Local Structure around Chloride Ion in Anion Exchange Resin

11337

2007, 111, 11337-11341 Published on Web 09/08/2007

Local Structure around Chloride Ion in Anion Exchange Resin Koji Yamanaka,*,† Yasuo Kameda,‡ Yuko Amo,‡ and Takeshi Usuki‡ R&D Center, Organo Corporation, Kawagishi 1-4-9, Toda, Saitama, 335-0015, Japan, and Department of Material and Biological Chemistry, Faculty of Science, Yamagata UniVersity, Kojirakawa-machi 1-4-12, Yamagata 990-8560, Japan ReceiVed: June 21, 2007; In Final Form: August 28, 2007

Neutron diffraction measurements on 35Cl/37Cl isotopically substituted anion exchange resins were carried out in order to obtain direct information on the local structure around the chloride ion absorbed in the resin. Structural parameters concerning the first nearest-neighbor interaction of chloride ions were determined through a least-squares fitting procedure of the observed first-order difference function, ∆Cl(Q). It has been revealed that the chloride ion is neighboring an ion exchange group (-CH2(CH3)3N+) with a Cl-‚‚‚N distance of 3.10(3) Å, and simultaneously bonded with 2.4(1) D2O molecules with a Cl-‚‚‚D distance of 2.25(2) Å. The second and third nearest water molecules around Cl- have also been observed. These results indicate that the direct ionic interaction between Cl- and -CH2(CH3)3N+ drastically reduces the number of first-neighbor water molecules around Cl- but enhances the long-distance structuring of the remaining water molecules in the environment surrounded by a hydrophobic polymer matrix.

Introduction Ion exchange resins have wide application in numerous fields of fundamental sciences and industries.1,2 However, detailed structural information concerning ion exchange mechanisms at the microscopic level is not available yet except for a few cases. The hydration structure of Ni2+ and Li+ in divinylbenzene crosslinked poly(stylene/sulfonate) cation exchange resins has been investigated by neutron diffraction with the isotopic substitution method.3 A decrease in the number of water molecules in the first hydration shell of Ni2+ has been reported that suggests a strong interaction between Ni2+ and the sulfonic group in the cation exchange resin.3 Recently, the hydrogen-bonded network within cation and anion exchange resins was examined by means of neutron diffraction with the H/D isotopic substitution technique.4 In the anion exchange resin, the hydrogen-bonded network among water molecules was found to be wellmaintained as in liquid water.4 Alternatively, the hydrogenbonded structure is revealed to be significantly modified in the cation exchange resin. The strong interaction between water molecules and the sulfonic group of the ion exchange resin was suggested.4 The local structures of Cl- and Br- in the anion exchange resins have also been examined by XAFS.5-7 The maximum number of water molecules neighboring Cl- and Brhave been reported to be 3.9(4) and 3.4(5), respectively, when they are bound to the ion exchange group.5 The nearest-neighbor Cl-‚‚‚C (or N) distance and coordination number in the dried resin were determined to be 3.27 and 4.52 Å, respectively.7 The result is consistent with the local configuration in which the * To whom correspondence should be addressed. E-mail: [email protected]. Fax: +81-48-441-7765. † Organo Corporation. ‡ Yamagata University.

10.1021/jp074862z CCC: $37.00

Cl- is present in the tripod consisting of three methyl groups of the ion exchange group.7 However, details of intermolecular Cl-‚‚‚water distance and coordination number have not been obtained because of difficulties in separating contributions from the halide ion-water molecule and halide ion-ion exchange group.7 Neutron diffraction with 35Cl/37Cl isotopic substitution is considered to be one of the most suitable experimental techniques that provides direct information on the local structure around Cl-, that is, orientational correlation of hydrated water molecules. In the present letter, we describe the results of neutron diffraction measurements for 35Cl/37Cl substituted anion exchange resins equilibrated with D2O. Information on the local structure of the chloride ion has been obtained from the firstorder difference function, ∆Cl(Q), and its Fourier transform, GCl(r). Structural parameters for the nearest-neighbor Cl-‚‚‚water and Cl-‚‚‚ion exchange group have been determined through a least-squares fitting analysis of the observed ∆Cl(Q). Experimental Section Materials. Anion exchange resin (AER, AMBERLITE IRA402BL, OH- form, divinylbenzene cross-linked poly(stylene/trimethylammonium hydroxide)) was packed in a column and washed by pure water, then converted into the HCO3- form by treating with aqueous 1 M NH4HCO3 (Kanto Chemical Co. Inc., guaranteed grade) solution to remove Cl-, which may remain as a contaminant in the OH- form resin, and then followed by washing with pure water. The AER was again converted to the OH- form by passing aqueous 1 M NaOH (Kanto Chemical Co. Inc., guaranteed grade) solution through the column followed by a pure water rinse. Deuteration of exchangeable hydrogen atoms within the AER was carried out © 2007 American Chemical Society

11338 J. Phys. Chem. B, Vol. 111, No. 39, 2007

Letters

TABLE 1: Isotopic Composition, Mean Scattering Length, bCl, of the Chloride Ion, Total Cross Section, and Number Density of Samples in the Stoichiometric Unit, (AER-*Cl)0.0679(D2O)0.9321, σt, and G, Respectively sample I (AER-35Cl)0.0679(D2O)0.9321 II (AER-natCl)0.0679(D2O)0.9321 a

35

Cl/%

99.0 24.2

37

Cl/%

1.0 75.8

bCl/10-12cm

σt/barnsa

F /Å-3

1.1563 0.9577

61.019 60.365

0.01877

For incident neutron wavelength of 1.092 Å.

by batch procedures. The obtained OH- form resin was soaked into more than 10 times the molar quantities of D2O (99.9% D, Kanto Chemical Co. Inc.) with respect to that of the water molecules swelling the resin. After equilibration for 24 h, extraneous heavy water outside the resin was then removed by decantation and filtration under dried air to prevent to exposure of the resin to the moisture of natural H2O in atmospheric air. This procedure was repeated 3 times. AER samples of the Clform with different 35Cl/37Cl isotopic ratios were prepared by column processes; that is, the resin in OD- form was treated with aqueous 1 M Na35Cl (99.0% 35Cl, Cambridge Isotope Laboratories, Inc.) and NanatCl (natCl, 75.8% 35Cl, natural abundance, Kanto Chemical Co. Inc., guaranteed grade) in D2O (99.9% D, Kanto Chemical Co. Inc.), followed by washing with D2O. The AER samples of the Cl- form were finally equilibrated with D2O saturated air to obtain samples I (AER-35Cl)0.0679(D2O)0.9321 and II (AER-natCl)0.0679(D2O)0.9321 and used for neutron diffraction measurements. The D2O contents in samples I and II were adjusted carefully to obtain a complete cancellation of partial structure factors that do not involve the Cl- contribution in deriving the difference function. The molar ratios of D2O to Cl- were confirmed to be the same, 13.7, by weight reduction during vacuum-dry at 40 °C for 10 h. The resin beads were sealed into a cylindrical fused quartz cell (12.0 mm in inner diameter and 1.1 mm in wall thickness). The sample parameters used in the present study are listed in Table 1. Neutron Diffraction Measurements. Neutron diffraction measurements were carried out at 25 °C using an ISSP diffractometer 4G (GPTAS) installed at the JRR-3M research reactor operated at 20 MW in the Japan Atomic Energy Agency (JAEA), Tokai, Japan. The incident neutron wavelength, λ ) 1.092(3) Å, was determined by Bragg reflections from the KCl powder. Beam collimations were 40′-80′-80′ in going from the reactor to the detector. The aperture of the collimated beam was 20 mm in width and 40 mm in height. Scattered neutrons were collected over the angular range 3 e 2θ e 118°, corresponding to a scattering vector magnitude range of 0.30 e Q e 9.86 Å-1 (Q ) 4π sin θ/λ). The step intervals were chosen to be ∆2θ ) 0.5° in the range 3 e 2θ e 40° and ∆2θ ) 1° in the range 41 e 2θ e 118°, respectively. The preset time was 410 s for each data point. The total number of observed counts was in the range of 1.1 × 106 to 1.8 × 106, corresponding to the statistical uncertainty below 0.1%. Scattering intensities were measured for the empty cell, vanadium rod of 10 mm in diameter, and instrumental background. Data Reduction. Observed scattering intensities from the sample were corrected for instrumental background, absorption,8 and multiple scattering.9 The observed count rate for the sample was converted to absolute scale by using corrected scattering intensities from the vanadium rod. Details of the data correction and normalization procedures have been described in previous papers.4,10,11 The first-order difference function,12-14 ∆Cl(Q) was obtained as the numerical difference between normalized scattering cross

TABLE 2: Values of the Coefficients of aij(Q) in Equation 1 A/barns

B/barns

C/barns

D/barns

E/barns

F/barns

0.0128

0.0295

-0.0103

0.0126

0.0013

0.0015

section from samples I and II, which are identical except for the isotopic composition of the chloride ion

∆Cl(Q) ) A[aClO(Q) - 1] + B[aClD(Q) - 1] + C[aClH(Q) - 1] + D[aClC(Q) - 1] + E[aClN(Q) - 1] + F[aClCl(Q) - 1] (1) where

A ) 2cClcO(b35Cl - bnatCl)bO B ) 2cClcD(b35Cl - bnatCl)bD C ) 2cClcH(b35Cl - bnatCl)bH D ) 2cClcC(b35Cl - bnatCl)bC E ) 2cClcN(b35Cl - bnatCl)bN and

F ) cCl2(b35Cl2 - bnatCl2) Weighting factors A-F in eq 1 are numerically listed in Table 2. The distribution function, GCl(r), describing the local structure around the chloride ion is obtained by the Fourier transform of the observed ∆Cl(Q)

GCl(r) ) 1 + (A + B + C + D + E + F)-1 (2π2Fr)-1

∫0Q

max

Q∆Cl(Q) sin(Qr) dQ ) [AgClO(r) +

BgClD(r) + CgClH(r) + DgClC(r) + EgClN(r) + FgClCl(r)] × (A + B + C + D + E + F)-1 (2) The upper limit of the integral, Qmax, was set to 9.86 Å-1. Structural parameters concerning the first hydration shell of the chloride ion were determined through a least-squares fitting procedure for the observed ∆Cl(Q), employing the model function, ∆Clcalc(Q), involving both the short- and long-range contributions15-17

∆Clcalc(Q) ) Σ 2cClnClR(b35Cl - bnatCl)bR exp(-lClR2Q2/2) sin(QrClR)/(QrClR) + 4πF (A + B + C + D + E + F) exp(-l02Q2/2)[Qr0 cos(Qr0) - sin(Qr0)]Q-3 (3) where, nClR denotes the coordination number of the R atom around the chloride ion. Parameters lClR and rClR are the rootmean-square amplitude and internuclear distance for the Cl-R pair, respectively. The long-range parameter, r0, corresponds to the distance beyond which a continuous distribution of atoms

Letters

J. Phys. Chem. B, Vol. 111, No. 39, 2007 11339

Figure 2. (a) Difference function, ∆Cl(Q), observed for heavy water equilibrated anion exchange resin (dots). The best-fit of the calculated ∆Clcalc(Q) is shown by a solid line. (b) Residual functions (dot).

Figure 1. Scattering cross section, (dσ/dΩ)obs, observed for the heavy water equilibrated anion exchange resins involving 35Cl (99.0% 35Cl) and natCl (75.8% 35Cl, natural abundance). The first-order difference function ∆Cl(Q) is indicated below.

around the chloride ion can be assumed. The parameter l0 describes the sharpness of the boundary at r0. Structural parameters, nClR, lClR, rClR, r0, and l0, are determined from the least-squares fit to the observed ∆Cl(Q). In the present analysis, the fitting procedure was performed in the range of 0.80 e Q e 9.86 Å-1 with the SALS program,18 assuming that statistical uncertainties distribute uniformly. Results and Discussion Observed scattering cross sections, (dσ/dΩ)obs, for AER samples with different 35Cl/37Cl isotopic ratios, are shown in Figure 1. The decrease in (dσ/dΩ)obs in the higher-Q region is due to the inelasticity effect arising mainly from hydrogen atoms involved in the resin. The overall features of (dσ/dΩ)obs for two samples look very similar because of the smaller contribution of Cl-‚‚‚j interactions. However, the first-order difference function ∆Cl(Q) derived from present scattering cross sections indicates an oscillational feature that is expected to involve information on the local structure around Cl-. A sharp rise below 0.4 Å-1 in ∆Cl(Q) can be caused by increasing uncertainty at lower scattering angles in background subtraction procedure or may arise from small-angle scattering given by confinement effects on water molecules and Cl- ions restricted in spaces surrounded by a three-dimensional cross-linked polymer network. In the Fourier transforming procedure, ∆Cl(Q) values in this region of Q dominantly influence quite long distances, r > 16 Å, in GCl(r). Therefore, in the present least-squares fitting procedure we have employed a Q range of 0.80 e Q e 9.86 Å-1 and discussed the local structure around Cl- within ca. 6 Å. Small-angle scattering experiments should reveal long distance information, such as nanoscale agglomerations of water molecules around ions, and complement interpretation of the rise in ∆Cl(Q) in low-Q region. Distribution function around Cl-, GCl(r), was obtained from the Fourier transform of ∆Cl(Q). In the preliminary analysis, it was found that unphysical ripples appearing in the GCl(r) were

Figure 3. Distribution function, GCl(r), around the chloride ion in the anion exchange resin (solid line). Fourier transform of the calculated ∆Clcalc(Q) is shown by a thick broken line. The contributions from the short- and long-range interactions are denoted by thin-broken and thindotted lines, respectively.

much reduced by applying a moving average procedure to the observed ∆Cl(Q). The number of the data points adopted in the data-averaging procedure was decided carefully considering the following criteria. (a) Oscillatory features involved in the observed ∆Cl(Q) should not be smeared. This was confirmed by the sharpness of the short-range peaks appearing in the transformed GCl(r). (b) Unphysical ripples in GCl(r) are suppressed sufficiently. In the present analysis, a three-point moving average was adopted for the observed ∆Cl(Q) and used for the subsequent analysis. The averaged difference function, ∆Cl(Q), and distribution function around the chloride ion, GCl(r), are represented in Figures 2 and 3, respectively. The present GCl(r) is characterized by a well-resolved first peak at r ) 2.15 Å and a second peak appearing at r ) 3.8 Å. The position of this first peak is in good agreement with the nearest-neighbor Cl-‚‚‚D(D2O) distance that has been reported for various aqueous solutions,12,19-22 implying that the chloride ion in the anion exchange resin has a stable hydration shell. In the preliminary analysis, the Cl‚‚‚D coordination number was estimated to be 1.7 from the integrated value of the present GCl(r) in the range of 1.4 e r e 2.7 Å. This coordination number is considerably smaller than that expected for the completely hydrated Cl- in the aqueous solution (nCl‚‚‚D ≈ 6),12,19-22 which suggests that the first coordination

11340 J. Phys. Chem. B, Vol. 111, No. 39, 2007 shell of the Cl- in the AER certainly involves both interactions between Cl- and the nearest-neighbor D2O, and Cl- and the ion exchange group of the AER, -CH2(CH3)3N+. Because the H atom in the methyl group of the ion exchange group has a negative scattering length, the nearest-neighbor Cl-‚‚‚H(CH3) interaction must contribute as a negative peak in the present GCl(r). A small negative peak appearing at r ∼ 1 Å in GCl(r) cannot be attributable to any intermolecular interaction between Cl- and the other atoms. The peak position of this peak is close to that for the intramolecular O-D distance within the D2O molecule and that for the covalently bonded C-H distance within the resin. This peak might have arisen from incomplete cancellation of the O-D and C-H contributions between the two samples; however, the very small integrated intensity of this negative peak indicates the validity of data correction and normalization procedures employed in the present analysis. To obtain structural parameters for the nearest-neighbor coordination shell around the Cl-, we applied a least-squares refinement procedure to the observed ∆Cl(Q). In the fitting procedure, the following assumptions were adopted in evaluating the model function in eq 3. (a) Parameters for the first nearestneighbor Cl-‚‚‚D2O interaction, rCl‚‚‚D, lCl‚‚‚D, nCl‚‚‚D, the tilt angle R between the Cl-‚‚‚DW1 axis and the DW1-OW bond (DW and OW denote the water deuterium and water oxygen atoms, respectively), and the dihedral angle β between the plane involving the Cl-‚‚‚DW1-OW atoms and the molecular plane of the D2O, were treated as independent parameters. The geometry of the D2O molecule was fixed to that reported for liquid heavy water (rOD ) 0.983 Å, rDD ) 1.55 Å).23,24 (b) Structural parameters for the nearest-neighbor Cl-‚‚‚-CH2(CH3)3N+ interaction, rCl‚‚‚N, lCl‚‚‚N, nCl‚‚‚N, were refined independently. To take into account all of the possible configurations between Cl- and -CH2(CH3)3N+, we also independently refined the bond angle γ (∠Cl-‚‚‚N-C(methylene)) and the dihedral angle δ between the plane involving Cl-‚‚‚N-C(methylene) atoms and the plane formed by Cl-‚‚‚N-C(methyl) atoms. Intramolecular parameters for the -CH2(CH3)3N+ group were taken from the literature values for the tetramethylammonium ion determined from single-crystal X-ray diffraction studies.25-27 In the present fitting procedure, interactions between Cl- and atoms within the methylene group binding with the ion exchange group were also included in evaluating the model function. (c) The second and third nearest-neighbor Cl-‚‚‚D2O interactions were taken into account in the model function in which each contribution was treated as a single interaction with the coherent scattering length in eq 3, bR, being 2bD + bO. (d) Structural parameters for long-range random distribution of atoms, l0 and r0, were allowed to vary independently. The results of the least-squares fit for the observed ∆Cl(Q) are shown in Figure 2a. Satisfactory agreement was obtained between observed and calculated ∆Cl(Q) functions. The Fourier transform of the calculated ∆Clcalc(Q) was also in good agreement with the observed GCl(r) as represented in Figure 3. Final values of all independent parameters are listed in Table 3. The value of the nearest-neighbor Cl-‚‚‚DW1 distance (2.25(2) Å) and the tilt angle R (5(12)°) are in excellent agreement with those reported for the hydrated chloride ion determined by neutron diffraction studies with the 35Cl/37Cl isotopic substitution method (rCl‚‚‚DW1 ) 2.22 ∼ 2.29 Å, R ) 0 ∼ 10°),12,19-22 which confirms the stable hydration shell around Cl- in the AER. Alternatively, a small value of the hydration number for the first hydration shell around Cl- (nCl‚‚‚DW1 ) 2.4(1)) indicates partial dehydration caused by a strong ionic interaction between Cl- and the ion exchange group, -CH2(CH3)3N+. Negative

Letters TABLE 3: Results of the Least-Squares Refinement for the ∆Cl(Q) Observed for the Anion Exchange Resina interaction

rCl‚‚‚j/Å

lCl‚‚‚j/Å

nCl‚‚‚j

0.25(8) β ) 0(20)° c 0.40(6) δ ) -2(10)° e 0.4(1) 0.5(1)

2.4(1)

Cl-‚‚‚D2O(II) Cl-‚‚‚D2O(III)

2.25(2) R ) 5(12)° b 3.10(3) γ ) 179(2)° d 4.05(5) 5.15(5)

long-range

r0/Å 5.2(3)

l0/Å 1.3(1)

Cl-‚‚‚DW1 Cl-‚‚‚N

1.0(3) 4.0(7) 3.5(5)

a Estimated errors are given in parentheses. b Tilt angle between the Cl-‚‚‚DW1 and DW1-OW axes. c Dihedral angle between the plane involving Cl-‚‚‚DW1-OW atoms and the molecular plane of D2O. d Angle ∠Cl-‚‚‚N-C(methylene). e Dihedral angle between the plane involving Cl-‚‚‚N-C(methylene) atoms and the plane formed by Cl-‚‚‚N-C(methyl) atoms.

contribution in GCl(r) arising from the Cl-‚‚‚H(CH3) interaction was taken into account in eq 3 in the refining procedure. Fourier transform of optimized ∆Clcalc(Q) reproduces the observed GCl(r) well and supports the ascriptions of these interactions around Cl-. The present values of the angle γ ) 179(2)°, between Cl-‚‚‚N and N‚‚‚C(methylene) axes, and the coordination number nCl‚‚‚N ) 1.0(3), indicate that the Cl- is bound within almost the center of the tripod formed by three methyl groups of an ion exchange group, which is compatible with the result obtained by XAFS measurement on dried resin.7 The present nearest-neighbor Cl-‚‚‚N distance (3.10(3) Å) is slightly shorter than the sum of ionic radius of the Cl- (1.67 Å)28 and the van der Waals radius of the nitrogen atom (1.55 Å),29 which also suggests that strong intermolecular interactions are present between Cl- and ion exchange groups. The second and third nearest-neighbor water molecules were found to be located at r ) 4.05(5) and 5.15(5) Å, respectively. This second nearestneighbor water molecules are considered to form hydrogen bonds with water molecules in the first hydration shell of the Cl-. In the hydrated anion exchange resin, Cl- might then have a more structured hydration shell system than that in aqueous solution, in which the Cl- has a stable first hydration shell but no indication beyond the second hydration shell. Acknowledgment. We thank the Institute of Solid-State Physics (ISSP), the University of Tokyo, for allowing us to use the 4G(GPTAS) diffractometer. We are grateful to Prof. Taku J. Sato (ISSP, the University of Tokyo) for his help during the course of neutron diffraction measurements. We acknowledge Prof. Hideki Yoshizawa (ISSP, the University of Tokyo) and Mr. Yoshihisa Kawamura (ISSP, the University of Tokyo) for their stimulated discussion and encouragement. All calculations were carried out in the Yamagata University Networking and Computing Center. This work was partially supported by Grantin-Aid for Scientific Research (C) (no. 16550049), Scientific Research on Priority Areas (no. 1641205), and Creative Scientific Research (no. 16GS0417), from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References and Notes (1) Ion Exchange Technology; Naden, D., Streat, M., Eds.; Ellis Horwood Limited: West Sussex, England, 1984. (2) Ion Exchange for Industry; Streat, M., Ed.; Ellis Horwood Limited: West Sussex, England, 1988. (3) Tromp, R. H.; Neilson, G. W. J. Phys. Chem. 1996, 100, 7380. (4) Kameda, Y.; Yamanaka, K.; Sasaki, M.; Amo, Y.; Usuki, T. Bull. Chem. Soc. Jpn. 2006, 79, 1032. (5) Okada, T.; Harada, M. Anal. Chem. 2004, 76, 4564.

Letters (6) Harada, M.; Okada, T.; Watanabe, I. J. Phys. Chem. B 2002, 106, 34. (7) Harada, M.; Okada, T. J. Chromatogr., A 2005, 1085, 3. (8) Paalman, H. H.; Pings, C. J. J. Appl. Phys. 1962, 33, 2635. (9) Blech, I. A.; Averbach, B. L. Phys. ReV. 1965, 137, A1113. (10) Kameda, Y.; Uemura, O. Bull. Chem. Soc. Jpn. 1993, 66, 384. (11) Kameda, Y.; Usuki, T.; Uemura, O. Bull. Chem. Soc. Jpn. 1998, 71, 1305. (12) Soper, A. K.; Neilson, G. W.; Enderby, J. E.; Howe, R. A. J. Phys. C: Solid State Phys. 1977, 10, 1793. (13) Enderby, J. E.; Neilson, G. W. Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1979; Vol. 6, p 1. (14) Enderby, J. E. Chem. Soc. ReV. 1995, 24, 159. (15) Narten, A. H.; Danford, M. D.; Levy, H. A. Discuss. Faraday Soc. 1967, 43, 97. (16) Caminiti, R.; Cucca, P.; Monduzzi, M.; Saba, G.; Crisponi, G. J. Chem. Phys. 1984, 81, 543. (17) Ohtaki, H.; Fukushima, N. J. Solution Chem. 1992, 21, 23.

J. Phys. Chem. B, Vol. 111, No. 39, 2007 11341 (18) Nakagawa, T.; Oyanagi, Y. Recent DeVelopments in Statistical Inference and Data Analysis; North-Holland: Amsterdam, 1980; p 221. (19) Enderby, J. E.; Cummings, S.; Herdman, G. J.; Neilson, G. W.; Salmon, P. S.; Skipper, N. J. Phys. Chem. 1987, 91, 5851. (20) Powell, D. H.; Barnes, A. C.; Enderby, J. E.; Neilson, G. W. Faraday Discuss. Chem. Soc. 1988, 85, 137. (21) Powell, D. H.; Neilson, G. W.; Enderby, J. E. J. Phys.: Condens. Matter 1993, 5, 5723. (22) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93, 1157. (23) Powles, J. G. Mol. Phys. 1981, 42, 755. (24) Kameda, Y.; Uemura, O. Bull. Chem. Soc. Jpn. 1992, 65, 2021. (25) Yukawa, Y.; Igarashi, S.; Masuda, Y.; Oguni, M. J. Mol. Struct. 2002, 605, 277. (26) Trombe, J. C.; Mohanu, A. Solid State Sci. 2004, 6, 1403. (27) Yang, X. Mater. Res. Bull. 2006, 41, 54. (28) Shannon, R. D. Acta Crystallogr. 1976, A32, 751. (29) Bondi, A. J. Phys. Chem. 1964, 68, 441.