J. Phys. Chem. 1994,98, 7455-7451
7455
Supercooling of Water below the Anomalous Range near 226 K Lawrence S. Bartell’ and Jinfan Huang Department of Chemistry, University of Michigan, Ann Arbor, Michigan 481 09 Received: May 16, 19940
Large clusters of supercooled water undergoing evaporative cooling show no evidence of abrupt structural changes until they reach about 200 K. At that temperature they begin to freeze to cubic ice. Results of monitoring the cooling clusters by electron diffraction are described and discussed in the light of incompletely resolved anomalies in the properties of supercooled water.
We report the supercoolingof submicroscopicdroplets of water to 200 K by a technique that allows their structure to be followed continuously during the cooling process. This is of some interest in connection with speculations about anomalies in the behavior of highly supercooled water.’-’ The properties of supercooled water are well known to be strikingly different from those of typical liquids. It has been suggested that changes in its heat capacity, coefficient of thermal expansion, compressibility, and other properties as it is cooled indicate the existence of some sort of instability or critical phenomenon in the vicinity of 226 K,a temperature we shall call Ts.3-SJ This conjecture and Angell’s challenging remarks of a decade agog have led to a considerable amount of research that seems to have ruled out the existence of critical fluctuations1° near 226 K but which has not yet fully laid the problem to rest. In a seminal review of the evidence, Angel1 wrote? ‘The lowest temperature to which even the smallest and purest droplets of water have ever been supercooled seems to be -42 “C-[but]-an extension of this range for ultra-fast measurements (not yet designed) is perpaps possible in principle for measurements performed on microscopic particles during cooling processes at rates of the order of lo7 deg s e d . ” The reason experiments had been unable to explore in detail the phenomena in the immediate vicinity of TS is that water had always frozen 10-20 deg higher than Ts. It was suggested1that a ‘homogeneous nucleation temperature” THat -235 K limited the supercooling to which bulk water or even finely dispersed droplets could be subjected without crystallizing. SinceAngell’s review appeared, several workers have succeeded in cooling water considerably below Ts and vitrifying it in the process.IlJ2 In all cases water was in the form of finely divided particles, either in an emulsion or in an aerosol, and cooling was accomplishedby plunging the dropletsinto a cryogen or depositing them at supersonic speeds onto a very cold surface. These experiments left no doubt that water could be cooled through the anomalous region without crystallizing but, by their nature, the techniquesprevented the continuous examination of water during the cooling. The present investigation introduces an alternative method for cooling water well below Ts, which allows at least some of its properties to be monitored continuously. The method is the evaporative cooling of large molecular clusters produced by condensationof water vapor in supersonicflow through a miniature Laval nozzle. Thevapor, initially at a temperature near 100 “C, is seeded into neon carrier gas (water concentration 20-40 mol %). Liquid water clusters up to 74 A in diameter containing 6600 molecules are generated, although it is possible to produce much larger clusters by changing initial conditions. Adjustments of flow conditions make the cluster’s temperature upon emerging from the nozzle into the vacuum chamber comfortably above the hypothesized instability temperature. Clusters in free flight *Abstract published in Advunce ACS Absrrucrs, July
15, 1994.
0022-3654/94/2098-1455$04.50/0
I
”
I
I
0.5
’
t
I
1.5
I
I
I
1
2.5
s (A’)
I
I
I
I
3.5
I
4.5
Figure 1. Electron diffraction patterns of water clusters taken at 3.6-ps time-of-flight intervals, showing the transition from liquid to cubic ice. I
*
I
I
I
I
J
0
10
20
30
40
230
-20
-10
t, microsec Figure 2. Temperature profile computed for liquid water clusters. The
time origincorresponds to the emergence of clustersfrom the Lavalnozzle. Arrows indicatethe times at which the patterns of Figure 1 wererecorded. beyond the nozzle are probed at various timeof-flight intervals by electron diffraction13and could also have been interrogated continuously by Nibler’s technique of coherent Raman spectroscopy.14 Our clusters are observed to freeze, to crystals of somewhat disordered cubic ice, in the vicinity of 200 K. It is the diffraction peak breadths that provide the information about the size of the clusters. Typical difftaction patterns showingthe transformation are reproduced in Figure 1. The cooling of such small droplets to their so-called “evaporative cooling temperature”, Tcvp,is extremely rapid after they emerge into the vacuum, as illustrated in Figure 2. In cooling from 235 to 200 K droplets lose about 4% of their bulk by evaporation. Shortly after clusters leave the nozzle the cooling rate is lo7deg s-l if they are as small as those of the present investigation. Larger clusters would cool at predictable but correspondingly lower rates. Several rules-ofthumb for estimating Tcvp~3J5J6 correctly forecast our cluster’s temperature some dozens of microseconds after unimpeded evaporation had begun. The thermal history of the clusters was
-
0 1994 American Chemical Society
Letters
7456 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994
characterized more definitely by integrating the coupled differential equations governing the gas dynamics in the expanding medium, the nucleation and growth of the clusters, and evaporation, condensation, and thermal a c c ~ m m o d a t i o n . ~ If ~ - the ~~ clusters depart the nozzle at temperatures appreciably above TW, as they do in the present experiments, the cluster’s temperature profile T(t) beyond the nozzle tip is insensitive to the details of the processes taking place inside the nozzle and to the exact exit temperature. The external region is of primary concern in the present investigation. It is worth noting that the electron diffraction patterns clearly show the clusters remaining liquid until after they have cooled substantially below THand Ts. That they are liquid and not glassy solids is corroborated by their extremely rapid transformation to cubic ice once the nucleation rate, accelerated by the increasing supercooling, reaches a sufficientlyhigh value for freezing to take place on the microsecond time scale of the experiments. According to our modeling of the formation of critical nuclei,13 the rate of nucleation drops far below the observed rate when the liquid viscosity rises to that characteristic of a glass. Moreover, the glassy solid produced by chilling liquid microdrops on very cold surfaces has been shown to melt to the liquid at temperatures well below those encountered in the present work before it freezes (also to cubic That the clusters freeze in a few microseconds when they reach 200 K seems to imply that they do not experience the viscosity divergence at 228 K postulated recently by Angell.21 It is unexceptional that our clusters remain liquid far below the commonly accepted “temperature of homogeneous nucleation”, TH. In all examples we have examined so far, we have found the freezing of large molecular clusters to take place well below the temperatures recorded in prior studies of the freezing of macroscopic droplets of the same substance. It must not be supposed that the “nucleation temperature” THis lowered as a size effect in the same way as the freezing point. According to the treatment of Buffat and Borel,z2 the freezing point depression of a cluster composed of 5000 water molecules would be approximately 20 deg (if the surface tension of ice is estimated with the help of turn bull'^^^ and ant on ow'^^^ relations). Only about 3 deg of this lowering, that due to the Laplace pressure, would apply to TH. As explained by Reiss, Mirabel, and Whetten,25 the degree of supercooling (which does govern the nuclear rate) is reckoned from the bulk melting temperature, not from that of the cluster (according to the inherent basis of the classical capillary treatment adopted by Buffat and Borel). Our low nucleation temperatures for clusters are adequately accounted for by our high rates of evaporative cooling and small volumes available for nucleation. What is more interesting is the undisturbed passage of our clusters through the anomalous region near Ts. In view of the uncertain nature of the anomaly it is not clear whether TSshould be expected to exhibit a size effect analogous to that for the melting point. If, as recent evidence suggests,lo the region in question contains no critical point, there is nothing special about the survival of the liquid below Ts. Even if we assumed, for sake of argument, that the phenomenon near TSwere a true singularity and that the physical properties of water near TS obeyed the scaling laws characteristic of true critical points,26 our small droplets would not be expected to encounter serious instabilities during their cooling. Any critical fluctuations of density responsible for anomalies in compressibility, heat capacity, and other properties of the fluid would be frustrated by the small dimensions and short time scale of experiments. Accordingly, the thermodynamic properties should presumably more or less follow those of Angell’s “normal component” of water.27 How valid this conclusion would be for larger clusters is uncertain. The present clusters are probably far smaller than needed to pass through the anomalous region in the liquid state by the present technique. We plan to carry out experiments on progressively larger clusters to find whether interesting behavior is encountered at any stage. In this regard should be mentioned suggestionss.2”30
to the effect that water confined to small dimensions may not behave like true liquid water. In addition to the limitation imposed by small dimensions on any large density fluctuations possibly encounterd near Ts,other factors may be involved. Perturbations induced by the surface structure may disturb the molecular organization toward the interior. Therefore, some would argue that experimentson molecular clusters could never, by themselves, resolve questions about phenomena occurring in bulk water at temperatures near Ts. Other authors, however, question the importance of such perturbations over distances of more than a few molecular length^.^^.'^ Irrespective of the resolution of the latter controversy, even if there is nothing particularly surprising about the uneventful passage of our liquid clusters through the postulated range of instability, experiments of the present kind offer significant extensions of research on water. They demonstratean alternative method of deep cooling that permits a continuous observation of physical properties. Even more importantly, they yield a direct measure of nucleation rates in freezing, and at much higher supercoolings than had ever been reached in prior research on the crystallization of water.33934 Our analyses of nucleation rates will be presented elsewhere.
Note Added in hoof. One of the referees kindly pointed out that a viscosity divergence2’ need not rule out a rapid freezing. Despite the fact that molecular jump frequencies in classical theories of nucleation and crystallizationrates are based on models of viscous flow, it has been observed experimentally that growth rates of crystals in glasses can be explosively fast. Acknowledgment. This research was supported by a grant from the National Science Foundation. We are indebted to Paul Lennon for his valuable contributions to the diffraction experiments. References and Notes (1) Angell, C. A. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum: New Yorlc, 1982; Vol. 7, p 1. (2) Lang, E. W.; Liideman, H.-D. Angew Chem.,Int Ed. Engl. 1982,21, 315. (3) Speedy, R. J.; Angell, C. A. J. Chem. Phys. 1976,65, 851. (4) Speedy, R. J. J . Phys. Chem. 1982,86,982. ( 5 ) Speedy, R. J. J . Phys. Chem. 1982,86,3002. (6) Poole, P. H.;Sciortino.F.; Essmann, U.;Stanley, H. E. Nature 1992, 360, 324. (7) Stanley, H. E.; Teixeria, J. J. Chem. Phys. 1980, 73, 3404. (8) Vedamuthu, M.; Singh, S.; Robinson, G. W. J. Phys. Chem. 1994, 98,2222. These authors propax on the basis of their faithful modeling of its density that water is a mixture of two structural components. The authors argue that the smooth change in proportions of the two structural types is responsible for the evolution of water’s properties as temperature falls. No low-temperature instability is associated with the model. The curious coincidence that this model exhibits a discontinuity in the slope of p ( T ) at a temperature indistinguishable from TSseems not to be an essential property of the model. (9) Angell, C. A. Annu. Rev. Phys. Chem. 1983,34, 593. (10) Xie, Y.; Ludwig, K. F., Jr., Morales, G.; Hare, D. E.; Sorensen, C. M. Phys. Rev. Lett. 1993, 71, 2050. ( 1 1 ) Mayer, E. J. Microsc. 1986, 140, 3. (12) Hage, W.; Hallbrucker, A,; Mayer, E.; Johari, G. P. J. Chem. Phys. 1994, 100 2143. (13) See, for example: Bartell, L. S.; Dibble, T. S. J . Phys. Chem. 1991, 95, 1 1 59. (14) Beck, R. D.; Hineman, M. F.; Nibler, J. W. J . Chem. Phys. 1990, 92, 7068. (1 5 ) Gspann, J. In Physics of Electronic and Atomic Collisions;Datz, S., Ed.;Hemisphere: Washington, DC. 1976. (16) Klots. C. J . Phys. Chem. 1988.92, 5864. (17) Bartell, L. S. J . Phys. Chem. 1990, 94, 5102. (18) Bartell, L. S.; Machonkh, R. A. J. Phys. Chem. 1990,94,6468. (19) Furthermore, our clusters are well above the observed glass temperatureof water reported by: Angell, C. A; Sare, J. M.; Sare, E. J. J. Phys. Chem. 1978,82,2622. (20) R. J. Speedy [J.Phys. Chem. 1992.91.23221, however,suggests that the liquid phase produced when the vitrified water melts is a phase distinct from normal liquid water. (21) Angell, C. A. J . Phys. Chem. 1993,97,6339. (22) Buffat, P.; Borel, J.-P. Phys. Reo. A 1976, 13, 2287.
Letters (23) (24) (25) 7241. (26)
Turnbull, D. J. Appl. Phys. 1950,21, 1022. Antonow, G.N. J. Chim. Phys. 1907,5,372; Koll. Z . 1932,59,7. Reiss, H.; Mirabel, P.; Whetten, R. L. J. Phys. Chem. 1988, 92,
Anisimov, M. A. Critical Phenomenain LiquidsandLiquid Crystals; Gordon and Breach: Philadelphia, 1991. (27) Oguni, M.; Angell, C. A. J. Chem. Phys. 1983, 78,7334. (28) Robinson, G. W.; Zhu, S.-B. In Reaction Dynamics in Clusters and Condensed Phases; Jortner, J., Ed.; Kluwer Academic: Amsterdam, 1994; p 423.
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7457 (29) Zhu, S.-B.;Singh, S.;Robinson, G. W.In Modern Nonlinear Optics, Part 3; Evans, M., Kielich, S.,Eds.; Wiley: New York, 1994; p 627. (30) Stillinger, F. H. ACS Symp. Ser. 1980, 127, 11. (31) Derbyshire, W. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1982; Vol. 7, Chapter 4. (32) Clifford, J. In Water: A Comprehensive Treatise; Franks, F., .Ed:; Plenum: New York, 1982; Vol. 5, Chapter 2. (33) Wood, G. R.; Walton, A. G. J. Appl. Phys. 1970, 41, 3027. (34) Butorin, G.T.; Skripov, V. P. Sou. Phys.-Crystallop. (Engl. Transl.) 1972, 17, 322.
