J. Phys. Chem. C 2008, 112, 14549–14554
14549
Particle Size Effect on the Electronic Conductivity of Electroactive LixWO3 · H2O Powders: A Study from 103 to 1010 Hz J.-C. Badot,*,† L. Beluze,†,‡ and O. Dubrunfaut§ Laboratoire de Chimie de la Matie`re Condense´e de Paris, CNRS UMR 7574, ENSCP, ParisTech, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France, Laboratoire de Re´actiVite´ et de Chimie des Solides, CNRS UMR 6007, UniVersite´ Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France, and Laboratoire de Ge´nie Electrique de Paris, CNRS UMR 8507, SUPELEC, UniVersite´ Paris 06, UniVersite´ Paris-Sud, 11 rue Joliot Curie, Plateau de Moulon, 91192 Gif-sur-YVette Cedex, France ReceiVed: April 9, 2008; ReVised Manuscript ReceiVed: May 30, 2008
We report on the electrical transport properties and the permittivity of LixWO3 · H2O powders which may be used as infrared reflectivity modulators. Broad-band dielectric and resistivity spectra of LixWO3 · H2O powders were recorded in a frequency range of 103-1010 Hz at temperatures varying between 200 and 300 K. The role of the powder morphology has been investigated on two types of compounds, the first one being constituted by nanoparticles and the second by microparticles. Complex resistivity diagrams have enabled us to obtain thermal behaviors of both dc conductivity. The transport properties are shown be consistent with smallpolaron conduction models. Particle size effect is evidenced, arising from the surface layer conduction of the nanoparticles. Two dielectric relaxations are found, attributed to water molecule motions and small-polaron hopping in Li0.35WO3. A discussion is given concerning the different behaviors which have been observed. 1. Introduction The attention in studying the electrical properties of tungsten trioxide monohydrate WO3 · H2O was stimulated by its promise as regards use as a basic compound in infrared emissivity/ reflectivity flexible modulators driven by the electrochemical insertion of lithium ions.1-4 The injection of electrons comes with the insertion of these cations in the compound. Hence, the variation in electron population can induce the simultaneous changes in optical and electrical behaviors. WO3 · H2O is an electrochromic compound which commutes faster than WO3 owing to the presence of water molecules which facilitates more easily cation diffusion.5 A previous paper has shown that WO3 · H2O powder embedded in a plastic matrix could be used as the active component in the LiCoO2/Li electrolyte/WO3 · H2O system. With Li+ intercalation the optical behavior has been well described by a Drude-Lorentz model which is often correlated to the existence of free electrons and/or to a high electronic conductivity.3 The role of the WO3 · H2O powder morphology was investigated on two types of compounds obtained by two different elaboration methods,2-4,6,7 the first one being constituted by microparticles (Figure 1a) and the second by nanoparticles (Figure 1b). The study has evidenced a larger improvement in IR modulation properties with the increase of the particle size. Strong differences have been observed in the thermal behaviors of the electrical conductivities and of the permittivities.4 For temperature above 268 K, the conductivities due to the existence of oxygen vacancies (i.e., W5+) are thermally activated with activation energies of about 0.19 and 0.79 eV for micro- and nanoparticles, respectively. Stronger electron localization (small polaron) was thus evidenced on the nanoparticles giving rise to higher activation energy and limiting thus the interparticle electron transfer. Below * Corresponding author. E-mail:
[email protected]. † CNRS UMR 7574, ENSCP. ‡ CNRS UMR 6007, Universite ´ Jules Verne. § CNRS UMR 8507, SUPELEC.
Figure 1. SEM micrographs (refs 2 and 4) of WO3 · H2O powders containing (a) microparticles and (b) nanoparticles.
268 K, the conductivities of both compounds have the same activation energy (W ) 0.08 eV), which has been attributed to a charge transfer from an occupied to a neighboring unoccupied donor (oxygen vacancy). This type of charge transfer (impurity conduction) occurs in a two-step process: (i) the first one consists to extract the electron from the electrostatic field of the defect (oxygen vacancy) 4,8 with a probability proportional to exp(-W/ kT), whereas (ii) the second is a tunneling transfer to a neighboring site.4,8,9 WO3 · H2O exhibits a layered orthorhombic structure with Pnmb space group (Figure 2.) The lattice parameters are a ) 5.247 Å, b ) 10.712 Å, and c ) 5.137 Å. The structure consists of sheets of distorted octahedral units of tungsten atoms coordinated by five oxygen atoms and a water molecule. The sheets are linked by hydrogen bonding between the water molecules and the neighboring oxygen atoms of the adjacent layer. Lithium ions can thus easily intercalate between the tungsten trioxide sheets: LixWO3 · H2O compounds are thus obtained. Lithium ions are compensated by excess electrons,
10.1021/jp8030732 CCC: $40.75 2008 American Chemical Society Published on Web 08/20/2008
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Badot et al. based on a sol-gel route, which enables us to obtain plateletshaped particles (“microparticles”) with size of about 3000 × 5000 × 40 nm3 (Figure 1a). The second,7 which is based on a rapid precipitation of the compound, yields smaller parallelepiped-shaped particles (“nanoparticles”) with size of about 120 × 120 × 40 nm3 (Figure 1b). Particle sizes have been determined from scanning electron microscopy (SEM) micrographs2 obtained with a Philips FEG XL 30 microscope for microparticles powders and with a Hitachi S2500 microscope for nanoparticles powders. LixWO3 · H2O compounds were prepared by electrochemical lithium insertion of the different powders according to the following reaction:
WO3 · H2O + xLi++xe- f LixWO3 · H2O
Figure 2. Schematic representation of the WO3 · H2O orthorhombic unit cell (refs 2 and 4).
reducing W6+ into W5+ and contributing to the electronic conductivity of LixWO3 · H2O. In previous works,10,11 electrochemical data were correlated to structural data revealing successive intercalation phases noted R (until x ) 0.35), β (0.6 < x < 0.8), γ (1.3 < x < 1.6), and δ ( x > 2.67) as the lithium concentration increases. It has been found that potential cycling over the R phase does not lead to any major degradation of the structure, the structural change being small.10,11 The study of electrical transport properties presents some difficulties because LixWO3 · H2O is in the form of a powder. So, the conductivity measurements by usual dc techniques cannot provide any information on the electrical transport properties owing to the existence of microstructures and/or nanostructures. On the other hand, broad-band dielectric spectroscopy (BDS) techniques are powerful tools for the electrical characterization of powdered materials. The BDS probes the interaction of a material with a time-dependent electric field. The resulting response is due to charge density (or current) fluctuations which are described by relaxations up to millimeter wavelengths. The time scale (or relaxation time) of these fluctuations depends on the nature, the morphology, and the structure of the sample. The measured response is either expressed by the frequency-dependent complex permittivity ε, conductivity σ, or resistivity F. The above-mentioned fluctuations generally arise from the reorientation of the dipoles (vs water in hydrates) or from the charge local hopping (e.g., ions or polarons) at higher frequencies. Other possible mechanisms include the appearance of interfacial polarizations due to the existence of microstructures or nanostructures (e.g., polarization reversal due to the grain boundaries) at lower frequencies. In the present paper, we report the first detailed study concerning the broad-band dielectric (or resistivity) spectroscopy of LixWO3 · H2O microparticles (x ) 0.06 and 0.35) and nanoparticles (x ) 0.27) obtained by both the Furusawa6 and Freedman7 methods. The spectra were recorded within the temperature range of 200-300 K. The influence of the particle size and the lithium content will also be discussed in order to understand the electrical properties of LixWO3 · H2O. 2. Experimental Section 2.1. Synthesis and Structure. The WO3 · H2O powders were synthesized according to two methods as has been described in previous papers.2,4,6,7 The first one6 is a crystal-growth method
(1)
Swagelock-type cells were used to intercalate Li+ in WO3 · H2O at room temperature. The working electrode is a thin pellet which is only constituted of WO3 · H2O powder (20-30 mg). The counter electrode is a Li-metal disk. A separator made with glass fiber (Whatman) soaked with liquid electrolyte is between the two electrodes. The electrolyte was a 1 M solution of LiPF6 dissolved in a 50:50 volume mixture of ethylene carbonate and dimethyl carbonate (EC-DMC). The cell was assembled in a glovebox under a dry argon atmosphere. Li+ intercalation was driven by a low current (a few microamps) producing a decrease of the potential. After a time t corresponding to a fixed value of x, the current is stopped and a relaxation of potential occurs up to an equilibrium which is effective about 12 h. The composition tends to be homogenized owing to the lithium diffusion in the WO3 · H2O particles. After the intercalation reaction, powders were washed with DMC and dried under vacuum at room temperature. 2.2. Broad-Band Dielectric Spectroscopy. Complex resistivity and permittivity spectra were recorded over a broad frequency range of 103-1010 Hz, using simultaneously an impedance analyzer (Agilent 4294) and a network analyzer (HP 8510). The experimental device, fully described in previous papers,4,12,13 consists of a coaxial cell (APC7 standard) in which the cylindrically shaped sample (radius ) 1.5 mm and thickness ) 1 mm) with silver-plated front faces fills the gap between the inner conductor and a short circuit. After a relevant calibration of the analyzers, the complex (relative) permittivity ε(ω) ) ε′(ω) - iε′′(ω) of the sample is computed from its admittance Ys according to the expression4,12,13
YS ) i
2πksrs J1(ksrs) ωµ0ds J0(ksrs)
(2)
where i ) (-1)1/2, µ0 is the free space permeability, k0 ) ω/c (c ) 3 × 108 m · s-1), and ks ) k0(ε(ω))1/2. ds and rs are the thickness and the radius of the sample, respectively. J0 and J1 are zero- and first-order Bessel functions of the first kind, respectively. For frequency below 108 Hz, where generally |ksrs|, 1, the electric field is quasi-uniform in the sample and expression 2 is simplified to that of the “parallel-plate capacitor” (quasi-static approximation):
YS ) iωε0ε(ω)
πrs2 ds
(3)
Complete dielectric spectra were made from about 400 measurements with an accuracy of approximately 3-5% in the experimental frequency range. The knowledge of the complex permittivity enables the calculation of the complex resistivity F ) F′ - iF′′ ) (iωε0ε)-1 (ε0 being the vacuum permittivity). The samples are compacted powders at 1 GPa, and the
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Figure 3. Dielectric spectra of Li0.35WO3 · H2O microparticles (m) and Li0.27WO3 · H2O nanoparticles (n): (a) real part ε′ and (b) imaginary part ε′′ of the permittivity vs frequency ν (ν ) ω/2π) at T ) 285 K.
measurements were made in the temperature range of 200-300 K under dry N2 flux. 3. Results and Discussion The frequency dependence of the real and imaginary parts ε′ and ε′′ of the permittivity ε of microparticles (x ) 0.35) and nanoparticles (x ) 0.27) is shown in Figure 3 at 300 K. All dielectric spectra have similar shapes whatever the temperature of the samples. The real part of the permittivity ε′ versus frequency decreases by about 3 orders of magnitude from 103 to 1010 Hz (Figure 3a). At frequencies around 103 Hz, the values of ε′ are between 103 and 105, which indicate a strong capacitive effect due to interfacial polarization (e.g., interface silver electrodes/sample, grain boundaries). On the other hand, dielectric losses ε′′ versus frequency (Figure 3b) vary by about 5-6 orders of magnitude from 103 to 1010 Hz. As the relaxations are not clearly shown in dielectric spectra, the use of Nyquist plots for complex parameters (F′′ vs F′ and ε′′ vs ε′) is helpful.12-14 The complex resistivity plots are useful to determine the grain bulk dc conductivity in powdered compounds (compacted or sintered). 3.1. Microparticles. Figure 4a shows the entire complex resistivity diagram, F′′ versus F′ of Li0.35WO3 · H2O at 285 K. To provide evidence for the different electrical relaxations we used a decomposition procedure of the Nyquist plots, which has been described elsewhere.11-13 This procedure is obtained by successive subtractions of the different contributions from low to high frequencies. As an illustration of the decomposition process, the first dispersion domain R1 is well fitted by a circular arc in the low-frequency part of the plot (Figure 3a). R1 corresponds to resistivity relaxation described by the complex function
F ) FH +
FL - FH R
1 + (iωτF)
(4)
where FL and FH are, respectively, the low- and high-frequency limits of the resistivity, R is a fitting parameter, and τF is a
Figure 4. Nyquist plot of the imaginary part F′′(ω) vs the real part F′(ω) of the complex resistivity at 285 K for Li0.35WO3 · H2O micrometric powder: (a) entire plot from 103 to 1010 Hz (evidence of the first relaxation domain R1); (b) graph obtained upon subtracting the contribution of the relaxation domain R1 (evidence of the second relaxation domain R2).
(resistivity) relaxation time. The relaxation domain R2, which is represented by a circular arc and described by an expression similar to eq 4, is plotted after subtracting the contribution R1. Domain R1 is due to contact resistances and capacitances between the sample and the silver electrodes. The second contribution R2 (Figure 4b) is thus due to contact resistances and capacitances between the grains (crystallites). The grain dc conductivity σg ) (Fg)-1 is determined from the intersection of the high-frequency part of the domain R2 with the real F′axis (Figure 4b). Moreover, an additional phenomenon appears for frequencies above 1 GHz. The latter is due to bulk (grain) contribution such as small-polaron motion and water molecule reorientation (see below). Similar resistivity diagrams were obtained whatever the temperature and the lithium content x. Figure 5 shows the resulting temperature dependence of σg for both compounds Li0.06WO3 · H2O and Li0.35WO3 · H2O. Two conductivity regimes are evidenced with transition temperatures Tt ) 258 and 248 K for x ) 0.06 and 0.35, respectively. Starting from the lowest temperature, σg drops steeply with increasing temperature. Above Tt, σg increases with increasing temperature. The same type of temperature dependence was also observed for YBa2Cu3O7-d9 and LaTiO3.41.15 Such behavior is due to the existence of small polarons in these compounds as explained in different theoretical models. Among them, the small-polaron model of Holstein shows that the transition temperature Tt marks the transition between polaron band and hopping regimes.16-19 The dc conductivity of Holstein small polarons is the sum of the two terms, one for hopping σh and another for tunneling σt:
σ ) σh + σt
(5)
In the high-temperature region (T > Tt), the hopping conductivity σh dominates according to the expression
σh )
nx(1 - x)(ea)2 2πνh kT
(6)
where νh ) ν0 exp(-Wh/kT) and Wh ) γ(pωph)/2. Here νh is the hopping frequency, ν0 is the attempt frequency, Wh is the hopping activation energy, ωph is the phonon frequency (in s-1),
14552 J. Phys. Chem. C, Vol. 112, No. 37, 2008
Badot et al. (Figure 6a.) In the low-frequency part of the plot, the first relaxation domain P1 is well fitted by a circular arc. The second relaxation domain P2, which is plotted after subtracting the contribution P1 (Figure 6b), is represented by a circular arc. The permittivity εG of a microparticle can be thus described by a sum of two Cole-Cole (CC) functions
εG(ω) ) ε∞ +
Figure 5. (a) Direct current conductivity σg as a function of inverse temperature T-1 (log σT vs T-1) for LixWO3 · H2O microparticles; (b) plot of σs/(x(1 - x)) vs the reduced temperature T/Tt. Tt is the transition temperature between band and hopping regimes. x ) 0.06 (b) and x ) 0.35 (9). Dotted lines corresponds to fits of eqs 6 and 7.
γ is the electron-phonon coupling constant, n ) 1.33 × 1028 m-3 is the tungsten content, x is the lithium content, a ≈ 3 Å is the hopping distance. Moreover, a bandlike (tunneling) conduction dominates in the low-temperature region (T < Tt). The resulting expression for σt reads9,16,18
σt )
[ ( )] (
pωph 2nx(1 - x)(ea)2 pωph γ csch p kT π 2kT
1/2
×
( ))
exp -2γcsch
pωph 2kT
(7)
where csch(x) ) 1/sinh(x). The experimental results in Figure 5 are well fitted by expressions 5-7. Table 1 contains fitting parameters for the samples. The phonon energies (frequencies) are close to that of the basic compound WO3 · H2O. It is important to note that the transition temperatures, Tt ) 0.42pωph/ kT, reported in Table 1, are in the range of (0.25-0.50)pωph as previously shown in Holstein theory.16 The reported values of γ are compatible with strong electron-phonon couplings. Since the attempt frequencies ν0 are close to the phonon frequencies, the high-temperature conductivity is due to an adiabatic smallpolaron hopping between neighboring tungsten sites. In conclusion, the temperature dependence of the conductivity can be analyzed in terms of delocalized (low-temperature regime) and localized (high-temperature regime) charge carriers. Otherwise, if the resistivity due to interfacial and grain boundary polarizations (domains R1 and R2) is subtracted from the sample resistivity F(ω), the grain bulk resistivity is
FG(ω) ) F(ω) -
F1 - F2 R1
1 + (iωτ1)
-
F2 - Fg R2
1 + (iωτ2)
(8)
where τ1 and τ2 are the relaxation times of the domains R1 and R2, respectively. The bulk complex permittivity εG ) (iωε0FG)-1 of the particle is obtained as a frequency-dependent function. The dielectric spectrum of Li0.35WO3 · H2O microparticles is drawn on a Cole-Cole plot, i.e., εG′′ versus εG′, after subtraction of the contribution σg/ε0ω of the microparticles dc conductivity
ε2 - ε∞ 1 + (iωτε2)
β2
+
ε1 - ε2 1 + (iωτε1)β1
(9)
where τε1 and τε2 are the relaxation times of the two relaxation domains P1 and P2, respectively. ε∞ is the high-frequency limit of the permittivity; β1 and β2 are fitting parameters of P1 and P2 that are here, respectively, equal to 0.67 and 0.81 whatever the temperature. The permittivity ε∞ is approximately 15 (whatever the temperature), which is similar to that of WO3 · H2O,4 and corresponds to the lattice (vibrations) and electronic contributions of the polarizability. The relaxation domain P1 is due to cooperative “windscreen wiper” motions of the water molecules as previously shown in the case of WO3 · H2O.4 The relaxation frequency of water molecules, i.e., νε1 ) (2πτε1)-1 ) 1.5 × 108 Hz at 300 K, has the same value as that in WO3 · H2O.4 Our attention will be focused on the relaxation P2, whose frequency is νε2 ) (2πτε2)-1 ) 2.2 × 109 Hz at 300 K (Figure 6b). The relaxation P2 corresponds to a fast motion of charges in the crystal lattice. From expression 6, the small-polaron hopping frequency νh is calculated and equal to 2.7 × 109 Hz at room temperature. Since νh ≈ νε2, we can attribute the relaxation P2 to small-polaron hopping between neighbor tungsten sites. This result shows that the dc conductivity is well correlated to the experimental parameters obtained from dielectric spectra. 3.2. Nanoparticles and Size Effect. Figure 7a shows the whole complex resistivity plot (F′′ vs F′ at 287 K) of the sample, which is composed of Li0.27WO3 · H2O nanoparticles. This plot is well fitted in the whole frequency range by the HavriliakNegami (HN) function20-23 of the complex resistivity
F)
Fs (1 + (iωτF)R)β
(10)
where Fs is the low-frequency limit (ω f 0) of the resistivity. τF is the average relaxation time which is related to the inverse of the relaxation frequency νF ) (2πτF)-1. R and γ are fitting parameters in the range of 0-1. The relaxation parameters are νF ≈ 2 × 107 Hz at 287 K and R ≈ 0.83, β ≈ 0.48 whatever the temperature. As the high-frequency part of this plot crosses the origin, it seems thus like that of a bulk contribution over the experimental frequency range. We obtain the bulk dc resistivity Fs (or dc conductivity σs ) Fs-1) of the sample from the intersection of the low-frequency part of the plot with the real F′-axis. We note that the contribution of the interfacial polarization (interface sample/silver) is negligible in complex resistivity representation. For frequencies above 5 × 108 Hz, the corresponding complex conductivity plot (Figure 7b) shows that the frequency dependence of the conductivity obeys a power law24,25
σ(ω) ) C(iω)s
(11)
where C is the prefactor and s ) 0.4 whatever the temperature. Since ωτF . 1, expression 11 is also deduced from expression 10 with s ) Rβ and C ) (τFRβ/Fs). The electrical behavior of Li0.27WO3 · H2O nanoparticles is thus similar to that of disordered materials. Figure 8 shows the resulting temperature dependence of the dc conductivity σs. Two conductivity regimes are also evidenced with a transition temperature Tt ≈ 253 K and are
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TABLE 1: Room-Temperature dc Conductivity (σ), Transition Temperature (Tt), High- and Low-Temperature Activation Energies Wh and W, Electron-Phonon Coupling Constant (γ), Phonon Energy (pωph), and Attempt Frequency (ν0) of LixWO3 · H2O Microparticles for Three Different Lithium Contents (x) x
σ (S · cm-1) at 300 K
Tt (K)
Wh (eV) for T > Tt
W (eV) for T < Tt
γ
pωph (meV)
ν0 (Hz) hν0 (meV)
0.00a
1.0 × 9.0 × 10-2 3.6 × 10-1
268 258 248
0.20 0.22 0.22
0.09
5.2 7.3 7.8
77.0 60.0 52.0
1.78 × 1013 (74) 1.78 × 1013 (74)
0.06 0.35 a
10-3
Ref 4.
Figure 6. Cole-Cole plot of the imaginary εG′′(ω) vs the real part εG′(ω) of the complex permittivity εG(ω) at T ) 285 K for Li0.35WO3 · H2O. The contributions of the dc conductivity and the interfacial (grain boundary type) polarizations have been subtracted. (a) Evidence of the first relaxation domain P1; (b) graph obtained upon subtracting the relaxation domain P1 (evidence of the second relaxation domain P2).
Figure 7. Nyquist plots of (a) the complex resistivity (imaginary part F′′(ω) vs real part F′(ω)) and (b) the complex conductivity (imaginary part σ′′(ω) vs real part σ′(ω)) at 285 K for Li0.27WO3 · H2O nanoparticles.
ruled by two Arrhenius plots following the equation
σs )
A W exp T kT
( )
(12)
where A and W are the conductivity prefactor and activation energy, respectively. Room temperature dc conductivity, transition temperature Tt and activation energies are given in Table 2. Note that the transition temperatures Tt are similar for the two types of particles as shown by Tables 1 and 2. Unlike the microparticles, the conductivity behavior of the nanoparticles is thus strongly different when we compare the Figures 5a and 8. Above Tt, the conductivity of the Li0.27WO3 · H2O nanoparticles has activation energy much lower than those of the microparticles (Table 1). The conductivity of the Li0.27WO3 · H2O nanoparticles can be thus due to polaron hopping on their surface layer. This phenomenon originates from the smaller size of the particles, which facilitates the lithium ions’ segregation (with excess electrons) on their surface. We can consider that the conductivity of particles’ inner core is lower than that of their surface layer. The sample constituted by nanoparticles is thus similar to a disordered continuous medium. As σs is calculated from total thickness and area of the sample (see expression 3), its intrinsic value should be higher owing to a low volume fraction of the conductive phase (surface layer of nanoparticles) in the sample. For T < Tt, the transport of the polarons can be governed by impurity conduction, which corresponds to the transfer from an occupied to a neighboring unoccupied donor
Figure 8. Direct current conductivity σs as function of inverse temperature T-1 (log σT vs T-1) for Li0.27WO3 · H2O nanoparticles.
TABLE 2: Room-Temperature dc Conductivity (σ), Transition Temperature (Tt), High- and Low-Temperature Activation Energies Wh and W of LixWO3 · H2O Nanoparticles for Two Different Lithium Contents (x) x
σ (S · cm-1) at 300 K
Tt (K)
Wh (eV) at T > Tt
W (eV) at T < Tt
0.00a 0.27
6.0 × 10-4 5.0 × 10-2
268 253
0.80 0.08
0.09 0.03
a
Ref 4.
in the surface layer of the nanoparticles. This transport consists of two-step process: (a) the first one consists to extract the electron from the electrostatic field of the lithium ion8 with a probability proportional to exp(-W/kT); (b) the second is a tunneling transfer to a neighboring site.8,16-19 The number of polarons is thus temperature-dependent for the low-temperature regime. In conclusion, no theoretical model is relevant to understand and fit the surface conductivity of the nanoparticles.
14554 J. Phys. Chem. C, Vol. 112, No. 37, 2008 4. Conclusion In this paper is reported the first determination of the conductivity and the permittivity of LixWO3 · H2O compacted powders (micro- and nanoparticles) over a wide frequency range of 103-1010 Hz. Interpretation of the spectra was made possible through the knowledge of the micro- and nanostructure previously studied by SEM. Complex resistivity and permittivity diagrams have allowed the determination of the electrical transport properties of LixWO3 · H2O micro- and nanoparticles with the temperature from 200 to 300 K. For microparticles, resistivity relaxations are attributed to interfacial and grain boundary polarization phenomena in the samples. In this way, bulk dc conductivities of microparticles were obtained versus temperature by taking into account the interfacial phenomena. We have suggested a segregation of lithium ions on the surface layer of the nanoparticles. This hypothesis agrees with experimental evidence of a better reversibility of Li insertion-deinsertion for the nanoparticles after several electrochemical cycles.2 Consequently, insertion and deinsertion of lithium ions would be faster, since charge carrier diffusion on the surface layer of the nanoparticles requires lower energy than in the particle inner core. Acknowledgment. This work was supported by DGA and EADS Company. The authors are thankful to Professor J. M. Tarascon (LRCS, Amiens, France), Dr. B. Viana (LCMCP, Paris, France), and Professor A. Kreisler (LGEP, Gif-sur-Yvette, France) for their interest in the work. References and Notes (1) Bessie`re, A.; Marcel, C.; Marquette, M.; Tarascon, J. M.; Lucas, V.; Viana, B.; Baffier, N. J. Appl. Phys. 2002, 91, 1589.
Badot et al. (2) Bessie`re, A.; Beluze, L.; Morcrette, M.; Lucas, V.; Viana, B.; Badot, J. C. Chem. Mater. 2003, 13, 2577. (3) Bessie`re, A.; Beluze, L.; Morcrette, M.; Viana, B.; Frigerio, J. M.; Andraud, C.; Lucas, V. J. Appl. Phys. 2004, 95 (12), 7701. (4) Beluze, L.; Badot, J. C.; Weil, R.; Lucas, V. J. Phys. Chem. B 2006, 110, 7304. (5) Judeinstein, P.; Livage, J. Mater. Sci. Eng. 1989, B3, 129. (6) Furusawa, K.; Hachisu, S. Sci. Light 1966, 15 (2), 115. (7) Freedman, M. L. J. Am. Chem. Soc. 1959, 81, 3834. (8) Sanchez, C.; Henry, M.; Grenet, J. C.; Livage, J. J. Phys. C: Solid State Phys. 1982, 15, 7133. (9) Thorn, R. J. Physica C 1992, 190, 193. (10) Beluze, L. Ph.D. Thesis, Universite´ Pierre et Marie Curie (Paris 06), Paris, France, 2004. (11) Bessie`re, A.; Beluze, L.; Morcrette, M.; Lucas, V.; Baffier, N. Solid State Ionics 2003, 165, 23. (12) Ragot, F.; Badot, J. C.; Baffier, N.; Fourrier-Lamer, A. J. Mater. Chem. 1995, 5, 1155. (13) Badot, J. C.; Bianchi, V.; Baffier, N.; Belhadj-Tahar, N. E. J. Phys.: Condens. Matter 2002, 14, 6917. (14) Rotenberg, B.; Cade`ne, A.; Dufreˆche, J. F.; Durand-Vidal, S.; Badot, J. C.; Turq, P. J. Phys. Chem. B 2005, 109, 15548. (15) Kuntscher, C. A.; Van der Marel, D.; Dressel, M.; Lichtenberg, F.; Mannhart, J. Phys. ReV. B 2003, 67, 035105. (16) Holstein, T. Ann. Phys. (NY) 1959, 8, 343. (17) Bosman, A. J.; van Daal, A. J. AdV. Phys. 1970, 19, 1. (18) Bo¨ttger, H.; Bryksin, V.V. Hopping Conduction in Solids; VCH Publishers: Deerfield Beach, FL, 1985. (19) Alexandrov, A. S.; Mott, N. Polarons and Bipolarons; World Scientific: Singapore, 1998. (20) Zorn, R. J. Chem. Phys. 2002, 116 (8), 3204. (21) Bergman, R. J. Appl. Phys. 2000, 88 (2), 1356. (22) Alvarez, F.; Alegria, A.; Colmenero, J. Phys. ReV. B 1991, 44, 7306. (23) Alvarez, F.; Alegria, A.; Colmenero, J. Phys. ReV. B 1993, 47, 125. (24) Jonscher, A. K. Dielectric Relaxation in Solids; Chelsea Dielectrics: London, 1983. (25) Jonscher, A. K. IEEE Trans. Electr. Insul. 1992, 27 (3), 407.
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