M. Moors

Calculation of the impedance of noncylindrical pores Part I: Introduction of a matrix calculation method

In this paper a new method is proposed for the calculation of the impedance of arbitrary electrodes containing noncylindrical pores and/or having place-dependent impedances. The method is based on splitting up the pore and the surrounding material into N discs. For the equivalent circuit of each disc a transmission line with constant impedances is adopted. By matrix calculations the impedance of the porous electrode can be obtained. A comparison is made between this, very general, matrix method and a recursion method developed by Keiser et al. for purely capacitive interface behaviour of pores in an electrode material with negligible impedance. It is shown that the matrix method requires much smaller N-values owing to the use of transmission lines for each disc. This makes it more appropriate to be used in curve fitting procedures. Moreover, it is shown that the typical behaviour of the pore impedance at low penetration depths is much better simulated with the matrix method. Furthermore, an attempt is made to provide more general knowledge about the impedance behaviour of noncylindrical pores as a function of the penetration depth of the a.c. signal. Finally, the theory is enlarged using constant phase elements instead of capacities to describe the behaviour of the electrode/electrolyte interfaces.

The influence of the anodization temperature and voltage on the porosity of the anodization layer on aluminium

Abstract The pore-filling method is a known process for measuring the porosity of porous anodic oxide layers on aluminium. This method has been used to study the relationship between the anodizing conditions and the porosity of the porous anodic film. In a series of experiments, the influence of the anodization voltage and temperature on the porosity, of an anodization layer formed in 15 wt.% sulphuric acid was investigated. From these results a mathematical equation was deduced that gives the porosity as a function of the anodization voltage and temperature. In the second part of the study the height of the voltage jump, on which the thickness of the barrier layer at the start of the re-anodization process depends, was investigated as a function of the anodization voltage. A linear relationship was found between the voltage jump and the anodization voltage.

Calculation of the impedance of noncylindrical pores Part II: Experimental verification on pores drilled into stainless steel

The method of one-dimensional modelling of the pore impedance is validated on pores drilled in AISI 316 stainless steel. Impedance measurements were carried out in 0.511 sulphuric acid solution. Experimentally, it is found that, for cylindrical pores with a radius/pore length-ratio smaller than 0.5, the one-dimensionality condition is satisfied. Furthermore, impedance measurements on noncylindrical, scaled-up pores provide evidence that a geometric constant Ag has to be introduced, as in Part I. In accordance with this theory it is found that for pores with narrowing cross section Ag is less than 1/3, while for pores with a broadening cross section Ag is greater than 1/3. Moreover, it is shown that the matrix method, presented in Part I, provides a way of calculating the impedance of a non-cylindrical pore by using a highly reduced number of discs, N, compared to the recursion method of Keiser et al. This is an advantage in fitting procedures.

Electrostatic Splitting of the Emulsion Used in Liquid Surfactant Membranes Process for Metals Separation

Abstract A study has been carried out to investigate the effect of different parameters on the splitting process of the emulsion used in the liquid surfactant membranes process for metals separation. The influence of electric field strength, frequency of the applied ac voltage, and membrane recycling on emulsion stability have been studied. The investigations have revealed that there exists a unique optimal frequency range in which the best separation of the emulsion phases is obtained. The effect of the membrane composition and the variation of tri-n-butyl phosphate (TBP) concentration has been shown to vary linearly with the splitting efficiency. This finding correlates quite well with Sadek and Hendricks equation on the force causing coalescence in an electric field.

The estimation of the charge transfer resistance by graphical analysis of inclined semicircular complex impedance diagrams

Recently a graphical method for the determination of the charge transfer resistance, obtained from impedance measurements, was developed. The original method was limited to perfect, semicircular Nyquist plots. Extension to inclined or depressed semicircular arcs is made possible by a few simple mathematical and graphical manipulations.

Estimating the barrier layer thickness of porous aluminium oxide films with A.C. impedance measurements

Abstract The a.c. impedance behaviour of porous aluminium oxide films has been investigated. According to the characteristics of the equivalent circuit, the capacitance corresponding to the porous film layer can be obtained for the frequency ω → ∞. As the capacitance is related to the thickness of the layer, it provides a method for the evaluation of the thickness of the porous aluminium oxide film. Measurements were performed in the range from 2 mHz to 100 kHz. Results showed that the capacitance measured does not correspond to that of the porous film. Since the capacitance attained at high frequencies is closely related to the anodization voltage, and since it is independent of the anodization time, it can be ascribed to the thin barrier layer.

The application of the pore-filling method to the study of the structure of porous anodic films on aluminium

Abstract The process in which aluminium covered with a porous layer is re-anodized to obtain a compact layer is known as the pore-filling method. The purpose of this work was to study the relationship between anodizing conditions and the structure of the porous anodic film on aluminium by application of the pore-filling method. In a first series of experiments the influence of the anodization voltage on the porosity was examined. It was found that the inverse of the porosity is a function of the square root of the anodization voltage. The second part of our investigations consisted in studying the dependence of the thickness of the barrier layer on the anodization voltage. At each stage of the anodization process this barrier layer thickness is a function of the anodization voltage. Moreover, there is some evidence of a variation in the thickness of the barrier layer during an anodization process performed at a constant voltage.

AC impedance measurements on high copper dental amalgams

In recent years alloys with a high copper content were developed to improve the corrosion resistance of dental amalgam by elimination of the gamma 2 (Sn-Hg) phase. The purpose of the present investigation was to compare the electrochemical behaviour of high copper amalgams obtained from single composition amalgam alloys (Indiloy; Shofu, Dental Corp., Menlo Park, USA) with those that used the additive mode of copper alloying (Dispersalloy; Johnson & Johnson, East Windsor, USA).

Correlation between the thickness and the specific mass of an anodization layer on aluminium and the measured current transient

Abstract For anodizing of aluminium in a sulphuric acid (15 mass%) solution at constant voltage, the current initially jumps to a high value and decreases rapidly to a low value in the first few seconds; thereafter the current rises to a constant level. The course of the current versus time is common for all applied voltages and temperatures. However, the higher the voltage and temperature are, the faster and higher the rise and constant level will be. The shape of this current-time curve is representative for the specific anodization layer. Exponential relations has been found for the different characteristic points (minimum, maximum and steady-state current and the corresponding times) of the current density-time curve versus voltage and temperature. Also for the thickness and the apparent specific mass of the oxide layer, exponential functions versus voltage and temperature were found. In this work it has been proved that a correlation exists between the measured steady-state current density, the thickness and the apparent specific mass of the layer. For the formed oxide layers the measured mean real specific mass value is the same as that one which has already been published.