1730
J . Phys. Chem. 1985,89, 1730-1735
Transport and Relaxation Properties of Dimethyl Sulfoxide-Water Mixtures at High Pressure Ellen S. Baker and Jiri Jonas* Department of Chemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 (Received: October 2, 1984)
The pressure dependence of the deuterium T I in Me2SO-D20 mixtures and the proton T Iand H 2 0 self-diffusion coefficients in Me2SO-d6-H20 mixtures has been measured at 25 OC. The observation of increased motional freedom of H 2 0 with the initial application of pressure in mixtures up to 30 wt % Me2S0 (xMczso= 0.1) indicates that small amounts Me2S0 do not perturb in a major way the overall hydrogen-bond network in H20. The Debye equation describes well the reorientation of water molecules at 1 bar, but it fails at high pressure due to changes in the coupling between rotational and translational motions. The decreased pressure dependence of the rotational-translational coupling in solutions for xMCw 50.2, as compared to pure water, indicates that Me2S0 enhances the water structure at low Me2S0 concentration. The pressure dependence of the intramolecular and intermolecular proton dipolar relaxation rates of H 2 0 in Me2SO-d6-H20is also reported.
Introduction The complexity of the properties of water and aqueous solutions is reflected in the large number of theoretical and experimental studies of these systems. In this laboratory, work has centered on determining the effect of varying the density, as well as the temperature, on the dynamics of liquid water.’ Measurements have been made of the nuclear magnetic resonance spin-lattice relaxation time^^,^ and self-diffusion coefficient^^*^ of liquid water and heavy water over a wide temperature and pressure range. The results illustrate the importance of using pressure as a variable to separate the effects of temperature and density in the study of the dynamic structure of liquids. In addition to our studies of pure water, the pressure dependence of spin-lattice relaxation times in aqueous solutions of electrol y t e ~ ~and , ’ nonelectrolytes* have been examined to determine the effects of “structure-making” and “structure-breaking” solutes. Aqueous solutions of nonelectrolytes are some of the most complex and least well understood classes of liquids? The binary system dimethyl sulfoxide (Me2SO)-water is an excellent example. Many articles have been published describing experiments on this system. The experiments include measurements of physical, thermodynamic, and spectroscopic properties of H20, Me2S0, and their solutions as a function of temperature and Me,SO concentration. The interest in the system is due in part to the wide use of M e 2 S 0 and its aqueous solutions as solvents and reaction media. The utility of M e 2 S 0 as a cryoprotective agent for the prevention of damage to living cells at low temperatures was first noted in 1959 by Lovelock and Bishop.” The studies indicate a strong interaction between Me2S0 and = 0.3-0.4. water, particularly in the mole fraction range xMleZSO When plotted against concentration, many properties of the mixture such as density,” viscosity,” spin-lattice relaxation rate^,'^^'^ partial molar enthalpies,I4 and heats of mixingI5 go
through minima or maxima at about xM = 0.35. The behavior of the thermodynamic excess functions1“s“as a function of Me2S0 concentration is consistent with Rowlinson’s9 picture of aqueous nonelectrolytes. According to this theory, the thermodynamic results indicate that there are very strong and/or a large number of hydrogen bonds between H 2 0 and Me2S0. The general conclusion is that, at this concentration, molecular mobility is at a minimum, and Me2SO-H20 interactions at a maximum, due to the formation of Me2SO-H20 hydrogen bonds. There is some disagreement as to whether actual hydrogen-bonded complexes are f ~ r m e d , what ” ~ ~ the ~ ~Me2SO:H20 ~~ ratio is in the c ~ m p l e x , and ’ ~ how long such complexes exist.12x20 The effect of small amounts of MezSO on the structure of liquid water is in dispute. Some of the most convincing evidence to support the theory that Me2S0is a water structure maker at low concentration comes from a study by Safford and associates.21 They used IR, neutron inelastic scattering, and X-ray diffraction techniques to study the structure of the solutions and found that 10.1)produced a cooperative small quantities of Me2S0 (xMeZSO ordering of water molecules, increasing the long-range structure. Similarities in the results between Me,SO and Me2S02,despite the fact that M q S O forms stronger hydrogen bonds than Me2S02, suggest that dipole-dipole forces as well as hydrogen bonding contribute to this cooperative orientation. The breakdown of the water structure due to the formation of hydrogen-bonded complexes was apparent by xhi& = 0.2. On the other hand, infrared studies,22as well as density and partial molar volume measurem e n t ~ indicate , ~ ~ that small amounts of Me2S0 have little or no effect on the water hydrogen bonding. Dimethyl sulfoxide has been classified as a water structure breaker in small quantities on the basis of ionic c o n d ~ c t a n c e temperature ,~~ of maximum density,25and ultrasonic measurements.26 (15) Fox, Malcolm F.; Whittingham, K. P. J . Chem. Soc., Faraday Trans. 1407. (16) Kenttamaa, J.; Lindberg, J. J. Suom. Kemistil. B 1960, 33, 98. (17) Lindberg, J. J.; Majani, C. Acta Chem. Scand. 1963, 17, 1477. (18) Madigosky, W. M.; Warfield, R. W. J. Chem. Phys. 1983,78, 1912. (19) Glasel, J. A. J . Am. Chem. SOC.1970, 92, 372. (20) Higashigaki, Y.; Christiansen, D. H.; Wang, C. H. J . Phys. Chem. 1981, 85, 2531.(21) Safford, G.J.; Schaffer, P. C.; Leung, P. S.; Doebbler, G. F.; Brady, G. W.; Lvden. E. F. X. J. Chem. Phvs. 1969, 50, 2140. (22) Brink, G.;Falk, M. J. Mol. 3truct. 1970, 5 , 27. (23) de Visser, C.; Henvelsland, W. J. M.; Dum, L. A,; Somsen, G. J. Chem. Sor., Faraday Trans. 1 1978, 74, 1159. (24) Petrella, G.; Petrella, M.; Castagnolo, M.; Dell’Atti, A,; DeGiglio, A. J . Solution Chem. 1981, 10, 129. (25) MacDonald, D. D.; Smith, M. D.; Hyne, J. B. Can. J . Chem. 1971, 49, 2817. (26) Subbarangaiah, K.; Murthy, N. M.; Subrahmanyam, S. V. Bull. Chem. SOC.Jpn. 1981, 54, 2200. 1 1975, 71,
( I ) Jonas, J. Comments Solid State Phys. 1977, 8, 29. (2) Jonas, J.; DeFries, T.; Wilbur, D. J. J. Chem. Phys. 1976, 65, 582. (3) Wilbur, D. J.; DeFries, T.; Jonas, J. J . Chem. Phys. 1976, 65, 1783. (4) DeFries, T.; Jonas, J. J. Chem. Phys. 1977, 66, 896. (5) DeFries, T.; Jonas, J. J. Chem. Phys. 1977, 66, 5393. (6) Lee, Y.; Jonas, J. J. Magn. Reson. 1971, 5 , 267. (7) Lee, Y.; Campbell, J. H.; Jonas, J. J . Chem. Phys. 1974, 60, 3537. (8) Lee, Y.; Jonas, J. J. Chem. Phys. 1973, 59, 4845. (9) Rowlinson, J. S . ; Swinton, F. L. “Liquids and Liquid Mixtures”, 3rd ed.; Butterworth: London, 1982. (10) Lovelock, J. E.; Bishop, M. W. H. Nature (London)1959, 183, 1394. ( I I ) Cowie, J. M. G.; Toporowski, P. M. Can. J. Chem. 1961, 39, 2240. (12) Packer, K. J., Tomlinson, D. J. Trans. Faraday Sot. 1971,67, 1302. (13) Tokuhiro, T.; Menafra, L.; Szmant, H. H. J . Chem. Phys. 1974.61, 2275. (14) Rallo, F.; Rodante, F.; Silvestroni, P. Thermochim. Acta 1970, I , 31 1,
0022-3654/85/2089-1730$01.50/0
0 1985 American Chemical Society
Me2SO-Water Mixtures at High Pressure The technique of nuclear magnetic resonance spectroscopy has been used by several g r o ~ p s ~ ~to- ’investigate ~*’~ the dynamics of aqueous M e 2 S 0 solutions. Packer and TomlinsonI2 measured proton Tl’s and molecular self-diffusion coefficients of H20 and M q S O over the entire concentration range and a wide temperature range. Tokuhiro, Menafra, and Szmant” measured proton Tl’s and chemical shifts and attempted to separate the inter- and intramolecular contributions to the total proton relaxation rate. Glasel19 measured deuterium Tl’s in Me2SO-D20 solutions as a function of M e 2 S 0 concentration a t room temperature. No pressure experiments of any kind have been performed on aqueous MezSO solutions, although MezSO has been used as a solvent for high-pressure kinetics s t ~ d i e s . ~ ~ ~ ~ ~ In view of the interest shown in the Me2SO-H20 system, as well as the useful information which can be obtained from high-pressure experiments, we carried out experiments to determine the pressure dependence of the spin-lattice relaxation times and self-diffusion coefficients of water and heavy water in aqueous Me2S0. Measurements were made of the deuterium T I in Me2SO-D20 mixtures and the proton TIand H20self-diffusion coefficients in Me2SO-d6-H20 mixtures. In addition, densities of Me2SO-H20 solutions were measured over a corresponding range of pressure and concentration. Since we are mainly interested in pressure trends, these data will be used as an approximation for the densities of the Me2SO-d6-H20 solutions. There are several main goals of the present study. The first is to find whether the anomalous increase of motional freedom of water molecules with the initial application of pressure persists even when small amounts of M e 2 S 0 are added. The second is to check whether the Debye equation is applicable for the description of reorientation of water molecules in Me2SO-H20 mixtures at high pressure. The third is to determine the pressure effects on the intramolecular and intermolecular dipolar proton relaxation rates of H 2 0 in MezSO-d6-Hz0 mixtures.
Experimental Section The measurements of the spin-lattice relaxation times and self-diffusion coefficients were made by using a 14.1-kG electromagnet for a resonance frequency of 9.21 MHz for deuterium and 60 M H z for protons. The relaxation times were measured by using the inversion recovery pulse sequence, with an estimated accuracy of &3%. The diffusion coefficients were determined by using the Hahn spin-echo sequence,2gwith an estimated accuracy of &5%. The spectrometer system and high-pressure equipment have been described p r e v i o ~ s l y . ~The ~ system is automated for the measurement of relaxation times” and diffusion coefficient^.^^ The calibration of the magnetic field gradient for the diffusion cm2/s measurements was based on the value of D = 2.299 X for pure water at 25 O C and 1 bar.33 This value was used to calibrate the field gradient in a temperature probe, and then the diffusion coefficient of water in each Me2SO-d6-H20 mixture at 25 “C and 1 bar was determined by using this probe. The 1-bar value of the coefficient for each mixture was then used to calibrate the field gradient of the pressure probe for the determination of the pressure dependence of the coefficient for that mixture. This procedure accounted for the minor changes in the relative placement of the sample and the diffusion coils when the samples were changed. All samples were prepared by weight and were thoroughly degassed by the freeze-pumpthaw method before transfer to Pyrex sample cells in an oxygen-free glovebox. The atmospheric (27) Brower, K. R.; Ernst, R. L.; Chen, J. S . J . Phys. Chem. 1964, 68, 3814. (28) Fuchs, A. H.; Ghelfenstein,M.; Szwarc, H. J. Chem. Eng. Data 1980, 25, 206. (29) Hahn, E. L. Phys. Reu. 1950, 80, 580. (30) Jonas, J. In “Proceedings of a NATO AS1 on High Pressure Chemistry”; Kelm, H., Ed.; Reidel: Dordrecht, Holland, 1978; p 65. (31) Cantor, D. M.; Jonas, J. Anal. Chem. 1976, 48, 1904. (3’2) Cantor, D. M.; Jonas, J. J. Magn. Reson. 1977, 28, 157. (33) Mills, R. J . Phys. Chem. 1973, 77, 685.
The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 1731 TABLE I: Tait Equation Parameters for the Densities of Me2SO-H20 Mixtures xhis$30
T,O C
press. range, bar
PR,bar
0.005 0.012 0.025
25 25 25 25 25 25 25
1-4500 1-4500 1-4500 1-4400 1-3520 1-3200 1-1800
1 1 1 1 1 1 1
0.036 0.19 0.33 0.48
g/cm’ 0.9995 1.0033 1.0099 1.0170 1.0700 1.0990 1.0982
PR’,
B, bar
C
2222 2192 2525 2547 3049 2577 2019
0.0976 0.1042 0.1038 0.1153 0.1005 0.1015 0.0795
Reference 11. Proton TI in DMSO-d6-H20 Mixtures
Pressure (bar)
Figure 1. Proton T Iin Me2SO-d6-H20 mixtures. Numbers of each curve give the weight percent of Me2SO-d, in the mixture. 1.01
,
1
Deuteron TI in DMSO-D20 Mixtures 0.7
Pressure (bar1
Figure 2. Deuteron TI in Me2SO-D20 mixtures. Numbers of each curve give the weight percent of M e 2 S 0 in the mixture.
TIvalue was checked after each pressure cycle to check for any contamination from the pressurizing fluid (CS,). The densities of the MezSO-HzO mixtures were measured by using a high-pressure densitometer which has been described p r e v i o ~ s l y . ~The ~ reference values for the calibration of the densitometer were obtained from ref 11. The density data are conveniently expressed in terms of the Tait equation35
(34) Akai, J. A. Ph.D. Thesis, University of Illinois, Urbana, IL, 1977.
Baker and Jonas 3.0O
,
yo
Diffusion in DMSO-d6-t+0 Mixtures
-
H 2.0-
. I
-
0
\ r O . ‘ -
: I
0.1
30
0
2000
4000
Pressure (bar1
Figure 3. Water self-diffusion coefficient in Me2SO-d6-H20 mixtures. Numbers of each curve give the weight percent of Me,SO-d, in the mixture.
where pp is the density in g/cm3 at a pressure P,in bar, pR is the reference density at pressure PR for the Tait fit, and B and C a r e the empirical constants. The parameters for the Tait fit are given in Table I. Low conductivity glass distilled water was used for the Me2SO-d6-H20 and Me2SO-H20 solutions. The deuterated M e 2 S 0 (Merck Sharp and Dohme Canada Ltd.) had a stated minimum purity of 99.5 atom % D. The Me2SO-D20 and Me2SO-H20 solutions were made with reagent-grade Me2S0 (E. K. Industries, Inc.) and deuterated water (Bio-Rad Laboratories) with a stated purity of 99.8%.
Results and Discussion The N M R data are presented in Figures 1-3. The plots of the proton and deuteron spin-lattice relaxation times and water self-diffusion coefficients illustrate that as M e 2 S 0 is added to water, the values of T1 and D decrease. The rotational and translational motions of the water molecules are progressively slowed down with increased M e 2 S 0 concentration. The most notable feature of the plots is that the initial increase in proton and deuteron T,’s and self-diffusion coefficients with pressure, observed for pure ~ a t e r , ~is” maintained .~ in the more dilute aqueous M e 2 S 0 solutions. In pure water, the initial application of pressure enhances the rotational and translational mobility of the water molecules due to the distortion of the hydrogen-bonded network.’ Further compression results in closer packing of the molecules and restricts the mobility. The Tl’sand self-diffusion coefficients then decrease. The lower the temperature, the more pronounced is the anomaly; above -40 OC, the effect is no longer noticeable. In contrast, more “typical” liquids, without the strong directional forces present in liquid water, show increasingly restricted mobility with increasing pressure (density). The persistence o f the anomaly in the dilute Me2S0 solutions indicates that the long-range hydrogen-bonded structure of water has not been broken up until at least 30% Me2S0 (xMMo= 0.1). The smaller magnitude of the T,’s and D’s at lower concentrations reflects the “rigidifying” effect2I of Me2S0 on the water structure as observed in the neutron scattering studies. At higher M e 2 S 0 concentrations, the decreased mobility is due to strong hydrogen-bonding interactions between H 2 0 and Me2S0. The 1-bar values for the proton Tl’s in Me2SO-d6-H20 at 25 OC are in excellent agreement with the results of Packer and Tomlinson.I2 There are no data in the literature for deuteron T,’s
in Me2SO-D20 a t this temperature. GlaselI9 measured Tl’sat 31 OC and 1 bar. Our results compare well if the 6-deg temperature difference is taken into account. Our 1-bar values of the water self-diffusion coefficients are approximately the same as those obtained by Packer and Tomlinson12 at 26 OC. The differences can be largely explained by the difference in the value measured for pure water. We used a reference value33 of D = 2.299 X cm2/s for the calibration of the magnetic field gradient, so all subsequent diffusion coefficients are referenced to this number. Packer and Tom1insonl2 report a value of apcm2/s for pure water at 25 OC. If this proximately 2.55 X difference is accounted for, then our results fall on the same curve, within experimental error. Packer and Tomlinson also observe a minimum in the curve at around M q S O mole fraction 0.3, while our curve is smooth. However, the difference which they observe is within our experimental error. Our results for the pressure dependence of diffusion in pure water at 25 OC are in excellent agreement with Krynicki et al.36 It has been shown37that the spin rotation and intra- and intermolecular dipolar contributions to the deuterium spin-lattice relaxation rate in D 2 0 can be neglected. Relaxation is due to quadrupolar interactions. Therefore, the reorientational correlation times for the D 2 0 molecules in the Me2SO-D20 mixtures were calculated from the experimental spin-lattice relaxation times by use of the equation for the quadrupolar i n t e r a ~ t i o n ~ ~
1 = i3( 1 + $/3) (e2$ T1
where is the electric field gradient asymmetry parameter, ( e 2 q Q / h )is the quadrupolar coupling constant (QC), and 7,g is the correlation time. The asymmetry parameter was neglected as it is very srnalL5 Since there are no reported studies of the deuterium quadrupole coupling constant in MqSO-D20 mixtures, the QC value for pure heavy water, 230 f 10 kHz,2v37was used. We will assume that the coupling constant is independent of pressure and composition. A study of the effects of compression on heavy water by Jonas, DeFries, and Wilbur2 showed that the deuterium quadrupolar coupling constant did not change significantly for pressures up to 9 kbar-the average value remained 230 kHz. Hindman, Svirmickas, and Wood39studied the deuterium T1 relaxation of D 2 0 in various organic solvents and used the following relationship, developed by Chiba,40 between the Q C and the -OH stretching frequency in the mixture to calculate the quadrupolar coupling constant of D 2 0 in the mixture 2aQC = 2.26 X 10-2(~oH)2
(3) where 2 4 Q C ) is in Hz and vOH is wavenumbers. A study of the -OH and -OD band profiles in aqueous Me2S0 mixtures by Brink and FalkZ2showed no change in frequency or half-width of vOH or vOD upon the addition of MezSO to H 2 0or D 2 0 for concentrations up to 20 mol % Me2S0. This result, combined with Chiba’s relationship (eq 3), implies that the Q C also remains constant with M e 2 S 0 concentration up to 20 mol % at 1 bar. In order to determine whether the hydrodynamic equations describe the reorientation of D 2 0 in Me2SO-D20 mixtures, we look at the equation which relates the correlation time to the macroscopic viscosity 4 7ra3grc re=--
3 kT
where a = 1.38 A, the hydrodynamic radius of D20, g is the viscosity in poise of the mixtures, and K is the McClung-Kivelson ( 3 6 ) Krynicki, K.; Green, C. D.; Sawyer, D. W. Faraday Discuss. Chem. SOC.1919,-66, 199. (37) Powles, J. G.; Rhodes, M.; Strange, J. H. Mol. Phys. 1966,11,515.
Oxford 138) Abranam. A. “The Princioles of Nuclear Magnetism”; University P G s : London, 1961. (39) Hindman, J. C.; Svirmickas, A.; Wood, M. J . Phys. Chem. 1968.72, 4188. (40) Chiba, T. J . Chem. Phys. 1964, 41, 1352. ’
(35) Skinner, J. F.; Cussler, E. L.; Fuoss, R. M. J . Phys. Chem. 1968, 72, 1057.
(4)
The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 1733
Me2SO-Water Mixtures at High Pressure
Equation 7 was derived by use of the Stokes-Einstein equation which relates diffusion to the macroscopic viscosity by
TABLE II: Applicability of Debye Equation at 1 bar f
0.02 0.05 0.10 0.15
0.50 0.80
Te(exp), ps 3.06 3.27 3.58
q’Tl/T X lo5 1.61
4.00
9.32 12.6
K~
KC
0.98 1.00
1.63
0.99 0.99 0.97 0.98
1.54 1.18
1.04 1.35
1.61 1.65
D=- kT Crus
0.94 0.94 0.94 1.17
“Weight fraction of Me2S0 in the Me2SO-D20 mixtures. b~ as determined from deuteron T I and viscosity data. c~ as determined from deuteron TI and diffusion data. parameter.41 For K = 1, the above expression is the Debye equation. The parameter K is equal to the ratio between the intermolecular torques on the solute molecules to the intermolecular forces on the solvent molecules. Physically, K is interpreted in terms of the coupling between the rotational and translational motions of the molecule, with K = 1 for complete coupling, and K = 0 for no coupling. For most molecular liquids, K is small (-0. l ) , but it has been shown by both dielectri~?Z~~ and NMRmeasurements that K = 1 for H 2 0 and D 2 0 over a range of temperatures at 1 bar. The Debye equation describes well the reorientation of H 2 0 at 1 bar, but pressure studies have shown that it breaks down with increasing density.233”The parameter K decreases due to decreased rotational-translational coupling. In the study of reorientation of D20 in dioxanewater mixtures: it was found that the Debye equation describes well the reorientation of DzO molecules as a function of composition and temperature (30-50 “ C ) a t 1 bar. The parameter K was equal to 1 and was constant, while the T I and viscosity changed by a factor of 2. However, the Debye equation did not describe the reorientation of the dioxane-d8 molecules; K was equal to -0.06-0.15 and varied with concentration. If we combine eq 4 with eq 2 , we obtain the expression
5=+) T aa3 K(QC)’
(5)
Therefore, if the Debye equation is an appropriate description of the reorientation of D2O in aqueous M e 2 S 0 solutions at 1 bar, the product q T , / T should remain constant with changes in concentration (since we have concluded that the QC is concentration independent). The results for 1 bar, where q is known, are given in Table 11. Viscosity data for the deuterated solutions are not available, but we can approximate the difference using an equation of the form
where is the mixture viscosity corrected for deuteration, qmix is the viscosity of the nondeuterated solutions,” x is the weight fraction of Me2S0 in the Me2SO-D20 mixture, and q D 2 0 / ~ H 2 0 is the experimentally4’ determined ratio of viscosities of heavy and light water, equal to 1.231. Also included in Table I1 are the K values obtained by using the measured diffusion coefficients of water in aqueous Me2S0, using an equation similar to eq 5 (7) ~
~ ~ _ _ _ _ _ _ _ _ _
(41) McClung, R. E. D.; Kivelson, D. J . Chem. Phys. 1968, 49, 3380. (42) Collie, C. H.; Hasted, J. B.; Ritson, D. M. Proc. Phys. Sac., London, Sect. B 1948, 60, 145. (43) Grant, E. H. J . Chem. Phys. 1957, 26, 1575. (44) Woessner, D. E. J . Chem. Phys. 1964, 40, 2341. (45) Smith, D. W. G.; Powles, J. G. Mol. Phys. 1966, IO, 451. (46) Krynicki, K. Physica (Amsterdam) 1966, 32, 167. (47) Millero, F. J.; Dexter, R.; Hoff, E. J . Chem. Eng. Dura 1971, 16, 85.
(8)
where C = 4 in the slip limit and C = 6 in the stick limit. The Stokes-Einstein equation has been found to be valid for water over a wide range of temperature and pressure36with C = 4.6 f 0.3. The difference between the diffusion coefficients of light and heavy water was accounted for by the experimental ratio D p z O / D D z O = 1.228 given by Mills.33 The variation of this factor with concentration should be insignificant. The results of these calculations show that the product q T , / T stays constant, with K = 1 within experimental error, up to the 80 wt 5% solution (Me2S0mole fraction 0.51). This implies that the Debye equation does describe the reorientation of the D 2 0 = in solution at 1 bar, at least through the mole fraction xMeZSO 0.2. The agreement between the values of the parameter K determined by the two methods indicates that the Stokes-Einstein equation, with C = 4.6, holds for the diffusion of water in the mixtures at 1 bar. There have been no previous studies reported on the applicability of the Debye equation to the reorientation of water in these solutions, although a few articles do mention the reorientation of the M e 2 S 0 molecule. Tokuhiro et al.I3 carried out isotopic dilution studies to separate the inter- and intramolecular contributions to the M e 2 S 0 proton T I as a function of composition and temperature at 1 bar. Wang et aL20 studied the reorientation of the M e 2 S 0 molecules in aqueous solution by measuring the Rayleigh relaxation times as a function of temperature and composition at 1 bar. The conclusions of the two studies are that the Debye equation describes the reorientation of M e 2 S 0 molecules in pure M e 2 S 0 but not when water is added. The discrepancy is largest at low M e 2 S 0 concentrations and becomes O 0.65. less significant after X M ~ ~ S= To summarize, the Debye equation satisfactorily describes the reorientation of each pure component at 1 bar. The hydrodynamic model continues to describe the water reorientation in the mixtures, at least up to X M ~ ~ S=O 0.2, and possibly higher. The equation fails to predict the reorientation of M e 2 S 0 in the mixtures, particularly at the lower M e 2 S 0 concentrations. The available data are too sparse at high Me2S0 concentrations (xMezpo > 0.8) to see if the hydrodynamic equations are a valid description for M e 2 S 0 reorientation in this region. We can extend our analysis of the validity of the Debye equation to high pressures by use of eq 7. As noted earlier, for pure water K decreases from approximately 1.0 to a value of about 0.62 for a pressure increase from 1 bar to 5 kbar, reflecting the decrease in rotational-translational coupling due to the distortion of the hydrogen-bonded network. In an earlier studys of the reorientational motion of DzO in D20-dioxane solutions, the pressure ~ determined from viscosity and dependence of the K ( Q C )term, deuterium T I data, was determined as a function of dioxane concentration. As noted in the article, dioxane is considered to enhance the water structure up to 0.2 mole fraction. At higher concentrations, the random hydrogen-bond network in water is disrupted by the addition of dioxane. The plot of the K ( Q C )values ~ at 30 O C , normalized to the 1-bar value, as a function of pressure (Figure 3 in ref 8) indicates that the higher the dioxane content in the mixture, the stronger is the pressure dependence. However, ~ for an error was made in this plot, as it shows the K ( Q C )value pure water decreasing only 10% by 3000 bar, rather than the actual decrease of approximately 30%. The revised plot shows that for solutions with dioxane mole fractions of 0.05 and 0.10, the pressure dependence of the quantity K(QC)’is actually less than or about equal to that of pure water. In other words, the enhanced structure of the low dioxane concentration solutions leads to increased resistance of the rotational-translational coupling to the application of pressure. For higher dioxane concentrations (dioxane mole fraction equal to 0.29, 0.59, and 0.73), where dioxane is known to disrupt the hydrogen-bnded structure of the
-
Baker and Jonas I.Or
0.9-
I
I
@
*
6
9
x0 ’0
-
N!
)r
8
0.0-
:
8
0
8
I
I-
t
I
.
‘V
l t
! I
Relaxation Rates at Atmospheric Pressure
1 0
0
0.7’
I
I
0
b
1
.
I
*
4
water, the pressure dependence is much stronger than in pure water. The destruction of the water structure causes the mixtures to be less resistant to pressure, and the rotational-translational coupling decreases at a faster rate. In Figure 4 we plot the value of K ( Q C ) ~normalized , to values at 1 bar, vs. pressure for D 2 0 in Me2SO-D20 solutions up to a mole fraction of Me2S0equal to 0.2. The ratios were determined according to eq 7 by assuming the validity of the Stokes-Einstein equation over this concentration and pressure range. The agreement in the 1-bar K values calculated by using viscosity data and those calculated by using diffusion data (see Table 11) showed that the Stokes-Einstein equation is valid when extended to diffusion in the mixtures a t 1 bar, at least up to the 0.2 mole fraction M%SO. Considering this agreement, as well as the known validity of the equation for water at high pressures,36we believe the extension to mixtures at high pressures i s reasonable. The plot shows that as M e 2 S 0 is added to water, the pressure dependence of the quantity K(QC)’ decreases. In analogy with the study on dioxane, this confirms the atmospheric pressure measurements which show that the addition of M e 2 S 0 enhances the long-range hydrogen-bonded structure of pure water. At these low concentrations, M e 2 S 0 is a water “structure maker”. Of course, the possibility that the Q C is increasing with pressure cannot be conclusively ruled out. However, since the evidence suggests that the deuteron Q C is independent of concentration at 1 bar, and since it has been shown2 that the QC for pure D 2 0 is independent of pressure up to 9 kbar, the possibility that it increases with pressure in the mixtures is unlikely. In order to check the effect of added Me2S0 on the rotations and translations of the water molecules, the contributions of the intra- and intermolecular relaxation rates to the total observed proton relaxation rate of H 2 0in the Me2SO-d6-Hz0 solutions were separated. Since the spin rotation interaction is negligible for water a t these temperatures and pressure^,^' the relaxation is considered to be totally due to dipole-dipole interactions. The intermolecular contribution was calculated by using Hubbard’s4* equation for dipole-dipole relaxation for spin nuclei in the motionally narrowed limit
$)*I
(9) 5aD where N is the density of spins, a is the hydrodynamic radius of water, b is the distance of the proton to the center of the molecule, and D is the self-diffusion coefficient. The values of (I and b used were those for pure water ( a = 1.38 A, b = 0.92 A). The H 2 0 self-diffusion coefficients were those measured in the H20Me2SO-d6 mixtures. The values for the density of spins were derived from the experimentally measured macroscopic densities of the mixtures. The densities were corrected for deuteration by using the 1-bar density of a Me2SO-d6-H20 solution as the reference density for a Tait fit35of the measured nondeuterated densities. (48) Hubbard, P. S. Phys. Rev. 1963,131, 275.
(I/T!) Inter
-
Figure 4. Pressure dependence of K(QC)*,normalized to 1-bar values: (0)pure water; (A)X M ~ ~ S O 0.005;(V)X M ~ ~ S O 0.043; (0)X M ~ ~ S=O 0.084; (m) xMc2s0= 0.18; ( 0 )xMc2S0 = 0.20.
- - --Nay‘h2[ 1 + o m ( :)2 + ,.is(
0
1
1
I /TI) observed (I/Tl) intra
O( A.V
+-
0 0
I
0.1
0.2
I 0.3
1
Y
0.4
0.5
0,6
DMSO Mole Froctbn
Figure 5. Contributions to the total observed proton relaxation rate. l/?,, in Me2SO-d6-H20mixtures at 1 bar: (0) observed rate; (v) intramolecular contribution from method 1; (A)intramolecular contribution from method 2; (0)intermolecular contribution.
The intramolecular contribution could be estimated in either of two ways. In the first method, we use the correlation time calculated from the deuterium T I data as an estimate of T~ in the equation38
for the intramolecular dipole-dipole ratio for spin ‘I2nuclei in the motionally narrowed limit. The measured correlation time is adjusted by the ratio TH,o/rD20= 0.781 given by Lankhorst et al.49 Another alternative is to calculate the intermolecular contribution according to eq 9 and then subtract this from the observed proton relaxation rate to obtain the intramolecular contribution. The second method is quite common, but it is subject to error due to the experimental errors in measuring the self-diffusion coefficents and the densities, as well as errors introduced in correcting the densities for deuteration. For the first method we must use data from two different samples, unlike the second method, where the T I and D are measured on the same sample. The results of both methods are plotted as a function of concentration at 1 bar in Figure 5, along with the intermolecular contribution and the total observed rate. The values for the intramolecular rate all fall on the same smooth line, independent of the method of calculation, indicating that either method is appropriate. In addition, this agreement confirms that the assumptions made in the calculation of T~~~ and (1 / Tl)inter,lntra are valid. There are several notable features of the plot of relaxation rates vs. composition at 1 bar. The intramolecular contribution to the total rate is dominant at all concentrations and increases as the M e 2 S 0 concentration increases. This observation is consistent with that of Packer and Tomlinson;12 their results indicate that only rotations contribute to the relaxation of water protons for xMezSO 20.3. For mixtures with smaller Me2S0 concentrations, they see signs of increasing intermolecular contributions. The variation of the intermolecular contribution follows the variation of the solution density and viscosity, with a maximum between the SO% (xMW= 0.2) and 80% (xMe2M = 0.5) solutions. The intermolecular contribution becomes less significant with increasing Me2S0 concentration, so the change in the overall rate is dominated by the changes in intramolecular rate. The relaxation behavior of the water molecules is predominantly determined by the hindered rotational motion caused by interactions with the added Me2S0. The pressure dependence of the intra- and intermolecular contributions to the total relaxation rate is shown in Figure 6 for (49) Lanirhorst, D.; Schriever, J.;Leyte, J. C . Ber. Bunrenges. Phys. Chem. 1982, 86,215.
J . Phys. Chem. 1985,89, 1735-1741
1735
Summary
4l
I
'
'i
Pntwre (Bar)
Figure 6. Pressure dependence of the intramolecularand intermolecular proton relaxation rates, 1/ T I ,in Me2SO-d6-H20 mixtures, normalized to values at 1 bar. Open symbols represent intramolecular rates, full symbols represent intermolecular rates. (A)5 wt % Me2SO-d6;(0) 50 Wt % Me,SO-d& (0)80 Wt % Me$O-d6.
the 5 wt % (xMe,~0= 0.01), 50 wt % (xMule2S0 = 0.2), and 80 wt % ( ~ ~ $= 0.5) 0 solutions. The application of pressure increases both intra- and intermolecular relaxation rates for the more concentrated solutions, reflecting the restricted rotational and translational motions in the compressed liquids. However, in the 5% solution, the intermolecular rate increases, but the intramolecular rate decreases. The same behavior is observed in pure water at lower temperatures.2 The anomalous behavior of pure water is maintained in the low M e 2 S 0 concentration solutions. In general, as the concentration of M e 2 S 0 is increased, the relaxation rates become more sensitive to the changes in pressure. The behavior becomes more like that of nonassociated liquids. As expected, the intermolecular rate is more sensitive than the intramolecular rate, reflecting the greater sensitivity of translational motions to changes in density.
The persistence of the pressure anomaly in the relaxation and diffusion behavior of water in the mixtures up to 0.1 mole fraction M e 2 S 0 indicates that the water structure has not been broken up by the addition of small amounts of Me2S0. At low concentrations, M e 2 S 0 is in fact a water structure maker, reducing the mobility of the water molecules as reflected in the decreased Tl's and diffusion coefficients. The enhancement of the water structure is further confirmed by the decreased pressure dependence of the rotational-translational coupling in solutions for xMW5 0.2. At higher M q S O concentrations, the water struture has been extensively disrupted, as evidenced by the disappearance of the pressure anomaly. The addition of the M e 2 S 0 at these concentrations causes the relaxation and transport behavior of H20as a function of pressure to become more like that of a typical liquid. At 1 bar, the reorientation of the water molecules in aqueous MezSO can be described by the Debye equations, at least up to a concentration X M ~ ~ = ~O 0.2. . The Stokes-Einstein equation for the diffusion of water in the mixtures is also valid in this region. At all concentrations and pressure studied, the intramolecular contribution to the relaxation rate is dominant, becoming more so as the M e 2 S 0 concentration is increased. As expected, the intermolecular rate is more severly affected than the intramolecular rate by the increases in density.
Acknowledgment. We thank Dr. Donald R. Brown for his assistance with the measurements. This work was supported in part by the National Science Foundation under Grant NSF C H E 81-1 1176 and the Department of Energy under Grant DOE DEFG 22-82 PC 50800. Registry No. Me2S0, 67-68-5; deuterium, 7782-39-0.
X-ray Diffraction Study of the Phase Transition in Crystalline Tetracene U. Sondermann? A. Kutoglu? and H. Biissler* Fachbereich Geowissenschaften, und Fachbereieh Physikalische Chemie, Philipps- Universitat, 0-3550 Marburg, FRG (Received: October 18, 1984)
By applying X-ray diffraction techniques it has been established that crystalline tetracene undergoes a structural transition to a second triclinic phase below 200 K. The transition temperature depends on external parameters, such as the strength of mechanical coupling of the crystal to a supporting surface, and is subject to a hysteresis effect. The parameters of the new phase have been determined and a structure has been proposed on the basis of lattice energy calculations. It is concluded that the transition involves a rotation of the molecule at 1/z,1/2,0around the axis normal to the molecular plane. Translational displacement of the face-centered molecule, equivalent to a reduction of crystal symmetry from Pi to PI, stabilizes the new phase.
Introduction A peculiarity of crystalline tetracene (TC) is the occurrence of a phase transition whose parameters depend in a subtle way on sample history and preparation and which had not be characterized by diffraction methods. Prikhotko and Skorobogatko' were the first to note a temperature-driven phase transition near 70 K in freely mounted crystals accompanied both by a red shift of the optical absorption edge and by crystal shattering. However, if kept in good mechanical contact with a quartz substrate the crystals survived cooling and retained the spectral features characteristic of the high-temperature phase. Fluorescence excitation spectroscopy2as well as reflection spectroscopy3confirmed Fachbereich Geowissenschaften.
* Fachbereich Physikalische Chemie.
the existence of a temperature-induced red shift of the absorption spectrum yet indicated that the transition began already near 180 K. Vaubel and BasslerZ also noted pretransitional phenomena in a temperature interval of about 50 K above the transition temperature Tt and found a variation of Tt between 170 and 200 K depending on the way crystals had been mounted. Conducting a systematic study of polarized reflection spectra as a function of temperature and crystal mounting, Kolendritskii et aL4 found Tt 160 K for freely mounted crystals and confirmed the earlier
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(1) A. F. Prikhotko and A. F. Skorobogatko, Opt. Spectrosc., 20, 33 (1966). (2) G. Vaubel and H. Bassler, Mol. Cryst. Liq. Cryst., 12, 39 (1970). (3) J. M. Turlet and M. R. Philptt, J . Chem. Phys., 62, 4260 (1973). (4) D. D. Kolendritskii, M. V. Kurik, and Yu.P. Piryatinskii, Phys. Status Solidi b, 91, 741 (1979).
0022-3654/85/2089-1735$01.50/0 0 1985 American Chemical Society
