"a,b,c" Impedance

1
"a,b,c" Impedance
Daria Vladikova IEES - BAS, 10 Acad. G. Bonchev
St., 1113 Sofia, BULGARIA Centre of Excellence
Portable and Emergency Energy Sources E-mail
d.vladikova_at_astratec.net
2
SUMMARY
3
CONTENTS

• Introduction 5
• What is Electrochemical Impedance
  Spectroscopy 10
• Impedance of Electrochemical Systems 13
• 3.1. Basic Hypotheses 14
• 3.2. Impedance Presentation and Monitoring
• 3.3. Advantages and disadvantages of
  Electrochemical Impedance Spectroscopy 20
• Main Steps in the Classical Impedance
  Investigation 21
• Impedance Models 24
• 5.1. Impedance Elements 25
• 5.1.1. Lumped Elements
  26
• Resistance 26
• Capacitance 28
• Inductance 30
• 5.1.2. Frequency Dependent Elements 32
• Warburg Element 32

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CONTENTS
5
1. INTRODUCTION
INTERNATIONAL IMPEDANCE LIFE
6
1. INTRODUCTION
IMPEDANCE OFFERS IMPORTANT ADVANTAGES
From SCIENTIFIC point of view
From APPLIED point of view
7
BASIC IMPEDANCE LITERATURE
1. INTRODUCTION
 D. C. Graham, Chem. Rev., 1947, 41, 441.  P.
Delahay, New Instrumental Methods in
Electrochemistry, 1965, Wiley-Interscience, New
York.  P. Delahay, Double Layer and Electrode
Kinetics, 1965, Wiley-Interscience, New York.
D. E. Smith, Electroanalytical Chem. 1966,
1,1(Eds. A. J. Bard, Marcel Dekker), New
York.  M. Sluyters-Rehbach and J. H. Sluyters in
On the impedance of galvanic cell. The potential
dependence of the faradaic parameters for
electrode processes with coupled homogeneous
chemical reactions, Electroanalytical Chem. 1970,
4,1(Eds. A. J. Bard, Marcel Dekker), New
York.  J. R. Macdonald in Superionic Conductors,
(Eds. G. D. Mahan, W. L. Roth), Plenum Press, New
York, 1976, p.81.  J. R. Macdonald in Electrode
Processes in Solid State Ionics, (Eds. M. Kleitz
and J. Dupuy), Reidel, Dordrecht, Holland, 1976,
p.149.   M. C. H. McKubre and D. D. Macdonald in
A Comprehensive Treatise of Electrochemistry,
(Eds. J. OM Bockris, B. E. Conway and E.
Yeager), Plenum Press, New York, 1977.  D. D.
MacDonald, Transient Techiques in
Electrochemistry, Plenum Press, New York,
1977.  R. D. Armstrong, M. F. Bell and A. A.
Metcalfe, Electrochem. Chem. Soc. Spec. Rep.
1978, 6, 98.  W. I. Archer and R. D. Armstrong,
Electrochem. Chem. Soc. Spec. Rep. 1980, 7,
157.  C. Gabrielli, Identification of
Electrochemical Process by Freguency Response
Analysis, Monograph Reference 004 /83, Solartron
Instr.Group, Farnsborough, England, 1980. D. D.
Macdonald and M. C. H. McKubre, Electrochemical
Impedance Technigues in Corrosion Science
Electrochemical Corrosion Testing, STP 272, ASTM,
Philadelphia, PA, 1981.  J. R. Macdonald, IEEE
Trans. Electrical Insulation EI-15, 1981,
65.  D. D. Macdonald and M. C. H. McKubre,
Modern Aspects of Electrochemistry, (Eds. J. OM
Bockris, B. E. Conway and R. E. White), Plenum
Press, New, 1982, 14, 61. M. Sluyters-Rehbach
and J. H. Sluyters in Comprehensive Treatise of
Electrochemistry, (Eds. E. Yeager, J. O.M.
Bockris, B. E. Conway and S. Sarangapani), Plenum
Press, New York, 1984, p. 177.
8
BASIC IMPEDANCE LITERATURE
1. INTRODUCTION

•  C. Gabrielli, Identification of Electrochemical
  Processesby Frequency Respose Analysis, Technical
  Report ? 004, Solartron, Hampshire, 1984.(can be
  dounloaded from http//accessimpedance.iusi.bas.bg
  )
• J. R. Macdonald (Ed.), Impedance Spectroscopy -
  Emphasizing Solid Materials and Systems,
  Wiley-Interscience, New York, 1987.
•  C. Gabrielli, Use and Applications of
  Electrochemical Impedance Tecniques, Technical
  Report ? 024, Solartron, Hampshire, 1990.
•  Z. Stoynov, B. Grafov, B. Savova-Stoynova and
  V. Elkin, Electrochemical Impedance, 1991,
  Publishing House Science, Moscow (in Russian).
•  D. D. Macdonald in Tecniques for
  Characterization of Electrodes and
  Electrochemical Processes, (Eds. H. R. Varma and
  J. R. Selman, J.WileySons), New York, 1991,
  p.515.
•  F. Mansfeld and W. J. Lorenz in Tecniques for
  Characterization of Electrodes and
  Electrochemical Processes, (Eds. H. R. Varma and
  J. R. Selman, J.WileySons), New York, 1991,
  p.581.
•  C. M. A. Brett and A. M. Oliveira Brett,
  Electrochemistry, Principles, Methods and
  Applications, 1993, Oxford University Press.
•  A. Lasia, Electrochemical Impedance
  Spectroscopy and Its Applications, Modern Aspects
  of Electrochemistry, B. E. Conway, J. Bockris,
  and R. White, Edts., Kluwer Academic/Plenum
  Publishers, New York, 1999, Vol. 32, p. 143-248.
  http//www.wkap.nl/prod/b/0-306-45964-7
•  Second International Symposium on
  Electrochemical Impedance Spectroscopy,
  Electrochimica Acta, 38, 14, 1993.
•  Third International Symposium on
  Electrochemical Impedance Spectroscopy,
  Electrochimica Acta, 41, 7/8, 1996.
•  EIS98 Proceedings Impedance Spectroscopy
  Electrochimica Acta, 44, 24, 1999.
•  Fifth International Symposium on
  Electrochemical Impedance Spectroscopy,
  Electrochimica Acta, 47, 13/14, 2002.
• R. Cottis and St. Turgoose, Electrochemical
  Impedance and Noise, Eds. B. C. Syrett, NACE
  International, 1440, South Greek Drive, Houston,
  TX77084, 1999.

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2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTROSCOPY

• The Electrochemical Impedance Spectroscopy is
  based on the classical method of the TRANSFER
  FUNCTION (TF)

Linear System
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2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTROSCOPY

• k( iw) y( iw) / x( iw)

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2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTSCOPY
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3. IMPEDANCE OF ELECTROCHEMICAL SYSTEMS
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3. 1. Basic Working Hypotheses
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3. 1. Basic Working Hypotheses
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3. 1. Basic Working Hypotheses
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3. 1. Basic Working Hypotheses
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3. 2. Impedance Presentation and Monitoring
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3. 2. Impedance Presentation and Monitoring
3.2.1. Impedance monitoring (graphical
visualization) The problem of impedance
monitoring comes from the 3-dimensional nature of
the data, which should be plotted in a
2-dimensional pattern. The most common
presentations are the complex plane (Nyquist)
plot (in Cartesian coordinates) and Bode plots
(in polar coordinates).
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3.3. ADVANTAGES AND DIADVANTAGES OF
ELECROCHEMICAL IMPEDANCE SPECTROSCOPY
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4. MAIN STEPS IN THE CLASSICAL IMPEDANCE
INVESTIGATION
I STAGE
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II STAGE DATA ANALYSIS
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( D3 ?i, Rei, Imi )
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5. IMPEDANCE MODELS
There are few approaches for presentation of the
impedance models. The electrical circuit
modelling approach is very convenient for
impedance studies of electrical properties. In
this case the electrical circuit has a response
identical to that obtained from the measurement
of the investigated system. The electrical
circuit can be regarded as a construction of
different electrical and electrochemical elements
(structural elements) connected under given laws.
If the model is not formal, the values of its
elements could give a significant contribution to
the physical understanding of the investigated
system.
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5.1. IMPEDANCE ELEMENTS

• Impedance elements are described with one or
  more parameters, which determine their
  dimensions.
• Impedance elements can be divided it 2 basic
  groups
• Lumped elements resistance R capacitance C
  inductance L. They are directly adopted form
  electrotechniques, i.e. they are electrical
  elements and can describe homogeneous systems.
• Frequency dependent elements they describe
  frequency unhomogeneity. They are developed for
  descrption of some electrochmical processes,
  i.e. they are electrochemical elements.

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5.1.1. LUMPED ELEMENTS RESISTANCE R

• R is the simplest modelling element
• Modelling in the time (t) domain follows Ohms
  Law
• URR.I
• (UR - voltage drop I current)

Dimensions ohm (O) VA-1 m2kgA-2s-3
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5.1.1. LUMPED ELEMENTS RESISTANCE R
2. Modelling in the frequency (?) domain ZR (i?)
R only real part (ReR
Im 0)

• 3. Physical meaning
• description of energy losses dissipation of
  energy potential barrier electronic
  conductivity or conductivity of very fast
  carriers
• Electrolyte resistance - Zs(i?) Rs - for
  water based electrolytes
• Ohmic resistance - R? Rs Rm (Rm - R of
  metallic leads)

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5.1.1. LUMPED ELEMENTS CAPACITANCE C
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5.1.1. LUMPED ELEMENTS CAPACITANCE C

• 3. Physical meaning
• modelling of mass and charge accumulation,
  dielectric polarization, integral relation
  between parameters
• Double layer capacitance Cdl . The impedance of
  the double layer has a capacitive character.

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5.1.1. LUMPED ELEMENTS INDUCTANCE L
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5.1.1. LUMPED ELEMENTS INDUCTANCE L

• 3. Physical meaning
• Modelling of self inductance of the connecting
  cables, the measuring cell and investigated
  objects, self inductance of current flow or of
  charge carriers movement
• accumulation of magnetic energy

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5.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE

• For integer values of n ( n 1, 0, -1) CPE
  models respectively the lumped elements C, R
  and L.

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5.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE

• 3. Physical meaning of CPE.
• CPE may have direct physical meaning
• the generalized resistance n 0 - 0.2 may
  model conductance of ionic clouds or conductance
  connected with accumulation of magnetic or
  electrostatic energy
• the generalized capacitance n 0.8 - 1 may
  model surface roughness of the electrode or
  distribution of the charge carrier density, i.e.
  a double layer with complicated stricture
• The generalized Warburg n 0.4 - 0.6 may present
  non-ideal geometry of the diffusion layer
  presence of migration or convection diffusion
  connected with energy loses or accumulation of
  charges constrains of the host matrix to the
  diffusion of species,unhomogeneous diffusion
• CPE may be also used for formal better modelling
  of an external similarity with the measured
  impedance.

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5.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED ELEMENTS
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED WARBURG ELEMENT BW
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED WARBURG ELEMENT BW
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
4. Properties of BCP element the most
generalized element
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
4. Properties of BCP element

• criterion for verification of BCP
• ( a and b are the angles of the diagrams
  asymptotes respectively at low and high
  frequencies.

b 2a (n p/2)
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5.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
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5.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
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5.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
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5.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
Series connection
Z (iw) ZR(iw) ZC(iw)
Z (i?) ZR (i?) ZC (i?) R (i?C)-1 R -
i(?C)-1
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5.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
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5.3. BASIC ELECTROCHEMICAL MODELS5.3.1. MAIN
STRUCTURES OF ELECTROCHEMICAL MODELS

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5.3. BASIC ELECTROCHEMICAL MODELS5.3.1. MAIN
STRUCTURES OF ELECTROCHEMICAL MODELS

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5.3. BASIC ELECTROCHEMICAL MODELS5.3.2. MODEL
DESCRIPTION CONVENTIONS

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
IDEALLY POLARIZABLE ELECTRODE (IPE)

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
MODIFIED IDEALLY POLARIZABLE ELECTRODE (MIPE)

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)
Rct

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
MODIFIED POLARIZABLE ELECTRODE (MPE)
1. Structure La Rs CPEdl/ Rct 2. Application
one of the most applied model structures, which
describes the depression of the semicircle often
observed in real systems. 3. Physical meaning
the application of the MPE model may be a better,
but formal description of the investigated
system, or it may have a physical meaning
description of the electrodes surface roughness.

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5.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
FARADAIC REACTION WITH ONE ADSORBED SPECIES

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5.3.4. MODELS WITH DIFFUSION LIMITATIONS
RANDLES MODEL

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5.3.4. MODELS WITH DIFFUSION LIMITATIONS
RANDLES MODEL

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5.3.4. MODELS WITH DIFFUSION LIMITATIONS
MODIFIED RANDLES MODEL (MRN)