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.     

The fractal theory of electrochemical diffusion noise: Correlations of the third and fourth order

Based on the Langevin linear stochastic equation, the correlations of the 3rd and 4th order for thermal fluctuations of the electrode potential are studied in an electrochemical ac circuit involving an electric double layer capacitance, a resistance of steady-state diffusion, and a Warburg impedance. The presence of the noisy Warburg impedance in the ac circuit makes the Langevin linear stochastic equation fractal. The analogy with the steady-state diffusion noise and with the noise of the barrierless-activationless slow discharge is used. Equations for bispectrum and trispectrum of electrode-potential activation are shown. It is demonstrated that the intensity of bispectrum and trispectrum is determined exclusively by the noise of the steady-state diffusion resistance if one of frequency arguments in the polyspectrum is zero. It is found that in an electrochemical ac circuit containing the noisy Warburg impedance, the asymptotics of establishment of equilibrium values of asymmetry and excess of electrode-potential fluctuations (thermalization) obeys the power law rather than the exponential law. Furthermore, the excess thermalization proceeds faster as compared with asymmetry thermalization. The performed theoretical analysis of correlations of the 3rd and 4th order of the fractal noise of electrochemical diffusion is of practical interest. For instance, the concepts of the fractal electrochemical noise can be used in the noise diagnostics of devices of electrochemical power engineering and in the noise methods for studying corrosion systems.     

The Kramers-Moyal expansion for electrochemical stochastic diffusion

It is proved that there is a general stochastic equation, according to which any random process in the transient mode can be presented by spatially homogeneous Kramers-Moyal expansion. In the electrochemical stochastic diffusion, an integral of the fluctuation component of electrode potential over the time plays the role of spatial coordinate. Based on these two facts, we derived a spatially homogeneous Kramers-Moyal expansion for the propagator of electrochemical stochastic diffusion. By using the limiting transition to long observation times, we obtained a time and spatially homogeneous asymptotic Kramers-Moyal expansion for the propagator of asymmetric non-Gaussian electrochemical stochastic diffusion. Under the conditions of Gaussian electrochemical noise, the asymptotic Kramers-Moyal expansion turns into the Einstein stochastic diffusion equation. The method of determining time and spatially homogeneous asymptotic Kramers-Moyal expansion for the propagator of asymmetric non-Gaussian electrochemical stochastic diffusion may be useful in the stochastic theory of slow electrochemical discharge and in the electrochemical noise diagnostics.     

Theory of the first encounter with the boundary by a stochastic diffusion process in an equilibrium electrochemical <Emphasis Type="Italic">RC</Emphasis>-circuit

The methodology of electrochemial impedance is used for finding the characteristic function of the random time of the first encounter with the boundary by a process of electrochemical stochastic diffusion in an equilibrium ac circuit containing a double layer capacitance and a noisy charge-transfer resistance. The Nyquist diagram of the characteristic function suggests that the method of the first random encounter with the boundary by electrochemical stochastic diffusion may prove to be useful in the noise diagnosis of objects and devices of electrochemical power engineering and also in comparative studies of electrochemical corrosion processes.     

In situ NMR diffusion coefficients assessment of lithium ion conductor using electrochemical priors and Arrhenius constraint——A computational study

In situ NMR measurements of the diffusion coefficients,including an estimate of signal strength,of lithium ion conductor using diffusion-weighting pulse sequence are performed in this study.A cascade bilinear model is proposed to estimate the diffusion sensitivity factors of pulsed-field gradient using prior information of the electrochemical performance and Arrhenius constraint.The model postulates that the active lithium nuclei participating electrochemical reaction are relevant to the NMR signal intensity,when discharge rate or temperature condition is varying.The electrochemical data and the NMR signal strength show a highly fit with the proposed model according our simulation and experiments.Furthermore,the diffusion time is constrained by temperature based on Arrhenius equation of reaction rates dependence.An experimental calculation of Li_4Ti_5O_(12)(LTO)/carbon nanotubes(CNTs) with the electrolyte evaluating at 20 ℃ is presented,which the b factor is estimated by the discharge rate.     

Software and Instrumentational Methods of Enhancing the Resolution in Electrochemical Noise Measurements

Several methods of enhancing the signal-to-noise ratio for instrumentation designed to measure electrochemical noise are practically tested. The experiments are carried out using model RC-circuits and lielectrolyte electrochemical cells. Strong limitations in the tested objects’ impedance values are found due to the input current noise of the instrumentation, especially during the parallel connection of several channels. The advantages of a two-channel scheme for automatically compensating the instrument’s self noise are demonstrated. Different methods of lowering the dispersion of the frequency dependences of the spectral power density of electrochemical noise are compared. It is shown that averaging over segments with an overlap is the most effective method but averaging over frequencies can lead to large distortions when investigating electrochemical systems.

     

Sensing mechanism of non-equilibrium solid-electrolyte-based chemical sensors

Solid electrolytes can be used in several different types of chemical sensors. A common approach is to use the equilibrium potential generated across a solid electrolyte given by the Nernst equation as the sensing signal. However, in some cases, stable electrode materials are not available to establish equilibrium potentials, so non-equilibrium approaches are necessary. The sensing signal generated by such sensors is often described by the mixed potential theory, in which a pair of electrochemical reactions establishes a steady state at the electrode, such that the electrons produced by an oxidation reaction are consumed by a reduction reaction. The rates of both reactions depend on several factors, such as electron exchange, active area, and gas phase diffusion, so establishment of the steady-state potential is complex and alternative explanations have been proposed. This paper will review and discuss the mechanisms proposed to explain the sensor response of non-equilibrium-based electrochemical sensors.     

A macrokinetic model of redox sorption on metal–ion exchanger nanocomposites at electrochemical polarization

A conceptual macrokinetic model of redox sorption on metal–ion exchanger nanocomposites upon electrochemical polarization is formulated and a corresponding mathematical model is constructed. The solution to a multi-point boundary value problem for the concentration of a sorbed substance (oxygen) is given. The concentration front of the sorbed substance is characterized by a concentration gradient in the near-surface layer of the solution, by layers of the products of metal oxidation in the composite forming due to both external and internal diffusion transfer, and by chemical and electrochemical reactions at the interphase boundaries. A considerable reduction in the concentration gradient of the sorbate in layers of the products of oxidation of metal and the growth of the diffusion layer of the solution with polarizing currents weaker than the limiting diffusion current are noted.     

Understanding the effects of diffusion coefficient and exchange current density on the electrochemical model of lithium-ion batteries

The diffusion coefficient and exchange current density are the two dominant parameters that determine the electrochemical characteristics of the electrochemical battery model. Nevertheless, both parameter values are generally adopted from well-known literature or experimental data measured under limited conditions and are sometimes overfitted to match actual electrochemical behaviors without full consideration. Herein, the diffusion coefficients and exchange current densities of a LiNi_0·4Mn_0·3Co_0·3O₂/Li cell are measured and applied to the electrochemical model (based on Newman's model) using four different electrochemical methods: galvanostatic intermittent titration technique (GITT), potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS), and cyclic voltammetry (CV). Without any fitting, the model adopting the diffusion coefficient and exchange current density measured from PITT and EIS, respectively, simulates the actual voltage–capacity profiles well. Thus, this case study provides a valuable opportunity to understand the advantages and disadvantages of each measurement method in obtaining key experimental parameters for electrochemical battery models.     

Theory of Electrochemical Transducer of an Alternating Flux, Based on a Two-dimensional Cathode-Grid Model

Alternating diffusion current, caused by small oscillations of flow rate, is calculated using a two-dimensional model of an electrochemical flux transducer containing numerous parallel cylindrical cathodes. Fields of the flow velocity and depolarizer concentration in the interelectrode space are determined by numerically solving equations of hydrodynamics and convective diffusion. Frequency dependences of amplitude and phase of a harmonic diffusion current are obtained for a wide frequency range.     

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.     

Electrochemical reactivity at redox-molecule-based nanoelectrode ensembles

A model describing electrochemical reactivity at nanoelectrode ensembles consisting of redox-molecule-based active sites immobilized on otherwise passivated electrode surfaces is presented. A mathematical treatment in terms of hemispherical diffusion of redox-active solutes to a layer of independent molecule-based nanoelectrode sites is shown to be equivalent to one in terms of a bimolecular diffusion-limited reaction between a layer of immobilized redox molecules and a reservoir of redox-active solutes. This equivalence derives from the fact that in both cases the mass-transfer problem is essentially that of hemispherical diffusion. The model is further developed to consider rate limitation by both the bimolecular redox reaction between the active-site molecule and redox molecules in solution and the heterogeneous redox reaction between the electrode and the active-site molecule. Analytical expressions are derived for the current–voltage relation corresponding to catalyzed electron transfer at an ensemble of redox-molecule-based nanoelectrode sites, and the expressions are used to interpret preliminary data for ultrasensitive electrochemical detection in flow streams via an electrochemical amplification process that is thought to involve redox mediation by individual analyte molecules adsorbed onto monolayer-coated electrodes.     

Bayesian uncertainty quantification in inverse modeling of electrochemical systems

This present study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modeling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are transported in electrolyte solutions under an applied current. Such systems are typically described by the Planck-Nernst equation in which the unknown material properties are the diffusion coefficient and the transference number assumed constant or concentration-dependent. These material properties can be optimally reconstructed from time- and space-resolved concentration profiles measured during experiments using the magnetic resonance imaging (MRI) technique. However, as the measurement data is usually noisy, it is important to quantify how the presence of noise affects the uncertainty of the reconstructed material properties. We address this problem by developing a state-of-the-art Bayesian approach to uncertainty quantification in which the reconstructed material properties are recast in terms of probability distributions, allowing us to rigorously determine suitable confidence intervals. The proposed approach is first thoroughly validated using “manufactured” data exhibiting the expected behavior as the magnitude of noise is varied. Then, this approach is applied to quantify the uncertainty of the diffusion coefficient and the transference number reconstructed from experimental data revealing interesting insights. © 2018 Wiley Periodicals, Inc.     

Gas Diffusion Electrodes for Use in an Amperometric Enzyme Biosensor

The preparation of gas diffusion electrodes and their use in an amperometric enzyme biosensor for the direct detection of a gaseous analyte is described. The gas diffusion electrodes are prepared by covering a PTFE membrane (thickness 250 μm, pore size 2 μm, porosity 35%) with gold, platinum, or a graphite/PTFE mixture. Gold and platinum are deposited by e‐beam sputtering, whereas the graphite/PTFE layer is prepared by vacuum filtration of a respective aqueous suspension. These gas diffusion electrodes are exemplarily implemented as working electrodes in an amperometric biosensor for gaseous formaldehyde containing NAD‐dependent formaldehyde dehydrogenase from P. putida [EC. 1.2.1.46] as enzyme and 1,2‐naphthoquinone‐4‐sulfonic acid as electrochemical mediator. The resulting sensors are compared with regard to background current, signal noise, linear range, sensitivity, and detection limit. In this respect, sensors with gold or graphite/PTFE covered membranes outclass ones with platinum for this particular analyte and sensor configuration.     

瞬时离子释放扩散模型及熔盐电解固态WS_2制备纳米W的液相扩散研究

固态化合物熔盐电解冶金在21世纪初被提出后受到学术界和工业界的广泛关注.根据固态化合物电解的动态三相电化学界线模型,固态金属氧(硫)化物阴极在电解还原过程中,涉及O2?(S2?)在电解生成的多孔金属层中的液相扩散,但由于一直以来缺乏方便可靠的理论和实验方法,相关传质过程动力学的研究鲜有文献报道.本文引入多孔电极瞬时离子释放扩散模型,以粉末微腔电极为微型多孔电极,设计双电势阶跃实验研究了WS2在等摩尔比NaCl+KCl熔盐中电解时固态阴极中的液相扩散.实验结果与理论模型符合良好,973 K时,硫离子在孔隙率为69%的多孔金属钨层中的扩散系数为0.92×10?5 cm2/s,扩散活化能为53.4 kJ/mol.研究表明,二硫化钨在NaCl+KCl混盐体系中能够快速电解还原生成纳米金属钨,其中,S2?的扩散传质是整个电解过程的速度控制步骤.     

吡虫啉电化学性能研究

应用循环伏安法研究了吡虫啉（IDP）在玻碳电极的电化学行为. 结果表明：IDP的还原反应是不可逆的,且受扩散控制,电子转移数4,扩散系数DR 2.44×10-6cm2?s-1,反应活化能Ed 9.33 kJ?mol-1.     

Two-parameter stochastic resonance in a model of electrochemical oxidation of formic acid on Pt

Stochastic resonance (SR) is shown in a two-parameter system, a model of electrochemical oxidation of formic acid on Pt. The driving current and the saturation coverage for carbon monoxide are two control parameters in this model. Modulation of an excitable focal stable state close to a Hopf bifurcation by a weak periodic signal in one parameter and noise in the other parameter is found to give rise to SR. The results indicate that the noise can enlarge a weak periodic signal and lead the system to be ordered. The scenario and novel aspects of SR in this system are discussed.     

The effect of partial charge transfer on the electrochemical turbulent noise

Theoretical analysis of the effect of electrode potential on the spectral density of random alternating current emerged in electrochemical cell under the action of turbulent pulsations of the electrolyte solution velocity is carried out. An impedance model of metal electrode dissolution reaction, including two adsorption stages, is suggested, with allowance for the oxidized ion diffusion in electrolyte solution. It is known that in terms of the Ershler-Randles model, at low frequencies the experimentally measured slope of bilogarithmic frequency dependence of spectral density equals 3, which is characteristic of the diffusion control; at high frequencies the slope equals 4, which is characteristic of the kinetic control. It is shown that for the model of impedance of the two-stage adsorption oxidation process, in the middle segment of the spectrum the local slope must decrease down to 2, provided the first oxidation stage, which proceeds within the inner electrical double layer, is slow; the local slope must increase up to 6 (or 5, for diffusion control), provided the second oxidation stage (the partially oxidized ion desorption to solution) is slow. The “height” and “width” of the slope local changes appeared explicitly depending on the parameters of the partial charge transfer. This makes the turbulent noise method somewhat superior to the impedance method in the studying of the above-specified reaction type.     

Étude des comportements déterministe et stochastique de l'interface électrochimique à l'aide de corrélateurs numériques

It is shown that correlation methods are particularly suited for analysing the deterministic and stochastic behaviour of an electrochemical interface. The electrode impedance, which exhibits the deterministic behaviour, can be measured by correlation by means of a white noise; this method allows us to perform very fast measurements. The electrochemical noise, which exhibits the stochastic behaviour, is measured by a crosscorrelation method. Characteristics and performances of these methods are analysed in detail taking account of requirements of the polarization control. These methods are applied to the experimental study of some electrochemical interfaces.     

Electrochemical noise of a hydrogen-air polymer electrolyte fuel cell operating at different loads

The electrochemical noise of a polymer membrane hydrogen-air fuel cell operating at different load currents was measured in serial experiments. Spectral power densities of the noise are shown to be divided into three regions. At frequencies greater than 3–10 Hz, the spectrum dependence has a constant slope of ??2 in the bilogarithmic coordinates. At frequencies 0.3–5 Hz, there is a horizontal plateau in which length is determined by the value of a load. At frequencies less than 0.3 Hz, the dependence of spectral power density has a slope of ??2. Medium-frequency plateau and high-frequency slope of spectral power densities of the noise were approximated by model RC circuits. The values of Faradic resistance and double-layer capacitance connected in parallel were obtained from the electrochemical impedance data. At load voltages higher 0.5 V, the height of the plateau was shown to be proportional to the 2.68 power of the load current value.