Langmuir 2000, 16, 10559-10563
Interlayer Water Molecules in Vanadium Pentoxide Hydrate, V2O5‚nH2O. 7. Quasi-elastic Neutron Scattering Study Shuichi Takahara and Shigeharu Kittaka* Department of Chemistry, Faculty of Science, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan Yasushige Kuroda Department of Chemistry, Faculty of Science, Okayama University, Tsushima, Okayama 700-8530, Japan Toshio Yamaguchi and Hiroyuki Fujii Department of Chemistry, Faculty of Science, Fukuoka University, Nanakuma, Jyonan-ku, Fukuoka 814-0180, Japan Marie-Claire Bellissent-Funel Laboratoire Le´ on Brillouin (CEA-CNRS), CE Saclay, 91191 Gif-sur-Yvette Cedex, France Received June 15, 2000. In Final Form: September 25, 2000
Introduction Vanadium pentoxide hydrate, V2O5‚nH2O, is a compound with layered structure, and water molecules are confined in the two-dimensional (2D) interlayer space.1-3 Physicochemical properties of this material are similar to those of smectite type clay minerals.4,5 We have been interested in the structural and physicochemical properties of the 2D water that have been investigated by XRD, calorimetry, FTIR, etc.1,6-9 The results obtained so far are as follows. (1) The adsorption isotherm of water for this material is stepwise with the first, second and higher water layers.1 This was confirmed by XRD measurements in which the interlayer distances of the compound increase stepwise as a function of water vapor pressure.1 (2) No phase changes of the interlayer water, such as freezing, were detected by calorimetry at the water content below n ) 3.8,10 (3) By polarized FTIR spectroscopy, it was found that the interlayer water molecules are isotropic in the ab * Author for correspondence. E-mail:
[email protected]. FAX: +81-86-254-2891. TEL: +81-86-256-9433. (1) Kittaka, S.; Ayatsuka, Y.; Ohtani, K.; Uchida, N. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3825. (2) Aldebert, P.; Baffier, N.; Gharbi, N.; Livage, J. Mater. Res. Bull. 1981, 16, 669. (3) Yao, T.; Oka, Y.; Yamamoto, N. Mater. Res. Bull. 1992, 27, 669. (4) Moony, R.; Keenan, A. G.; Wood, L. A. J. Am. Chem. Soc. 1952, 74, 1371. (5) Olphen, H. V. An Introduction to Clay Colloid Chemistry; Interscience Publishers: New York and London, 1963. (6) Kittaka, S.; Uchida, N.; Miyahara, H.; Yokota, Y. Mater. Res. Bull. 1991, 26, 391. (7) Kittaka, S.; Suetsugi, T.; Kuroki, R.; Nagao, M. J. Colloid Interface Sci. 1992, 154, 216. (8) Kittaka, S.; Suetsugi, T.; Morikawa, S.; Uchida, N. Langmuir 1993, 9, 1104. (9) Kittaka, S.; Hamaguchi, H.; Shinno, T.; Takenaka, T. Langmuir 1996, 12, 1078. (10) Abello, L.; Pommier, C. J. Chim. Phys. Phys.-Chim. Biol. 1983, 80, 373.
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plane.9 This implies that the water molecules are arranged randomly in the 2D interlayer space. These results suggest that the interlayer water in V2O5‚nH2O is a 2D nonfreezing liquid. However, direct evidence for this model such as determination of the structure of the interlayer water from diffraction experiments has not been shown yet. In the present study, we have analyzed the dynamics of the monolayer water molecules in V2O5‚nH2O by quasielastic neutron scattering (QENS). Here, the applicability of a model including both translational and rotational diffusion was tested. To get precise information about the two diffusion modes, QENS spectra using 9 and 6 Å wavelength neutrons were measured; the former covers mainly the translational diffusion and the latter the rotational one. Experimental Section Material. V2O5‚nH2O samples were prepared by an ionexchange polymerization method from an aqueous solution of recrystallized NH4VO3, as described previously.1 To obtain a concentrated solution (0.2 mol dm-3) of vanadic acid, NH4VO3 was dissolved in a NaOH solution and then heated to remove NH4+ as NH3. A reddish brown sol thus formed was aged under ambient conditions for more than 2 months until it changed to a thick gel and was finally freeze-dried. Neutron Scattering. Dry and monolayer samples for QENS measurements were prepared by the following procedure. V2O5‚ nH2O powder was packed into a flat aluminum cell (1 × 30 × 48 mm3). The sample cell was set in a vacuum chamber and evacuated. For preparation of the monolayer sample, the dried sample was exposed to water vapor of 1.4 kPa for 2 h at 298 K. The prepared sample corresponded to V2O5‚1.5 H2O which has monolayer water on the basis of the adsorption isotherm. Finally, helium gas was introduced in the vacuum system to adjust the internal pressure to 1 atm, and the cell was sealed using indium wire. The dry sample was prepared by evacuation of the sample at 373 K for 2 h, followed by filling with helium gas and sealing. The composition for this sample was expressed by V2O5‚0.14H2O. The remaining water molecules in the dry sample are strongly adsorbed on the layer surface and can stand heating to ∼600 K.7 The transmission factors were estimated to be 88% for the monolayer sample and 95% for the dry sample. The QENS spectra of the dry and monolayer samples were measured by using neutron beams with wavelengths of 9 and 6 Å, on the spectrometer MIBEMOL (G6-2)11 of LLB, Saclay. The energy resolutions for 9 and 6 Å measurements were 14 and 48 µeV (half-width at half-maximum, HWHM), respectively. The flat sample cell was oriented by 40° to the incident neutron beam, and the QENS spectra were measured in a reflection mode. The sample temperature was adjusted to 298 or 253 K by circulating a liquid medium in a sample holder with a temperature controlling unit. The temperature was controlled to within (0.2 K. The resolution function of the spectrometer was determined by measuring a vanadium plate.
Results and Discussion Typical examples of the QENS spectra are shown in Figures 1 and 2. The spectra for the monolayer sample (n ) 1.5) at 298 K and at Q ) 1.30 and 1.95 Å-1 are shown in Figure 1 at the 6 and 9 Å resolutions, together with those of the dry sample (n ) 0.14) and the vanadium plate (the resolution function of the instrument). Here, all the spectra are normalized by coinciding the peak maximum to emphasize the quasielastic wings of the spectra. The quasielastic component of the monolayer sample is clearly (11) Laboratoire Le´on Brillouin Equipements Experimentaux; 1995.
10.1021/la000831i CCC: $19.00 © 2000 American Chemical Society Published on Web 11/23/2000
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Figure 1. Quasielastic neutron scattering spectra for the monolayer sample V2O5‚1.5 H2O (b), the dry sample V2O5‚0.14 H2O (×), and the vanadium plate (bold solid line) at 298 K measured with (a) 9 Å wavelength neutrons at Q ) 1.30 Å-1 and (b) 6 Å wavelength neutrons at Q ) 1.95 Å-1. All the spectra are normalized by coinciding the peak maximum to emphasize the quasielastic wings.
seen, while the spectra of the dry sample are almost the same as those of vanadium. This shows that the water molecules remaining in the dry sample are immobile on the experimental time scale. Figure 2 shows the Qdependence of the spectra at the 6 and 9 Å resolutions for the monolayer sample at 298 K. A Bragg peak due to 001 diffraction was observed for both the dry and monolayer samples, but the Q-values for the peak were different from each other. This is because the interlayer distance changes depending on the water content, as mentioned above.1 Therefore, we could not use a difference spectrum technique, which is usually applied to adsorbed systems.12 In the analysis of the monolayer sample, we did not use the spectrum at the lowest Q ) 0.59 Å-1, because it contained a large contribution from the coherent scattering. The spectra of the monolayer sample were analyzed by a model modified from that developed by Teixeira et al.13 (12) Clark, J. W.; Hall, P. G.; Pidduck, A. J.; Wright, C. J. J. Chem. Soc., Faraday Trans. 1 1985, 81, 2067. (13) Teixeira, J.; Bellissent-Funel, M.-C.; Chen, S. H.; Dianoux, A. J. Phys. Rev. A 1985, 31, 1913.
for bulk water. The scattering law S(Q,ω) employed in the analysis is as follows,
S(Q,ω) ) 〈u2〉 2 Q [Aδ(ω) + (1 - A)SR(Q,ω)XST(Q,ω)] + exp 3 B(Q) (1)
(
)
Here, the first factor represents the Debye-Waller factor. δ(ω) is a δ-function and A is the fraction of elastic component. SR(Q,ω) and ST(Q,ω) represent the contributions from rotational and translational diffusion, respectively. X means convolution in ω. B(Q) represents the ω-independent background due to vibrational motion. In eq 1, Aδ(ω) corresponds to the elastic component due to contributions from the atoms in V2O5 and from the strongly adsorbed water molecules. The term (1 - A)SR(Q,ω)XST(Q,ω) corresponds to a quasielastic component ascribed to the diffusive motions of the water molecules. According to the FTIR data,9 the transition moments of the interlayer water molecules in V2O5‚nH2O are
Notes
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Figure 2. Q-dependence of the quasielastic neutron scattering spectra for the monolayer sample at 298 K measured with (a) 9 Å and (b) 6 Å wavelength neutrons, respectively. Closed circles indicate the experimental data. Solid, dotted and broken lines are for the total fit, the quasielastic component, and the background, respectively.
oriented partly along the c-axis. This implies that the rotational motion of the interlayer water molecules is not perfectly isotropic. For the sake of simplicity, however, we assumed that rotational diffusion can be expressed by the isotropic diffusion model:14
SR(Q,ω) ) j20(Qa)δ(ω) +
(
3j21(Qa)L ω,
)
( )
1 1 + 5j22(Qa)L ω, (2) 3τR τR
Here, jn are the spherical Bessel functions of the nth order. L(ω,Γ) is the Lorentzian function with HWHM Γ. a stands for the radius of rotation, taken as 0.98 Å (the O-H distance of water molecule). τR denotes the relaxation time of rotational diffusion. The higher order terms in eq 2 are negligible in our experimental Q-range. For translational diffusion, a single Lorentzian with HWHM ΓT was adopted as ST(Q,ω):
ST(Q,ω) ) L(ω,ΓT)
(3)
Strictly speaking, the scattering law of powder averaged 2D translational diffusion is given by
ST(Q,ω) )
1 2π
∫0πL(ω,ΓT,2D(Q|))sin θ dθ
(4)
where θ is the angle between the scattering vector Q and the normal to the water layer. Q| is the component of Q (14) Sears, V. F. Can. J. Phys. 1966, 44, 1299; 1966, 45, 237.
parallel to the water layer and given by Q| ) Q sinθ. ST(Q,ω) given by eq 4 is not a single Lorentzian, but a function having logarithmic singularity at ω ) 0.15 However, if ΓT is small compared to the resolution width of the instrument, an experimental spectrum can approximately be described by a convolution of the resolution function with a Lorentzian, although it is more peaked at ω ≈ 0.15 In the fitting procedure, the more peaked shape of the spectrum results in extra magnitude of elastic scattering. To estimate this effect, we generated a spectrum of 2D translational diffusion by using eq 4. Separating the simulated spectrum into both elastic and quasielastic components, this extra magnitude was evaluated to be less than 10% of the total intensity. This indicates that the single Lorentzian approximation (eq 3) does not seriously affect the fitting results. The spectra were analyzed in a least-squares refinement procedure by using the program KIWI,16 in which the experimental data were fitted by S(Q,ω) convoluted with the resolution function of the instrument. In this procedure, 15 spectra measured in different ranges of scattering angles by using 9 and 6 Å wavelength neutrons were fitted simultaneously by the model function described in eqs 1-3. The values of the fitting parameters obtained depended on their initial values, and each result gave almost the same standard deviation. The reason would be that this least-squares fitting has many variables to determine (37 parameters) and a large nonlinearity. However, we could determine the possible ranges of each parameter value by fitting with various initial values for the variables. Examples of the least-squares fitting are shown in Figure 2. As shown in this figure, all the spectra were fitted well by the model function. The values and errors of parameters A and τR obtained by the fitting are listed in Table 1, together with the literature data for bulk water.17 At 253 K, the line width of the quasielastic component became narrower, which caused a large ambiguity of the fitting. The experiment with higher resolution is needed to investigate the dynamics of the interlayer water at low temperature. Thus, we concentrate our discussion on the data at 298 K as follows. The fraction A of the elastic component corresponds to the ratio of intensity of incoherent scattering from immobile atoms to the total intensity. In this experiment, this value should be equal to the ratio of the total scattering intensity of the dry sample to that of the monolayer sample at the Q-range where a Bragg peak does not exist, because all the atoms in the dry sample are immobile, as mentioned above. The ratio estimated was ∼0.3, which almost coincides with the value of A. A slightly larger value of A may be explained by the extra magnitude of elastic scattering due to the single Lorentzian approximation of ST(Q,ω). The value of τR indicates that the water molecules in V2O5‚nH2O rotate a little bit slower than those in bulk water. We also tried the fit without fixing the radius of rotation a to 0.98 Å. The value of a became 0.93 Å, which is close to the reported value 0.98 Å. The obtained values of other parameters were almost the same as those with fixing a. This indicates the validity of the present model function. Figure 3 shows the Q-dependence of ΓT obtained by the fitting. The vertical lines represent the error bars. As (15) Renouprez, A.; Fouilloux, P.; Stockmeyer, R.; Conrad, H. M.; Goeltz, G. Ber. Bunsen-Ges. 1977, 81, 429. (16) A fitting program for quasielastic data analysis, KIWI ver. 1.01 made by Fanjat, N. (17) Bellissent-Funel, M.-C.; Chen, S. H.; Zanotti, J.-M. Phys. Rev. E 1995, 51, 4558.
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Table 1. Parameters Obtained by the Analysis of the Neutron Scattering Spectra sample
T/K
A
τR/ps
F/Å
τΤ/ps
DT/10-10 m2 s-1
V2O5‚nH2O
298 253a 298
0.38 ( 0.05 0.52 ( 0.21 s
2.4 ( 0.4 4.2 ( 1.5 1.10
2.5 ( 0.3 s 1.23c
47 ( 7 s 1.10
3.3 ( 0.8 s 23.0
bulk waterb a
The fitting contains a large ambiguity because of the narrowing of the line width. b The literature values of bulk water in ref 17. c The mean jump length calculated from τT and the diffusion constant in ref 17.
Figure 3. Q-dependence of ΓT of the monolayer water at 298 K measured with 9 Å (b) and 6 Å (O) wavelength neutrons. Vertical lines represent the error bars. Solid curve indicates a fitting result by use of eq 5.
shown in this figure, ΓT values have rather large errors, but we can find a broad maximum at Q2 ≈ 2Å-2. This shape is given by the jump-diffusion models in which the jump length is fixed.18 According to the random-jumpdiffusion model,19 in which the jump length is randomly distributed, ΓT should increase monotonically with Q. The fixed jump length model is reasonable for the present system since the monolayer water molecules must jump between the physisorption sites on the V2O5 sheets. Thus, we adopted the fixed jump length model for 2D translational diffusion to fit the ΓT data as was adopted by Renouprez et al. for the data analysis of hydrogen adsorbed on a nickel catalyst.15 In this model, ΓT is given by
ΓT ) [1 - JO(QF)]/τT
(5)
Here, J0 is the cylindrical Bessel function of zeroth order, F is the diffusion step length, and τT is the mean residence time of translational diffusion. The result of the fitting is shown in Figure 3 by a solid curve. The values obtained for F and τT are listed in Table 1 together with the literature data for bulk water.17 The value in the column for the jump length of bulk water is a mean jump length L, which was calculated from the values of τT and the diffusion constant DT in ref 17 by using the relation L ) (6τTDT)1/2. The estimated F value for the interlayer water is larger than the mean jump length for bulk water, but is not an unreasonably large value. This value of 2.5 Å may be related with the structure of the V2O5 layer sheet; the nearest neighbor V-V distance in the ab plane parallel to the V2O5 sheet ranges ∼2.5 Å (a-direction) and 3.6 Å (b-direction).6 The residence time τT for the interlayer (18) Bee, M. Quasielastic Neutron Scattering; Adam Hilger: Bristol and Philadelphia, 1987. (19) Egelstaff, P. A. An Introduction to the Liquid State; Academic Press: London and New York, 1967.
water at 298 K is ∼40 times longer than that for bulk water, indicating that the water molecules in V2O5‚nH2O translate more slowly than those in bulk water. The 2D translational diffusion constant was calculated from the values of F and τT by using the relation DT ) F2/4τ,15 and is listed in Table 1. The obtained values of F, τT, and DT are similar to those for monolayer water in Li-montmorillonite given by Cebula et al.20 (L ) 3.2 Å, τT ) 43 ps, DT ) 4 × 10-10 m2s-1). Both τR and τT of the water molecule in V2O5‚nH2O were larger than those for bulk liquid water, but much shorter than those in bulk ice; both τR21 and τT22 of water molecules in bulk ice are ∼10-5 s just below the melting point. This implies that the interlayer water is not a 2D crystal but a liquid. Conclusions The dynamics of interlayer water molecules in V2O5‚ nH2O was investigated by quasielastic neutron scattering. The spectra of the dry sample have no quasielastic wing, indicating that the strongly adsorbed water molecules on the V2O5 sheets are immobile on the experimental time scale. The spectra of the monolayer sample were analyzed by assuming a model in which dynamic motion of the interlayer water molecules is composed of isotropic rotational diffusion and 2D translational diffusion. For both translational and rotational diffusion, the water molecules in V2O5‚nH2O are less mobile than those in bulk liquid water but much more mobile than those in bulk ice. This implies that the interlayer water is a 2D liquid. (20) Cebula, D. J.; Thomas, R. K.; White, J. W. Clays Clay Miner. 1981, 29, 241. (21) Auty, R. P.; Cole, R. H. J. Chem. Phys. 1952, 20, 1309. (22) Franks, F., Ed. Water, A Comprehensive Treatise; Plenum Press: New York and London, 1972; Vol. 1. τT value in bulk ice was evaluated from DT ≈ 2 × 10-15 m2s-1 and F ) 2.76 Å (O-O distance in bulk ice) by using the relation τT ) F2/6DT.
Notes
Acknowledgment. The authors express sincere thanks to Dr. Remi Kahn of LLB for his kind suggestions and help in QENS experiments and data analysis. The authors are indebted to Mr. Hidekazu Mizuno for his help with the data analysis. This work was partly supported by a Grant-in-Aid for Science Research No. 0643060 from
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the Ministry of Education, Science and Culture of Japan and by a Special Grant for Cooperative Research administered by Japan Private School Promotion Foundation. LA000831I
