98
STEVEN A. SCHICHMAN AND RALPHL. AMEY
Viscosity and Local Liquid Structure in Dimethyl Sulfoxide-Water Mixtures1
by Steven A. Schichman and Ralph L. Amey" Departmmt of Chemistry, Occidental College, Los Angeles, California 90041
(Received September 16, 1969)
Publication costs assisted by The Petroleum Research Fund of the American Chemical Society
The shear viscosity and density of ten dimethyl sulfoxide (DMSO)-water mixtures have been measured over the concentration range 0.1 to 0.8 mole fraction (mf) DMSO and over the temperature range 213 5 T 5 293'K. Density data are reported and have been fitted to a quadratic equation of the form p = a bT cT2. The maximum in the viscosity-concentration curve observed by others at elevated temperatures is found to sharpen considerably at low temperatures. The very large positive AS,* calculated for viscous flow in the region of 0.33 mole fraction DMSO at low temperatures is indicative of an extensive disordering process. Analysis in terms of WLF theory yields To= 120' in the region of 0.3 mf DMSO.
+ +
Introduction Recent interest in the DMSO-water system and of its role in biochemical processes has spurred the measurement of some of its excess properties. Analysis is hindered by 1,he fact that it represents one of the more complicated binary systems, namely an associating component plus a second component which is capable of forming hydrogen bonds with the first. The likelihood of resolving this problem at present is small, since the complete answer must await an intimate linowledge of the intermolecular potential governing the system. As has been pointed out by Rice and his coworkers, however, much can be accomplished to describe liquid behavior if experimental data are available against which theoretical constructs may be tested. Viscosity studies at elevated temperatures on mixtures of dimethyl sulfoxide (DMSO) and water have led several i n ~ e s t i g a t o r s ~t-o~ suggest strong association between DMSO and water. Cowie and Toporowski3 and Lindberg and Ilaureh5have proposed the existence of a 2: 1 \vater-Di\lSO association complex in liquid mixtures. The former's analysis was based upon the method of Geddes6 in which he measured the greatest deviation from linearity for a viscosity vs. mole fraction plot at constant temperature. They concluded that the complex was thermally labile and could exist in an undissociated state only at low temperatures. It has been noted by others, however, that the freezing point-composition curve indicates a eutectic rather than compound formation7 at an approxinlate DMSO mole fraction of 0.33. Furthermore, the lack of any observed splitting in the R~~~~ sulfur-oxygen stretching band hakj been submitted as evidence by Lindberg and Rlajaini that there is no H-bonded complex formed be tween the components.8 ,4S part of our study Of aprOtiC solvent Systems We The Journal of Physical Chemistry, Vol. '76,No. 1, 19'72
have extended the viscosity measurements on DMSOwater mixtures to much lower temperatures. In this paper we report viscosity and density data on ten mole fractions talien at several subambient, temperatures. The results are discussed in terms of several model systems. Experimental Section Materials. Reagent grade dimethyl sulfoxide (J. T. Baker, and Matheson Coleman and Bell) was used directly without further purification. Maximum original water content as stated on the label was 0.03%. The mixtures were prepared with distilled u-ater by an addition method using a top loading balance. Density Measuremeiats. Densities were obtained with a Sprengel-Ostwald-type pycnometer of approximately 11-ml capacity. The pycnometer was calibrated above 0" with distilled waterg and below 0" with absolute methanol.1o The temperature bath used was a Lauda Type NB circulator with an average temperature control accuracy of *0.02". The circulator liquid was methanol, and the circulator thermometer was cali(1) A portion of this work was presented a t the 158th National Meeting of the American Chemical Society, New York, N . Y., Sept 11, 1969. (2) S. A. Rice, J. P. Boon, and H. T. Davis in "Simple Dense Fluids," H. L. Frisch and 2. W. Salsburg, Ed., Academic Press, New York, N. Y., 1968, p 251. (3) J. M. G. Cowie and P. M.Toporowski, Can. J . Chem., 39, 2240 (1961). (4) R . J. Fort and W. R. Moore, Trans. Faraday Soc., 62, 1112 (1966). (5) J. J. Lindberg and R. Lauren', Finska Kemiskzamfundets Medd., 719 37 (19G2). (6) J. A. Geddes, J . Amer. Chem. Sot., 55,4532 (1933). (7) R. K. Wolford, J . Phys. Chem., 68, 3392 (1964). (8) J. 3. Lindberg and C. Majani, Acta Chem. Scand., 17(5), 1477 (1963). (9) G. S. Kell, J . Chem. Eng. Data, 12, 66 (1967). (io) S. Young and E. C. Fortey, J . Chem. SOC., 81, 717 (1902).
Vrscarw~~r ANDI LOCAL LIQUIDSTRUCTUREIN DMSO-H20
99 __9___11--
Table II : Densitirs id 1.bMSO-H,O -Mixtures ad Several Temperatures"
0.10 0.20 0.25 0.30 0.33 0.35 0.40
1.159~
11.143 1i.155 li.159 11.160 li.167
1.121 1.136 1.147 1.151 1.151 1.158
1,140 1.151 1.154 1.156 1.162
0.50
1.112 1.125 1.134 1.137 1.139 1.145 1.151
1.062 1.101 1.113 1.121 1.124 1.126 1.131 1.136
0.60
1.060 1.098 1.110 1.118 1.120 1.121 1.127 1,132 1.132
1.050 1.082 1.093 1.100 1.104 1.104 1,108 1.112 1.112 1.112
1.055 1.090 1.101 1.109 1.112 1.113 1.117 1.122 1.122
0.80 a
Temperatures in degrees Celsius.
* Mole fraction DMSO.
1.048 1.079 1.090 1.096 1,099 1.100
1.104 1.108 11.108
1.107
1.045 1.076 1.086 1.092 I . 096 I .096 1,099 1,103 I.103 I , LO2
The relative error ( A p l p ) of each density is 10.1270.
brated at the o-xylene melting point (-25.19"), the ice point of distilled water, and 20.00". A nonlinear calibration curve was obtained for the pycnometer. Densities of the ten DM SO-water mixtures were obtained in each case over their liquid range. P ~ S C OA4Seasurtments. ~~ZJ Viscosity data were obtained with a 1Haali.e RIodel B precision falling ball viscometer. Ball constants were supplied by the manufacturer and compared favorably with those obtained with standard calibration fluids. Falling times were measured to an accuracy of 3~0.05see. Low-temperature operation wag maintained with a Dry Ice heat exchanger in conjunatjon xvith the Lauda NB circulator.
2.5
\
2.3
/--\
2.1
-50
-45
I .9
I.? P
Re SUI ts Table 1 liste the densities of ten DMSO-water mixtures in gram8) per cubic centimeter over the temperature sange 213 7' 293°K. Table I1 presents the
<
ionof mole fraction for several isotherms. The Journal of Physical Chemistry, Vol, 76, N o . 1 , 1971
STEVEN A. SCHICHMAN AND RALPH L. AMEY
100 ~
Table I11 : Viscosities of DMSO-H20 Mixtures at Several Temperatures" - 60
570b
-55 341.3" 339.4c 339.6" 336.8~ 283.10
- 50
213.7" 214.7" 214.7" 212.6~ 181.1~
- 46
118.gd 138.00 139.90 140.20 139.3" 123.8"
- 30
Viscosity, oP, at t =-------
36.1tjd 42.60d 43.81d 43.47d 43.OOd 4O.0Od 29.37d
- 15
8.12* 14.7gb 17.13d 18.25d 18.25d 18.17d 17.20d 13.5kV
-lob
6.41 11.43 13.24 14.20 14.27 14.23 13.43 10.91 9.15
Temperatures i n degrees Celsius. Average relative error = =t0.55%. relative error = d ~ 0 . 3 4 7 ~e .Extrapolated value. Q
Error Analysis
1
_ _ _ _ _ _ _ I I _
Ob
lob
15b
2ob
XDn1so
4.205 7.27 8.46 9.07 9.16 9.17 8.71 7.37 6.25
2.941 4.899 5.72 6.09 6.17 6.16 5.94 5.19 5.30 3.362
2.496 4.097 4.719 5.10 5.18 j.19 5 02 4.445 3.904 2.964
2.152 3.455 4 . OOe 4.310 4.383 4.398 4.267 3.838 3,398 2.627
0.10 0.20 0.25 0.30 0.33 0.35 0.40 0.50 0.60
Average relative error = 2~0.41%.
for DMSO-water mixtures. However, upon extrapolation of our highest temperature values (20°),good agreement is reached with published density data measured at 25°.3- j t l 2 Our reported relative error of about 0.5% for the viscosity (see Table 111) reflects what is thought to be a conservative estimate of the accuracy of our data. Comparison of our viscosity results with the literature is compatible with our error figure when it is recognized that bhere is little agreement among the present literaturevalues for this system. As can be seen from 'Table I V , our value falls between the two reported literature values. Due to the high melting points of DMSO (18.51') and water, it is not possible to calculate partial molal excess functions for the binary mixtures at low temperatures. Thus we are deprived of one of the most important parameters for the comparison of nonelectrolyte mixtures"l3 The measured isotherms of viscosity vs. mole fraction demonstrate a progressively sharper maximum at lower temperatures occurring in the region of 0.3 mole fraction DMSO. This is consistent with the observations of othcr workers at higher temperatures. 3-6 The Journal of Physical Chemistry, Vot. 76,No. 1, 1971
0.80 d
Average
Table IV : Comparison of Densities and
The viscosity of a liquid when measured by a falling Viscosities with Literature Values ball viscometer may be calculated from q = FDK where Mole ------Density F is the falling time in seconds, D is the difference befraction Forttween ball and liquid densities at a specified temperaMoorea DMSO ture, and K is the ball constant supplied by the manu0.20 1.0742 facturer (and rechecked against standard calibration 0.25 1.0816 liquids). The total uncertainty in the viscosity was 1 . 0885d 0.30 1.0989 0.40 taken to be due to the uncertainties in the falling time (estimated as =k0.05 see), the liquid density, and the ----Viscosity Mole fraction Fortspecified temperature (typically =!=0.05to =!=0.2"). DMSO Moorea The relative errors in the viscosity, A q / v , were calcu0.20 3.156 lated in the usual manner." These are included in 0.40 3.799 Table 111. 0.60 3.008
Discussion No other low-temperature values have been reported
I
--.
in g/cms at 25"--SchichmanCowieAmeyb ToporowskiC
1.072 1.082 1.088 1.095
1.0717 1.0809 1.0880 1.0956
in OPat 25°------SohiohmanCowieAmeyb ToporowskP
3.045
2.97 3.69 2.98
a Reference 4. Calculated according t o quadratic coefInficients. c Interpolated from published values, ref 3. terpolated value.
Figure 1 shows these isotherms in terms of log q to facilitate display of all the data on a single graph. Because of the nature of the logarithmic function, the peaking of the isotherms is not as apparent as it would be on a viscosity-mole fraction plot. At present, no successful quantitative analysis of such maxima in associated mixtures has been made.13*14Although vis(11) (a) E. B. Wilson, Jr., "An Introduction to Scientific Research," McGraw-Hill, New York, N. Y., 1952, p 272. (b) The viscosity of both distilled water and reagent grade glycerol was measured a t 20° and was found to be accurate in each case to within a t least 0.3%. This is less than any relative error which we have reported in Table I11 for our data. Due to the uncertainties in (and unavailability of) low-temperature density and viscosity data, comparable direct accuracy checks at low temperatures are less satisfactory. However, measurements made by us on glycerol-water mixtures a t low temperatures indicate that we are justified in reporting our error in a comparable manner to that reported at higher temperatures. (12) R . G. Lebel and D. A . I. Goring, J . Chem. Eng. Data, 7, 100 (1962).
(13) R. L. Scott and D. V. Fenby, Ann. REV.Phys. Chem., 20, 111 (1969) * (14) A. Bondi in "Rheology:
Theory and Applications," Vol. 4, F. R. Eirich, Ed., Academic Press, New York, N. Y., 1967, p 75.
cannot be ascribed uniquely to a single phenomenon nor to a particular model systeni. ~ ~ c ~ and ~ a ~ ~ ~ Ubbelohde have treated deviations from Arrhenius behavior in a number of liquids as a, consequence of cluster formatlion near the melting Such an interpretation of behavior in the DMSO-water system is tempting but not feasible by the ~ ~ ~ c-1Jbbe~ ~ ~ ~ ~ lohde method due t o the greater compJcxi.ly of the DMSO-water interaction. Jeaorek and hlark,15 in their discussion of this type of system, indicate that ~ may ~ ~ ~ ~ an extensive network of branched ~ ~ ~fwnm be responsible for many of the properties of DMSOwater mixtures. An alternative vi@m might) m x m e an equilibrium between a Dn~ISCt-watereo~73pRexknilar to the one previously mentioned arid an n-mer cluster of complex units. The question of whether one is dealing with branched polymeric chains or j cannot be answered readily from present data. From a fit of the linear high-tem-per,2dure region of each curve in Figure 2 to the Arrhenius expression
2.5
2.0
1.5 60
0
II
1.0
values of the parameter E, were obhained. By identification of E, with the ent,halpy of activation for viscous flow, AH,*, and use of the Eyring rate equation
0.5
Figure 2. Log viscosity of several DMSO-Ht0 mixtures as a function of reciprocal Kelvin temperature.
cosity maxima of thirg type are frequently identified with compound formatjon, there are several experimental observations M hich appear t o be in conflict with such an interpretation. The lack of compound formation has been identified with the presence of a eutectic rather than LL maximum at 0.33 mole fraction DMSO in the DnISO-N20 phase diagram.’ Lindberg and Rfaj ani have measured the Raman spectra of DMSO-€120 mixtures.8 They find 110 splitting in the sulfur-oxygen stretching band and conclude from this that no Hbonded complex can be present. NeverthelesF,, significant evidence to support the presence of an t:quilibriurn of the form
+
D,~/ISO 211~0
complex
appears to be available from calorimetric, nmr, and earlier viscosity rebults. These have been adequately summarized by both Wolford’ and Jezorek and Mark15 and will not be repeated here. Typical of the nonlinear deviation from Arrhenius behavior observed at lower temperatures is the plot of log v us. reciprocal Kelvin temperature shown in Figure 2 for several DhW2 mole fractions. Such nonlinearity
the entropy of activation, AX,*, for each mole fraction was obtained. At, the lowest temperatures obtainable with each mole fraction-usually t h e melting pointstangents were drawn to the curves, and the appropriate parameters were obtained. These are listed in Table V. ~
Table V : Activation Parameters of Viscous Flow for DMSO-H20 Mixtures c-----T
>> Tmp-----
----Near
AS,*,
T’mp----
AS,.,
cal/mol-
XDJISO
E,, kcal
dea
kcal
0.10 0.20 0.30 0.40 0.50 0.60 0.80
2.02 2.24 2.50 2.17 2.04 1.92 1.65
f4.14 +4.68 +4.80 $4.52 +4.24 f4.08 +3.52
2.0 4.4
&I,
(7.7) 1.2 3.0 2.4 1.6
cal/moldeg
4-4.1 $13.3 (4-28) 4-12.6
4-7.9 4-5.8 +3.5
Examination of the high temperature calculations in&cate a sharp increase in AX,* in the region of 0.3 mole fraction DMSO. This suggests that viscous flow in (15) J. R. Jesorek and H. B. Mark, Jr., J . Phys. Ghem., 74, 1627 (1970). (16) R. K. Hind, E. MoLaughlin, and A. R. Ubbelohdo, Trans. Faraday Sac., 56, 328, 331 (1960).
The Journal of Physical Chemistry, Vol. 75, N o . I , 1971
STEVEN A. SCHICHMAN AND RALPH L. AMEY
102
& A
2.5
m
I
0.25 0.30
f
Table VI: WLFD Parameters for D~vISO-H~O Mixtures XDNSO
0.25 0.30
0.33
0.33
TO
B
120 rt 1 116 rt 1 122 f 1
435 f 2 458 i 2 397 rt 2
free volume, discussions utilizing free volume models are necessarily qualitative in nature.14 Tommila and Pajunenlg have measured the dielectric constants and surface tensions of DMSO-water mixtures at 20-75O. As one would expect of high dielectric constant components, the ratio (E - l ) / ( e 3. 2) changes little with mole fraction. Hence the total molar polarization appears t o vary linearly with concentration and is rather insensitive as a probe of local liquid structure in = Eobsd this case. The excess dielectric constant, (Xlel XZeZ), exhibits a maximum value at a DMSO mole fraction of 0.28, whereas the excess viscosity maxi= 0.33. The difmum at 25” occurs a t about XDMW ference probably is not significant, although since the mechanisms for dielectric polarization and viscous flow are not identical there is no need to expect agreement among their excess functions.
2.0
1.5 F 0,
0 -I
+
1.0
0.5
Conclusions
Figure 3. Log viscosii y of several DMSO-H20 mixtures plotted as a function of (T - TO)-1, Values for To,obtained by least-squares aiialyeiis, are listed in Table VI.
this mixture involves an extensive disordering process at low temperatures. The dramatic increase in viscosity, particularly in the region of0.3mole fraction, may suggest the onset of a glassy state.’? With this in mind we have analyzed our data in terms of the Williams-Landel-FerryDoolittle (WLFD) free volume model of viscous flow.18 The results of fitting the data by least-squares computation t o an expression of the form
(4) are presented in Figure 3 and Table VI. The fundamental parameter, To,is defined as the temperature below which the viscosity becomes essentially infinite, and within the framework of the WLFD theory, defines the temperature below which free volume is no longer available for viscous flow. Bondi has observed that since viscosity is a function of more than just the
The Journal of Physical Chemistry, VoE. 76, N o . 1 , 1971
Despite the considerable efforts made by investigators to determine the origin of behavior in DMSO-H20 mixtures, little of certainty yet can be said. Viscosity data seem t o indicate an increase in local order-perhaps through the formation of polymeric structures-with a decrease in temperature. The very large positive AS,* calculated for viscous flow in the region of 0.33 mole fraction D,1(ISO at low temperatures is indicative of an extensive disordering process and may be suggestive of the important role which the DMSO-HzO ratio plays in local liquid structure at these temperatures. However, evidence for establishing the exact nature of its local liquid structure remains inconclusive. Analysis of such systems in terms of eq 4 and the free volume model, although necessarily qualitative at present, appears to hold more promise than one which employs any expression which assumes Arrhenius behavior.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the National Science Foundation for partial support of this work. (17) A. Bondi, “Physical Properties of Molecular Crystals, Liquids and Glasses,” Wiley, New York, N. Y., 1968, p 350. (18) M. L. Williams, R. F. Landel, and J. D. Ferry, J . Amer. Chem. Soc., 77, 3701 (1955). (19) E. Tommila and A. Pajunen, Suom. KemistiEehti B, 41, 172 (1968).
