Supplimentary Document 1
Wagner's DC Polarization Method
For a solid electrolyte to be used as a separator in electrochemical devices, such as rechargeable batteries, fuel cells, supercapacitorsetc, the electronicconductivity must be negligibly small compared to the ionic conductivity in order to minimize the internal short circuiting and to achievehigher power densities. Due to its simplicity, the most widely used technique to estimate the ionic and electronic contributions to the total conductivity in a solid electrolytehas been the Hebb-Wagner polarizationmethodwhich is also known as the Wagner DC polarization method.
In the usual Wagner DC polarization technique, the electrolyte sample is sandwiched between two ion blocking electrodes and a constant D.C. potential of about 1 V is applied across the sample by a potentiostat and the resulting current is monitored by a sensitive digital multimeteras afunction of time. Under the influence of the D.C. field,cations migrate to the negative electrode andanions to the positive electrode. As the cell polarizes charge carriers blocked at inner dielectric boundary layers (on the mesoscopic scale) or external electrodes (on a macroscopic scale) lead to a separation of charges.When the back potential created by the concentration gradient exactlyopposes the applied potential the ions no longer carry current and the cell is completelypolarized with respect to the ionic species. Thus, any resulting steady state current is only due to electronic contribution.
When solid electrolytes possess conductivity due to both ionic and electronic transport, it is necessary to know the fraction of the conductivity due to ions and electrons. For example, in solid electrolytes used for battery applications, the electroniccontributions to the total conductivity should be minimized. The use of solid electrolyte materials in practical electrochemical devices usually requires that they exhibit little or no electronic conductivity. i.e,the transport number of ions,ti should be ideally greater than 0.99
In a solid electrolyte, the total conductivity is the sum of the ionic and
electronic contributions.
The total conductivity (t) is the sum of the conductivity due to ions (i) and theconductivity due to electrons (e).
t = i + e
Ionic and electronic transport numbers can be calculated from the following equations.
Ionic transport number, ti = i/t
and electronic transport number te = e/t
For a purely ionic conductor, ti= 1 and for a purely electronic conductor te= 1. For a mixed conductorstiand te have values between 0and 1. There are several methods for determining the ionic transport number of mobile ions in solid electrolytes and out of these, Wagner DC Polarization method appears to be the simplest.
A typical circuit used for Wagner DC polarization test is shown in the figure. Just after the circuit is switched on, the initial total current It starts to quickly decrease with time, corresponding to the polarization of ionic species in the electrolyte and becomes constant in the fully polarized situation. At this stage, the residual current is only electronic current (Ie).
The total current (It) flowing in the system at any instant is the sum of the current due to ions (Ii) and thecurrent due to electrons (Ie).
It = Ii + Ie
By measuring the It and Ie, Ii can be calculated.
Ionic and electronic transport numbers can also be calculated using the measured currents from the following equations.
Ionic transport number ti, = Ii/It
and electronic transport number te = Ie/It
Alternatively, the voltage drop over a fixed resistor which has been installed in theexternal circuit is measured. Voltage drop due to external resistance and lead wire is compensated from measured current and voltage values. Moredetailed information about operating principle of the Wagnerpolarization experiment is easily found in the literature [1,2].
Limitations
When determining partial conductivity by Wagner DC polarizationmethod, however we have to premise several critical assumptions regarding electrode geometry, defect equilibrium, current blocking condition as well as electrode over-potential. In most cases, neglecting the electrode over-potentialunder conventional two electrode configuration may lead toinaccurate results.
For a measurement with reasonable accuracy, the measurement of partial conductivityvia polarization method potential drop at the electrodes should benegligible. There are few studies which have considered electrode over-potential problem. In early 1980s, Dudley [4] introduced powerful technique for electrochemical investigation, which had symmetric 4 point electrode arrangement. To measure partial ionic and electronic conductivity he used two additional ionic and electronic probes respectably. By using additional ionic and electronic probes in symmetric 4 point electrode arrangement electrode over-potential could be neglected.Another inherent limitation of this method is the experimental difficulty in measuring the initial (at time = 0) current accurately.
References
1.WagnerC (1933) ZPhysikChem B21: 25-47
2. HebbMH (1952), J ChemPhys 20:185-190
3. Reassessment of conventional polarization technique to measure partial electronic
conductivity of electrolytes
Lee Kyung-Ryul, Lee Jong-Ho, Yoo Han-Ill (2010) Solid State Ionics 181:724–729
4. Dudley GJ, Steele BCH(1980), J Solid State Chem 31: 233