Fakultät Maschinenwesen | Institut für Energietechnik | Professur für Technische Thermodynamik
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Lecture Series at Fritz-Haber-Institute Berlin
„Modern Methods in Heterogeneous Catalysis“
7.12.2012
Impedance Spectroscopy
Old Technique – New Applications
Cornelia Breitkopf
For personal use only!
Outline
o Why old technique?
o What mathematics necessary?
o What measurement principle?
o Which applications in general and in heterogeneous catalysis?
Papers and citations
concept of electrical impedance was first introduced by HEAVYSIDE in the 1880s
Transient methods – general approach
Black Box
disturbance
analysis
TAP …temporal analysis of products
concentration
change in
Porous solid
pulse
shape of pulse
FR …frequency response
volume
Porous solid
modulation
sine-wave
Porous solid
voltage
modulation
see former lectures
pressure
at FHI
detection
EIS …electrical impedance spectroscopy
MS detection = f(t)
of reactants and
products
Electrochemical impedance spectroscopy (EIS) …
…. is now established as a powerful tool
o for investigating the mechanisms of electrochemical reactions
o for measuring the dielectric and transport properties of materials
o for exploring the properties of porous electrodes
o for investigating passive surfaces
Reflections on the history of electrochemical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
Electrochemical impedance spectroscopy (EIS)
The power of the technique arises from:
o it is a linear technique and results are interpreted in terms of Linaer Systems Theory
o if measured of an infinite frequency range, the impedance delivers all information
from a system by linear electrical pertubation/response techniques
o high experimental efficiency
o validation of data is quite easy via integral transform techniques (Kramers-Kronig)
that are independent of the physical processes
…however, EIS data interpretation requires a high level of mathematical skills
Reflections on the history of electrochmical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
Mathematics behind….
…. some examples
Electrochemistry basics behind….
…. some examples
Introduction to impedance
o EIS - Electrochemical Impedance Spectroscopy
o measures dielectric properties of a medium as a function of frequency
o permittivity: interaction of an external field with the electric dipole moment of the
sample
o characterization of electrochemical systems
o impedance…complex electrical resistance
Principle – Representation of Complex Impedance
o Impedance …ability to resist the flow of electric current without limitations of
Ohm´s law
o Electrochemical impedance measurement
 applying an AC potential to an electrochemical cell
 measure then the current through the cell
 analyze via Fourier series
o General principle similar to TAP, Frequency response (see lectures for
diffusion)
Black Box
Sinusoidal
Excitation
Response
Analysis
Principle – Representation of Complex Impedance
o electrical resistance – ability of a circuit element to resist the flow of electrical
current
R=
o Ohm´s law
•
E
I
R resistance
E voltage
I current
ideal resistor
 valid at all E, I levels
 R independent of frequency
 AC current and voltage are in phase
•
ideal capacitor
 AC current and voltage are completely out of
phase, current follows voltage
Principle – Representation of Complex Impedance
o ideal resistor
o ideal capacitor
𝑑
𝑅 = 𝐴
𝐶=
R

d
A

resistance []
electrical resistivity [ cm]
distance [cm]
area [cm2]
conductivity 1/
0  𝐴
𝑑
C capacitance [F]
0 electrical permittivity of vacuum (8.85 *10-14 F/cm)
 relative electrical permittivity of material [-]
water
= 80,1
polymers = 2…8
vacuum = 1
Principle – Representation of Complex Impedance
o replace the simple concept of resistance/capacitance by impedance
o impedance is a more general circuit parameter
o it takes the phase differences between input voltage and output current into account
Impedance can be defined
…as a complex resistance
…realized when a current flows through a circuit
…composed of various resistors, capacitors or inductors.
…it is valid for direct current (DC) and alternating current (AC).
Linearity of electrochemical systems
o systems can be viewed as linear and non-linear systems
o impedance analysis of linear circuits is much easier
o definition of linear systems (by Oppenheim and Willsky in Signals and Systems):
…A linear system ….is one that possesses the important property of
superposition: if the input consists of the weighted sum of several signals, then
the output is simply the superposition (weighted sum) of the responses of the
system to each of the signals
in case of an electrochemical cell: input is potential, output is current
o electrochemical cells are not linear (doubling voltage = double the current)
Pseudo-linearity of electrochemical systems
o at small AC signals (1 – 10 mV), electrochemical cells become pseudo-linear
o linear systems do not produce any harmonics of the excitation frequency
o thus, presence and absence of significant harmonic responses can be used to
check for linearity
Conditions for measurement
o systems being measured must be at steady state
o systems which change with time may cause problems in standard EIS
measurements
o reasons for being not at steady state
o adsorption of solution impurities
o growth of an oxide layer
o build up of reaction products
o coating degradation
o temperature changes
…however, these problems may be solved by faster
detection techniques (see applications) and thus open
opportunity to follow such phenomena
Principle – Representation of Complex Impedance
o for small excitations a pseudo-linear response results with characteristic phase shifts
o excitation signal as function of time
Principle – Representation of Complex Impedance
o excitation as f(t)
Et = Eo sin(t)
Et
E0

f
o response signal
potential at time t
amplitude
radial frequency = 2p f
frequency
It = Io sin(t + )
It
I0

response at time t
amplitude
phase
Principle – Representation of Complex Impedance
o expression similar to Ohm´s law
Z
Et
Eo sin(t )
sin(t )

 Zo
I t I o sin(t   )
sin(t   )
Z
Z0
impedance
magnitude
o E(t) on x-axis, response I(t) on y-axis  Lissajous figure
Principle – Representation of Complex Impedance
o EULER relationship
exp(j) = cos+ j sin
o representation of impedance as a complex function
Et = Eo exp(jt)
It = Io exp(jt - i)
Z () =
Z ( ) 
𝐸𝑡
𝐼𝑡
Et
Eo .exp( jt )

 Z o (cos   j sin  )  Z Re  jZ Im
I t I o .exp( jt   )
Principle – Representation of Complex Impedance
Z () = Z0 (cos + j sin)
o Z() is composed of a real and an imaginary part
o plot on x-axis  real part
o plot on y-axis  imaginary part
Nyquist plot
Principle – Nyquist plot
Each point on the Nyquist plot is the impedance at one frequency
impedance is represented as
vector with length IZI
negative!
angle between vector and x-axis is
phase angle 
high frequencies
low frequencies
Principle – Nyquist plot
Nyquist plots
…..
are based on ……..
o semicircle is characteristic of a single time constant
equivalent circuits
Principle – Bode plot
BODE plot as another presentation opportunity. It shows frequency information.
absolute value of IZI
log frequency
phase shift
log frequency
Models and analogs interpretation
analogs
tools to
interprete
impedance data
physical models
o analogs which always take the form
of electrical equivilant circuits
o aim to reproduce the phenomena
of interest
o simply reproduce the properties
o account for the mechanism of the
processes in terms of valid concepts
o do not pretend to describe physicoelectrochemical properties of the
system
Electrical circuit elements
o Equivilant circuits serve as analysis/evaluation tool for EIS data
o EIS data are fitted to a model representing an equivilant circuit
o common circuit elements: resistors, capacitors, inductors*
o properties of basic models determine the dependency of frequency
* Basics of EIS. www.gamry.com
Physical Electrochemistry – Electrolyte resistance
o solution resistance is a significant factor
o resistance in ionic solution is determined by ionic concentration, type of ion,
temperature, area of cell
o k as conductivity of solution (see standard textbooks and tables for data)
o problem: uniformity of current through an electrolyte area
Basics of EIS. www.gamry.com
Physical Electrochemistry – Double layer capacitance
o existance of electrical double layer on the interface between an electrode and its
surrounding electrolyte
o double layer forms by "sticking" ions on the electrode surface  charged electrode
is separated from charged ions  formation of a capacitor
o value of double layer capacitance depends on electrode potential, temperature,
ionic concentrations, type of ions, oxide layers, electrode roughness, adsorption of
impurities….
Basics of EIS. www.gamry.com
Physical Electrochemistry – Polarization/charge transfer
o polarization occurs via electrochemical reactions at electrode surface
o mixed potentials
o amount of current depends on kinetics of reaction and diffusion of reactants
towards and away from electrode
o example: corrosion
o single kinetically controlled reaction causes a charge transfer resistance
o no mixed potentials
o example: metal substrate in an electrolyte
o charge transfer speed depends on kind of reaction, temperature, concentration of
reaction products, applied potential
Basics of EIS. www.gamry.com
Physical Electrochemistry – Examples
…for combination of electrolyte resistance R1, charge transfer resistance R2,
double layer cpacitance C
R2
R1
C
demonstration examples
Physical Electrochemistry – Examples
…for diffusion and kinetic controlled electrochemical reactions
(dependencies between rate constant k0, transfer coefficient a, bulk solution
concentration cbulk, diffusion coefficient D)
o reaction control by kinetics or by diffusion
demonstration examples
Physical Electrochemistry - Diffusion
o diffusion creates an impedance which is called WARBURG impedance
o impdedance depends on pertubation frequency
 at high frequency a small Warburg impedance results
 at low frequency a higher Warburg impedance is generated
Warburg impedance appears in
Nyquist plot as diagonal line
with slope of 45 °
Example for mixed kinetic and diffusion control
o Warburg impedance is the diffusional impedance for the diffusion layer of infinite
thickness which is characterized for the macroelectrode
o W is given by
with l as relative parameter of charge transfer k and diffusion coefficient D
with kf and kb heterogeneous kinetics on electrodes and D as diffusion coefficient
o RANDLES cell: equivalent circuit with mixed kinetic and charge transfer/diffusion control
Physical Electrochemistry - Diffusion
o Randles cell – equivalent circuit
o electrolyte resistance Re (4700), charge transfer resistance Rct (44000), double
layer cpacitance Cdl (5*e-9), l =7
demonstration examples
graph with Warburg impedance according to values
History – some important theories and names
o concept of electrical impedance was first introduced by HEAVYSIDE in the 1880s
o improvement by KENNELLY and STEINMETZ via use of vector diagrams and
complex numbers representation
o Warburg (1899) determined impedance of diffusional transport of an electroactive
species to an electrode surface
History – some important theories and names
o Kramers-Kronig transforms (1920s)
o validate data consistency
o independent check for validity
o originally to treat optical data
o based on Cauchy theorem which
provides theoretical basis for
causality
from: Reflections on the history of electrochemical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
History – some important theories and names
o introduction of double-layer theory by FRUMKIN and GRAHAM resulted in use of
equivalent circuit modeling approach by RANDLES (1947)
from: Reflections on the history of electrochemical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
History – some important theories and names
o coupling of electrochemical reactions with diffusion by GERISHER and adsorption
by EPPELBOIN
o important electrochemical processes and reactions could be described for the first
time
 hydrogen and electrode reactions
 metal dissolution
 passivity
 corrosion
from: Reflections on the history of electrochemical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
History – some important theories and names
o effects of porous surfaces on electrochemical kinetics  theory of porous
electrodes developed by de LEVIE in the 1960s
from: Reflections on the history of electrochemical impedance spectroscopy.
D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.
History – some important theories and names
o de LEVIE
from: Reflections on the history of
electrochemical impedance
spectroscopy.
D. D. Macdonald. Electrochimica
Acta 51 (2006) 1376-1388.
History – some important theories and names
o data analysis improved by further development of mathematical methods
o improvement of computer and measurements techniques in last 40 years
o new applications: dielectric spectroscopy analysis of conduction in bulk polymers
or cell suspensions, surface corrosion kinetics, analysis of state of biomedical
implants
Example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
…possible to describe also gas diffusion ?
Example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
…and comparison to TAP results ?
373 K
Methan
30
25
Ethan
2
Deff [cm /s]
Neon
Propan
20
Butan
14
3*10 Moleküle/Puls
14
1.5*10 Moleküle/Puls
15
0,10
0,15
0,20
0,25
0.5
1/(M )
Knudsen diffusion of gases over corund determined by TAP (C. Breitkopf)
Example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
o comparison of surface modified samples
o modification with pyridine
o loading of sample with n-butane
o remeasure properties as time resolved responses
example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
o equivilant circuit
Example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
Example: gas diffusion in porous systems
Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H:
Impedance spectroscopy on solid sulfated zirconia catalysts
Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.
Literature example:
The rate of hydrogen and iodine adsorption at Platinum
o
aim of study:
evaluation of adsorption rate of hydrogen in presence of iodine in solution
on the surface of crystal Pt(111) and polycrystalline Pt by EIS
o
why interesting?:
- former investigation of adsorption of hydrogen on Pt, Rh in acid solution
- using iodine can increase adsorption of hydrogen on the surface
R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133
Literature example:
The rate of hydrogen and iodine adsorption at Platinum (experiment)
Sample
- single-crystall Pt(111) and polycrstalline Pt with 10mm
in diameter
- electrolyte: alkaline: KOH addition KI with pH= 13; 14
Set up of experiment
- carrying out in standard electrochemical cell
- using 3 electrodes: counter- (Pt sheet), working (Pt or
Pt (111))-, and reference electrode
Method
- cyclic voltammetry (CV): check the surface orientation
- electrochemical impedance: evaluation of hydrogen
and iodine adsorption
Standard electrochemical cell
R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133
Literature example:
The rate of hydrogen and iodine adsorption on Platinum (equivalent circuit)
o
•
for reversible adsorption (Langmuir) and irreversible adsorption (Frumkin)
equivalent circuit for adsorption control: (Fig. 1)
CD- double-layer capacitance
RadH, CadH- resistance and capacitance of
hydrogen adsorption
Re-solution resistance
Figure 1
R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133
Literature example:
The rate of hydrogen and iodine adsorption at Platinum (results and discussion)
1. Single-crystal Pt(111)
- evaluation of several series and parallel equivilant circuits
- adsorption of iodine is very fast (Fig.3)
- adsorption of hydrogen is slow (Fig.3)
R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133
The rate of hydrogen and iodine adsorption at Platinum
(results and discussion)
2. Polycrystalline Pt
- rate of iodine adsorption in polycrystalline Pt < Pt(111)
- structure-activity relations with respect to water dissiciation
R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133
Literature example:
Impedance spectroscopy on porous materials: A general model of lithium-ion
batteries
Aim of study
- general model to fit electrochemical impedance spectra experimental data considering
adsorption of species at the electrode’s surface of lithium-ion batteries
Reasons
- essential information about processes at graphite electrodes from electrochemical
impedance: charge transfer at interface, diffusion inside, adsorption at the interface,
geometric limitation.
- understanding of limitations in order to obtain maximum performance of electro-active
materials
Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121
Literature example:
Impedance spectroscopy on porous materials: A general model of lithium-ion
batteries (experiment)
1. Structure of cell (Fig.4)
- working electrode: prepared from graphite powder
mixture with binder
- reference electrode: lithium
- current collector: titanium wire
- counter electrode: lithium
- electrolyte: ethylene carbonate (EC) mixture dimethyl
carbonate (DMC) in 1M LiPF6
2. Approach
EIS: using a Potentiostatic/Galvanostat by Princeton
Applied Reseach at 25oC, DC potential of 1.5V,
frequency 100kHz down to 10mHz, amplitude 2mV
Cyclic voltammetry: potential between 1.5V and 0.9V
at sweep rate of 0.2mVs-1
Table 1
3. Materials (Table 1)
Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121
Literature example:
Impedance spectroscopy on porous materials: A general model of lithium-ion
batteries (results)
o
o
Figs. represent the modulus of impedance
spectra with different graphite materials in
Bode plot
 impedance correlates with
irreversible charge consumption on
SEI layer (solid electrolyte interface).
(processes cannot be analyzed from
these diagrams)
Modulus of the electrochemical impedance of a GN44
electrode in EC:DMC at 1.5V vs. Li/Li+
influence of the BET on impedance
 impedance of KS sample at low
frequencies significantly different
Modulus of specific the electrochemical impedance for
different graphite samples in EC:DMC at 1.5V vs. Li/Li+
Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121
Literature example:
Impedance spectroscopy on porous materials: A general model of lithium-ion
batteries (expressions of model)
A general model interpretation of EIS experimental data:
• Based on resistivity of both electrolyte solution and
electrode, eq (6):
  d ln Ap    RT
Cw   S   E
 x  dx   x  FC (1  2t ) x   a. A


S

p
•
Describing the behavior of a porous electrode, mass
transport equations, electrochemical reaction at the
surface, eqs (19,20)
 S  E
  d ln Ap   
RT
j
 x  dx  x    FC (1  2t )Cw  
a

 
S

C
t
•
(6)
x 0, x

  d ln Ap   
 2 D(1  t )  


dx   x x 0, x 
 x
(19)
Electrical equivalent circuit representing the
current lines and reacting sites in porous electrode
(20)
Eqs(19,20) be used for AC response of porous electrodes with assumption in timedomain and steady-state by eq (45)
l  cosh(k l )    
ZT ( ) 
 

NAp  k l sinh(k l )
2
(45)
with
 S2   E2

;
S  E

2  S . E
 S2   E2
Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121
Literature example:
Impedance spectroscopy on porous materials: A general model of lithium-ion
batteries (Fitting experimental data with model)
o equation (45) used for fitting experimental impedance spectra
o impedance spectra were analyzed using Kramer-Kronig transformation
Nyquist plot of electrochemial impedance of GN44
electrode in EC:DMC at 1.5V vs. Li/Li+
Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121
Applications of EIS (current and future)
o impedance of electroactive polymer films with respect to their special properties
such as flexible solution and melt processability manufacturing, blendability with
commodity polymers, ambient stability, unconventional electrical and optical
properties
 new materials in value-added industrial and consumer products as
electroactive inks, paints, coatings, and adhesives
 electrochromic smart windows
 electrically conductive transparent and corrosion-protective films
 supercapacitive materials
 conductive high-performance fibers
 electrochemical sensors, enzyme-modified conductive polymers
from: Impedance spectroscopy – applications to electrochemical and dielectric
phenomena. Vadim F. Lvovich. Wiley 2012.
Applications of EIS (current and future)
o impedance of industrial colloids and lubricants
 reduction of friction processes in industry and automobiles
 opportunity by EIS to resolve a complicated lubricant system both spatially
and chemically to analyze specific parts of that system
o cell suspensions, protein adsorption, and implantable biomedical devices
o insulating films and coatings
o electro-rheological fluids
o impedance of metal-oxide films and alloys
o corrosion monitoring
from: Impedance spectroscopy – applications to electrochemical and dielectric
phenomena. Vadim F. Lvovich. Wiley 2012.
Modifications of EIS (current and future)
o AC voltammetry
o potentiodynamic and (fast) Fourier-transform impedance spectroscopy
o non-linear higher-harmonics impedance analysis
o local EIS
o scanning photo-induced impedance microscopy (SPIM)
from: Impedance spectroscopy – applications to electrochemical and dielectric
phenomena. Vadim F. Lvovich. Wiley 2012.
Thanks for the attention !
Questions please send to:
Cornelia.Breitkopf@tu-dresden.de