J. Phys. Chem. 1902, 86,5205-5208
that Fermi resonance is not important in this case. (D) Deviations from the Birge-Sponer line have been observed for the aromatic high overtones, but these shifts are temperature dependent. The dependence is viewed as evidence against Fermi resonance for the aromatic. The temperature-dependent shift and broadening of the durene bands suggests that some dephasing or exchange process is involved. (E) The analysis of the Birge-Sponer plots gives frequencies and anharmonicities for the in- and out-of-plane methyl bands and for the aromatic band. The frequencies suggest a trend of the bond lengths: r,,, < rin.plane< r,t-of-plane.The computed bond dissociation energies follow the reverse trend. (F) The narrow bandwidths of the methyl modes suggests that the relaxation times of these modes may be long (20.5 ps) compared to previous estimates of CH stretching overtone relaxation times (50.1 ps). These times are perhaps on the order of those needed to enhance reactions
5205
for example of neighboring molecules in matrices, where the collision frequencies are high. (G) The well-resolved bands due to various inequivalent hydrogens (assigned experimentally with polarized light) implies that bond-selective and stereoselective excitation is possible and that laser-induced reaction with such selectivity is feasible, especially at low temperature. (H) Finally, the comparison of the durene results with those of gas-phase CHD3 shows that the effect of the increased density of states of durene is not as expected from the total density, i.e., the coupling involves a restricted density of some form.
Acknowledgment. This work was supported by a grant from the National Science Foundation, No. CHE8112833. We thank Professor G. Rossman of the Department of Geology at the California Institute of Technology for the use of the Cary-17 spectrophotometer. We also thank Professor B. Henry for useful comments and suggestions.
Effective Ionic Radii of NO2- and SCN- Estimated In Terms of the Bottcher Equation and the Lorentz-Lorenz Equation Y. Iwadate, K. Kawamura, Research Laboratory for Nuclear Reactors, Tokyo InstirUte of Technoiogy, Ookayarna, Meguro-ku, Tokyo 152, Japan
K. Igarashl, and J. Mochlnaga' Department of Synthetic Chemistry, Faculty of Englneerlng, Chiba University, Yayoi-cho, Chlba-shi, Chib8 260, J8pm (Received: July 2, 1982: I n Final Form: September 8, 1982)
The electronic polarizabilities of NOL and SCN- ions have been estimated from the refractive index data by use of the Lorentz-Lorenz equation and the Bottcher equation. The effective ionic radii of NOz- and SCNhave been evaluated from the obtained electronic polarizabilities to be 1.77-1.81 A (320 "C) and 2.15-2.20 A (300 "C), respectively, by using the correlation between the third power of the ionic radius and the electronic polarizability of an ion and also taking into account the structure of the ion. It has been concluded that the Bottcher equation does not hold good for molten ionic liquids such as NaNOz and LiSCN in the optical frequency region.
Introduction There exists much current interest in polarization phenomenon of an ion in ionic For estimating the electronic polarizability of an ion, two methods are usually employed such as measurements of the dielectric constant6*'and the refractive i n d e ~ . ~The , ~ latter is of greater advantage than the former in the sense that it is carried out more easily and accurately. For an accurate evaluation of electronic polarizability we have to attain the refractive index at infinite wavelength by extrapolating the indexes obtained at several wavelengths. However, there (1)E,, Karawacki, Ph.D. Thesis, Chalmers Univ. Tech., Goteborg, Sweden, 1977. (2) R. Aronsson and E. Karawacki, 2.Naturjorsch. A, 35,694(1980). (3)Y. Iwadate, K. Kawamura, and J. Mochinaga, J.Phys. Chem., 85, 1947 (1981). (4)Y. Iwadate, J. Mochinaga, and K. Kawamura, J. Phys. Chem., 85, 3708 (1981). ( 5 ) Y. Iwadate, K. Kawamura, K. Murakami, K. Igarashi, and J. Mochinaga, submitted for publication in J. Chem. Phys. (6) C. J. F. Bthtcher, "Theory of Electric Polarization", 2nd ed., Vol. 1, Elsevier, New York, 1973,p 196. (7) C. J. F. Bottcher, Physica, 9,945 (1942). (8)C.J. F.Bottcher, R e d . Trau. Chim. Pays-Bas., 62,325(1943);62, 503 (1943);65,19,91 (1946). (9)H. R.Petty, J. A. Crumb, V. E. Anderson, E. T. Arakawa, and J. K. Baird, J. Phys. Chem., 81,696 (1977). 0022-3654/82/2086-5205$01.25/0
are few data on the refractive indexes of ionic melts available to calculate the electronic polarizability. Based on the definition of polarizability, the Lorentz-Lorenz equation has been used to determine the electronic polarizability of an ion, from which the Bottcher equation has been also derived with some corrections. The Bottcher equation has already been applied to aqueous electrolyte solution^^^^ and organic solvents,1°but not to molten salts with the exception of molten alkali nitrates.' Here we report the electronic polarizabilities and the effective ionic radii of NOz- and SCN- calculated by using (1)the Lorentz-Lorenz equation, (2) the Bottcher equation, and (3) a correlation between the third power of the ionic radius and the electronic polarizability of an ion. We also examine the applicability of the Lorentz-Lorenz equation and the Bottcher equation to molten salts.
Calculation Process As indicated previ~usly,~ the polarizability discussed here is the electronic one, which is reduced to a scalar in the case of molten salts. The electronic polarizability of a molecule (a)is defined by the Clausius-Mossotti equa(10)J. D.Olson and F. H. Horne, J. Chem. Phys., 56, 2321 (1973).
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86,No.
Iwadate et al.
26, 1982
tion analogous to the Lorentz-Lorenz equation, in which the optical dielectric constant is replaced by the refractive index according to the Maxwell relation ~ ( w =) n(o)2
TABLE I: Electronic Polarizability ( 0 1 ) and Effective Radius ( r ) of NaNO, and LiSCN Molecules Estimated from Eq 5
d m ) = [3/(4XN~)l[(n(W)~ - l)/(n(o)2 2)1vm (1)
molecule
where the symbols NA, V,, and o refer to Avogadro's number, the molar volume, and the frequency used, respectively, and also the refractive index n is designated as a function of w. For a substance composed of ions, an alternative expression is introduced on the basis of the additivity for the electronic polarizability (n(mI2- l)/(n(w)2 + 2) = (4~/3)(CNi.i)
NaNO,
w aveleng t 11 / nm 632.8 m
LiSCN
632.8 m
a
~
3.84 3.23 12.21 - 14.90
~
3
rlX 2.84 1.87 -2.22 -1.35
(2)
I
where Ni and cyi are the number of the i-th ion in unit volume and the electronic polarizability of the i-th ion, respectively. However, the refractive index at infinite wavelength n, should be known to obtain the electronic polarizability. Taking into consideration that the refractive index is dependent on both wavelength and temperature (density), one obtains the value of n, by the following which is based on Cauchy's approximation n(h,t) = ( P + Q/X2 + R/X4) + (P, + Qt/X2 + R t / X 4 ) t (3) where h and t are the wavelength in nanometers and the temperature in "C, respectively. The constants P to R, are determined by a least-squares method. With the aid of eq 3, the n, is reduced to P + Ptt and the refractive index and its temperature coefficient at an arbitrary temperature and wavelength are reproducible. Furthermore, in the present calculation the electronic polarizability of a Li' ion is taken as a reference," viz., 0.03 A3. A detailed explanation and the validity of the assumption have been described el~ewhere.~ As shown below, the Bottcher equation is expressed as a function of the dielectric constant e, the density d, the effective molecular radius P, and the molecular electronic polarizability a. Starting with the Onsager approximation to the local field acting on a molecule in the liquid, we have 127rCd -----M M 2e-2 (4) ( E - I)(& 1) NAa NAr3 2~ 1
+
+
Equation 4 can also be converted by the Maxwell relation c = n2 in the optical frequency region 12rn2d M M 2n2-2 ----(5) (n2 - l)(2n2+ 1) N A ~NA1'3 2n2 + 1 The plot 12an2d/[(n2- 1)(2n2+ l ) ] vs. (2n2- 2)/(2n2 + 1) gives information on a and r from the intercept and the slope, respectively, of the straight line ordinarily obtained.
Results and Discussion The refractive index equations used in this work are as follow~,~ which J ~ were obtained with goniometry: NaNOz n = 1.4475 - (1.280 X 10-4)t
( t / " C ) at 632.8 nm
n, = 1.4400 - (1.415 X 10-4)t
(t/"C) at infinite wavelength LiSCN n = 1.6571 - (1.629 X 10-4)t
(t/"C) at 632.8 nm
n, = 1.6086 - (1.019 X lOW4)t ( t / " C ) at infinite wavelength (11)L. Pauling, Proc. R. SOC.London, Ser. A , 114, 181 (1927).
r3/A3 Figure 1. Correlation between the electronic polarizability of an ion (a,)and the ionic radius ( r ) : (a) Mg2+, (b) Li', (c) Ca2+, (d) Y3+, ($ ,'aN (rl K', (9) Rb', (h) Cs', (i) CI-, (i) N O F (k) Br-, (1) SO:-, (m) Dy" , (n) Gd3+, ( 0 )d ' , (p) La3+, (4)Ag', (r) TI , (s) Zn2+,(t) SCN-, (u) NOT.
The density data were taken from the literature.12J3 According to eq 5 and the above empirical equations, the electronic polarizability and the effective radius of a molecule were estimated as listed in Table I. Bottcher's expression was extended successfully to aqueous solutions and organic solvents.g8 Petty et al.9 have reported the electronic polarizability and the ionic radius of a bulky tungstosilicic ion in aqueous solution by converting eq 5 into the differential form. In applying eq 5 to the ions in molten nitrates, Karawacki' found reasonable values for the ionic polarizabilities but the positive slopes required the estimated values for the effective ionic radii to be negative. As shown in Table I, the effective radius of a LiSCN molecule becomes negative and that of a NaNOz molecule varies largely from wavelength to wavelength. In agreement with Karawacki,l it may be concluded that Bottcher's expression remains inapplicable to molten ionic liquids. The inapplicability of Bottcher's expression to molten NaN02and LiSCN may be caused by the fact that the assumed molecular structures are not spherical. Here, we also report the electronic polarizabilities of NO2- and SCN- in molten NaN02 and LiSCN to be 3.24 A3 at 320 "C and 6.10 A3 at 300 "C, respectively, using eq 1 and 2. We have already shown the correlation between the third power of the ionic radius and the electronic polarizability of an ion (see Figure l),which has been confirmed to be applicable to polyatomic ions such as NO3and S042-. When this correlation is applied to the NO2and the SCN-, we find graphically that the electronic polarizabilities of NOz-and SCN- correspond to the effective (12) J. Mochinaga, Y. Sasaki, K. Igarashi, and T. Suda, Nippon Kagaku Kaishi, 947 (1982). (13) Y. Iwadate, I. Okada, and K. Kawamura,J. Chem. Eng. Data, in press.
The Journal of Physical Chemistry, Vol. 86, No. 26, 1982 5207
Effective Ionic Radii of NO2- and SCN-
ionic radii in the ranges 1.77-1.81 8, and 2.15-2.20 A,respectively. The obtained electronic polarizability and the effective ionic radius of NO2- are smaller than those of NO - which have been evaluated to be 4.13 A3 and 1.89-1.94 as described in the previous paper.4 Greenberg and Hallgren14 have reported that the NO, ion as it exists in molten salts may be represented as the configuration of a plane equilateral triangle having the symmetry Dsh with a nitrogen atom in the center. From the measurements of Raman spectra, additional support for the D3hmodel assumed for the NO3- ion in the molten salts was given by Janz and James.15 Current concepts on the bonding and the electron density distribution in the NO3- ion have pointed out that hybridization of one s orbital and two p orbitals makes a N-0 bond which gives a plane triangle structure with a bond angle LO-N-0 = 120’ and that there exist 7r bondings. As for the NO2- ion, Greenberg and Hallgren14 have also predicted that the ion may be represented as an isosceles triangle having CZ0symmetry with an apex angle of 90”. But Fukushima and Suzuki16have determined the intraradical structure of the NO2- ion in molten NaN02 and KN02 by means of a time-of-flight pulsed neutron diffraction experiment. Their results are as follows: the bond lengths of N-0 and 0-0 are 1.261 and 2.178 A for NaN02,and the correspondinglengths for KN02are 1.263 and 2.171 A,respectively. These values lead to 119.4’ for NaN02 and 118.5’ for KN02 as an 0-N-0 bond angle, respectively. This estimation suggests that the NO; possesses sp2hybrid orbitals and it has such an isosceles triangle structure. One can imagine one oxygen being taken away from the NO3- ion, since Fukushima and Suzuki17have already reported the N-0 bond length of the NO, ion to be 1.26 A. It should also be noted that nitrogen possesses a lone pair of electrons. I t could be concluded from the above discussion that the effective ionic radius of the NO2- ion should at least be smaller than that of the NO< ion, which leads to the validity of our estimate. For further interpretation of polarization phenomena and the prediction of the electronic polarizabilities of unknown ions, we have tried in our previous work4 to assign the electronic polarizability of the NO3- ion to constituent species such as oxygen and nitrogen by extending the application of eq 2. The values tentatively assigned to oxygen and nitrogen are 1.4 and 0 A3, respectively. The electronic polarizability of the NO2- ion is, therefore, estimated to be 2.80 A3 in all. However, Ohba et al.’* have presented the deformation-density map of the NO2- ion calculated from the molecular orbital theory, which indicates that the electron cloud of nitrogen is spread largely on the opposite side of oxygen. The polarizability increment 0.44 A3 (=3.24 - 2.80) is thought to arise from the contribution of a lone pair of electrons on nitrogen. An additional remark should be made that the accurate assignment of electronic polarizability to oxygen or nitrogen is quite difficult since the charge distribution of the NOC ion is not always equal to that of the NO3- ion as indicated by Wyatt et al.19 As for the crystal structure of KSCN, K1ug2Ohas found that the unit cell is orthorhombic with linear S-C-N
From the above discussion, it can be concluded that the predominating structure is designated as -S-C=N in molten salts, which characterizes the dimension of the ion. The results on the bond lengths so far reported are tabulated in Table 11. Here we employ the neutron diffraction data taking into account the accuracy of the data. Pauling’s covalent bond lengths25are determined to be 0.77 A for C with single bond, 0.60 A for C with triple bond, and 0.55 A for N with triple bond. For S with single bond the value 1.04 A is assigned but this cannot be used because sulfur has a charge of 1- which will spread the electron cloud of S to the opposite side of a C-N group. If sulfur has an ionic character, it will be treated hypothetically as an ion with a charge of 1-. Shannon26has given for the ionic radii of sulfur the following: S2-, 1.84 A; S4+,0.37 A; and S6+,0.12 A. Since the ionic radius of sulfur is thought to be a function of its oxidation state, we fitted the radius ( r ) and the oxidation state ( x ) to the function r = A exp(Bx). A and B were estimated by a least-squares method to be 1.030 and -0.324, respectively. From this equation, the radius of S1- is evaluated to be 1.42 A. According to the above tentative calculation, the SCN- ion is regarded as a cylinder 1.42 A in radius and 4.77 A in height. The volume of the cylinder is 30.22 A3, which corresponds to that of a sphere with an effective radius of 1.93 A. This value may be underestimated since the extent of orbital
(14)J. Greenberg and L. J. Hallgren, J. Chem. Phys., 33,900(1960). (15)G. J. Janz and D. W. James, J. Chem. Phys., 35, 739 (1961). (16)Y.Fukushima and K. Suzuki, Res. Rep. Lab. Nucl. Sci., Tohoku Uniu., 9,103 (1976). (17)Y. Fukushima and K. Suzuki, Res. Rep. Lab. Nucl. Sci., Tohoku Uniu., 8,288 (1975). (18)S. Ohba, K. Toriumi, S. Sato, and Y. Saito, Acta Crystallogr., Sect. B, 34,3535 (1978). (19)J. F. Wyatt, I. H. Hillier, V. R. Saunders, J. A. Connor, and M. Barber, J. Chem. Phys., 54, 5311 (1971). (20)H. P.Klug, 2. Kristallogr., 85, 214 (1933).
(21)L. H.Jones, J. Chem. Phys., 25, 1069 (1956). (22)C. B. Baddiel and G. J. Janz, Trans. Faraday SOC.,60, 2009 (1964). (23)L.D.Sipio, L. Oleari, and G. D. Michelis, Coord. Chem. Reu., 1, 7 (1966). (24)H.Ohno, M. Sakamoto, H. Motohashi, K. Furukawa, K. Igarashi, and J. Mochinaga, “Proceeding of the 15th Symposium on Molten Salt Chemistry, Osaka, Nov 10-11, 1981“,p 51. (25)L. Pauling, “The Nature of the Chemical Bond”, 3rd ed., Cornell University Press, Ithaca, NY, 1960,pp 224,228. (26)R.D.Shannon, Acta Crystallogr., Sect. A , 32, 751 (1976).
1
TABLE 11: Bond Lengths of C - N . C-S. and N-S species
i C C N
rijlA
j
X-raya
NDa,b
IRC
Ramand
N S S
1.13
1.15 1.65
1.17
1.61
2.80
2.78
1.18 1.59 2.77
1.67 2.80
a Reference 24. N D : neutron diffraction. ence 21. Reference 22.
Refer-
groups lying in parallel planes, and in each plane the linear S-C-N groups are perpendicular to neighboring S-C-N groups. This suggests that the S-C-N groups are oriented in any direction after melting, which makes estimating an effective ionic radius worthwhile. On the basis of Badger’s rule and the infrared spectra of aqueous and solid KSCN, Jones21has proposed that the SCN- ion possesses three resonating structures as follows: N=C-S- (71%), -N= C = S (12%),-2N-C=”+ (17%). Baddiel and have reported that the Raman spectral data are consistent with a C,, poinbgroup symmetry for the SCN- ion and that the linear form -S-C=N, whose triple-bond character is enhanced in the case of LiSCN to stabilize the -S-C=N structure itself, is predominant in ionic melts. Sipio et al.23 have calculated the charge distribution in the ion from the obtained molecular orbitals and found q s = -0.48
qc = -0.01
qN = -0.51
which is in good agreement with the values obtained from the resonance structure given by Jones21 4s = -0.54
qc = 0.00
qN = -0.46
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J. Phys. Chem. 1982, 86, 5208-5219
electrons is not taken into consideration, and individual species such as S, C, and N are assumed to be rigid. Accordingly, the real effective ionic radius is expected to be larger than 1.93 A. Jindal and HarringtonZ7have already pointed out that the effective ionic radii of NO< and SCNare calculated to be 1.60 and 1.86 A, respectively, and (27) H. R. Jindal and G . W. Harrington, J. Phys. Chem., 71, 1688 (1967).
concluded that these values are small compared with the published data (see the literature4 where the ionic radii so far reported are summarized). Therefore, our value 2.15-2.20 A evaluated as the effective ionic radius of SCNis thought to be reasonable. The above discussion implies that the electronic polarizability of an ion can be used to estimate the effective ionic radius. Further investigation, a md%” orbital study, is necessary to clarify the true nature of electronic polarization.
Cross-Polarization/Magic-Angle-Spinning Silicon-29 Nuclear Magnetlc Resonance Study of Silica Gel Using Trimethylsilane Bonding as a Probe of Surface Geometry and Reactivity Dean W. Slndorf and Gary E. Maciel’ Department of Chemistty, Colorado State University, Fort Collins, Colorado 80523 (Received: August 2, 1982)
29SiNMR experiments, using cross polarization (CP) and magic-angle spinning (MAS), were carried out on a variety of silica gels and the products of their trimethylsilylation reactions with the silylating agent, hexamethyldisilazane (HMDS). A methodology has been developed to provide quantitative relationships on structure and reactivity from the 29SiCP/MAS spectra. Geminal-hydroxyl silanol sites were found to be more reactive to HMDS than lone-hydroxyl silanol sites. Measured surface hydroxyl densities and trimethylsilane coverages are discussed in terms of structural models.
Introduction Previous reports have demonstrated the potential of ?3i NMR techniques, using cross polarization (CP) and magic-angle spinning (MAS) in the study of the surface chemistry of silica The 29SiCP/MAS approach has characterized surface silicon atoms of the (=SiO),Si(OH)2,(=SiO),SiOH, and (=SiO)4Si types on unreacted silica gels1t2and attached silane silicons of the -0-Si*-R type in silylated ~ilicas.~A Relaxation studies1p2have shown that the resonances of those silicons to which hydroxyl groups are directly attached are suitable for quantitative interpretations. The fact that the CP process discriminates against 29Sinuclei far removed from protons renders %i CP/MAS NMR essentially a surface technique for these systems. Representative 29SiCP/MAS spectra of a silica gel and its trimethylsilyl (TRMS) derivative are shown in Figure 1, A and B, respectively. In Figure 1B the sharp resonance at 15 ppm can be assigned unambiguously to the directly attached trimethylsiloxyl species indicated by d in the figure diagram. (The diagrams in Figure 1 are intended to illustrate the applicable silicon chemical environment, not specific structural configurations.) Single-hydroxyl silanol centers (b of Figure 1A) that undergo the silylation reaction are converted into species containing four siloxane bonds (a’ of Figure 1B). Since previous work1v5v6has shown (1) G. E. Maciel and D. W. Sindorf, J. Am. Chem. SOC.,102, 7607 (1980). (2) D. W. Sindorf, Ph.D. Dissertation, Colorado State University, June 1982. (3) G. E. Maciel, D. W. Sindorf, and V. J. Bartuska, J. Chronatogr., 205, 438 (1981). (4) D. W . Sindorf and G. E. Maciel, J . Am. Chem. SOC.,103, 4263 (1981).
(5) H. C. Marsmann, 2. Naturforsch. B , 29,495 (1974).
0022-3654/82/2086-5208$0 1.25/0
that the substitution of a siloxane bond for a hydroxyl group at the silicon environment will be accompanied by a -9- to -10-ppm 29Sichemical shift, this process should result in a buildup of intensity a -109 ppm in the 29Si spectrum and a decrease in intensity at -100 ppm. Similarly, reaction of a single hydroxyl group on geminalhydroxyl silanol sites (c of Figure 1A) converts such species into sites that contain three siloxane bonds and one hydroxyl (b’ of Figure 1B) and should result in a redistribution of spectral intensity from -91 to -100 ppm. Both of these expectations are qualitatively consistent with changes evident in the “silica” region (-80 to -120 ppm) of the spectra of Figure 1. These simple relationships suggest that a more rigorous analysis of 29SiNMR intensities obtained for reacted and unreacted silica samples may allow for quantitative studies of normal and silylated silica surfaces. The methodology necessary for such investigations is developed in this paper, which is concerned with the reactivities of surface silanol sites of silica gels with the trimethylsilylating agent hexamethyldisilazane (HMDS). Experimental Section N M R Measurements. Solid-state 29SiNMR spectra were obtained at 11.88 MHz on a prototype JEOL FX6OQS NMR spectrometer and at 39.75 MHz on a modified Nicolet NT-200 spectrometer. Details of these spectrometer systems are described elsewhere.2 Magic-angle sample spinning was routinely carried out at 2.0-2.3-KHz spinning rates on the FX-6OQS spectrometer and at 3.5-4.0 KHz on the NT-200, using bullet-type Kel-f or Delrin rotors containing 0.5 cm3 of sample. (6) R: K. Harris and B. E. Mann, ‘NMR and the Periodic Table”, Academic Press, New York, 1978.
0 1982 American Chemical Society
