J. Phys. Chem. B 2008, 112, 4687-4693
4687
Partial Pair Correlation Functions of Low-Density Supercritical Water Determined by Neutron Diffraction with the H/D Isotopic Substitution Method Toshiya Otomo,† Hiroki Iwase,†,# Yasuo Kameda,*,‡ Nobuyuki Matubayasi,§ Keiji Itoh,| Susumu Ikeda,† and Masaru Nakahara§ Institute of Material Structure Science, KEK, Tsukuba, Ibaraki 305-0801, Japan, Department of Material and Biological Chemistry, Faculty of Science, Yamagata UniVersity, Yamagata, Yamagata 990-8560, Japan, Institute of Chemical Research, Kyoto UniVersity, Uji, Kyoto 611-0011, Japan, Research Reactor Institute, Kyoto UniVersity, Kumatori, Osaka 590-0494, Japan, and AdVanced Science Research Center, JAEA, Tokai, Ibaraki 319-1195, Japan ReceiVed: December 4, 2007; In Final Form: February 13, 2008
Neutron diffraction measurements were carried out on H/ D isotopically substituted water in the low-density supercritical condition (T ) 673 K, P ) 26.3 MPa, and F ) 0.0068 molecules·Å-3) in order to obtain direct information on the intermolecular partial structure functions, gHHinter(r), gOHinter(r), and gOOinter(r). In correspondence to the high-density supercritical water previously reported, the intermolecular nearest neighbor peaks in gHHinter(r), gOHinter(r), and gOOinter(r) are diffuse compared with the ambient ones. The nearest neighbor O‚‚‚O distance (3.3 Å) and its coordination number (2.6) were determined from the observed gOOinter(r). These results indicate that the orientational correlation between neighboring water molecules is considerably lost in low-density supercritical water. Small clusters involving a few water molecules are preferentially formed in low-density supercritical water, which is consistent with results obtained by previous IR and NMR studies.
Introduction Supercritical water (SCW) has received considerable interest because of its excellent properties as a solvent and also as a reactant for various chemical reactions,1-5 which are highly important in both fundamental and industrial chemical processes. Since the physical properties of SCW such as dielectric constant, viscosity, and dissociation constant can vary continuously over a wide range in the supercritical state, it is possible to tune the properties of the reaction medium to optimal values for a given chemical reaction by choosing pressure and temperature conditions.3 The properties of the SCW is considered to be governed by the hydrogen-bonding interaction between neighboring water molecules. Intermolecular hydrogen-bonded structure in the SCW has extensively been investigated by neutron diffraction,6-15 large angle16-18 and small angle19 X-ray diffraction, NMR,20-24 quasielastic25,26 and inelastic27-29 neutron scattering, inelastic X-ray scattering,30,31 IR,26,32 Raman scattering,29,33-37,71 X-ray Raman scattering,38 and molecular dynamics simulation2,5,6,22,39-46 methods. Temperature dependence of partial pair correlation functions, gHH(r), gOH(r), and gOO(r) in SCW (the number density of 0.0194 e F e 0.0381 molecules‚Å-3) was examined by neutron diffraction with H/D isotopic substitution method.6-14 The nearest neighbor hydrogen-bonded O‚‚‚H and H‚‚‚H peaks in the observed gOH(r) and gHH(r) functions become gradually smeared with increasing temperature,13 clearly indicating that the hydrogen-bonding interaction between the nearest neighbor water molecules is considerably weak in the high-density SCW * To whom correspondence should be addressed. E-mail: kameda@ sci.kj.yamagata-u.ac.jp, Fax: +81-23-628-4591. † Institute of Material Structure Science. ‡ Yamagata University. § Institute of Chemical Research, Kyoto University. | Research Reactor Institute, Kyoto University. # Advanced Science Research Center.
(we tentatively call the state in which the density is larger than 0.5 g‚cm-3 (F ) 0.0167 molecules‚Å-3) as “high-density SCW” in the present paper).13 The peak position of the nearest neighbor O‚‚‚O interaction has been reported to shift toward a longer distance with increasing temperature.9,13 In the high-density SCW, the width of the first O‚‚‚O peak exhibits significant increase compared with that in the ambient state,9,13 which is consistent with results from the X-ray diffraction studies.16-18 These results indicate the weaker interaction between the nearest neighbor water molecules in the high-density SCW. On the other hand, experimental determination of the partial pair correlation function has not yet been reported for low-density SCW. According to the results from the small-angle X-ray scattering study,19 the estimated correlation length in low-density SCW is ca. 7 Å (at T ) 677 K and the number density of F ) 0.0067 molecules‚Å-3), indicating the inhomogeneity in the dimension of length in low-density SCW is ca. 7 Å. The mean jump distance of hydrogen atoms in low-density SCW (ca. 4 Å at T ) 653 K and F ) 0.0067 molecules‚Å-3) obtained from the quasielastic incoherent neutron scattering exhibits a strong density dependence in the SCW, which suggests the nearest neighbor interaction between water molecules changes with the density.25,26 The density dependence of the proton chemical shift in the SCW (T ) 673 K) determined by NMR20,21 indicates that the average number of hydrogen bonds per one water molecule decreases from the value of ca. 1 in the high-density SCW to less than 0.5 in low-density SCW21 (note that in ref 21, the number of hydrogen bonds is normalized so that it is 4 in ice and is different from the definition in this paper by a factor of 2). The result suggests the number of hydrogen bonds decreases with decreasing density. The reorientational relaxation time, τ2R, determined for supercritical D2O at T ) 673 K is found to be ca. 1/102 of that observed at T ) 303 K,23 suggesting a shorter life time of the intermolecular hydrogen bonds in the
10.1021/jp711434n CCC: $40.75 © 2008 American Chemical Society Published on Web 03/25/2008
4688 J. Phys. Chem. B, Vol. 112, No. 15, 2008 SCW. The breakdown of the nearest neighbor hydrogen bonds in SCW has also been suggested from low-frequency Raman scattering studies.34-37 IR spectra in the O-H stretching region indicate that water dimers and trimers are dominant chemical speciesinlow-densitySCW(0.0017eFe0.0134molecules‚Å-3).32 Actually, because of the pressure elevation in supercritical conditions, supercritical water of wide use is often restricted to low- to medium-density regime. Information on intermolecular structure in the partial structure function level is thus necessary to elucidate the property of the short-range interaction between water molecules in low-density SCW. In order to obtain direct information on the local structure in low-density SCW, neutron diffraction with H/D isotopic substitution is considered to be the most suitable experimental technique. A complete set of partial structure functions can be deduced from at least three independent neutron scattering data for samples with different H/D isotopic compositions. In this study, neutron diffraction measurements for low-density supercritical D2O, H2O, and 0H2O (H/D ) 64/36, the average coherent scattering length of the hydrogen atom, bH, is set to be zero) have been carried out at T ) 673 K and the number density, F ) 0.0068 molecules‚Å-3. Intermolecular partial structure factors, aHHinter(Q), aOHinter(Q), and aOOinter(Q), are directly determined from the combination of the observed interference terms. In order to confirm the reliability of the data correction and normalization procedures employed, measurements for the ambient water were carried out in advance. Experimental Section Materials. Weighed amounts of the samples, H2O (resistivity of 18.2 MΩ), D2O (99.9% D, Aldrich Chemical Co., Inc.) and the “null” water (0H2O, H/D ) 64/36, bH ) 0), were introduced into the cylindrical high-pressure Ti-Zr null alloy cell (6.0 mm in inner diameter and 2.0 mm in wall thickness). The cell was sealed by a Ti-Zr cap with gold packing. Neutron Diffraction Measurements. Neutron diffraction measurements were carried out at T ) 673 K using the HIT-II spectrometer47 installed at the pulsed spallation neutron source (KENS) in the High-Energy Accelerator Research Organization (KEK), Tsukuba, Japan. The temperature of the sample was carefully controlled by an infrared image furnace. The number density of the sample at T ) 673 K was set to be F ) 0.0068 molecules‚Å-3, which was estimated by the molar quantity of the sample introduced in the cell and the fixed volume within the sample cell. The exposure time of H2O, D2O, and 0H2O samples were 16, 20, and 30 h, respectively. Scattered neutrons (incident neutron waveband of 0.08 e λ e 5.5 Å) were detected by 104 3He proportional counters covering the scattering angle range of 10 e 2θ e 157°. In order to confirm the reliability of the data correction and normalization procedures for the scattering data obtained by using the high-pressure Ti-Zr cell, measurements of H2O, D2O, and 0H2O within the high-pressure cell under ambient condition (T ) 298 K) were also performed. Scattering intensities were measured for the empty cell, vanadium rod of 6 mm in diameter, and the empty furnace as a background. Data Reduction. Observed scattering intensities for the sample were corrected for background, absorption of sample and cell,48 and multiple49 and incoherent scatterings. The coherent scattering lengths as well as the scattering and absorption cross-sections for constituent nuclei were referred to those tabulated by Sears.50 The wavelength dependence of total cross-sections for H and D nuclei was estimated from the observed total scattering cross-sections for H2O and D2O,
Otomo et al. respectively.51 The corrected intensities were converted to the absolute scale using the corrected scattering intensities from the vanadium rod. The inelasticity correction was applied by the use of the observed self-scattering intensities from the liquid 0H O.52 The magnitude of the inelasticity effect is roughly 2 proportional to sin2 θ;53-58 therefore, scattering data observed at the small scattering angle are preferred for the present samples involving considerable amounts of H and D nuclei. Since the observed total interference terms, i(Q), from 52 sets of forward angle detectors at 10 e 2θ e 25° agree well within the statistical uncertainties for H2O and 0H2O samples, they were combined at the Q-interval of 0.1 Å-1 and used for the subsequent analysis. In the case of D2O, scattering data from 64 sets of detectors at 10 e 2θ e 51° were employed. Observed total interference term, i(Q), is divided into the intra- and intermolecular contributions,
i(Q) ) iintra(Q) + iinter(Q)
(1)
where,
iintra(Q) ) 4bObHexp(-lOH2Q2/2)sin(QrOH)/(QrOH) + 2bH2exp(-lHH2Q2/2)sin(QrHH)/(QrHH) (2) Parameters lij and rij denote the root-mean-square displacement and internuclear distance of the i-j pair within a water molecule, respectively. In the present study, these structural parameters were determined through the least-squares refinement of the observed total interference term in the high-Q region (8 e Q e 25 Å-1), where contribution from the intermolecular interference term is negligibly small. The fitting procedure was performed by the SALS program,59 assuming that statistical uncertainties distribute uniformly over the Q-range employed. Prior to the fitting procedure, correction for the low-frequency systematic errors involved in the observed i(Q) was applied.60 The intermolecular interference term, iinter(Q), was evaluated by subtracting the calculated intramolecular interference term from the observed i(Q). Intermolecular partial structure factors, aHHinter(Q), aOHinter(Q), and aOOinter(Q), were determined by combining intermolecular interference terms observed for H2O, D2O, and 0H2O;
aHHinter(Q) - 1 ) [iinterD2O(Q) - iinter0H2O(Q)]/[4bD(bD - bH)] [iinterH2O(Q) - iinter0H2O(Q)]/[4bH(bD - bH)] (3) aOHinter(Q) - 1 ) bH[iinterD2O(Q) - iinter0H2O(Q)]/[4bObD(bH - bD)] bD[iinterH2O(Q) - iinter0H2O(Q)]/[4bObH(bH - bD)] (4) and
aOOinter(Q) - 1 ) iinter0H2O(Q)/bO2
(5)
The intermolecular pair correlation function, gijinter(r), was evaluated by the Fourier transform of the observed aijinter(Q);
gijinter(r) ) 1 + (2π2Fr)-1
∫0Q
max
Q[aijinter(Q) - 1] sin(Qr) dQ (6)
Structure of Low-Density Supercritical Water
J. Phys. Chem. B, Vol. 112, No. 15, 2008 4689 TABLE 1: Intramolecular Parameters for D2O and H2O Molecules Obtained from the Least-Squares Fitting Analysis of Observed Neutron Total Interference Terms for Room-Temperature Water and Supercritical Water in the Range of 8 e Q e 25 Å-1 a temp, K rOH(D), Å lOH(D), Å rHH(DD), Å lHH(DD), Å γ a
Figure 1. The observed total interference terms of D2O, H2O, and 0 H2O at T ) 298 K and number density of F ) 0.0333 molecules‚Å-3 (dots). Solid lines indicate the best-fit results of the intramolecular interference term for D2O and H2O. Residual functions, δ(Q), are shown below.
Since the oscillational amplitude of the intermolecular interference term decays more rapidly in the higher-Q region than that for the intramolecular ones, errors in the gijinter(r), mainly associated with the termination of the Fourier integral, are expected to be much reduced. The upper limit of the integral, Qmax, was set to be 20 Å-1 in the present analysis. The intermolecular running coordination number, nijinter(r), was evaluated by the following equation;
nijinter(r) ) 4πFcj
∫0r r′2gijinter(r′) dr′
(7)
where, cj denotes the number of atom j within a water molecule. Results and Discussion Observed interference term, i(Q), for D2O, H2O, and 0H2O under ambient condition (T ) 298 K, F ) 0.0333 molecules‚Å-3) is shown in Figure 1. Overall features of the present total i(Q) observed for D2O, H2O, and 0H2O samples are in good agreement with those reported in the literature.61-65 The oscillational feature extending to the high-Q region is clearly identified in the i(Q) observed for D2O and H2O, which is attributable to the intramolecular interference contribution within the water molecule. In order to confirm the reliability of the data correction and normalization procedures adopted in the present study, the least-squares fitting analysis of the total i(Q) observed for D2O and H2O was performed in the range of 8 e Q e 25 Å-1, where the intramolecular interference contribution is dominant. In the present fitting procedure, structural parameters, rOH(OD), rHH(DD), lOH(OH), lHH(DD), and the normalization factor, γ, defined by iobs(Q) ) γ × iintracalc(Q), were treated as independent parameters. The results of the least-squares refinement are summarized in Table 1. Present values of the intramolecular O-D and D‚‚‚D distances observed for the ambient liquid D2O are in excellent agreement with those reported for D2O molecule in the liquid state.60,61,64,66,67 The
D2O
D2O
H2O
H2O
298 0.984(3) 0.072(3) 1.56(2) 0.14(2) 1.04(5)
673 0.984(1) 0.062(1) 1.540(7) 0.124(6) 1.02(2)
298 0.981(2) 0.067(2) 1.46(2) 0.16(1) 1.13(4)
673 0.982(2) 0.054(3) 1.53(2) 0.12(1) 0.96(3)
Estimated errors are given in parentheses.
normalization factor γ was determined to 1.04(5), implying the overall normalization error for the observed total interference term is roughly estimated to be within 4%. The value of the intramolecular O-H distance obtained for the H2O under ambient conditions agrees well with the rOD value for the ambient liquid D2O. The intramolecular interference term, iintra(Q), was evaluated by eq 2 applying the intramolecular parameters which were determined by the least-squares refinement. The calculated iintra(Q) was then subtracted from the total interference term to obtain the intermolecular interference term, iinter(Q). On the other hand, the present value of the intramolecular H‚‚‚H distance of H2O in an ambient state seems too short compared with the D‚‚‚D distance observed for the ambient D2O. It is possible that the intramolecular H‚‚‚H contribution (appears as a positive peak in the distribution function) is overlapped with the nearest neighbor intermolecular O‚‚‚H contribution (negative peak) in the case of ambient liquid H2O, which may cause difficulties in determining the intramolecular rHH value. Then the intramolecular interference term for the liquid H2O at T ) 298 K was evaluated by adopting the rHH value of 1.56 Å, which was determined for the liquid D2O at 298 K. Calculated iintra(Q) was subtracted from the total i(Q) to derive the intermolecular iinter(Q). The total interference term i(Q) observed for low-density SCW is shown in Figure 2. The interference feature of the present i(Q) from D2O agrees well with that reported for the supercritical D2O at T ) 653 K and F ) 0.0069 molecules‚Å-3.10 In low-density supercritical D2O, the height of the first and second diffraction peaks located at Q ≈ 2 and 4 Å-1 (clearly observed in the ambient liquid D2O) is significantly decreased. An increase in intensity of i(Q) in the lower-Q region suggests that the clustering of water molecules occurs in low-density SCW, which is consistent with the results from a previous SAXS study.19 Diffraction peaks at Q ≈ 3, 5, and 8 Å-1 that appeared in the i(Q) for ambient H2O are considerably smeared out in low-density supercritical H2O, which indicates the same trend as the observation for high-density supercritical H2O.8,9,13 The molecular geometry of the water molecule in low-density SCW was determined through the least-squares fitting analysis of the observed i(Q) in the range of 8 e Q e 25 Å-1. All independent parameters are summarized in Table 1. The values of the intramolecular O-D and D‚‚‚D distances for low-density supercritical D2O agree well within the experimental error with those in liquid D2O at T ) 298 K, suggesting that the molecular geometry of D2O remain almost unchanged in low-density SCW. Structural parameters determined for low-density supercritical H2O are also in good agreement with those obtained for lowdensity supercritical D2O. The geometry of a water molecule reported for high- and low-density SCW suggests that there is no appreciable change when going from the liquid at ambient conditions to the supercritical state.7,10 The normalization factor γ was determined to 1.02(2) and 0.96(3) from the present low-
4690 J. Phys. Chem. B, Vol. 112, No. 15, 2008
Figure 2. The same notations as Figure 1 except for the condition of T ) 673 K and F ) 0.0068 molecules‚Å-3.
Figure 3. The observed intermolecular partial structure factors for water, aHHinter(Q), aOHinter(Q), and aOOinter(Q), at T ) 298 K and F ) 0.0333 molecules‚Å-3 (dots). The Fourier back-transform of the gijinter(r) in Figure 5 is shown by the solid line.
density supercritical D2O and H2O, respectively, implying that the overall normalization error for the amplitude of the total interference term is well within ca. 4%. These results suggest that the inelasticity effect of the interference term is sufficiently small under the present experimental conditions and that the data correction procedure is considered to be reliable. Figure 3 represents the intermolecular partial structure factors, aHHinter(Q), aOHinter(Q), and aOOinter(Q), for ambient water derived by the combination of observed total intermolecular interference terms. The interference features of the present aijinter(Q) functions for water at T ) 298 K are in excellent agreement with those
Otomo et al.
Figure 4. The same notations as in Figure 3 except for the condition at T ) 673 K and F ) 0.0068 molecules‚Å-3.
reported for ambient water,63,68 which confirms that the present data correction and normalization procedures are adequately carried out. The aijinter(Q) functions for low-density SCW are indicated in Figure 4. The observed aHHinter(Q) and aOHinter(Q) both exhibit considerably smaller oscillational amplitudes compared with those appeared in the ambient water. The data points of the observed O‚‚‚O partial structure factor are somewhat scattered due to the statistical uncertainties, although diffraction peaks at Q ≈ 2.5 and 4 Å-1 can be identified. These results indicate that the large difference is present in the intermolecular structure between ambient water and low-density SCW. Intermolecular partial pair correlation functions, gijinter(r), observed for the ambient water (T ) 298 K, F ) 0.0333 molecules‚Å-3) and low-density SCW (T ) 673 K, F ) 0.0068 molecules‚Å-3) are shown in Figures 5 and 6, respectively. In order to check the consistency of the observed gijinter(r) and aijinter(Q) functions, the following procedure was applied. Unphysical ripples appearing in the low-r region were eliminated by setting values of gijinter(r) to zero in the region below the first peak. The corrected gijinter(r) functions were then back Fourier transformed to aijinter(Q), which are shown in Figures 3 and 4. The back-transformed interference function agrees well with the observed data points except for statistical uncertainties that are involved in the observed data. The intermolecular running coordination number evaluated from the observed gijinter(r) is indicated in Figure 7. The first and second peak positions of gHHinter(r) observed for the ambient water, r ) 2.38 and 3.94 Å, respectively, are in good agreement with those reported in previous neutron diffraction studies.7,9,14,63,68 The values of the intermolecular running coordination number, nHHinter(r), derived from the present gHHinter(r) at r ) 2.38 Å (peak center of gHHinter(r)), was determined to be 2.0. If a symmetrical distribution of the intermolecular nearest neighbor H‚‚‚H interaction is assumed, the coordination number for this peak is estimated to be 4.0 () 2 ×nHHinter(r) at r ) 2.38 Å). This value is consistent with that expected for the tetrahedral local structure of the water molecule.
Structure of Low-Density Supercritical Water
Figure 5. Intermolecular partial pair correlation functions for water, gHHinter(r), gOHinter(r), and gOOinter(r), observed at T ) 298 K and F ) 0.0333 molecules‚Å-3.
Figure 6. The same notations as in Figure 5 except for the condition at T ) 673 K and F ) 0.0068 molecules‚Å-3.
The H‚‚‚H running coordination number integrated up to 2.99 Å (the first local minimum of the gHHinter(r)) is obtained to be 5.8, which agrees well with the previous nHH value of ca. 6 evaluated by an integration of the observed gHH(r) for ambient water in the range of r e 3.1 Å.63,69 The observed gOHinter(r) for the ambient water is characterized by well resolved first intermolecular peak located at r ) 1.78 Å and the second peak at r ) 3.28 Å. These peak positions are in good agreement with those found in the previous studies.7,9,14,63,68 The running coordination number, nOHinter(r) ) 2.2 at r ) 2.50 Å (the first local minimum of the gOHinter(r)) agrees well with that reported previously.7,63,69 This value also corresponds to the tetrahedral
J. Phys. Chem. B, Vol. 112, No. 15, 2008 4691
Figure 7. Intermolecular running coordination number for observed partial pair correlation functions for water.
hydrogen-bonded local structure at the ambient condition. The positions of dominant peaks in the present gOOinter(r), r ) 2.71 and 4.59 Å, are consistent with the tetrahedral local structure of the nearest neighbor water molecules. The present first nearest neighbor O‚‚‚O distance is slightly shorter than that determined in the previous neutron diffraction studies.63,65 The position of a small hump located at r ≈ 3.4 Å in the present gOOinter(r) is close to that for the contribution from the “interstitial” water molecules18,70 weakly interacted with the neighboring molecules; whereas, this small hump is not observed, and the position of this hump corresponds to the local minimum in the gOO(r) function from previous studies.7,9,14,63,65 It is possible that this small hump is associated with the termination effect in the Fourier transform of the relatively sharp nearest neighbor O‚‚‚O peak and statistical uncertainties involved in the observed aOOinter(Q). The running coordination number nOOinter(r) at r ) 3.4 Å is estimated to be 4.1 in the present gOOinter(r), and the value is in reasonable agreement with that observed previously. The present results for the ambient water indicate the reliability of derived partial structure functions, confirming the validity of data correction and normalization procedures employed in the present data analysis. Intermolecular pair correlation functions observed for lowdensity SCW represented in Figure 6 indicate a very different short-range structure from that in the ambient state. The position of the first intermolecular peak in the observed gHHinter(r) shifts from r ) 2.38 Å in the ambient state to r ) 2.26 Å in lowdensity SCW. The running coordination number of the peak at r ) 2.42 Å (the first minimum in gHHinter(r)) is found to be 0.43. This small value of the nearest neighbor H‚‚‚H coordination number implies that the intermolecular hydrogen bonds between neighboring water molecules are considerably collapsed in low-density SCW. The position of the second nearest neighbor H‚‚‚H peak (r ) 3.59 Å) also shifts toward ca. 0.3 Å shorter distance compared with that observed for the ambient water. The profile of the present gHHinter(r) in the first- and second-peak regions is less distinct compared with that in the ambient state. This is parallel to the behavior in the high-density
4692 J. Phys. Chem. B, Vol. 112, No. 15, 2008 SCW9,14 and shows the weakened orientational correlation between the neighboring water molecules. The gOHinter(r) for low-density SCW is characterized by the dominant intermolecular peak located at r ) 3.06 Å with a shoulder at r ≈ 2 Å on the lower-r side. This shoulder corresponds to the nearest neighbor hydrogen-bonded O‚‚‚H interaction, which appears as a well resolved peak in the gOHinter(r) for the ambient water. In the high-density SCW (673 K, F ) 0.0221 molecules‚Å-3), it is reported that the nearest neighbor O‚‚‚H peak is significantly broadened and appears to move to longer distance,9,14 which is very similar to that observed for the present low-density SCW. It is difficult to evaluate the nearest neighbor O‚‚‚H coordination number from the present gOHinter(r) for low-density SCW; the running coordination number of 0.3 is tentatively determined by integrating the gOHinter(r) up to r ) 2.50 Å, corresponding to the first local minimum in the gOHinter(r) of the ambient water. This value is consistent with the value (NHB ) 0.7 at the cutoff distance of 2.4 Å) determined by the NMR chemical shift21 (the values differ by a factor of 2 simply due to the difference in the definition of the coordination number). These results indicate that hydrogen bonds among water molecules are remarkably broken in low-density SCW. The gOOinter(r) observed for low-density SCW has a distinct peak at r ) 3.30 Å. According to this peak position, the distance between neighboring water molecules is elongated compared with that in the ambient state; this feature is common to that found in the high-density SCW.6-9,13,14 The present value of the nearest neighbor O‚‚‚O distance implies that the hydrogenbonding probability is closer to the simple, contact value in lowdensity SCW. If we assume a simple isotropic (homogeneous) expansion, the average intermolecular O‚‚‚O distance in lowdensity SCW (F ) 0.0068 molecules‚Å-3) is calculated to be ca. 1.7 times the O‚‚‚O distance in the ambient state (2.8 Å × 1.7 ) 4.76 Å). This shows that weakly interacting water clusters are present in low-density SCW. The existence of clusters involving a small number of water molecules in low-density SCW has been suggested by previous IR26,32 and NMR21,22 studies. The nearest neighbor O‚‚‚O coordination number estimated from the twice the value of the nOOinter(r) at r ) 3.30 Å (peak center) is 2.0. The running coordination number nOOinter(r) at r ) 4.30 Å (the first local minimum of the present gOOinter(r)) is evaluated to be 2.6. The present gOOinter(r) for low-density SCW exhibits a deeper first local minimum than that observed for the high-density SCW.6-9,13,14 This is consistent with the observation in molecular simulation that gOOinter(r) oscillates more strongly at a lower density.22 Formation of small clusters of water molecules can be suggested from the present partial structure functions for low-density SCW. Acknowledgment. We thank Prof. Toshiharu Fukunaga (Kyoto University) for his help during the course of neutron diffraction measurements. All calculations were carried out in the Yamagata University Networking and Computing Center. This work was partially supported by Grant-in-Aid for Creative Scientific Research (no. 16GS0417), from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References and Notes (1) Gopalan, S.; Savage, P. E. J. Phys. Chem. 1994, 98, 12646. (2) Flanagin, L. W.; Balbuena, P. B.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. 1995, 99, 5196. (3) Savage, P. E. Chem. ReV. 1999, 99, 603. (4) Akiya, N.; Savage, P. E. J. Phys. Chem. A 2000, 104, 4433. (5) Akiya, N.; Savage, P. E. J. Phys. Chem. A 2000, 104, 4441. (6) Postorino, P.; Tromp, R. H.; Ricci, M. A.; Soper, A. K.; Neilson, G. W. Nature 1993, 366, 668.
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