challenging task. We report here the first infrared spectra of model gas-phase cerium complexes and use the results as a benchmark to assist evaluation of the accuracy of ab initio calculations. Complexes containing [CeOH](2+) ligated by three- and four-acetone molecules were generated by electrospray ionization and characterized using wavelength-selective infrared multiple photon dissociation (IRMPD). The C[double bond, length as m-dash]O stretching frequency for the [CeOH(acetone)(4)](2+) species appeared at 1650 cm(-1) and was red-shifted by 90 cm(-1) compared to unligated acetone. The magnitude of this shift for the carbonyl frequency was even greater for the [CeOH(acetone)(3)](2+) complex: the IRMPD peak consisted of two dissociation channels, an initial elimination of acetone at 1635 cm(-1), and elimination of acetone concurrent with a charge separation producing [CeO(acetone)](+) at 1599 cm(-1), with the overall frequency centered at 1616 cm(-1). The increasing red shift observed as the number of acetone ligands decreases from four to three is consistent with transfer of more electron density per ligand in the less coordinated complexes. The lower frequency measured for the elimination/charge separation process is likely due to a combination of: (a) anharmonicity resulting from population of higher vibrational states, and (b) absorption by the initially formed photofragment [CeOH(acetone)(2)](2+). The C-C stretching frequency in the complexes is also influenced by coordination to the metal: it is blue-shifted compared to bare acetone, indicating a slight strengthening of the C-C bond in the complex, with the intensity of the absorption decreasing with decreasing ligation. Density functional theory (DFT) calculations using three different functionals (VWN, B3LYP, and PBE0) were used to predict the infrared spectra of the complexes. Calculated frequencies for the carbonyl stretch are within 40 cm(-1) of the IRMPD of the three-acetone complex measured using the single acetone loss, and within 60 cm(-1) of the measurement for the four-acetone complexes. The B3LYP functionals provided the best agreement with the measured spectra, with the VWN modestly lower and PBE0 modestly higher. The C-C stretching frequencies calculated using B3LYP are higher in energy than the measured values by approximately 30 cm(-1), and reproduce the observed trend which shows that the C-C stretching frequency decreases with increasing ligation. Agreement between C-C frequency and calculation was not as good using the VWN functional, but still within 70 cm(-1). The results provide an evaluation of changes in the acceptor properties of the metal center as ligands are added, and of the utility of DFT for modeling f-block coordination complexes.     

Analysis of electrochemical noise by means of bispectral technique

Nonlinear processes are often encountered in the practice of electrochemical and corrosion measurements. Especially, activation-controlled processes are inherently nonlinear. Taking into account investigations of electrode reactions, linear approximation is a popular approach. In this introductory paper, the possibility of extension of electrochemical noise (EN) measurements to the nonlinear regime is presented. Natural consequence of focusing on nonlinear processes is application of higher-order spectral techniques. Utilization of bispectral representation enables analysis of stationarity and linearity properties of EN. The authors present algorithm enabling assessment of both quantities and also exemplary analysis of noise generated during cathodic polarization, which is important for corrosion protection. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, 13–16 March 2005. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, March 13–16, 2005.     

Pitting corrosion in steel and electrochemical noise intensity

Electrochemical noise data in the presence of pitting corrosion were analyzed. A correlation between the intensity of the observed noise and mass loss of steel electrodes was recognized. The registered noise was decomposed into a set of band limited components using wavelet transform. It has been observed that the standard deviation of the chosen component was more strictly correlated with mass loss of electrodes than the standard deviation of the other components. The frequency band of the chosen component was adequate to the band where energy of transients, typical for pitting corrosion dominated. The measurement results were obtained only for the limited number of electrodes due to a very long time of noise observation.     

Theory of the shot noise in electrochemical bridge contacts

Correlation functions of the current and the noise power for a redox-group-containing electrochemical tunnel contact are calculated under the assumption on a shot character of the electron tunneling. Weak and strong interaction between the redox group and electrodes is considered. Overvoltage dependence of the Fano factor at different bias-potentials is found. The conditions of passing of the calculated dependences into the Schottky law are formulated.     

Calculation of noise resistance by use of the discrete wavelets transform

Discrete wavelet transform (DWT) was applied to the electrochemical noise analysis (ENA). The original potential noise and current noise were first decomposed into a series of details D_j and approximation A_j by DWT at increasing scale j. Then, the noise resistance R_n(j) was calculated as a ratio of the standard derivation of the reconstructed potential noise to the reconstructed current noise. The experimental results demonstrated that the DWT could improve the calculation of the classic noise resistance R_n and spectrum noise resistance R_sn(f) because it could remove the low frequency trend coupled in the potential or current fluctuations very well. In addition, the variation of R_n(j) with j may provide an insight into the prevalent corrosion mechanisms.     

Shot noise sets the limit of quantification in electrochemical measurements

Detection of single molecules, particles, and rapid redox events is a challenge of electrochemical investigations and requires either an amplification strategy or significant averaging for the electrochemical current to exceed the noise level. We consider the minimum number of electrons required to reach the limit of quantification in these electrochemical measurements. A survey of the literature indicates that the state-of-the-art limit in current detection for different types of measurements (e.g. voltammetry, single-molecule redox cycling, ion channel recordings of single molecules, metal nanoparticle collision, and phase nucleation) is independent of the nature of the measurement and increases linearly with reciprocal response time, Δt^?1, over ～5 orders of magnitude (from ～10 to ～10⁶ s^?1). We demonstrate that the practical limit of quantification requires cumulative measurement of ～2100 electrons during Δt and is determined by statistics of counting electrons, that is, the shot noise in the current.     

Monitoring the heterogeneity in single cell responses to drugs using electrochemical impedance and electrochemical noise

Impedance spectroscopy is a widely used technique for monitoring cell–surface interactions and morphological changes, typically based on averaged signals from thousands of cells. However, acquiring impedance data at the single cell level, can potentially reveal cell-to-cell heterogeneity for example in response to chemotherapeutic agents such as doxorubicin. Here, we present a generic platform where light is used to define and localize the electroactive area, thus enabling the impedance measurements for selected single cells. We firstly tested the platform to assess phenotypic changes in breast cancer cells, at the single cell level, using the change in the cell impedance. We next show that changes in electrochemical noise reflects instantaneous responses of the cells to drugs, prior to any phenotypical changes. We used doxorubicin and monensin as model drugs and found that both drug influx and efflux events affect the impedance noise signals. Finally, we show how the electrochemical noise signal can be combined with fluorescence microscopy, to show that the noise provides information on cell susceptibility and resistance to drugs at the single cell level. Together the combination of electrochemical impedance and electrochemical noise with fluorescence microscopy provides a unique approach to understanding the heterogeneity in the response of single cells to stimuli where there is not phenotypic change.

A light addressable single-cell impedance technique for cell adhesion monitoring and measurement of a cell''s drug response based on electrochemical noise is introduced.     

Pitting corrosion characterization by electrochemical noise measurements on asymmetric electrodes

Pitting corrosion of stainless steel electrodes can be detected by presence of characteristic transients in a current that flows between two short-circuited electrodes. Various methods for detection of these events are proposed in literature but still a more thorough analysis is needed. The authors present another method that preserves information about transient occurrence and their characteristic time constant. We suggest the application of the bispectrum or, even with better results, its integrated function for transient detection during metastable pitting. This method was successfully applied for noise recording at pitting corrosion of stainless steel 0H18N9 when exposed to electrolyte (1-M concentration of FeCl₃ in distilled water).     

A novel electrochemical noise sensor applied to detect food safety

A novel electrochemical noise (EN) sensor was elaborately designed to detect the metal residue in energy drinks. By calculating the characteristic parameter, noise resistance R _n, obtained from the EN data, the tin and iron residue can be semiquantitatively evaluated. In addition, R _n was further compared with the inductively coupled plasma mass spectrometer (ICP-MS) results. Accordingly, an interesting relationship was found between the EN data and ICP-MS results. The experimental results reveal that R _n can indirectly reflect the corrosion-induced metal release from the packaging materials; a lower R _n means a higher metal release. This electrochemical sensor has potential applications in evaluating food safety because of its fast, economic and in-situ features.