Electroanalytical features of non-uniformly doped conducting poly-3-(3,4,5-trifluorophenyl)thiophene films

Article abstract of DOI:10.1039/b303466f

Specially prepared, thin poly-3-(3,4,5-trifluorophenyl)thiophene, PTFPT, films were shown to possess stable p- and, most importantly, n-doping in TEABF₄/sulfolane (SF) solutions. Electrodes comprising PTFPT films were studied by cyclic voltammetry (CV), potentiostatic intermittent titration (PITT), and electrochemical impedance spectroscopy (EIS). A detailed analysis of the shape of the time-dependent current transients during PITT characterization of the PTFPT electrodes has been performed. The non-uniform character of the PTFPT film doping was proved. Plots of dlogl(t)/dlog t vs. t/τ_d were found to be useful for understanding the response of potentiostatic transients. The Cottrell time domain during potentiostatic transients was found to be very narrow, reflecting the drastic effect of the Ohmic potential drops (mainly across the film's bulk) on the semi-infinite diffusion current transient at the shortest times, and a wide distribution of the diffusion time constants. PITT and EIS characterizations provided converging results with respect to the relevant diffusion time constants and the non-uniform character of PTFPT film doping in the SF solution. EIS measurements were found to be very useful for the determination of diffusion time constants, as they allow more effective separation of the medium frequency, Warburg response from the Ohmic and the kinetic high-frequency responses.

Full text of DOI:10.1039/b303466f

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Electroanalytical features of non-uniformly doped conducting
poly-3-(3,4,5-trifluorophenyl)thiophene films
M. D. Levi,*a Y. Gofer,a M. Cherkinsky,a M. L. Birsa,a D. Aurbacha and A. Berlinb
a
Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
Centro Sintesi e Stereochimica Special Sistemi Organici—CNR Via C. Golgi,
1920133 Milano, Italy
b
Received 27th March 2003, Accepted 14th May 2003
First published as an Advance Article on the web 3rd June 2003
Specially prepared, thin poly-3-(3,4,5-trifluorophenyl)thiophene, PTFPT, films were shown to possess
stable p- and, most importantly, n-doping in TEABF4/sulfolane (SF) solutions. Electrodes comprising PTFPT
films were studied by cyclic voltammetry (CV), potentiostatic intermittent titration (PITT), and
electrochemical impedance spectroscopy (EIS). A detailed analysis of the shape of the time-dependent current
transients during PITT characterization of the PTFPT electrodes has been performed. The non-uniform
character of the PTFPT film doping was proved. Plots of dlog|I(t)|/dlog t vs. t/td were found to be useful for
understanding the response of potentiostatic transients. The Cottrell time domain during potentiostatic
transients was found to be very narrow, reflecting the drastic effect of the Ohmic potential drops (mainly across
the film’s bulk) on the semi-infinite diffusion current transient at the shortest times, and a wide distribution of
the diffusion time constants. PITT and EIS characterizations provided converging results with respect to the
relevant diffusion time constants and the non-uniform character of PTFPT film doping in the SF solution. EIS
measurements were found to be very useful for the determination of diffusion time constants, as they allow
more effective separation of the medium frequency, Warburg response from the Ohmic and the kinetic
high-frequency responses.
monomer resulted in thin poly-3-(3,4,5-trifluorophenyl)thio-
Introduction
phene, PTFPT films that showed a relatively high n-doping level.
The goal of the present work was to rigorously measure and
characterize the potential dependencies of the major equili-
brium and kinetic parameters related to n- and p-doped PTFPT
film: the differential intercalation capacitance, Cdif and the
chemical diffusion coefficient, Di , respectively. These were
obtained by the combined application of cyclic voltammetry
(CV), potentiostatic intermittent titration (PITT), and electro-
chemical impedance spectroscopy (EIS). The experimental
results attained were then treated using classical finite-space
diffusion models, from which a major feature of the electroche-
mical doping of the PTFPT electrodes, namely, the films’ non-
uniformity (heterogeneity), was envisaged. We then examined
how this heterogeneity was specifically reflected in different
kinds of electroanalytical measurements. This is expected to
contribute to a better application of these techniques for
quantitative characterization of highly heterogeneous electro-
chemical systems.
Practical applications of electronically conducting polymers
(CP) in LED devices, electrochemical transistors, electrochro-
mic windows, and rechargeable batteries are largely based on
the phenomenon of reversible p- and n-doping.1–6 By defini-
tion, simple p-doping is the removal of electrons from the
p-conjugated polymeric backbone (partial oxidation), which
is equivalent to the creation of a cation-radical species. The
latter is stabilized both by delocalization within the p-system,
and by anion insertion from the solution. N-doping (in its
simple form, without the participation of co-ions) by the
same principle is the partial reduction of the p-system with
the formation of anion-radicals, stabilized by cations coming
from the solution. Only a few CP among them, i.e., polyace-
tylene,7 poly-p-phenylene,8 and polythiophene,9 can be doped
in both directions. As a rule, repeated and stable n-doping/
neutralization of these polymers is much more difficult to
obtain, compared to p-doping. For example, numerous
attempts to increase the n-doping level of underivatized poly-
thiophene were not very successful: although the variation of
the solvent and electrolyte nature allowed this level to
increase to a certain extent, it was never as high as that of
the p-doping (see a comprehensive review10).
Experimental
Synthesis of the monomer
An important advantage of CP over conventional inorganic
ion-insertion cathodes and anodes for rechargeable batteries is
that a simple chemical derivatization of the CP structure may
lead to a drastic, targeted change of their unique molecular
properties.1 In order to balance the n- and p-doping levels, a
series of monomers based on (fluorophenyl) thiophenes has
been suggested and tested in experimental cells.11–13
In the present work, we obtained 3-(3,4,5-trifluoro-
phenyl)thiophene by modifying the synthetic procedure
reported in ref. 11. Further electropolymerization of this
3-(3,4,5-trifluorophenyl)thiophene was obtained by a modifica-
tion of the reported procedure11 related to the palladium cata-
lyzed coupling reaction of a zinc complex of trifluorobenzene
with 3-bromothiophene. Either dichlorobis(triphenylphosphine)
palladium(II) or tetrakis(triphenylphosphine) palladium(0) can
be used as a catalyst. However, the yield was better with the
former. The reaction was carried out in dry THF under Ar
atmosphere. The final product contained about 5% of a 3,4,5,-
30,40,50-hexafluoro-biphenyl by-product, which, however,
did not affect the subsequent electropolymerization of
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This journal is # The Owner Societies 2003
DOI: 10.1039/b303466f

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3-(3,4,5-trifluorophenyl)thiophene. The analytically pure 3-
(3,4,5-trifluorophenyl)thiophene can, however, be obtained by
the low-temperature precipitation of the biphenyl by-product
from hexane.
domain, with the use of appropriate characteristic current–
time plots.
EIS was performed at several potentials under constant
potential polarization. Before measurements, the PTFPT film
was preliminary polarized at the related potential for 10 min.
The amplitude of the ac voltage used was 5 mV. The frequency
range measured extended from 374 kHz to 50 mHz.
Techniques and equipment
PTFPT films were deposited potentiostatically on Pt wires
(: 0.5 mm, geometric surface area of 0.11 cm2). Pt wire
pre-treatment, as well as the construction of two electroche-
mical cells used in this work for electropolymerization
and electroanalytical characterization in a monomer-free
solution, was the same as that previously described for poly-
pyrrole films.14 For the electropolymerization, the counter-
electrode was a Pt grid, whereas a reversible Ag/0.1 M
AgNO3 in 0.25 M TEABF4/acetonitrile (AN) separated by
a glass frit from the working compartment served as the
reference electrode. This compartment was filled with 0.25
Results and discussion
PTFPT films were deposited on Pt wires, as described above.
The polymerization potential of 1.39 V was chosen to ensure
an optimal condition for growth of the polymer films (see
Fig. 1a). A moderate increase in the current after a delay of
more than 10 s corresponded to appearance of the polymer
nuclei on the current collector surface (the related surface
area increases) and further growing of the polymer coating.
When the charge passed, Qpolym , reached the value of 25
mC, the polarization was turned off. The film was neutralized
in the same solution in a potentiodynamic scan from 0.85 to
0 V at a scan rate of 50 mV sꢀ1 (see Fig. 1b). The neutraliza-
tion (undoping) of the oxidized film, as is seen from this
figure, is reflected by a characteristic peak at around 0.55 V;
the corresponding charge, Qneut , was equal to 2.5 mC. The
maximal doping level, x, was evaluated from the ratio of the
neutralization to polymerization charge, taking into account
the known stoichiometry of the polymerization reac-
tion11–13 and assuming a Faradaic efficiency of 100%: x/
(2 + x) ¼ Qneut/Qpolym , from which x ¼ 0.22 eꢀ per moiety
unit (e(mu)ꢀ1) was found. The high Faradaic efficiency esti-
mated for these reactions under the specified conditions is a
reasonable assumption that can be separately checked, e.g.,
by weighing the films deposited onto massive current collec-
tors (as was the case in the previous work13). The above value
of x coincides well with those reported earlier for PTFPT
films,11–13 and was not very different from that usually
obtained with pristine p-doped polythiophene.
M
TEABF4 in AN + 0.05 M 3-(3,4,5-trifluorophenyl)-
thiophene. Immediately after electropolymerization, the
doped film was neutralized by a linear potentiodynamic scan
in the same monomer-containing solution. The Pt electrode
with the deposited film was then removed from the cell,
rinsed several times with pure AN, and, finally, with the sol-
vent in which the doping process was studied. The film’s
electrode was then inserted into an undivided 3-electrode cell
for CV, PITT and EIS characterization. In this cell, the WE
wire with the deposited film was surrounded by a counter-
electrode (Pt cylinder). The reference electrode was either a
Li or an Ag wire in a thin plastic tube located in the vicinity
of the working electrode. Li was used as a quasi-reference
electrode in PC14,15 and SF,16 whereas Ag wire was used
in AN. We monitored the potential of the Li wire in the
above solvents and found it to be ꢀ3.65 and ꢀ3.67 V,
respectively, using a standard Fc/Fc+ electrode. Measure-
ments over a period of one day showed that the shift in
the potential was negligible, about several mV. Hence, the
use of this RE is fully justified, based on the stability mea-
surements and previous experience.
Note that the specified polymerization potential for electro-
synthesis of PTFPT films was chosen in order to maintain
sufficient rates of the films’ growth. A decrease in the
All measurements and manipulations were performed in a
glove box at room temperature, under highly pure Ar atmo-
sphere. The oxygen and water content did not exceed several
ppm. TEABF4 was battery grade from Tomiyama. The resi-
dual water content in the dry solutions did not exceed 20
ppm, as follows from Karl Fischer titrations.
CV, PITT, and EIS measurements were performed using
Autolab/PGSTAT20 potentiostat/galvanostat systems con-
taining FRA modules driven by Pentium II personal compu-
ters using GPES software from Eco Chemie (Utrecht, The
Netherlands). CV was performed in a staircase mode with
potential steps of 0.3 mV at a scan rate of 50 mV sꢀ1
.
PITT characterizations of the PTFPT electrodes were per-
formed as follows. The first potentiostatic titration of the films
was performed during the p-doping (oxidation of neutral film),
followed by the subsequent p-undoping (reduction of the oxi-
dized films). Then the potentiostatic titration was similarly
repeated for the n-doping (reduction of neutral films) and
the subsequent n-undoping (oxidation of the reduced film).
In each step the current was recorded for approximately 5
min. At the end of each step, at moderate doping levels, the
current dropped below 2 mA cmꢀ2. It was assumed that at this
condition complete equilibrium is maintained within the films.
Then the next potential step was applied. In the limit of high
doping levels, the current reached a time-independent, back-
ground value of 5 mA cmꢀ2, which was subtracted from the
measured values. The PITT data were first analyzed with the
use of finite-space diffusion models for homogeneous intercala-
tion electrodes.17,18 The pronounced deviation of the behavior
of the p- and n-doped PTFPT film from that predicted by the
finite-space diffusion models was observed for a wide time
Fig. 1 I vs. time curves for the potentiostatic synthesis of a PTFPT
film (a) and its neutralization under potentiodynamic conditions (b)
in a 0.25 M TEABF4/AN + 0.05 M (3,4,5)TFPT solution.
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polymerization potential with the corresponding increase in
the deposition time (to keep the same charge) resulted in poor
films, which were capable of p-doping but could not reach a
substantial n-doping level.
We estimated the film’s thickness as 0.6 mm using a com-
monly used method, namely, comparing the amount of charge
passed during the electropolymerization of the PTFPT films
with the charge required to prepare reference films of known
thickness, as previously reported.11
However, meaningful PITT and EIS characterizations are
only possible with insertion electrodes possessing long-term
stability (cyclability). Although as-prepared PTFPT films
showed more facile kinetics in AN and PC solutions compared
to that in SF, their charge and discharge capacities (mainly, for
n-doped films) deteriorated rapidly with the number of cycles
(or polarization time) in the former two solutions. In contrast,
despite the clearly poorer doping kinetics of PTFPT films
in SF solutions, long-term stability of the film, especially for
the n-doped film, was rather good. At the end of the PITT
and EIS characterizations, PTFPT electrodes usually lost 14
and 28% of their initial redox-charge during the p- and n-
doping, respectively. Interestingly, the Faradaic efficiency of
the n-doping of the PTFPT electrodes increased in the AN <
PC < SF sequence: 83, 88, and 91%, respectively, i.e., in the
reverse order with respect to the rate of the films’ doping in
these three solvents. Thus, the detailed electroanalytical charac-
terizations of PTFPT could be performed in SF, as only this
solvent enabled the required long-term stability of the
electrodes.
The solid lines in Figs. 3a and b reflect stable, steady-state,
voltammetric responses of the film during its repeated p- and
n-doping, respectively. However, for the sake of comparison
with the results obtained from PITT, the voltammetric curves
in these figures were normalized by the scan rate. In such a
way, the calculated quantity presents the so-called differential
capacitance of the doping/undoping process in terms of CV:
Cdif ¼ Icv/n. Here, Icv stands for the voltammetric current,
and n for the scan rate.
As-neutralized PTFPT films were immersed in monomer-
free, 0.25 M TEABF4 solutions in either acetonitrile (AN),
propylene carbonate (PC), or sulfolane (SF). CV curves mea-
sured with PTFPT electrodes at a scan rate of 50 mV sꢀ1 in
each of these three non-aqueous solutions, during both
p- and n-doping, are depicted in Fig. 2. It is seen that the
CV responses from the n-doped film are qualitatively similar
to those for the p-doped polymer. When analyzing the depen-
dence of the related peak-potential separations on the solvent
nature, the reversibility of both p- and n-doping processes
tends to increases in the SF ꢁ PC < AN sequence. Note that
during p-doping the films exhibited approximately the same
redox-charge, independent of the solvent nature, with rela-
tively high Faradaic efficiencies (92–94%).
The curves shown in Fig. 2 correspond to the stable CV
responses attained during consecutive cycling of the freshly
prepared films for different periods of time. Whereas only a
few cycles were necessary to reach the steady-state response
in AN and PC, more than 30 cycles were required to obtain
such a response in a SF-based solution. We thus suspected
that poorer kinetics of the p- and n-doping of PTFPT films
in the latter solution might be connected with the films’ slow
impregnation by the SF-based solution. A similar gradual
increase of the redox-charge related to the SF based solutions,
and its lower absolute value compared to that in PC-based
solutions was recently reported for poly(vinylferrocene)
(PVF) film electrodes.19
In order to determine the dependence of Di on the electro-
de’s potential using PITT, the current–time response for
each potential step should be treated in terms of the two
quantities:20 The first one is the differential (incremental)
The assumption about the important role of swelling in the
film’s redox kinetics was further checked using EIS and PITT.
CV, as a large-amplitude technique, could provide only gross
features of the kinetics of p- and n-doping of PTFPT electro-
des, reflected mainly by the value of the peak-potential separa-
tion. Small amplitude techniques, such as PITT and EIS, were
applied in this work in parallel, in order to study the kinetics of
the PTFPT electrodes as a function of both time (frequency)
and equilibrium potential (doping level).
Fig. 2 Stable (steady-state) CV curves measured with (the same or
similar) PTFPT film(s) of ca. 0.6 mm thick (prepared in an AN solu-
tion), which was p- and n-doped in SF, PC, and AN. Scan rate and
the solution compositions are indicated. For comparison, a CV curve
measured in an AN vs. Ag quasi-reference electrode is presented vs. a
Li electrode by shifting the potential by 3.32 V towards more positive
values.
Fig. 3 Comparison of the plots of the differential capacity, Cdif . vs.
potential, E, obtained by CV (solid lines) and PITT (dotted lines)
during p- and n-doping (a and b, respectively).
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capacity Cdif , defined as the ratio of the charge injected dur-
ing the whole potential step (DQ) to the width of this poten-
tial increment (DE):
decrease in titration time for each step; thus, the measured
response may deviate from the true, equilibrium value.
Once Cint was found, further calculation of Di by PITT
required the determination of the characteristic kinetic para-
meter It1/2 for each of the potential steps. Earlier, we proposed
treating the experimental PITT data related to the intercalation
electrodes, using It1/2 vs. log t plots (see ref. 20 and references
therein). This was helpful for the following reasons: (i) The plot
visualizes the separation between a short-time (Cottrell)
domain, and a portion of the plot, related to finite-space
Cdif ¼ DQ=DE;
ð1Þ
where DQ can be obtained by numerical integration of the
related I vs. t curve. The Cdif quantity is an important equili-
brium characteristic of the doped (undoped) film. The depen-
dencies of Cdif on the potential are shown in Figs. 3a and b
for the p- and for the n-doping, respectively. Comparing the
plots of Cdif vs. potential (E) obtained from PITT and from
CV (see Figs. 3a and b) shows that the former technique basi-
cally provides a closer approach to equilibrium state of the
film compared to the latter technique. The reason for this
is that the characteristic accessible time window of the CV
curves measured at the scan rate of 50 mV sꢀ1 appears to
be considerably less than that for the PITT measurements
(by approximately 6-fold). Ohmic potential drops, bulk film
resistance, and slow interfacial and diffusion kinetics will
broaden the CV curves measured (unless the potential scan
rate is very slow), whereas all these factors become insigni-
ficant when current transients during PITT are integrated
over a sufficiently long period of time. There is one shortcom-
ing of PITT compared to CV: The CV curves shown in Fig. 3
were measured in a stepped mode with a potential height of
0.3 mV. Thus the number of points corresponding to the
half-peak width exceeded 1300. In the PITT experiment, we
usually performed 8 titrations, 50 mV each step. Hence, the
Cdif curve contained 8 points. A further increase in the num-
ber of experimental points in the PITT experiments by redu-
cing potential step height, would lead to less accurate values
of Cdif calculated from each step. This is because the incre-
mental charge due to doping becomes comparable with the
parasitic charge consumed by inevitable background reac-
tions, which should be normally subtracted from the total
measured charge. On the other side, increasing the number
of experimental points (Cdif) measured accurately, require a
diffusion. A combination of the two parameters, Cint and
1=2
Cottrell
It
defines the related diffusion time constant td(E).20 (ii)
The normalized It1/2/It1C=o2ttrell vs. log t plot obtained for a vari-
ety of equilibrium potentials possesses a remarkable property
of congruency (for a homogeneous film): the shape of the curve
is invariant with respect to td(E).21 Deviation of the shape of
the experimental curves from the theoretical ones may clearly
reflect non-uniformity of the redox films.21,22 In an ideal case,
i.e., in the absence of Ohmic and kinetic limitations, the
Cottrell region appears in the It1/2 vs. log t plot as a horizontal
straight line.20 If, on the contrary, Ohmic and kinetic limita-
tions considerably affect the short-time current response, the
Cottrell domain, i.e., It1/2 vs. t or log t appears as a function
with maximum or minimum, depending on the sign of the
current.20
Fig. 4a shows a typical example of an It1/2 vs. log t plot
obtained from PITT measurements during n-doping of a PTFPT
electrode (a potential step from 1.55 to 1.50 V). The ordinate
value at the minimum, i.e., at log t ¼ ꢀ0.222 s, was taken as
1=2
Cottrell
the It
value, from which the diffusion time can be calcu-
at longer times is
1=2
Cottrell
lated. Deviation of It1/2 from the It
caused by finite-space diffusion, whereas deviation of It1/2
from the It
1=2
Cottrell
at shorter times is mainly due to Ohmic
potential drops (in the solution and in the bulk of the film,
especially, in its neutral state) and kinetic limitations (for a
detailed analysis of the latter case, see recent paper by
Montella23).
Fig. 4 Current response obtained from the PTFPT film in the SF solution during its n-doping from 1.55 to 1.50 V (vs. Li), treated in different
plots: It1/2 vs. log t (a), I vs. tꢀ1/2 (b), log|I| vs. t (c), and log|I(t)|/dlog t vs. t/td (d).
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An important feature of the curve shown in Fig. 4a is that,
along with the main peak falling on the short-time domain,
one can clearly see a portion of the curve of a relatively small
slope in the time domain from 50 to 125 s. An ideal uniform
film should have only one Cottrell domain (i.e., a single value
of td), and thus the above inflection on the It1/2 vs. log t curve
implies a secondary, less expressed Cottrell domain. It can be
formally related to a higher value of td due to the film’s
non-uniformity.21 This non-uniformity may originate from
either a distribution of CP fibrils thickness (although Di
remains the same), or, alternatively, from a distribution of Di
due to the different extent of swelling of different parts of the
PTFPT film. The latter factor of the film’s non-uniformity
seems to be in line with the relatively slow kinetics of its swel-
ling in the SF solution, as verified by CV. Note that the shape
of the It1/2 vs. log t curve (i.e., the presence of a major and a
secondary Cottrell domain) was qualitatively independent of
the equilibrium potential of the film (or the related doping
level). This latter observation substantiates, as a first approxi-
mation, the use of finite-space diffusion models (elaborated
for uniform intercalation electrodes)17,18 for the determination
of td related to a specific, particular domain of the non-
uniform intercalation electrode.
on the determination of td .23 As seen from the solid line in
Fig. 4d, the transition from the Cottrell domain to the finite-
space diffusion domain occurs within a narrow time range near
t/td ¼ 0.2.23 In the short-time domain, (dlog|I(t)|/dlog t) is
equal to ꢀ0.5 (Cottrell domain), whereas in the long-time
domain, (dlog|I(t)|/dlogt) ¼ ꢀ(p2t/4td).23 Aninterestingproperty
of the plot dlog|I(t)|/dlog t vs. t/td for the case of a uniform
electrode is that it does not depend on td . In view of the con-
siderable Ohmic potential drops and the kinetic contributions
to the current transient of the PTFPT film under considera-
tion, the horizontal plateau corresponding to (dlog|I(t)|/dlog
t) ¼ ꢀ0.5 at (t/td) < 0.2, is absent in the experimental curve
in Fig. 4d. In addition, in the range of (t/td) > 0.2, the experi-
mental curve does not approach to the limiting straight line,
and clearly demonstrates a concave shape. Comparison
between Figs. 4d and c shows that the concave curve in the for-
mer figure corresponds to a gradual increase in the local value
of td . Thus, such an analysis of the shape of the dlog|I(t)|/dlog
t vs. t/td plot appears to be very useful in identifying the
non-uniform character of doping of the PTFPT film under
consideration.
It was significant to study how the non-uniform character of
doping of the PTFPT film is reflected by parallel EIS measure-
ments. Fig. 5a shows typical Nyquist plots for the PTFPT film
during its n-doping at five selected potentials in the SF solu-
tion. In the high-frequency domain, a non-closed semicircle
(HFS) appears as a result of the relatively high bulk polymer
film resistance in the SF-based solution (see insert in Fig.
5a). This semicircle was absent in the impedance spectra of
the same electrodes in the AN- and the PC-based solutions.
Thus, the above high bulk film resistance deduced from the
Nyquist plots for the PTFPT film in the SF solution could
be the major reason for deviation of the current transients
described above, from the Cottrell behavior in the short-time
domain (see Fig. 4). This high, potential-dependent bulk film
resistance probably arises because of insufficient swelling of
the film in the SF solution. Thus, a correlation between the
related PITT, CV, and EIS characteristics of the PTFPT film
in the SF solution has been obtained.
Our major focus is on the portions of the Nyquist plots
related to the medium-to-low frequency domain, because they
reflect the impact of diffusion. The insert in Fig. 5a shows that
a potential-dependent, medium-frequency semicircle (MFS)
appears on the right-hand side of the HFS. Fitting the MFS
using a simple equivalent circuit analog shows that the capaci-
tance in its maximum is of the order of 6 mF cmꢀ2, i.e., close to
a typical double-layer capacitance. Taking into account the
fact that the coupled resistance decreases as the doping level
of the film increases, the MFS was ascribed to slow, interfacial
ion-transfer kinetics. At the beginning of the n-doping (E ¼
1.6 V vs. Li/Li+), as is seen from Fig. 5a, an extensive,
depressed, HFS overlaps with the MFS. This latter semicircle,
in turn, overlaps with the very narrow (in terms of the fre-
quency range) Warburg-type response, which approaches a
limiting, distributed capacitance behavior (constant-phase
element, CPE) in the limit of the very low frequencies.
Fig. 5b presents a detailed Nyquist plot measured with the
PTFPT film during its n-doping at 1.6 V (vs. a Li ref. elec-
trode). This plot is used as an example for the analysis of td
obtained by EIS in the high- and the low-frequency domains,
and for a comparison of the td values obtained by EIS and
PITT.
The potential dependence of td related to the short time
Cottrell domains of the PTFPT film can be conveniently calcu-
lated by a simple expression:20
2
tdðEÞ ¼ ½Cdif =ðp1=2It1=2=DEÞꢂ ;
ð2Þ
where td(E) is the characteristic diffusion time constant of
a specific part of the film from which the chemical diffusion
coefficient Di (related to this specific part) can be calculated:
Di(E) ¼ l2/td(E). It is assumed that the characteristic diffusion
length l is the film’s thickness. Note that this assumption affects
the absolute value of Di rather than the plot of log Di vs. poten-
tial, since the characteristic diffusion length is most probably
invariant with the potential. The calculated value, td ¼ 12.3 s,
is marked in Fig. 4a.
Instead of determining the Cottrell parameter as minimum
in Fig. 4a, one can use the conventional I vs. t1/2 plot (see Fig.
4b). A straight line tangential to the short-time domain of the
experimental curve, crossing the origin of the coordinates,
results in exactly the same value of td as that obtained from
Fig. 4a. Involvement of slow kinetics and the secondary Cot-
trell domain are indicated in Fig. 4b, and can be compared
with those marked in Fig. 4a.
It was interesting to examine the long-time domain of the
response. This can be done using different current–time plots.
In Fig. 4c we present the same experimental data in the form
of a log|I| vs. t curve, appropriate for the identification of an
exponential decay of the diffusion current with time, in the
finite-space (long-time) domain.17,18,20,23 The diffusion time
constants td can be found from the linear portions of this plot,
whose slope is ꢀp2/4td . From Fig. 4c it is seen that in the
range of 50 < t/s < 125 the plot is linear, and the related td is
120 s. However, in the range of 10 < t/s < 13, the effective
value of td is considerably smaller, about 53 s. Fig. 4c actually
provides evidence that in the range of 10 < t/s < 50, the slope
of the log I vs. t curve gradually decreases, and thus the effec-
tive values of td increase accordingly.
In order to complete the comparison of the shape of the cur-
rent transients for uniform and non-uniform films, we used the
plot of the differential quantity, dlog|I(t)|/dlog t vs. dimension-
less time, t/td proposed by Montella.23 The solid line in Fig. 4d
relates to the case of semi-infinite (Cottrell) diffusion in the
short-time domain, and to finite-space diffusion in the long-
time domain (uniform electrode). The current was calculated
with the use of the exponent series sum,21 which was previously
used by us for modeling Li-ion diffusion in composite graphite
electrodes,24 and by Montella in his detailed analysis of the
effect of charge-transfer kinetics and Ohmic potential drops
Similar to the short-time domain of the PITT response eqn.
(2), the high-frequency Warburg-type EIS response can be
conveniently treated in terms of the differential capacitance,
Cdif ¼ Qmdy/dE (equilibrium characteristic), and the Warburg
slope, Aw (a kinetic characteristic), where Aw ¼ DRe/Doꢀ1/2
¼
DIm/Doꢀ1/2 (DRe and DIm are the differences in the real
and the imaginary components of the impedance, respec-
tively, corresponding to a finite variation in the angular
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difference between the values of td obtained by the two techni-
ques in the same time domain that we have never seen before
during our study of a variety of lithiated inorganic host mate-
rials.20,26–28 Note, however, that the Ohmic potential drops
and the kinetic limitations for these latter materials in contact
with typical for Li-ion battery aprotic electrolyte solutions
were never so great as that for the PTFPT film, in contact with
SF solutions. We suggest that the large bulk film resistance in
the SF solution, as is seen from the insert in Fig. 5a, leads to
the fact that the It1C=o2ttrell, calculated is lower than the true value
because of the interference of the high resistance, which does
1=2
Cottrell
not allow It
to be measured precisely, from which td
is calculated. Thus, the minimum in It1/2 vs. log t, as seen in
Fig. 4a, can be considered only as a rough estimate of
ItC1=o2ttrell. The use of EIS for the determination of td should
be more advantageous, as this allows more effective separation
of the medium-frequency Warburg response from the Ohmic
and the bulk film impedance (see Fig. 5a). However, as is seen
in the same figure, separation between the Warburg domain
and the medium-frequency kinetic semicircle, especially at
low doping levels, is not very good (in the case of lithiated
inorganic hosts usually much better separation could be
obtained20). The above intrinsic difference between the two
techniques, as refers to their ability to discriminate between
the contributing high- and medium-frequency processes,
should always be kept in mind. Note also that the worst tech-
nique in this respect is CV, since such high-frequency charac-
teristics as the Ohmic potential drops in the solution and in
the film’s bulk directly affect the shape of the low-frequency
response, i.e., the shape of the CV curves.
It was interesting to evaluate td from the low-frequency
domain of the impedance spectra. The case of a finite-space
diffusion (low-frequency response) for uniform electrodes
could be conventionally treated in terms of a product of
the limiting, low-frequency capacitance CL(coinciding with
the earlier introduced Cdif), and the related low-frequency
resistance:25
t ¼ 3RLCL:
ð5Þ
Fig. 5 Nyquist plots measured with an n-doped PTFPT film in con-
tact with a SF-based electrolyte solution at five different potentials as
indicated (a) and the detailed Nyquist plot for the slightly doped film
(b). The Warburg and the low-frequency, distributed capacitance lines
are marked. Insert in Fig. 5a is an enlarged view of the high-frequency
domain of the plots shown in (a). For other details see the text.
The main problem related to the practical application of
eqn. (5), is the determination of RL and CL from the experi-
mental Nyquist plot, which shows a great deal of non-ideality
(see Fig. 5b): the low-frequency domain of these Nyquist plots
can be approximated by a constant-phase-element, CPE. We
estimated RL from the Nyquist plot as was proposed by Pickup
et al.,29–31 i.e., from the intercept between the Warburg line
and the sloping capacitive line (the CPE-like line), see Fig. 5b.
Calculation of td from the low-frequency domain using eqn.
(5), and the value for the low-frequency resistance RL , as indi-
cated in Fig. 5b, and CL , taken from the parallel PITT mea-
surements, results in tdlowo ¼ 4.1 s. Thus, the diffusion time
constant obtained from the low-frequency range, appears to
be almost three times smaller than that estimated from the
Warburg domain (thdigho ¼ 11.4 s), and about an order of mag-
nitude smaller than that obtained from PITT, tPdITT ¼ 40 s).
The most probable reason for the reduced value of tldowo is
an underestimation of RL obtained from the transitional, CPE-like
low-frequency line. In fact, the extrapolation procedure
depicted in Fig. 5b allows the determination of tldowo from
a limited, low-frequency domain of the film’s impedance
spectra. However, due to the film’s non-uniformity, this
transitional domain corresponds to a continuous distribution
of td , as we saw from the analysis of the PITT response
(Fig. 4c). Direct impedance modeling of such non-uniform
film’s response shows that extrapolation from a limited,
transitional domain to high frequencies may lead to severe
frequency of the ac current, Do). The diffusion time con-
stant, td , is then simply a product of both the above quan-
tities20 (compare with similar equation in ref. 25):
2
td ¼ 2½QmAwdy=dEꢂ ;
ð3Þ
where td ¼ l2/Di ; Qm is the maximal doping (undoping)
charge and y is the dimensionless doping level.
For ideally uniform films, the values of td obtained by PITT
in the short-time domain should coincide with those obtained
by EIS in the high frequency, Warburg region. This can be
easily proved: by equating the td from eqns. (2) and (3) one
obtains the intrinsic relation between the characteristic kinetic
parameters of the PITT and EIS responses, i.e., between It1/2
DE (DE is the amplitude of the potential step) and Aw :
/
Aw ¼ ð2pÞꢀ1=2DE=It1=2
:
ð4Þ
It is seen from eqn. (4) that the product of these parameters
is equal to (2p)ꢀ1/2, i.e., to a universal constant connecting
together the direct and the alternative current responses.
Determination of td for the PTFPT film polarized at 1.6 V
using eqn. (3) results in thdigho ¼ 11.4 s, i.e., 3.5 times less than
that found from PITT (tPdITT ¼ 40 s). Both these values are
indicated in Fig. 5b. Thus, we observed a pronounced
21
underestimation of RL (see also Fig. 4 in ref. 22 and
Fig. 5 in ref. 32). Careful analysis of the slope of these tran-
sitional impedance domains shows that only slight deviations
Phys. Chem. Chem. Phys., 2003, 5, 2886–2893
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of the film’s behavior from that typical for uniform films,
can justify the method of estimation of RL according to
Pickup et al.29–31
and undoping, is roughly the same, except for the slightly
undoped film. The absolute values of Di obtained from the
impedance data are approximately 4 times larger than that
which followed from PITT. The reason for this difference
has been discussed above. We can imagine two different cases
of the film’s non-uniformity. The first considers the film as a
variety of fibrils having a different, but potential-independent,
size. The extent of film swelling may be potential dependent
but identical for the fibrils of different size. In this case, Di will
be independent of the individual fibril sizes but there will be a
distribution of different td in the time domain of the related
measurement technique (i.e. PITT and EIS). If this is the case,
the Di in Fig. 6 could be interpreted as effective values of Di
obtained for a specific (short) time domain using conventional
finite-space models for uniform electrodes. Since for this parti-
cular case of the film’s non-uniformity the individual values of
Di at constant potential do not depend on the size of the fibrils,
potential dependences of effective Di obtained in the high-
frequency domain (i.e. of the Warburg-type) may reflect
true potential dependences of the individual Di . In order to
either confirm or refute this type of non-uniformity, reliable
models for quantitative treatments of non-uniformity are
required. Alternatively, if the fibrils have essentially the same
size, but have a different chemical environment (i.e., differently
impregnated with the solvent), a distribution of different Di
will certainly result in the related distribution of td . We cannot
distinguish this type of film non-uniformity from the former
one on the basis of electrochemical methods only. This is
because these methods actually provide the determination of
td , whereas Di is calculated from the simple expression for lin-
ear diffusion Di ¼ l2/td . Direct in situ observations of CP
films’ morphology at different doping levels may be desirable
for understanding the essential features of non-uniformity of
doped CP films.
Thus, both analyses of the current transients (PITT) and the
Nyquist plots (EIS) related to the PTFPT electrodes in SF
solutions indicate that doping the PTFPT film is essentially
non-uniform. This, of course, considerably complicates the
analysis of the potential dependences of td or the related Di .
In the case of uniformly doped CP films, with a single td for
the whole film electrode, the shape of the plot Di vs. E allows
the identification of the nature of the interaction between the
electronic and ionic species at their sites inside the film.20,26,33
When Di is independent of E, such interactions are absent, and
the doping can be expressed by a Langmuirian (Nernstian) iso-
therm.20,33 The curve with a maximum usually suggests repul-
sive interactions.20,26,33
It is clear that the analysis of the potential dependences of Di
for the non-uniform electrodes becomes very complicated.
Because of a considerable underestimation of RL , and thus
td and Di , when treating low-frequency impedance spectra,
we must exclude the related results from the discussion because
they are not sufficiently reliable. Thus, only the potential
dependences of Di obtained from PITT and high-frequency
impedance spectra should be compared. The chemical diffusion
coefficients of the inserted ions, calculated from the related td ,
are shown in Figs. 6a and b as a function of potential for the
p- and n-doping, respectively. As discussed above, the td
values calculated from PITT measurements of the PTFPT elec-
trodes in SF are not accurate. However, they reflect a clear
trend of the diffusion time constants, as a function of potential.
It can be seen that the plots, both for the doping and the
undoping, are peak-shaped, as is expected for repulsive inter-
actions between the inserted species. We assume that the shape
of the Di vs. E plots obtained from PITT for the non-uniform
electrode is also as meaningful as that calculated for uniform
electrodes, for certain, particular types of non-uniformity. This
can be proved by direct comparison of Di obtained from the
PITT and the high-frequency impedance measurements. As
seen in Fig. 6b, the shape of Di vs. E curves, both for n-doping
Conclusion
The electroanalytical characterization of PTFPT electrodes in
SF-based solutions using CV, PITT, and EIS, shows a great
deal of similarity in the mechanism of the film’s p- and n-
doping. This relates to the maximum stored charge and the
potential dependence of the differential capacity, Cdif , and
the chemical diffusion coefficient of the inserted ions, Di . We
analyzed the shape of the time-dependent current responses
during PITT characterizations. A major, short-time Cottrell
domain in the current transients was seen in all the individual
potential steps. In order to study the PTFPT film’s non-unifor-
mity during doping, we carefully analyzed experimental
current responses during potentiostatic titrations using
dlog|I(t)|/dlog t vs. t/td plots. A drastic diminution of the
length of the Cottrell domain in this plot has two different
sources. In the short-time limit, this diminution, as well as a
decrease in the Cottrell parameter, It
1=2
Cottrell
(compared to the
true one), reflects a strong effect of the Ohmic potential drop
across the film’s bulk measured (when doped in the SF solu-
tion) in the semi-infinite, diffusion domain. Very large bulk
film resistance, directly observed by EIS, is one of the most
characteristic features of PTFPT electrodes doped in SF solu-
tions. Unfortunately, this was not the only complication
related to quantitative description of the shape of the current
transients during PITT. At longer times, this transient tends
to show a continuous distribution of td rather than the
expected, logarithmic decay of the current with time, charac-
terized by the same td as that in the short-time domain. This
behavior is clear evidence of a non-uniform film doping. The
conclusion on the non-uniform PTFPT film doping in the SF
solution is in line with the sluggish kinetics of the film’s swel-
ling in this solution studied by CV. Further experimental stu-
dies on the effect of non-uniform doping of CP films, should
Fig. 6 Potential dependencies of the chemical diffusion coefficient,
log Di , for the p-doping/undoping (a) and the n-doping/undoping
(b). For the latter case, the values of Di were obtained from both PITT
and the high-frequency impedance spectrum of the film.
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9
G. Zotti and G. Schiavon, J. Electroanal. Chem., 1984, 163, 385.
probably include the use of galvanostatic intermittent titration
technique, for which the Ohmic potential drops can be easily
taken into account. New theoretical approaches to descrip-
tions of continuous distribution of diffusion time constants,
observed for highly non-uniform intercalation electrodes, are
required. The qualitative consideration of two simple models
of non-uniformly doped CP films leads us to conclude that
direct in situ observations of the film’s morphology at different
doping levels are highly desirable for probing the type of non-
uniformity of doped CP films.
10 C. Arbizzani and M. Mastragostino, Curr. Trends Polym. Sci.,
1997, 2, 217.
11 H. Sarker, Y. Gofer, J. G. Killian, T. O. Poehler and P. C.
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12 Y. Gofer, H. Sarker, J. G. Killian, J. Giaccai, T. O. Poehler and
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13 Y. Gofer, J. G. Killian, H. Sarker, T. O. Poehler and P. C.
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14 M. D. Levi, E. Lankri, Y. Gofer, D. Aurbach and T. Otero,
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16 K. Xu and C.A. Angell, J. Electrochem. Soc., 2002, 149, A920.
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Acknowledgements
18 W. Weppner and R. A. Huggins, Annu. Rev. Mater. Sci., 1978,
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19 W. S. Schlindwein, A. Kavvada, R. J. Latham and R. G. Linford,
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20 M. D. Levi and D. Aurbach, Electrochim. Acta, 1999, 45, 167.
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22 J.-P. Diard, B. Le Gorrec and C. Montella, J. Electroanal. Chem.,
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This work has been partially supported by the Ministry of
Science, Culture, and Sport of the State of Israel (MOS),
and the Consiglio Nazionaledelle Ricerche of the Republic of
Italy (CNR) within the framework of binational collaboration,
and by the BMBF, the German Ministry of Science, within the
framework of the DIP Program.
23 C. Montella, J. Electroanal. Chem., 2002, 518, 61.
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