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Energy Conversion and Storage
Double layer illustration
3 electrode setup
(1) working electrode; (2) auxiliary electrode;
(3) reference electrode
A reference electrode is an
electrode which has a stable
electrode potential.
The high stability of the electrode
potential is usually reached by
employing a redox system with
constant (buffered or saturated)
concentrations of each of the
participants of the redox reaction.
Eg saturated calomel electrode
+0.244 V vs. SHE at 25 °C
St Andrews
Impedance Spectroscopy
Introduction to EIS and process
Why use a spectroscopic technique for electrical characterisation?
dc measurements give "total" or "composite" response:
Grain boundaries
Electrode-sample interface
Film-substrate interface
Defect/compositional gradients
Space charge effects
Charge transfer
Impedance spectroscopy allows separation of different electroactive regions
i.e. Electrical Microstructure
deconvolution of bulk behaviour from other effects
V =V0 sin ωt
I = lo sin(ωt +Φ)
The impedance is given by Z =V/I
Impedance is a vector quantity and can be defined using
complex numbers
Z* =
Z’ – jZ”
Complex real imaginary
Note that this defines Z" as a positive value for a
capacitive reactance
Z' + jZ" also often used
Circuit Elements
Impedance, Z (essentially ac version of Ohm’s law):
Resistor, R:
No phase difference between current (lt) and voltage (Vt):
Capacitor, C:
Current (lt) leads voltage (Vt) by 90o
Inductor, L:
Current (lt) lags voltage (Vt) by 90o
What is Impedance Spectroscopy?
Apply an ac (sinusoidal) voltage of varying frequency:
(typically in the range 10-2 to 107 Hz)
Measure the current response
Determine IZI(ω) and Ɵ(ω),
or Z*(ω) = Z’(ω)-jZ"(ω):
Z and Ɵ (and Z', Z") vary with frequency
- varying R, C (and L) contributions
Separation in frequency domain of physical processes
giving rise to each type of behavior
electrical "composition" or microstructure
Physical origin of circuit elements
Capacitive: recoverable displacement of charge
elastic process
Dielectric constant (permittivity, e’)
polarsisation processes
Resistive: transfer of charge, energy loss inelastic process
Conductivity, dc or ac (semi-, conductors)
(long range migration of charge (electrons/ ions)
Inductance : storage of energy in magnetic field generated by
current – mainly conductors
tan δ (dielectrics/ insulators), ac only
ε”/ ε’
(dissipation, transient leakage)
Materials response to an ac field depends on frequency
Response can be represented by a combination of various R. C and L
=> Equivalent circuit
Electrode Processes