6017
J. Phys. Chem. 1992, 96,6017-6020
Dielectric Spectroscopy of 2-Butoxyethanoi/Water Mixtures in the Complete Composition Range U. Kaatze,* R. Pottel, and A. Schumacher Drittes Physikalisches Institut, Universitiit GBttingen, Biirgerstrasse 42-44, W-3400 GBttingen, Germany (Received: November 7, 1991; In Final Form: March 20, 1992)
At 25 OC the complex (dielectric) permittivity of butoxyethanol/water mixtures has been measured as a function of frequency v from 3 MHz to 70 GHz and of mole fraction x between 0 an 1. All spectra can be analytically represented by the Havriliak-Negami relaxation spectral function which reflects an unsymmetric continuous distribution of relaxation times. Depending on the composition of the liquids, the width of the relaxation time distribution function reaches considerable values. The principal relaxation time is small if compared to that of relevant alcohoi/water mixtures. This finding points at a substantial effect of the hydrogen bonding ether oxygens in the 2-butoxyethanol/water system. The effect of the ether groups is also visualized by a small relative maximum in the dependence upon composition of the principal relaxation time. The extrapolated low-frequencypermittivities indicate a striking similarity in the dipole orientation correlation between the 2-butoxyethanol/water mixtures and the system tert-butyl alcohol/water. Only at low water content some differences between the two series of binary liquids are found. These differences are again assumed to be due to the ether oxygen atom of 2-butoxyethanol.
Dielectric spectroscopy of associating liquids offers valuable insights into the microdynamics of fluctuating hydrogen bonded networks. Attention is in particular paid to the behavior of the principal dielectricrelaxation time. With control of the slow decay in the autocorrelation function @ ( t ) of the sample polarization P(t), it is basically a collective quantity. On favorable conditions, however, the macroscopic dielectric relaxation time can be identified with the molecular dipole autocorrelation time.’ For this reason it is frequently considered a reorientation time. Of particular interest in this connection is water with its outstanding importance in chemistry and biology. Recent computer simulation studies of water revealed a rather sophisticated picture of the microdynamics of this unique liquid. Each hydrogen bond of the percolating molecular network breaks up and reforms again within intervals, Tb, as small as 0.1 to 1 PS.~J Likewise small is the actual reorientation time of a molecule or its dipole vector ( T ~ 0.1 p ~ ~ , Hence ~ ) . the principal dielectric relaxation time of water (T, 10 ps at room temperature4) appears to predominantly reflect other propertiea of the associated liquid. The water molecule is capable of up to four hydrogen bonds with the relative number of j-fold bonded (j = 0, ...,4) molecules in the liquid following a binomial distribution f u n c t i ~ n .Obviously, ~ a significant rotation is only possible if a molecule is unbonded or single-bonded. Hence T, is mainly determined by the interval passing until, after an orientationaljump of a molecule, favorable conditions for another reorientational motion again originate from the thermal fluctuations. The suitable bond order is doubtless an important precondition for rotations of a molecule through nonnegligible angles. The computer simulations show, however, that simultaneously an appropriately positioned additional molecule has to be present. That molecule, sometimes called ‘the fifth neighbor”: has to be suitably orientated to offer the possibility for a new hydrogen bond. If this idea is accepted, the principal dielectric relaxation time is inherently assumed to noticeably depend on the spatial density of sites which are capable of forming hydrogen bonds. This view is supported not only by computer simulation studies6 but also by dielectric e p e c t r ~ p y of 7 water at densities up to 1.09 g ~ m - ~ . An example of the dependence of the principal dielectric relaxation time T , on a relevant density parameter p is presented in Figure 1 for aqueous solutions of some monohydric alcohols and for the series of pure primary normal alcohols. Parameter p is defined by the relation
-
Herein, c,, c,, and c denote the molar concentrations of H 2 0 in the solutions, of H 2 0 in pure water and of the nonaqueous con0022-3654/92/2096-6017%03.00/0
stituents, respectively. 2, is the number of hydrogen bonding groups per organic molecule. Hence with the liquids under consideration Z, = 1 throughout. Since we are only interested in the overall trends here, the T , values according to T,
= (27rvm)-’, dc”(v,)/dv
= 0, d2d’(v,)/dv2
99%) was purchased from Aldrich, Steinheim (FRG), and was used without additional purification. Water was distilled, and deionized by mixed-bed ion exchange. The mixtures were prepared by weighing appropriate amounts of the components into suitable flasks. The density p of the liquids was measured pycnometrically. The specific electric low-frequency conductivity u, measured in the usual manner at 1, 10, and 100 kHz, was negligibly small. Complex Permittivity Meamwments. Two well-tried frequency domain methods have been used to measure the complex relative (electric) permittivity ~ ( vof) the samples as a function of frequency v (3 MHz S v I70 GHz). Between 3 MHz and 3 GHz we utilized a computerantrolled network analyzer (Hewlett-Packard 8753A) to perform reflection coefficient measurement^'^-'^ on cells of the ‘cut-off“ variety.1618 With this type of cell the liquid under test is contained in a small piece of coaxial line/circular cylindrical waveguide transition. The waveguide is excited below
0 1992 American Chemical Society
Kaatze et al.
6018 The Journal of Physical Chemistry, Vol. 96, No. 14, 199’2 500
1
I
I
I
I
I
I
I
1.5
2
3
5
7
10
1”’ 1
i
I
1
I
B -’
I
I
1
I
I
I
1
I
I
I
15
Figure 1. Bilogarithmic plot of the relaxation time ratio T , , , / T ~ as a function of p-l (eq 1) for monohydric normal alcohols (CH3(CH2)w10H, m = 1, ..., 10, 20 O C , and for three series of monohydric alcohol/water mixtures ((CH,),CHOH, 25 OC, inverted triangles;” (CH3)$OH, 25 OC, circles;II CH3(CH2),0H,squares1*).Data for pure alcohols are indicated by closed symbols. The relaxation time T~ of pure water‘ has been taken at the respective temperature of measurement. The full line is drawn to accentuate the general trend in the data. It can be analytically represented by the power law T,,,/T, = 3-l.
its cut-off frequency. Depending on the frequency range under consideration and on the permittivity of the sample liquid, the length of the liquid-filled part of the coaxial line can be adjusted to yield maximum sensitivity in the measurements.18 Modal analysis” of the coaxial line/circular waveguide transition has been applied to show that the cell can be well represented by a capacitor network. The capacitances of this network have been determined by calibration measurements with appropriately chosen reference liquids. In the frequency range from 1 to about 70 GHz a traveling-wave method has been used in which a wave transmitted through a liquid-filled cell of precisely variable length is sensitively balanced against a reference wave.18-20Seven microwave double-beam interferometers, each matched to a narrow frequency band, were used to uninterruptedly cover the range from 1 to 70 GHz. One interferometer (u < 5 GHz) consisted of coaxial line components, the others were constructed with standard small-band waveguide devices. Experimental Accuracy. With all measurements the temperature of the sample liquid was controlled to within kO.05 K. The relative error Au/u in the measuring frequency was smaller than f0.001, Both methods of permittivity measurements have been carefully examined with respect to imperfections which could result in systematic errors. At frequencies below 3 GHz the reflection coefficient measurements have been repeatedly performed using cells with different length of the coaxial line. Additional tests were run in the lower frequency range in which the network analyzer was replaced by an impedance analyzer or a sensitive admittance bridge. In the upper frequency range unnoticed systemic errors are unliiely since we used different interferometers in the microwave region. The accuracy of the e’- and €’’-values has been judged by test measurements on liquids with well-known dielectric spectra and by multiple data recording utilizing different cells and different electronic and microwave devices. In most of the frequency range the relative errors Ae’/t‘ and Ad’le’’ are smaller than f1%. Above about 20 GHz At’lt’ and Ad’le’’ increase and reach a value of f3% at 70 GHz. Below 100 MHz the uncertainty in the t” data is higher (Ad’ = f l ) . Results and A ~ l y t i c Representation ~I of Data
In Figure 2, as an example, the complex dielectric spectrum is displayed for the 6.75 M aqueous solution of 2-butoxyethanol (mole fraction of solute x = 0.5). Here and in the following, only the dielectric contribution has been calculated by using the relation d’d( v) = E”( v) - / (f@) (4)
\ E(-)
-
\\ \
0’003 0.01 0.03
0.1
I
I
1
I
0.3
1
3
10
I
30GHz100
V
Figure 2. Real part e’(v) ( 0 )and dielectric contribution e’’&) to the negative imaginary part (0)of the complex permittivity semilogarithmically plotted versus frequency u for the equimolar 2-butoxyethanol/ water mixture at 25 OC. The full curves are the graphs of the Havriliak-Negami relaxation spectral function (eq 5) with the parameter values given in Table I. The dashed curve represents the frequency-dependent negative imaginary part of a dielectric spectrum with discrete relaxation time T~ (Debye-type relaxation, eq 5 with a = fi = 0).
to subtract the uninteresting (small) conductivity contributions A s V-I m-l from the measured t”(u). In eq 4 to = 8.854 X and w = 27ru. The dielectric spectrum shown in Figure 2 exhibits one dispersion (dd(u)/du < O)/dielectric loss (c”&) > 0) region only. This finding is common to all mixtures considered in this study and also to the pure constituents. Other than with pure water? however, the spectra of the solutions and of 2-butoxyethanol cannot be characterized by a discrete relaxation time but reflect the existence of a relaxation time distribution. In Figure 2 this is demonstrated by the dashed curve which appropriately normalized represents the frequency-dependent loss for a Debye-type2’ relaxation process with only one relaxation time, 7,. The deviations of the measured dielectric loss from the predictions by a Debye-type spectral function are particulary pronounced at frequencies above u, (=1/(27r7,)). This fact is a strong indication of an underlying unsymmetric relaxation time distribution. It is therefore an obvious attempt to analytically describe the measured dielectric spectra by the semiempirical Davidson4Ae relaxation spectral function.u We found, however, that at low content of butoxyethanol ( x < 0.2) the agreement between this function and the measured complex permittivity data is not perfect. Satisfactory fits for the complete set of liquids can be obtained by use of the Havriliak-Negami relaxation spectral functionz3which is given by the relation
In this function, parameters a and (3 measure the width of the underlying relaxation time distribution (0 Ia,(3 C 1). Equation 5 was fitted to all measured complex permittivity spectra by applying a nonlinear least-squarts regression analysis. At x > 0.2, in order to enhance the significance of the other parameters, a E 0 was used in this analysis. The results of the fitting procedure are presented in Table I. At (3 # 0 the relaxation time T~is no longer given by the frequency u, (eq 2). For this reason, the T , values are also given in Table I. The errors in the parameter values have been derived from further fitting procedures in which sets of pseudodata were considered. These pseudodata have been generated by adding, within the limits of
Dielectric Spectroscopy of 2-Butoxyethanol/Water Mixtures
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 6019
TABLE I: Mole Fraction x , Concentration c of the Organic Comtitwnt, Water Concentration c, Parameters of the Relaxation Spectral Function (Eq 5), and Relaxation Time T, (Eq 2) for Bmry Mixtures of 2-Butoxyetbnol with Water at 25 OC c, mol/ c,, mol/ x f0.195 L f 0.1% L f 0.1% e(=) 40) 78, P rm PS a f0.002 6 f0.05 0 0 55.33 5.2 f 0.1 78.36 f 0.05 8.27 f 0.03 ET. SO SO ~
1.52
6.75 3.04 0.84
7.64
0
2.1 f 0.5
0.500 0.704
0.900 1.ooo
49.75
f 1.5 f 1.5 f 1.0 f 1.0 f 0.7 2.6 f 0.6 2.4 0.5 2.2 f 0.5
0.85 2.24 3.46 4.66 5.87 6.75 7.23
0.017 0.053 0.099 0.170 0.303
4.5 4.0 3.0 2.8 2.7
39.86 31.66 22.61 13.52
*
71.7 56.9 44.7 33.6
f 0.3 f 0.3
f 0.3 f 0.3 23.5 f 0.2 16.7 f 0.2 12.9 i 0.2 10.4 f 0.1 9.3 f 0.1
10.9 f 0.3 14.8 f 0.3
21.9 f 0.5 38.2 f 1 61.4 f 3 87.5 f 4 115 f 6 126 f 6 118 f 6
16.8 f 0.3 14.2 f 0.3 19.0 f 0.5 28.4 f 0.7 44.2 f 1 61.6 f 3 73.9 f 3 74.6 f 3 67.0 f 3
1.5
0.070
0.0 1 0.05
0.076
0.15
0.036
0.031
0.30 0.34
10 EO SO
0.36 0.43 0.48 0.5 1
EO EO
2
3
4
4-’
0
001
003
01
I
I
I
I
03
1
3
10
I
30GHz100
V
Figure 3. Semilogarithmic plot of the dielectric contribution c ” ~ ( v to )
the negative imaginary part of the complex permittivity against frequency v for a 5.9 M aqueous solution of 2-butoxyethanol (circles, volume fraction of solute u = 0.76) and an 8 M aqueous solution of 1-butyric acid (triangles,I5u = 0.73) at 25 O C . experimental errors Ad, Ad’, random values to the original permittivity data.
Discussion Relaxation Spectral Function. The fact that only one dispersion/dielectric loss region is found with the binary 2-butoxyethanol/water mixtures attracts attention for several reasons. Obviously, the constituents do not noticeably contribute to the spectra with the pure liquid relaxation times T,(x=O) = T, and T,(x=~). These relaxation times differ from another by a factor of about 10 (Table I). Hence, if distinct contributions with T, and T,( 1) were present, these should become evident. Though the system 2-butoxyethanol/water exhibits a miscibility gap with a lower critical demixing point at x, = 0.0598 and T, = 49.3 0C,24the mixtures do not seem to be composed of microphases with different composition. As illustrated by Figure 3 the dielectric spectra for butyric acid/water mixtures, also far away from the critical demixing point of that system, clearly reveal the decomposition into such microphases with relaxation times T , , T~ # T,(x=O), T,(x=l). We therefore conclude that the 2-butoxyethanol/water mixtures form an almost homogeneous hydrogen-bonded network. The dielectric relaxation of this network, however, is subject to a continuous relaxation time distribution. Several effects may contribute to this distribution, among them concentration fluctuations, in particular at mole fractions around the critical x,, diffusion of defect^^^-^' like the above mentioned additional neighbor, perturbations of the water structure by the butoxyethanol molecules, existence of various states of association of butoxyethanol which may include a variety
Figure 4. Relaxation time ratio r,/rW bilogarithmically plotted as a function of the density parameter fi (eq 1) for the 2-butoxyethanol/water mixtures at 25 OC. The full symbol indicates the value for the pure organic liquid. The dashed line is the graph of the relation T , / T , = fi-2.5 representing the data of Figure 1. of dimers and oligomers with different lifetimes, and different modes of dipole orientation of butoxyethanol including crankshaft-like motions of the ether oxygen around the C-O bond. At the present there does not exist a sufficient amount of data on the relaxation time distribution of associating binary mixtures to enable a clear-cut conclusion on the relative importance of the various effects. Dielectric Relaxation Time. In Figure 4 the relaxation time ratio T,/T, of the butoxyethanol/water mixtures is displayed versus the density parameter j as defined by eq 1. For comparison with the data presented in Figure 1 T, is considered here instead of the principal relaxation time T, (eq 5, Table I). Both relaxation times show the same trends in their dependence upon the mixture composition though T, > T , if @ > 0. The dielectric relaxation time of pure 2-butoxyethanol (T,(x= 1) = 67 ps, T,(x=l) = 118 ps) is small if compared, for example, with that of l-heptanol(~,= 1290 ps at 20 OC*). This substantial difference in the T , values for liquids with nearly the same molecular structure and length strongly supports the above idea on dielectric relaxation of associating liquids. Substitution of a methyl group by an ether atom distinctly promotes the relaxation frequency since the spatial density of sites for the formation of hydrogen bonds is increased thereby. In addition, as mentioned above, rotational motions of the ether group also tend to reduce the relaxation time with respect to that of normal alcohols. The relaxation time ratio slightly increases if small amounts of water are added to 2-butoxyethanol. The same behavior has been found recently with polyether/water systems.I3 Obviously, the motions of the ether oxygen atoms are impeded by hydrogen bonding. Water seems to form comparatively stable linkages between different ether groups. Normally, the existence of a relative maximum in the dependence upon composition of the relaxation time seems to be characteristic of binary aqueous systems in which hydrogen bond accepting sites are the only hydrophilic parts of the other constituent. Prominent examples are mixtures of water with quinoxaline,28dimethyl sulfoxide,2s
6020 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
acetone,3sand a c e t ~ n i t t i l e .In ~ ~these systems the pure organic liquids cannot form normal hydrogen bonds. Hence addition of water first tends to promote association effects and, therefore, to enhance the dielectric relaxation time. Above a certain water concentration the tendency to reduce the relaxation time by the increasing availability of sites for the formation of hydrogen bonds (H-bond ‘switching”) predominates. As already discussed in the Introduction, the latter effect is characteristic of binary aqueous systems in which the pure organic constituent also forms hydrogen bonds. Well-known examples for such behavior are alcohol/water mixtures for which r, monotonously increases with x (Figure 1). The finding of a relative maximum in the relaxation time ratio (Figure 4), even if less pronounced, may thus be taken an indication of the dominant role of the ether oxygen atom in the microdynamics of 2-butoxyethanol/water mixtures. Static Permittivity. Below about 0.3 GHz the real part of the dielectric spectrum of the 2-butoxyethanol/water mixtures is nearly independent of frequency (Figure 2). For this reason the low-frequency permittivity e(0) is a well-defined quantity. It is very unlikely that there exist polarization mechanisms which at frequencies below our range of measurement add noticeable contributions to the spectrum. Hence the e(0) values can indeed be considered the static permittivities of the liquids. The static permittivity decreases monotonously when going from pure water (c(O,x=O) = c,(O) = 78.36) to pure 2-butoxyethanol (t(O,x=l) = 9.3). This is to the most part a reflection of the decreasing number density of electric dipolts within the liquids. The dipole of an isolated 2-butoxyethanol molecule ( p = 2.08 D) is even somewhat greater than that of water in the gaseous state (pw = 1.85 D). To gain some insights into the structural arrangements of the dipole moments, it is necessary to theoretically consider the relation between e(O), the molecular dipole moments, and the concentration of the constituents. This relation should include effects of various dipole orientation correlations. Since it is impossible to determine different orientation correlation factors from only one parameter, we evaluated the static permittivity data on the basis of a simplified model. With development of this model the Frahlich for the static permittivity of pure liquids has been extended to apply for binary mixtures. Disregarding at the outset any dipole orientation correlations, we consider the quantities
”(
D, = eokT
e(=) + 2 7) (cwpw2 + cp2)
(6)
and
N A (=6.02 (=1.38 X
X
mol-’) is Avogadro’s number herein and k
V A s K-I) the Boltzmann constant.
If indeed effects of dipole orientation correlation could be neglected and if, in addition, the proper high-frequency permittivity e(=) to be used in eqs 6 and 7 would be known, then DJD, = 1 should hold. The DJD, ratio for the 2-butoxyethanol/water mixtures and for the mixtures of tert-butyl alcohol with water is displayed as a function of mole fraction x in Figure 5. Though the DJD, values depend sensitively on the insufficiently known e(=), some interesting conclusions can be drawn. The surprisingly similar behavior of the two series of D,/D, data attracts attention since, due to its ether oxygen, 2-butoxyethanolis capable of a much greater variety of hydrogen-bonded molecular associations than terr-butyl alcohol. The strong increase at small x in the D,/D, ratio of both series of liquids may result from precritical concentration fluctuations (x, = 0,0598, T, = 49.3 O C , 2-butoxyethanol2‘). The D,/D,, ratio for both pure organic liquids has a distinctly higher value than for pure water. If water is added to tert-butyl alcohol the D,/D, ratio decreases. The parallel ordering of dipoles as characteristic for pure alcohols35is successively destroyed by the presence of water molecules and the additional possibilities of hydrogen bonds offered thereby. In contrast, water molecules added to 2-butoxyethanol obviously act as hydrogen-
I , .
. .
Kaatze et ai.
1.4
-
1.2
-
9= d
t/
b 0.8
0
06
0
02
06
04
08
1
X
Figure 5. Ratio DJD, (eqs 6 and 7) plotted versus the mole fraction x of the organic constituent for the mixtures of water with 2-butoxyethanol ( 0 )and of rert-butyl alcohol ( A l l ) a t 25 OC.
bonding linkages. In conformity with the characteristic relaxation time of the mixtures (Figure 4) the DJD, ratio is enhanced thereby. Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaftis gratefully acknowledged. Registry NO. HO(CHZ)~OBU,11 1-76-2. References and Notes (1) Kaatze, U.; Pottel, R. J . Mol. Liq., in press. (2) Tanaka, H.; Ohmin, I. J . Chem. Phys. 1987,87,6128. (3) Ohmine, I.; Tanaka, H.; Wolynea, P. G. J. Chem. Phys. 1988,89,5852. (4) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371. ( 5 ) Sciortino, F.; Fornili, S.L. J. Chem. Phys. 1989, 90, 2786. (6) Geiger, A.; Mausbach, P.; Schnitker, J. In Water and Aqueow Solutions; Neilson, G. W., Enderby, J. E., Eds.;Hilger: Bristol, 1986; p 15. (7) Pottel, R.; Asselborn, E.; Eck, R.; Tresp, V. Ber. Bunsen-Ges. Phys. Chem. 1989, 93,676. ( 8 ) Gestbolm, B.; Sjbblom, J. Acta Chem. Scand., Ser. A 1984, 38, 47. (9) Gestbolm, B.; Sjablom, J. Acta Chem. Scand., Ser. A 1984.38, 575. (10) Kaatze, U.; Schifer, M.; Pottel, R.Z . Phys. Chem. 1989, 165, 103. (1 1) Kaatze, U.;Schumacher, A.; Pottel, R. Ber. Bunsen-Ges.Phys. Chem. 1991, 95, 585. (12) Mashimo, S.; Kuwabara, S.J . Chem. Phys. 1989, 90, 3292. (13) Unnecke-Gabel, V. Doctoral Thesis, G6ttingen, 1990. (14) Kaatze, U.;L6nnecke-Gabe1, V. J . Mol. Liq. 1991, 48, 45. (15) Kaatze, U.;Menzel, K.; Pottel, R. J . Phys. Chem. 1991, 95, 324. (16) Kaatze, U.;Giese, K. J . Phys. E: Sci. Instrum. 1980, 13, 133. (17) Gattmann, 0.;Dittrich, A. J. Phys. E Sci. Instrum. 1984, 17, 772. (18) Kaatze, U.;Giese, K. J. Mol. LQ. 1987, 38, 15. (19) Pottel, R. Ber. Bunsen-Ges. Phys. Chem. 1965,69, 363. (20) Kaatze, U.Mikrowellen Magasin 1980, 6, 27. (21) Debye, P. Polare Molekeln; Hirzel: Leipzig, 1929. (22) Davidson, D. W.; Cole, R. H. J . Chem. Phys. 1950, 18, 1417. (23) Havriliek, S.;Negami, S . J. Polym. Sci., Part C 1966, 14, 99. (24) Muller-Kirschbaum, Th. Thesis, University of Kdn, 1988. (25) Glarum, S.H. J . Chem. Phys. 1960, 33,639. (26) Condat, C. A. Z . Phys. B 1989, 77, 313. (27) Bordewijk, P. Chcm. Phys. Lett. 1975, 32, 592. (28) Kaatze, U.;Pottel, R.; Schmidt, P. J . Phys. Chem. 1988, 92, 3669. (29) Kaatze, U.;Pottel, R.; SchHfer, M. J. Phys. Chem. 1989,93,5623. (30) Achadov, J. J. Dielectric Properties of Binary Solutions; Pergamon: Oxford, 1981. (31) McClellan, A. L. Tables of Experimental Dipole Momenrs; Freeman: San Fransisw, CA, 1963, Vol. I; Rahara, El Cerrito, 1974, Vol. 11. (32) Riddick, J. A.; Bunger, W. B. Organic Soluents; Wilcy: New York, 1970. (33) Frahlich, H. Theory of Dielectrics; Clarendon: Oxford, 1958. (34) Hill, N. E.In Dielectric Properties and Molecular Behauiour, Hill, N. E., Vaughan, W. E., Price, A. H.. Davies, M., Eds.; Van Nostrand Reinhold: London, 1969. (35) Davies, M. In Dielectric Properties and Molecular Behauiour; Hill, N. E., Vaughan. W. E..Price. A. H.: Davies, M.,Eds.;Van Nostrand Reinhold: Lodon, 1969.
