Title: (prerequsite training course)
1"a,b,c" Impedance
(prerequsite training course)
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_bas.bg
2SUMMARY
3CONTENTS
- 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
4CONTENTS
51. INTRODUCTION
INTERNATIONAL IMPEDANCE LIFE
61. INTRODUCTION
IMPEDANCE OFFERS IMPORTANT ADVANTAGES
From SCIENTIFIC point of view
From APPLIED point of view
7BASIC 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.
8BASIC 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.
9 2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTROSCOPY
- The Electrochemical Impedance Spectroscopy is
based on the classical method of the TRANSFER
FUNCTION (TF)
Linear System
10 2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTROSCOPY
11 2. WHAT IS ELECTROCHEMICAL IMPEDANCE
SPECTSCOPY
123. IMPEDANCE OF ELECTROCHEMICAL SYSTEMS
133. 1. Basic Working Hypotheses
143. 1. Basic Working Hypotheses
153. 1. Basic Working Hypotheses
163. 1. Basic Working Hypotheses
173. 2. Impedance Presentation and Monitoring
183. 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).
193.3. ADVANTAGES AND DIADVANTAGES OF
ELECROCHEMICAL IMPEDANCE SPECTROSCOPY
204. MAIN STEPS IN THE CLASSICAL IMPEDANCE
INVESTIGATION
I STAGE
21II STAGE DATA ANALYSIS
Data Analysis will be given in the lectures on
the Workshop
22( D3 ?i, Rei, Imi )
235. 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.
245.1. 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.
255.1.1. 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
265.1.1. 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)
275.1.1. LUMPED ELEMENTS CAPACITANCE C
285.1.1. 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.
295.1.1. LUMPED ELEMENTS INDUCTANCE L
305.1.1. 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
315.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
325.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
335.1.2. FREQUENCY DEPENDENT ELEMENTS
WARBURG ELEMENT W
345.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE
355.1.2. 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.
365.1.2. 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.
375.1.2. FREQUENCY DEPENDENT ELEMENTS
CONSTANT PHASE ELEMENT CPE
385.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED ELEMENTS
395.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED WARBURG ELEMENT BW
405.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED WARBURG ELEMENT BW
415.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
425.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
4. Properties of BCP element the most
generalized element
435.1.2. 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)
445.1.2. FREQUENCY DEPENDENT ELEMENTS
BOUNDED CONSTANT PHASE ELEMENT BCP
455.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
465.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
475.2. 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
485.2. SIMPLE CALCULATIONS EXAMPLE ON R AND C
ELEMENTS
495.3. BASIC ELECTROCHEMICAL MODELS5.3.1. MAIN
STRUCTURES OF ELECTROCHEMICAL MODELS
505.3. BASIC ELECTROCHEMICAL MODELS5.3.1. MAIN
STRUCTURES OF ELECTROCHEMICAL MODELS
515.3. BASIC ELECTROCHEMICAL MODELS5.3.2. MODEL
DESCRIPTION CONVENTIONS
525.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
IDEALLY POLARIZABLE ELECTRODE (IPE)
535.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
MODIFIED IDEALLY POLARIZABLE ELECTRODE (MIPE)
545.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)
Rct
555.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)
565.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
POLARIZABLE ELECTRODE (PE)
575.3.3. 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.
585.3.3. MODELS WITHOUT DIFFUSION LIMITATIONS
FARADAIC REACTION WITH ONE ADSORBED SPECIES
595.3.4. MODELS WITH DIFFUSION LIMITATIONS
RANDLES MODEL
605.3.4. MODELS WITH DIFFUSION LIMITATIONS
RANDLES MODEL
615.3.4. MODELS WITH DIFFUSION LIMITATIONS
MODIFIED RANDLES MODEL (MRN)