Transcript Electrochemical Techniques 1

Electrochemical Theory
© Bob Cottis 1998
Kinetics of Activation Controlled
Reactions
M  Mn+ + ne rate of reaction depends on potential
according to the Tafel equation:
 ia 
E  E   a ln 
 i0,a 
where Ea0  equilibrium potential for anodic reaction
0
a
a  Tafel coefficient for anodic reaction
ia  anodic current density
i0,a  anodic exchange current density
© Bob Cottis 1998
Tafel’s Law
b=2.303
Potenti
al
Slope b
E0a
i0,a
© Bob Cottis 1998
ln |i|
log
|i|
Charge Transfer Resistance

Charge transfer resistance = local slope of i
versus E curve (not log i)
 ia 
E  E  a ln 
 i0,a 
0
a
 E  Ea0 

ia  i0,a exp 
 a 
dia
1
ia


dE Rct ,a a
© Bob Cottis 1998
Charge Transfer Resistance
Note that charge transfer resistance is not a
constant, but depends on the applied current
density
 If we could measure the charge transfer
resistance, we could determine the current
density

© Bob Cottis 1998
Dependence of Kinetics on
Reactant Concentration
More reactant allows reaction to go faster,
hence rate is proportional to reactant
concentration
 e.g. oxygen reduction 

Ox + ne  Red
 (E - E0c ) 

i c = i 0 ,c C s exp  
c 

Surface concentration Minus sign because this
is a cathodic reaction
of oxygen
(and c is taken as positive)
© Bob Cottis 1998
Tafel’s Law
[O2]
Cathodic
reaction
Rate with
constant
[O2]
rate
increases
with
Rate
with
surface
surface concentration
decreasing
potential of
concentration
of oxygen
oxygen varying
[O2]
E0c
Potenti
al
i0,c
© Bob Cottis 1998
ln |i|
log
|i| ilim
Mixed Potential Theory
Net current density on freely-corroding
electrode must be zero.
 Therefore potential (Ecorr) will be that at which
anodic and cathodic current densities are
equal and opposite.
 Called a mixed equilibrium (not a true
electrochemical equilibrium)

© Bob Cottis 1998
Tafel’s Law
Potenti
al
log |i|
© Bob Cottis 1998
Tafel’s Law
E0c
Potenti
al
i0,c
© Bob Cottis 1998
ln |i|
log
|i| ilim
Electrical Units
© Bob Cottis 1998
Charge
Results from inbalance between electrons and
protons in a metal, or between anions and
cations in a solution
 Unit the coluomb, C
 Charge on the electron = 1.6 x 10-19 C

© Bob Cottis 1998
Current
Flow of charge past a point in a conductor
(either electron or ion)
 Unit the Amp, A

© Bob Cottis 1998
Conservation of Charge
Charge can be neither created nor destroyed
 Hence, the currents into and out of a point in
an electrical circuit must add up to zero
(Kirchoff’s Law)

© Bob Cottis 1998
Potential

The potential at a point in space is the work
done in moving a unit charge to that point
from infinity.

Units of volts, V (=J/C)
© Bob Cottis 1998
Potential Difference (or Voltage)

The potential difference or voltage is the
difference between the potentials at two
points, and hence the work done in moving a
unit charge from one point to the other.

Units of Volts
© Bob Cottis 1998
Resistance
A resistor (conventional symbol R) is a device
that produces a voltage across its terminals
when a current passes through it
 Ohm’s Law V=IR
 R is the resistance of the resistor
 Units Ohms, 
 1 V is produced by a current of 1 A through a
resistance of 1 

© Bob Cottis 1998
Capacitance
A capacitor (conventional symbol C) is a
device that stores charge when a current is
applied to it
 Units of capacitance Farads, F

I = C dV/dt
 A 1 F capacitor will produce a voltage
increase of 1 V/s when a current of 1 A flows
into it

© Bob Cottis 1998
Equivalent Circuits
An electrical circuit with the same properties
as a metal-solution interface
 The simplest circuit is a resistor,
corresponding to the polarization resistance,
in parallel with a capacitor, corresponding to
the double layer capacitance

Metal
© Bob Cottis 1998
Rct
Solution
Cdl
Equivalent Circuits
An electrical circuit with the same properties
as a metal-solution interface
 The Randles equivalent circuit adds a series
resistor, corresponding to the solution
resistance

Metal
Rct
Rct
Cdl
© Bob Cottis 1998
Solution
Potential Measurement
© Bob Cottis 1998
Electrode Potential
The potential of a metal electrode with
respect to a solution.
 BUT the charge carriers in a metal are
electrons, while the charge carriers in a
solution are ions.
 So how do we measure it?

© Bob Cottis 1998
Measurement of Electrode
Potential
Use arbitrary reference electrode to convert
from ion current to electron current.
 Conventional standard reference electrode is
based on the reaction

2H
Hydrogen
ions in
solution at
unit activity
© Bob Cottis 1998

 2e

Electrons in
the metal
 H2
Hydrogen gas
in solution at
unit activity
The Normal Hydrogen Electrode
(NHE)
© Bob Cottis 1998
Secondary Reference Electrodes

Reference electrodes of the first kind, a metal
in equilibrium with a soluble salt:
Cu  Cu
2
 2e

Potential controlled
by Cu2+
concentration
© Bob Cottis 1998
Secondary Reference Electrodes

Reference electrodes of the second kind, a
metal in equilibrium with a sparingly soluble
salt and a solution containing anions of the
salt:
Ag+ concentration

Ag  Ag  e

 controls equilibrium
potential
AgCl  Ag  Cl

Chloride concentration controls
Ag+ concentration
[Ag+][Cl-] = const
© Bob Cottis 1998
The Ag/AgCl Electrode
© Bob Cottis 1998
Potentials of Common Reference
Electrodes
Common Name
Electrode
V vs NHE
Saturated Calomel Electrode (SCE)
Hg/Hg2Cl2/sat. KCl
+0.241
Calomel
Hg/Hg2Cl2/1M KCl
+0.280
Mercurous sulphate
Hg/Hg2SO4/sat. K2SO4
+0.640
Mercurous oxide
Hg/HgO/1M NaOH
+0.098
Silver chloride
Ag/AgCl/sat. KCl
+0.197
Copper sulphate
Cu/sat. CuSO4
+0.316
Zinc in seawater
Zn/seawater
~ -0.8
© Bob Cottis 1998
Practical Potential Measurement
© Bob Cottis 1998
Potential Measurement
Requirements - Input Resistance
High input resistance to minimize errors due
to source resistance.
 For most corrosion work 107 ohm is sufficient,
but for high resistance systems (paints,
passive metals etc.) 109 ohm or more may be
better.

© Bob Cottis 1998
Potential Measurement
Requirements - Frequency
Response

Frequency response (ability to detect rapid
changes). Often not important for corrosion
measurements.
– Measurements at around 1 Hz are quite easy
– Measurements above 1kHz are rather more
difficult
– Measurements at around 50 Hz are difficult (due
to mains frequency interference).
© Bob Cottis 1998
Potential Measurement
Requirements - Resolution

Resolution is the ability to detect small
changes in a large value
– for most corrosion measurements 1 mV is
adequate
– for electrochemical noise and similar studies, 1mV
may be necessary
© Bob Cottis 1998
Potential Measurement
Requirements - Sensitivity
Resolution is the ability to detect small
changes in a large value
 Sensitivity is the ability to measure small
values

– e.g. it is relatively easy to obtain a sensitivity of 1
mV when measuring 1 mV, but it is very difficult
to obtain a resolution of 1 mV when measuring a
10 V signal
– not usually a problem for corrosion measurements
© Bob Cottis 1998
Potential Measurement
Requirements - Precision
Resolution is the ability to detect small
changes in a large value
 Sensitivity is the ability to measure small
values
 Precision or accuracy is the ability to measure
the ‘true’ value

© Bob Cottis 1998
Potential Measurement Methods

Analogue meter (moving coil)
–
–
–
–
–
© Bob Cottis 1998
low impedance (typically 20 kohm/V)
poor frequency response (~1 Hz)
low sensitivity (~1 mV)
low resolution (~1%)
low precision (~3%)
Potential Measurement Methods

Analogue meter (electronic)
–
–
–
–
–
© Bob Cottis 1998
high impedance (typically 10 Mohm)
poor frequency response (~1 Hz)
possibly high sensitivity (~1mV)
low resolution (~1%)
low precision (~3%)
Potential Measurement Methods

Digital meter
–
–
–
–
–
© Bob Cottis 1998
high impedance (typically 10 Mohm or more)
poor frequency response (around 3 Hz)
high sensitivity (10 mV to 100 nV)
high resolution (0.1% to 0.0001%)
high precision (0.1% to 0.0001%)
Potential Measurement Methods

Electrometer (digital)
–
–
–
–
–
© Bob Cottis 1998
very high impedance (~1014 ohm)
poor frequency response (<1 Hz)
high sensitivity (1 mV to 100 nV)
high resolution (0.1% to 0.001%)
high precision (0.1% to 0.001%)
Potential Measurement Methods

Chart recorder
– impedance depends on instrument (from 103 to
107 ohm)
– moderate frequency response (~10 Hz)
– moderate sensitivity (~10mV)
– moderate resolution (~0.1%)
– moderate precision (~0.1%)
© Bob Cottis 1998
Potential Measurement Methods

Oscilloscope
–
–
–
–
–
© Bob Cottis 1998
high impedance (106 to 107 ohm)
high frequency response (10 MHz or more)
moderate sensitivity (~100mV)
poor resolution (~1%)
poor precision (~1%)
Potential Measurement Methods

Computer data acquisition
– high impedance (~107 ohm)
– variable frequency response (10 Hz to 1 MHz or
more)
– moderate to good sensitivity (~10 mV)
– moderate to good resolution (0.5 to 0.01%)
– moderate to good precision (0.5 to 0.01%)
– facilitates subsequent plotting and analysis
© Bob Cottis 1998
Practical Current Measurement
© Bob Cottis 1998
Current Measurement
Requirements - Input Resistance
Low input resistance to minimize errors due
to voltage drop across measuring device.
 For most corrosion work 1 mV voltage drop
will have little effect.
 A wide dynamic range (ratio of largest current
to smallest current) is required for many
corrosion measurements.

© Bob Cottis 1998
Current Measurement Methods

Analogue meter (moving coil)
– usually poor input resistance (~ 75 mV drop at full
scale)
– poor frequency response (around 1 Hz)
– low resolution (around 1%)
– low precision (around 3%)
– dynamic range acceptable using range switching
© Bob Cottis 1998
Current Measurement Methods

Analogue meter (electronic)
– usually poor input resistance (~100 mV drop at
full scale)
– poor frequency response (around 1 Hz)
– low resolution (around 1%)
– low precision (around 3%)
– dynamic range acceptable using range switching
© Bob Cottis 1998
Current Measurement Methods

Digital multimeter
– often poor input impedance (~100 mV drop at full
scale)
– poor frequency response (around 3 Hz)
– high resolution (0.1% to 0.0001%)
– high precision (0.1% to 0.0001%)
– often poor sensitivity (100 mA to 1 mA)
– dynamic range acceptable using autoranging
© Bob Cottis 1998
Current Measurement Methods

Electrometer (digital)
–
–
–
–
–
© Bob Cottis 1998
essentially zero input impedance
poor frequency response (<1 Hz)
high resolution (0.1% to 0.001%)
high precision (0.1% to 0.001%)
good dynamic range using range switching or
autoranging
Current Measurement Methods

Chart recorder
– resistor used to convert current to voltage, hence
voltage drop depends on sensitivity
– moderate frequency response (~10 Hz)
– moderate resolution (~0.1%)
– moderate precision (~0.1%)
– acceptable dynamic range providing range
switching is used
© Bob Cottis 1998
Current Measurement Methods

Oscilloscope
– resistor used to convert current to voltage, hence
voltage drop depends on sensitivity
– high frequency response (10 MHz or more)
– poor resolution (~1%)
– poor precision (~1%)
– poor dynamic range
© Bob Cottis 1998
Current Measurement Methods

Computer data acquisition
– resistor used to convert current to voltage, hence
voltage drop depends on sensitivity
– variable frequency response (10 Hz to 1 MHz or
more)
– moderate to good resolution (0.5 to 0.01%)
– moderate to good precision (0.5 to 0.01%)
– dynamic range often limited
– facilitates subsequent plotting and analysis
© Bob Cottis 1998