Langmuir 2005, 21, 1389-1397
1389
Interlayer Water Molecules in Vanadium Pentoxide Hydrate. 8. Dynamic Properties by Quasi-Elastic Neutron Scattering Shigeharu Kittaka,*,† Shuichi Takahara,† Toshio Yamaguchi,‡ and Marie-Claire Bellissent Funel§ Department of Chemistry, Faculty of Science, Okayama University of Science, Ridaicho, Okayama 700-0005, Japan, Advanced Materials Institute and Department of Chemistry, Faculty of Science, Fukuoka University, Nanakuma, Jyonan-ku, Fukuoka 814-0180, Japan, and Laboratoire Le´ on Brillouin, CEA-CNRS Saclay, 91191 Gif-sur-Yvette Cedex, France Received July 20, 2004. In Final Form: November 15, 2004 The dynamics of water molecules in the layered vanadium pentoxide hydrate, V2O5‚nH2O, were studied by quasi-elastic neutron scattering (QENS) measurements. Heterogeneity of the dynamic properties was confirmed by R-relaxation model analysis. Translational diffusion of monolayer and double-layer water molecules is by site-to-site diffusion and is reduced relative to that of bulk water. Water molecules lose their mobility markedly and solidify with decreasing temperature. However, mobile water remains at 253 K. Rotational diffusion coefficients are unaffected by confinement and are very similar to the bulk values determined at temperatures in the range 253-298 K. The dynamic speed characterized by QENS is much faster than that expected from the data determined by deuterium NMR (DNMR) measurements at low temperatures.
Introduction Vanadium pentoxide hydrate is an orthorhombiclayered compound whose physicochemical properties are very similar to those of smectite-type clay minerals.1,2 As in montmorillonite, water layers are introduced stepwise up to three layers and continuously above it.3,4 Polar molecules such as alcohols, NH3, and acetonitrile are easily intercalated between the layers.3-6 Interlayer protons stemming from the hydroxyl groups of the layer sheets are exchangeable with cationic species such as metal ions, alkylamines, and complex species.6,7 One of the marked differences of the properties of V2O5‚nH2O from those of clay minerals is its chemical reactivity; for example, V5+ is readily reduced by metals having a lower oxidation and/ or organic materials, which gives rise to high electrical conductivity, and polaron hopping taking place under an electric field.8 Additional electrical conductivity of the sample also arises from protons liberated from interlayer water molecules.9 Thus, the underlying mechanism of conduction should be related to the dynamic motions of water molecules, that is, rotation and translation, which are confined between the layers: protons are transferred * Corresponding author. Phone: 81 86 256 9433. Fax: 81 86 256 9757. E-mail:
[email protected]. † Okayama University of Science. ‡ Fukuoka University. § CEA-CNRS Saclay. (1) Aldebert, P.; Baffier, N.; Gharbi, N.; Livage, J. Mater. Res. Bull. 1981, 16, 669. (2) Kittaka, S.; Uchida, N.; Miyahara, H.; Yokota, Y. Mater. Res. Bull. 1991, 26, 391. (3) Kittaka, S.; Ayatsuka, Y.; Uchida, N. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3825. (4) Kamiyama, T.; Itoh, T.; Suzuki, K. J. Non-Cryst. Solids 1988, 100, 466. (5) Kittaka, S.; Yamamoto, H.; Higuma, S.; Sasaki, T. J. Chem. Soc., Faraday Trans. 1992, 5, 715. (6) Kittaka, S.; Hamaguchi, H.; Umezu, T.; Endoh, T.; Takenaka, T. Langmuir 1997, 13, 1352. (7) Kittaka, S.; Uchida, N.; Katayama, M.; Doi, A.; Fukuhara, M. Colloid Polym. Sci. 1991, 269, 835. (8) Sanche, C.; Barbonneau, F.; Morrineau, R.; Livage, J. Philos. Mag. B 1983, 47, 279. (9) Kittaka, S.; Uchida, N. J. Phys. Chem. 1994, 98, 2129.
from one water molecule to another one or from a water molecule to a hydroxyl of the substrate layer surface and vice versa. Thus, some detailed analysis on the structures of interlayer water molecules as well as on dynamic properties is needed. Among various techniques for studying the dynamic properties of water at interfaces, dielectric relaxation,10 quasi-elastic neutron scattering (QENS),11 and deuterium NMR (DNMR)12 are complementary methods for covering a wide dynamic range.13 A QENS experiment on the water in V2O5‚nH2O was previously conducted by the present authors, but only for a monolayer water at 298 K.14 In previous DNMR measurements of V2O5‚nH2O (n ) 1.5 and 2.6), it was found that water molecules had two rotational motions, a C4 rotational motion and a C2 flip motion along the dipole of the water molecule, presenting some tilt angle from the former axis.12 The present study reports experiments on water at monolayer and double-layer water coverages over a temperature range from 298 down to 253 K. Lowtemperature Fourier transform infrared (FT-IR) measurements were also made to examine the vibration mode of the adsorbed water. Experimental Section Materials. Vanadium pentoxide hydrate, V2O5‚nH2O, sol was prepared by hydrating high-purity V2O5 (Aldrich, 99.99%) after ball-milling to give an amorphous state for 2 h using a Frisch P7 instrument.15 This method was derived after Mu¨ller-sol preparation.16 Hydration of V2O5 was completed to give a reddish sol after a few days. The sol was then aged for more than 1 month in the dark and was freeze-dried before use. The dried samples are flaky particles, and the crystal structure with c-planes is in parallel with layers. The crystal structure was confirmed by X-ray diffraction (XRD) and electron microscope studies. (10) Bergman, R.; Swenson, J. Nature 2000, 403, 283. (11) Bellissent Funel, M.-C.; Chen, S. H.; Zanotti, J. M. Phys. Rev. E 1995, 51, 4558. (12) Takeda, S.; Gotoh, Y.; Maruta, G.; Takahara, S.; Kittaka, S. Z. Naturforsch., A 2002, 57, 419. (13) Bellissent Funel, M.-C. Eur. Phys. J. E 2003, 12, 83. (14) Takahara, S.; Kittaka, S.; Kuroda, Y.; Fujii, H.; Yamaguchi, T.; Bellissent Funel, M.-C. Langmuir 2000, 16, 10559.
10.1021/la0401009 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/19/2005
1390
Langmuir, Vol. 21, No. 4, 2005
Kittaka et al.
QENS Measurements. QENS measurements were performed by the use of a MIBEMOL high-resolution time-of-flight spectrometer in Laboratoire Le´on Brillouin at Saclay in France. The neutron beams used are wavelengths of 6 Å (resolution 51 µeV, which is given by the half-width at half-maximum (hwhm) of the spectrum of a vanadium plate) and 9 Å (15 µeV). A sample was packed in a rectangular aluminum cell. The thickness of the samples was adjusted so that the transmission was around 90% to avoid multiple scattering. Three kinds of samples were prepared by exposing dry samples to water vapor that was regulated according to an adsorption isotherm:3 monolayer water (MLW, 1.5H2O/V2O5), double-layer water (DLW, 2.8H2O/V2O5), and dried sample (dried, 0.21H2O/V2O5) obtained by evacuation at 373 K for 6 h. The resolution functions of the spectrometer were determined by the use of a vanadium plate. All the measurements were performed in a transmission mode by tilting the sample cell by 135° with respect to the incident neutron beam. Measurements were conducted for 10 h at temperatures of 298, 283, 273, 263, and 253 K. FT-IR Measurements. A thick V2O5‚nH2O sol was spread over stainless steel mesh and dried in air. The specimen was mounted in a cryostat that permits measurements at temperatures down to 243 K under controlled humidity. FT-IR spectra were measured on a JEOL JIR-100 instrument at a resolution of 4 cm-1.
Theoretical The QENS experiment provides us with information on the dynamic motions covering the time range from 10-10 to 10-12 s, that is, vibrations, translations, and rotations. The scattering intensity, I, or the doubledifferential scattering cross section, is proportional to the dynamic structure factor, S(Q,ω).
σinc ks d2σ I) ) N S(Q,ω) dΩ d 4π ki
(1)
where N is the number of nuclei, σinc is the incoherent scattering cross section of a nucleus, B ki and B ks are the incident and scattered neutron wave vectors, respectively, ki| is the momentum transfer. Then, S(Q,ω) and Q ) |k Bs - B is expressed by eq 2.
-Q2〈u2〉 [Aδ(ω) + (1 - A)ST X SR] (2) S(Q,ω) ) exp 3 where the exponential factor is the Debye-Waller factor including the mean square amplitude of proton vibration, u. Aδ(ω) accounts for the contribution of immobile species, A is the elastic incoherent structure factor (EISF), and ST and SR are the dynamic scattering laws for translational and rotational motions of molecules, respectively. X signifies a convolution. Translational Diffusion. When the translational diffusion takes place in a single mode, ST can be
L ) x6DTτ0
(5)
It is known that the dynamic scattering law of the translational motion of supercooled water molecules, STS, is expressed by the Fourier transform of the intermediate scattering factor described by a stretched exponential function, as given by eq 6.
[ (τt) ]
Fs(Q,t) ) exp STS(Q,ω) )
β
(6)
∫0∞dt cos ωt exp[- (τt) ]
1 π
β
(7)
where τ is a correlation time and β a stretched exponent.17 When β is unity, eq 7 becomes eq 3. β stands for the heterogeneity of the translational motion of water in the system and thus should appear as a value lower than unity for molecules confined as in the present case. The average relaxation time, τav, is expressed by eq 8.
τav )
∫0∞dt exp[- (τt) ] ) βτ Γ(β1) β
(8)
where Γ(1/β) is the gamma function of 1/β. τav can be transformed into the average energy transfer by eq 9.
Γav )
1 τav
(9)
To simplify the treatment, rotational diffusion is expressed isotropically by eq 10
SR(Q,ω) ) j02 δ(ω) + 3j12(Qa) L(ω,ΓR1) + 5j22(Qa) L(ω,ΓR2) + ... (10) where ji is the ith Bessel function,18 a is the radius of rotation of the molecule, δ(ω) is the delta function of ω, and L(ω,ΓRi) is the Lorentzian function with energy transfer, ω, and hwhm, ΓRi, of the peak.
ΓR1 )
1 1 and ΓR2 ) 3τR τR
(11)
In the simplest case, in which the motion is assumed to be a single translational mode, that is, it is expressed by eq 3, and the first two terms are taken from the righthand side of eq 10 for rotational motion, eq 2 is transformed through eq 12 to give eq 13.
S(Q,ω) ) exp
(
)
S(Q,ω) ) exp
(
)
-Q2〈u2〉 (A δ(ω) + (1 - A) LT(ω,Q) X 3 2 [j0 (Qa) δ(ω,Q) + 3j12(Qa) LR(ω,Q)]) (12)
(3)
-Q2〈u2〉 [A δ(ω) + 3 B1L1(ω,ΓT) + B2L2(ω,ΓT + ΓR)] (13)
expressed by a Lorentzian function, where ΓT is the hwhm of the spectrum. When the translational motion of the H2O molecule is described by a jump-diffusion model, ΓT is related with a self-diffusion constant, DT, and a residence time, τT, as shown by eq 4.
where B1 and B2 are constants for the Lorentzian functions. By fitting the spectrum with eq 13, one can determine the values of ΓT and ΓR. When either translational or rotational motion is not detectable, the spectrum is fitted with a delta function and a single Lorentzian function. In such a case, one can define the mode of dynamic motion of the species by analyzing the relation EISF-Q.19
ST(Q,ω) ) L(ω,ΓT) )
ΓT
1 π ω2 + Γ
2
T
ΓT )
DTQ2 1 + DTQ2τ0
(4)
The mean jump-diffusion length, L, is expressed by eq 5.
(15) Kittaka, S.; Nishida, S.; Iwashita, T.; Ohtani, T. J. Solid State Chem. 2002, 164, 144. (16) Muiller, E. Z. Chem. Ind. Kolloide 1911, 8, 302. (17) Zanotti, J.-M.; Bellissent Funel, M.-C.; Chen, S.-H. Phys. Rev. E 1999, 59, 3084. (18) Sears, V. F. Can. J. Phys. 1966, 44, 1299; 1999, 45, 237.
Dynamics of Water of Layered Vanadium Oxide Hydrate
Figure 1. Raw QENS spectra of monolayer water (MLW) and double-layer water (DLW) adsorbed on V2O5‚nH2O, dried V2O5‚nH2O, and vanadium at Q ) 1.115 Å-1 and 298 K by using the 9 Å neutron beam. The peak heights of the spectra were adjusted to coincide with each other. One channel corresponds to 17.4 µs.
Langmuir, Vol. 21, No. 4, 2005 1391
Figure 2. QENS spectral intensities of DLW, MLW, and dried samples measured over a range of 0.4 Å-1 < Q 0.5 Å-2) by applying eq 4. On the other hand, ΓT values in the smaller Q2 regions converge to some nonzero value on the ordinate rather than to the origin. These facts suggest that the translational motion of the water molecules can be expressed by the jump-diffusion model and is forbidden across the layer planes.21 This experimental fact differs from that of Ca-type montmorillonite.22 Translational diffusion coefficients and residence times, and jump lengths thus evaluated, are given in Table 2. In the case of MLW, the observed plots are dispersed compared with those for the DLW (Figure 9b). The 6 Å neutron data were not used in this Q2 range due to the (21) Volino, F.; Dianoux, A. J. Mol. Phys. 1980, 41, 271. (22) Tuck, J. J.; Hall, P. L.; Hayes M. H. B. J. Chem. Soc., Faraday Trans. 1 1984, 80, 309.
Dynamics of Water of Layered Vanadium Oxide Hydrate
Langmuir, Vol. 21, No. 4, 2005 1395
Figure 11. Arrhenius plots of diffusion coefficients for DLW, MLW, and bulk water.
low resolution of the spectra. The fact that the ΓT value is detectable at a low temperature of 263 K indicates that there are water molecules migrating between the layers. The ΓT value starts from some definite value in the low Q2 range and increases gradually with Q2, in agreement with a jump-diffusion model of water molecules in a confined geometry.21 Figure 11 shows an Arrhenius plot of the diffusion coefficients. It is clear that the diffusion coefficient at 298 K is strongly dependent on the confinement and smaller than that of bulk water. It is reasonable to attribute these relatively large values of the diffusion coefficient compared to that (5.0 × 10-10 m2 s-1 at 298 K) estimated by the R-relaxation model to the fact that the analysis using a Lorentzian function is limited to the faster translational motions at the resolution of the spectrometer. That is, slower motions were not detectable and could only contribute to the δ-function. Interesting is the fact that the jump length is almost constant at varying temperatures (∼2.4 Å), which is very similar to the value (2.5 Å) reported in the previous work.14 This distance corresponds to the repetition length of the similar sites arranged in a zigzag mode to the b-direction between the layers.2 Rotational Motions. According to eq 13, spectra observed with the 6 Å neutron beam (Figure 10) can be analyzed with one delta function and two Lorentzian functions. From these Lorentzian functions, one can calculate ΓR from the third term of the right-hand side of eq 13. Figure 12 shows the ΓR values as a function of momentum transfer, Q. The plotted ΓR values for all the systems are all constant against Q values. This constancy indicates that the dynamic motion producing this relation is due to the rotational motion of the water molecules.11 On the basis of these values, the relaxation times, τR, for the rotational motion of water molecules were calculated according to eq 11 and are given in Table 3 and shown as rotational rate in Figure 13. It is concluded that the rotational motion of water molecules confined in V2O5‚ nH2O is very similar to that in bulk water at the temperatures investigated. Discussion Translational Motion of Interlayer Water Molecules in V2O5‚nH2O. Parts a and b of Figure 14 respectively show the elastic incoherent structure factor (EISF, the ratio of the elastic component to the total scattering intensity) values for DLW and MLW that have been determined from the 9 Å neutron beam experiments,
Figure 12. ΓR (half-width at half-maximum)-Q relations of interlayer water extracted from QENS spectra determined with the 6 Å wavelength neutron beam at various temperatures: (a) DLW; (b) MLW. Table 3. Relaxation Times, τR, of the Rotational Motion of Monolayer Water (MLW), Double-Layer Water (DLW), and Bulk Water MLW DLW
bulk
T/K
τR/ps
298 283 273 298 283 273 263 298 278 268 258
1.53 1.27 1.45 1.42 1.37 1.42 2.04 1.10 1.37 1.56 1.91
in which the Bragg component at lower Q ranges was subtracted. The plots for DLW show that EISF values at 298 K decrease with an increase in the Q value and finally approach zero. The final values for the data measured at lower temperatures approach the upper values. This indicates that mobile water molecules observed with the 9 Å neutron beam, which probes the decrease in translational motion, are reduced when the temperature is decreased down to 253 K. As can reasonably be anticipated, more significant is the case of MLW in Figure 14b. The increase of EISF in the lower Q range for either case suggests the existence of a confined diffusion of water between the layers. This is substantiated by the fact that the ΓT converges to a definite value in the decreasing Q range (Figure 9). Table 2 shows that the temperature dependence of the diffusion coefficient is smaller than that of bulk water,20 which apparently suggests that the activation energy for translational motion of water between the layers is small. In the case of bulk water, the diffusion coefficient decreased
1396
Langmuir, Vol. 21, No. 4, 2005
Figure 13. Rotational rates, 1/τR, of MLW and DLW determined by QENS: (O) DLW; (b) MLW; (() bulk water.
Figure 14. Elastic incoherent scattering factor (EISF)-Q relations of interlayer water molecules determined at various temperatures by the 9 Å neutron beam: (a) DLW; (b) MLW.
significantly with temperature, implying a larger activation energy of translational diffusion. As discussed above, however, the observed translational diffusion is limited only for more mobile water molecules in V2O5‚nH2O. Thus, one should consider that faster water molecules remain at lower temperatures of 253 K, although its proportion decreases. Rotational Motion of Water Molecules between the Layers. In a previous work,12 two modes of the rotational motion of water molecules were proposed to explain the NMR spectra observed at temperatures lower than those of the present QENS experiments. They are the following: (1) a flip rotation around the C2 axis of water, which coincides with the direction of the dipole moment of water and (2) the precession rotation of the flip rotation axis of water around the C4 axis, in which the former is tilted by some angle.12 In Figure 15, the rotational
Kittaka et al.
Figure 15. Rotational rates, 1/τR, of water at various temperatures, determined by QENS, dielectrics, and NMR. Above 230 K: V2O5‚nH2O (Ο) DLW; (b) MLW (present data); (]) bulk water;20 (*) vermiculite Li‚1H2O;21 (×) Li‚2H2O;22 (0) vermiculite Na‚1H2O24; (9) 2H2O. Below 230 K: DLW (O) C2, (b) C4; MLW (4) C2, (2) C4; (]) bulk water (ice);10 (0) vermiculite Na‚2H2O;10 (*) H2O in the polymer.25
rates determined by NMR, which are determined from the inverse of the rotational relaxation time, are plotted in an Arrhenius representation, in which data from neutron experiments are also added, from Figure 13. The difference between monolayer and double-layer water is not significant. The flip rotation is faster than the rotation around the C4 axis, and they approach each other as the temperature is increased. However, dynamic properties at temperatures higher than this temperature cannot be analyzed by NMR because the dynamic motion of water is too fast to be observed. The rotational motion for this temperature range can be characterized by QENS measurements. In the case of QENS measurements, however, it is not possible to distinguish between the above two rotation modes due to the lack of resolution; that is, the observed information derives from the overall rotation. The dynamic speed determined by QENS is much larger than that extrapolated from DNMR data, which have been determined below 230 K. This discontinuous change can be seen in the display of the dynamics of water molecules in various systems, as shown in Figure 15,21,23-25 where rotation speeds were observed by either NMR, dielectric relaxation, or neutron scattering measurements. In both temperature ranges, the dynamic speed of water molecules in V2O5‚nH2O is faster than those in clays with Na and/or Li ions. This makes us believe that water molecules occluded in V2O5‚nH2O without strong coordination to the surface are more mobile than those hydrating the interlayer ions in clay systems. Conclusions (1) The dynamic properties of the interlayer water molecules of V2O5‚nH2O are characterized by heterogeneous distributions. (2) Mobile interlayer water molecules decrease in number as the temperature is decreased. The jumpdiffusion length of the remaining mobile water molecules is unchanged with temperature, suggesting that the translational diffusion of a water molecule occurs from site to site in the two-dimensional field. (23) Swenson, J.; Bergman, R.; Howells, W. S. J. Chem. Phys. 2000, 113, 2873. (24) Poinsignon, C.; Estrade-Szwarckopf, H.; Conard, J.; Dianoux, A. J. Physica B 1989, 156-157, 140. (25) Johari, G. P. J. Chem. Phys. 1996, 105, 7079.
Dynamics of Water of Layered Vanadium Oxide Hydrate
(3) Rotational motion is faster than that in clay minerals and is similar to that of bulk water. Interaction of water molecules with surface hydroxyls on the surface layer is smaller than that with the intercalated metal ions. Acknowledgment. The authors express sincere thanks to Mr. Remi Kahn of LLB for his help in the neutron scattering experiments and suggestions in the analyses
Langmuir, Vol. 21, No. 4, 2005 1397
of the data. Financial aid is appreciated from a Grant in Aid for Science Research No. 0643060 from the Ministry of Education, Science and Culture of Japan and a Special Grant for Cooperative Research Administered by Japan Private School Promotion Foundation, 13HK11. LA0401009
