1. NorFERM 2008 The EMF technique
Henrik Bentzer
NorFERM 2008
The EMF technique

2. Outline
The definition of transport numbers and why they are interesting
The basics of the EMF method
A typical EMF setup
EMF measurements on proton conductors
Pitfalls and problems
Corrections for electrode polarisation resistance: When are they needed and how are they made
Hydrogen isotopes, complimentary methods

3. Ionic conducting oxides
Numerous oxides are known to conduct oxide ions (e.g. YSZ and CGO) or protons (e.g. acceptor doped strontium cerates and lanthanum niobate).
All materials have some component of electronic conductivity, ranging from minor to dominating.
Ionic conducting ceramics may find use in many different fields, such as fuel cells, membranes, sensors etc.
Wether or not electronic conductivity is desired depends on the intended use of the material

4. The transport number The transport number for species i is defined as
For example, the oxide-ion transport number in an oxide-ion conducting oxide is
The sum of all transport numbers equals 1
For use in fuel cell electrolytes, sensor applications etc., ionic conductivity should be as pure as possible, that is, the transport number should be as close to unity as possible under applicable conditions, to avoid current leaks.

5. Ambipolar transport
In other applications, such as membranes and electrode materials, mixed ionic electronic conductivity (MIEC) is desireable.
The (non-galvanic) transport of oxygen or hydrogen through a membrane material is governed by the so called ambipolar conductivity. Taking a mixed proton/electron conductor as an example, the ambipolar conductivity is
which is maximised when

6. The electromotive force technique
The EMF technique for transport number determination is based on open cell voltage measurements on a sample equipped with two reversible electrodes and subjected to a gradient in chemical potential.

7. The setup Thermocouple Spring-loaded alumina hood Gold seals
Electrodes
Alumina tubing
Platinum wires
Sample

8. How it works: The simple equations
What ”creates” the voltage? The Nernst equation:
What we measure:
The maths part:

9. How it works: A more formal derivation
The flux and partial current density of a species i in an electrochemical potential gradient are:
The net current density is the sum of all partials:
Assuming the sample is connected to an external circuit, the following expression for the electric potential is achieved:

10. Since chemical potentials for charged species are not well defined, corresponding neutral species and electrons are used instead:
We can now integrate over the sample thickness:
Under open circuit conditions, using equal, intert electrodes, we get:

11. For gaseous species:
and so, for our one species i we get
From here, we just need our assumption that ti is constant, and there we go.

12. Proton conductors – 3 conducting species
In proton conducting oxides, the protons are usually created by water uptake in oxygen vacancies.
Hydrogen and water will under the right circumstances react and form water:
Using the equations derived above, the total voltage over a sample subjected to a gradient in hydrogen and/or oxygen partial pressure is

13. The equilibrium between water, oxygen and hydrogen allows us to rewrite the EMF equation,
which allows us to, theoretically, set up a number of experiments to determine transport numbers for oxide ions and protons under varying conditions

14. Transport number determined
Different setups
Experimental setup
Gas, outer compartment
Gas, inner
compartment, constant
compartment, varied
Conditions
Transport number determined A
O2/N2 - O2
Dry, High pO2 tO B
H2/N2 H2
Dry, Low pO2 tH C
O2/N2/H2O
O2/H2O ratio (H2)
O2, H2O
Wet, High pO2 D
H2/N2/H2O
H2/H2O ratio (O2)
H2, H2O
Wet, Low pO2 E
H2O F G
N2/H2O
Wet
tO-tH

15. Gas setup Air or H2/N2 Air or H2/N2 N2, Air or H2/N2 Furnace Sample
Inner tube
Exhaust

16. Oxide ion transport number measurements on SrCe0.95Y0.05O3

17. Oxide ion transport number measurements on SrCe0.95Y0.05O3

18. Difficulties with the method
Samples need to be dense, and seals need to be gas-tight
Impurities in gas mixtures must be avoided
The gas mixture in each chamber should be uniform, that is, partial pressures at the sample surface should be the same as the known gas bulk partial pressures
Thermo-emf’s must be either avoided or corrected for by reversing and averaging
The electrodes should be reversible

19. The problem of electrode polarisation
The assumption that the electrodes are completely reversible does not hold
The figure shows the relative error made by ignoring the electrode polarisation resistance as calculated by Kharton and Marques.

20. Approach I: The Gorelov method
Gorelov suggested using a variable resistor in parallel to the sample
By making a series of voltage measurements while varying the resistance, a plot can be constructed and the electronic resistance found.
An EIS measurement allows a determination of the polarisation resistance.

21. Approach II: The Liu-Hu method
Liu and Hu instead suggested using only impedance measurements, using both the high and low frequency limit measurements.
The high frequency measurement gives the bulk resistance, Rb , while the low frequency measurement gives the total resistance of the cell, RT.
Individual resistances can then be found as

22. Polarisation corrections for protonic conductors

23. The hydrogen isotope cell
If a cell is set up with H2/H2O in one compartment and the same partial pressures of D2/D2O in the other, a voltage might develop over the cell.
If the sample is a pure proton conductor, the voltage can be calculated as
If the sample is an oxide ion conductor, a negative EMF will develop, due to the different equilibrium constants of the H2/H2O/O2 and D2/D2O/O2 reactions.

24. Hydrogen isotope cell measurements

25. Alternative methods: Faradaic efficiency measurements
Faradaic efficiency measurments are based on the same theory as the EMF technique, however, the measurements are performed on a closed circuit.
A current is applied over the sample, and the flux of species i is measured
The partial current density of species i is calculated from the flux, and divided by the total current to yield the transport number.
Many of the problems from the EMF technique also apply to faradaic efficiency measurements.

26. Alternative methods: Hebb-Wagner technique
The Hebb-Wagner technique utilizes conductivity measurements with and without blocking electrodes to find the transport number.
For example, YSZ is a very pure oxide ion conductor, and can be used to block electrons in measurements of oxide-ion transport numbers.
Obstacles include making a setup where complete blocking is actually achieved.

27. Alternative methods: Conductivity measurements
Conductivity measurements, especially if a series of measurements where partial pressures of oxygen and water as well as temperature is varied will give you a lot of information.
While conductivity measurements do not allow for very precise determination of the transport number, the extra information gained might be worth it.

28. Recommended reading (references)
Basic equations: C. Wagner, Z. Phys. Chem. (1933) T. Norby’s Defect Chemistry Course D. P. Sutija, T. Norby and P. Björnbom, SSI 77 (1995)
Electrode polarisation resistance V. P. Gorelov, Elektrokhimiya, 24 (1988) M. Liu, H. Hu, J. Elchem. Soc. 143 (1996) V. V. Kharton, F. M. B. Marques, SSI 140 (2001)
Hydrogen isotope cells H. Matsumoto, K. Takeuchi, H. Iwahara, J. Elchem. Soc. 146 (1999) H. Matsumoto, K. Takeuchi, H. Iwahara, SSI 125 (1999) V. I. Tsidilkovski, SSI , (2003)