JOURNAl, OF COLLOID AND INTERFACE SCIENCE 25, 192--205 (1967)

Liquid-Like (Transition) Layer on Ice 1

H. H. G. JELLINEK

Department of Chemistry, Clarkson College of Technology, Potsdam, New York Received August 1, 1966

The concept of a liquid-like layer on ice even below the freezing point of water has become of increasing importance, because it can account for the surprising surface properties of ice. This concept has a very interesting history involving many famous scientists of the last century such as Faraday, Lord Kelvin, J. Thomson, Helmholtz, and Tyndall. Actually, an appreciable amount of research was carried out on ice about 100 years ago. A survey of the concept of the liquid-like layer covering approximately the last hundred years will be given here.

A. EARLY WORK at that time and Faraday carried out a In 1850, M. Faraday (1,2) described a number of experiments with other substances phenomenon shown by ice, which soon at their melting points, but they did not became the object of a lively controversy show this behavior. between such famous scientists as Faraday Tyndall accepted Faraday's view, and and Tyndall, on the one side, and J. Thom- the term regelation (refreezing) was first son, his brother W. Thomson (later Lord coined by him in a paper with Huxley (3). Kelvin), and Helmholtz, on the other side. Tyndall attempted to explain the '.'flow" of Faraday's observation was a very simple glaciers by regelation. His idea was that the one: If two pieces of ice at 0°C. or at a higher ice in glaciers fractures in many places, ambient temperature are brought into slight takes up new positions, and reunites by contact, they freeze together. Faraday regelation. points out in various papers that water can Somewhat before Faraday's discovery of be supercooled and superheated. However, regelation, J. Thomson (4) (a brother of when an ice crystal is placed into supercooled W. Thomson (5), later Lord Kelvin) made water, crystallization takes place at once. a quantitative theoretical study of the effect He ascribes this freezing to the effect of of pressure on the melting point of ice by "cohesive" forces exerted on the neighboring thermodynamic reasoning. The final result water "particles." This effect is intensified, is in the form of the Clausins-Clapeyron according to him, if a water film is situated equation. Thomson tried at once to explain between two ice surfaces--a situation which regelation by pressure melting and opposed is brought about by contacting two pieces Faraday's and Tyndall's views. J. D. Forbes of ice; the cohesive forces are then so effec- (6,7) was also interested in regelation phe- tive that freezing takes place even when the nomena at that time, but his theory of ambient temperature is above 0°C. This regelation was certainly incorrect and is of property of ice was a very remarkable one only historical interest today. In response to Thomson's criticisms of 1 This survey appeared as special report $70, Faraday's views on regelation, the latter October 1964, U. S. Army Cold Region Research (2) performed a number of simple but very and Engineering Laboratories, Hanover, New Hampshire. The author wishes to express his ap- ingenious experiments. However, J. Thom- preciation for support of this work by the above son (5) was not convinced. organization. Thus, Faraday and Thomson were dead- 192 LIQUID-LIKE (TRANSITION) LAYER ON ICE 193 locked, although Faraday conceded that, 2.86,~ under appropriate conditions, pressure melt- i ~---,~ ing could play a role. Helmholtz (3) also o Oo ,0 supported Thomson's views and carried out I experiments on regelation, but Tyndall (3) C' remarks in his book that he and Helmholtz © ¢ eventually agreed that regelation could not be properly explained at that time. It is clear that if only experiments at 0°C. I or above are considered, a definite decision o + cannot be made. Thomson's views eventually I I prevailed and found their way into the © o textbooks. I i ii~--o, 2o A Further progress came when more became © known about crystal lattices and forces acting in the surface of solids and when experiments were carried out at tempera- 2.81A tures below the melting point of ice. Fie. 1. Surface layer of a sodium chloride B. RECENT WORK crystal lattiee showing displacement of anions and cations forming an electrical double layer, 0.20 A Progress was made concerning the problem thick (9). of regelation by Weyl (8) in 1951. He pointed out that in an ionic crystal lattice there is reaching consequences for the surface prop- polarization in the surface distorting the erties of water and ice. Thus for water, there lattice in the uppermost surface layer. A should be a disturbance in the surface layers; good example is a crystal of sodiunl chloride in other words, the properties of water in (9). The anions are more polarizable than the surface are different from the bulk the cations, and the surface free energy is properties of water. decreased when the anions are displaced A transition layer several hundred Ang- with respect to the cations in the surface stroms thick is needed, according to Weyl layer as shown in Fig. 1. to pass from the configuration of the outer- An electrical double layer is formed owing most layer to the proper bulk ice structure. to the distortion of the lattice. The actual Thus, he assumes a liquid-like layer, which values for this distortion depend, of course, on the one side has the properties of a water on assumptions made about potential energy surface which changes continuously across curves, etc. This introduces uncertainties in a certain film thickness until the crystal the quantitative evaluation. However, it structure of ice is reeehed. Such a layer, seems to be agreed that such distortion and according to him, exists not only very near double !ayer formation actually take place. the melting point but considerably below An appreciable decrease in surface free the melting point, eventually disappearing energy accompanies such distortion. Weyl as the temperature decreases. Such a film suggested a similar phenomenon for the is in equilibrium with water vapor on the structure of the ice surface. Water molecules one side and bulk ice on the other. It is consist of dipoles, and the surface free energy neither liquid water nor ordinary ice, but is of a water surface and also of an ice surface a transition film which has properties some- in contact with air or in a vacuum would where between those of ice and water. He be considerably reduced if the water dipoles goes even further and postulates that such a were oriented in such a way that the negative liquid-like transition film exists not only at charges (the oxygen atoms) were situated an ice/air interface but also on ice/solid at the outer surface, directed towards the interfaces. The properties and thickness of air or vacuum. In such a way an electrical the transition film will then be influenced by double layer would be formed at the surface the nature of the respective solid. of the water or ice. This postulate has far- The assumption of a liquid-like layer on 194 JELLINEK

ice below 0°C. throws new light on all regela- sodium chloride will, of course, have thicker tion phenomena and allows a distinction to transition films and the rolling action will be made between the views of Faraday and be increased. Tyndall on the one side and those of Thom- It will be very difficult to explain this son on the other. In other words, regelation phenomenon in any other way; for instance, phenomena should occur say at -5°C., by pressure melting. It could be assumed where 615 kg./em. 2 are needed to depress that on contact, large pressures are devel- the melting point of ice to such a value. oped owing to the small contact area and Nakaya and Matsumoto (10) were the that some melting and refreezing takes first to carry out some experimental work place; however, breaks should take place in order to verify Weyl's assumptions. They without any rolIing action, although there prepared ice spheres, which were suspended is a small rotational momentum. Similar from cotton threads like pendulums. One of experiments, more accurately controlled, these pendulums could be moved laterally however, were carried out by Hosler, Jensen, making the two spheres touch each other and Goldshlak (11). under a ve[y slight force estimated by the Their apparatus is shown in Fig. 2. It authors to be less than 0.01 dyne. The ice consists of a heated insulated box which spheres prepared from distilled water had could be cooled to -80°C. Here A and B diameters ranging from 1.5 to 4 mm. are the ice spheres, C a microscope, D a Separation of the two spheres was wormserew, and E a calibrated knob. Lateral achieved by moving the suspension point movements to an accuracy of 0.001 inch of one sphere laterally. This separation took could be measured. The force of separation place when each thread formed an angle 0 is again measured by finding the angle 0, with the vertical. An interesting phe- nomenon was observed by these authors. It happened quite frequently at the angle 0, I H that the two spheres started sliding or rolling over each other before finally separating. Rotation was more frequent near the melting point but also occurred at -7.0°C. The strength tended to decrease with increasing temperature, but increased (larger contact c tl'f:],ltl Z. i ~ I ~1 ~*,'Tim'~-J ,:> \l,s)lt ~: ~,'~ I I ITt,~Vllq£'~(~l area) the larger the force by which the two E \y,l',t i, .~.4 [1, +l spheres were brought together. Experiments were also earned out with spheres made from water containing 0.1% sodium chloride. In these cases, the rotation was much more pronounced and frequent; rotation could often be observed down to a temperature of - 14°C. The authors accepted Weyl's assumption of a transition layer on the surface of ice at temperatures lower than 0°C., to explain their results. Their view is as follows: when the two spheres come into contact, the liquid-like fluid at the contact point is FIG. 2. Apparatus for measuring force of sepa- transformed into ice. This bond is then ration of ice spheres. A--outer cell of heat insu- lated box, B--fiberglass, C--inner shell, F--ap- broken when a definite angle 0 is reached; paratus chamber, D--cooling chamber packed however, instead of the spheres separating with dry ice, E--copper plates, G and H--brass immediately, a rolling action takes place clips holding the ice spheres, L--worm screw, J-- owing to the surface tension of the film, knob for turning screw measuring linear move- and eventually actual separation takes place ment of H (minimum 1 X 10-3) (11), K--thermo- at an angle 0 -F AO. The spheres containing couple, L--lucite rod windows (11, 12). LIQUID-LIKE (TRANSITION) LAYER ON ICE 195

.J the logarithms of the separation force against the reciprocal absolute temperature T, ~~ (SR2) i yielding an apparent energy of activiation E = 10.6 kcal.; R is the ideal gas constant; A and A' is a constant. If the assumption is now made that the contact area A where freezing is taking place is proportional to some power n of the transition layer thick- ness d, we have: F = F1A = kFl.d n, [2] where F is the tensile strength of the bond Fro. 3. Initial and final positions of spheres. Force of separation F = weight of sphere )< tan; and /c a constant of proportionality. From horizontal distance one sphere has moved = Eqs. [I] and [2], we obtain: (SR 2 - SR 1)/2 = D, A = length of suspending A' -~/Rr thread, hence tan 0 = D/A (11, 12).

giving a force of F =mg tan 0, where mg or is the weight of one sphere. This is illustrated in Fig. 3. The horizontal distance each sphere -E' ~ A' log d - 2.303RT + log [3] has moved is given by (SR2 - SR1)/2 -- D; n kF1 ' hence tan 0 = D/A, where A is the length where E ~ = E/n. Hence the logarithm of of the suspending thread. The spheres were the layer thickness plotted against the prepared in Lucite molds and had a radius reciprocal absolute temperature should also of 0.29 inch. The authors worked in dry and water vapor saturated atmospheres. Be- tween -80 ° and -40°C. no adhesion oc- 600 ' ' L i I curred. The results obtained in the two different environments are shown in Fig. 4. There is a very striking difference between the experiments carried out in a saturated n 5OO o tll and those carried out in a dry environment. Z The lowest temperature at which adhesion {D could be measured in a saturated atmosphere W was about -25°C., whereas in a dry atmos- 4O0 gu phere adhesion practically ceased at -3°C. {o Again these results can best be explained o by Weyl's theory of a transition layer on llJ 300 o o o o the surface of ice below 0°C. In the ease of fig the dry environment, this transition layer bl evaporates very quickly and proper equilib- {D 0 200 rium cannot be obtained; thus the liquid-like I-- layer practically disappears at a temperature of --3°C., whereas in the saturated atmos- ,o, phere equilibrium is always maintained and t~ oo a noticeable layer still exists at -25°C. The W force of separation observed by Hosler ,9 / ~o et al. (11) as a function of temperature can 0 ~ I I " -80 -25 -20 -15 "10 -5 0 be represented by the following equation: TEMPERATURE ° C

F = A'e-E] Rr. [1] FIG. 4. Separation force as a function of tem- perature: A--water vapor saturated atmosphere; The data give a good straight line by plotting B--dry atmosphere (11, 12). 196 JELLINEK give a straight line, with an energy of activa- various surfaces, such as stainless steel, tion E' differing by a factor 1/n from the optical flat quartz surfaces, and surfaces apparent energy of activation E for the of various polymers. He observed that only separating force. That this is actually the cohesive breaks occurred with tensile experi- case will be discussed subsequently. ments, however finely polished the surface It would be very difficult to account for was. But shear experiments gave adhesive these experimental results on the basis of breaks, the strength of which depended on the pressure melting theory. Some simple the rate of shear, surface finish, and tern- calculations were performed by Jensen (12) perature. The temperature relationship is to illustrate this. For instance, if the spheres shown in Fig. 5, where the adhesive strength were brought together at -5°C., a pressure is plotted as a function of temperature; P-5 of about 600 atmospheres is needed to down to -13°C., this relationship is linear, achieve pressure melting. This would occur the adhesive strength increasing with de- if the contact area between the spheres is creasing temperature. A sharp break occurs A-5 era. 2. Suppose the spheres are brought at -13°C.; below this temperature only together with the same force at -20°C., cohesive breaks are observed, the tensile then the pressure P-20 for melting would strength being practically independent of have to be 1910 atmospheres. The corre- temperature. Adhesive strength as a function sponding contact area would be A_20cm. 2. of surface finish is shown in Fig. 6. The Hence, the separating forces at these two adhesive strength decreases with decreasing temperatures would be given by F_5 = roughness of the surface. Figures 7 and 8 P_sA_a and F-20 = P-2oA-2o or since F_5 = show the adhesive strength as a function of F-20 rate of shear for mirror-polished stainless steel and optically flat quartz surfaces, A_5 P-20 respectively; linear relationships are found.

A-20 P-5 " Some adhesion experiments were also carried out by Raraty and Tabor (15) which The contact area at -5°C. would have to be are substantially in agreement with Jellinek's 3.2 times larger than that at -20°C. if the data. The latter has made use of Weyl's same force was used in both cases for con- postulate of a liquid-like or transition layer tacting. If the tensile strength is the same at the ice/solid interface. This provides the in both cases, the force of separation should be 3.2 times as great at -5°C. as at -20°C. These separating forces can be obtained from experimental data. The actual ratio t4 is 10.5. One should rather expect that the tensile strength decreases somewhat with increasing temperatures. Jensen also computed the actual contact 8 areas from his experimental data, taking 17.4 kg./cm. 2 as the tensile strength of ice. 6 The result is that the actual pressures on 4- the contact areas are 3000 to 10,000 times 2 smaller than those which are required for 0 i i f I i i i i i i i i i i I I i I melting. -t0 -20 -50 The difference observed in the saturated Ternperafure (°c) and dry environments is also in contradiction to the pressure melting theory. The environ- FIG. 5. Strength as a function of temperature for snow-ice sandwiched between stainless steel ment should have a negligible influence in disks, obtained by shear. Cross-sectional area 1.54 case of pressure melting. cm.~, height 0.2 to 0.4 cm. Adhesive breaks down Jellinek (13,14) investigated the adhesive to --13°C; cohesive breaks below --13°C). Each properties of ice by carrying out tensile point represents the average of at least 12 tests and shear experiments with ice frozen to (13, 14). LIQUID-LIKE (TRANSITION) LAYER ON ICE 197

6.0 value far above the bulk tensile strength of ice. Hence only cohesive breaks will take place for tensile experiments. The situation becomes more complicated if the surface of the solid is not completely wetted by the 5.0 liquid-like layer, as in such a case the contact ® angle is greater than zero. The situation is quite different for shear experiments. If the surface of the solid were 4.0 ideally flat, the smallest shear force should start the solid moving across the ice provided the transition layer has no yield point. (There are, however, indications of a small

3o yield point; see Figs. 7 and 8.) Experimental data indicate that this is actually the case for fused quartz optical flats. The ratio of the viscosity to the thickness of the liquid-like layer is given by: 2.0 ~/L = c/S/dr [51 if it is assumed as a first approximation that the transition layer is Newtonian. Here t.0 is the viscosity, S the shear strength, and V the velocity of shear. It has also to be remembered that ~ is an average value, as the properties of the layer change continually from the solid/liquid layer interface until 0 t0 20 50 40 50 60 70 the proper ice crystal lattice is reached. Time (SEC) The relationship between cohesive strength and rate of shear was found to be linear: FIG. 6. Typical stress vs. time curves for stain- less steel disks of different roughness and for a for ice/stainless steel: fused quartz optical fiat (rates of shear are similar in all cases): (i) Snow-ice--stainless steel, steel dS/dV = n/L = 69.9 kg. see.. surface finished on lathe. (2) Snow-ice--stainless cm. steel, mat polish. (3) Snow-ice--stainless steel, mirror polish. (4) Snow-ice--stainless steel, mirror polish. (5) Snow-ice--fused quartz optical fiat

(flat to within i/g waveband), temperature -4.5°C t.4 (14). 1.2 only reasonable explanation for the observed (D !.0 phenomena. The situation is indicated in v Fig. 9, where the solid is completely wettable 08 F by water. In such a case, there is a pressure 2 difference across the curved surface given 06 by the following equation: 04 x_ 2~ [4] 0.2 Ap- L • Here ~, is the interfacial tension at the liquid- 0 0.5 1.0 I 5 20 like layer/air interface and L the thickness Rate of shear (tOZxCM/SEC) of the layer. If we suppose that L --- 2 X FIG. 7. Relationship between average adhesive 10-6 era. and ~ = 76.4 dynes/era., the pres- strength and rate of shear for snow-ice--stainless sure Ap becomes 7 X 107 dynes/cm.2--a steel (mirror polish). Temperature -4.5°C (14). 198 JELLINEK

O.S - i -- i i :~ 0.7 o 0.6 -- 05

mF 0.4 x x 0.3 >~ 0.2 OA

t.0 20 50 4.0 Rate of shear (fO 2 x CM/SEC) FIG. 8. l%elationship between average adhesive strength and rate of shear for snow-ice--fused quartz optical fiat. Temperature -4.5°C (14).

ported that cohesional breaks took place ~ 2R ~- I for ice frozen to various solids on shearing. The apparent discrepancy between Jellinek's (13,14) results and those of Ford and Nichols is probably due to the high rate of pressure application (20 p.s.i./sec.) used by LIQUIDLIKE LAYER the latter authors. This rate is so high that the liquid-like layer has not sufficient thne to accommodate the change in pressures. Kingery (17) carried out some interesting STEEL ] experiments on the growing together of ice spheres. Growing together of particles or sintering is a general phenomenon taking FIG. 9. Liquid-like transition layer sandwiched place at temperatures not too far below the between ice and stainless steel. Pressure difference melting point of a substance. The driving Ap across curved surface is Ap = 2,,//L, where force for the sintering is the decrease in is the surface tension of the liquid like layer, V is surface free energy. Ice, of course, is usually the velocity of the stainless steel disk for shear studied very near the melting point and experiments (13). sintering should be readily apparent. How- ever, ice seems to have a special position for ice/quartz: because of the dipole nature of the water molecule, and the disturbance (transition dS/dV = n/L = 15.1 kg._see. layer) in its surface is particularly pro- cm. nounced. The general relationship between the radius X of the neck between two spheres A reasonable assumption considering the and the radius of the spheres is given by the roughness of the various surfaces involved following equation (see Fig. 10) :2 gives an estimate for L, and approximate values for the viscosity can then be obtained. (x) ~ F (~) For L varying from 10-5 to 10-G em. at - Ro_ ~ . [6] -4.5°C. one obtains for v at an ice/steel interface 70 to 700 poises and for ice/quartz Here F(T) is a function of the surface free 15 to 150 poises. This is the first rough energy and n and m are exponents which are estimate of the viscosity of the liquid-like characteristic of the respective growth layer, and it does not seem to be unreason- able, lying between the viscosity of super- See in this connection, corrections for Eq. cooled water (2.1 X 10 -~ poises at -5°C.) [6], H. H. G. Jellinek and S. H. Ibrahim, "Sintering and ice (ca. 101~ poises). of Ice Spheres," paper presented in this Sympo- T. E. Ford and O. D. Nichols (16) re- sium. LIQUID-LIKE (TRANSITION) LAYER ON ICE 199

assumption of such a transition layer (19). He also remarks that if such a film were present, a discontinuity in the surface diffu- sion properties should become apparent with change of temperature. As a matter of fact, the rate of diffusion as a function of the reciprocal absolute temperature suggests such a discontinuity. If the two points FIG. 10. Growing together of ice spheres (18). corresponding to the two highest tempera- tures are considered, an energy of activation process: of about 180 keal./mole/deg, is derived. Kuroiwa (20) also carried out experiments n = 2, fr~ = 1 Viscous flow on the growing together of ice spheres. His n= 3, m= 1 Evaporation-condensation ice spheres had radii smaller than 10.2 era. n = 5, m= 2 Volume diffusion (20 to 80 ~) over a range of temperatures n = 7, m = 3 Surface diffusion from -15.5 ° to -2°C. However, no attempt Kingery carried out growth experiments was made to calculate diffusion coefficients with ice spheres having radii varying from and energies of activation. Experiments 0.011 to 0.328 cm. over a temperature range were also carried out under kerosene. The from -2.2°C. to -25.1°C. In all eases, the experiments indicated that volume and average values for n were near 7 and those surface diffusion were involved. Evapora- for m about 3, indicating surface diffusion. tion-condensation was definitely excluded Two remarkable features were noted: The by means of the experiments under kerosene. diffusion coefficient (DO -- 1022) was found The only paper in recent years in which to be several magnitudes larger than ex- the concept of a liquid-like transition layer pected and the energy of activation is very of ice is opposed, is that by Hobbs and high: Mason (20a). They maintain that observing under the microscope two ice spheres grow- Ds = 1022 exp (--27500/RT) ing together, they found no evidence for such a layer, except when the surface is (no dimensions were given for Ds). contaminated (e.g., NaC1). In this particular The energy of activation (27500 cal./ ease, a rapid growth of the "neck" takes mole/deg.) suggested to Kingery that the place, whereas in the ease of "pure" ice, rate-determining process was that of diffu- this growth is quite slow. It is an easy matter sion of water molecules from the ice into to show that the thickness of the transition the surface layer. The above relationship layer is far below the resolving power of may be compared with that obtained by an optical microscope. Thus what was ob- Murphy (18) for the bipedal walk of a water served with "pure" ice spheres is just what molecule on an ideal ice surface. In this would be expected. Only careful experiments ease, only one hydrogen bond has to be with two ice pendulums would reveal the broken at the time: transition layer. D, = 3.5 X 10 .4 exp (--5200/RT) cm?/sec. Jellinek and Ibrahim (20b) (see paper this symposium) have studied the sintering of The energy of activation for this process is ice spheres (radius 0.5tL) over a range of about half that for the heat of evaporation temperatures. Surface areas were determined of water (strength of hydrogen bond). by the BET method before and after sinter- Kingery does not think it necessary to ing. It was ascertained that sintering of ice assume a transition film on ice but only a spheres of small magnitude is due to plastic very highly mobile surface layer, one or two flow caused by surface tension forces. The molecules thick. However, in view of all results are compatible with a transition the evidence presented here for the existence layer on ice. of a liquid-like layer on ice, it is clear that Fletcher (21) was the first to attempt to Kingery's results agree very well with the show quantitatively that a transition layer 200 JELLINEK exists on an ice surface and also on a water the possible hydrogen bonds are broken. It surface. His arguments are partly thermo- should also be mentioned that evidence for dynamic and partly statistical. The main liquids' having surface transition layers was point is to show that ice having such a collected by Henniker (22). transition layer on its surface has a lower The surface molecules of water are sup- free energy G than ice with an ordinary posed to have their oxygen atoms pointing surface and no disturbance in the surface outward whereas the hydrogen atoms are layer; in fact, the equilibrium state is given pointing inward. The energy gained (nega- when G shows a minimum. Suppose there tive AH) per molecule by changing from a is a definite amount of ice with an ideal random orientation to the orientation as ice surface at a given temperature T; this indicated above is about e ~ 10-12 erg/ means it has a perfect ice crystal lattice molecule or 14.34 kcal./mole. This value throughout. The free energy G of the system can be estimated in the following ways: is given by: (a) The energy gained by orienting one proton in a water surface from pointing G = H -- TS, [71 outward to the opposite direction is approxi- where H is the enthalpy, T the absolute mately equal to the energy of formation of a temperature, and S the entropy of the hydrogen bond. This leads to a value for E system. The essential point is the following: of about 4 × 10-18 erg. (b) Estimates using Suppose all the water molecules in the first electrostatic energies lead to e ~ 10 -12 erg. surface layer are oriented in such a way that (c) Measurements of the surface entropy of all oxygen atoms are pointing outward and water (26) showed that this was lower by all hydrogen atoms inward. This, of course, 1.7 k (k is Boltzmann's constant) per mole- creates a disturbance in the crystal lattice eule than the entropy expected from a and there will be a decreasing orientation randomly oriented surface. In a random in neighboring layers until eventually the surface, half of the molecules are oriented proper ice structure is reached. If this inward, the other half outward. For the process is connected with a decrease in G oriented surface to be stable this decrease then ice will have such a transition layer. in entropy must be compensated by the This decrease can be brought about by a enthalpy e per molecule gained for the decrease in enthalpy and an increase in process; hence: entropy or any combination of changes in e/2 > 1.7 dT, both as long as: which gives for T = 273°K. AG = AH -- TAS e > 1.2 X 10-13 erg. is negative; an equilibrium state will be Although the orientation decreases the reached when G is at a minimum. This is enthalpy of the surface, it does not neces- essentially the basis of Fleteher's paper. sarily follow that the free energy will be Fletcher points out that the treatment decreased since, owing to the orientation, a is only an approximate one, since the struc- diminution of the entropy takes place. As ture of polar liquids is not yet well under- long as the decrease of TAS is smaller than stood; however, he maintains that his that of the enthalpy, a decrease in AG occurs. results are at least of a semiquantitative Fletcher's calculations lead to an apploXi- nature. mate expression for the change in free energy The surface structure of water is con- per molecule from changing the surface and sidered first. Supercooled water or water underlying layers from a random orientation near the freezing point has a short-range to a preferred orientation of the outermost ice-like structure. This means that there are layer with decreasing orientation of the small domains which have the structure of underlying layers: ice and which continually fluctuate and change in space and time. This mobility is AG~ --(so-- }~) e +~V(a0-- ~)~ largely due to the fact that about 13 % of + kT(ao -- 1/~)'/2v, [8] LIQUID-LIKE (TRANSITION) LAYER ON ICE 201 where a0 is a measure of the degree of +0.5 orientation (a0 = 1 for complete orientation and a0 = }~ for random orientation), e is 0-- the change in enthalpy per molecule, 5 is a factor connected with the fraction of time g -0.5 each molecule remains in the oriented state, k is Boltzmann's constant, and ~, is a con- -ohc-- -t.0 stant. This equation has a mininmm for a positive value of (a0 -- }~). By choosing -t .5 reasonable values for e, y, and 8 and taking o_ D a0 = 1 (complete orientation of the upper- -2.0 I I most layer), Fletcher comes to the conclusion -S0 -20 -10 0 that at equilibrium, near the freezing point, Tempera fure °C water has a transition layer of about 13 FIG. 11. Upper bound to the amount AG by molecules (26 A) with the outermost layer which the free energy of the equilibrium liquid oriented in such a way that the oxygen atoms film surface exceeds that of a solid crystalline ice point outward. surface. AG is given per surface molecule (21). The structure of the ice surface is treated similarly to that of water. The free energy temperatures from 0 to --13°C. AG is defi- would not decrease, owing to the large de- nitely negative; at lower temperatures AG crease in entropy, by just orienting the becomes very slightly positive; in actual outermost layer. The disturbance has to go fact, however, even in the range from -13 ° very much deeper than that. Fletcher to -30°C., AG may be negative, as the treated the case of a transition layer on ice calculations are only approximate. The as envisaged by Weyl (8). The transition thickness of the transition layer is given by starts with one oriented layer of water 40 molecules at the top, decreasing in orienta- d ~ 2.8 X 10 .7 log ~ - 0.4 em., [10] tion until eventually the random arrange- ment of the ice crystal lattice is reached. where At is in centigrades. This relationship The change in enthalpy per molecule for the is depicted in Fig. 12. Log d as a function water/air {nterface is e~ ~ 5 × 10 -~a erg; of the reciprocal absolute temperature further e2 is the change in enthMpy for the actually gives a straight line between -2°C. breaking of a single hydrogen bond. Similarly and -24°C. with an apparent energy of as before, he obtains an expression for the activation of about 14 keal./mole/deg. This change in free energy from an ideal ice relationship may be compared with the surface to a transition layer of thickness d, results of Hosler and co-workers where the separation force for two ice spheres decreased /cT & zXTd + - 1/2) exponentially with temperature. The ratio of the energies of activation for Hosler's [1 -- exp (-- 2yd)] + ~3' (a0 -- 1/2) 2 (11) data and Fletcher's theoretical results is [9] given by - (a0 - 1/2) [e~ - e2 exp (- 3'd)]. 10.6 Here ASp is the entropy of fusion which is n - -- - 0.75. connected with the free energy of fusion for 14.0 water supercooled by AT as follows: Although Fleteher's theoretical considera- AGF = ASFAT. tions contain uncertainties and approxima- tions, as clearly pointed out by him, his Minimization is more complicated than results seem to be reasonable and fit in well for the previous case; however, it can be with all the experimental evidence presented approximately carried out numerically. previously. Figure 11 shows an upper limit for AG as a In a note, Watts-Tobin (23) criticizes function of temperature. For a range of Fletcher's paper for neglecting the dipole- 202 JELLINEK

50 I00 fixed load of 2.1 kg., and a temperature control of about -/-0.02°C. The movement 40 80 of the wire was recorded, and a sensitivity of 1 cm. on the chart for a movement of o 30 60 ~- 4 X 10.3 cm. was achieved. The migration of the wire in four blocks were measured. -~ 2o 4o .E_ The mean velocities as a function of tem- perature are shown in Fig. 13. Between t0 20 -3.5°C. and -0.7°C. a straight-line rela- tionship is obtained for the logarithms of the 0 0 velocity as a function of the logarithms of - 30 -20 -10 0 the temperature in centigrades, the velocities Temper0fure in °C ranging from about 10-7 era. see. -1 to 10.6 FIG. 12. Thickness d of the equilibrium liquid em. see?-1. Above --0.7°C. the velocity film on the surface of ice as a function of tempera- increased enormously, by a factor of about ture (21). 200 at -0.5°C. This increased velocity is attributed to pressure melting. A pressure dipole interaction between water molecules, of about 45 atmospheres is exerted by the which would produce a strong depolarizing wire, which is enough to depress the melting effect; however, Fletcher himself has pointed point of ice by about 0.5°C. The migration out that his results are at best semiquantita- of the wire at lower temperatures than tire. It is the first attempt at a quantitative -0.5°C., which was completely missed by treatment and is therefore of great impor- other workers, cannot be attributed to tance in spite of its shortcomings. pressure melting. The authors accept the In a recent reply to Watts-Tobin criticism assumption of a transition layer between Fletcher (23a) points out that taking into the wire and the ice, and consider the move- account the dipole-dipole interaction will ment to be due to the flow of this viscous not alter the whole picture essentially but layer around the wire. The flow is assumed will affect only the quantitative aspects. to be Newtonian as a first approximation. He also points out an error in equation 26 (Eq. [9] in this report) of his paper: "The third term on the right hand side 50 I I I I I I I I I should contain an additional factor [i - Pressure melting exp (-2 d)]. Minimization of this free V: 4× tO-*cm.s-~ energy expression by numerical methods gives a curve closely similar to that of Fig. 2 [our Fig. 12], above --5°C., but below this t0 o o temperature the film thickness decreases ~_o Experi more rapidly and the film vanishes at x --12°C. '' T~ 5 Recently, Telford and Turner (24) made a very careful study of the passage of a thin steel wire through a block of ice over a 2 ~ × range of temperatures from -0.5°C. to ~/ Theoretical -3.5°C. Similar experiments had been t.0 carried out previously by various other X workers, but not under well-defined and controlled conditions. The older experiments 0.5 Ill I [ I I I I were all explained in terms of pressure - 0 -5 -2 -10 -0.5 -0.2 melting. Telford and Turner worked with a Temperafure (degrees cenfigrade) steel wire 0.045 era. in diameter, polycrystal- FIG. 13. Velocity of a wire moving through ice line ice blocks of about 1 era. thickness, a as a function of temperature (24). LIQUID-LIKE (TRANSITION) LAYER ON ICE 203

Such movement is described by the following of a transition layer on ice very likely. What equation: is needed now is more information about the actual properties of such a transition layer. At present, there are only very rough esti- 12~n ' [10] mates available. From the adhesion measure- ments we know that the thickness of the where V is the velocity of the wire, F the layer at an ice/metal and ice/quartz inter- load per unit length of the wire, d the thick- face is approximately between 10-5 and ness of the transition layer, n its viscosity, 10-6 cm. and its viscosity s~veral hundred and a the radius of the wire. The authors poises at about -4°C. From theoretical inserted Fletcher's values for the appropriate considerations, the thickness is known to be temperatures into Eq. [10] and corresponding about 100 A near the melting point, de- viscosities for supercooled water. The values creasing exponentially with decreasing tem- thus obtained for the velocities are indicated peratures until it vanishes at about -30°C. in Fig. 13. This, of course, is only a very It is not known whether the layer is New- approximate treatment; the authors are tonian as far as viscosity is concerned. aware of this, since they ascertained that Probably it is not. Moreover, all its prop- the rate of travel increased with the cube erties will vary continuously from one side of the load. of the fihn to the other. An alternative to the preceding explana- Some of the possible methods will now tion of a liquid-like layer would be that the be considered briefly, which may yield more movement of the wire is due to creep of ice. direct information about the properties of However, a plot of the logarithm of the rate the transition layer: of travel as a function of the reciprocal (a) A direct method of measuring film absolute temperature gives a straight line; thickness is that of ellipsometry. Plane the energy of activation derived from this polarized light reflected from a surface which plot is 180 kcal./mole/deg. This is a very is coated with a thin layer or with a transi- much higher value than that for creep, which tion layer, shows an elliptic component in amounts at the most to 31.8 kcal./mole/deg. its reflected beam. The amount of ellipticity, Thus the experimental results are in sub- which can be measured, is a function of the stantial agreement with the assumption of a film thickness; however, the refractive transition layer at the ice/metal interface. indices of the two boundaries or the refrac- It is of interest to note that Mason, tive index as a function of surface layer Bryant, and Van den Heuvel (25) studied depth have to be known to obtain actual the growth of ice crystals and pointed out values for the layer thickness. The effect is the importance of surface migration. They quite pronounced for opaque substances; suggest that some of their results may be however, transparent media such as glass or explained in terms of a liquid-like layer on water and ice are expected to show much the surface of ice crystals. smaller effects (26). Some ellipsometry has It would lead too far here to discuss all been carried out, for instance, by McBain, the phenomena which are related to the Bacon, and Bruce (27) on water surfaces. present topic of a transition layer on ice. The least possible thickness which could be Into this category fall all the experimental calculated from the data was 2.26 A. This data for systems where the surface or inter- was calculated with a refractive index facial properties are predominant, such as 1.1558 = (mtL2)1/~, where ~z = 1.0000 is the freezing of droplets, freezing in capillaries refractive index for air and ~2 = 1.3359 is or porous systems, frictional properties of that for water at 20.0°C. However, this is a ice, and properties of thin water films. Some fairly arbitrary way of choosing the refrac- relevant papers are noted in reference 19. tive indices especially if the layer is a transi- tion layer and hence a large number of layer C. CONCLUSION AND OUTLOOK thicknesses could be eMeulated choosing The experimental and theoretical evidence other combinations for the refractive indices. presented in this survey makes the existence No data are as yet available for ice. 204 JELLINEK

(b) Electron diffraction should prove a Mfiller-Pouillet, ed., "Lehrbuch der Phy- useful tool in this connection, especially sik," 9th ed., Vol. 2, Pt. 2, p. 595. Braun- low-angle diffraction, as the electron beam schweig (1898). does not penetrate the material deeply in 3. TYNDALL, J., AND HUXLEY, T. H., "On the contrast to X-rays (28). structure and motion of glaciers," Phil. (c) Infrared spectra especially reflection- Trans. Roy. Soc. (London) 147, 327 (1857); see also TYNDALL, J., "Glaciers of the Alps," spectra should be of help, as their sensitivity ... Vol. 20, pp. 446. Tickner and Fields, for hydrogen bonds is very great (29). Boston, 1861. pp. 419.2nd edition in German: (d) Nuclear magnetic resonance spectra "In den Alpen .... , "Friedrich Vieweg (NMR) may also be of help (30). and Sohn, 1899. See especially Chapter 4, (e) Surface potentials are also of interest "Helmholtz fiber Eis und Gletcher," pp. but are not very reproducible (31). 334-358; see also "Remarks on ice and (f) Surface conductance (32) and surface glaciers," Phil. Mag. [4th series] 17, 91 diffusion would constitute indirect methods (1859). which would be of value. Surface diffusion 4. THOMSON, J., "Theoretical considerations on of radioactive molecules such as tritriated the effect of pressure in lowering the freezing point of water," Trans. Roy. Soc. (Edin- water would not be suitable for an ice/air burgh) 16,575 (1849). See also "On the effect (gas) interface, because of exchange reac- of pressure in lowering the freezing point of tions, vaporization, and condensation; the water and on the plasticity of ice," Belfast, same holds true for H20 is or D20. A study Natural History and Philosophical Society, of surface diffusion of large molecules tagged pp. 1-4 (1858) ; and "A quantitative investiga- with radioactive isotopes would be more tion of certain relations between the gaseous feasible. and the solid states of water substance," (g) Contact angle measurements would Proc. Roy. Soc. (London) 22, 27 (1874). be informative, as the contact angle of a 5. THOMSON, W., "The effect of pressure in hydrocarbon on an ice surface will be de- lowering the freezing point of water experi- mentally demonstrated," Proc. Roy. Soc. pendent on the presence of a transition (Edinburgh) 2, 267 (1850); also THOMSON, J., layer. "On recent theories and experiments re- SUMMARY garding ice at or near its melting point," Proe. Roy. Soc. (London) 10, 152 (1860); also A survey of the literature covering about "Note oil Prof. Faraday's recent experi- the last hundred years is presented concern- ments on regelation," Proc. Roy. Soc. (Lon- ing the existence of a liquid-like transition don) 11, 198 (1861). layer on ice below its melting point. The 6. FORBES, J. D., "On some properties of ice conclusion is reached that the available near its melting point," Proc. Roy. Soc. evidence is very strongly in favor of the (Edinburgh) 4, 103 (1858). 7. PERSON, Compt. Rend. 30, 526 (1850). existence of such a layer. However, more 8. WEYL, W, A., "Surface structures of water direct measurements of the properties of and some of its physical and chemical such a layer are needed and possible methods manifestations," J. Colloid Sci. 6,389 (1951). for obtaining such information are indicated. 9. GREGO, S. J., "Surface Chemistry of Solids," 2nd ed., p. 22. Chapman, London, 1961. REFERENCES 10. NAKAYA,U., AND MATSUMOTO, A., "Evidence 1. FARADAY, M., Lecture given at the Royal of the existence of a liquid like film on ice Institution, London, June 7, 1850, reported surfaces," U. S. Army Snow, Ice and Perma- in Athenaeum 1850, p. 640; see also Forbes, frost Res. Estab. Res. Paper 4, (1953). J. D., "Occasional Papers on the Theory of 11. HOSLER, C. L., JENSEN, D. C., AND GOLD- Glaciers," p. 266. Adam and Charles Black, SHLAK, L., "On the aggregation of ice crys- North Bridge, Edinburgh, (1859). tals to form snow," J. Meterol. 14,415 (1957) ; 2. FARADAY, M., "Note on regelation," Proc. also Hosler, C. L., and Hallgren, R. E., Roy. Soc. (London) 10, 440 (1860); also "On DisCussions Faraday Soc. 30, 200 (1960). regelation," Phil. Mag. [4th series] 17, 162 12. JENSEN, D. C., "On the cohesion of ice," (1859); "Researches in chemistry and phys- Pennsylvania State University, M. S. Thesis, ics," pp. 373-378. Faraday's Diary, Bell, State College, Pennsylvania, 1956. London, 1933; also PFAUNDLER, L., in 13. JELLINEK, H. H. G., "Tensile properties of LIQUID-LIKE (TRANSITION) LAYER ON ICE 205

ice adhering to stainless steel," U. S. Army 23. WATSON-TOBIN, R. J., "Surface structure of Snow, Ice and Permafrost Res. Estab. Res. water and ice," Phil. Mag. 8,333 (1963). Rept. 23, (1957). 23a. FLETCHER, N. H., "Surface structure of 14. JELLINEK, H. H. G., "Adhesive properties of water and ice--a reply and a correction," ice," U. S. Army Snow, lee and Perma~ros Phil. Mag., August, p. 1425 (1963). Res. Estab. Res. Rept. 38, (1957); also '!Ad- 24. TELFORD, J. W., AND TURNER, J. S., "The hesive properties of ice, Part II," ibid. 62, motion of a wire through ice," Phil. Mag. 8, (1960); see also J. Colloid Sci. 14, 268 (1959) 527 (1963). and Can. J. Phys. 40, 1294 (1962). 25. MASON, B. J., BRYANT, G. W., AND VAN DER 15. RARATY, L. E., AND TABOR, D., "Adhesion I~IEUVEL, "The growth habits and surface and strength properties of ice," Proc. Roy. structure of ice crystals," Phil. Mag. 8, 505 Soc. (London) A245, 184 (1958). (1963). 16. FonD, T. F., AND NICHOLS, O. D., "Shear 26. JELLINEK, ]7I. H. G., AND KoPP, M., Bimonthly characteristics of ice in bulk at ice/solid Progress Report, January-February (1963) interfaces, and at ice/lubricants solid in- (DA-Eng. 27-021-62-G1) constituting an terfaces in a laboratory device," Naval Res. Annual Report for 1962 on a "Study of Lab. Rept., p. 5662 (1961). Surface and Interfacial Properties of Ice." 17. KINGERY, W. D., "Regelation, surface dif- 27. McBAIN, Y. W., BACON, R. C., AND BRUCE, H. fusion and ice sintering," J. Appl. Phys. 31, D., "Optical surface thickness of pure 833 (1960). water," J. Chem. Phys. 7, 818 (1939). 18. Mu~PI~Y, E. J., J. Chem. Phys. 21, 1831 (1953). 28. GREGG, S. J., "The Surface Chemistry of 19. JELLINEK, H. ~I. G., "Liquid-like layers on Solids," 2nd ed., p. 281. Chapman, London, ice," J. Appl. Phys. 32, 1793 (1961). 1961. 20. I(UROIWA, D., "A study of ice sintering," 29. FAI-IRENFORT, J., "Attenuated total reflec- U.S. Army Cold Regions Res. Eng. Lab. Res. tion," Spectrochim. Acta 17,698 (1961). : Rept. 86, (1962). 20a. HOBBS, P, V., AND MASON, B. J., Phil. Mag. 30. KUME, :K., "Proton-spin-mugaetic resona~lce 9, No. 98, 181 (1964). of ice," J. PAys: Soc. Japan 15, 1493 (1969)i 20b. JELLINEK, ]-I. H. G., AND IBRAHIM, S. H., 16, 290 (196I). This Symposium. 31. BRILL, R., AND CAMP, P. R. "Pr'operties of 21. FLETCHER, N. H., "Surface structure of water ice," U. S. Army, Snow, Ice and Permafrost and ice," Phil. Mag. 7,255 (1962). Res. Estab. R~s. Rept. 68. 22. HENNIKER, J. C., "The depth of the surface 32. KoPP, M., "Conduetivitd electrique de la zone of a liquid," Rev. Mod. Phys. 21, 322 neige, au courant continu," Z. angew. Math. (1949). PAys: 13,431 (1962).