Potentiodynamic electrochemical impedance spectroscopy

Article abstract of DOI:10.1016/j.electacta.2004.10.055

Potentiodynamic electrochemical impedance spectroscopy (PDEIS) uses virtual instruments to acquire, by means of a common potentiostat, multidimensional dependencies that characterise variations of dc current and frequency response in the same potential scan. Unlike classical EIS, which finds the whole equivalent circuit in stationary states, PDEIS finds, in potentiodynamic systems, only those elements of equivalent circuits that are needed to decompose the ac response in a limited range of frequencies. The decomposition of ac response into components belonging to different elements is provided by a built-in spectrum analyser, which gives dependences of equivalent circuit parameters on variable potential. The new technique develops the idea, originally suggested by D.E. Smith, of versatile characterisation of the electrochemical response in a simple computerised experiment. PDEIS solves this problem with the use of multi-frequency potentiodynamic probing based on analysis of streams of wavelets. The use of the additional variable (electrode potential) helps to disambiguate the equivalent circuit analysis. The PDEIS performance is illustrated on systems of different kind: a reversible system (ferricyanide redox transformations on glassy carbon and platinum electrodes), a system that is locally reversible but shows different responses in forward and backward scans (Bi upd on Au) and strongly irreversible variable system (initial stages of aniline electropolymerisation on gold).

Full text of DOI:10.1016/j.electacta.2004.10.055

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Electrochimica Acta 50 (2005) 1553–1563
Potentiodynamic electrochemical impedance spectroscopy
G.A. Ragoisha∗, A.S. Bondarenko
Physico-Chemical Research Institute, Belarusian State University, 220050 Minsk, Belarus
Available online 23 November 2004
Abstract
Potentiodynamic electrochemical impedance spectroscopy (PDEIS) uses virtual instruments to acquire, by means of a common potentiostat,
multidimensional dependencies that characterise variations of dc current and frequency response in the same potential scan. Unlike classical
EIS, which finds the whole equivalent circuit in stationary states, PDEIS finds, in potentiodynamic systems, only those elements of equivalent
circuits that are needed to decompose the ac response in a limited range of frequencies. The decomposition of ac response into components
belonging to different elements is provided by a built-in spectrum analyser, which gives dependences of equivalent circuit parameters on
variable potential. The new technique develops the idea, originally suggested by D.E. Smith, of versatile characterisation of the electrochemical
response in a simple computerised experiment. PDEIS solves this problem with the use of multi-frequency potentiodynamic probing based on
analysis of streams of wavelets. The use of the additional variable (electrode potential) helps to disambiguate the equivalent circuit analysis.
The PDEIS performance is illustrated on systems of different kind: a reversible system (ferricyanide redox transformations on glassy carbon
and platinum electrodes), a system that is locally reversible but shows different responses in forward and backward scans (Bi upd on Au) and
strongly irreversible variable system (initial stages of aniline electropolymerisation on gold).
© 2004 Elsevier Ltd. All rights reserved.
Keywords: Electrochemical impedance; PDEIS; Underpotential deposition; Bismuth; Electropolymerisation; Polyaniline
1. Introduction
of the components of the electrochemical response has a no-
table potential for interfacial studies: a double electric layer
is the thinnest probe, which helps to detect even the slightest
changes on the interface by the variation of the double layer
capacitance, the Faradaic responses are remarkably sensitive
as well as selective, and the responses of electronic processes
in semiconductor space charge layers on electrochemical in-
terfaces provide unique possibilities for investigation of tiny
semiconductor structures. However, on the whole, the tech-
niques of electrochemistry are often considered in surface
science among supplementary techniques [3]. The losses of
opportunities originate from the above-mentioned disintegra-
tion of the electrochemical probing between different tech-
niques and the difficulties of components separation in com-
plex responses, which hinder the development of practically
feasible integrated probing procedures for the comprehensive
characterisation of electrochemical systems.
Electrochemical responses contain valuable information
both on interfacial structures and dynamics of interfacial pro-
cesses. The established practice of the electrochemical char-
acterisationimpliessequentialprobingoftheelectrochemical
system with various techniques, highly specialised in partic-
ular aspects of ac and dc responses [1,2]. The separate analy-
sis of the frequency and potential variance of the response, as
well as the separate investigation of ac and dc responses has
been inherited by the present-day computerised techniques
from the analog predecessors that were unable to monitor
the multidimensional dependences in a single potential scan.
The dispersal of the electrochemical response investigation
among different techniques is very disadvantageous, espe-
cially to the mutable and non-stable systems characterisation,
and this is one of the main limitations for a wider applica-
tion of electrochemical techniques in surface science. Each
The idea of versatile characterisation of the electrochem-
ical response in a single computerised experiment was first
suggested by Smith with co-workers [4–8], who developed
the concept of Fourier transform electrochemical instrumen-
∗
Corresponding author. Fax: +375 17 2264696.
E-mail address: ragoishag@bsu.by (G.A. Ragoisha).
0013-4686/$ – see front matter © 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2004.10.055

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G.A. Ragoisha, A.S. Bondarenko / Electrochimica Acta 50 (2005) 1553–1563
tation, which was elaborated later [9–11] for application
on personal computers. Fourier transform electrochemical
instrumentation uses simultaneous multi-frequency probing
and gives the transfer function by comparing the current sig-
nal spectrum with the voltage spectrum [5]. Repetitions of
the same procedure on each step of a staircase potential scan
give frequency responses as functions of electrode poten-
tial. Though the Fourier transform electrochemical instru-
mentation has been elaborated for three decades, it has not
replaced the common ac and dc voltammetry. The main prob-
lem with that technique comes from a very low intensity of
the constituent responses and their non-uniformity. The si-
multaneous analysis of multi-frequency responses is much
morerestrictedthanthesingle-frequencyanalysis. Responses
in different frequencies may differ in orders of magnitude;
therefore even small nonlinearity of the most intensive com-
ponent, which might be insignificant in the single-frequency
probing, hinders considerably the acquisition of low-level
components. The hindrance depends on the properties of the
system under investigation and therefore cannot be taken into
account before the measurement. For this reason the optimi-
sation of phases, which allows composing the probing signal
with the amplitude much lower than the sum of the con-
stituents [11], does not always result in the optimal response.
Equivalent electric circuit (EEC) analysis with Fourier trans-
form electrochemical instrumentation is difficult and very
few publications (see e.g. [12,13]) are available on the appli-
cation of that technique for decomposition of the potentiody-
namic frequency response into constituents related to EEC
elements.
The fundamental alternative to frequency response ac-
quisition with Fourier transform techniques that overcomes
intrinsic limitations in accuracy of simultaneous frequency
response analysis is the application of wavelets [14,15].
Wavelets are small waves terminated on the time scale. Due
to the termination, each frequency can be treated individu-
ally in streams composed of many wavelets, and this gives
the benefit of better response protection from the effects of
nonlinearity and noise. However, frequency scanning with
wavelets requires sophisticated real-time virtual instruments
capable of precise positioning of the probing and analysis in
the streams of responses (in the wavelet approach the fre-
quency response is analysed locally in different parts of the
time series, unlike the case with FFT, when the whole signal
is analysed simultaneously).
thousand times during the potential scan (the scan may be
either unidirectional or cyclic) with real-time representation
of the variation of the frequency response and dc current on a
computer screen. The EEC analysis in PDEIS is implemented
in the virtual spectrometer subroutine that utilises three dif-
ferent minimisation algorithms in order to provide reliable
fitting. PDEIS was used for characterisation of Cu upd on
gold [16], Pb upd on Te [17] and Ag upd on Pt [18].
In this work PDEIS was applied to systems of various
kind: (i) reversible, (ii) locally reversible but irreversible in
a wider potential range, and (iii) completely irreversible. In
each of the cases PDEIS provided different but substantial
opportunity for diversified fast characterisation of objects
under investigation. The combination of impedance spec-
troscopy, which is originally a stationary technique, with
the intrinsically non-stationary approach of potentiodynamic
techniques, appears to be constructive and helpful, despite
some self-contradiction of joining seemingly opposite ap-
proaches. The contradiction is actually just seeming, as the
impedance itself is not a stationary characteristic but just a
relation of the ac voltage to the ac current, which makes sense
both for stationary and nonstationary systems. The stationar-
ity in common EIS is required mainly for measurements in
infralow frequencies, therefore the latter have to be cut off in
potentiodynamic measurements. As a trade-off, the EECs ob-
tained by PDEIS can be incomplete. PDEIS does not attempt
to derive a complete EEC for an object under investigation.
Unlike common EIS, PDEIS investigates just a part of a trans-
fer function and concentrates on the evolution of the acquired
part of frequency response in the potential scan. The situation
with EIS and PDEIS is similar to the situation with station-
ary and potentiodynamic, in particular cyclic, voltammetry.
Both the voltammetries have different applications, and only
in certain cases they can be interchangeable. The main desti-
nation of PDEIS is the characterisation of variable interfaces.
This aspect of PDEIS was considered recently [17] on the ex-
ample of irreversible Pb upd on Te, the system complicated
by a spontaneous interaction of Pb monolayer with the sub-
strate. By applying PDEIS in this work to systems of various
kinds, we tried to present a wider view of the possibilities
of the versatile potentiodynamic response characterisation in
the systems with different extent of irreversibility.
2. Experimental
The potentiodynamic electrochemical impedance spec-
troscopy (PDEIS) [15] uses a common potentiostat and vir-
tual instruments on a personal computer for electrochem-
ical system probing with streams of mutually coordinated
wavelets and real-time analysis of the response. Similarly
to the Fourier transform electrochemical instrumentation,
PDEIS superimposes ac probing on the staircase potential
scan for the acquisition of frequency response variation. Due
to high power of modern computers and low-level optimi-
sation of virtual instruments, the snapshots of the frequency
response can be taken in PDEIS for hundreds or even several
PDEIS spectra were recorded using a technique that was
described in [15]. PDEIS virtual spectrometer is a computer
program that acquires ac and dc responses by means of a com-
mon potentiostat. The control of the PDEIS spectra record-
ing is very similar to the control of CV acquisition in com-
mon computerised potentiostats. The potential and frequency
ranges, periodicity of frequency response snapshots, scan
rate, number of cycles of the potential scan, ac amplitude
and several other parameters were set from the interface of
PDEIS 1.4 program before the scan. Ac amplitude of the

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G.A. Ragoisha, A.S. Bondarenko / Electrochimica Acta 50 (2005) 1553–1563
1555
probing signal was from 5 to 10 mV and the potential steps in
the potential scan were always set to be several times smaller
than the ac amplitude. This secured the continuity of spectra.
Similarly to CV, PDEIS requires continuity of the record-
ing to give accurate representation of the dynamics of the
response variation on the potential scale.
of the stationary impedance spectroscopy but actually most
spectroscopic techniques deal with small frequency ranges,
as well as kinetic studies are often limited in certain ranges
of time constants.
PDEIS can analyse short-cut spectra not only due to the
above mentioned optimisations but also, and mainly, due to
the additional variable, the potential that helps to check the
consistency of the fitting which could be otherwise very am-
biguous.
Actually, PDEIS solves the problem in three dimensions,
unlike stationary EIS, which operates on 2D data. We have
implemented two strategies of finding the EEC with the built-
infittingroutine. Thefirstoneisusedforthesystemsthathave
no theoretically predicted models. This strategy utilises the
automatic enumeration of possibilities on several constant
potential sections of the 3D spectrum from more than 20 cir-
cuits (most often used in EIS analysis) with the automatic
rating, which reduces the number to very few circuits for a
subsequent more detailed analysis of the behaviour on the
potential scale. This strategy has been used in the investiga-
tion of the initial stages of polyaniline film growth in aniline
electropolymerisation (Section 5), as there was no presup-
posed model for the nonstationary ac response of that system.
The other strategy proceeds from theoretical assumptions that
give fewer models for trying. Thus, the Randles circuit was
tried as the first approximation for simple reversible reactions
considered in Section 3, and models of reversible adsorption
gave the possible variants for the EEC of Bi upd. The next
paragraph explains the strategy of deriving the EEC of Bi upd
on gold.
Using very small potential steps was also important for
data clearance from random noise and compensation of drift
effects, which could be generated by the potential scanning.
Interpolation in sequences of repeatedly acquired impedance
spectra is a usual way of drift compensation in nonstationary
impedance measurements [19]. PDEIS utilises this possibil-
ity in the smoothing of 3D data along the potential scale
before EEC fitting of the data in constant potential sections.
Distances on the potential scale between neighbouring 2D
sections of 3D PDEIS spectrum are smaller than the ac am-
plitude. This enables addition of information from several
neighbouring sections to each 2D section by applying a mov-
ing average smoothing in the range commensurable with the
ac amplitude, which results in more reliable fitting in the
constant potential sections of the spectrum.
It is well known [20] that the accuracy of impedance data
is very dependent on the frequency. Common nonlinear least
squares fitting spreads the errors from the least accurate part
of the spectrum over the whole spectrum, however local fit-
ting for the most accurate part of the spectrum gives much
better result for that part of the spectrum. PDEIS benefits
from this possibility by using relatively narrow fractions of
EIS spectra in the ranges of the maximal accuracy of the
equipment. In the examples that will be considered in this
work the spectra were previewed in the range from 5 Hz to
3 kHz and recorded for quantitative analysis in the following
ranges:
A linear component of the ac electrochemical response of
an upd at a small perturbation of the electrode potential ꢀE
may be presented in the following functional form [21,22]:
(i) [Fe(CN)6]3− reduction on glassy carbon: from 20 to
351 Hz;
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
∂i
∂i
∂i
ꢀi =
ꢀE +
ꢀθ +
ꢀCs
(1)
∂E
∂θ
∂Cs
(ii) [Fe(CN)6]3− reduction on Pt: from 14 to 1750 Hz;
(iii) Bi upd on Au: from 27 to 877 Hz;
where ꢀi, ꢀCs, ꢀθ are the respective variations of the cur-
rent, metal cation surface concentration and surface coverage
of metal adatoms formed as a result of upd. In the case of re-
versible upd the first term produces a resistance, the second –
the adsorption capacitance, and the third – the impedance of
diffusion. In the upd with anion coadsorption, depending on
the mechanisms, the adsorption of cations and anions may
appear in frequency response either as a single process, or
as two separate processes. Assuming additivity of the both
adsorption processes and the double layer charging [23], one
obtains two RCW branches in parallel with the double layer
capacitance [12,13], where R is the resistance, C the adsorp-
tion capacitance and W is the Warburg element in the EEC.
Inseparable adsorption of cations and anions would produce
just one RCW branch for the Faradaic part of impedance. In
all cases a serial resistance should be added to account for
the damping effect of solution. Also, reduced versions, lack-
ing some of the above-mentioned components of the Faraday
impedance, should be tried, to take account of the shortcut-
(iv) aniline electropolymerisation on Au: from 12 to 433 Hz.
We would like to emphasise that the EEC fitting in such
narrow ranges purposes the decomposition of the actual ac-
quired response, and PDEIS does not attempt to derive a
complete EEC, which might probably require much wider
spectra. Even in ac voltammetry, which acquires a single
frequency response, the response originates from different
EEC elements, but the ac voltammetry has no means to de-
compose its responses, because the decomposition requires
the knowledge of the frequency response. Fortunately, only
a part of the transfer function is needed to decompose the
ac response at a certain frequency, and this makes the basis
for the potentiodynamic frequency response analysis. Thus,
PDEIS solves a quite different problem than the stationary
EIS does – this new technique investigates the evolution in
the potential scan of those EEC elements whose responses
fall into the analyser window. The narrow frequency range
used in PDEIS may seem unusual from the point of view

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Fig. 3. Illustration of impedance data unstable fitting with the model shown
in Fig. 1b (Ca variation in the cyclic potential scan).
tinguishable in certain 2D sections of the PDEIS spectrum.
However, with the variable potential the minimisation pro-
cedure for the model (b) appeared to be unstable (Fig. 3, the
higher value of Ca is the upper limit of the minimisation pro-
cedure which was excessively assigned to be of 500 ␮F). The
abrupt transitions of Ca were physically unlikely with the po-
tential changes smaller than the amplitude of ac perturbation
and also accuracy of fit (χ2 and relative errors for individ-
ual elements) in general was not sufficient to accept model
(b) even for limited ranges of the potential. On the contrary,
model (a) gave reasonable potential dependences of the EEC
elements with χ2 far below 10−4 and low relative errors for
individual elements. The dependences of the EEC elements
for this model will be considered in Section 4.
Thus, the EEC fitting can be ambiguous in single short-cut
spectra, but the knowledge of the variation of the frequency
response with the potential helps to resolve the ambiguity.
Due to variation of contributions of different processes to the
total response, it is hardly possible to obtain smooth fitting in
three dimensions for incorrect model, though the ambiguity
of single spectra is a common problem in EIS.
Because of the variable potential, the EEC fitting in PDEIS
differences from the fitting in common EIS also in the amount
of calculations. The processing of thousands of spectra was
difficult with common CNLS programs, as the stability of
the fitting procedures turned to be very important in the au-
tomated processing. This made us to implement a coherent
processing of large sets of the 2D sections of the 3D PDEIS
spectrum in the spectrometer built-in fitting routine. Upon
trying manually various reasonable models at several poten-
tialsor ratingthem automatically, the fitting to the prospective
model runs automatically along the potential scale in such
a way that the solution obtained in one section is used as
the first approximation for the minimisation in the next sec-
tion. The resulting coherency of the analysis, together with
the use of three minimisation algorithms [15] and permanent
control of χ2 and relative errors of EEC elements, provided
stability and reasonable reliability of the automatic fitting.
Good models keep χ2 below 10−4 in the whole range of
the potential, while sharp changes in χ2 and in relative er-
rors for individual elements disclose either incorrectness of
the model, or inappropriateness of presumed limits for the
parameters (presumptions on possible limits for parameters
Fig. 1. Equivalent circuits for Bi upd on Au that were selected at preliminary
examination of spectra.
ting of the spectra. Not all of the three components of Faraday
impedanceareequallypronouncedindifferentupdprocesses.
In a reversible upd the out-of-phase component of the Fara-
day impedance is predominantly capacitive [24,25], while in
the irreversible upd it turns to be completely diffusional [17].
In the latter case adsorption capacitance vanishes, because
the oscillation of the adatom coverage, which produces this
EEC element, requires the overlap of the potential ranges of
the upd and the monolayer desorption. In Pb upd on Te [17]
and Ag upd on Pt [18] the cathodic and anodic processes
did not overlap and therefore no capacitance of adsorption
showed up in the EEC. On the contrary, Bi upd on Au has
been found in this work to behave typically capacitive, due
to overlap of cathodic and anodic processes.
Fig. 1 shows a subset of the three circuits that remained af-
ter preliminary rating of the EECs from the above-mentioned
wider set, and Fig. 2 gives two examples of Nyquist plots with
the best fit lines for the three models. The circuit (c) showed
insufficient fit and thus was easily excluded, but the circuits
(a) and (b) both fitted to the data with χ2 less than 10−4 in
the constant potential sections shown in Fig. 2. In terms of
a single spectrum analysis this two models seem to be indis-
Fig. 2. Examples of Nyquist plots for two constant potential sections of
PDEIS spectrum of Bi upd on Au in perchloric medium with the best fit
lines corresponding to different circuits from Fig. 1: (a) solid, (b) dashed,
and (c) dotted.