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