DIELECTRIC RELAXATION IN CLATHRATE HYDRATES OF CYCLICETHERS
1889
Dielectric Relaxation in the Clathrate Hydrates of Some Cyclic Ethers
by R. E. Hawkins and D. W. Davidson Contrihzition S o . S R C 9041 f r o m the DiFiswn of Applied Chemistry, S a t w n a l Research Council, Ottawa, Caimda (Receined December 14,1965)
By comparison of the low-frequency dielectric properties of the propylene oxide-, trimethylene oxide-, and dihydrofuran-water systems with those of the known clathrate hydrate of tetrahydrofuran, it is shown that these cyclic ethers (11) also form gas hydrates of von Stackelberg's structure 11, with compositions close to A1.17Hz0. The shapes and aniplitudes of the dispersion curves associated with reorientation of the water molecules are identical within the experimental error for all four hydrates. The shapes are slightly broader than Debye curves. The relaxation times of the water structure depend somewhat on the nature of the encaged molecules 31. The extremely rapid reorientation of the 11 molecules gives a contribution to the high-frequency dielectric constant which is proportional to pnl2 and somewhat higher than predicted by the Onsager cavity model. Trimethylene oxide, the smallest of these molecules, forms a second clathrate hydrate, probably of structure I. I n it the water molecules relax more rapidly than in structure 11.
Gas hydrates are now known to be clathrates in which small molecules of a variety of types occupy cages in rigid, hydrogen-bonded water lattices. From X-ray powder diffraction patterns of some 20 simple gas hydrates, von Stackelberg and his collaborators' inferred the existence of two distinct cubic forms, characterized as structures I and 11. Nore recently, Jeffrey and his co-workers have shown the existence of two additional noncubic types of clathrate hydrate, as exemplified by bromine hydrate2 and a hydrate of trimethylamine.3 They have also used single-crystal X-ray studies to characterize the structural parameters of the ethylene oxide structure I hydrate4 and the structure I1 double hydrate of tetrahydrofuran and
HzSe5 Previous dielectric study6 has established for the hydrates of ethylene oxide and tetrahydrofuran the presence of two widely separated regions of dielectric absorption. One, in the radiofrequency range, is associated with the rotational relaxation of the water molecules in the lattice; the other, at microwave frequencies, with the slightly hindered rotation of the encaged ethylene oxide or tetrahydrofuran molecules. Here we present the results of low-frequency dielectric studies of the tetrahydrofuran hydrate and of previously unreported hydrates of propylene oxide, trimethylene oxide, and 2,5-dihydrofuran.
Experimental Methods After distillation of the commercial products, vapor phase chromatographic analyses showed tetrahydrofuran and propylene oxide to contain less than 0.1% nonaqueous impurities. Commercial samples of trimethylene oxide and dihydrofuran were found to contain less than 0.1 and 0.3y0 impurities, respectively, and were used without purification. Samples for dielectric study were usually prepared by freezing solutions in conductivity water which were slightly more concentrated in ether AI than 11 17Hz0. This meant that the hydrates contained a small quantity of 11-rich liquid which interfered less with the dielectric dispersion of the hydrate than ice would have done and enabled the hydrate compositions to be checked from the small changes in dielectric constant which occurred at the eutectic points. Because of 9
(1) 111. von Stackelberg and H. R. Mtiller, Z . Elektrochem., 58, 25 (1954); M.von Stackelberg and B. Meuthen, ibid., 62, 130 (1958). (2) K. W. Allen and G. A. Jeffrey, J . Chem. P h y s . , 38, 2304 (1963). (3) G. A. Jeffrey, R. K. Rlchfullan, and T. C. W. Mak, Bozeman Meeting, American Crystallographers Association, 1964. (4) R. K. RIcMullan and G. A. Jeffrey, J . Chenz. Phys., 4 2 , 2725 (1965). (5) T. C. W.RIak and R. K. McMullan, ihid., 4 2 , 2732 (1965). (6) D. W. Dabidson, M. 11. Davies, and K. Williams, ihid., 40, 3449 (1964).
V o l u m e 70,N u m b e r 6
June 1966
R. E. HAWKINS AND D. W. DAVIDSON
1890
and Eutectic ( T E )Temperatures of Ether-Water Systems (in "C) Table I : Hydrate-Decomposition (TH) Ether 1zI
Tetrahydrofuran 2,5-Dihgdrofuran Propylene oxide Trimethylene oxide
Fp of M
- 107.8," - 108.5* -88.7 -111 gs - 99*
TE
f5.1," +4.4d -1.2 -4.4f -13.1 -20.8
TE(~)
-1.Od -3.3 -4.71
-107.8 -89.2 -112.7 -101.5
a B. Rice, J. A. Livasy, and G. W. Schaeffer, J . Am. Chem. SOC., 77, 2750 (1955). * H. H. Sisler, H. H. Batey, B. Pfahler, and R. Mattair, ibid., 70, 3821 (1948). H. A. Palmer, Dissertation, University of Oklahoma, 1950. J. Erva, Suomen Kemistilehti, 29B, 183 (1956). e F. L. Oetting, J . Chem. Phys., 41, 149 (1964). J. N. Wickert, W. S. Tamplin, and R. L. Shank, Chem. Engr. Progr. Symp. Ser., 121 48,92 (1952). H. H. Sisler and P. E. Perkins, J.Am. Chem. SOC.,78, 1135 (1956).
the more complicated phase relationships in the trimethylene oxide-water system, solutions of 12 different concentratioris were studied. The measuring and temperature-control circuits were the same as in the study' of the ethanol-water system. Two three-electrode cells were used. Cell 1 had coaxial cylindrical stainless steel electrodes and a cell constant of 5 pf. The upper electrode assembly of cell 2 consisted of concentric coplanar guard and guarded electrodes mounted on a shaft to permit variation of the separation from the lower fixed electrode. Electrodes were of gold-plated brass. Cooling liquid was circulated through a copper coil mounted within the cell and above the upper electrodes to control the rate of initial freezing, which was observed through Lucite windows in the cell wall. Results for tetrahydrofuran and propylene oxide hydrates in the two cells showed no systematic differences except for somewhat lower low-frequency space-charge effects in cell 1. Dihydrofuran and trimethylene oxide hydrates were studied in cell 1 only.
Results Formation of Structure II Clathrate Hydrates. Examples of complex dielectric constant plots for samples (in cell 1) of composition approaching 17 water molecules per molecule of ether RI are given in Figures 1 to 4. As discussed below, the limiting values of the dielectric constants reached at high frequencies and the similarities between the dispersion-absorption curves of the four systems strongly suggest that clathrate hydrates similar to the well-known tetrahydrofuran hydrate are also formed by the other three ethers. This is also indicated by the maxima which occur in the freezing point curves of propylene oxide and dihydrofuran (see Table I) a t compositions close to 31. 17Hz0. The corresponding hydrate of trimethylene oxide decomposes incongruently at - 13". A second clathrate hydrate is formed at higher trimethylThe Journal of Physical Chemistry
Figure 1. Complex dielectric constant loci of tetrahydrofuran hydrate; sample composition TMO. 16.1H10. Numbers on curves identify frequencies in kc sec-l.
ene oxide concentrations (see below) and decomposes at -21". Complex Dielectric Constant Loci. The shapes of the complex loci of Figures 1 to 4 are slightly broader than semicircular and conform approximately to circular arcs. A few representative results are given in Table I1 in terms of the parameters of the Cole-Cole circular arc description. There are, however, clear systematic departures from this description, particularly at relatively high frequencies, where, as is clear from the results a t low temperatures, the experimental loci intersect the E' axis at right angles at a value here This behavior is inconsistent with a called ~(1). finite value of the distribution parameter a. The additional increase in absorption and dispersion at low frequencies is probably associated with the presence of ionic space charges. The magnitude varied with sample and time and was considerably reduced by application to the solid sample of a dc (7) A. D. Potts and D. W. Davidson, J . P h y s . Chem., 69,996 (1965).
DIELECTRIC RELAXATION IN CLATHRATE HYDRATES OF CYCLIC ETHERS
1891
Table I1 : Measured Dielectric Parameters of Hydrate Systems Temp, System
Cell
O C
*(arc)
THF.16.lHzO
1
-1.4 -40.5 -70.0 -94.8 -120.6 -144.7
61.1 68.3 74.3 78.5 74
-22.5 -48.4 -83.5 -113.0
61.4 67.6 80.2 86.8
-20.8 -58.2 -95.4 -113.2 -151.4
66.5 75.8 86.0 90.5
-6.3 -53.8 -84.9 -98.5 -138.3
67 78.5 91 96
-43.3 -93.2 - 196
74 87
-24.3 -49.0 -91.0 -134.4 -170.2
63.4 65 67 69
-24.6 -74.2 -101.8 -123.1 -155.5
50.6 44.3 45.1 45.2
T H F .16.5H20
D H F .16.3HzO
2
1
1
2
1
TMO *7.63H20
1
field of 1500 to 3000 v cm-' for some hours. The effect of the presence of a small residual quantity of ice in the trimethylene oxide hydrate sample of Figure 4 is to be seen as a low-frequency shoulder. Multiple absorption regions in the trimethylene oxide-water system will be considered below. Dielectric Parameters of the Structure 11 Hydrates. The experimental dielectric constants listed in Table I1 differ somewhat from the true values for the hydrates because of the presence of some ether-rich liquid phase and, at low temperatures, of air gaps and cracks in the samples. At - 15" the apparent static dielectric constants €,(arc) for the first six samples of Table I1 were all within l t 3 of 63. Estimated corrections for the presence of small quantities of liquid gave the value 66 f
em
(1)
4.7 5.04 5.21 5.50
4.85 5.10 4.6 4.90 5.10 5.58
5.74 5.93 6.60 5.90 8.48
5.59 6.09 6.85
11.0 11.8 10.2
T O ,sec
(I
1.04 X 1 . 0 1 x 10-6 1.12 x 10-4 2.09 x 10-3
0.025 0.036 0.042 0,050
3 . 0 x 10-7 1.87 X 3.61 x 10-5 8 . 1 x 10-4
0.029 0.043 0,058
4 . 4 x 10-7 6.0 x 1.40 x 10-4 8.6 X
0.025 0.043 0,055
2 . 1 x 10-7 6.1 X 9 . 9 x 10-6 3 . 9 x 10-4
0.028 0.05 0.06
2.65 X 1.95 x 10-4
0,030 0.057
9 . 7 x 10-7 2.50 x 10-6 2 . 4 x 10-3
0.033 0.044 0.052
x x x
0.10 0.09
2.92 3.06 3.41
10-7 10-5
2 for the static dielectric constant of all four structure I1 hydrates at -15". Samples in cell 2 showed no visible cracks a t relatively high temperatures. With decrease of temperature, cracking of the samples eventually became evident (usually near - 65") from visual examination and reduction of the slopes of €,(arc) us. 1/T curves. Extrapolation of the high-temperature linear portion of these curves, slightly adjusted for liquid content, gave eo values of approximately 78 at -60" and 97 at -105". The experimental co(arc) values near -105" may be accounted for by series air gaps of effective thickness eO.002 of the sample thickness except for the sample of trimethylene oxide hydrate for which a gap of about 0.004 is required. Small corrections were applied to the experimental values of at -105" to give the em(H20)values Volume 70.Number 6 June 1966
1892
R. E. HAWKIKS AND D. W. DAVIDSON
-
1I0
I 20
I 30
+
! 40
I
50
60 I
!
70 I
I
E'
Figure 4. Complex dielectric constant loci of trimethylene oxide hydrate (structure 11),after conditioning 5 days a t -25'; sample composition TMO. 16.4H20.
Figure 2 . Complex dielectric constant loci of dihydrofuran hydrate; sample composition D H F . 16.3H20.
+ 4
0
,
*-----zo---
I
I
I
--lo---+,
I -40
c,50
,
60
,8
/
I'
1
) I : 70
80
I 90
Figure 3. Complex dielectric constant loci of propylene oxide hydrate; sample composition PO 16.4H20.
listed in Table 111. The correction for liquid content was estimated from the increase in e m ( I)observed when the sample was heated through the eutectic temperature and was never more than 0.05, a result consistent only with hydrate compositions close to 119.17HzO. The air-gap correction, which amounts to 0.04, for example, for em = 5 and a gap of 0.002 of sample thickness, was of similar magnitude but opposite sign.
Table I11 : Relation between Experimental em( HzO) and Calculated eO(M) of Structure I1 Hydrates a t - 105" M
em (Hz0)
Tetrahydrofuran Dihydrofuran Propylene oxide Trimethylene oxide
5.06 5.03 5.94 5.63
T h e Journal of Physical Chemistry
dgas),
U,
D.
AB
m(M)
7.93 7.74 6.18 6.23
4.88 4.67 5.45 5.29
1.63 1.54(CeH~) 2.00 1.93
The most probable relaxation times T~ derived for the circular-arc approximation are plotted against 1/T in Figure 5 . These curves run nearly parallel to one another. The high-temperature linear portions correspond to Arrhenius energies of 8 kcal mole-', but there is a pronounced decrease of slope with decreasing temperature. The change in temperature dependence is much too large and too consistent to be attributed to the effect of the small series air gaps already discussed. Except for some of the low-temperature loci of propylene oxide hydrate, for which the overlap with the space-charge polarization was greatest, all the values of the Cole-Cole parameter a which fitted the data best lay within 0.010 of a straight line on a 1/T plot extending from 0.024 at -15" to 0.045 at -105". There appear to be no appreciable differences in the breadths of the dispersion curves for the different structure I1 hydrates. The Second Hydrate of Trimethylene Oxide. I n addition to the region of absorption shown in Figure 4, two other distinct absorption-dispersion regions were observed in the trimethylene oxide-water system. One of these occurred at relatively low frequencies (a maximum in e" initially appeared a t -1 kc sec-l in a sample of composition TR/IO. 14.3H20 at -55", for example) and can be ascribed to ice. Ice was generally the first solid to form when the solutions were cooled. The other absorption appeared, for samples relatively rich in trimethylene oxide, on the high-frequency side of the structure I1 hydrate absorption. It was finally obtained as an isolated absorption region in a sample of composition TMO .7.63H20 which had been rapidly cooled to -80", conditioned for 4 days at -27", and subsequently recooled. Some data for
DIELECTRIC RELAXATION IN CLATHRATE HYDRATES OF CYCLIC ETHERS
-2
-3
-
phases proceeds very slowly, particularly for sample I compositions intermediate between the compositions of the two hydrates. Relaxation of water molecules in the second hydrate is 20 times as fast as in structure 11. Relaxation times measured at ten temperatures between -74 and - 144" are given by log TO = -12.899 1265,7/T to within an average deviation in T~ of 1%. The Arrhenius energy is 5.8 kea1 mole-l. The dispersion loci are somewhat broader than for structure I1 hydrates.
-
+
-4-
s
I
rp -5
1893
-
B
c
o
DHF.
16.3 H p O
THF * 16.1 H20 + THF * 16.5
D
H20
TMO. 16.4 H20 + TMO. 14.3 H 2 0
Figure 5. Temperature dependence of Cole-Cole relaxation times T ~ .
20
Figure 6. Complex dielectric constant locus of the trimethylene oxide-rich hydrate; sample composition TMO 7.63H20.
-
this sample are included in Table 11. Its dispersion locus (Figure 6) showed no more than a trace of structure I1 hydrate. No discontinuity in dielectric properties was detected in the eutectic region near -100". This absorption region therefore appears to be associated with a second hydrate whose composition is close to T_140.72/3H~0, the composition of a structure I hydrate with fully occupied tetrakaidecahedral, but empty dodecahedral, cages. The values of ,E for the second hydrate (Figure 6) are about twice as great as for the structure I1 hydrate (Figure 4)) as expected for a higher density of encaged trimethylene oxide molecules. The results of dielectric and thermal analysis studies of samples of a number of compositions support the existence of a second hydrate which decomposes at -21". The establishment of equilibrium among the
Discussion Properties Characteristic of the Structure 11 Lattice. The static dielectric constants and the shapes of the dispersion loci of the four structure I1 hydrates depend primarily on the structure of the water lattice. To the static dielectric constant of 66 at -15" the water molecules contribute about 64. This is twothirds of the value for ordinary ice, in which the density of water molecules is 18% greater. I t is apparent that the correlation of neighboring water dipoles increases the dielectric constant to a similar, if smaller, extent. For n2 = 1.60, derived from n2 = 1.72 for ice by use of the Lorentz-Lorenz equation, the value of the Kirkwood correlation parameter g is 2.7. This value falls within the range of g values of 2.7 to 3.4 foundSfor ices I, 111,V, and VI and is of the magnitude expected from the four-coordinated distorted-tetrahedra1 structure of the hydrate lattice. The water molecules possess the same long-range orientational disorder as these ices and therefore a similar residual entropy. The details of the departures of the shapes of the dispersion-absorption loci from simple semicircles are reminiscent of the departures which occur in some of the high-pressure ices8 and probably again reflect the presence of nonequivalent sites and hydrogen bonds, of which there are three and four, respectively, in the structure I1 hydrate lattice. For this to be so, the relaxation process must involve the reorientation of only a very few molecules at a time, as in the wellknown Bjerrum mechanism of diffusion of rotational defects. Small differences in local molecular environment would not be reflected in the relaxation behavior if "melting" of large groups of molecules was required. Properties Dependent on the Molecules Encaged in the Structure 11 Lattice. Because of the absence of dispersion at frequencies between the widely separated relaxation regions of 11 and mater,6 E,(H~O)= eo(11), the "static" dielectric constant appropriate to reorientation of hl molecules in a rigid HzO lattice. This quantity is dependent on the dipole moment of 11. The ~
(8) G. J. Wilson, R. K. Chan, D. W. Davidson, and E. Whalley, J . Chem. Phys., 4 3 , 2384 (1965).
Volume 70,Number 6
June 1.966
R. E. HAWKINS AND D. W. DAVIDSON
1894
nearly spherical shape of the cages and the isolation of the encaged molecules provide an opportunity of testing the Onsager cavity model of the reaction field. For a solution of polar molecules R/I in a "nonpolar" lattice the Onsager result may be writteng
4nN~ 1-f W M
[,, amfzl PM2
+
where EO = EO(N) = em(H20),em0 is the dielectric constant of the empty (rigid) lattice, and N Mis the number density, P M the dipole moment, and a~ the polarizability of molecule 11. fnf is the reaction field factor EO - 1)/[a3(2~, l ) ]for a spherical cavity of radius a, normally, in applications to liquids, taken to be given by 4 a N a 3 / 3 = Ti, where N is Avogadro's number and V the molar volume. Here, however, we take a to be the "free radius" of the physical cage, that is, to be 3.2 A at -105". The introduction of RI molecules is assumed not to affect the contribution of the empty lattice given by the first term. The value of E,O cannot be measured directly, nor, as is known from the examples of the ices,8 can it be related simply to the polarizability of water molecules derived from the optical n2. Since, however, the local mater structure in the hydrates is similar to that in ice, the contribution of the empty lattice may be estimated from the corresponding contribution for ice itself, reduced by the ratio of the number of water molecules/cm3 in the hydrate to the number in ice. We have measured €,(ice) = 3.27 f 0.04 at -12". With the cubic cell parameter taken as 17.12 A for the hydrates at -105", the contribution of the empty lattice becomes 1.540, equivalent to E,O = 2.98. All the large cages are assumed to be occupied and N M = 1.59 X loz1at - 105". Table I11 gives the values of EO(RI) calculated from the listed polarizabilities and dipole moments. The calculated contributions of the encaged molecules to e o ( l I j range from 82 to 91% of the amounts necessary to account for the experimental values of ~,(H20). The differences exceed the experimental errors. It does not seem possible to increase em0 or f b f , each of which is probably already a little too large. The polarizabilities CYM are underestimated since they are based on sodium D refractive indices. They would, however, need to be raised by an average of 35% to provide agreement with experiment. For the structure I1 hydrates examined, the Onsager equation therefore consistently underestimates the contribution of encaged molecules to the dielectric
+
The Journal of Physical Chemistry
constant. The success of the Onsager equation for many nonhydrogen-bonded polar liquids may be related to the cancellation of errors produced by the introduction of the approximation that a is given by 4rNa3/3 = V . The dielectric relaxation times of the hydrates increase, a t a definite temperature, in the order trimethylene oxide, tetrahydrofuran, dihydrofuran, and propylene oxide. This is also the order in which the largest molecular diameter increases, from ca. 5.5 to 6.5 A. This suggests that in hydrates with relatively small encaged molecules more space is available for the formation and diffusion of orientational defects. There may also be more "intrinsic" lattice imperfections in the form of misplaced 31 molecules to serve as sources of defects. Thus, the non-Arrhenius behavior at low temperatures (Figure 5) resembles the low-temperature behavior of the relaxation times in slightly impure and strained samples of ice. Relatively high dipole moments may lead to instability of the lattice. The hydrate of acetonelo ( p = 2.9 D.), which resembles propylene oxide in its largest diameter, relaxes as fast as trimethylene oxide hydrate. Attempts to form a hydrate of acetonitrile failed, perhaps because its dipole moment (4.0 D.) is too large. The Structure I Hydrate of Trimethylene Oxide. The molecule of trimethylene oxide fits the geometrical requirements laid down by von Stackelberg' for formation of a structure I hydrate in which only the larger cages are occupied. I n its maximum diameter (ea. 5.5 A) it resembles the structure I hydrate-formers CH8SH and COS, which are considered' to occupy only the tetrakaiclecahedral cages. These cages are much less spherical than the hexakaidecahedra of structure 11. In the structure I hydrate of ethylene oxide there is a variation of 0.6 A in the distances of the cage oxygen atoms from the cage enter.^ If, however, an average free cage radius of 2.9 A is assumed at -125", e o ( l l j = e,(H20) = 10.0 is calculated by the method already applied to the structure I1 hydrates. Since the experimental value e m ( l ) = 11.7 at -125" (for T110.7.63Hz0j is undoubtedly somewhat low because of air gaps in the sample a t this temperature, the calculated value is considerably too low.
Acknowledgment. We are indebted to A. D. Potts for some of the measurements. (9) C. J. F. Bottcher, "Theory of Electric Polarisation," Elsevier Publishing Co., Amsterdam, 1952, p 191. (10) G. J. Wilson and D. W. Davidson, Can. J. Chem., 41, 264 (1963).
