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.     

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.     

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.     

靛红掺杂聚吡咯膜修饰电极的电荷传输

利用交流阻抗法研究了靛红掺杂聚吡咯膜内的电荷传输，通过非线性最小二乘法拟合，得出了体系的等效电路，并计算出其电荷扩散系数和异相电子传递反应速率常数。实验结果表明，随着膜厚的增加，活性点增多，异相电子传递反应速率常数增大，同时表观扩散系数也增大。     

Electrochemical impedance spectroscopy investigations of a microelectrode behavior in a thin-layer cell: Experimental and theoretical studies

Electrochemical impedance spectroscopy experiments were performed on a microdisk electrode in a thin-layer cell using a scanning electrochemical microscope for controlling the cell geometry. Experimental data showed that when the thin-layer thickness diminished, an additional low-frequency response appeared. It was ascribed to the radial diffusion of the electroactive species and was strongly dependent on the thin-layer dimensions (both thickness and diameter). Moreover, the numerical simulation of the impedance diagrams by finite element method calculations confirmed this behavior. An equivalent circuit based on a Randles-type circuit was proposed. Thus, the diffusion was described by introducing two electrical elements: one for the spherical diffusion and the other for the radial contribution. A nonlinear Simplex algorithm was used, and this circuit was shown to fit the impedance diagrams with a good accuracy.     

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.     

受主方程控制的化学反应体系非平衡定态宏观稳定性判据之随机推广

借助扰动按分布参数分离法及主方程的Kramers-Moyal展开证明,随机熵相应于对最可几路径偏离的偏超量之时间导数与体系对外部扰动的响应性直接相关.该演变速率等价于偏超随机熵产生,并与根据随机位方法提出的随机超熵产生速率等效.对Poisson分布,该量表现为Gibbs超熵产生的等价量.局域平衡假定失效后,化学反应体系的宏观稳定性即决定于这个新的随机量.     

A Stochastic Extension of Macroscopic Stability Criterion of Nonequilibrium Steady State in Chemical Reaction Systems Governed by Master Equation

By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .     

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.     

Enhanced diffusion in conic channels by means of geometric stochastic resonance

Geometric stochastic resonance of Brownian particles diffusing across a converging conic channel subject to oscillating forces is studied in this paper. Conic channel geometries have been previously considered as a model for transport of particles in biological membranes, zeolites, and nanostructures. For this system, a broad excess peak of the effective diffusion above the free diffusion limit is exhibited over a wide range of frequencies, suggesting a synchronization effect in the confining geometry as particles respond to the periodic modulation of the external force. This indicates that the geometric stochastic resonance effect with unbiased ac forces can be exploited for improving the transport of particles in complex geometries.     

Thermal behavior of polarized Pd/D electrodes prepared by co-deposition

Thermal behavior of polarized Pd/D electrode, prepared by the co-deposition technique, serving as a cathode in the Dewar-type electrochemical cell/calorimeter is examined. It is shown that: (i) excess enthalpy is generated during and after the completion of the co-deposition process; (ii) rates of excess enthalpy generation are somewhat higher than when Pd wires or other forms of Pd electrodes are used; (iii) positive feedback and heat-after-death effects were observed; and (iv) rates of excess power generation were found to increase with an increase in both cell current and cell temperature, the latter being higher.     

Small-signal ac response theory for systems exhibiting diffusion and trapping of an electroactive species

A theoretical expression is derived for the interfacial admittance of an electrochemical system in which a product species diffuses into (or along internal surfaces of) an electrode subject to reversible trapping at one or more types of stationary sites in the electrode. The admittance obtained in a generalization of earlier results for diffusion without trapping and is exactly representable by an equivalent electrical circuit involving a lossy transmission line. Representative numerical data are given for the impedance of this distributed element. Trapping effects are found to be significant primarily when the number of trapped atoms is comparable to the number of mobile atoms. The results obtained may therefore be of greatest interest in the case of polycrystalline or amorphous electrodes.     

聚苯胺纳米管在阳极氧化铝模板中电聚合的生长机理

利用阶跃电位、循环伏安等电化学方法，应用金属电沉积理论,研究聚苯胺纳米管在阳极氧化铝模板（AAO）内电聚合的生长机理.结果表明：电聚合初始，苯胺二维非扩散控制的瞬时成核生长形成聚苯胺晶胞链段单层,单层形成以后，聚苯胺的生长过程变为线性扩散控制. XRD实验进一步证实电聚合的聚苯胺同时包含结晶相和无定型相结构.     

二茂铁及其与DNA复合物的电化学行为

在Tris-NaCl(pH=7.2)缓冲溶液中, 应用循环伏安法、微分脉冲伏安法、旋转圆盘电极实验、电化学阻抗谱等技术研究了二茂铁在旋转碳纳米管(CNT)修饰电极上的电化学行为及其与小牛胸腺DNA的相互作用. 结果表明, 二茂铁及其与双链DNA的电活性产物在静止的CNT修饰电极上均呈现一对基本可逆的氧化还原峰；在旋转电极上呈现出明显的极限扩散电流, 电化学阻抗谱呈现一个压扁的半圆. 二茂铁与DNA的作用在扩散控制过程中表现为峰电流和极限扩散电流随DNA浓度增大而减小；电化学控制过程则表现为电化学反应电阻随DNA浓度增大而增大, 条件电位下的速度常数也有一定程度的减小.     

Determination of amino acids, vitamins, and drug substances in aqueous solutions using new potentiometric sensors with Donnan potential as analytical signal

Basic principles of a new potentiometric sensor are considered. Its analytical signal is the Donnan potential at the ion-exchange polymer/studied solution of electrolyte interface. Assessments of potential drops at individual interfaces are presented, same as estimates of diffusion potentials in the electrochemical circuit for measurement of the sensor response. It is shown that the overall contribution of the values of all potentials to EMF of the electrochemical circuit, except for the Donnan potential, at the ion-exchange polymer/studied solution interface are negligibly low as compared to the experimental values of the circuit EMF in the studied systems. Certain regularities of the Donnan potential formation are studied in the systems with the polymers of different structure and solutions containing inorganic ions and organic electrolytes in different ionic forms. The possibility is shown of using a sensor with such an analytical signal as the Donnan potential for assay of amino acids, vitamins, and drug substances in aqueous solutions. The sensor was used as a selective electrode for determination of lysine in aqueous solutions with neutral amino acids in the range of pH 5.0–7.0 and glycine in aqueous alkali solutions in the range of pH 9.00–11.00. The developed sensor is introduced as a cross-sensitive electrode into the array of multisensor systems for multicomponent quantitative analysis of the lysine monohydrochloride, thiamine chloride, novocaine hydrochloride, lidocaine hydrochloride solutions containing potassium and sodium chlorides. The measurement error of electrolytes in aqueous solutions did not exceed 10%.     

A Better Understanding of Diethylstilbestrol Electro-oxidation: Towards the Design of an Electrochemical Sensor

The obstacle for the development of a reliable electrochemical technique to trace diethylstilbestrol (DES) lies in the complex electrochemical behavior of this illicit hormone. The present study targeted to thoroughly investigate and understand the electro-oxidation of DES in acetonitrile on gold electrode by cyclic voltammetry (CV) and square wave voltammetry (SWV) techniques. DES voltammogram has shown two anodic peaks, implicating two successive and irreversible processes. Adsorption and diffusion properties were studied and characterized using electrochemical, spectroscopic and morphological techniques. Avoiding adsorption, and under diffusion process only, a good linear correlation between peak current and DES concentration in the range of 0.25 to 1000 μmol/L was obtained with a detection and quantification limits of 0.2 μmol/L and 0.7 μmol/L, respectively, and a sensitivity of 0.016 A/mM. Competitivity tests, between DES and its structural analog hexestrol (HS), were carried out by chronoamperometry and SWV. HS even added in excess was found to merely affect DES electrochemical measurement. The established method exhibited high precision and reproducibility, and allows the easy and successful determination of DES in poultry feed sample. With a deep insight into its complex electrochemical behavior, this work paves the way to the development of selective, sensitive and easy-to-use electrochemical sensors directed towards this synthetic hormone and the related chemicals such as phenolic compounds.     

Cu(2)O nanowires in an alumina template: electrochemical conditions for the synthesis and photoluminescence characteristics.

Cu2O nanowires, mainly consisting of (100) and (200) polycrystalline structures with a length of 4 mum are prepared by electrochemical deposition using a porous alumina template. It is found that the optimized electrochemical conditions to prepare Cu2O nanowires are different from those for the formation of a bulk thin Cu2O layer since different pH values are found between the tip of the pores and the bulk, due to diffusion limits in porous alumina with an extremely high aspect ratio of 300. We point out that Cu2O (200), Cu2O (111), Cu, and co-deposited alloys can be obtained under specific electrochemical conditions. In addition, the optical band gap of the prepared Cu2O nanowires with a length of 4 microm and a diameter of 200 nm is estimated to be 2.17 eV from photoluminescence measurements.     

气体扩散电极参数对阴离子交换膜燃料电池性能的影响

优化了碱性阴离子交换膜燃料电池（AAEMFC）使用的气体扩散电极（GDE）,发现催化层中PTFE含量与催化剂担载量对电池性能与其电化学动力学特征影响很大.采用i-V曲线,开路电压,电池内阻与在线的电化学阻抗谱与动力学分析,评估了所制GDE的电化学性能.在所研究的AAEMFC电极催化层中,PTFE的最佳含量是20%,Pt载量对膜电极三相界面、催化层导电性与催化剂利用率的影响极大.当制备的GDE催化层中Pt/C的Pt载量为1.0mg/cm²,PTFE含量为20%时,AAEMFC的峰电流密度在50^oC达到了213mW/cm².兼顾Pt催化剂的利用率与成本,在没有明显影响电池性能的情况下,Pt的担载量可降至0.5mg/cm².