J . Phys. Chem. 1988, 92, 2013-2015
2013
Vapor-Phase Cotton-Mouton Effects of Methane, Methyl Chloride, Chloroform, and Carbon Tetrachloride Philip B. Lukins'" and Geoffrey L. D. Ritchie*Ib School of Chemistry, University of Sydney, New South Wales 2006, Australia, and Department of Chemistry, University of New England, New South Wales 2351, Australia (Received: August 12, 1987)
Measurements of the vapor-phase Cotton-Mouton effects of methane, methyl chloride, chloroform, and carbon tetrachloride over a range of temperature and pressure are reported. Analysis of the results shows that the magnetic hyperpolarizability anisotropy (lOS0Aq/C m2 V-' T2) is positive in sign for all four molecules and tends, overall, to increase in magnitude as the number of chlorine substituents increases (CHI, 11.3 & 1.5; CH3CI, 47 & 33; CHC13, 150 f 70; CC14,75 i 23). Reliable values of the magnetic anisotropies (1029Ax/J T-2) of methyl chloride and chloroform are obtained (CH3C1, -15.0 f 1.3; CHCl,, 22.7 f 1.9), and these, in combination with the known mean magnetizabilities, yield the individual components of the molecular magnetizability tensors.
Introduction The phenomenon of magnetic-field-induced birefringence (the Cotton-Mouton effect) is of considerable importance as a route to magnetic anisotropies and other electric and magnetic properties of molecules. In previously reported studies of the temperature dependence of the effect in gases and vapors we have shown that for strongly anisotropic molecules (for example, benzene and substituted benzenes2)the magnetic hyperpolarizability anisotropy, Aq, which arises from distortion of the electronic structure by the magnetic field, makes only a very small contribution at normal temperatures. On the other hand, evidence for weakly anisotropic molecules (for example, cyclopropane3 and sulfur dioxide4) indicates that the contribution from this source may be significant and that it must be taken into account in order to derive reliable magnetic anisotropies, Ax, for such molecules. In order to further elucidate the nature and importance of Aq we have now extended the investigation to the series methane, methyl chloride, chloroform, and carbon tetrachloride. Analyses of the vapor-phase Cotton-Mouton effects of these molecules have allowed us to quantify the contribution made by Aq and also to derive reliable values of Ax for the two anisotropically polarizable species. Theory Relevant theory has already been summarized; symbols and other details not explicitly mentioned here are as in the earlier
report^.^-^ The low-density molar Cotton-Mouton constant C , of a diamagnetic and axially symmetric species is, in SI units5 C , = 2 n V , ~ ~ [ 3 ( n+~2)2]-'[(nll - n,)B2],,,
(la)
where eq l a is a measure of the refractive index difference nIln,, induced in the gas by the magnetic induction B and eq l b is the theoretical relationship6 between the observed birefringence - 1 / 3 qaa,sa), and fundamental molecular properties; Aq Aa (=CY,,- CY,,), and Ax ( y Z z- xx,) are the anisotropies in the magnetic hyperpolarizability, the optical-frequency electric polarizability, and the magnetizability, respectively. If the molecular symmetry is such that the polarizability and magnetizability tensors are isotropic rather than anisotropic, eq 1b reduces to (1) (a) University of Sydney. (b) University of New England. (2) (a) Lukins, P. B.; Buckingham, A. D.; Ritchie, G. L. D. J . Phys. Chem. 1984, 88, 2414-2418. (b) Lukins, P. B.; Ritchie, G. L. D. J . Phys. Chem. 1985, 89, 1312-1314. (3) Lukins, P. B.; Laver, D. R.; Buckingham, A. D.; Ritchie, G. L. D. J . Phys. Chem. 1985, 89, 1309-1312. (4) Lukins, P. B.; Ritchie, G. L. D. J . Phys. Chem. 1985,89, 3409-341 1. (5) See ref 3 for a summary of the algebraic and numerical factors required to convert the relevant electric and magnetic properties from SI to cgs units. (6) Buckingham, A. D.; Pople, J. A. Proc. Phys. Soc., London, Sect. B 1956, 69, 1133-1138.
0022-3654/88/2092-2013$01.50/0
C , =(NAcLO~/~~O~AV
(2)
so that the molar Cotton-Mouton constant is independent of temperature; measurements at a single temperature therefore serve to define Aq. In other cases Aq can be obtained if the effect is measured over a range of temperature such that a plot of C , against T'can be reliably extrapolated to give the intercept at T I = 0; the slope yields Ax, provided ACYis known. Experimental Section Apparatus as previously described24 was used to determine the vapor-state magnetic-field-induced birefringences of the compounds. Under the conditions of our experiments both methane and carbon tetrachloride exhibited retardances of only about 1 X 10" rad, and although the molar Cotton-Mouton constant of carbon tetrachloride is significantly larger than that of methane, it was less well determined, because of the lower vapor pressures which were attainable and the higher cell-window temperatures ( ~ 8 0 "C) which were required. In consequence it was necessary, particularly in the case of carbon tetrachloride, to employ additional noise reduction techniques. Data acquired over 8, 16, or 32 cycles of the magnetic field (0.0125 Hz) were digitized, averaged, smoothed, and Fourier transformed on an LSI- 1 1/3 microcomputer. Repetitive measurements on, alternately, the filled and the evacuated cell, at fixed time intervals, were used to correlate the observed retardance with the gas pressure. Under favorable circumstances these procedures allowed the detection of effects as small as 1 X lo-' rad. For methyl chloride and chloroform, the ranges of temperature over which accurate data could be obtained were limited by the available vapor pressure at lower temperatures and the diminution of the effect at higher temperatures. The samples were as follows: methane (Matheson) and methyl chloride (Matheson), used without further treatment; chloroform (Merck analytical-reagent grade), washed with water, extracted, and twice distilled from phosphorus pentoxide; and carbon tetrachloride (Merck spectroscopic grade), distilled. Gas-chromatographic and mass-spectrometric analyses confirmed the purities of all four as 399.9%. In addition, the two liquids were subjected to several freeze-pumpthaw-distill cycles in the vapor-handling system immediately prior to the commencement of each set of pressure-dependence measurements. The definition of the molar Cotton-Mouton constant in terms of experimental observables is (3) in which SB2 dl = 3.289 f 0.045 T2 m, 6' = (2?r1/X)9n(n2 + 2)-2(nll- n l ) is a measure of the birefringence induced in the gas by the magnetic field, and V,-' is the reciprocal of the molar volume. Recorded density virial coefficients' were used to calculate
0 1988 American Chemical Society
2014
Lukins and Ritchie
The Journal of Physical Chemistry, Vol. 92, No. 7 , 1988
TABLE I: Cotton-Mouton Effects of Methane, Methyl Chloride, Chloroform, and Carbon Tetrachloride at 632.8 nm TI K IO~T~/K-' no. of press. p/kPa no. of measurements 106E/m3mol-' 294.4
3.397
26
407.6 400.7 363.8 320.4 305.8 294.6 28 1.2 252.0
2.453 2.496 2.749 3.121 3.270 3.394 3.556 3.968
5
471.2 454.0 430.0 413.3 392.6 376.9 361.1 347.5 332.3 319.0
2.122 2.203 2.326 2.420 2.547 2.653 2.769 2.878 3.009 3.135
396.6
2.521
Methane 94-1 009
208
-44.3 1
102',C/m5 AW2mol-' 0.045 f 0.006
Methyl Chloride 140-250 30-250 48-270 11 1-400 109-501 I 1 8-436 1 10-245 100-1 0 2
15 9 7
18 18 7 5
40 120 72 35 90 90 35 25
-203 -212 -259 -345 -376 -419 -466 -656
-0.95 -1.11 -1.15 -1.29 -1.38 -1.51 -1.56 -1.73
f 0.08
80 85 50 11s 90 75 50 85 90 55
-430 -446 -480 -520 -590 -656 -734 -815 -914 -1010
-2.24 -2.24 -2.28 -2.49 -2.80 -2.94 -3.14 -3.21 -3.18 -3.45
f 0.12 f 0.07 f 0.13 f 0.16 f 0.10 f 0.15 f 0.10 f 0.09 f0.12 f 0.16
248
-900
f 0.06 f 0.04
f 0.05 f 0.03 f 0.02 f 0.03 f 0.05
Chloroform 102-1 10 103-1 14 108-1 I 1 107-121 107-117 77-91 77-80 70-75 60-69 48-57
16 17 10
23 18
15 10 17 18 11
Carbon Tetrachloride 31
23-76
0.30 f 0.09
TABLE 11: Analysis of the Cotton-Mouton Effects of Methane, Methyl Chloride, Chloroform, and Carbon Tetrachloride
lO2'(intercept)/m5 A-2 mol-' 1024(slope)/m5A-2 K mol'' IOS0A77/Cm2 V-I TZ 1o4O~a/C m2 V-' 1 0 2 9 ~ T-2 ~ / ~
IO'Ax/J TW2 mol-' 1029x/J T-Zb 1 0 2 9 T~-~~ C ~ ~
CH,
CHKI
CHCI,
CCI,
0.045 f 0.006
0.19 f 0.13 -0.492 f 0.039 4 1 f 33 1.705 f 0.054 -15.0 f 1.3 -9.05 f 0.77 --53.1 f 1.0 -63.1 f 1.3 -48.1 f 1 . 1
0.58 f 0.27 -1.29 f 0.10 I50 f 70 -2.974 f 0.100 22.7 f 1.9 13.6 f 1.1 -98.5 f 2.0 -83.4 f 2.4 -106.1 f 2.1
0.30 f 0.09
11.3 f 1.5 0 0 0 -28.9 f 1 . 3
J
1 0 2 9 ~ T-Z ~ ~c
"Optical-frequency polarizability anisotropies from ref 21. *Mean molecular magnetizabilities, x = (Zx,, 'Directions of molecular axes: x and J'. which are equivalent, in a plane perpendicular to z . the C, axis. the values of V,-' from the measured pressures; third virial coefficients were included in the case of methyl chloride but gave negligibly small corrections for the other gases under the conditions of our experiments. The results are summarized in Table I, where the uncertainties shown are based on the standard deviations derived from the least-squares fitting of straight lines to the density-dependence data, together with appropriate allowance for systematic errors. Second Cotton-Mouton virial coefficients were not observable. Previously reported molar Cotton-Mouton constants (quoted here as 102',C/m5 A-2 mol-') for these four molecules can be compared with values from Table I (shown in parentheses). In the case of methane, observations of the effect at 546.1 nm and at 632.8 nm gave values of 0.08 rt 0.05* and 0.08 f 0.049 (present work, 632.8 nm. 0.045 f 0.006); however, the earlier measurements were performed at pressures up to 5000 kPa, much higher than in the present work, and the contribution from the second Cotton-Mouton virial coefficient may not have been negligible. The only previous determinations of the effect in methyl chloride and chloroform are single-temperature values reported by Corfield:9 CH3C1,632.8 nm, 23 "C, -1.48 f 0.05 (present work, 632.8 nm, 23 "C, -1.47 k 0.02); CHCI3, 632.8 nm, 100 OC, -1.9 f 0.5 (present work, 632.8 nm, 100 OC, -2.89 f 0.10). Obviously, agreement is satisfactory for methyl chloride but not for chloroform. There are no previous estimates o f the vapor-state ( 7 ) Dymond, J. H.; Smith. E. B. The Virial Coefficients of Pure Cases and Mixtures; Clarendon Press: Oxford, 1980. (8) Buckingham, A . D.: Prichard. u'.H.: Whiffen, D. H. Trans. Furadax SOC.1967, 63, 1057-1064. (9) Corfield, M . G. Ph.D. Thesis, University of Bristol. 1969.
+ x,,)/3,
75 f 23 0 0 0 -111 f 3
from ref 22 and 23.
Cotton-Mouton constant of carbon tetrachloride; in fact, under the conditions of temperature and pressure used in the present study, the magnetic birefringence exhibited by this species is an order of magnitude smaller than the resolution of earlier versions of the equipment.*,9
Discussion From eq I b it can be seen that the molar Cotton-Mouton constants of CH4 and CCI4, for which Aa and 1 x are zero, are independent of temperature, while those of CH3C1 and CHCI3 should exhibit a linear dependence on the reciprocal of the absolute temperature. Figure 1 shows plots of ,C against T I for the latter; Table I1 contains the intercepts and slopes of the weighted-fit least-squares straight lines and an analysis of the Cotton-Mouton effects of all four molecules in terms of the magnetic hyperpolarizability, the magnetic anisotropy, and the individual components of the magnetizability. The magnetic hyperpolarizability anisotropy, AT, is positive for all four molecules and, within the limits imposed by the experimental errors, appears to increase in magnitude as the number of chlorine substituents increases. It is of interest to compare the present result for CH4, in particular, with recently measured values (quoted here as lOS0A7/Cm 2 V-' T-2) for the inert gases'" (Ar, 4.5 f 0.7; Kr, 6.5 f 0.7; and Xe, 15.1 f 0.6). Values of 37 have also been reported for a range of other molecules (H2;"." 02:'3a ( I O ) Carusotto, S.;Iacopini, E.; Polacco, E.; Scuri, F.: Stefanini. G.: ZaOpt. Phj'x. 1984, I , 635-640. ( 1 1 ) Scuri, F.; Stefanini, G.; Zavattini, E.; Carusotto, S.; lacopini, E.: Polacco, E. J . Chem. Phys. 1986, 85, 1789-1794. ( 1 2 ) Buckingham. .4. D.; Williams. J . H. J L'hrn:. PhI \ . 1987. 86. 5883--5884.
vattini. E. J . Opt. SOC.A m . B.
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 2015
Vapor-Phase Cotton-Mouton Effects -0.8r
CHBCl
10 T -l/K
-l
Figure 1. Temperature dependence of the vapor-state Cotton-Mouton effects of methyl chloride and chloroform.
N2, CO, NNO;13bOCO, OCS, SCS;13b C2H2, C2H4, C2H,5;I3' C3H6;3C6H6, C6H3F3, C6F62"3d),but few, if any, trends are as yet discernible. However, we note that in the cases of CH3C1 and CHC13 the temperature-independent and temperature-dependent contributions to the Cotton-Mouton constants once again have opposite signs and that H2 is, to date, the only diamagnetic molecule for which the two contributions have been found to have the same sign. The consequence of this opposition of terms is that the contribution from Aq has the effect of increasing the slope , against T I and thereby the magnitude of the of the plot of C derived magnetic anisotropy beyond the values that would be obtained if this term were assumed to be zero, as has been done in solution-phase studies.I4 For CH3CI and CHC13 the proportions of the molar Cotton-Mouton constants at 298 K which originate in the temperature-independent contribution (CH3Cl, -1 3%; CHC13, -15%) are actually the largest yet observed in these laboratories, and failure to take account of such contributions would lead to serious underestimates of the magnetic anisotropies. It is of particular interest that for CC14 the molar CottonMouton constants found in the present work for the vapor (0.30 f 0.09) and previously reported for the liquid (-0.166 f 0.006;9 -0.30 f 0.07;14-0.165 f 0.00315)are of opposite sign. In consequence, it can be inferred that there are contributions to the magnetic birefringence of CCI4 in the liquid state which predominate over that from the intrinsic, free-molecule magnetic hyperpolarizability anisotropy. Factors that may be involved are (13) (a) Kling, H.; Dreier, E.; Hiittner, W. J . Chem. Phys. 1983, 78, 4309-4314. (b) Kling, H.; Hiittner, W. Chem. Phys. 1984,90,207-214. (c) Kling, H.; Geschka, H.; Hiittner, W. Chem. Phys. Lett. 1983, 96, 631-635.
(dt, Geschka. H.: Pferrer. S.: Haussler., H.:, Hiittner. W. Ber. Bunsen-Ges. P h p . Chem.' 1982,86, 790-795. (14) Battaglia, M. R.; Ritchie, G. L. D. J . Chem. SOC.,Faraday Trans. ~
~~~~
1977. 209-221. -2 .. . , 73. ., .. __. .
(15) Batchelor, P. J.; Champion, J. V.; Meeten, G. H. J . Chem. Soc., Faraday Trans. 2 1980, 76, 1610-1617.
correlated collision-inducedtransient anisotropies in the molecular properties;I5-l8the existence of local order in the liquid, as indicated by X-rayIg and neutron20 diffraction; and variation in A7 in the condensed medium, because of molecular interaction^.'^ The matter clearly deserves further attention. The magnetic anisotropies, A x , and the magnetizability components, xzzand xxx,of CH3CI and CHCl, were calculated from the slopes of the plots of C , against T I together with the known polarizability anisotropies21and mean magneti~abilities~~-~~ of these molecules (Table 11). In the case of CH3C1, the magnetic anisotropy (quoted here as 1 0 2 9 A ~ / JT2)so deduced (-15.0 f 1.3) is in reasonable agreement with that obtained by Vanderhart and F l ~ g a r from e ~ ~ a microwave Zeeman spectroscopic study (-1 3.2 f 1.0). Because of the complications that arise from nuclear quadrupolar interactions, the Zeeman method is not readily applicable to CHC13, so that the temperature dependence of the vapor-phase Cotton-Mouton effect provides by far the most useful and perhaps the only direct route to the magnetic anisotropy of the free molecule. Our result for the magnetic anisotropy of CHC13 (22.7 f 1.9) can, however, be compared with an earlier estimate (31 f 6) from single-temperature measurements of the Cotton-Mouton and Kerr effects of dilute solutions14 and with a recently reported value (25.4) deduced by a new procedure that exploits the quadrupole splitting in the high-resolution ZHN M R spectra of chloroform and other halomethanes in the pure-liquid or solution states.25 In relation to the first of these two condensed-phase methods,I4 it must be noted that although observations on dilute solutions have yielded reliable magnetic anisotropies for highly anisotropic molecules, application of the same procedure to weakly anisotropic molecules, particularly dipolar species such as chloroform, is likely to give unreliable results unless appropriate allowance is made for the several relevant electric and magnetic hyperpolarizabilities.
Summary The present study of the temperature dependence of the vapor-state magnetic-field-induced birefringence of methane, methyl chloride, chloroform, and carbon tetrachloride has shown that the magnetic hyperpolarizability anisotropy is positive in sign for all four molecules and increases in magnitude as the number of chlorine substituents increases. As expected, the molar CottonMouton constants of methyl chloride and chloroform at 298 K are dominated by the temperature-dependent contributions, which arise from molecular orientation; however, the temperature-independent contributions, which originate in the magnetic hyperpolarizability anisotropy, are not negligible and amount to =-15% of the effects that are observed at this temperature. Reliable free-molecule magnetic anisotropies and magnetizability components have been obtained for methyl chloride and chloroform. Acknowledgment. The award of a University of Sydney Special Project Research Scholarship (to P.B.L.), financial support from the Australian Research Grants Scheme (to G.L.D.R.), and the valuable assistance of Dr. D. R. Laver are gratefully acknowledged. Registry No. MeH, 74-82-8; MeCI, 74-87-3; CHC13, 67-66-3; CCl,, 56-23-5. (16) Buckingham, A. D.Pure Appl. Chem. 1980. 52, 2253-2260. (171 Battaelia. M. R. Chem. Phvs. Lett. 1978. 54. 124-127. (18j Champion, J. V.; Dandridge, A.; Meeten, G.'H. Faraday Discuss. Chem. SOC.1918,66, 266-276. (19) Narten, A. H.; Danford, M. D.; Levy, H.A. J. Chem. Phys. 1967, 46, 4875-4880. (20) Egelstaff, P. A,; Page, D. I.; Powles, J. G. Mol. Phys. 1971, 20, 881-894. (21) Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.; White, A. H. J . Chem. SOC.,Faraday Trans. 1 1978, 74, 3008-3015. (22) Barter, C.; Meisenheimer, R. G.; Stevenson, D. P. J . Phys. Chem. 1960, 64, 1312-1316. (23) Lundolt-Bornstein Zahlenwerte und Funktionen, Vol. 2, Part 10, Magnetische Eigenschaften ZI; Springer-Verlag: Berlin, 1967. (24) Vanderhart, D. L.; Flygare, W. H. Mol. Phys. 1970, 18, 77-93. (25) Bothner-By, A. A,; Dadok, J.; Mishra, P. K.; Van Zijl, P. C. M. J . Am. Chem. SOC.1987, 109, 4180-4184.
