J. Phys. Chem. 1992,96, 10477-10483 (4) Klein, M. L.; Lewis, L. J. Chem. Rev. 1990, 90, 459. (5) Rao, C. N. R.; Yashonath, S. J . Solid Stare Chem. 1987, 68, 193. (6) Subramanian, G.; Davis, H. T. Mol. Phys. 1979,38, 1061. (7) Powles, J. G.; Dornforth-Smith, A.; Evans, W. A. B. Phys. Rev. Lett. 1991, 66, 1177. (8) MacElroy, J. M. D.; Suh, S.-H. Mol. Simular. 1989, 2, 313. (9) Derouane, E. G. Chem. Phys. Lert. 1987, 142, 200. (IO) Politowicz, P. A.; Kozak, J. J. Mol. Phys. 1987, 62, 939. (1 1) Woods, G. B.; Panagiotopoulos, A. Z.; Rowlinson, J. S. Mol. Phys. 1988,63,49. (12) Vetrivel, R.; Catlow, C. R. A.; Colbourn, E. A. J. Chem. Soc. Faraday Trans. 2 1989,85, 497-503. (13) June, R. L.; Bell, T. A,; Theodorou, D. N. J . Phys. Chem. 1990,94, 1508. (14) June, R. L.; Bell, T. A,; Theodorou, D. N. J . Phys. Chem. 1990,94, 8232. (IS) Pickett, S. D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.; Swift, J. F. P.; Cheetham, A. K.; den Ouden, C. J. J.; Smit, B.; Post, M. F. M.J . Phys. Chem. 1990,94, 1233. (16) Demontis, P.; Suffriti, G. B.; Quartieri, S.; Fois, E. S.; Gamba, A. Zeolites 1987, 7, 552. (17) Demontis, P.; Fois, E. S.; Suffriti, G. B.; Quartieri, S. J. Phys. Chem. 1990,94,4329. (18) Smit, B.; den Ouden, C. J. J. J . Phys. Chem. 1988,92, 7169. (19) Leherte, L.; Lie, G. C.; Swamy, K. N.; Clementi, E.; Derouane, E. G.; Andre, J. M. Chem. Phys. Lett. 1988, 145, 237. (20) Rowlinson, J. S.; Woods, G. B. Physica A 1990, 164, 117. (21) Woods,G. B.; Rowlinson, J. S . J. Chem. Soc., Faraday Trans. 2 1989, 85, 765. (22) Barrer, ,R. M.; Sutherland, J. W. Proc. R . Soc. London, Ser A 1956, 237, 439. (23) Fomkin, A. A.; Serpinskii, V. V.; Bering, B. P. Bull. Acad. Sci. USSR, Dlv. Chem. Sci. 1975, 24, 1114. (24) Chkhaidze, V. E.; Fomkin, A. A.; Serpinskii, V. V.; Tsitsishili, V. G. Izv. Akad. Nauk. SSSR, Ser. Khim. 1986, 276.
10477
(25) Yashonath, S.; Thomas, J. M.; Nowak, A. K.; Cheetham, A. K. Nature 1988, 331, 601. (26) Yashonath. S.: Demontis. P.: Klein, M. L. Chem. Phvs. h t . 1988. 153, 551. (27) Yashonath, S.; Demontis, P.; Klein, M. L. J. Phys. Chem. 1991,95, 588 1. (28) Yashonath, S. J. Phys. Chem. 1991, 95, 5877. (29) Demontis, P.; Yashonath, S.; Klein, M. L. J. Phys. Chem. 1989, 93, 5016. (30) Fitch, A. N.; Jobic, H.; Renouprez, A. J. Phys. Chem. 1986.90, 1311. (31) Olson,D. H. J. Phys. Chem. 1968, 72, 4366. (32) Kiselev, A. V.; Du, P. Q. J. Chem. Soc., Faraday Trans. 2 1981,77, 1. (33) Yashonath, S. Chem. Phys. Lett. 1991, 177, 54. (34) Hirschfelder, 0. J.; Curtiss, F. C.; Bird, B. R. Molecular Theory of Gases and Liquids; John Wiley: Chichester, U.K., 1954. (35) Kushick, J.; Berne, J. B. In Statistical Mechanics, Part E: Timedependent processes; Beme, J. B., Ed.; 1977; Chapter 2. (36) Yashonath, S.; Santikary, P. Submitted for publication in J . Phys. Chem. (37) Cohen de Lara, E.; Kahn, R. J . Phys. 1981, 42, 1029. (38) de Mallmann, A.; Barthomeuf, D. Zeolites 1988, 8, 292. (39) Yashonath, S.; Rao, C. N. R. Proc. R . SOC.(London) 1985, A400, 61. (40) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Phys. Chem. 1984, 106, 6638. (41) Friassard. J.: Ito. T. Zeolites 1988. 8. 350. (42j Grosse, R.;Burmeister, R.; Boddent&, B.; Gedeon, A.; Fraissard, J. J. Phys. Chem. 1991, 95, 2443. (43) van Kampen, N. G. Stochastic Processes in Phvsics and Chemistrv: .. North-Holland: Amsterdam, 198 1. (44) Chandrashekar, S. Rev. Mod. Phys. 1943, 15, 1. (45) Uhlenbeck, G. E.; Ornstein, L. S. Phys. Rev. 1930, 36, 3. (46) Haus, J. W.; Kehr, K. W. Phys. Rep. 1987, 150, 263. (47) Fruede, D. Zeolites 1986, 6, 12.
Measurements of the Cotton-Mouton Effect of Water and of Several Aqueous Solutions Jeffrey H. Williams* and Jim Torbett Institut hue-Langevin 156X, 38042 Grenoble Cedex, France, and Max Planck Institute for High Magnetic Fields 166X, 38042 Grenoble Cedex, France (Received: June 22, 1992; In Final Form: September 8, 1992)
We report a new measurement of the Cotton-Mouton constant, at 632.8 nm of liquid water, together with measurements, at the same wavelength of the Cotton-Mouton effect in several aqueous ionic solutions of varying concentration. We show how these results may be combined with literature values of optical Kerr measurements in the same solutions to separate the optical and magnetic susceptibility contributions to the Cotton-Mouton effect. These results will be of interest to those seeking to measure electrooptic effects in aqeuous solutions as the combination of the two experiments will give new information on the nature of the aqueous state.
Even though the aqueous state is ubiquitous, a detailed understanding of its microscopic structure remains elusive. We are nearly completely ignorant of the electric and magnetic properties of the ions which constitute the solution. This state of affairs is mainly the result of the lack of suitable techniques for the study of the electmoptic properties of solvated ions. We have, therefore, undertaken a series of measurements of the Cotton-Mouton effect in aqueous solutions. These experiments have demonstrated the suitability of this technique for such studies. We were also motivated by recent epidemiological evidence’ which suggests that electromagnetic fields produced, for example, by power cables and household electrical appliances could be harmful to health. As these electromagneticfields oscillate slowly (-60 Hz),it is conceivable that their magnetic field component induces small orientational fluctuationsin ionic distributionswithin tissue thus influencing in vivo interactions. Application of an intense electromagneticfield to a fluid induces an anisotropy in its physical properties. The Cotton-Mouton +Presentaddress: Department of Biochemistry, University of Edinburgh, George Square, Edinburgh EH89XD, U.K.
effect, for example, is the response of a fluid to a strong uniform magnetic field. The field gives rise to differences between the components of the refractive index parallel and perpendicular to the field; thus a beam of linearly polarized light propagating perpendicular to the field direction becomes elliptically polarized on passage through the fluid. Physically, the molecules are being oriented by the magnetic field and the fluid is thus behaving as a uniaxial crystal, with its optic axis parallel to the applied field direction. The Cotton-Mouton constant, C, is defined as C = (n,, - n , ) v / B 2 (1) where n,, - n, is the difference between the components of the refractive index, n, for electromagnetic waves of wavenumber Y with electric vectors parallel and perpedicular to the field direction, the magnetic field, B, being uniform and normal to the optical path. For a pure material, a molar Cotton-Mouton constant, ,C, may then be defined
where V, is the molar volume and po the vacuum permeability.
0022-3654/92/2096-10477%03.00/00 1992 American Chemical Society
10478 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Williams and Torbet
Bitter -Type Magnet
_ L 9 Amplifier
Frequency Generator
Fturr 1. Diagramatic representation of the experimental setup used for our measurements of the Cotton-Mouton effect. P1 and P2 are Glan polarizers. BSC is a Babinet-Solei1 compensator, PEM is a photoelastic modulator, and PSD represents the phase-sensitive detector.
The full theory of the Cotton-Mouton effect has been described previously2+ and has long been used as a means of obtaining and, more recently, exploring the solution molecular inf0rmation~9~ properties and dynamics of biological macr~molecules.~*~ In brief, for a system of noninteracting, diamagnetic molecules the molar Cotton-Mouton constant, in SI units, is3
(3) where Au is the anisotropy of the molecular polarizability which for a molecule with a rotational axis C,,,n 1 3, is Aa e all - al, where aI = a,, and aL = a,, = ayy;Ax is the anisotropy of the molecular magnetizability (the sum of diamagnetic and paramagnetic parts) whose components are defined in the same way as for the molecular polarizability, AT is a hypermagnetizability describing the dependence of the differential polarizability on Bz and is the sole cause of the Cotton-Mouton effect in fluids consisting of isotropically polarizable molecules, Le., when Aa = Ax = 0. The other terms in eq 3 have their usual meaning. As the above equation contains a temperaturedependentpart,in principle it should be possible to independently determine the relative importance of the orientational, temperature dependent, and hypermagnetizability, temperature-independent,components. Evidence suggests, however, that the hypermagnetizabilityterm is small.* In the experiments recoded here, the molecules interact strongly and one has to modify eq 3 to take this strong interaction into account. For a gas or a nonpolarizable fluid, n = 1 and one may go directly from eq 2 to eq 3 with a factor 2/27. However, this is not so straightforward when n is very different from unity. When one considers concentrated aqueous solutions or highly polarizable organic liquids one applies an internal or local field correction to the measured data to take account of molecular interactions. This internal field correction has been much studied,lo*lIbut there is no general solution. This correction for solutions has been, perhaps, most successfully achieved in the Cotton-Mouton effect measurements of solution made by LeFivre et ale5who considered the molar Cotton-Mouton constant at infinite dilution. Their form of analysis requires detailed measurements of the solute concentration dependence of not only the Cotton-Mouton constant but also the index of refraction and the density of the solution samples under investigation. Instead, we will keep our measurements as specific CottonMouton constants and show certain empirical trends which may be inferred from our data. We will, however, show in a few cases the type of information which is available, in principle, from these preliminary measurements. The primary molecule under consideration here, H20, is of C, symmetry and the orientational part of the induced effect is more complicated, 2AaAx being replaced by {(a,,- ay )(x,, - xy ) + (ayy- azz)(xyy - XI,) + (azz- axx)(xzz - xxx)t part 4om measurement of the Cotton-Mouton constant of pure water we have investigated this effect in a variety of aqueous solutions and we must therefore consider the additivity or nonadditivity of the Cotton-Mouton effect.
The first worker to analyze solution Cotton-Mouton effect measurements in terms of the additive contribution of the mole fractions of the specific effect of solute and solvent present was LeF€~re.~ He based his analysis on that previously devised and successfully applied to solution electrooptic Kerr effect measurements. Following Buckingham's study of the Kerr effect of solutions? we write the Cotton-Mouton constant for a multicomponent system, that is, of the solution, as (4)
where xi are the molar fractions of the components with 0')being the complementary Cotton-Mouton constant. In eq 4 the first term on the right-hand side represents the additivity rule, while the subsequent terms account for any deviations from additivity. Experimeatal Section The main details of the experimental setup are shown in Figure 1. Our experiments were conducted at the Max Planck Institute for High Magnetic Fields, Grenoble. The magnetic field is generated inside a water-cooled, Bittertype solenoid, and it is vertical with a 5.0 cm diameter cylindrical bore; maximum field strengths are of order 13 T. The light source in these experiments is a helium-neon laser, X = 632.8 nm, propagating horizontally through a radial bore in the solenoid. Polarization of the laser beam is achieved with Glan polarizers, P1 and P2, and the analyzer, P2,is crossed with respect to the polarizer, at 4 5 O to the magnetic field direction. In electric birefringence experiments, to facilitate observation of the induced effect, the applied electric field is modulated at a frequency w and the detector output is monitored via a lock-in amplifier. Unfortunately, it is not possible to modulate a large magnetic field in the same manner; consequently, a different strategy has to be adopted to observe an induced magnetic birefringence signal. A photoelastic modulator aligned with its optical axis parallel to the magnetic field direction produces a sinusoidal variation of the phase difference, 4, between the horizontally and vertically polarized light components at a frequency w 50 kHz and an amplitude of A# 0.2r, 4 = A$ sin ut. If the polarizers are well crossed, then the light level at the detector is given by
-
I = Io sin2 4/2
(5)
Zo being the light intensity incident upon the analyzer. The detector will then see a light signal alternating at 20. For small 4, Z is
proportional to @. If a number of birefringent elements are placed between the crossed p o l a h , then the light level at the detector is proportional to the sum of the square of individual birefringences, i.e. I
%
Io(C4i)2
(6)
I
Thus, in addition to the alternating component, arising from the photoelastic modulator, there will be a steady phase difference, +o, made up of the induced Cotton-Mouton effect, ~ C M the ,
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10479
Cotton-Mouton Effect of Water birefringence arising from the Babinet-Solei1 compensator, c#I=, and any stray birefringence induced by optical components or windows, t#Jext 40
4CM
+ 4BS + 4 e x t
Thus, the detector signal is I = (10/4)(A+2 sin2 or
+ 2A+& sin ot + 4 ~ ~ ' )
(7)
where the different alternating components can be separated by w of a phase-sensitive detector. The noise level of the experiment is dependent upon the total light level passed by the analyzer and thus strongly dependent upon the induced static birefringence. This dc output is used as an error signal in a feed-back loop involving a parity-converting integrator, a high-voltage amplifier, and a longitudinal Pockels cell. As the birefringence, r#+, of the Pockels cell is linear in the applied voltage, c$o can be continuously compensated by 4 , i.e., #o = -t#Jp. We thus have a means of determining the magnitude and sign of the induced magnetic birefringence, provided the other source of static birefringence are removed. This is achieved with the Babinet-Solei1 compensator, which is used to minimize t j before ~ ~ the ~ magnetic ~ field is applied to the sample. The induced magnetic birefringence is monitored directly via this feed-back loop as the magnetic field is run up to full strength. The time constant for the loop depends upon the expected signal-to-noise ratio. Calibration of the apparatus is obtained by measuring the voltage acroB8 the Pockels cell for various settings of the calibrated Babinet-Solei1 compensator. The samples for the experiments reported here, deionized water and solutions of readily dissociated salts in deionized water, were contained in a quartz cuvette 3.0 cm in length. A single cuvette was used and in each case the signal for the empty cuvette was subtracted from the result of the cuvette plus water or solution experiment. Our measurements on water were made over a period of 18 months with a variety of samples, and an analysis of variance was used to obtain the error in our final result. This statistical analysis yielded (-10.35 f 1.3) X 1 V 6G-2cm-' for the Cotton-Mouton constant for water at 632.8 nm. Our experiments were undertaken at a variety of temperatures; however, in deriving this value we have only included those results taken between 10 and 20 OC. The error is quite large, but the effect for water is small being only about twice that of the empty quartz cell. The signal observed for the concentrated solutions is much greater, between 10 and 100 times that for pure water. Consequently, the large error in the water measurement will not greatly influence these results. There will, however, be a small error arising from solution preparation and dilution. For the apparatus described above the smallest measurable induced retardation, 4, is of order lo4 radian; this gives as the smallest detectable Cotton-Mouton constant l@l7 G-2cm-I. It is likely that our sensitivity is limited by stray induced birefringences, lack of precision in cuvette geometry, and temperature fluctuations. Also it is possible that there are end effects in the sample, it is very short, and the field is very strong. We did not investigate this latter point as it would have necessitated the use of cuvettes of smaller path lengths, thereby increasing the difficulty of our measurement.
+
Discdon We have measured the molar Cotton-Mouton constantm ,C, for water at X = 632.8 nm and at temperatures between 10 and 20 OC in magnetic fields up to 13.0 T (13.0 X 10" G), our mean 1.3) X 1Wt6G-2cm-I for C or (-1.18 f 0.15) value is (-10.35 X lW1*G-2an3mol-' for ,C in cgs units which is (-1.86 f 0.23) X ms A-2 mol-' in SI units. There appears to be no recent measurements with which to compare ours; however, Landolt and B6msteint2quote a value of -39 X 1W16G-2cm-' for water measured with a white light source. There is also a value for water, measured with a white G-2cm-l.I3 light source, due to Ramanadham, of -110 X
*
0
2
4
6
8
10
12
14
Solute Concentration (moles/lltre)
Figure 2. Plot of (Cmlut,on - xHz0CH2?)versus solute concentration, in moles/liter, for different aqueous solutions. The error bars are given by
the vertical lines through the data points.
E
,
6 1
.
-k
I
p
LiNO,
0
-t
%
I
0
alland P a is negative as is the case for benzene. It is necessary to consider the phase of together with that of in the interpretation of values of which may be extracted from the data in Table I with a suitable model of the local field contribution. It is seen from the measurements displayed in Figure 5 that, as the mean spacing between ions changes, that is, as the concentration of ions in solution changes, so the measured polarizability anisotropy fluctuates. Of the solutions whose polarizability anisotropies have been investigated the nitrates will always have a significant effect; NO3will at all dilutions contribute strongly to the measured optical Kerr effect. However, as in other liquids there will be a significant collision-induced contribution of the measured optical Kerr effect. That is, we may consider the measured polarizability anisotropy, Aa, as the sum of the isolated ion polarizability anisotropy and a term arising through molecular interactions, varying as R3and @ which will be a function of the distance between ions R , in the solution; Z i = + A ~ ( R ) .his type of model is exemplified by NH4Cl. Here the two component ions have no intrinsic polarizability anisotropy; thus Aa = 0 and at low concentration should have no measurable optical Kerr effect, Le., be indistinguishable from the optical Kerr effect of the solvent. However, at higher concentrations the ions polarize themselves and give rise to a collision-induced polarizability anisotropy.
a
I
s, _ -
0
4
8
12
16
20
Solute Concentration (molesllitre)
Figure 4. Plot of (B+,tion- xH2&.,fl]/X+c versus solute concentration, in moles/liter, for different aqueous solutions. The data are taken from the optical Kerr effect measurementsof Paillette and show the presence of intcrmolccular interactions. The dashed line gives the signal level for pure water. The error bars are given by the vertical lines through the
data points. 632.8 nm gives 2.45 X 10-l6V2m. The large difference between
mX1 and , ,KO arises because of the loss of the large dipolar contribution to the temperature-dependent orientation term; see eqs 10 and 11. In eq 10, Auo corresponds to the polarizability of the molecule appropriate for the frequency of the orienting field, the static polarizability in convensional dc Kerr effect measurements. In the optical Kerr effect, Aao will correspond to the frequency of the powerful orienting laser and Aa to the frequency of the weaker probe laser. As we are dealing with systems which have no absorption features in the visible region of the spectrum, it is only necessary to scale Au by the ratio of two wavelengths to observe the magnitude change on changing wavelength. From the measurements of PailletteIg we have extracted the data which we have analyzed obtain the mean polarizability - toanisotropy, assuming Aao = Aa; these are displayed in Table 11. In Table 11, Bsoluleis the Kerr constant for the solution corrected for the signal arising from water, of mole fraction x,, and for the mole fraction of solute present. That is, we have used the Kerr constant equivalent of eq 8 for our analysis. The concentration dependence of these derived apparent Bsolutc are displayed in Figure 4. The error bars are determined by our ability
z,
a.
z,
a
10482 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
For the solutions of intrinsically anisotropic ions we see that as the concentration increases the measured polarizability anisotropy falls. This is, however, contrary to what one might expect. As the solution becomes more concentrated, Le., as the average interionic spacing falls, the interaction-induced contribution to the total polarizability anisotropy, Aa(R), should increase. However, an explanation may lie in the nature of the hydration process. At low concentrationsall the X+ and NO3- ions will be completely solvated. This polarization of the aqueous medium by the field of the ions produces large-scale structures in the solution which may well have substantially larger polarizability anisotropies than the bare NO< ion or water molecule. However, as the solution becomes more concentrated, there are simply not enough water molecules available to maintain these extended solvent sheaths. For example, in 6 M NaN03 solution where each Na+ ion requires 6 water molecules and each NO3- ion requires at least 2 molecules for solvation. There is barely enough water present to give a first completed solvent sheath around each ion. We have, therefore, a picture of long-range, polarizable structures established at low concentrations which are disrupted by the strong ionic forces produced by the addition of further solute. In Figure 5 we see that the derived values of are tending to some limiting value. A solution of ammonium nitrate with 19.53 mol/L of solute is likely to be fairly viscous; indeed it is probably better described as a glass. The same is likely to be the case for all of the stronger solutions. We pointed out above how at these concentrations there are not enough water molecules available to completely solvate all the ions. In the limit of large concentration we would have a completely disordered ionic glass and we have to consider how and why tends to some limiting value for such systems. Equation 11 gives the answer; in the optical Ken effect there is a temperature-independent term and a temperaturedependent term which contribute to the measurement. The former describes the distortion of the polarizability of the subject molecule, NO), by the applied oscillating electric field. The latter describes the orientation of the NOy ion induced by the torque arising through the interaction of the ions polarizability and the applied field. In the case of strongly associated ionic glasses it is only the temperature-independent distortion which will survive. The induced orientational torque will not be large enough to overcome the strong ionic intermolecular interactions present in the disordered material. We are therefore seeing the loss of this temperaturedependent contribution to the optical Kerr effect when we look at the decrease in as a function of concentration in Figure 5 . At the high concentrations we are left only with the electronic contribution to the optical susceptibility, which we see from Figure 5 can be a sizable fraction of the total polarizability. This being the case, the Ken and indeed the Cotton-Mouton constants for very concentrated solutions should be very similar to those measured in the crystalline solid and be independent of temperature.
z
a
Discussion of Ionic Solutions As an example of the type of analysis which is, in principle, possible with our Cotton-Mouton data, we find from the optical Kerr effect measurements values of (Y for the NaN03 solutions. These may be used, see eq 3, to obtain from our CottonMouton results at similar concentrations. It is clearly seen that both and are concentration dependent. For the purpose of an order of magnitude calculation, we assume we may account for the solute concentration dependence of the solution refractive index and the magnetic field induced anisotropy in the refractive may then obtain from our specific Cotton-Mouton index; weconstant, AaAx = 2.7 X Cz m2 T2for N a N 0 3 at a concentration of 9.28 M, from which we obtain Ax = -2.1 X J T2 for the NaN03solution, at 9.28 M, when we have extracted the relevant from Figure 5 ( z ( N a N 0 3 ) = -13.25 X lo4 Cz mz J-I), taking care of the phases of the various molecular terms. These data are not available from any other source. For
hx
hx
z
Williams and Torbet a comparison, the mean magnetizability, x, in concentrated aqueous solution for this material is z(NaNO3) = -4.38 X 10-28 J T2.', From the data in Landolt and B6msteinZZwe may obtain the separate ion contributions to the mean magnetic susceptibility; it is seen that NO) is, in comparison to the cations present in our experiments, by far the biggest contributor. For example, for the sequence Na+, K+,NH4+ and NO3-, the values of the -21.6 X magnetic susceptibility are given asZZx = -8.3 X -19.1 X and -33.2 X J Tz, respectively. With regard to the anisotropy of 2, NO3- being intrinsically optically anisotropic will be the dominant contribution to the CottonMouton effect of aqueous nitrate solutions. It is the nitrate ion which is giving the observable effect, and the cation is not really contributing. Assuming similar absolute values of for the nitrate and nitrite anions (see Table 11), it is curious that the values of for NOy and NO, are so different, ICdU&iO2l 3 lCdu&iO;l. This difference may also be seen in the comparison of the Cotton-Mouton constants measured here for KN03and the data for KNO, extracted from Landolt and Bbmstein (see Table I). However, it may well be that here we are okserving a paramagnetic contribution. The neutral species NO2 is an open-shell molecule; however, one would expect a purely diamagnetic behavior from the NOz- ion. Perhaps in the intense applied magnetic field we have a mixing of low-lying r states, which could give rise to an induced paramagnetic current density. Its form would be the same as the current that exists when the orbitals are degenerate and the molecule is in a state of well-defined orbital angular momentum, the difference being one of magnitude. We may make similar qualitative analysis with regard to the other Cotton-Mouton results presented in Table I. For those salts which have no intrinsically anisotropically polarizable ions the measured effect arises through molecular interactions, e&, NaCl and KCl. These ion pairs at infinite separation have neither anisotropy in magnetizability nor polarizability. They will, however, still have a Cotton-Mouton effect due to the temperature-independent term seen in eq 3. Indeed, this hypermagnetizability for a completely solvated ion may be quite appreciable; however, as these two closed-shell ions approach one another an induced polarizability anisotropy will arise through molecular interactions. We may also interpret this difference in the Cotton-Mouton effect of pure water and in aqueous solutions of NaCl and KCI as arising because of the break up of the complex hydrogen bonded structure of water. The statistical average over the angular coordinates of the molecules in the presence of the applied electromagnetic fields which is involved in deriving eqs 3, 10, and 11 is made more complicated in water because of the presence of the strong hydrogen bonds which make up the liquid. When small spherical ions are, however, present, they polarize the medium and disrupt these hydrogen bonds obtaining a solvent sheath in the process. If we assume that the ions make no net contribution to the measurement, i.e., they are unobservable electrooptically, then the Cotton-Mouton effect for aqueous solutions of spherical ions such as Na+Cl- and K+Cl- give a measure of the Cotton-Mouton effect in disordered water. We see from the second column of Table I that the CottonMouton constant for solvated NaCl is positive while that for KCl is smaller and negative; however, a difference in the solvation podynamics of Na+ and K+ is ~ e l l - k n o w n . ~The ~ - ~smaller, ~ larizing Na+ cation is termed a structuremaking cation while the K+ cation, being larger and less able to polarize the medium, is considered a structurebreaking cati0n.2~J~As to this difference in magnitude and phase of Cdutoit is first necessary to note that the ion pairs, Na+, C1- and K+, Cl-, are closed-shell spherical ions, Le., with no intrinsic anisotropic polarizability or magnetizability. At these ionic concentrations the dielectric measurements of Wei et a1.26give hydration numbers for these cations of 4.75 0.25 for Na+(aq) and 3.75 f 0.25 for K+(aq). Similarly the neutron scattering measurements for Nielson and Enderbyz3and Skipper and Nielson" give hydration numbers of 5 for Na+(aq)
-
*
Cotton-Mouton Effect of Water and 4 for K+(aq) at these solute concentrations. With four water molecules, which from space requirements would be tetrahedrally disposed around the K+ cation, this solvated aqua ion will have neither anisotropic polarizability nor anisotropic magnetizability, being spherically symmetric. In the case of Na+, however, solvated with 5 water molecules, the structure will be such as to possess an anisotropic polarizability and an anisotropicmagnetizability. Both solvated cations will have a, possibly large, temperatureindependent hypermagnetizability contribution to the observed Cotton-Mouton effect. If because of the tetrahedral symmetry Aa = Ax = 0 for the solvated potassium cation then it may well be that for this system the hypermagnetizability is negative as observed in Table I. provided we are not at solution cOncentratiOIlS which are so large as to prevent the formation of complete solvent sheaths, it is not unreasonable, considering the nonspherical symmetry of the solvated sodium cation, that the measured Cotton-Mouton constant of aqueous NaCl is very different from that of aqueous KCl. The larger positive temperature-dependent contribution to the Cotton-Mouton effect in solvated sodium cations (positive AaAx arisiig from negative h,see Table 11, and negative, diamagnetic, Ax) cancelling the smaller negative hypermagnetizability contribution, seen in the potassium solution, giving the phase change observed between the two solutions. The CI- anion at these concentrations is believed to be solvated with 6 water molecules25 and, consequently, with such an octahedral disposition of water ligands will have neither Aa or Ax. From such an analysis of the contribution of the solvent shell to this type of electrooptic experiment, it may be predicted that aqueous Li+ solutions will behave like those of K+. The Li+ ion, being a strongly polarizing cation, takes 6 water molecules into its solvent shell,2sthereby producing an octahedral solvation complex which will possess neither Aa nor Ax. With ZnBr2, ZnC12, and HgC12 it is possible that there are chemical effects present in aqueous solution which contribute to the measurement. It is well-known that the zinc halides have a complex chemistry in aqueous solution2’ and that some of the complex cations formed may well have a disproportionately large Cotton-Mouton constant. In the case of HgC12 there is the possibility of covalent behavior in solution, i.e., very little dissociation into ion pairs. It has a large Cotton-Mouton effect for a comparativelysmall amount of material. Such observations raise the possibility of using the Cotton-Mouton effect as a probe of aqueous solution chemistry. For example, Raman spectra2’ show that, depending on the concentration, the species present in aqueous solutions of ZnC12 are [Zn(H20),J2+, ZnCl+, ZnCl,, and [ZnC14(H20)2]2-, using the Cotton-Mouton effect to probe the magnitude of the induced optical anisotropy, may allow one to place estimates on the relative quantities of these species, of differing intrinsic optical anisotropy, present at a particular concentration. The above analysis of the electrooptic properties of water and of several aqueous solutions is very qualitative and makes many approximations. However, we believe it points the way for further experiments with greater precision and more detailed considerations of concentration effects in a system which is of such importance but whose electromagnetic properties are so little un-
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10483 derstood in the condensed phase. Our measurements do show that there is an appreciable effect due to an applied magnetic field on the distribution of ions within aqueous solutions. However, with regard to our earlier point concerning the biological implications of these experiments the magnetic fields associated with the propagation of large currents through power cables and electrical appliances are quite small (-0.1-1.0 G). Thus it is unlikely that the orientational effect on the solvated ions of the magnetic component of such electromagnetic fields is of significance in this context. Acknowledgment. The authors are indebted to the management of the Max Planck Institute for High Magnetic Fields, Grenoble, for making available the apparatus used in these measurements; in particular, we wish to thank Dr. G. Maret. J. T. would like to thank the British Heart Foundation for support during the latter stages of this work and J. H. W. would like to acknowledge Prof. A. D. Buckingham, FRS,for many helpful suggestions.
References and Notes (1) Pool, R. Science 1990,249, 1096. Pool, R. Science 1990,249, 1378. (2) Buckingham, A. D.; Pople, J. A. Proc. Phys. SOC.B 1956,69, 1133. Buckingham, A. D.; Pople, J. A. Proc. Phys. Soc. B 1955, 68,905. (3) Battaglia, M. R.; Ritchie, G. L. D. Chem. Soc., Faraday Trans. 2 1977, 73, 209. (4) Buckingham, A. D.; Prichard, W. H.; Whiffen, D. H. Trans. Faraday SOC.1%7,63, 1057. Bogaard, M. P.; Buckingham, A. D.; Corfield, M. G.; Dunmur, D. A,; White, A. H. Chem. Phys. Lett. 1972,12, 558. (5) LeF&re, R. J. W.; Williams, P. H.; Eckert, J. M. Aust. J. Chem. 1965, 18, 1133. See also subsequent papers by; R. J. W. LeFevre and collaborators in the same journal (1966-1971). (6) Cheng, C. L.; Murphy, D. S. N.; Ritchie, G. L. D. Mol. Phys. 1971, 22, 1137. (7) Maret, G.; Well, G. Biopolymers 1983, 22, 2727. (8) Torbet, J. Trends Biochem. Sci. 1987, 12, 327, (9) Buckingham, A. D. Trans. Faraday SOC.1956,52, 61 1. (IO) Burnham, A. K.; Alms, G. R.; Flygare, W. H. J. Chem. Phys. 1975, 62, 3289. (1 1) Buckingham, A. D.; Pople, J. A. Discuss. Faraday Soc. 1956,22,17. (12) Landolt-Bhstein; Springer Verlag: New York, 1962; 6 Auflage Zahlenwerte und Funktionen, I1 Band, Vol. 8, p 5-827. In particular: Haque, M. A.; C. R. Stances Acad. Sci. Paris, 1930, 190, 789. (13) Ramanadham, M. Indian J. Phys. 1929.4, 15. (14) Cotton, A.; Mouton, H. C. R. Seance Acad. Sci. Paris 1912, l54,930. Cotton, A.; Mouton, H. Ann. Chim. 1913,28, 209. Cotton, A.; Tsai Belling C. R. Stance Acad. Sci. Paris 1934, 198, 1889. (15) Chinchalker, S.W. Indian J. Phys. 1931,6, 165. Ramanadham, M. Indian J. Phys. 1929, 4, 109. (16) Buckingham, A. D. In Molecular Electro-optics; O’Konski, C . T., Ed.; Marcel Dekker: Dordrecht, 1976; p 27. (17) Chen, Y.-J.;Orttung, W. H. J. Phys. Chem. 1972,76,216. Khanna, R. K.; Dempsey, E.; Parry Jones, G. Chem. Phys. Lett. 1978, 53, 542. (18) Buckingham, A. D. Proc. Phys. SOC.1956,869, 344. (19) Paillette, M. Ann. Phys. (Paris) 1969, 4 , 671. (20) Aroney, M. J.; Battaglia, M. R.; Ferfoglia, R.; Miller, D.; Pierens, R. K. Trans. Faraday SOC.1976, 72, 724. (21) Orttung, W. H.; Meyers, J. A. J. Phys. Chem. 1963.67, 1905. (22) Landolt-Bornstein; Springer Verlag: New York, 1986 New Series, Vol. 16, p 402. (23) Neilson, G. W.; Enderby, J. E., Adu. Inorg. Chem. 1989, 34, 195. (24) Skipper, N. T.; Neilson, G. W. J. Phys.: Condensed Matter 1989, I, 4141. (25) Howell, I.; Neilson, G. W.; Chieux, P. J. Mol. Struct. 1991, 250, 281. (26) Wei, Y.-Z.; Chiang, P.; Sridhar, S. J. Chem. Phys. 1992, 96,4569. (27) Cotton, F. A.; Wilkinson, G. Aduanced Inorganic Chemistry; Wiley: New York, 1972; Chapter 18.
