JOURNAL OF COLLOID AND INTERFACE SCIENCE
ARTICLE NO.
180, 116–121 (1996)
0280
Electrical Behavior of an Inorganic Film from ac and dc Measurements
J. BENAVENTE,* ,1 J. R. RAMOS-BARRADO,
AND
A. CABEZA†
*Departamento de Fı́sica Aplicada, and †Departamento de Quı́mica Inorgánica, Facultad de Ciencias,
Universidad de Málaga, E-29071 Málaga, Spain
Received July 19, 1995; accepted October 18, 1995
The electrical behavior of a supported inorganic film (hydrogen
uranyl phosphate or UPP) in contact with electrolytes containing
inorganic precipitate generating ions was studied by ac and dc
measurements. The equivalent circuit for the system UO2 (NO3 )2 /
UPP film/H2O3PC6H5 was determined by impedance spectroscopy.
This technique permits us to obtain three different electrical contributions for the whole system: (i) film/electrolytes interface; (ii)
bulk film; (iii) electrolyte solutions. Film and interface electrical
parameters, such as the film resistence and capacitance (R f and
C feq), the charge transfer resistance ( Rct ), and double layer capacieq
tance (C dl
), were obtained for different concentrations of the external solutions. For comparison, measurements with the same
electrolytes at both sides of the UPP film were also made. From
dc measurements the asymmetry of the current–voltage curves,
depending on the polarity of the external voltage applied to the
system, was also obtained. This asymmetry can be taken as a
measure of the film efficiency for electric current rectification.
Concentration dependence for the i–v curves was also considered.
q 1996 Academic Press, Inc.
Key Words: ac measurements; dc measurements; inorganic films;
uranyl phenylphosphonate.
1. INTRODUCTION
Uranyl phenylphosphonates (UPP) are a new class of
materials having bi-dimensional structure, which can be seen
as an organic pillared layer–inorganic structure. In general,
metal organophosphonates have been developed as alternatives to Langmuir–Blodgett and siloxane multilayers for
electronic and optical devices. The electrical properties are
an important characteristic of these materials (1–2), which
can be used as catalysts, ion exchangers, and material for
the derivation of electrode surfaces (3–5).
In previous papers (6, 7) we have determined some electrical parameters ( z -potential, electrophoretic mobility, salt
permeability, or cation transport numbers) for a film of uranyl phenylphosphonate, when it was in contact with solutions of each one of the precipitate generating electrolytes
(the same solution at each side of the film). In this paper,
1
To whom correspondence should be addressed.
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2. EXPERIMENTAL
Material
The UO2 (O3PC6H5 ) or UPP was prepared by mixing phenylphosphonic acid solution (0.3 M) and uranyl nitrate solution
(0.3 M) in a molar ratio P/U Å 3 following the procedure
indicated in Ref. (6). The UPP is thermally stable below 3307C
and very insoluble in water, acetone, and other common solvents. It is also stable and insoluble in strong acid solutions
116
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All rights of reproduction in any form reserved.
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the electrical behavior of the system UO2 (NO3 )2 /UPP film/
H2O3PC6H5 is studied using alternating (ac) and direct (dc)
current measurements, and some characteristic parameters
have been determined.
Impedance spectroscopy (IS) is a powerful technique for
studying electrical and electrochemical properties of a large
variety of systems (8). Concerning the use of IS to study
thin film in contact with electrolyte solutions, three different
contributions, bulk, interfacial, and electrolytes, can be determined. Using equivalent circuits as models, some characteristic parameters of both UPP film and electrolyte/film
interfaces, which are related to the different electrochemical
processes in the system, can be obtained. A parallel RQ
association (resistance, R, and nonideal capacitor, Q) was
obtained for both UPP film and interface. From these results,
the film resistance and equivalent capacitance as well as the
charge transference resistance and double layer capacitance
values for different electrolyte solutions (10 04 õ c (M) õ
10 02 ) were determined. IS measurements with the UPP film
separating the same electrolyte solution, UO2 (NO3 )2 /UPP
film/UO2 (NO3 )2 and H2O3PC6H5 /UPP film/H2O3PC6H5 ,
were also carried out, and a comparison among the different
electrical parameters was also made.
On the other hand, dc measurements show the asymmetry
of the current–voltage curves depending on the polarity of
the external voltage (9, 10), which can be taken as a measure
of the rectifier behavior of the UO2 (NO3 )2 /UPP film/
H2O3PC6H5 system. This asymmetry is due to the ion adsorbed layers at the film/electrolyte solution interfaces, and
is related to the different ions responsible for the driving
current under each external voltage polarity.
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ELECTRICAL BEHAVIOR OF INORGANIC FILM
until c Å 0.5 M and in basic dilute solutions. The X-ray diffraction study reveals a lamellar structure, with basal spacing of
14.6 Å and good crystallinity. Its layer space does not swell
and contains the phenyl groups (6). The supported film
was prepared by deposition of an aqueous suspension of
UO2 (O3PC6H5 ) on an alumina porous filter (Anopore).
or by a set of n first order differential equations. Hence if
£ (t) is a sine wave input,
£ (t) Å V0 sin vt,
[2]
the current intensity i(t) is also a sine wave,
Impedance Measurement
The measuring cell has already been described (11). Measurements were carried out at room temperature (257C) with
aqueous solutions of the precipitate generating electrolytes
at five different concentrations (10 04 õ c (M) õ 10 02 ). The
UPP film was placed separating UO2 (NO3 )2 and H2O3PC6H5
solutions at the same concentration.
For impedance measurements one pair of gold electrodes
was placed in each half-cell and connected to a frequency
response analyzer (Solartron 1255), from which data can be
sent to a computer for further treatment and storage. Experimental data were corrected by software as well as by other
parasite capacitances (12). The measurements were carried out
for 120 different frequencies in the range from 1002 to 10 7 Hz,
and a maximum voltage of 0.025 V was used. For comparison,
measurements with the UPP film and the same electrolyte
(UO2 (NO3 )2 or H2O3PC6H5 , respectively) and concentration
at both sides of the film were also made.
For dc measurements two kinds of electrodes were used,
gold electrodes for injecting current and platinum electrodes
to measure the potential difference at both sides of the UPP
film. Due to the asymmetry of the UO2 (NO3 )2 /UPP film/
H2O3PC6H5 system, different values of the electrical resistance depending on the direction of the current were measured, which are called R(h) and R(d).
3. THEORETICAL FRAMEWORK
Let us consider a film which interposed between two isothermal media allows a mass transfer between them. When
the interface is perturbed from its equilibrium by means of
an external energy source, permanent flow of charge and
matter appears across it. This may be due to the existence
of electrochemical reactions allowing the electric charge
transfer or gradients of electric and chemical potentials,
which make possible the transport of reacting species. Although these systems must be considered as nonlinear systems, they can be considered in a linear regime for small
external perturbation (13).
When a linear system is perturbed by a small £ (t) voltage,
its response, the electric current, i(t) is determined by a
differential equation of nth order in i(t),
b0
d ni(t)
d n0 1i(t)
/
b
/rrr/ bni(t)
1
dt n
dt n0 1
Å a0
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d n£ (t)
d n0 1£ (t)
/
a
/rrr/ an£ (t),
1
dt n
dt
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[1]
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i(t) Å I0 sin( vt / f ),
[3]
and a transfer function, the admittance function, can be defined as
Y *( v ) Å ÉY ( v )É e j f ,
[4]
where ÉY ( v )É Å I0 /V0 , and ÉY ( v )É and f are the modulus
and the phase shift of the admittance function. The impedance function, Z( v ), is the inverse of the admittance function:
Z *( v ) Å [Y *( v )] 01 .
[5]
The impedance Z *( v ) of these systems is a complex number, which can be represented in cartesian coordinates by
Z *( v ) Å Z * / jZ 9,
[6]
where Z * and Z 9 are the real and imaginary part of the
impedance.
Two types of plots are used to describe these relationships
and they are illustrated with an example for the equivalent
circuit corresponding to an electrochemical cell, which is
represented by a parallel association of a resistance ( R) and
a capacitor (C). Figure 1a shows a plot of the impedance
imaginary part ( 0Z 9 ) versus the real part (Z * ) in the complex plane Z *, where the angular frequency ( v ) increases
from the right to the left (Nyquist plot), while Fig. 1b shows
the impedance imaginary part against log v (Bode plot).
The analysis of ac data is often carried out by the complex
plane method, which involves plotting the impedance imaginary part against the real part ( 0Z * vs Z 9 ). When plotted
on a linear scale, the equation for a parallel RC circuit,
which can represent an electrochemical cell, gives rise to a
semicircle in the Z * plane (8). The semicircle has intercepts
on the Z * Å Zreal axis at R` ( v Å ` ) and R0 ( v Å 0), where
(R` 0 R0 ) is the resistance of the system. The maximum of
the semicircle is 0.5(R` 0 R0 ) and occurs at a frequency
such that vRC Å 1, RC being the relaxation time.
Complex systems may present different relaxation
times. In these cases, the impedance plot is a depressed
semicircle, and a nonideal capacitor, called a constant
phase element ( CPE ) , is considered; the CPE admittance
is expressed by ( 8 )
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BENAVENTE, RAMOS-BARRADO, AND CABEZA
Q( v ) Å Y0 ( j v ) n ,
[7]
where Y0 ( Vs 0n ) and n are two empirical parameters (0 õ
n õ 1). In these cases an equivalent capacitance, C eq , can
be determined by the relationship
C eq Å (R0Y0 ) 1 / n /R0 .
[8]
These expressions indicate that electrical parameters for homogeneous or heterogeneous systems can be obtained from
impedance spectroscopy results.
4. RESULTS AND DISCUSSION
Figure 2 shows the impedance plot for the UO2 (NO3 )2 /
UPP film/H2O3PC6H5 system, at a given concentration (c Å
0.005 M) for the whole frequency range. The total experimental impedance values, for each concentration, were fitted
FIG. 2. Nyquist plot and equivalent circuit for the system UO2 (NO3 )2 /
UPP film/H2O3PC6H5 , at a given concentration (c Å 0.005 M).
to a circuit which consists of a series association of three
parts (electrolyte, bulk film, and film/electrolyte interface),
as is also indicated in Fig. 2:
(i) The electrolyte part, which corresponds to the highest
frequencies ( f ú 10 5 Hz), consists of a resistance, Re , in
parallel with a capacitor, Ce , and it is represented by (ReCe ).
We will not consider this contribution in the following discussion.
(ii) The film equivalent circuit, for frequencies ranging
between 100 and 10 5 Hz, consists of a parallel asociation
of a resistance, R f , and a nonideal capacitor or CPE, Q f ,
and it is written as (RfQ f ).
(iii) The film/electrolyte interface contribution appears
at low frequencies (0.01 Hz õ f õ 100 Hz), and it also
consists of a resistance, Rct , and a nonideal capacitor, Qdl .
These two elements are associated to the charge transference
resistance and the electrical double layer capacitance, and
the equivalent circuit is represented by (RctQdl ).
FIG. 1. Equivalent circuit of an electrochemical cell, which consists of
a parallel association of a resistor, R, and a capacitor, C. (a) representation
in the Z * plane or Nyquist plot ( 0Z 9 vs Z * ); (b) Bode plot ( 0Z 9 vs log
v ).
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For further comparison, the impedance measurements for
two systems, UO2 (NO3 )2 /UPP film/UO2 (NO3 )2 and
H2O3PC6H5 /UPP film/H2O3PC6H5 , which correspond to the
UPP film in contact with each one of the electrolytes containing the generating precipitate ions, were also carried out
and the impedance plots are shown in Fig. 3. In both cases,
the film equivalent circuit also consists in a parallel association of a resistance (Rur or Rf f ) and a nonideal capacitor
(Qur or Qf f ). No significant interface contributions were
observed for these systems. A comparison of these results
with those corresponding to the UO2 (NO3 )2 /UPP film/
H2O3PC6H5 system shows that the equivalent circuit associated to the UPP film itself is similar with both kind of
systems (although differences in the characteristic parameters could exist, as it will be discussed), but the adsortion
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ELECTRICAL BEHAVIOR OF INORGANIC FILM
TABLE 1
Calculated Parameters, R* and a, and Correlation Coefficient,
r, of the UPP Film for Different Systems Studied
R* (kV)
System
H2O3PC6H5/UPP/H2O3PC6H5
UO2(NO3)2/UPP/UO2(NO3)2
UO2(NO3)2/UPP/H2O3PC6H5
4.33
5.65
90.81
R(c) Å R*c 0a .
FIG. 3. Nyquist plot for the UPP film with the same electrolyte at both
sides at c Å 0.005 M. ( s ) H2O3PC6H5 ; ( n ) UO2 (NO3 )2 .
of ions at the film/electrolyte interfaces, which originates
the double layer in the composite system, is not so important
in the case of both single systems.
The fitting of the experimental data, by means of a nonlinear program (14), permits us to determine both the resistance and capacitance values for the electrolyte, the UPP
film, and the interface, for the different concentrations studied. In all cases, differences between experimental and calculated values were lower than 8%.
Concentration dependence for the film resistance with the
different systems studied is shown in Fig. 4. These results
show that the resistance values are strongly dependent on
salt concentration, which is attributed to the electrolyte invasion into the film structure (15, 16), but for the composite
UO2 (NO3 )2 /UPP film/H2O3PC6H5 system a kind of limit
value is obtained at high concentrations. In this case, the
electrolyte invasion will originate the formation of more
precipitate during the experiments until an almost complete
compaction of the precipitate. Resistance values were fitted
to an exponential expression:
a
r
00.763
00.708
00.490
0.999
0.988
0.992
[9]
Values of the empirical R* and a parameters for the three
systems studied are shown in Table 1. From these results,
it can be seen than the electrical response of both simple
systems (UO2 (NO3 )2 /UPP film/UO2 (NO3 )2 and H2O3PC6H5 /
UPP film/H2O3PC6H5 ) are very similar to each other, but
important differences exist if they are compared with the
resistance determined for the composite UO2 (NO3 )2 /UPP
film/H2O3PC6H5 system. This difference can be attributed
to the UPP film itself (adsorption of ions to the membrane/
film interfaces) or to the formation/compaction of the UPP
precipitate during the measurements as was previously indicated. This results in an important increase of the film electrical resistance.
The charge transference resistance, Rct , for the
UO2 (NO3 )2 /UPP film/H2O3PC6H5 system was also determined and its values are indicated in Table 2. Much higher
values are obtained for Rct than for R f (almost two orders
of magnitude) and also a concentration dependence was
found, this behavior being similar to that indicated in the
literature for other inorganic films (17).
From the impedance data the equivalent capacitances for
eq
the UPP film, C eq
f , and the double layer, C dl , were also
determined by means of Eq. [8], and their values, as a
function of the electrolyte concentration, are also indicated
in Table 2. From this table, it can be seen that at low concentrations C eq
dl values increase when the concentration increases
but an almost constant value is reached at high concentrations. This can be explained assuming that at a given concentration, around 0.001 M, the electrical double layer built up
TABLE 2
Charge Transfer Resistance, Rct , and Film and Double Layer
eq
Equivalent Capacitances, C feq and C dl
, for the System UO2 (NO3)2 /
UPP Film/H2O3PC6H5
FIG. 4. Film resistance versus concentration for the different systems:
( s ) H2O3PC6H5 /UPP film/H2O3PC6H5 ; ( n ) UO2 (NO3 )2 /UPP film/
UO2 (NO3 )2 ; (x) UO2 (NO3 )2 /UPP film/H2O3PC6H5 .
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c (M)
Rct (MV)
C eq
f (mF)
C eq
dl (mF)
1004
5 1 1004
1003
5 1 1002
1002
15.00
1.80
1.35
0.96
0.26
0.137
0.158
0.251
0.334
0.447
12.2
26.0
28.3
32.2
33.8
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BENAVENTE, RAMOS-BARRADO, AND CABEZA
TABLE 3
Extrapolated Equivalent Capacitance at C Å 0, C eq
0 , and Average
eq
Capacitance »C ur
… and »C eq
ff … for the System Studied
C eq
0 (F)
System
H2O3PC6H5 /UPP/H2O3PC6H5
UO2(NO3)2 /UPP/UO2(NO3)2
UO2(NO3)2 /UPP/H2O3PC6H5
»C eq… (F)
(9.7 { 1.6)1008
(8.4 { 2.2)1008
08
13.8 1 10
by the adsorption of the UPP precipitate-generating ions at
the UPP film/electrolyte interface is completely developed
and it is not greatly affected by an extra amount of ions in
the solutions (high concentrations). However, C eq
f values
present linear increases when the concentration increases,
and its extrapolated value at c Å 0, C eq
f (0), is shown in
Table 3. An explanation for this fact will be provided by
the formation/compaction of the precipitate layer previously
indicated, which would mainly affect the geometrical parameters of the UPP film.
eq
C eq values for the two simple systems (C eq
f f and C ur ) were
also determined; they do not present a clear concentration
dependence (no chages in the precipitate layer should exist
in these systems) and not important differences depending
on the electrolyte considered were also obtained, as can be
eq
seen from their average values, » C eq
f f … and » C ur … , which are
also indicated in Table 3. A comparison of these three values
shows the similarity of results when no adsorbed layer at
the UPP film interfaces are considered.
From dc measurements, current–voltage curves for the
UO2 (NO3 )2 /UPP film/H2O3PC6H5 system were obtained,
and they are shown in Fig. 5, for different electrolytes con-
centrations. The asymmetry of the i–v curves, which is a
characteristic of the inorganic precipitation systems (9, 10),
is clearly shown in this picture. In Fig. 5, two different zones
(h and d) can be seen depending on the polarity of the
external applied voltage:
—Zone h corresponds to the hyperpolarizing (or positive)
voltage, which drives to the UPP film the ions forming the
precipitate. In this situation two oppositely charged layers appear, one at each film/electrolyte interface, and only a residual
or limit current (I0 ) crosses the system, which is mainly due
to the H / and OH 0 ions from the solvent (water).
—Zone d corresponds to the depolarizing (or negative)
voltage, and in this case no restriction to the ions’ movement
exists and the system behaves as an ohmic conductor.
From the slopes of the straight lines shown in Fig. 5, R(h)
and R(d) values were determined for each concentration.
The R(h)/R(d) ratio represents a measure of the film current
rectification efficiency, and its values are indicated in Table
4. As can be seen from these results, at the low concentration
used (c Å 10 04 M) no current rectification exists, which
indicated the necessity of a minimum value for the concentration of precipitate-generating ions in the electrolyte solutions, in order to observe the rectification effect; this might
permit us to use the system as a sensor to detect the presence
of the inorganic precipitate-generating ions, (UO/2
2 ) and
HO3PC6H 50 in this case, among other ions in mixed solutions.
The other parameter related to the current rectification is the
limit intensity, I0 , which was determined by the interception
of the straight lines obtained for each current polarity (17).
I0 values are also indicated in Table 4. An increase of both
parameters R(h)/R(d) and I0 when the electrolytes concen-
FIG. 5. Current–voltage curves at different concentrations for the system UO2 (NO3 )2 /UPP film/H2O3PC6H5 . (x) c Å 10 04 M; ( L ) C Å 5 1 10 04
M; ( n ) c Å 5 1 10 03 M; ( s ) C Å 10 02 M.
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ELECTRICAL BEHAVIOR OF INORGANIC FILM
TABLE 4
Concentration Dependence for the Film Resistance Ratio,
R (h)/R (d), and the Limit Current, I0
c (M)
R (h)/R (d)
I0 (mA)
1004
5 1 1004
1003
5 1 1002
1002
1.00
1.90
2.75
5.48
5.05
0.08
0.55
1.35
2.20
5.56
could be used to detect the presence of some of the precipitate-generating ions in the solutions bathing the inorganic
0
film (in this case, (UO/2
2 ) and HO3PC6H 5 ), and it gives to
the inorganic precipitate films the posibility of being used
as sensors for electrolytic systems.
ACKNOWLEDGMENTS
We thank the Ministerio de Educación y Ciencias (ESPAÑA) for the
project CICYT MAT90-917 and Junta de Andalucı́a (Research group 6064)
for financial support.
REFERENCES
tration increases was found, which means that the increase
of precipitate-generating ions in the solution not only increases the adsorbed layers at the UPP film interfaces but
also affects the transport of charges across the film, which
should be considered for further applications of these kinds
of systems.
The electrical response of the system UO2 (NO3 )2 /UPP
film/H2O3PC6H5 was studied by alternating and direct current measurements for different electrolyte concentrations.
Impedance spectroscopy can be used for studying heterogeneous systems with different dielectric properties, such as
solid/salt solution systems. In this case, IS measurements
permit us to determine separately the electrical contributions
of salt solutions, solids, and solid/liquid interfaces. Taking
into account IS results, the film and interface electrical resistances and capacitances were obtained. Concentration dependence for these parameters was also considered. A comparison with the results obtained for the same UPP film in contact
with each one of the electrolytes is also made.
The asymmetry of the current–voltage curves determined
with dc measurements shows the rectifier behavior of this
system, for concentrations higher than 10 04 M. This property
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9. Ayalon, A., J. Membr. Sci. 20, 91 (1984).
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11. Cabeza, A., Martinez, M., Benavente, J., and Bruque, S., Solid State
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13. Gabrielli, C., Tech. Report No. 004/83, Solartron Instruments, 1980.
14. Boukamp, B. A., Solid State Ionics 18 and 19, 136 (1986).
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Sci. 20, 103 (1984).
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