Transcript Inverse problem in the potentiodynamic electrochemical

Inverse problem in potentiodynamic
electrochemical impedance spectroscopy
A.S. Bondarenko, G.A. Ragoisha
Belarusian State University, Minsk, Belarus
E-mail: [email protected]
Outline
• Multidimensional data acquisition in
potentiodynamic electrochemical
impedance spectroscopy (PDEIS)
• Analysis of 3D PDEIS spectra
• Applications
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
Impedance Z is a two-dimensional physical quantity
Impedance spectrum
shows implicitly the
frequency response
In complex impedance notation Z’ and Z’’characterise 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 threedimensional
Data acquisition and analysis in PDEIS.
Data
acquisition
(1) Data
acquisition
gives 3D impedance spectra
and dc current as functions
of the electrode potential
Inverse
problem
solving
(2) Inverse
problem
solving
PDEIS spectra analysis
in terms of equivalent
electric circuits
Circuit parameters as
functions of the
electrode potential
Deduction of theoretical models
DO – digital output, AO – analog output, AI – analog input
The view of the PDEIS spectrometer screen in cyclic
potential scanning (3D data acquisition)
3D PDEIS spectrum
2D “slices” of
PDEIS
spectrum in
different
coordinates
Cyclic voltammogram
PDEIS spectrum represents electrochemical response
by means of a 3D graph
Imaginary part of impedance (Z’’)
Ferrocyanide reversible
redox transformation
Real part of impedance (Z’)
dc current (I)
Aniline electropolymerisation
Electrode potential (E)
…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
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’’ / Ω
Z’ / Ω
Each “slice” will be processed
separately in the automatic
mode along the potential axis
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
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
Each interfacial process is modeled by its own EEC element
simultaneously.
…
Spectrum analyser fits 2D slices of a PDEIS spectrum to
equivalent circuits sequentially along the potential axis
Equivalent electric circuit
parameters obtained
Equivalent
electric
circuit
Experimental data
(2D “slice” of PDEIS spectrum)
and fitted curve
The spectrum analyser window of the virtual spectrometer
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
Analysis of constituent responses (1)
Equivalent circuit
Zw= σ /(jω)0.5
Warburg
constant
Calculated curve (solid line)
These curves
characterise
the diffusion
of reagents
Diffusion of reagent in ferrocyanide redox transformations on glassy carbon
Analysis of constituent responses (2)
Thus, information on
different aspects
of interfacial dynamics
is obtained from the same
PDEIS spectrum
Pt passivation does not affect diffusional
parameter…
…but affects
charge transfer
Analysis of the constituent responses (3)
Anions co-adsorption during metal monolayer formation
Separate monitoring of simultaneous processes
and
theoretical models development
Inverse problem solving
Multivariate data
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.А. 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.А. 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/physchem/0301005
G.А. 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