Download The EMF technique

NorFERM 2008
The EMF technique
Henrik Bentzer
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
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
The transport number
• The transport number for species i is defined as

ti  i
 tot
• For example, the oxide-ion transport number in an oxide-ion
conducting oxide is
tO 
O
O  e
• 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.
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
 amb
 H e

H e
which is maximised when
 H   e  0.5
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.
The setup
Thermocouple
Spring-loaded alumina hood
Gold seals
V
Electrodes
Alumina tubing
Platinum wires
Sample
How it works: The simple equations
• What ”creates” the voltage? The Nernst equation:
ENernst
RT p2

ln
nF p1
• What we measure:
RT
Eth  
nF

II
I
ti d ln pi
• The maths part:
tavg 
Eth
ENernst
How it works: A more formal derivation
• The flux and partial current density of a species i in an electrochemical
potential gradient are:
ji 
 i  dµi
d 

z
e
i

2 
dx
dx

 zi e  
ii  zi eji
• The net current density is the sum of all partials:
 k  dµk
d 
itot  
 zk e 
2 
dx 
k  zk e   dx
• Assuming the sample is connected to an external circuit, the following
expression for the electric potential is achieved:
i
t dµk
d
  tot   k
dx
 tot k zk e dx
• Since chemical potentials for charged species are not well defined,
corresponding neutral species and electrons are used instead:
i
t dµn 1 dµe
d
  tot   n

dx
 tot n zn e dx e dx
• We can now integrate over the sample thickness:
II
II
II
II
itot
tn
1
I d   I  tot dx  I n zne dµn  I e dµe
• Under open circuit conditions, using equal, intert electrodes, we get:
II
tn
E   
dµn
n I zn e
• For gaseous species:
µn( g )  µn0( g )  kT ln pn
• and so, for our one species i we get
II
kT
E
ti d ln pi

zi e I
• From here, we just need our assumption that ti is constant, and there we go.
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:
½O2  H 2
H 2O
• Using the equations derived above, the total voltage over a sample
subjected to a gradient in hydrogen and/or oxygen partial pressure is
pO22 RT
pH2 2
RT
Eth 
 tO  ln 1   tH  ln 1
4F
pO2 2 F
pH 2
• The equilibrium between water, oxygen and hydrogen allows us to
rewrite the EMF equation,
Eth 
pO2 2
pH2 2O
RT
RT
t

t
ln

 O H 1
 tH  ln 1
4F
pO2 2 F
pH 2O
• Or
pH2 2O RT
pH2 2
RT
Eth 
 tO  ln 1   tO  tH  ln 1
2F
pH 2O 2 F
pH 2
• which allows us to, theoretically, set up a number of experiments to
determine transport numbers for oxide ions and protons under
varying conditions
Different setups
Experiment
al setup
Gas, outer
compartment
Gas, inner
compartment,
constant
Gas, inner
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
tO
D
H2/N2/H2O
H2/H2O ratio (O2)
H2, H2O
Wet, Low
pO2
tH
E
O2/N2/H2O
O2
H2O
Wet, High
pO2
tH
F
H2/N2/H2O
H2
H2O
Wet, Low
pO2
tO
G
N2/H2O
-
H2O
Wet
tO-tH
Gas setup
Air or
H2/N2
Furnace
Sample
Inner tube
Exhaust
Air or
H2/N2
N2, Air
or
H2/N2
Oxide ion transport number measurements on SrCe0.95Y0.05O3
600°C
Oxide ion transport number measurements on SrCe0.95Y0.05O3
800°C
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
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.


Eobs
 tO 1 

ENernst
R

R
O
e 

R
1
Approach I: The Gorelov method
• Gorelov suggested using a variable resistor in
parallel to the sample
R 

Eobs
 tO 1 

ENernst
 RO  Re 
1
R  R
ENernst
1  O
Eobs
Re
 1
ENernst
1 
 1   RO  R    
Eobs
 Re Rb 
• 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.
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.
Rb 
RO Re
RO  Re
RT 
( RO  R ) Re
( RO  R )  Re
• Individual resistances can then be found as
Re 
Rt
E
1  meas
ENernst
R 
Rb
RO 
1
Rb
RT

Emeas
1


 ENernst



RT  Rb
Emeas
ENernst
 Rb
1 
 RT

Emeas 
1



E
Nernst 

Polarisation corrections for protonic conductors
Emeas
EO
EH

RO  RO RH  R H

1
1
1


RO  RO RH  R H Re
EO EH

RO RH
Eth 
1
1
1


RO RH Re
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
Eth


 
2µD0  µD0 2  2µH0  µH0 2
2F
  RT ln p
2F
 D2 uD2
pD  H2 uH2
H2
2
• 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.
Hydrogen isotope cell measurements
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.
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.
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.
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 162-163, (2003)