Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

The characterization of porous electrodes by impedance measurements

Impedances of a gold-powder and a Raney-gold electrode were measured over a wide frequency range, and were found to be very similar to those of cylindrical pore of finite depth. The simulation calculation for sphere-packed electrode impedance was performed. It was observed that even though each sphere-layer shows the impedance related to an occluded pore-shape, the overall impedance is similar to that of a cylindrical pore electrode. When the penetration depth approaches the pore depth, the shape of the pore wall has little influence on the impedance. Thus, impedance measurement techniques can be applied to porous electrodes of more intricate pore-texture, and evaluate the radius, depth and pore number of its equivalent cylindrical pore electrode. These values determined for a Raney-gold electrode are in very good agreement with those determined by other methods. The case of a more realistic fuel cell electrode such as Raney-nickel with a metal-electrolyte-gas system, was also tentatively examined.     

The dissolution and passivation of Fe and FeCr alloys in acidified sulphate medium: Influences of pH and Cr content

The steady state polarization curves of ferritic FeCr alloys, containing 7–12% Cr and immersed in 1M H₂SO₄, exhibit two current maxima, i.e. two passivating processes take place at the electrode interface within two different voltage ranges. The origin of these two passivation phenomena was investigated by plotting the steady state polarization curves and also by measuring the electrode impedance along with different polarization points. These results are then compared to those obtained with Fe electrode immersed in sulphate solutions of various pH value (0–5) since the steady state polarization curves of this electrode exhibit also two current maxima in a weakly acid medium, i.e. at solution pH greater than 4. However, even in a strongly acid solution in which only one current maximum is observed for the Fe electrode, the electrode impedance showed two passivation processes are occurring at the electrode interface. Therefore, the Fe dissolution involves at least two dissolution paths and the current at which one dissolution path overtakes the other is dependent upon the solution pH. The impedance diagrams of FeCr alloy electrode are similar to those of Fe electrode especially when the comparison is made with the Fe electrode immersed in a less acid solution, i.e. the addition of Cr in Fe enhances the appearance of two passivation phenomena with increase of solution pH.     

A theoretical approach of impedance spectroscopy during the passivation of steel in alkaline media

A theoretical impedance function is deduced for a proposed mechanism of passive film formation of steel in contact with alkaline aqueous media involving two reaction intermediates: mixed oxide with similar stoichiometry to magnetite and Fe(III)-oxides. The reduction reaction of dissolved oxygen is considered as the only cathodic reaction compensating the anodic current induced by the formation of iron oxides at open circuit potential. The iron dissolution takes place through a chemical dissolution of ferric oxide. A two-layered passive film with 3D structure is considered. A satisfactory agreement between the digital simulations on the basis of the theoretical impedance function and experimental spectra validates the proposed model.     

Corrosion and scale inhibition of low carbon steel in cooling water system by 2-propargyl-5-o-hydroxyphenyltetrazole

The 2-propargyl-5-o-hydroxyphenyltetrazole (PHPT) has been tested as corrosion inhibitor for low carbon steel in simulated cooling water. The polarization curves showed that PHPT acts as mixed-type inhibitor. Its inhibition efficiency was found to enhance with increase of the inhibitor concentration and immersion time due to the formation of the inhibitor film on the metal surface as indicated by electrochemical impedance spectroscopy measurements.To complete the formulation further, a non oxidizing biocide was added. Its presence with PHPT does not affect its inhibitory performance and it can be served as a basic component of the formulation for cooling water system.     

Use of impedance measurements for the determination of the instant rate of metal corrosion

The various methods of evaluating corrosion rate and charge transfer resistance have been critically reviewed on the basis of the recent developments on the measurement and interpretation of faradaic impedances. It is demonstrated that the entity which is most accurately correlated with corrosion rate is the transfer resistance, the limit of the faradaic impedance at infinite frequency. In the case of iron, with and without inhibitor (propargylic alcohol), it has been ascertained, under various experimental conditions, that the measurement of this resistance constitutes nowadays the best electrochemical test for corrosion, and allows thea priori calculation of corrosion rate.This paper constitutes a chapter of H. Takenouti's University thesis, which was presented in Paris on June 25, 1971 [1]     

Impedance measurements of corroding mild steel in an automotive fuel ethanol with and without inhibitor in a two and three electrode cell

The impedance measurements in a highly resistive electrolyte medium are difficult. The use of two identical electrode cells having a large surface area may overcome this difficulty, but measurements have to be restricted to the corrosion potential. The advantages of each type of cell are discussed. The electrochemical system tested in this work was the corrosion of mild steel in an automotive fuel ethanol with or without ethanolamines as corrosion inhibitors. It was found that in a three electrode cell, the use of a special electronic circuit increasing the input impedance of reference electrode was necessary to perform correct measurements. No particular care was needed in the impedance measurements in a two electrode cell. If the two electrode plates were set too close, the measured impedance was significantly great, thus leading to an erroneous prediction of the corrosion behaviour. A tentative explanation to this phenomenon is given.     

Electrochemical impedance spectroscopy for studying passive layers on steel rebars immersed in alkaline solutions simulating concrete pores

Present paper deals with the use of the electrochemical impedance spectroscopy to identify different processes in the passive layer growth over steel rebar surface immersed in an alkaline media simulating the concrete pore solution. Two cases have been considered: a passive layer spontaneously grown in a high alkaline media and a passive layer assisted by the application of an anodic potential in the same media. The application of electric equivalent circuits allows distinguishing between the different mechanisms occurring in this passive layer when grows in different conditions. An electric equivalent circuit with two RC loops connected in parallel is often used for fitting the EIS diagrams obtained for spontaneous growth of passive layers in the alkaline solution simulating the concrete pores. However, when the passive layer is formed under anodic polarization, a Warburg element must be introduced in the equivalent circuit. According to the Point Defect Model (PDM), this Warburg element is allocated to the transport of oxygen vacancies through the passive layer, which concentration changes with the potential.