Theory of asymmetric electrochemical stochastic diffusion

Strict analysis of electrochemical strochastic diffusion due to asymmetric Brownian motion of electric charge in an equilibrium electrochemical ac circuit containing double electric layer capacitance and noisy Faradaic resistance is carried out. Cumulant analogs (for 3rd and 5th order correlations) of the Einstein formula are obtained. It is proved that equilibrium asymmetric (nongauss) stochastic diffusion is in agreement with the central limiting theorem of the probability theory. The Hurst exponent was found in the case of the nongauss components of the process of equilibrium stochastic diffusion. Apart from electrochemistry, the performed stochastic analysis of equilibrium electrochemical nongauss diffusion is also of general theoretical interest, including its application in the stochastic theory of asymmetric anomalous transport and strict theory of fluctuations at large deviations from equilibrium.     

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.     

Electrochemical symmetric stochastic diffusion

Symmetric stochastic diffusion in an equilibrium electrochemical ac circuit is studied theoretically. The electrochemical circuit included double layer capacitance and slow discharge resistance. Electrochemical analog of the stochastic Einstein formula is found. An equation is obtained for the excess of electrochemical stochastic diffusion. It is shown that an excess of electrochemical stochastic diffusion increases at high relaxation times in proportion to the observation time. It is found that excess is related to correlation between the phenomenon of electrochemical stochastic diffusion and the central limiting theorem.     

Dual Fluctuation–Dissipation Relationships between Tri- and Bispectra of the Brownian Motion

A fluctuation–dissipation analysis of nonlinear noise accompanying Brownian motion (BM) in electric systems is carried out. It is shown that, for symmetrical BM, there exists a linear set of dual fluctuation–dissipation relationships linking an equilibrium trispectrum to a derivative of a bispectrum with respect to a direct electric current (or voltage), taken at equilibrium. Analysis of an electrochemical model of BM in the form of a symmetrical slow discharge yields a proportionality coefficient.     

Impedance studies of porous lanthanum-phosphate-bonded nickel electrodes in concentrated sodium hydroxide solution

The hydrogen evolution reaction (HER) was investigated on a lanthanum-phosphate-bonded nickel (LPBN) powder electrode in 30 wt.% NaOH at 70°C using ac impedance and steady-state polarization techniques. Circuits containing one or two constant-phase elements (CPEs) in parallel with a resistance and corresponding to fractal and porous electrode models were tested in order to interpret the ac impedance data. The experimental impedance spectra were well described by the porous electrode model and the circuit containing two CPEs. The results obtained from the ac impedance and steady-state measurements allowed the mechanism and kinetics of the HER to be evaluated. Comparison of these parameters with those obtained on the polycrystalline nickel electrode in 1 M alkaline solution at 25°C indicates that an increase in activity is principally due to an increase in the real surface area.     

Electrochemical noise generated by anodic dissolution or diffusion processes

A model of the noise generated by electrochemical reactions and by diffusion is proposed. The elementary fluctuations are supposed to be the particle fluxes which are Poisson white noise. This model is successfully used to describe the experimental stochastic behaviour of two cases of non-equilibrium electrochemical interfaces: the noise generated by anodic dissolution of iron in acidic medium and that by diffusion of a reacting species in the bulk of the electrolyte.     

多壁纳米碳管空气电极的交流阻抗研究

研究了多壁纳米碳管、活性炭和石墨等空气电极的交流阻抗特性.结果表明,纳米碳管空气电极的阻抗谱由两个半圆组成,高频区半圆对应欧姆极化阻抗,低频区半圆对应电化学极化阻抗.催化剂Pt以纳米颗粒的形式沉积在碳管的外表面,明显减小了电极的欧姆阻抗和电化学极化阻抗,提高了氧还原反应的电催化活性.活性炭电极除存在电化学阻抗外,还存在薄液膜扩散阻抗(Nernst扩散),石墨电极形成的薄液膜反应区域较小,电极反应呈Warburg扩散阻抗特征,相应的电催化活性较低.采用交流阻抗等效电路分析方法,对拟合的动力学数据进行了解释.     

Cyclic Voltammetry and the Impedance of Electrodes Modified by Indium(III) Hexacyanoferrate Films

The results of studying indium(III) hexacyanoferrate films by the cyclic voltammetry and faradaic impedance methods are presented. It is shown that the synthesis from solutions with different contents of potassium salts leads to the appearance of films with different electrochemical properties. The impedance spectra exhibit semicircles corresponding to the Randles circuit and portions of the Warburg dependence. Parameters of the equivalent circuit corresponding to the obtained spectra are determined.     

How noise statistics impact models of enzyme cycles

Theoretical tools for adequately treating stochastic effects are important for understanding their role in biological processes. Although master equations provide rigorous means for investigating effects associated with fluctuations of discrete molecular copy numbers, they can be very challenging to treat analytically and numerically. Approaches based on the Langevin approximation are often more tractable, but care must be used to ensure that it is justified in each situation. Here, we examine a model of an enzyme cycle for which noise qualitatively alters the behavior of the system: fluctuations in the population of an enzyme can result in amplification and multistability in the distribution of its product. We compare master equation and Langevin treatments of this system and show that results derived previously with a white noise Langevin equation [M. Samoilov et al., Proc. Natl. Acad. Sci. U.S.A. 102, 2310 (2005)] are inconsistent with the master equation. A colored noise Langevin equation captures some, but not all, of the essential physics of the system. The advantages and disadvantages of the Langevin approximation for modeling biological processes are discussed.     

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making the physical significance of the variational method more transparent. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational Ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.     

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.     

Effect of the protonation level of poly(o-phenylenediamine) (PoPD) on the ac impedance of humidity-sensitive PoPD/poly(vinyl alcohol) composite film

A composite film consisting of poly(o-phenylenediamine) (PoPD) and poly(vinyl alcohol) (PVA) has been prepared, and the effect of the protonation level of PoPD on the response of the composite to humidity been investigated by ac impedance measurements. The electrochemical system of the PoPD/PVA composite in a humid atmosphere is represented by an electrochemical equivalent circuit containing film (R_film, C_film), Warburg (W) and interfacial (R_ct, C_dl) impedance. R_film was increased with decreasing protonation level of the PoPD in relative humidity regions higher than 40%, but it was almost independent of the protonation level in humidity regions lower than this percentage.     

尖晶石锂锰氧化物锂离子嵌脱过程的交流阻抗谱研究

用粉末微电极研究了尖晶石锂锰氧化物在不同嵌锂状态下嵌脱锂过程的交流阻 抗图谱，提出了新的等效电路模型。描述锂离子在固体中扩散的Warburg阻抗与累 积或消耗的嵌入电容在Lix MnO4中的x≤0．5时串联，0．5＜x≤1时并联。用提出 的等效电路模型分阶段拟合了实验所得的交流阻抗谱，拟合值与实验值相当吻合， 由拟合结果得到不同电位下锂离子在表面膜中的迁移电阻和电容，界面电荷传递电 阻，双层电容，锂离子在固体中扩散系数和累积或消耗的嵌入电容。     

Interfacial properties of precipitate-based ion-selective electrodes : Rotating disk impedance measurements of the Ag2S/Ag (aqueous) interface

Three-electrode rotating disk impedance measurements were made from 31.6 kHz to 0.0178 Hz on Ag₂S/Ag⁺ (aqueous) and Ag₂S/Ag systems. Membranes were prepared from materials precipitated in excess of silver or sulfide ions, and stoichiometric mixtures. Impedances were analyzed, as a function of rotation rate and bathing activities, to isolate bulk conductivities, internal diffusion, surface kinetic and dissolution/crystallization impedances. High-frequency bulk resistivities, R_∞, varied by four with precipitation and pressing conditions. Resistivities were the same for solution and ohmic configurations for each preparation. For ohmic contacts, R_∞ and R(DC) were identical. Solution contact cells in 10^-1 M and 10^-2 M bathing silver ion solution gave identical frequency-dependent impedances which were independent of rotation rate. Thus, solution diffusional impedances and solution dependent surface kinetics were eliminated, and a finite Warburg, interior-Ag⁺-defect, diffusion impedance was indicated. Summation of bulk membrane and contact resistances, and this Warburg impedance served as a 'background' correction in analyzing dilute bathing solution interfacial impedances for surface effects. Corrected impedances in 10^-3 –10^-5 M AgNO₃ showed solution diffusional behaviour combined with surface kinetic and dissolution impedances. An iterative linear least-squares method resolved these quantities. The surface resistance suggests a potential-dependent rate constant; dissolution time constants were solution-independent and smaller than those for solution diffusion. Thus, dissolution can be a rate-limiting step in establishment of steady-state potentials.     

Protective Properties of Zinc-Rich Coatings: An Impedance Method Estimate

The impedance of zinc-rich polymer coatings on steel in a 3-% NaCl solution is studied. The electrochemical behavior of the electrode is satisfactorily described by an equivalent circuit that contains a constant-phase element, which reflects fractal properties of the zinc surface in the binder. From the results of calculations of the circuit elements for metal-rich electrodes with different zinc contents computed are fractions of the active area of the surface of the coating and its fractal dimensionality.     

Dielectric properties and frequency response of self-assembled monolayers of alkanethiols

This paper presents dielectric properties of alkanethiol self-assembled monolayers (SAMs) under an ac electric field. Using a Hg-SAM/SAM-Hg junction, we measured the ac impedance of alkanethiol SAMs using a sinusoidal perturbation of 30 mV (peak-to-peak) with frequency ranging from 1 Hz to 1 MHz at zero bias. Semicircles at higher frequencies and at middle frequencies along with Warburg lines at lower frequencies were observed in complex plane impedance plots, that is, Nyquist plots. The frequency response of SAMs was analyzed by modeling the junction using an equivalent circuit and fitting the Nyquist plots. The semicircles at higher frequencies are attributed to the effect of the SAM/SAM interfaces, and the ones at middle frequencies are attributed to the effect of alkanethiol SAMs. The comparison in the plots of the imaginary part of the impedance Z against frequency for the bare Hg electrodes (in pure ethanal) and the SAM-covered Hg electrodes (in alkanethiol solution) supports the analysis. The Warburg lines are attributed to a certain ionic impurity. The dielectric loss spectra are further analyzed. Chain-length-dependent peaks, which correspond to different relaxation mechanisms, at higher frequencies and middle frequencies were observed in the spectra of the dissipation factor (tan delta vs frequency). The peaks move to small frequency with the increase of chain length of alkanethiols. Using a correlation of peak position with the chain length, we then derived active energies of 39-99 meV for alkanethiol SAMs of C7-C18 under an ac electric field.     

Comparing the Method and Hardware for Electrochemical Impedance with the Method of Measuring and Analyzing Electrochemical Noise

Russian Journal of Electrochemistry - The experimental techniques of the methods of impedance with an ac current and electrochemical noise are considered in detail. The main features,...     

Modeling the surface phenomena in carbon paste electrodes by low frequency impedance and double-layer capacitance measurements

Impedance and capacitance studies have been performed with covalently coupled Glucose oxidase (GOD) enzyme, covalently coupled flavin adenine dinucleotide (FAD), reconstituted GOD enzyme and blank carbon paste electrodes to study the changes in the electrochemical interfacial properties. Impedance studies were performed using a low frequency impedance technique and the electrochemical surface capacitance was measured by a pulse technique. We have attempted to fit the experimental values to an equivalent circuit model. The Randles' cell circuit with Warburg impedance modeled well the experimental values and the behavior of the enzyme electrodes. The individual components of the model were calculated and the parameters were explained. The blank paste electrode showed a constant phase element behavior.     

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.