Dielectric study of V2O5-1.6 H2O xerogel
in the broad frequency range (105-1010 Hz)
J. C. Badot (*), A. Fourrier-Lamer (**) and N. Baffier (*)
(*) Laboratoire de Chimie de la Matière Condensée, UA 302, ENSCP, 11, rue P. et M. Curie, 75231 Paris Cedex 05,
France.
(**) Laboratoire de Dispositifs Infrarouge, UA 836, T12 E2 Université P. et M. Curie, 4 Place Jussieu, 75230 Paris Cedex 05, France.
(Reçu le 19 mars 1985, accepté le 23 juillet 1985)
Résumé. 2014 Les premiers résultats expérimentaux concernant les propriétés diélectriques dans une large bande de fréquences (105-1010 Hz) du xérogel d’oxyde de vanadium (V2O5-1,6 H2O) sont présentés entre 198 K et 296 K.
Les spectres diélectriques montrent quatre types de comportements : a) un effet de basse fréquence dû à la diffusion des porteurs de charges (protons H+); b) deux relaxations diélectriques dues aux deux sortes d’eau : une eau forte-
ment liée et une eau faiblement liée au feuillet de V2O5 ; c) une relaxation diélectrique qui serait due à une rotation
rapide des ions H3O+. Une compréhension de ces mécanismes en fonction des résultats expérimentaux est proposée.
Abstract 2014 The first experimental results concerning the dielectric properties of V2O5-1.6 H2O xerogel in a broad frequency range (105-1010 Hz) are presented between the temperatures 198 K and 296 K. The dielectric spectra exhibit four behaviour types : a) a low frequency effect due to the diffusion of charge carriers H+ protons ; b) two dielectric relaxations due to the two kinds of water : water strongly-bonded and water weakly-bonded to the V2O5 ribbon; c) a dielectric relaxation which would be due to a fast rotation of the H3O+ ions. One explanation
of these mechanisms with respect to the experimental results is proposed.
Classification Physics Abstracts
77.40
1. Introduction.
A gel is a two-phases system which is constituted of solvent molecules confined in a solid particle network.
The material behaviour does not only depend on the
solvent and solid properties but also on the solid- liquid interface. Thus it is not possible to artificially distinguish between the solvent and the solid network components. Strong correlations exist as a result of the presence of the solid liquid interface, hence the importance of the study of this interface.
Transition metal oxide gels (V205, W03, Mo03) [1], made by polycondensation of vanadic, tungsdic
or molybdic acids, are mixed valence components in which the same metallic element can show several oxidation states. The resulting properties of electron transfer can confer on the material semi-conducting (V205) and electrochromic (W03) properties [2, 3].
These materials are hydrogels, i.e. they contain the
water as solvent confined in the V205 or W03 solid particle network. The water contained in the oxides
can exist in different forms : OH or H20 groups
fixed on the oxide surface or, almost free water molecules confined into the interfoliar space.
The equilibrium of the system is made by electro-
static compensation of the repulsion forces between
negatively charged solid particles and the attractive forces between the solvent cations (here the protons
H + /H 3 0 + ) and the negative charges of the solid network. A hydrogen-bond also occurs between the solvent and the network. The proton diffusion which results from this is at the origin of the high proton
conductivity observed in these materials [4]. The
dielectric study appears to be a method well suited to the characterization of the dynamigs of charge
carriers and the rotational motion of the different kinds of water. Up to now, the experimental results concerning the dielectric properties of similar systems such as montmorillonite clays have given rise to many
publications relative to the small frequencies range
[5-7]. To our knowledge, these dielectric studies of
V2O5-gels in the broad frequency range are the first
obtained.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198500460120210700
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2. Structure and properties of the xerogel V205-
1.6 H20.
The vanadium oxide gels formed by polycondensation
of vanadic acid correspond to the formula V20.1
n H20. According to the value of n, we have a gel (n 300) or a colloidal solution (n > 300). By drying
at room temperature we obtain a xerogel with the composition V205-1.6 H20. Electron microscope
observations have shown that the xerogel is formed
of entangled fibres which are flat and ribbon-shaped
with dimensions 10 x 102 x 103 A3 [8].
X-rays diffraction studies show a layered structure resulting from the parallel arrangement of the elemen- tary fibres into the corrugated ribbons [8, 9]. The
basic distance is a function of the water content in the
gel, e.g. d = 11.6 A for the V20s-1.6 H20 xerogel
and d = 8.8 A for the V205-0.5 H20 xerogel formed
after a stronger drying. The difference, Ad = 2.8 A,
between these two values corresponds to the dimen-
sions of the water molecule. Different kinds of water were observed by differential thermal analysis (DTA) : weakly-bonded water and water strongly-bonded to
the ribbon. The electrical properties study shows two
different behaviours [4] : one is electronic and concerns
essentially the solid network, the other concerns
rather the solvent molecules. Ionic conductivity of xerogel is due to proton diffusion into the inter-
layered water between the oxide ribbons. Thus, the conductivity becomes remarkably high 7 ~ 3 x
10- 3 at room temperature, with an acti- vation energy of 0.35 eV. This depends upon the water content in the gel and on the water pressure above the sample [4].
3. Dielectric relaxation.
Under the action of an alternating electric field the electrical response of a system having dipolar inter-
actions may be characterized by the complex per-
mittivity, 8*(W) = 8’(W) - The real part 8’(W) represents the dielectric permittivity and the ima-
ginary part 8"(W) is known as the dielectric loss.
The conventional model used in the description
of the dielectric relaxation is the Debye model [10]
which gives the frequency dependent complex per- mittivity with :
where 800 and 88 are limit values of 8*(W) as W approa- ches + oo and 0 respectively. i is known as the (Debye)
relaxation time and fp = 1/2 ~~ denotes the loss
peak frequency. The relaxation time i is a measure
of the nominal time scale on which molecular reorien- tation can take place. In the Debye model, the dipoles
are assumed to be non-interacting with each other.
Consequently, the Cole-Cole plot (s" vs. e’) [11]
corresponding to (1) is a Debye « semi-circle » centred
on the axis at with a radius
However, when the experimental Cole-Cole plot
is a circular arc with its centre below the 8’ axis, one
can use a formal empirical expression designed to fit experimental data [ 11 ].
here a is an empirical parameter (0 a 1) which
measures the degree of departure from ideal Debye
behaviour. In this case, the dipoles interact with each other.
Generally, in the classical theory of diffusion the temperature dependence of the relaxation time r follows an Arrhenius law :
where W is the activation energy for the rotation of the molecules and the prefactor To is equal to the
inverse of the oscillation frequency of the dipole
in its potential well.
4. Experimental procedure.
The xerogel samples are compacted pellets with as
diameter 2 a = 3 mm and a thickness d = 1 mm.
The same cell was used for both low and high frequency measurements. This cell is a circular coaxial line whose inner conductor is interrupted by
the sample (Fig. la). It is loaded with the characte- ristic impedance Zo (r = 0 and Zo = 50 0). This
means that the sample is connected in series with the load The equivalent network is shown on figure 1 b.
The study of the real and imaginary parts of the complex dielectric permittivity was performed in the
broad frequency range from 100 kHz to 12 GHz,
with different automatic devices :
- between 100 KHz and 1 MHz : LF impedance analyser model HP4192A
- between 1 MHz and 1 GHz = RF impedance analyser model HP4191A
- between 1 GHz and 12 GHz = network ana-
lysers model HP8746.
4.1 SAMPLE ELECTROMAGNETIC FIELD DISTRIBUTION. -
The sample and the inner conductor axis are identical.
The excitation and the sizes of the sample (d ~,/2)
involve a radial propagation and therefore only the z-component Ez of the electric field and the 0-compo-
nent 7~ of the magnetic field exist in the sample (Fig lc).
For this type of propagation, we define the impe-
dance Z(yr) of the sample at r = a, Z( ya), where y is the radial propagation constant.
Fig. 1. - (a) sample loaded with the characteristic impedance; (b) equivalent network corresponding to (a); (c) sample electromagnetic field distribution; (d) sample loaded with the short-circuit; (e) equivalent network corresponding to (d).
The electromagnetic field distribution and the
boundary conditions are the same as if the sample
was placed in a gap between the inner conductor and a short-circuit plane (H. Kolodziej [12, 13];
Fig. Id and 1 e). Consequently, we have used Kolod-
ziej’s results which give Z(ya). But, we have preferred
to use our own cell (sample between inner conductor and characteristic impedance) because the presence of a short-circuit produces spurious resonances at
higher frequencies, which increase experimental errors
in Z(ya).
4.2 MEASUREMENTS OF THE SAMPLE IMPEDANCE
Z(ya). - Letp the phase reference plane in our system and Zp the impedance measured in this plane (Fig. l a).
In this figure p’ is a plane tangential to the cylindrical sample where Z(ya) is the sample impedance defined
in the radial propagation.
0 is the electrical angle between the p and p’ planes
and is determined in the following way :
(i) we replace the characteristic impedance by a
short circuit and the xerogel sample by a metallic sample with the same dimensions.
(ii) we measure the phase shift between the p’
plane tangential to the metallic sample and the p
plane because d 03BB/2, (note : if d > /!/2 we measure
the phase shift between p" and p where p" is the
short circuit plane (Fig. 1 d).
Thus, when we know Zp’ we can calculate :
(i) Zp from to the relation
(ii) Z(ya) from to the relation Z(ya) = Zp - Zo,
because the sample in the gap is connected in series with Zo.
In this work, we have assumed the shunt gap capa- citances C’ between the inner and outer conductors to be negligible because of the high xerogel permitti- vity : cC figure 1 b where Z(ya) = (G +
4.3 CALCULATION OF S’ e". - According to Kolod- ziej :
where
9* = 8’ - i8", is the relative permittivity of the sample.
Jo, J1 are respectively zero order and first order Bessel functions.
(G + is the admittance of the sample where G
and C are respectively the conductance Ind the capa- citance of the sample : E’ and 8" are deduced from
equation (4).
Formula (4) is used in the frequency range 1 GHz- 12 GHz. For frequencies below 1 GHz, where 1, the equation becomes :
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with and ya/2 ; so = (36 x x 109) -1 F/m.
The values determined for BaTi409 and a A’203,
whose permittivities are known [14], are in good agreement with our calculations. We have obtained s’ = 9.6 for a Al203 and s’ = 36 for BaTi409.
In conclusion, our method presents the following advantage. It allows the use of the same cell and thus the same formalism (4) for both low and high fre-
quency measurements.
5. Experimental results.
The experiments are done in the broad frequency
range at various temperatures (T = 296 K, 258 K, 230 K, 213 K, 198 K). The relative experimental
errors in s’ and 8" are approximatively 2 % for lower frequencies and 5 % for higher frequencies. The Cole-
Cole plot (s" vs. s’) shows a strong dispersion for 8’
and s" (Fig. 2). The decomposition of these plots
shows two kinds of behaviour. One is represented by
a straight line (domain I) and the other by semi-
circles or circular arcs (domains II, III and IV). These
behaviours are also shown in log-log representation (log s" vs. log f) (Fig. 3).
To understand the decomposition procedure of the
Cole-Cole plot, one example is given for T = 296 K
on figure 4.
(i) The low frequency part of the Cole-Cole plot
is a straight line (C, curve on domain I) with a slope :
p = cotg (n03C0/2) ; E1 2 is the dielectric permittivity value
where C1 intersects the 8’ axis: 81 = 70. This straight
line C, denotes a behaviour of type 81(W) = 81 + where n = 0.3 [15].
(ii) We subtract the values from the mea-
sured values 8(W) (C curve) and we obtain the C’
curve which represents relaxation behaviour. The
C~ curve can be decomposed into two relaxation
domains : domain II (C2 curve) and domain III
(C3 curve), which correspond to both circular arcs
C2 and C3 where a parameters values are given on figure 5 and table I. The same procedure is used to
obtain domain IV for T = 198 K, 213 K, 230 K.
5 .1 DOMAIN I. - This domain is situated in the low
frequency range and is represented by a straight line
with a slope of 2 which characterizes effects due to the electrical conduction [ 15] (cf. Figs. 2a and 4).
5.2 DOMAIN II, III, IV. - The domains II (« middle- frequency » range), III (o high-frequency » range),
IV (o very-high-frequency » range) are represented by a loss peak or circular arcs characterizing dielectric
relaxations (Figs. 2 and 3). Our experimental results
as well as those of ice and liquid water are printed on
table I. We remark that the relaxation times i of the domains II and III, located between those of ice and
liquid water, are closer to the relaxation time corres-
ponding to liquid water. The temperature dependence
of the relaxation time i follows an Arrhenius law
(cf. expression (3)). We have calculated the prefactors
To and the activation energies W for each domain
(cf. Table I). We have used the notation ~2, W2 for
domain II, i3, W3 for domain III and i4, W4 for
domain IV. Domain IV, which could be observed
partially at 230 K, 213 K and almost wholly at 198 K, corresponds to a Debye behaviour. At 213 K and 198 K, the experiments were made between 500 MHz
and 12 GHz for the study of domain IV. By decompo-
sition of the Cole-Cole plot we have obtained a small part of domain III which is represented by circular
arcs (cf. Table I and Figs. 2b and 3b with extrapolated
values of i, As and a). By extrapolation, at T = 296 K,
we obtained with activation energy
W4 ~ 0.14 eV for domain IV. For domain III, the activation energy is 0.21 eV in the temperature range 198 K-296 K. The temperature dependence of T
is shown in figure 5.
The relaxations of domains II and III are described by the equation (2); the corresponding a are shown figure 5 and table I.
With regard to the variations in dielectric permitti- vity (As = 8s - 8~J for each domain (see Table I),
we can see a decrease in å8 in relation to liquid water
values. In each domain As is decreasing with respect d
to temperature : d (å8) 0.
The 800 values (cf. Table I) determined for domain IV
(at T = 230 K, 213 K, 198 K) seem to be quite large (10 to 11.5); this could perhaps suggest the presence of other absorption bands at higher frequencies and/or
relevant contributions in the far-infrared region.
6. Discussion.
6.1 DOMAINS II AND III. - Generally when the
interaction of the water molecules (dipoles) with
their environment becomes stronger, their rotational motion is slower and the relaxation time T is larger.
It seems thus reasonable to assign the relaxation of the strongly-bonded water (hereafter called X-water)
to domain II and the relaxation of the weakly-bonded
water (hereafter called Y-water) to domain III.
It is generally assumed that the activation energy for the dielectric relaxation of the water molecule is connected to the breaking and reforming energy of the hydrogen-bonds (H-bonds) [16, 17]. This energy is stronger in the case of the X-water ( W2 N 0.27 eV),
than in the case of the Y-water ( W3 N 0.21 eV) in the
temperature range 198 K-296 K.
The increase in the relaxation times of X- and Y-waters, in comparison with the relaxation time of the free liquid water, can be explained by the « slowing
up » of the molecular motion due to the electrostatic field induced by the negatively charged ribbon and the counter ions (H + /H3 0 + ). Generally this very intense electrostatic field (10+5-10’ V/cm) [18] increases
when the molecule-ribbon distance diminishes. This electrostatic field whose direction is perpendicular to
Fig. 2. - Cole-Cole (s" vs. e") : (a) T = 296 K (8-. -) T = 258 K (A- -), T = 230 K (....); (b) T = 213 K (....), T =
198 K (1- -) (experimental errors on s’ and s" are not specified for clarity; the frequencies are indicated in MHz).
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Fig. 3. - Log-log representation (log E" vs. logf) : (a) T = 296 K (0- -) T = 258 K (A- -), T = 230 K (~ ... ); (b) T = 213 K (~ ... ), T = 198 K (8- - ) (experimental errors on s’ and s" are not specified for clarity).
Fig. 4. - Decomposition procedure of the Cole-Cole plot at T = 296 K (the frequencies are indicated in MHz).
Fig. 5. - Temperature dependence of relaxation frequency fp and empirical parameter a : III(e); IV(A).
the plane of the ribbon is thus opposed to the motion
of the water molecule as a result of this strong coupling
with the electric dipole of the molecule. So, it seems that the existence of two kinds of water is due to this local electric field effect :
- the X-water in the vicinity of the ribbon whose motion is « very frozen »
- the Y-water further from the ribbon, whose
motion is only a « little frozen ».
We note that the Y-water motion is probably per- turbed by the diffusion of the protons.
The diminution of As for the domains II and III in. relation to liquid water values is also a consequence of the dielectric saturation [19] due to the local elec-
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Table L- Different parameters obtained in V205-1.6 H20.
(*) Extrapolated values.
trostatic field in the interlayered water. The same phenomenon exists in the case of adsorbed water at solid surfaces [19].
The values of a parameter for X- and Y-waters in xerogel are close to 0.2-0.3 (cf. Fig. 5 and Table I),
in contrast to the situation in free liquid water and ice, where a is near zero (0.01-0.02). Large values of a
are also observed for adsorbed water on clays [5 to 7].
The values obtained in xerogels indicate that X and Y types of water molecules experience a broad variety
of molecular environments compared to free liquid
water and ice : ribbon-water interactions, presence of
charge carriers ... Usually the a para- meter is connected to continuous distributions of relaxation times (DRT) around the value 1 (cf (2))
calculated by approximate methods from macro-
scopic [11, 20, 22] or microscopic models [21].
Some authors [15, 23, 24] have criticized the DRT
approach and propose that the non-Debye behaviour
could arise from correlated states (Ngai’s Infrared Divergence Model [23, 24]). These excitations can
take place only through the action of sudden changes
of the potential resulting from jumping between
orientations of dipoles during a time related to
experimental value i (i.e., T2 and i3). Ngai’s theory [23, 24] is only valid for frequencies below 1010 Hz.
With respect to the physical sense of a, DRT or the
nature of correlated states, the correspondence bet-
ween these quantities and the different interactions,
which can occur in the water of V205-1.6 H20 xerogel, is not clearly established. In this way, other
spectroscopic techniques (QNS, RMN...) would be perhaps of great interest in this subject.
When the temperature is lower than 273 K, the relaxation times of water in the gel are smaller than those of ice and the evolution of As is not discontinued:
the interlayered water is a supercooled one. The
existence of this supercooled water was shown by
neutrons diffraction experiments in V205 xerogel [25].
This result was also observed for clays, biological systems and microcapillaries [5, 16].
6.2 DOMAIN IV. - This very high-frequency domain
is characterized by a near Debye dielectric relaxation
(a = 0). In the interlayered water, with the existence of the species H +, HO+, H20, we may consider three types of motion :
- rotation of the water molecules (domains II, III)
- rotation of the dipolar ions H30 +
- proton jumps.
The H30 + ion is pyramidal [26] with a HOH angle varying from 103° to 118° with its anionic environment.
This geometric conformation confers to the H30+ ion
a dipolar character. Thus the dielectric relaxation
represented by domain IV would be due to a fast
rotational motion of the H3 0 + dipoles (!4 ~ 2 x 10-12 s at T = 296 K) with a low activation energy
W4 of 0.14 eV. This type of rotation has been already
studied by QNS in proton conductors [27] such as
HUP (HU02PO4, 4 H~O) : 1 = 4 x 10-12 s at
T = 303 K with low activation energy.
