Inverse problem in potentiodynamic electrochemical impedance spectroscopy

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Inverse problem in potentiodynamic
electrochemical impedance spectroscopy

• A.S. Bondarenko, G.A. RagoishaBelarusian State
  University, Minsk, Belarus
• E-mail bondarenkoas_at_bsu.by

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Outline

• Multidimensional data acquisition in
  potentiodynamic electrochemical impedance
  spectroscopy (PDEIS)
• Analysis of 3D PDEIS spectra
• Applications

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Electrochemical impedance Z is the complex
opposition of electrochemical system to
alternative current. Z is a two-dimensional
value, which is usually represented in complex
notation by real impedance Z and imaginary
impedance Z. Electrochemical impedance
characterises electrochemical reaction and
electrode surface
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Impedance Z is a two-dimensional physical quantity
Impedance spectrum shows implicitly the frequency
response
In complex impedance notation Z and
Zcharacterise different parts of a complex ac
response Z - the in-phase part Z the
out-of-phase part With variable potential E the
response becomes three-dimensional
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Data acquisition and analysis in PDEIS.
Data acquisition
Inverse problem solving
(2) Inverse problem solving
(1) Data acquisition gives 3D impedance
spectra and dc current as functions of the
electrode potential
Circuit parameters as functions of the
electrode potential
DO digital output, AO analog output, AI
analog input
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The view of the PDEIS spectrometer screen in
cyclic potential scanning (3D data acquisition)
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PDEIS spectrum represents electrochemical
response by means of a 3D graph
Ferrocyanide reversible redox transformation
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more examples of 3D PDEIS spectra
PDEIS spectra can be used either as visual
signatures of systems under investigation, or
subjected to further analysis The solution of
inverse problem in PDEIS gives more detailed
information about the system
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3D PDEIS spectrum is considered as a collection
of 2D data (the spectrum is cut into 2D
slices on the potential scale with each slice
representing impedance spectrum for a certain
electrode potential)
-Z / O
Each slice will be processed separately in the
automatic mode along the potential axis
Z / O
E / mV
For each of the 2D slices the minimisation
problem is solved with complex nonlinear least
squares routine, and this gives the parameters of
equivalent electric circuits as functions of the
potential
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Electrochemical interface modeling by equivalent
electric circuits (EEC) is a key procedure in the
solution of inverse problem
EEC comprises common electric circuit elements
(resistors, capacitors etc.) and specific
electrochemical elements, e.g.impedance of
diffusion (Warburg impedance).
By means of EEC the total acquired response is
decomposed into constituents related to different
interfacial processes that take place
simultaneously.

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Spectrum analyser fits 2D slices of a PDEIS
spectrum to equivalent circuits sequentially
along the potential axis
The spectrum analyser window of the virtual
spectrometer
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The built-in analyser produces the dependences of
EEC parameters on the electrode
potential(examples )
The dependences of EEC parameters on the
electrode potential characterise dynamics of
various interfacial processes. Additional
information comes from comparison of EEC
parameters dependences with theoretical models
Cu and Bi monolayers formation accompanied by
coadsorption of anions
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Analysis of constituent responses (1)
Equivalent circuit
Zw s /(j?)0.5
Warburg constant
Diffusion of reagent in ferrocyanide redox
transformations on glassy carbon
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Analysis of constituent responses (2)
Thus, information on different aspects of
interfacial dynamics is obtained from the
same PDEIS spectrum
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Analysis of the constituent responses (3)
Anions co-adsorption during metal monolayer
formation
Separate monitoring of simultaneous
processes and theoretical models development
Multivariate data
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Conclusions
Computer program for analysis of 3D PDEIS spectra
has been developed and integrated with the
program of PDEIS virtual spectrometer A new
approach to investigation of simultaneous
nonstationary processes on the electrochemical
interface has been developed on the base of
analysis of 3D PDEIS spectra
Full-text articles about PDEIS available free on
Chemweb G.?. Ragoisha and A.S. Bondarenko,
Potentiodynamic electrochemical impedance
spectroscopy for solid state chemistry, Solid
State Phenom. 90-91 (2003) 103-108.
http//preprint.chemweb.com/physchem/0301002 G.?.
Ragoisha and A.S. Bondarenko, Investigation of
monolayers by potentiodynamic electrochemical
impedance spectroscopy, Physics, Chemistry and
Application of Nanostructures, World Scientific,
2003, 373-376. http//preprint.chemweb.com/physche
m/0301005 G.?. Ragoisha and A.S. Bondarenko,
Potentiodynamic electrochemical impedance
spectroscopy. A review, Proc. Phys-Chem. Res.
Inst., BSU, Minsk, 2003, 138-150
http//preprint.chemweb.com/physchem/0308001 G.A.
Ragoisha, A.S. Bondarenko. Potentiodynamic
electrochemical impedance spectroscopy of silver
on platinum in underpotential and overpotential
deposition. Surf. Sci. in press.
http//arxiv.org/e-print/cond-mat/0310449