The Hebb-Wagner Method

When performing a Hebb-Wagner polarization experiment one has to take the following aspects into careful consideration  

1) Depending on the sample geometry, the resulting currents may be in the pico-and subpico-ampere range. It is essential either to change the sample geometry or to make sure that the experimental setup resolves these small currents. 

2) The I-E plots may be extended to higher voltages in order to obtain the decomposition voltage of the sample. 

3) The temperature dependence of the I-E plots gives important information about the electrolyte, and also opens up the possibility of extrapolating the electronic properties to lower and higher temperatures. 

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The partial ionic or electronic currents and conductivities can also be measured by setting the driving force for the other partial current to zero. If one examines the Hebb-Wagner method, it becomes apparent that this nullification also occurs there. Because of the extreme resistance of the ion-blocking electrode to ionic current, the driving force for ionic motion in the MI EC vanishes (V/iion = 0). 

The Analog of the Hebb-Wagner Method for Determining Oj Selective Probes... 

FIGURE 8.3. Cell arrangement for the measurement of the partial electronie conductivity according to the Hebb-Wagner method. Specifie example the MIEC conducts 0 ions and electrons/holes. The polarity of the... 

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. 

Approaches for the description of interfacial processes involving various solid materials, particularly - ion conductors, and the theoretical background for the determination of minor contributions to the total conductivity of solids. These achievements made it possible to develop the measurement methods, which today have principal importance for the field of solid-state electrochemistry (see also -> diffusion determination in solids and - Hebb-Wagner method). 

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. 

Riess, I. (19%). Review of the limitation of the Hebb-Wagner polarization method for measuring partial conductivities in mixed ionic electronic conductors. Solid State Ionics, Vol. 91, pp. 221-232... 

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... 

The steady-state result (Eq. (77)) can be directly used to separate ionic and electronic conductivities the disadvantage of the technique is that it presupposes gas-separation. If not special measures are taken, it becomes unreliable for the ionic transport number less than 1%. Thus, this method well complements the Wagner-Hebb method which is very sensitive to small transference numbers. The partial conductivities of PbO shown in Figure 48 have been de-convoluted by the emf technique just described.3... 

Historically, this method was suggested by Wagner [i] following the work by Hebb [ii], who first proposed to use ion- or electron-blocking electrodes for the determination of partial conductivities in a 4-probe arrange-... 

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