DIELECTRIC PROPERTIES
OF
QUATERNARY AMMONITJ~V SALT HYDRATES
While it is difficult t o determine unambiguously the differences in thermal relaxation energies between the cation and neutral species derived from 9-anthroic acid, due exclusively t o rotation of the carboxyl group and conjugation with the anthracene ring in ground and excited states, the much greater sensitivity of the position of the fluorescence maxima to protonation and dissociation suggests that this effect is more pronounced in the excited state. Moreover, it is possible t o estimate the differences in solvent cage relaxation energies by observing the effect of a low dielectric solvent upon the fluorescence maxima. Thus in chloroform the fluorescence maximum of the neutral molecule is the same as in water while the fluorescence maximum of
1999
the cation lies 1000 cm-' to higher frequencies than in water (Table I). This establishes that the cation is more polar in the excited state than in the ground state and that a solvent relaxation error of 2.1 units in pK,' from this source alone would be incurred if absorption shifts alone, or an error of 1.1units would occur if the averaging technique were employed to calculate pK,". Thus because the employment of absorption shifts in the Forster cycle fails to account for substantial differences in rotational, conjugative, and solvational stabilization of the excited cation and neutral molecule derived from 9-anthroic acid, the employment of fluorescence shifts produced by excited-state prototropism provides the best estimation of pK,".
Dielectric Properties of Quaternary Ammonium Salt Hydrates by George T. Koide*l and Edwin L. Carstensen Department of Electrical Engineering, College of Engineering and Applied Science, University of Rochester, Rochester, New York (Received February $4, 2973) Publication costs assisted by the University of Rochester
The quaternary ammonium halide hydrates undergo dielectric dispersion in the frequency range lo2 to l o 7 Hz. Low-frequency dielectric constants, which can be attributed to bulk properties of the sample material rather than electrode phenomena, range from less than 100 t o values in excess of 1000. The dielectric data expressed as a function of hydration number show a discontinuity near critical hydration numbers which are in close agreement with values which have been obtained by X-ray diffraction. In general, the low-frequency limit of the dielectric constant increases with temperature-in some cases with marked changes occurring near 0". It appears that the dominant contribution t o the dielectric polarization at low frequencies comes from dipoles created by movement of anions either in liquid or crystalline water relative to cations which have been trapped in the clathrate structure. Of all the hydrates studied, only that of tetra-n-butylammonium hydroxide hydrate relaxes at frequencies above 10 MHz. The polarization, the high conductivities, and high relaxation frequencies of this hydrate are probably related to the high effective mobility of the hydroxyl ion in the crystalline structure. Introduction Water in several structural forms has been studied by dielectric techniques. I n the liquid state, near O", water has a relaxation frequency of approximately 9 G H z . ~ With the phase transition to hexagonal ice, its relaxation frequency falls abruptly to 7 kHza3 Although the relaxation' frequency changes by many orders of magnitude, the lowfrequency limit of the dielectric constant is affected very little by the phase transition and, in fact, to a good approximation goes as the reciprocal of the absolute temperature both above and below 0". Davidson and his coworkers have found that several "gas" clathrate hydrates and high pressure ices have relaxation frequencies which are near 1 MHz, if extrapolated to OO.*-10
Dielectric studies of protein solutions show a dispersion a t uhf-vhf frequencies. 11-15 Pennock and Schwan suggest that the disperion above 100 MHz re(1) Address correspondence to this author at the Department of Electrical Engineering, Rochester Institute of Technology, Rochester, N. Y. (2) C. H. Collie, J. B. Hasted, and D. M. Ritson, Proc. Phys. Soc., 60, 145 (1948). (3) L. Onsager and M. Dupuis in "Electrolytes," Pergamon Press, New York, E.Y., 1962. (4) D . W. Davidson and G. J. Wilson, Can. J. Chem., 41, 1424 (1963). (5) G. J. Wilson and D . W. Davidson, Can. J . Chem., 41, 264 (1963). (6) G. J. Wilson, P. K. Chan, D. W. Davidson, and E. Whalley, J . Chem. Phvs., 43, 2384 (1965). (7) A. D. Potts and D. W. Davidson, J . Phys. Chem., 69, 996 (1965). (8) R. E. Hawkins and D. W. Davidson, ibid., 70, 1889 (1966).
The Journal of Physical Chemistry, Vol. 76, N o . 14, 1979
2000 sults from a rotational relaxation of the water bound to the protein. Since the protein itself may contribute to the relaxation in this frequency range, it is difficult to show unequivocally which of the componentsprotein or bound water--are responsible for the dispersion at uhf frequencies. In fact, there is no clear evidence as yet that water in any of its forms relaxes at uhf frequencies. The clathrate hydrates are fascinating structural forms of water. Under the stabilizing influence of appropriatc guest molecules, water is able to form open crystalline cages which are stable at temperatures above 30” in certain cases. In fact, it has been suggested that the bound water of proteins may have a crystalline structure similar to the clathrate hydrates.16 The quaternary ammonium salt hydrates differ from the gas hydrates both in crystal structure and in the fact that ions are involved. The cations serve as guest molecules in the clathrate cavities and the anions are believed to be included in the clathrate water structure.’? This study was initiated to determine whether the kind of structural water found in the quaternary ammonium salt hydrates would provide a clear example of water with a rotational relaxation frequency in the uhf range. Instead, the dielectric propeties of these hydrates are dominated by a lowfrequency relaxation which is probably related to the movement of ions in trapped liquid or protons in the crystalline structure.
Experimental Section Methods and Materials. The salts used in this study were supplied by Distillation Products Industries, Division of Eastman Kodali- Co. Water concentrations mere determined by drying the samples under vacuum at 100” for 24 hr. In this investigation measurements were carried out on hydrates which in some cases contain more and in other cases less water than the amount required to form a complete clathrate structure around each of the cations. The term hydration number here is used to mean simply the ratio of the number of water molecules to the number of solute molecules in a given sample. The precise hydration number required to provide a complete clathrate shell for each guest molecule is called the critical hydration number. In this report, the hydration number follows the name of the salt; e.g., tetraisoamylammonium chloride 41 indicates a sample of this salt with a hydration number of 41. Precise measurements of the concentration of tetran-butylammonium hydroxide by the dry weight method were not possible because the compound sublimes. In this case samples with roughly the critical hydration number were prepared by first forming the hydrates at low temperature in an excess of water. The mixture of hydrate and water was filtered and the crystals wcre collected and dried on blotter paper for approxThe Journal of Phgsical Chemistry, VoE. 76, No. 1.6,19’7.8
GEORGET. KOIDEAND EDWINL. CARSTENSEN imately 1 hr at 5”. These samples were then melted and poured into the measuring cell and recrystallized for measurements. A simple calorimeter for measurements with the hydrates consisted of a 5-ml beaker containing the sample, heating elements, and a thermistor. This assembly was placed in a dewar. Starting a t -20”, a power of about 50-100 mW was applied to the heating coil and the temperature of the sample was monitored as a function of time. The unit was calibrated with water. Dielectric measurements in the frequency range 1-200 MHz were made using a Boonton Measurements Corp. 250A RX meter, those in the frequency range 0.1-4 X H z were made on a Wayne 1 h - r capacitance-conductance bridge B201, and those at low frequencies were performed with a special admittance bridge using techniques which have been described previously. 18-21 Observations of the dielectric properties of doped ice have been interpreted in part as an electrode phenomenon.z2 In our case the apparent low-frequency dielectric properties of the materials studied were shown to be independent of electrode spacing for separations ranging over a factor of 10. Thus the data reported here refer to the properties of the materials which constitute the samples and are independent of sample geometry and properties of the electrodes. In a few cases with highly conducting samples there was evidence that electrode polarizationz3 affected the data a t low frequencies. In these cases, data were corrected by standard techniques to remove the influence of polarization.20 (9) E. Whalley, D. W. Davidson, and J. B. R. Heath, J . Chem. Phys., 45, 3976 (1966). (10) A. Venkateswaran, J. R. Easterfield, and D. W. Davidson, Can. J . Chem., 45, 884 (1967). (11) H. P. Schwan, Advan. Biol. Med. Phys., 5 , 147 (1957). (12) H. P. Schwan, Ann. .V. Y . Acad. Sci., 125 (2), 344 (1965). (13) M.W. Aaron, E. H. Grant, and S. E. Young, Chem. SOC.Spec. Publ., 20, 77 (1966). (14) E. H. Grant, Phys. Med. Biol., 2 , 17 (1957). (15) B. E. Pennock and H. P. Schwan, J . Phys. Chem., 73, 2600 (1969). (16) I. M. Klotz in “Protein Structure and Function,” Brookhaven Symposia in Biology, No. 13, 1960, p 25. (17) G. A. Jeffrey, Sonderduck Dechema-Monogr., 47, 849 (1962). (18) H. Pauly and H. P. Schwan, Biophys. J., 6 , 621 (1966). (19) H. P. Schwan and K. Sittel, I E E E Trans. Commun. Electron., 72, 114 (1953). (20) H. P. Schwan in “Physical Techniques in Biological Research,” Vol. 6, Part B, W. L. Nastuk, Ed., Academic Press, New York, N. Y., 1963, p 323. (21) C. W. Einolf, Jr., and E. L. Carstensen, Biochim. Biophys. Acta, 148, 506 (1967). (22) M.Ida and S. Kawada, J . Phys. SOC.Jap., 21, 561 (1966). (23) This particular study and the general question of electrode polarization and space charge effects are discussed in detail in an internal report (Electrical Engineering Technical Report NO. GM09933-16, “The Dielectric Properties of Structured Water,” by G. T . Koide and E. L. Carstensen) which may be made available to the interested reader. This is also available from University Microfilms, Ann Arbor, Mich., order no. 70-2884.
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DIELECTRIC PROPERTIES OF QUATERNARY AMMONIUM SALTHYDRATES
Frequency (Hz)
Figure 1. Dielectric constant ( 0 ) and conductivity (0)of tetraisoamylammonium chloride 36 hydrate; temperature 5'. 10001
be present in other samples but is simply obscured by the high static conductivity. The relative loss factor curves in Figure 2 show the phen~rnenon.?~For the same solute but with a slight excess of water the conductivity at 5" increases so much that the maximum in the K" curve is almost obscured. However, when this sample is cooled to - 18" the low-frequency conductivity drops by nearly two orders of magnitude and the maximum in K" reappears this time shifted to about 0.1 MHz. As mentioned above, the tetraisoamylammonium chloride hydrate is the exception rather than the rule. I n general, the quaternary ammonium salt hydrates have higher conductivities and appear to have a broad distribution of relaxation freTable I : Low-Frequency Limits of the Dielectric Constants of Samples of Quaternary Ammonium Hydrates for Various Temperatures"
Frequency (Hz)
Figure 2. Dielectric loss factor K" for hydrates of tetraisoamylammonium chloride: a, hydration number, 36; temperature, 5 O ; b, hydration number, 41 ; temperature 5"; c, hydration number, 41; temperature, -18'.
Experimental Observations This investigation included dielectric studies of hydrates formed with both the tetra-n-butylammonium cation and the tetraisoamylammonium cation as guests in the clathrate structure and the anions F-, C1-, Br-, Cz04-, C2H303-,NOa-, and OH- as a part of the water structure. I n many cases, the measurements extended from 20 Hz to 200 MHz and included a wide range of temperature and solute concentrations. Of all the quaternary ammonium salt hydrates studied thus far, only one, tetra-n-butylammonium hydroxide, shows a relaxation in the uhf range. Even this may not represent rotational relaxation of water. However, in all the other quaternary ammonium hydrates studied, it is clear that water is either irrotational or characterized by relaxation frequencies of the order of 1 MHz or less. I n all of the hydrates, there are low-frequency dispersion processes. The data presented here are intended to illustrate the great diversity which is found in the dielectric behavior of this class of h ~ d r a t e s . 2 ~ Frequency Dependence. Figure 1 gives the relative dielectric constant and conductivity for the hydrate of tetraisoamylammonium chloride with approximately the critical amount of water necessary to form the complete clathrate structure for all of the solutions. The conductivity a t low frequencies in this hydrate is unusually low. However, because of this fact, it is possible to see a relaxation at around 0.5 MHz which may
T,
Low-freq.
Sample
OC
limit for
Tetra-n-butylammonium bromide 12
- 34
- 15
- 10 -5 1
Tetra-n-butylammonium chloride 32 Tetraisoamylammonium bromide 41 Tetraisoamylammonium chloride 35
Tetraisoamylammonium chloride 41
5 - 25 15 -6 5 - 34 - 20 - 11 2 - 30 15 -8 6 10 15 20 - 34 - 18
-
-
- 10
1 3 10 15 20
K
800 850 900 1000 1100 500 280 300 350 700 650 (100 Hz) 975 (100 Hz) 1600 (100 Hz) 4000 (100 Hz) 50 250 250 250 250 340 500 50 50 50 150 350 350 380 420
a Asymptotic values corrected for electrode polarization where it exists are reported. At low frequencies the tetraisoamylammonium bromide hydrate did not show electrode polarization but neither did it appear to be approaching a static limit. The 100-Hz data give an indication of the properties of these samples.
(24) A much more complete description of these hydrates and their dielectric properties is given in the internal report mentioned in footnote 23. (25) The relative loss factor K" = u/eow where c is the conductivity, eo = 8.85 X 10-13 F / m is the permittivity of free space, and w is the angular frequency.
The Journal of Physical Chemistry, Vol. 76, No. 14, 2978
GEORGET. KOIDEAND EDWIN L. CARSTENSEN
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(b)
T
'I
.-
10-'
B
u$
5-
.cI
E
6P
I0 ' 5-
IO MHz
IO' 2-
$
.g
54
IO?-
t
IO
,
,
, ,
,
20 30 Hydration Number
, 40
-% 100 MHz
20 30 40 Hydration Number
Figure 4. Relative dielectric constant for hydrates of tetra-n-butylammonium bromide: a, temperature, 5" ; b, temperature, -20". The discontinuities in the curves at high temperatures occur near the critical hydration number for this salt.
2
20
2%
2-
30
40
50
Hydration Number
Figure 3. Relative dielectric constant of hydrates of tetraisoamylammonium chloride ; temperature, 5". Note the sharp minimum near the critical hydration number for this salt.
quencies extending up to roughly lo6 Hz. The results of a large number of observations are summarized in Table I by giving just the low-frequency limit of the dielectric constant of the hydrate samples. Xote that the dielectric constant is reduced at low temperatures. Concentration. The critical hydration number for most of the quaternary ammonium hydrates shows clearly in the dielectric data. The dielectric constants for tetraisoamylammonium chloride (Figure 3) are typical for most of the samples studied. In these there is a sharp minimum in the dielectric constant when the water content of the sample reaches the critical value. An exception to the general pattern is found in the data for tetra-n-butylammonium bromide (Figure 4). In this case, the dielectric constant increases monotonically with hydration number but has an abrupt increase after passing beyond the critical number. At low temperatures, where presumably most of the liquid water has been frozen out (Figure 4b), the dielectric behavior is qualitatively different. Not only are the dielectric constant values significantly lower at all frequencies but there are no longer marked discontinuities in the data associated with the critical hydration number. Temperature Dependence. The dielectric constants of all the samples increase with temperature. For most of the salts this increase is more or less continuous up to the melting temperature of the hydrates a t which point the dielectric constant takes on the freThe Journal of Ph&cal Chemistry, Vol. 76, No. 14, 1972
5
-io
-2'0
-10 0 Temperature ("C)
1'0
Figure 5 . Relative dielectric constant for tetra-n-butylammonium chloride 36 hydrates. The dashed line at high temperatures is the frequency-independent dielectric constant which is characteristic of this sample in its liquid state.
quency independent value of the liquid solution. The data for tetra-n-butylammonium chloride with a hydration number of 36 in Figure 5 is fairly representative of most of the samples tested. In contrast, data for tetraisoamylammonium chloride 41 show an almost discontinuous increase of about 300 units in the relative dielectric constant near 0". This must be related to the thawing of the excess liquid water in the sample (See Table I and Figure 6). There is a similar, although less marked, discontinuity near 0' in the low-frequency dielectric constant data for tetraisoamylammonium bromide 40. As discussed below, the low-frequency dielectric constants appear to be related in part to movement of ions in liquid. With calorimetry it is possible to dem-
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DIELECTRIC PROPERTIES OF QUATERNARY AMMONIUM SALTHYDRATES
4 1 O-Asympatic low frequency values 300-
e-50 Hz
11
I: If
;r
A-I kHz
k
I /I
II
*.
li
4.u
200-
1
a
i .g
IQO-
B
I
-
e
Figure 6. Relative dielectric constant for tetraisoamylammonium chloride 41 hydrates,
Frequency (MHz)
Figure 8. Dielectric constants and conductivities of tetra-n-butylammonium hydroxide hydrate: a, 5"; b, -6" ; c, -20,"; d, -38". See Methods section for preparation of the sample and estimates of hydration number. The apparent dispersion in the dielectric constant below 5 MHz in curves a and b probably results from electrode polarization.
b
25
50 Time (rnin.)
75
Figure 7. Heating curve for tetraisoamylammonium chloride 40; sample weight, 4.4 g; input heat, 56 mW. The dashed curve is that for a sample with the same amount of water (2.9 g) as contained in the hydrate sample and with 56 mW input heat.
drates an order of magnitude or more higher than the others but from the appearance of the data in Figure 8 the relaxation frequency at temperatures around 0" must occur well above 100 MHz. The dielectric properties of tetraisoamylammonium hydroxide hydrates are similar to those of the halide hydrates.
Discussion onstrate that some water exists in the liquid state in the samples at temperatures well below 0". Figure 7 shoxs the heating curve for tetraisoamylammonium chloride 40. Note the slope change which begins at about -7" indicating that some of the water begins to change state a t this temperature. All samples tested showed evidence of liquid forming at temperatures below 0" with t>heexception of tetra-n-butylammonium bromide at below critical hydration numbers. The hydrates of this compound were unique in that the dielectric constants for samples of low water content were lower than those for samples near the critical hydration number (Figure 4). The Hydroxide Hydrates. Tetra-n-butylammonium hydroxide hydrates are unique among the samples studied. Not only are the conductivities of these hy-
Let us consider two general classes of relaxation processes which can lead to dispersion in the frequency range of these observations. One involves the preferred orientation of preexisting molecular dipoles; the other arises from the creation of dipoles by the displacement of ions of opposite sign relative to each other,26, In pure water only the first of these is important. The phenomenon of the rotation of polar molecules in the liquid state has been treated with some success (26) ~M,axwell-Wagner2' relaxation arising from the presence of conducting liquid "pockets" in an insulating solid would contribute minimally to the dispersion; e.g., if 10% of the medium were highly conducting, the magnitude of the dispersion in the dielectric constant AK would be only 1.05 K I where K I is the relative dielectric constant of the insulating portion of the medium. (27) K. w. Wagner, Arch. Elektrotech. (Berlin), 3 , 83 (1914).
The Journal of Ph&cal
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GEORGE T. KOIDEAND EDWIN L. CARSTENSEN
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by Onsager,28 KirkwoodJZ9DebyeJ30 and others. In the solid state, an answer to the question of how the molecules are able to "rotate" in the crystalline structure has been given by Bjerrum3I in terms of lattice defects. Even though the relaxation frequency changes by many orders of magnitude with the changes in state of water, the contribution of the polar molecules to the lowfrequency limit of the dielectric constant is of the order of 80-100 in all cases. The presence of ions in liquid water has only a minor effect on rotational relaxation frequency32 and the magnitude of the dielectric constant. The case for ice is somewhat different. The movement of ionic defects in ice may actually result in rotation of water molecules in a direction opposite to the electric field. As a consequence, the contribution of molecular dipoles to the dielectric constant is reduced.33 Jaccard predicts a reduction in dielectric constant with an increase in ion concentration. The effect has been observed in ice doped by HF.34835Thus, whereas in pure ice and water the rotation of permanent molecular dipoles is the only mechanism which contributes to the polarization , this effect can be reduced in ice by even small concentrations of ions. The other genersl class of polarization phenomena, the creation of dipoles by relative motion of ions, is not understood in detail but there are numerous examples of this kind of process in the work of others. The S c h ~ a r zmechanism, ~~ involving the movement of counterions relative to fixed surface charges, would fall into this category. There are many examples of high dielectric constants for doped ice (e.g., ice doped with KOH and ice doped with NH3).37'3*I n the most general terms, one would expect for this mechanism a low-frequency dielectric constant which would depend more or less directly upon the concentration of mobile ions and a relaxation frequency which is roughly proportional to the mobility of the counterions. In the case of the quaternary ammonium salt hydrates, since the cation is trapped in the clathrate structure, it is most reasonable to assume that the mobile ions are the anions. Halide ions in ice have mobilities which are lower by a factor of 104 than in water.3g Thus halide ions can be considered mobile only if they are able to move in liquid water. On the other hand, hydronium and hydroxyl ions have an even higher effective mobility in ice than in water.39 Assuming that the mobility characteristics of the ions are the same in the clathrate structure as in ice, it appears that a very wide range of dielectric constants and relaxation frequencies might be anticipated for the quaternary ammonium hydrates. The studies reported in the preceding section were designed to determine whether rotational relaxation of water contributes to the dispersion of the quaternary ammonium hydrates and insofar as possible to determinc the pathway for the movement of ions. The Journal of Physical Chemistry, Vol. 76, JVo.
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Since it is apparent simply from the magnitudes of the low-frequency dielectric constants of the hydrates that rotational relaxation of water alone cannot explain the dielectric phenomena, let us first consider the mechanism involving ion movement. Movement of Ions. From the relatively crude calorimetry illustrated in Figure 7, it is clear that many of the hydrate samples contain liquid water at temperatures as low as - 10". There is other evidence to suggest that liquid water may provide a pathway for the movement of ions in these samples, The abrupt shift in the low-frequency dielectric constants of tetraisoamylammonium chloride 41 with change in temperature near 0" (Table I) would be difficult to explain on any other basis. The gradual increase in dielectric constant with temperature up to 0" of most of the samples summarized in Table I would be consistent with a thawing of the hexagonal ice in the samples. On the other hand, although tetra-n-butylammonium bromidc 32 seems to have a pronounced shift in relaxation frequency with temperature, its low-frequency dielectric constant holds at roughly 1000 independent of temperature (Table I). In this case it appears that the concentration 6f relaxing elements is relatively constant but that the mobility of the charge carriers depends strongly on temperature. The ions involved in this relaxation cannot be identified with any assurance from these studies. The possibility that the bromide ions move in trace amounts of liquid water cannot be ruled out but it is difficult to see that very much liquid water could remain in the samples at temperatures below -30". Assuming that some liquid is present a t these low temperatures, it would appear likely that a large fraction of the counterions would be immobilized as the freezing out process continues. Yet the magnitude of the dielectric constant remains above 800 even at the lowest temperature of observation. In fact, all halide hydrates measured with the exception of tetraisoamylammonium chloride have low-frequency-low-temperature dielectric constants well above 100. Liquid samples of tetra-n-butylammonium bromide and chloride had pH values close to 7. Among the (28) L. Onsager, J . Amer. Chem. Soc., 58, 1486 (1936). (29) J. G. Kirkwood, J . Chem. Phys., 7, 911 (1939). (30) P.Debye, "Polar Molecules," Dover Publications, New York, N. Y., 1929. (31) N. Bjerrum, Science, 115, 385 (1952). (32) G. H. Harris, J. P. Hasted, and T. S. Buchanan, J . Chem. Phys., 20, 1452 (1952). (33) C. Jaccard, Hela. Phys. Acta, 32, 89 (1959). (34) A. Steinmann and H. Granicher, ibid., 30, 553 (1957). (35) H. Granicher, Phys. Kondens. Mater., 1 , 1 (1963). (36) A. Schwarz, J . Phys. Chem., 66, 2636 (1962). (37) ILI. Ida and S. Kawada, J . Phys. Soc. Jap., 21, 561 (1966). (38) A. Arias, L. Levi, and L. Lubert, Trans. Faraday Soc., 62, 1955 (1966). (39) M. Eigen and L. DeMaeyer, Proc. Roy. Soc., Ser. A , 247, 505 (1958).
DIELECTRIC PROPERTIES OF QUATERNARY AMMONIUM SALTHYDRATES tetra-n-butylammonium salt hydrates, hydroxyl hydrates have a melting temperature vhich is significantly higher than chloride and bromide hydrates. It is conceivable that upon lowering temperature, hydroxide hydrates are formed from the small number of hydroxyl ions in the solution in preference to the halide ions. As tetra-n-butylammonium hydroxide hydrates are formed more hydroxyl ions are created to satisfy the equilibrium constant. Thus, for the tetra-n-butylammonium salt hydrates, it may be possible that a higher concentration of hydroxide hydrates exist than would be anticipated from the pH of the liquid sample. This might account for the high conductivity and relaxation frequency of these hydrates. Rotational Relaxation of Water. It appears that thc dominant contribution to dielectric polarization at low frequencies comes from dipoles created by the movement of ions either in liquid or crystalline water. Whether there is any contribution from rotational relaxation of water is difficult to tell in the presence of the ionic mechanism. If a liquid pathway were important for the movement of these ions, it might be possible to suppress the low-frequency mechanism by “freezing out” this water. This would not be expected to reduce the magnitude of the rotational relaxation of the clathrate water, but merely to shift its relaxation frequency. Of the experiments described in the previous sections this technique was “successful” only for the tetraisoamylammonium chloride samples. With tetraisoamylammonium chloride 36 at 5” (Figure 2 ) there appears to be a maximum in K” at about 500 kHz. The dielectric constant (around 100 a t 100 kHz) is too high to be accounted for by the amount of water present in the sample. When a little more water is present in the sample (tetraisoamylammonium chloride 41, Figure 2) the low-frequency dielectric constant and conductivity increase and the maximum in K” nearly disappears. When the temperature of this sample is reduced to -18” the maximum in K” again appears, this time at about 100 kHz. The dielectric constant is low enough at this temperature that it could be accounted for by the amount of water present in the sample. This evidence is far from conclusive but it leaves open the possibility that a rotational relaxation exists in the quaternary ammonium salt hydrates which is similar to that found by Davidson and coworkers for the gas clathrates and high-pressure ices. Hydroxide Hydrates. The movement of ions in crystalline water was suggested above as a possible mechanism for the observed dispersion in the halide hydrates a t temperatures below freezing. It is clear that such a mechanism must be considercd with the hydroxide hydrates. The hydroxyl ion has a high mobility in ice.39 If it has a similar mobility in the clathrates this may explain the high conductivities and high relaxation frequencies of tetra-n-butylam-
2005
monium hydroxide hydrate. Whether rotational relaxation of the water molecules is involved at all is open to question. Since roughly 40% of the clathrate is occupied by the nonpolar quaternary ammonium cation, the dielectric constant of the samples above -6” is too high to be accounted for by the water present in the sample.
Conclusions The magnitude of the dielectric constant a t low frequencies in most samples is too great to be accounted for by the preferred orientation of molecular dipoles. Instead it appears that the polarization results from the creation of dipoles by movement of ions relative to other ions which have been trapped in the crystal structure. Calorimetry has shown that liquid water exists in the samples a t temperatures somewhat below 0”. Thus it is possible that some of the ions may move in liquid water. Movement of hydronium or hydroxyl ions in the crystal structure may also contribute to the polarization. The relaxation frequencies of tetra-n-butylammonium hydroxide hydrate are higher than those of the halide hydrates. The polarization, the high conductivities, and high relaxation frequencies of these hydrates are probably related to the high concentration and effective mobility of the hydroxyl ions in the crystalline structure. I n all of the observations there is no clear-cut evidence for rotational relaxation of the polar water molecules. It may exist but could simply be obscured by the ionic mechanism. The experiment with tetraisoamylammonium chloride 41 keeps this possibility open. However, this study of the quaternary ammonium salt hydrates contributes no positive support to the postulate that bound water is responsible for the relaxation of protein solutions a t vhf-uhf frequenies. All of the clathrates relax at much lower frequencies with the exception of the tetra-n-butylammonium hydroxide hydrate. Even in the hydroxide hydrate it is unlikely that the vhf dispersion results from a simple rotational relaxation of water. Acknowledgments. The authors are indebted to Mr. R. W. Smearing and Mr. J. Lozina for extensive help in the initial stages of this investigation and to Mrs. Sally Child for continued technical assistance throughout the investigation. The authors wish to thank Dr. D. W. Davidson, Kational Research Council, Ottawa, Canada, Dr. W. Y. Wen of Clark University, Drs. W. F. Newman, S. Shapiro, D. W. Healy, Jr., W. Streifer, and J. A. Kampmeier, all of the University of Rochester for helpful discussions. This work was supported in part by U.S. P. H. S. Grant No. 63109933. Dr. Koide was an N. I. H. Fellow under U. S. P. H. S. Grant No. 2TIGN540. The Journal of Physical Chemistry, Vol. 76, No. 14, 1973
