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Spin-Lattice Relaxation of D20 in Supercooled Water electron trapped in a cavity formed probably by the first solvation layer and moving without, or a t least with a minimal friction, in the medium. This concept of a friction "free" solvated electron should be kept in mind in studies meant to determine physical properties specific to the solvated electron from the overall properties of a solvated electron interacting with the solvent systems. It is worth noting that the "free" HMPA-solvated electron might not be a mere construct, and the approach to its direct observation could be sought for. For example, we anticipate that the esr signal from a nearly "free" HMPA-soluated electron might be observed when HMPA-solvated electrons are introduced in solvents such as liquid hydrocarbons since the viscosity coefficients of the latter are low and their ability to replace HMPA molecules in the electron solvation layer is weak.23 References a n d Notes This article will be included in G. Dodin's doctoral thesis, University ParisVII. V. Nicely and J. L. Dye, J. Chem. Phys., 53, 119 (1970),and references cited therein. R. Catterall, J. Slater, and M. C. R. Symons, J. Chem. Phys., 52, 1003 (1970). R. Catterall, I. Hurley. and M. C. R. Symons. J. Chem. SOC.,Dalton Trans., 139 (1972). V. L. Pollak, J. Chem. Phys., 34,864 (1961).
(6) D. E. O'Reilly, J. Chem. Phys., 35,1856 (1961). (7) J. Kaplan and C. Kittel, J. Chem, Phys., 21, 1429 (1953).
F. J. Dewald and G. Lepoutre, J. Amer. Chem. Soc., 78, 2953 (1956). (9) C. Lambert, "Metal-Ammonia Solutions." J. J. Lagowski and M. J. Sienko, Ed., Butterworths, London, 1970.
(8)
(10) R. Catterall, L. P. Stodulski. and M. C. R. Svmons. J. Chem. SOC. A, 437 (1968). (11) N. M. Alpatova, A. D. Grishlna, and M. G. Formicheva, Sov. Eiectrochem., 8, 248 (1972);translation published Sept 1972 by Consultant Bureau. (12) Mei Tak Lok, F. J. Tehan, and J. L. Dye, J. Phys. Chem., 76, 2975 (1972),and references cited therein. (13) G . Dodin, C. Lambert, and J. V. Acrivos, to be presented at the Coiloque ArnpBre. Kracovie, Poland, Sept 1973. (14) J. C. Dumais and Y. Merle d'Aubigne, Proc. Coiloq. AMPERE (At. Mol. Etud. Radio Elec.), X U / , 7970, l(1971). (15) J. S. Hyde and H. W. Brown, J. Chem. Phys., 37,368 (1962). (16) G. AlquiB, Thesis, Orsay, 1967. (17) S. I. Chan, J. A. Austin, and 0 . A. Paez, "Metal-Ammonia Solutions," J. J. Lagowski and M. J. Sienko, Ed., Butterworths, London,
1970. (18) C. P. Poole, "Electron Spin Resonance," interscience, New York, N. Y., 1967,p 695. (19) K. Halbach, Helv. Phys. Acta, 27,259 (1954). (20) A tunneling effect accounting for both hyperfine coupling modulation and electrical conductivity of the solutions as assumed for NaNH3 soiutionsg is unlikely to be valid in Na-HMPA solutions since the energy barrier for the electrical conductivities we have measured is expected to be much higher than the modulation barrier (which has the same order of magnitude as in Na-NH3),; (21) A. Abragam, "The Principles of Nuclear Magnetism, Oxford University Press, London, 1961,p 308. (22) J. Y. Gal and C. Moliton-Bouchetout, Bull. Soc. Chim. Fr., 2, 464
(1973). (23) A. Mozumder, J. Phys. Chem., 76,3824 (1972)
Relaxation Processes in Water. Spin-Lattice Relaxation of D20 in Supercooled Water' J. C. Hindman" and A. Svirmickas Chemistry Division, Argonne National Laboratory, Argonne, lllinois 60439 (Received June 5, 1973) Publication costs assisted by Argonne National Laboratory
Spin-lattice relaxation times, 2'1, for D2O have been measured in the supercooled region down to the homogeneous nucleation temperature using an emulsion of DzO in n-heptane. Using a double exponential form of the relaxation equation, an activation energy of 14.9 i 0.6 kcal mol-I and an entropy of 46.3 i 2.6 cal deg-l rno1-l have been derived for the low-temperature relaxation process. It is suggested that these large values for the entropy and energy may reflect a relaxation process involving cooperative motion of several water molecules.
It has become increasingly clear that the development and testing of models relating structure to relaxation in liquid water requires experimental data for transport processes over as wide a temperature range as possible. In particular, the marked non-Arrhenius behavior observed a t low temperatures emphasizes the importance of measurements in the supercooled region. The development of an emulsion technique2 for stabilizing small droplets (3.5 p in diameter) without significant alteration in the liquid properties has made it possible to measure various physical properties in the supercooled region2J down t o the homogeneous nucleation t e m p e r a t ~ r e .In ~ the present communication we describe the results of a study of the spinlattice relaxa.tion time, T I , for the deuteron in D20 down
to -37". An analysis of the results in terms of the twoprocess model is given.5 Experimental Section The procedures for the T measurements have been described e l ~ e w h e r e .The ~ emulsions of D2O in n-heptane were prepared according to Rasmussen's procedure.2 Emulsions of 25 and 50 vol Yo D2O were used. No significant difference in behavior was noted as indicated by the data given in Table I. Comparisons with a D2O sample run at the same time (values plotted in Figure 1) also showed that no significant differences could be detected in the relaxation time behavior a t temperature where measurements could be made on both kinds of samples, The Journal of Physical Chemistry, Voi. 77, No. 20, 1973
2488
J. C. Hindman and A. Svirmickas
TABLE I: Spin-Lattice Relaxation Time of DzO in n-Heptane Emulsion Temp, "K
TI, sec
Temp, "K
50 VOI % D 2 0
287.6 278.4 275.8 275.2 270.7 265.8 260.9 254.5 249.6 244.6 240.4 236.1 258.4 251.8 246.8 242.9 239.5 236.5
0.346 0.257 0.218 0.214 0.178 0.143 0.108 0.0726 0.0496 0.0306 0.0205 0.0138 0.0959 0.0604 0.0385 0.0247 0.0150 0.0127
L ' T I , sec
50 VOI % DzO 257.3 0.0872 0.0876 251.7 0.0603 0.0595 242.4 0.0255 0.0243 237.9 0.0146 0.0156 237.2 0.0126a 0.01 19 25 Vol % D20 257.3 0.0866 0.0885 251.7 0.0622 0.0600 0.0252 242.4 0.0251 237.9 0.0137 0.0135 237.2 0.0121a
IOOOlT, in
TABLE II: Fitting
a b
Eza
The Journal of Physical Chemistry, Voi. 77,
No. 20, 1973
OK
Parameters for Eq 1 D20,5 temp interval - 18 to 178"
d
I
4 00
DPO-DzO in n-heptane, temp interval -37 to 144"
I
€1 a
- In T,= [ a e 5 icedlT (1) The fitting parameters for the equation are given in Table 11. Close examination of Figure 1 as well as the larger standard deviation obtained in the present case indicates that the fit of this equation is not as good as previously obtained5 in studies where the measurements were not made to as low a temperature (see Table 11). As a consequence of the large number of observations the fit of the equation in the present case is forced with respect to the low-temperature points so that the deviations are most apparent in the high-temperature region. As a result the activation energy for the low-temperature process is more accurately defined than that for the high-temperature process. Actually, if we ignore the possibility of experimental uncertainties, the results suggest that we may need to consider more than two simple processes. Since the behavior of a variety of transport data in the hightemperature region is adequately represented by a simple Arrhenius equation, the complexity would necessarily be associated with the behavior in the low-temperature region. If, as suggested later in the text, the relaxation in the low-temperature region involves the cooperative motion of several water molecules. it would not appear im-
3 00
Figure 1. Spin-lattice relaxation time of DpO: 0 , D20 in n-heptane; +, D20, present experimental data.
Indication of partial freezing
Results The experimental T I values are given in Table I. It was found that the freezing of the water in the emulsion did not appear to affect its properties. On warming and recooling, T I values in essential agreement were obtained. The only apparent difference was that, whereas in the initial cooling, T I values could be obtained slightly below the reported homonucleation temperature, in subsequent cooling, incipient freezing was noted at this temperature. Values of -In 2'1 for the DzO and DzO in n-heptane as a function of the reciprocal temperature are shown in Figure 1. Also shown in the figure is a least-squares computed curve for the double exponential equation
I
-2001 2 00
C a
A
a
1.7323 X 5.152 X l o 3 7.010 X 1.660 X 1O3 10.24 & 0.29 3.30 f 0.06
1.2637 X 7.479 x 103 3.3670 X 1.928 x 103 14.86 f 0.64 3.83 i 0.13
Activation energies in kcal mol-' (95% level).
plausible to assume that the number of such molecules might exhibit a temperature variation with a consequent variation in the apparent activation parameters. The magnitude of the activation energy, 14.9 k 0.6 kcal mol-l, associated with the low-temperature process is comparable with those reported for the Tl(IH),6 E = 14.1 kcal mol-I, d i f f u ~ i o n ,E~ = 14.5 kcal mol-1, and dielectric,s E N 14 kcal mol-l, relaxation processes in ice. The comparability of these activation energies supports the view that the hydrogen-bonded structure associated with the relaxing molecules is well defined in the liquid at the lower temperatures. It is therefore of interest to determine how closely the rotational relaxation in the liquid resembles that in the solid. That there appears to be a significant difference can be shown by using transition state rate theory to derive the activation entropies for the relaxation in the two cases. Assuming that the correlation times associated with the 2'1 and dielectric relaxation are related in the solid as they appear to be in the liquid, we can use the equation5
k = 1 / r = [ehT/h] exp(AS,*/R) e x p ( - E / R T )
(2)
where the frequency factor, A, for the Arrhenius equation is
.4
[ e h T / h ] exp(AS,*/R)
(3)
For dielectric relaxation in ice, AS,* N 8.8 cal deg-I mol-l, while for the low-temperature, T I process in the liquid we calculate, ASc* = 46.3 cal deg-I rnol-l, an obviously significant difference. The actual magnitudes of the energy and entropy terms are the significant factors with respect to the mechanism of relaxation. The energy value indicates that several hydrogen bonds are broken in the activation process. The
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Spin-Lattice Relaxation of D20 in Supercooled Water present data can be interpreted in terms of the proposed kinetic model which assumes that hydrogen bond breaking and rotation is a single p r o c e ~ s Fundamental .~ questions are as follows. How many hydrogen bonds are broken? How many water molecules are involved? Does the relaxation correspond to the dissolution of a “cluster” of water molecules as suggested by Frank and Wen?lo If we follow Kauznnann and consider that the dissolution of a cluster corresponds to a “vaporization” of molecules in a local region of the liquid, the ratio of AS,* to the molar entropy of vaporization should be approximately equal to the number of molecules involved in the activation.ll This molar entropy of vaporization, ASlvap, is that for the vaporization of liquid water to water vapor occupying a volume equal to the “free volume” of the appropriate lattice configuration in the liquid, i.e. =
AS,,, - R In Wvapor/Vfree)
(4)
Weissmann and Blum have used the cell theory of fluids to calculate the “free volume” for water a t varying temperatures and intermolecular separations in an expanded ice lattice.12 Their calculations would suggest approximately 10 eu a s m upper limit for ASlvap, i.e., that more than four waiter molecules are involved. A similar calculation can be based on the ratio between the activation energy and the enthalpy for breaking a hydrogen bond. If we use the value of 2.5 kcal mol-1 for the breaking of the
bond in an 0-D-0 unit,13 we would calculate that approximately three water molecules are involved. These results lend some support to the idea that the relaxation does involve cooperative motion of a group of water molecules although the uncertainties in the various parameters are too large at present to allow us to specify the number of molecules involved. References a n d Notes Work performed under the auspices of the U. S. Atomic Energy Commission. D. H. Rasmussen and A. P. Mackenzie in “Water Structure at the Water-Polymer Interface,” H. H. G. Jellinek, Ed., Plenum Press, New York, N. Y., 1972, p 126. C. A. Angell, J. Shuppert, and J. C. Tucker, submitted for publication in J. Phys. Chem. 9. J. Mason, Advan. Phys.. 7 , 221 (1958). J. C. Hindman, A. J. Zielen, A. Svirmickas, and M. Wood, J. Chem. Phys., 54, 621 (1971). D. E. Barnall and I. J. Lowe, J. Chem. Phys.. 48, 4614 (1968). H. Blicks, 0. Dengel, and N. Riehl, Phys. Kondens. Mater., 4, 375 (1966): 0.Dengei, E. Jacobs, and N . Riehl, ibid., 5 , 58 (1966). R. H. Cole, J. Chem. Phys., 27, 33 (1957): R . Ruepp and M. Kass in “Physics of Ice,” N. Riehl, B. Bullemer, and H. Engelhardt, Ed., Plenum Press, New York, N. Y . , 1969, p 5 5 5 . J. C. Hindman, submitted for publication in J. Chem. Phys. H. S. Frank and W. Y . Wen, Discuss. faraday SOC.. 24, 133 (1957). See D. Eisenberg and W.Kauzmann, “The Structure and Properties of Water,” Oxford University Press, New York, N. Y., 1969, pp 212. 213. M. Weissmann,and L. Blum, Trans. faceday Soc., 64, 2605 (1968). G. E. Wairafen in “Water,” F. Franks, Ed., Plenum Press, New York, N. Y., 1972, Chapter 5.
The Journal of Physicai Chemistry, Vol. 77, No. 20. 1973
