Study of Prussian Blue (PB) films by ac-electrogravimetry: Influence of PB morphology on ions movement

Article abstract of DOI:10.1016/S0013-4686(00)00470-9

The electrochemical response of Prussian Blue films in NaCl solutions was studied. It was proved that the stability with cycling of PB films increased when these films are covered with a Nafion membrane. This fact allows PB films to be studied in NaCl solutions under steady state conditions by impedance spectroscopy and ac-electrogravimetry. A model, which can explain the differences between the electrochemical behaviour of amorphous PB films and crystalline PB films in NaCl solutions, is proposed. This model is based on the hypothesis of a partial dehydration of the sodium ions before the electrochemical reactions take place, allowing the transport of sodium ions through the zeolitic channels of Prussian Blue.

Full text of DOI:10.1016/S0013-4686(00)00470-9

Electrochimica Acta 45 (2000) 3765–3776
www.elsevier.nl/locate/electacta
Study of Prussian Blue (PB) films by ac-electrogravimetry:
influence of PB morphology on ions movement
J.J. Garc´ıa-Jaren˜o a,b, A. Sanmat´ıas a, F. Vicente a, C. Gabrielli b,
M. Keddam b, H. Perrot b,*
a Department Qu´ımica-F´ısica, Facultad de Qu´ımica, Uni6ersidad de Valencia, C/Dr. Moliner 50, 46100 Burjassot, Spain
b LPLE, UPR 15 du CNRS, Uni6ersite´ Pierre de Marie Curie, Physique des Liquides et Electrochimie, Tour 22,
4 Place Jussieu, 75252 Paris, France
Received 28 July 1999; received in revised form 5 January 2000
Abstract
The electrochemical response of Prussian Blue films in NaCl solutions was studied. It was proved that the stability
with cycling of PB films increased when these films are covered with a Nafion® membrane. This fact allows PB films
to be studied in NaCl solutions under steady state conditions by impedance spectroscopy and ac-electrogravimetry.
A model, which can explain the differences between the electrochemical behaviour of amorphous PB films and
crystalline PB films in NaCl solutions, is proposed. This model is based on the hypothesis of a partial dehydration
of the sodium ions before the electrochemical reactions take place, allowing the transport of sodium ions through the
zeolitic channels of Prussian Blue. © 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Prussian Blue Films; Nafion®; Sodium countercation; Quartz crystal microbalance
1. Introduction
gree of order in the structure of the films [2,11]. The
order in the structure has proved to be dependent on
the electrogeneration conditions. More amorphous PB
films are obtained by applying larger currents during
the electrodeposition reaction (a-PB films), while for
lower electrodeposition currents more crystalline PB
films (c-PB films) are obtained.
Prussian Blue films in their insoluble structure, as
they are deposited according to Itaya et al. [2–4], can
be reduced to the colourless compound Everitt’s Salt
(ES) by means of the following reaction [2]:
Prussian Blue (PB) films deposited on the surface of
an electrode were first obtained by V.D. Neff [1] in
1978. Their use in electrochromic devices, rechargeable
batteries or for electrocatalytic applications described
in literature have increased their technological inter-
est. On the other hand, the possibility of obtaining
films with an extremely ordered inner structure makes
these films one of the most widely studied systems
[2–10].
Several papers have suggested the possibility of dif-
ferent electrochemical behaviours depending on the de-
“
FeI4II [FeII(CN)6]3+4K++4e− K4FeI4I[FeII(CN)6]3 (i)
’
Prussian Blue
Everitts Salt
* Corresponding author. Tel.: +33-1-4427-7216; fax: +33-
1-4427-4074.
E-mail address: perrot@ccr.jussieu.fr (H. Perrot).
and oxidized to the Prussian Yellow (PY) form in
solutions containing Cl− anions by:
0013-4686/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved.
PII: S0013-4686(00)00470-9

3766
J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
“
’
The possibility of covering the PB film by a Nafion®
layer was shown to be of special interest in the develop-
ment of electrochromic devices [16,17], but also, in
electrocatalytic applications by fixing the catalyst on
the PB films by covering the electrode with the Nafion®
membrane [18]. However, the presence of Nafion® lay-
ers also modifies the electrochemical response of PB
films in KCl solutions as has been shown in a recent
study [19]. This membrane represents an additional
resistance to ion transport, but also the dehydration
process of the Nafion® membrane, in contact with the
KCl solution, causes the dehydration of the inner PB
film.
FeI4II[FeII(CN)6]3+3Cl− FeI4II[FeIII(CN)6]3Cl3+3e− (ii)
insoluble PB
insoluble PY
Anyway, it is known that insoluble PB films are
converted to a soluble structure of the films by succes-
sive cycling around the reduction system PBUES in
KCl solutions [10,12]. The reduction to the ES form
and the oxidation to the PY form are described in KCl
solutions for the soluble PB structure by [2]:
“
KFeIIIFeII(CN)6+K++e− K2FeIIFeII(CN)6
(iii)
’
soluble PB
soluble ES
It has been proved that the degree of hydration of
the PB films plays an important role during these
electrochemical processes [7,20–23]. Therefore, the
number of hydration of counterions should be a very
important factor to be considered in the analysis of
experimental results.
for the reduction process and:
“
KFeIIIFeII(CN)6+Cl− KFeIIIFeIII(CN)6Cl+e− (iv)
’
soluble PB
soluble PY
From voltammetric or electrochemical impedance re-
sults it is not possible to obtain information on the
number of hydration of the ions that are inserted or
expelled from the film during electrochemical experi-
ments. Therefore, it is necessary to obtain other data by
another experimental technique which permits the mea-
surement of mass changes inside the film associated
with the electrochemical processes in addition to the
measured electrical current. This information can be
provided by quartz crystal microbalance (QCM)
measurements.
Moreover, to get a better analysis of the various
processes the QCM was also used under alternative
regime: ac electrogravimetry allows the mass response
to a small potential perturbation to be analysed thanks
to a fast quartz crystal microbalance used in dynamic
regime [24–30]. This technique has been already used
for other polymers [24,30–33] and oxides ib28‘‘\[28]
where attractive informations were collected for clarify-
ing the species movement involved in the various
reactions.
for the oxidation process. It should be noted that the
name of ‘soluble PB’ is related to the incorporation of
potassium ions inside the insoluble PB after several
potential cycling.
According to reactions i and iii, during the electro-
chemical reduction of PB films to the ES form, some
countercations should enter the film in order to main-
tain electroneutrality. As the structure of PB films has
been described as a zeolitic building with channels of
,
3.2 A in diameter [13,14], only a few counterions with
hydrated radius smaller than the size of the pore of the
PB films can be transported through the PB structure.
That way, only voltammetric studies of PB films in
solutions containing K+, NH4+, Cs+ and Rb+ ions
showed good results of stability during the repetitive
voltammetric cycles around the PBUES process [2,15].
The diameter of the Na+ hydrated ion is about 3.66 A,
,
which is slightly larger than the size of the pore in the
PB structure. Therefore, electrochemical studies of PB
films in NaCl solutions have shown poor stability re-
sults [2]. However, it has been proved that this reduc-
tion process takes place [2] when more amorphous PB
films are studied. This electrochemical behaviour has
been explained by assuming that the sodium ion can
move through the amorphous Prussian Blue films as the
size of their inner pores is larger than for more crys-
talline films.
2. Theory
The motion of counterions through the film accom-
panies the transport of electrons to maintain the elec-
troneutrality of the film. In some polymers it is the
counterion transport which is the rate controlling step
of charge transport. In other polymers, the rate of
charge transport is controlled by the slow transport of
electron through the film. In both cases, the expressions
that represent the rate of charge transport through the
electroactive films are mathematically identical and
whichever the species which move through the elec-
troactive film, the process can be characterised by
means of an apparent coefficient of diffusion of elec-
trons or counterions [34–36].
Nevertheless, these results are not clarified yet con-
sidering that the electric charge measured from the
voltammetric peak of an amorphous PB film in a NaCl
solution is very close to the electrodeposition charge.
This fact implies that the whole PB film be electroac-
tive, and therefore it must be necessary that sodium
ions move inside the zeolitic channels of PB films
during the redox processes, which is not possible since
the diameter of the hydrated sodium ion is larger than
the size of the zeolitic channel.

J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
3767
(5)
Fig. 1 shows the scheme of the electrode/PB film/so-
2.2. Steady-state and quasi steady-state
lution. Since PB films are studied in acidic NaCl solu-
tions, both hydronium and sodium ions, c1 and c2,
chloride anion, a, and water, s, can eventually move
through the film during the charge transport process.
The geometry of the modified electrode is shown in
Fig. 1. By definition, the fluxes of species i, Ji, are
positive for outgoing ions:
At steady-state, it was shown that [37,38]:
dCi(E) bi−b’i
Ci −Ci
max min
=
dE
4
(b’ −b )(E−E0−E )
ꢀ
n
i i i i
cosh2
2
and has a maximum for E=E0i +Ei equal to:
dC
(Ci −Ci
)
ꢁ ꢂ
max
min
(b’i−bi)
(6)
(7)
Ji\0 for x\0
(1)
=
dE
4
max
The charge transfer mechanism, which occurs at the
film/electrolyte interface during an oxidation or reduc-
tion reaction of the film in aqueous media, can be
modelled by assuming that the transport of the species
in the electrolyte is sufficiently fast and is not a limiting
step.
where Ei is such as:
k’
C0i i0=exp[−(b’i−bi)Ei]
ki0
2.3. Dynamic beha6iour
In dynamic regime, by linearizing the equations
which govern the process and using the boundary con-
ditions, it can be shown that [37,38]
2.1. Boundary conditions
The following boundary conditions are supposed to
be applied at the electrode/film interface as anions,
cations and solvent cannot cross the interface:
DJi(d)
DE
Gi
=
i=a, c, s
(8)
jꢀ
ꢁ ' ꢂ
coth d
1+Ki
At x=0 Ja(0)=Jc1(0)=Jc2(0)=JS(0)=0
(2)
Di
On the other hand, as outwards positive fluxes give
negative currents for expelled cations, by assuming
monovalent ions at the polymer/electrolyte interface:
ꢃjꢀDi
where Gi and Ki can be calculated from Eq. (4), d is the
film thickness and Di the diffusion coefficient of the
species i.
Considering the behaviour in the frequency domain,
the electrochemical impedance, ZF(ꢀ), and the electro-
gravimetric transfer function (Dm/DE)(ꢀ), are
obtained:
IF
At x=d −Ja(d)+Jc1(d)+Jc2(d)=
(3)
F
where IF is the Faradaic current density, d is the
thickness of the film and F the Faraday number.
The generalized insertion rates, according to classical
heterogeneous kinetic laws, for the species i are sup-
posed to be such as:
DJa(d) DJc1(d) DJ (d)
ꢁ
ꢂ
c2
Z-F1(ꢀ)=F −
+
+
(9)
DE
DE
DE
Dm
DE
−A
jꢀ
DJ
DJ
DJ
DJ
ꢀ
n
s
a+m
c1+m
c2+m
Ji(d)=ki(Ci−Ci )−k’i(Ci −Ci)Ci0 i=a, c (4)
(ꢀ)=
m
aDE
c1 DE
c2 DE
sDE
min
max
where Ci , is the maximum concentration of sites
(10)
max
available for ion insertion, Ci
is the minimum con-
centration of sites occupied bymiinons i in the host mate-
rial and C0i is the concentration of species i in the
solution.
where ma, mc1, mc2, and mS are the atomic masses of
anions, cations and solvent (the mass of the electron is
supposed to be zero). Obviously, the charged species,
anions and cations, are involved in ZF(ꢀ), whereas
(Dm/DE) (ꢀ)depends on anions, cations and solvent all
together.
Another quantity, (Dm/Dq)(ꢀ), such as
Dm
Dq
Dm
(ꢀ)=jꢀZ
(ꢀ)
(11)
FDE
can provide information on the mass of the species
which is inserted or expelled at each frequency.
2.4. Diagnostic criteria
From Eqs. (9) and (10), it is possible to eliminate the
contribution of Cl− anions from the Dm/DE function
by considering:
Fig. 1. Scheme of the electrode/PB film/NaCl solution.

3768
J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
the unloaded quartz crystal resonance frequency and A
Dm−Cl
DE
Dm mCl
1
−
−
=
−
(12)
is the piezoelectrically active area. The conditions of
applicability of this equation imply that the film de-
posited onto the gold electrode is sufficiently rigid.
Unfortunately, this condition was not valid for our PB
film, which exhibited a pronounced viscoelastic be-
haviour according to electroacoustic admittance analy-
sis. But with very thin PB layers, d=0.14 mm, this
viscoelastic behaviour does not affect drastically the
mass sensitivity coefficient and moreover remained
constant when the potential was changed [40].
DE
jꢀ FZF
which takes into account only the contribution of
cations and solvent. This operation was performed in
order to check the efficiency of the Nafion layer: in-
deed, if this latter play the role of blocking barrier for
chloride ion, the previous calculated partial mass/poten-
tial transfer function will be equal to the experimental
and initial Dm/DE.
This partial electrogravimetric transfer function is
equal to:
Therefore, if PB films were grown on one of the gold
electrode of the quartz crystal it is possible to simulta-
neously obtain the voltammetric curve (current vs. po-
tential) and the mass change against the cycled
potential.
On the other hand, a sinusoidal signal with a small
amplitude perturbation was applied to the electrode
at a fixed potential after stabilisation where a zero
current was reached. From the analysis of the response
of the electrode in a large frequency range the im-
pedance,(DE/DI)(ꢀ), and the electrogravimetric trans-
fert function (Dm/DE)(ꢀ) were simultaneously ob-
tained.
PB films were galvanostatically deposited on ITO
(Indian Tin Oxide) electrodes (Ageom=1 cm2,
GLASSTRON) [2] for classical voltammetric curves.
FeCl3 (chemically pure), K3Fe(CN)6, KCl, NaCl and
HCl (p.a.) (A.R. PANREAC) were used for the syn-
thesis of PB films. Water was distilled and deionised
(Milli Q-plus-MILLIPORE). ITO electrodes were im-
mersed into K3(Fe(CN)6) 0.02 M, FeCl3 0.02 M and
HCl 0.01 M solution and a controlled cathodic current
of ic=40 mA/cm2 was applied for 150s for c-PB elec-
trodeposition. When this current was increased to 600
mA/cm2, a-PB films were obtained. For gravimetric
measurements, PB was deposited onto gold electrodes
following the same procedure.
Dm−Cl
−(ꢀ)
DE
1
DJNa+(d)
DE
ꢀ
=−
(mCl−+mNa )
+
jꢀ
DJH O+(d)
DJH O(d)
n
3
2
+(mCl−+mH O
)
+mH O
(13)
+
2
3
DE
DE
It should be noted that the Na+ and H3O+ contri-
butions calculated above are emphasised as their re-
spective DJi/DE terms are multiplied by an increased
mass, respectively, mCl− +m +and mCl− +mH O if
+
compared with the original ENqa. (10).
3
In the same way, if the sodium contribution is elimi-
nated in the mass change function, the partial electro-
gravimetric transfer functions resulting is:
Dm−Na
DE
Dm mNa
DE
1
+
+
=
+
(14)
jꢀ FZF
Dm−Na
DE
+(ꢀ)
1
= −
jꢀ
DJCl−(d)
ꢀ
(mCl− +mNa
)
+
DE
DJH O+(d)
DJH O(d)
n
3
2
+(mH O+ −mNa
)
+mH O
2
+
3
DE
DE
(15)
From the plot of the partial electrogravimetric trans-
fer functions the number of species involved in the
charge compensation process can be evaluated without
any doubt.
The Nafion® (perfluorinated ion-exchange mem-
brane) 5 wt.% stock solution in low aliphatic alcohols
and 10% water was supplied by Aldrich (Ref. 27,470-
4). Nafion® films were deposited on the PB film by
extending the appropriate volume of Nafion® solution
and allowing the solvent to evaporate at room temper-
ature: 25 ml for the ITO/PB electrode (A=1 cm2) and
4 ml of a 2:5 diluted Nafion®: aliphatic alcohols solu-
tion on the gold/PB system (A=0.25 cm2). The thick-
ness of the Nafion® film was calculated from the
electrode surface area assuming a dry Nafion® density
of 1.98 g/cm3 and an about 1 g/cm3 solution density
(about 6 mm for ITO/PB electrodes and 1.5 mm for
gold/PB electrodes).
3. Experimental
The changes of the resonance frequency of the
quartz crystal, Df can be related to changes of the mass
of the film deposited on the gold electrode, Dm, by
means of the Sauerbrey equation [39]:
2f20 Dm
Df= −
(16)
A
ꢃzQvQ
where zQ is the quartz density (2.648 g/cm3), vQ is the
quartz shear modulus (2.947×1011 dynes/cm2), f0 is
Electrochemical experiments were carried out by
means of a typical three electrodes cell where the PB/

J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
3769
non-linear least squares procedure based on the Mar-
quardt algorithm for function optimisation [41].
4. Results
4.1. Crystalline PB film
4.1.1. Cyclic 6oltammetry
The presence of a Nafion® layer covering the PB
films modifies their electrochemical properties [19].
Fig. 2A shows the voltammograms of an ITO/insolu-
ble (potassium-free) c-PB (crystalline) film covered by
a 6-mm thick Nafion® membrane in a 1-M NaCl
aqueous solution and acid pH (pH 2.2). It can be
observed that after 15 cycles the voltammetric wave
shape was still well defined, and furthermore, the elec-
tric charge enclosed in the voltammetric peak (6.1×
10−3 C) was in agreement with the electrodeposition
charge (6 mC). These PB films were generated at a 40
mA/cm2 current deposition, which corresponds to an
ordered structure (c-PB films). When they were not
covered by Nafion® layers their voltammetric response
in NaCl solutions had a very poor stability [2]. When
these PB/Nafion® films were studied along the whole
voltammogram, PYUPBUES, the film degradated
quickly and the electrochemical response disappeared
in a few cycles as shown in Fig. 2B. This behaviour is
typical for the insoluble PB films as it has been proved
in previous studies of stability of PB films for the
successive cyclings [42,43]. In fact, the voltammetric
response of insoluble PB films covered by Nafion®
layers around the PBUES process in KCl solutions
shown that the transformation to the soluble PB struc-
ture did not take place [19]. Here, in NaCl solutions a
similar behaviour was obtained, and during the first
cycles around the PBUES process, as shown in Fig.
2A, the shape of the peaks did not vary, and the
transformation to the soluble PB structure did not
occur. This means that this poor stability of PB films
should be attributed to the fact that the PB films were
in the insoluble form.
Fig. 2. Voltammograms of an ‘insoluble’ c-PB film covered by
a Nafion® layer (6 mm thickness) in a NaCl 1 M solution and
acid pH 3.0. Voltammograms are carried out at 0.02 V/s, (A)
from 0.6 to −0.2 V against the reference electrode Ag/AgCl/
NaCl (1 M) and (B) from 0.6 to −0.2 V and the reverse sweep
from −0.2 to 1.2 V against the reference electrode Ag/AgCl/
NaCl (1 M).
Nafion® films deposited on the ITO glass or gold were
used as the working electrode, a platinum plate (4
cm2) was the counter electrode and Ag/AgCl/KCl (1
M) or Ag/AgCl/NaCl (1 M) and SCE were used as
reference electrodes in various measurements. A four-
channel frequency response analyser SOLARTRON
1254 and SOTELEM P.G.STAT.Z.1 potentiostat were
used for the studies. Electrochemical experiments were
carried out in 1 M and 0.5 M NaCl [2–9].
The impedance and electrogravimetric response were
measured in the 0.01 Hz to 105 Hz frequency range
and 10 mV of signal amplitude. The fitting of experi-
mental impedance and electrogravimetric data to the
theoretical expression was carried out by means of a
The study of the electrochemical response of soluble
(with inner potassium) c-PB films covered by Nafion®
layers in NaCl solutions were also attractive. Soluble
PB films were obtained by cycling 15 times insoluble
PB films around the reduction system peaks PBUES
in a 1-M KCl solution before the PB films were cov-
ered by the Nafion® layers. Fig. 3A shows the voltam-
metric curves obtained for these films in a 1-M NaCl
solution: no difference appeared between the succes-
sive cycles. Furthermore, the stability of the voltam-
mogram (PYUPBUES) was also strongly increased as
shown in Fig. 3B, if compared with Fig. 2B.
It is important to note that a well defined system of
peaks appeared corresponding to the PBUPY process,

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J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
and the colour change from blue to yellow can be
observed. The system of peaks can only be clearly
observed in KCl and NaCl solutions, while for PB
films in NH4Cl or CsCl solutions this system of peaks
is poorly observed [15]. This system of peaks was either
observed when the films of Prussian Blue were covered
with Nafion® in CsCl and NH4Cl solution (Fig. 4).
Some features were not clear. The first one was the
fact that during the oxidation process, according
to reactions ii and iv, Cl− anions should enter the PB
film to maintain electroneutrality. However, it is
known that the transport of anions is almost entirely
suppressed through the Nafion® membrane [44]. This
perm-selectivity of Nafion® membranes implies that the
oxidation process to the yellow form cannot take place
according to reactions ii and iv. Some authors have
pointed up the possibility that the compensation of
the electric charge within the film occurs by the exit
of countercations instead of the entrance of the anions
during the oxidation process [5,9,45]. This idea is sup-
ported by several experimental results such as the in-
dependence of the formal potential for this system
of peaks on the nature of the counteranion [42] or
the dependence of this potential on the potassium
concentration [9,12,45]. Also, impedance studies of PB
films in NH4Cl, CsCl and KCl solutions at po-
tentials corresponding to the PBUPY process, have
shown that the countercations should play an import-
ant role during the oxidation process [15]. This is sup-
ported by the fact that the potential at which the re-
sistance of charge transport through the film [6,7],
reach minimum values is different in the three studied
solutions.
Another questionable point is the fact that although
the Na+ hydrated ions cannot be transported through
the PB films, the electrochemical processes which need
the entrance of countercations into the film can, never-
theless take place when c-PB films are covered by
Nafion® layers or that their structure is more amor-
phous [2]. In the case of c-PB films covered by Nafion®
layers, a very simple explanation is to consider that
sodium ions can lose a part of their hydration sphere
during the transport through the Nafion®. So, the
effective radius or size of the ion decreases and as the
size of the pore is only slightly smaller than the size of
the hydrated ion, a small decrease in the effective size
of the latter allows this ion to be transported through
the film.
Fig. 3. Voltammograms for a ‘soluble’ (previously cycled in a
KCl solution) c-PB film covered by a Nafion® layer (6 mm
thickness) in a NaCl 1 M solution and acid pH 3.0. Voltam-
mograms are carried out at 0.02 V/s, (A) from 0.6 to −0.2
against the reference electrode Ag/AgCl/NaCl (1 M) and (B)
from −0.2 to 1.2 V against reference electrode Ag/AgCl/NaCl
(1 M).
4.1.2. Cyclic EQCM
To confirm this hypothesis, ‘soluble’ c-PB films de-
posited on the gold electrode of a quartz crystal were
studied by cyclic voltammetry and QCM investigation.
Fig. 5 shows the variation of current and mass against
the applied potential. During the reduction process the
charge compensation takes place by the incorporation
Fig. 4. Whole voltammograms of c-PB films covered by a
Nafion® layer (6 mm thickness) in CsCl and NH4Cl 0.5 M
solutions and acid pH (between 2.5 and 2.7). Voltammograms
are carried out at 0.02 V from 0.6 to −0.2 V and the reverse
sweep from −0.2 to 1.2 V against the reference electrode
Ag/AgCl/NaCl (1 M).

J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
3771
(12)–(15) for a c-PB film covered with a Nafion® layer
in a NaCl solution at 0.1 and 0.05 V potentials. It is
observed that when the contribution of sodium ions is
eliminated, the residual function, which includes the
contributions of solvent, hydrated proton and anions is
almost zero for these potentials. So, the Dm/DE loop
can be attributed, without doubt, to the Na+ move-
ment and the sign of the Dm/DE low frequency limit
corroborates the shape of the mass/potential curve.
Indeed, a negative real value was obtained for this limit
(Fig. 6) which indicates that when the potential de-
creases the Na+ ions are inserted inside the film. This is
a result coherent with the mass increase observed dur-
ing the PB reduction (Fig. 5) in steady state
experiments.
Fig. 5. Curves current versus potential and mass versus poten-
tial of a c-PB film covered by a Nafion® layer (1.5 mm) in a
0.5-M NaCl solution, and acid pH. Scan rate=0.01 V/s, from
0.6 to −0.2 V against the SCE reference electrode.
of sodium cations within the PB film, and no participa-
tion of Cl− anions is expected since PB films are
covered by Nafion®. It is possible to partly evaluate the
mass of the cation that enters the PB film by the
following relationship:
F Dm
Q
mc=
(17)
where F is the Faraday (96 500 C/mol), Q the electric
charge enclosed within the voltammogram (C/cm2) and
Dm the change of mass associated to the reduction of
the PB form to the ES form (g/cm2). The electric charge
measured is 0.0086 C/cm2 and Dm=2 mg/cm2 and then,
the mass of the cation which enters the PB film is 22.4
g/mol. By comparing this value with the sodium atomic
mass, 23 g/mol, it is concluded that sodium cations are
not hydrated when they are inserted within the PB film.
To confirm this result, ac electrogravimetry was per-
formed with the same sample. Indeed, this atomic mass
value obtained can be questionable because the calcula-
tion (Eq. (17)) was used for a QCM measurement on a
whole cycle: this QCM response appears as a global
mass response taking into account all the motion of the
species. On the contrary, ac electrogravimetry can sepa-
rate the various species motions as the perturbation
frequency changes allows the various kinetic processes
to be reached.
Fig. 6. Global and partial electrogravimetric transfer functions
(Dmi/DE) for a c-PB film covered by a Nafion® layer (1.5 mm)
in a 0.5-M NaCl solution, and acid pH. Potential, E=0.1 V
(A) and E=0.05 V (B). Reference electrode SCE. Perturbation
signal amplitude DE=0.02 V.
4.1.3. ac electrogra6imetry
Fig. 6 shows the global, Dm/DE, and partial ac-elec-
trogravimetric transfer functions obtained from Eqs.

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J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
4.2.2. ac electrogra6imetry
When a-PB films are studied by electrogravimetry at
various potentials between the totally reduced form,
Everitt’s salt, and the mixed valence compound, Prussian
blue, similar conclusions can be drawn. Fig. 8 shows the
global and partial electrogravimetric transfer functions at
0.1 and 0.05 V (near the redox potential of the PBUES
reaction). In both cases, the partial contribution that
corresponds to the elimination of non-hydrated sodium
contribution is negligible. Besides, the F(Dm/Dq) func-
tion reaches values near 23 g/mol for the lowest frequen-
cies at these potentials which clearly prove that sodium
cations enter the PB film without water whatever the PB
film structure.
Fig. 7. Curves current versus potential and mass versus poten-
tial of an a-PB film in a 0.5-M NaCl solution, and acid pH.
Scan rate=0.01 V/s, from 0.6 to −0.2 V against the SCE
reference electrode.
When PB/Nafion® films are studied in NaCl
solutions by means of simultaneous impedance spectro-
scopy and ac-electrogravimetry at various potentials it
is also possible to obtain information on the cation
mass which enters the PB film at these potentials. From
the Faradaic impedance and the electrogravimetric
transfer function, the Dm/Dq function is obtained (Eq.
(11)). This function provides information on the mass
of the cation that enters the film. If this function is
multiplied by the Faraday (96 500 C/mol) the mass of
the ion which participates in the charge compensation
process is directly obtained. The real part of this
function reaches values of 22 g/mol at E=0.1 V and 25
g/mol at E=0.05 V.
4.2. Amorphous PB film
4.2.1. Voltammetry and EQCM measurements
To confirm this dehydration process, amorphous PB
films (a-PB films) deposited onto the gold electrode of a
quartz crystal were studied by cyclic voltammetry and
gravimetry. Fig. 7 shows the current and mass changes
against the applied potential. Following the same proce-
dure as for the c-PB/Nafion® system, it is possible to
estimate the mass of the cation, which enters the a-PB film
during the reduction process. In this case, the electric
charge enclosed within the voltammetric curve is Q=
0.0083 C/cm2 and the change in mass associated to this
process is Dm=2.02 mg/cm2. Therefore, the estimated
mass of the countercation is 23.4 g/mol which corre-
sponds to the non-hydrated sodium cation mass (23
g/mol).
Fig. 8. Global and partial electrogravimetric transfer functions
(Dmi/DE) for an a-PB film in a 0.5-M NaCl solution, and acid
pH. Potential, E=0.1 V (A) and E=0.05 V (B). Reference
electrode SCE. Perturbation signal amplitude DE=0.02 V.

J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
3773
[47,48]. In this case it is also possible to consider that
the Nafion® membrane cannot accept more water
molecules, and even if the dehydration process takes
place at the PB/Nafion® interface, water molecules will
be expelled to the outer solution. Therefore, Nafion® in
contact with a salt solution loses water since there is an
equilibrium between the outer solution and the solution
within the Nafion® membrane.
In this case, it is possible to consider that only
sodium cations participate to the charge compensation
process. Then, from the low frequency limits of the
electrogravimetric transfer functions it was possible to
obtain the values of the derivative of the insertion
isotherms dC/dE (Eq. (15)) for the sodium ion at
different potentials which are plotted in Fig. 9 for the
a-PB film. dC/dE was calculated from the low fre-
quency limit of Dm/DEby the following equation:
dC(E)
dE
1
Dm
DE
Fig. 9. Derivative of insertion rate for Na+ ions in amorphous
PB films. These values are evaluated from the electrogravimet-
ric curves by extrapolating at lower frequencies.
=
limit(
)
(18)
ꢀ“0
d×mNa
+
If compared with Fig. 7, a good correlation, about
the shape, is observed between the voltammogram and
the derivative of the insertion isotherm curve. The
minimum in Fig. 9 corresponds to the peak potential in
Fig. 7. According to Eq. (6) this potential (0.08 V),
which is equal to E0i +Ei, represents the redox potential
of the PBUES process in NaCl solutions.
If only one charged species participate in the charge
compensation process, from Eqs. (8) and (9) the
faradaic impedance can be written such as:
5. Discussion
In both cases, PB films (a-PB/Nafion® and c-PB/
Nafion®) in NaCl solutions show a good electrochemi-
cal response and it is corroborated that sodium cations
lose their hydration sphere before insertion into the
film. Therefore this process takes place at the film/solu-
tion interface. The modification of the surface of the PB
film allows the dehydration of the cation.
In the case of c-PB films in KCl solutions, it has been
also proposed that K+ ions enter the PB film without
water [46]. The energy needed to dehydrate the cation is
smaller for the K+ cation than for the Na+ cation and
also, the number of hydration of Na+ is larger than the
number of hydration of K+ in the solution. Na+
cations can enter the a-PB film and not the c-PB film
because the more amorphous surface allows the adsorp-
tion of sodium cations before the entrance in the film
and then catalyse the dehydration process. This process
can be expressed as:
DJNa
DE
GNa
+
Z−F 1(ꢀ)=F
+ =F
d2
ꢁ' ꢂ
coth
jꢀ
KNa
d
DNa
+
+
1+
DNa
'
+
jꢀ
d2
(19)
According to these results, no important transport of
water molecules, associated to the sodium insertion/ex-
pulsion process, is observed. Therefore, the electro-
gravimetric transfer function can be written, according
to Eqs. (8) and (10), such as:
Dm
DE
A
DJ
DE
ꢀ n
+
Na
(ꢀ)= −
mNa
+
jꢀ
“
“
’
(Na+·x(H2O))solution (Na+·x(H2O))adsorbed
A
mNa+GNa
+
’
= −
(20)
jꢀ
d2
ꢁ' ꢂ
(Na+)inserted+x(H2O)solution(A)(B)(C)
(v)
coth
jꢀ
KNa
DNa
+
+
1+
where x represents the number of water molecules that
hydrate the Na+ cation in the solution.
d
DNa
d2
'
+
jꢀ
For Nafion®/PB films it is also concluded that
sodium cations enter the PB film without water
molecules. That means that the dehydration process
takes place at the Nafion®/solution interface. However,
it has been reported that sodium cation is transported
through Nafion® membranes with water molecules
A good way to test the validity of the model pro-
posed here is to fit experimental data of impedance
spectra to Eq. (19) and the experimental electrogravi-
metric data to Eq. (20) and to compare the results
obtained. Figs. 10 and 11 show the good correlation

3774
J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
insertion rates here evaluated are close to that plotted
in Fig. 9 which are graphically evaluated. They were
calculated by combining Eqs. (8) and (10), which leads
to:
dC(E) GNa
=
(21)
dE
KNa
It should be noted that the accurate value found for
the atomic mass of sodium support the hypothesis
about the validity of the Sauerbrey equation in the
whole potential range, with a potential independant
sensitivity coefficient.
6. Conclusion
Crystalline PB films can be studied in NaCl solutions
by covering them with a Nafion® layer. These crys-
talline PB films without the presence of the pro-
tective Nafion® membrane are not stable in NaCl solu-
tion. The use of the QCM allows the atomic mass
of the cations involved in the charge compensation
process to be estimated. It shows that a dehydration of
sodium ions takes place before they enter the PB film,
decreasing the effective size of the ion and allowing
their entrance into the PB film structure during
the electrochemical processes. Therefore, the Nafion®
Fig. 10. Experimental impedance spectra (ꢀ) and simulated-
fitted impedance spectra (— —). E=0.05 V and amorphous
PB film.
between fitted-simulated data and the experimental
data for the impedance spectra and the electrogravimet-
ric transfer function.
Table 1 shows the values of the parameters obtained
from the fitting of impedance spectra to Eq. (19) and
electrogravimetric data to Eq. (20). It is shown that the
parameters evaluated from both techniques agree very
well, especially in the range of 0.2–0 V, near the redox
potential of the PBUES process. The changes of GNa
and KNa with potential were determined: the equivalent
diffusion coefficient of Na+ increased when the poten-
tial became more anodic. Besides, the derivative of
membrane acts not only as
a sieve that allows
the transport of some ions and that prevents the trans-
port of anions, but also participates in the electro-
chemical reactions allowing the dehydration of sodium
ions.
The results also proved that in the case of a-PB films,
sodium cations lose water molecules before they enter
the film. In both cases, sodium cations are non-hy-
drated within PB films. This is a very interesting aspect
in this study, since it could be applicable, i.e. to other
electrocatalytic systems, which need the entrance of
bigger hydrated ions.
The oxidation process from PB to PY is also
observed in PB films covered by Nafion® layers in NaCl
solutions. As the Cl− anion transport through the
Nafion® membranes is almost entirely suppressed, the
electric charge compensation during the oxidation
process should take place by the exit of some counter-
cations from the film instead of the entrance of
anions.
The good agreement of parameters evaluated from
the fitting of impedance spectra to Eq. (19) and electro-
gravimetric data to Eq. (20) proves the validity of the
models here proposed. By coupling these two tech-
niques, new informations can be obtained and for
example, the inserted/expelled species are identified
without doubt. In addition, the kinetic parameters, G
and K, can be determined at each potentials.
Fig. 11. Experimental electrogravimetric data (ꢀ) and simu-
lated-fitted electrogravimetric function (— —). E=0.05 V
and amorphous PB film.

Table 1
Parameters evaluated from the fitting of impedance spectra data to Eq. (19) and electrogravimetric data to Eq. (21)a
b
c
dC/dEb
dC/dEc
KNa
d
KNa
d
d2
d2
E (V)
mNa+GNa
mNa+GNa
+
+
+
+
b
c
b
c
(s)
(s)
(mg/s per V per cm2)
(mg/s per V per cm2)
(mol/V per cm3)
(mol/V per cm3)
DNa
DNa
+
+
(s−1
)
(s−1
)
/
0.30 −17.5
−10.2
−17.2
−26.2
−30.5
−23.3
−12.0
−5.3
17.9
21.4
11.9
6.9
3.7
1.9
8.3
10.7
8.7
5.4
3.1
1.8
1.1
0.8
1.2
0.6
0.5
0.6
0.9
1.6
2.0
5.4
0.7
0.5
0.5
0.6
1.0
1.6
3.0
7.8
−0.28
−0.42
−0.78
−1.50
−2.04
−2.07
−1.64
−0.93
−0.35
−0.50
−0.93
−1.78
−2.30
−2.00
−1.42
−0.78
0.25 −31.9
0.20 −31.5
0.15 −33.4
0.10 −24.3
0.05 −12.5
0.00
−0.05
−4.3
−1.3
0.8
0.4
4
−1.8
(
a dC/dE represents the derivative of insertion rates evaluated such as dC/dE=G+Na/K+Na and d=0.14 mm.
b Evaluated from the electrogravimetric data.
3
c Evaluated from the electrochemical impedance data.
3

3776
J.J. Garc´ıa-Jaren˜o et al. / Electrochimica Acta 45 (2000) 3765–3776
[22] J.J. Garc´ıa-Jaren˜o, A. Sanmat´ıas, J. Navarro-Laboulais,
Acknowledgements
F. Vicente, Electrochim. Acta 44 (1998) 395.
[23] J.J. Garc´ıa-Jaren˜o, Thesis University of Valencia, 1998.
[24] C. Barbero, M.C. Miras, R. Kotz, O. Haas, J. Elec-
troanal. Chem. 437 (1997) 191.
Part of this work has been supported by CICYT
PTR 95-0329-OP and CNRS-France.
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