Post on 16-Dec-2015
Inverse problem in potentiodynamic electrochemical impedance spectroscopy
A.S. Bondarenko, G.A. RagoishaBelarusian State University, Minsk, Belarus
E-mail: bondarenkoas@bsu.by
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
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 three-
dimensional
Impedance spectrumshows implicitly thefrequency response
Impedance Z is a two-dimensional physical quantity
(1) Data acquisition
gives 3D impedance spectra and dc current as functions
of the electrode potential
(2) Inverse problem solving
CCircuit parameters as ircuit parameters as functions of the functions of the
electrode potentialelectrode potential
Deduction of theoretical modelsDeduction of theoretical models
DO – digital output, AO – analog output, AI – analog input
Data acquisitionData acquisition Inverse problem solvingInverse problem solving
PDEIS spectra analysis PDEIS spectra analysis in terms ofin terms of equivalent equivalent
electric circuitselectric circuits
Data acquisition and analysis in PDEIS.
The view of the PDEIS spectrometer screen in cyclic potential scanning (3D data acquisition)
3D PDEIS spectrum3D PDEIS spectrum
Cyclic voltammogramCyclic voltammogram
2D “slices” of 2D “slices” of PDEISPDEIS
spectrum inspectrum in differentdifferent
coordinatescoordinates
PDEIS spectrum represents electrochemical response
by means of a 3D graph
Ferrocyanide reversibleFerrocyanide reversible redox transformationredox transformation
Aniline electropolymerisationAniline electropolymerisation
Electrode potential (E)
Imaginary part of impedance (Z’’)
Real part of impedance (Z’)
dc current (I)
…more examples of 3D PDEIS spectra
PDEIS spectra can be used either as visual signatures ofsystems 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)
Each “slice” will be processedEach “slice” will be processedseparately in the automaticseparately in the automatic
mode along the potential axismode along the potential axis
E / mVZ’ / Ω
-Z’’ / Ω
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 problemEEC comprises common electric circuit elements (resistors, capacitors etc.) andspecific electrochemical elements, e.g.impedance of diffusion (Warburg impedance).
Each interfacial process is modeled by its own EEC element
…
By means of EEC the total acquired response is decomposed into
constituents related to different interfacial processes that take place
simultaneously.
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
EEquivalentquivalent electric electric circuitcircuit
EEquivalent electric circuitquivalent electric circuitparameters obtainedparameters obtained
Experimental data Experimental data (2D “slice” of PDEIS spectrum)(2D “slice” of PDEIS spectrum)
and fitted curveand fitted curve
Cu and Bi monolayers formation accompanied by coadsorption of anions
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
Analysis of constituent responses (1)Equivalent circuitEquivalent circuit
Zw= σ /(jω)0.5 These curves characterise
the diffusion of reagents
Calculated curve (solid line)
Warburgconstant
Diffusion of reagent in ferrocyanide redox transformations on glassy carbon
Analysis of constituent responses (2)
…but affects charge transfer
Pt passivation does not affect diffusionalparameter…
Thus, information on different aspects
of interfacial dynamicsis obtained from the same
PDEIS spectrum
Analysis of the constituent responses (3)
Anions co-adsorption during metal monolayer formationAnions co-adsorption during metal monolayer formation
Multivariate dataMultivariate data
Separate monitoring of simultaneous processesSeparate monitoring of simultaneous processesandand
theoretical models developmenttheoretical models development
Inverse problem solvingInverse problem solving
ConclusionsComputer program for analysis of 3D PDEIS spectra has beendeveloped and integrated with the program of PDEISvirtual spectrometer
A new approach to investigation of simultaneous nonstationaryprocesses on the electrochemical interface has been developedon 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/0301002G.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/0301005G.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/0308001G.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