Wagner polarization method

Riess, I. (1992). Four point Hebb-Wagner polarization method for determining the electronic conductivity in mixed ionic-electronic conductors. Solid State Ionics, Vol. 51, No 3-4, pp. 219-229... 

Since the concentration of the minor carriers (electrons and/or holes) determines the chemical leakage of oxygen when oxide ion conductor is used as the electrolyte in SOFCs [33], analysis of the performance of electron and hole conduction is an important subject for the electrolyte materials. Partial electronic conduction is commonly analyzed by the ion blocking method, the so-called Wagner polarization method. Partial electronic conductivity is the sum of electronic and hole contribution to the total conductivity, and each conductivity is proportional to a carrier density. Therefore, the total electronic conductivity can be expressed as follows ... 

Polarization method according to Hebb-Wagner (steady state)... 

Polarization Method According to Hebb-Wagner (Steady State)... 

The Hebb-Wagner polarization technique has been developed either for the determination of electron and hole conductivity in ionic conductors [Hebb, 1952 Joshi Wagner, 1975 Wagner, 1957] or for the measurement of ionic conductivity in MIECs [Riess, 1996 Wiemhofer et al., 2002]. Basically, the method consists in using a reversible electrode and blocking electrodes to suppress the predominant charge carrier and thus enable measurement of the minority sp>ecies. The main limitations of the method have been reviewed [Riess, 19%] and new experimental set-ups have been proposed. 

Determination of hole and electron conductivities and transport numbers of oxide ion in LaGa03-based oxides were performed by the polarization method by Baker et al. [21], Yamajiet al. [35], and Kimand Yoo [36]. Kim et al. reported that Pq2 dependence of hole and electron conductivity is proportional to Pcn and respectively, and well obeys the Hebb-Wagner theory. The results... 

Similar approaches are used for most steady-state measurement techniques developed for mixed ionic-electronic conductors (see -> conductors and -> conducting solids). These include the measurements of concentration-cell - electromotive force, experiments with ion- or electron-blocking electrodes, determination of - electrolytic permeability, and various combined techniques [ii-vii]. In all cases, the results may be affected by electrode polarization this influence should be avoided optimizing experimental procedures and/or taken into account via appropriate modeling. See also -> Wagner equation, -> Hebb-Wagner method, and -> ambipolar conductivity. 

Mansfeld has described a method to determine Tafel slopes from the nonlinearity found in small magnitude linear polarization measurements [15]. The approach is similar to the fitting method described earlier for fitting potentiodynamic polarization curves to the Wagner-Traud equation, Eq. (3). Mansfeld showed that the fit can be made with only two parameters, the Tafel slopes, instead of four. The values of Ecorr and Ep can be determined, and icon- can be eliminated from Eq. (3) by insertion of Eq. (4)... 

Cathodic protection (CP) is defined as the reduction or elimination of corrosion by making the metal a cathode by means of impressed current or sacrificial anode (usually magnesimn, aluminum, or zinc) [11]. This method uses cathodic polarization to control electrode kinetics occurring on the metal-electrolyte interface. The principle of cathodic protection can be explained by the Wagner-Traud mixed potential theory [12]. 

To study the effects of interaction of starch with silica, the broadband DRS method was applied to the starch/modified silica system at different hydration degrees. Several relaxations are observed for this system, and their temperature and frequency (i.e., relaxation time) depend on hydration of starch/silica (Figures 5.6 and 5.7). The relaxation at very low frequencies (/< 1 Hz) can be assigned to the Maxwell-Wagner-Sillars (MWS) mechanism associated with interfacial polarization and space charge polarization (which leads to diminution of 1 in Havriliak-Negami equation) or the 5 relaxation, which can be faster because of the water effect (Figures 5.8 and 5.9). 

The purpose of this tutorial paper is to review the theory, the method of measurement and treatment of the data for experiments on polarized solid electrolytes according to the theory of C. Wagner and the developments of H. Rickert, K. Weiss, D. 0. Raleigh, A. Joshi and others. Methods to obtain the total and electronic conductivities, transport number, number and mobility of electronic charge carriers and the double layer capacitance at the electrolyte-electrode interface are to be discussed. Examples will be chosen which exhibit good agreement with theory— primarily the silver and copper halides. 

In any event the measurement of the electronic conductivity in a mixed conductor is very precisely and accurately carried out by using C. Wagner s asymmetric polarization cell method which is the primary subject of the present paper. 

The main concept that most of the corrosion data interpretation is based on was first introduced by Wagner and Traud (1938), according to which galvanic corrosion is an electrochemical process with anodic and cathodic reactions taking place as statistically distributed events at the corroding surface. The corresponding partial anodic and cathodic currents are balanced so that the overall current density is zero. This concept has proven to be very useful, since it allowed all aspects of corrosion to be included into the framework of electrochemical kinetics. Directly deduced from this were the methods of corrosion rate measurement by Tafel line extrapolation, or the determination of the polarization resistance Rp from the slope of the polarization curve at the open circuit corrosion potential... 

The AC impedance technique coupled to the complex plane method of analysis is a powerful tool to determine a variety of electrochemical parameters. To make the measurements, instrumentation is somewhat more complex than with other techniques. It requires a Wheatstone bridge arrangement with series capacitance and resistance in the comparison arm, a tuned amplifier/detector, and an oscillator with an isolation transformer. A Wagner ground is required to maintain bridge sensitivity, and a suitably large inductance should be incorporated in the electrode polarization circuit to prevent interference from the low impedance of this ancillary circuitry. Sophisticated measurement instruments or frequency response analyzers with frequency sweep and computer interface are currently available such as the Solartron frequency response analyzers. Data obtained can be analyzed or fitted into proper equivalent circuit using appropriate software. 

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