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Adhesive properties of ice
JOURNAL OF COLLOID SCIENCE
14, 268-280 (1959)
A D H E S I V E P R O P E R T I E S OF ICE H. H. G. JeUinek 1 U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Wilmette, Illinois Received January 9, I959 INTRODUCTION
The adhesive properties of ice have scarcely been studied experimentally from a fundamental point of view. There are numerous papers in the literature on ice-releasing substances, which have been investigated especially with regard to airplane de-icing, but all this work has been done from the applied point of view. Some fundamental experimental work on tensile properties of ice sandwiched between metal plugs and some theoretical work using heat of immersion and adsorption data have been carried out (1, 2). Attempts have also been made to calculate adhesive strength (3). However, these approaches, though of intrinsic value, consider only some of the problems concerned with adhesion. It is generally true that substances with which water forms a large contact angle adhere less to ice than those which show a small contact angle. But the contact angle can be considered only as a guide. It is well known that ice and indeed all solid substances have imperfections statistically distributed throughout their mass. Thus, the actual cohesive strength of ice is many magnitudes smaller than the one expected from theory (1). The same is true for the adhesive strength. Moreover, the plastic-elastic properties of the substances involved will also play an important role for the adhesive strength. Another complication is caused by adsorption of gases at the interfaces. U~fless extreme precautions are taken, adhesion between two substances does not take place between two clean surfaces but between surfaces which have gases adsorbed. Another complication arises owing to slight solubilities in each other of the substances involved. Last, the surface roughness down to molecular dimensions also plays a role. Thus, it is seen that adhesive studies deal with a complex situation. A realistic approach to adhesion will have to start with a systematic collection of experimental data, obtained under rigid experimental conditions. In the present work, a beginning has been made in the study of the ad1 Presented at the 134th Meeting of the American Chemical Society, Chicago, September 8, 1958. 268
ADHESIVE PROPERTIES OF ICE
269
hesive properties of ice with respect to stainless steel, polystyrene, and polymethylmethacrylate as a function of cross-sectional area and thickness of the ice specimen and also of temperature. Experiments were carried out by applying forces in shear and in tension. EXPERIMENTAL
Materials
Stainless steel was grade 304/A with polished surface; the finishing polish was obtained with Lapping Compound No. 38-900 A, U. S. Products Company. Cast polystyrene and polymethylmethacrylate (Lucite) sheets were selected such that no unevenness could be detected by visual inspection. Distilled water was passed through exchange resin and boiled out continuously; the procedure will be described subsequently. Snow-ice was prepared as described previously (4). All cleaning fluids such as methanol and benzene were of reagent grade. Apparatus
The tensile apparatus and the corresponding mounting device were the same as described in a previous paper (1). The shear apparatus was similar to the tensile apparatus except that the mounting apparatus and the shear apparatus were combined. (For details see ref. 5.) The ice was sandwiched between two metal disks or between a metal disk and a plastic disk. One of the disks had a hook which was constructed in such a way that the force was acting in line with the disk-ice interface. PROCEDURE
Tensile Experiments
The mounting, carried out at -10°C., was critical and had to be standardized rigidly. The polystyrene, polymethylmethacrylate, and metal disks were cleaned carefully with methanol before each test. That this cleaning procedure is satisfactory was shown by contact angle measurements (6). Thus, polymethylmethacrylate and polystyrene gave--using similar cleaning procedures--initial contact angles of 87 ° and 90 °, respectively. A metal disk was fixed into the steel rod of the vertical mounting device (see reference 1, Fig. 1) and the plastic disk was fixed into the lower part. A flask with water boiling on a hot plate was always ready next to the mounting apparatus and water was squeezed out directly (wash bottle fashion) on to the plastic disk, forming a large drop which covered the whole surface. The drop was left to cool for a standardized time, which had to be found by trial for each cross-sectional area. Then the water at the edge of the plastic surface was touched with a pointed ice crystal; if the conditions were right,
270
JELLINEK
the water froze so t h a t the crystals traveled first across the plastic-water interface, driving residual air from the interface. As quickly as possible, the stainless steel rod carrying the metal disk was lowered to a predetermined distance; the whole a s s e m b l y was left for at least 20 minutes and subsequently transferred to the tensile strength apparatus. I t was noticed t h a t the surface of the plastic disks became crazed and cloudy after a number of tests; thus, not more than three tests were carried out with each plastic disk.
Shear Experiments With stainless steel disks, only snow-ice was used. Cylinders were turned on a lathe at - 1 0 ° C . and frozen to one of the steel disks. The snow-ice cylinder was then cut to the desired height and mounted (for details see reference 5). In the case of a plastic disk, the seeding procedure as described in the previous section was used (see reference 5). EXPERIMENTAL
RESULTS
Shear Experiments Shear experiments for snow-ice (density ca. 0.886 g./cm, s) sandwiched between polished steel plates were carried out as a function of cross-sectional area at - 5 ° C . (Table I ) and as a function of temperature for constant cross section (Fig. 1, for details see reference 5). As can be seen from Table I, the adhesive strength of ice/stainless steel is independent of the cross-sectional area of the specimens and of the thickness of the ice. The adhesive strength of ice/stainless steel as a function of t e m p e r a t u r e rises linearly with decreasing temperature as is apparent from Fig. 1. I t shows a very a b r u p t change from adhesive breaks to cohesive breaks in the TABLE I Adhesive Strength of Snow Ice~Stainless Steel Obtained from shear experiments as a function of cross-sectional area at -5°C. All breaks were purely adhesive. Thickness of ice layer 0.2 to 0.4 cm. Adhesive strength
(kg./cm?)
Cross section
(em'~) 1.54 3.14 4.91 6.61
Mean
Standard deviation
5.44 5.50 5.32 5.41
d= 0.40 =t= 0.72 =t= 1.14 =h 0.49
Standard error of mean 2=0.12 ±0.19 -+-0.32 ±0.15
Time of load application (sec.) 14 23 28 41
ADHESIVE
PROPERTIES
OF
271
ICE
17 -®__
16 15 14
13 12
c~
II ~0 9 8
z w
7 6 5 ,4 3 2 I
0
/ r
I
r
q
L ~
-I0
i
h
,
,
-20
I
i
i
i
i
i
-50
TEMPERATURE (~C)
Fie. 1. Strength as a function of temperature for snow-ice, sandwiched between stainless steel disks, obtained by shear. Cross-sectional area 1.54 cm. 2, height 0.2 to 0.4 cm. Adhesive breaks only down to -13°C.; cohesive breaks only below -13°C. Each point represents the average of at least 12 tests. neighborhood of - 1 3 ° C . Below this temperature, practically all breaks are cohesive and show only a very slight decrease with temperature. The adhesive branch of the curve in Fig. 1 can be represented by the equation: S~ = - 1.24t -- 0.18 kg./cm. 2,
[1]
where S~ is the average adhesive strength and t the temperature in degrees centigrade. The magnitude of the cohesive strength is similar to that of the cohesive breaks by tension, reported in a previous paper (1). For instance, the tensile strength of snow-ice of height 0.5 cm. was found at - 4 . 5 ° C . to be 15.5 kg./cm. 2 at a stress rate of 0.64 kg./cm.2-sec., which is of slightly smaller magnitude than the cohesive strength values found by shear. The average stress rate for the shear experiments at --14, --20, and - 3 4 . 3 ° C . was 0.52 kg./cm.2-sec. The cohesive breaks are actually of similar shape to the most frequent type obtained previously under tension (see reference 1, Fig. 4A). Shear experiments were MSO carried out with ice frozen to polystyrene disks (for detailed data, see reference 5). The cross-sectionM areas in the range from 3.14 to 9.6 cm. ~ have no influence on the adhesive strength. The shear data on the adhesive strength of ice/polystyrene as a function
272
JELLINEK
/
0.50
0.40 (,9 .,,r
0.30
/
Z hi Q: t'-
co 0.20 IM o') w
:c a
0.10
0
-20
-I0
TEMPERATURE (°C)
FIG. 2. A d h e s i v e s t r e n g t h of i c e / p o l y s t y r e n e as a f u n c t i o n of t e m p e r a t u r e , o b t a i n e d b y s h e a r . C r o s s - s e c t i o n a l a r e a 9.61 c m ? , h e i g h t 7.6 × 10 -2 c m . E a c h p o i n t r e p r e s e n t s t h e a v e r a g e of a t l e a s t 12 t e s t s . TABLE
II
Adhesive Strength of Ice/Polystyrene O b t a i n e d f r o m t e n s i l e e x p e r i m e n t s , (a) a t - 5 ° C . for t w o c r o s s - s e c t i o n a l a r e a s ; (b) as a f u n c t i o n of r a t e of s t r e s s a p p l i c a t i o n a t a r e a 1.54 c m . ~ T h i c k n e s s 0.1 c m . Adhesive strength (kg./cm2.) (a) Cross section (em.~)
1.54 3.14
Type of break
--
]
__
I
Standard error of mean
I
3.3 2.1
~-2.4 4-0.16
~-0.7 ~-0.05
1.9 2.1
4-0.34 ±0.50
4-0.10 ±0.16
All a d h e s i v e
! i ! i
(b) a Rate Of Stress application kg/vm.~Sec. 0.3 1.0
Standard deviation
M an t t 1 ]Mean, adhesive e , oa breaks only
3.7
All a d h e s i v e ~ 10 a d h e s i v e [ 2 cohesive
F o r r a t e 0.55 kg./cm.2/sec., see u n d e r (a).
of temperature at constant cross section are plotted in Fig. 2 and can be expressed by the equation: Sa = - 2 . 8 X 10-2t kg./cm. 2.
[2]
These experiments also had an approximately constant rate of stress application (see reference 5).
ADHESIVE
PROPERTIES
OF
273
ICE
/-
6.0 5.0 o ~D
4.0 "1" Q9 Z bO~
3.0
W
>
2.0
w
1.0
I
o
i
I
I
I
t
I
1
-IO
I
I
I
I,
-2o
TEMPERATURE (°C)
FIG. 3. Adhesive strength of ice/polystyrene as a function of temperature, obtained by tension. Cross-sectional area 1.54 cm3, height 0.1 cm. Each point represents the average of at least 12 tests. Atmospheric pressure should be subtracted from strength values.
Tensile Experiments Tensile experiments were carried out with ice frozen to polystyrene and polymethylmethaerylate (Lucite). The data for two different cross-sectional areas for polystyrene obtained at - 5 ° C . are shown in Table I I (a). Apparently, the cross-sectional areas have little influence in this range of areas. The strength was also investigated as a function of temperature keeping the cross section constant. The m e a n adhesive values are plotted against temperature in Fig. 3 and can be represented b y SA = - 0 . 1 7 3 t ~- 1.81 kg./cm. 2.
[3]
For the tensile experiments also, the rate of stress application was found to be approximately constant. (For details, see reference 5). A number of experiments on the system ice/polystyrene were carried out at different rates of stress application (different speeds of motor). The results, listed in Table I I (b), show t h a t the rate of stress application in the range investigated has no effect on the adhesive strength. A number of experiments were also carried out on adhesion of ice to polymethylmethacrylate (Lucite) at - 5 ° C . For a cross-sectional area of 0.785 cm. 2, thickness 0.1 cm. and rate of stress application of ca. 1.1 k g . / cm.2/see, a mean adhesive strength of 4.4 k g . / c m J was found (standard d e ~ a t i o n ± 2 . 9 , standard error of mean 4-0.7). There were 19 adhesive
274
JELLINEK
breaks and 4 borderline cases. These data indicate that the adhesive strength of ice/polymethylmethacrylateis larger than the adhesive strength of ice/polystyrene. DISCUSSION The shear experiments where snow-ice was sandwiched between two stainless steel plates will be discussed first. These experiments bring out three remarkable characteristics: First, the adhesive strength is independent of cross-sectional area; second, the adhesive strength is independent of the thickness of the ice layer (only a small range has been investigated); and third, adhesive strength is a linear function of the temperature until it becomes larger than the cohesive strength of ice at about -13°C., where a very sharp transition from adhesive to cohesive breaks takes place. The only experiments by other authors which are of interest in this connection are those by Itunsaker et al. (7). Their experiments on the adhesive strength of ice/brass as a function of temperature show a striking similarity to the results obtained here with stainless steel. The transition point from adhesive to cohesive breaks was found by these investigators to be about -12°C. whereas the one found in the present work lies at about - 13°C. Similarly, as in the case of tensile strength (cohesive strength) of ice (1), the experimental adhesive strength is several magnitudes smaller than expected from theory. Czyzak (3) has calculated the adhesive strength of water adhering to iron by a classical and a quantum-mechanical method. The classical adhesive strength at 300°K. was calculated as 13050 kg./cm. ~ and the quantum-mechanical one as 6770 kg./cm. 2. Moreover, this strength should be almost independent of temperature. The experimental adhesive strength at 268°K. was found in the present work to be about 6 kg./cm. 2. In a previous paper (1), the present author accounted for this discrepancy by the assumption of imperfections randomly distributed in the ice; these imperfections were assumed to have a definite strength distribution. It was found that the tensile strength increases very rapidly as the height of the ice disks decreases. Two theoretical cases can be distinguished. First: as soon as the strength of the weakest imperfection of the specimen is reached, rupture of the specimen takes place. For such a case, the average tensile strength should be a function of the volume of the specimens only. Second, when the strength of the weakest imperfection in the specimen is reached, a crack of definite average length is produced, then the next weakest imperfection opens up until in cascade fashion the specimen is ruptured. In this second case, the average tensile strength will depend not only on the volume but also on the cross-sectional area. Similar assumptions can be made in the case of adhesion. If adhesive rupture takes place when the strength of the weakest imperfection is reached, the adhesive strength--using a Weibull distribution (1)--is given by
A D H E S I V E P R O P E R T I E S OF ICE
S.~ = k l A -1I~ + C
275
[4]
where SA is the average adhesive strength, ~, kl, and C are constants, and A is the cross-sectional area of the specimen. In the second case, where rupture takes place in cascade fashion (for derivations, see references 1 and 5), the adhesive strength is independent of cross-sectionM area, in agreement with the experimental results. .Mthough the assumption of imperfections in or near the interface explains the low experimental adhesive strength as compared with the theoretically expected one, it fails completely to account for the marked difference found in the behavior of the ice disks in tension and in shear. If the ice is assumed to adhere directly to the stainless steel, there is no apparent reason at all why the adhesive bond should be so small in the case of shear and so large in tension. The adhesive strength at -5°C. was about 6 kg./cm. 2 in shear; in tension, if the ice disk was thin enough, 70 kg./cm. 2 could be applied without obtaining an adhesive break, and there is no reason why a larger stress could not be applied if the disk could be made still thinner. As a matter of fact, the bulk tensile strength of snow-ice is of similar magnitude as the bulk shear strength and also as that of the torsional shear strength (8), and they are only slightly dependent on the temperature. The ]arge temperature dependence of the adhesive strength is indicative rather of a viscous process in a liquid than of shear strength of polycrystalline solids. This contradictory behavior under shear and tension can, however, be reconciled if the assumption is made that a liquidlike layer, an amorphous layer, with properties somewhere intermediate between ice and water is situated in the interface. The suggestion that a liquidlike layer exists on ice in the neighborhood of the melting point is not new. Faraday (9) suggested such a theory in 1859 to explain the phenomenon of regelation. Tyndall (10) supported Faraday's idea (see also Dorsey (11)), but J. Thomson (12) and W. Thomson (Lord Kelvin) (13) argued against it and put forward the idea of pressure melting. However, very large pressures are needed to depress the melting point of ice (e.g., under 590 atm. the melting point of ice is - 5 ° C . ) , and this theory does not seem to be tenable. In this connection, Bowden's and Tabor's (14) discussion of a liquid layer on ice produced by friction is of interest (see also Bowden (15)). More recently, Weyl (16) assumed a liquidlike layer on ice for energetic reasons. Nakaya and Matsumoto (17) carried out experiments on the cohesion of ice spheres and found quite frequently that the spheres rotated before separating, which is a good indication of liquid layers on the ice spheres. Similar experiments in a more quantitative way were carried out by Jensen (18) supporting the conclusions of the Japanese workers. Hori (19) performed interesting experiments on the freezing and evaporation of thin water films. Observations
276
JELL:[NEK
indicated, though not with certainty, that very thin supercooled water films (ca. 1 u thick) did not crystallize even when seeded. On the basis of these observations, it is not unreasonable to assume that ice has a liquidlike layer on its surface not only when in contact with air but also when it is in contact with other substances, such as steel and polymers. The properties of such a film would be influenced by the nature of the solid surface. Thus, it is not to be expected that the liquidlike layer is of the same consistency and thickness when in contact with metal as when in contact with various polymers. The consequence for shear and tensile experiments of assuming a liquidlike layer in the interface will now be considered. Such a discussion must be semiquantitative at best, as practically nothing is known quantitatively of the viscosity, thickness, and other properties of such films. In the case of shear, the liquidlike layer will be assumed to be a Newtonian liquid as a first approximation. For a film between two parallel plates of which one is stationary and the other moves with a velocity vt at time t, a relationship is valid as follows: zt
~v~ L
-
[5]
'
where zt is the shear stress at time t; v the effective viscosity coefficient and L the thickness of the liquidlike layer; and vt the velocity of the metal plate at time t. As the adhesive strength was found to be independent of the cross-sectional area, boundary effects do not seem to be important. In Eq. [5] 7, L, and vt are not known experimentally; only the breaking stress and total deformation velocity are known; the latter is given by the movement of the threaded steel rod. In the present instance, the total deformation rate was always 9 X 10-3 cm./sec. However, this total deformation velocity is shared between the test sample and the chain connecting the sample to the load ceil. It was shown in a previous paper (1) t h a t practically all the deformation takes place in the chain. Thus, the system can be considered to be composed of a dashpot and spring in series (Maxwell unit), whose total rate of deformation is constant; hence __ F t L
c
12
wR ~ + E =
dFt
d--t'
[6]
where c is the constant total deformation rate; Ft is the load at time t, ~ the viscosity coefficient and L the thickness of the liquidlike layer; 12the length and E Young's modulus of the chain and R the radius of the specimen. Equation [6] can be written as: dt
-
12
c
~rR2/.
[7]
ADHESIVE PROPERTIES OF ICE
277
Actually, the rate of stress application WaS f0urid to be nearly constant. This means that the second term in the parentheses of Eq. [7] should be small compared with the first one. An upper limit of L/v can thus be estimated. At - 5 ° C . , for instance, the adhesive strength for ice/steel was found to be 5.5 kg./cm. 2 = 5.5 X 106 dynes/cm. 2 and c = 9 X 10-3 cm./sec.; hence
Ft L wR 2
(~t L -
v~
iS]
should not be larger than about 1 X 10-3 cm./sec. This gives:
L/V = 1.8 X 10-1° cm.3/dyne-sec. According to Weyl (16) the liquidlike layer should be several hundred molecules thick. If one puts L = 10-6 cm., then ~ = 5 X 10~ poises. Such a viscosity coefficient can be considered an effective viscosity only over the whole layer and will be appreciably influenced by surface irregularities of the confining solids. I t may be remarked that the viscosity of supercooled water at - 5 ° C . is 2.1 X 10-2 poise and that of crystalline ice is about 1014 poises (4). The large difference in the adhesive strength for the tensile and shear experiments can now be accounted for readily by assuming a liquidlike layer between the ice and the stainless steel plates. Surface tension forces will be considered first. The situation is shown in Fig. 4. The two solid phases are bound together by surface tension forces. In the present case the contact angles between ice, steel, and the liquidlike layer are assumed to be zero 2 and the pressure difference Ap is given b y Ap = 2~/L, where is the surface tension of the liquid and L the layer thickness. An upper estimate of the thickness of L can be obtained easily. It was found previously (1), when the cohesive strength of ice was investigated as a function of ice thickness, that the thinnest ice specimen, 2.5 X 10-2 cm. thick, showed a purely cohesive break with strength of 70 kg./cm. 2 at - 5 ° C . Hence, the adhesive strength under tension must be at least 70 kg./cm. 2, probably appreciably higher. Taking Ap = 7 X 107 dynes/cm. 2 and ~ = 76.4 dynes/ cm., which is the surface tension of water at - 5 ° C . , one obtains an upper estimate for L of 2 X 10-6 cm. Hence, an ice cylinder of several millimeters height as used in these experiments will break in cohesion long before the surface tension forces are overcome. Even if the surface tension forces were small, the viscosity would play 2 In a recent paper by L. E. R a r a t y and D. Tabor [Proc. Roy. Soc. (London) A245, 184 (1958)] it is s t a t e d t h a t electrolytically degreased stainless steel has a zero contact angle, whereas stainless steel refluxed in benzene has an advancing contact angle of 55 ° and a receding angle of 30 °, which would reduce Ap by half if the ice/liquid and steel/liquid contact angles are b o t h taken as 60 ° (cos 60 ° = ~ ) .
278
JELLINEK
I I
ICE !{ LIQUIDLIKLAYER E STEEL
FIG. 4. Liquidlike layer between ice and solid material.
an important role when the two plates are pulled apart over time intervals of 10 to 20 seconds. The force F t holding the plates together, assuming the liquid to be Newtonian, is given b y (20) Ft -
3~TrR~ 8tL ~
where n is the viscosity, L the thickness of the liquidlike layer, t the time of complete separation of the plates, and R the initial radius of the liquid specimen. For ,1 = 5 X 103 poises, L = 10-6 era., t = 10 to 20 see., the ice will break in cohesion long before the separation of the plates is effected. The experimental results obtained with polystyrene and polymethylmethacrylate can also be accounted for on the basis of a liquidlike layer in the interface. In the ease of the shear experiments with polystyrene, an adhesive strength of about 0.13 kg./cm. 2 was found at - 5 ° C . Again using vt - 1 X 10-3 cm./sec., the ratio L / n becomes 7.7 X 10-9 cm.3/dyne-sec. Taking again n = 5 X 103 poises, which is probably not permissible, L becomes 3.9 X 10-5 cm. The ease of tension is more complicated because of the finite contact angle. Though only a qualitative picture of the processes involved has been given here, it is believed that the assumption of a liquidlike layer is necessary for an understanding of the experimental results. ACKNOWLEDGMENTS It is the author's pleasure to thank Mr. G. M. Walker and Mr. R. D. Setzer for the competent performance of the tensile and shear experiments, respectively, tte also thanks Dr. J. K. Landauer for helpful discussions, Mr. B. L. Hansen for advice in the construction of the apparatus, and Dr. H. Bader and Fir. J. A. Bender for their interest in this work. SUMMARY
An apparatus has been constructed for the investigation of the adhesive strength of ice by shear experiments.
ADHESIVE PROPERTIES OF ICE
279
For the system snow-ice/stainless steel, shear experiments yielded pure adhesive breaks down to a temperature of about - 1 3 ° C . , where a sharp transition to cohesive breaks took place. The adhesive strength for this system is a linear function of the temperature, and is independent of the cross-sectional area and height of specimens in the ranges investigated. The system ice/polystyrene gave pure adhesive breaks on shear. The adhesive strength was found to be a linear function of temperature down to a temperature of - 15°C. and independent of cross-sectional area. Tensile experiments on the system ice/polystyrene yielded a linear relationship between adhesive strength and temperature in a range from - 2 to - 2 5 . 5 ° C . Cross-sectional area and rate of stress application had no effect on the adhesive strength in the ranges investigated. The system ice/polymethylmethacrylate showed a larger adhesive strength than the system ice/polystyrene. The experimental results are explained by the assumption of a liquidlike layer between ice and the solid interface. The thickness and consistency of this liquidlike layer are a function of temperature and the nature of the solid interface. The surface tension forces and frictional forces operative in the liquidlike layer are discussed. REFERENCES 1. JELLINEK, ]-~. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 23; also JELLINEK, H. H. G., Proc. Phys. Soc. (London) 71,797 (1958). 2. BERGHAUSEN, P. E., GOOD, R. J., KRAus, G., PODOLSKY, B., AND SOLLER, W., WADC Technical Report 53-461, (1953) and WADC Technical Report 55-44, (1955). 3. CZYSAK,S. J., in "Adhesion and Adhesives, Fundamentals and Practice, Society of Chemical Industry," p. 16. Wiley, New York, 1954. 4. JELLINEK, I~. ~-L G., AND BRILL, R., J. Appl. Phys. 27, 1198 (1956). 5. JELLINEK, H. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 38 (1957). 6. JELLINEK, H. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 36 (1957). 7. HUNSAKER,J. C., KEYES, F. G., HOUGHTON,H. G., JOHNSON, C. A., AND DOTSON, J. V., Progress Report to National Academy of Sciences, M.I.T., Report No. 1 (1940). 8. BUTKOVICH,W. R., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Paper 11 (1954). 9. FARADAY, M., Phil. Mag. [4] 17, 162 (1859); also Proc. Roy. Soc. (London) 10, 440 (1860). 10. TYNDALL,J., Proc. Roy. Soc. (London) Ag, 141 (1858). 11. ]:)ORSEY, N. E., Properties of Ordinary Water Substance, p. 412. Reinhold, New York, 1926. 12. THOMSON,J., Proc. Roy. Soc. (London) A10,152 (1859) ; ibid. A l l , 198, 473 (1861). 13. THOMSON,W., Proc. Roy. Soc. (London) Ag, 761 (1858). 14. BOWDEN, F. P., AND TABOR, D., "The Friction and Lubrication of Solids," p. 65 and Chapter 15. Oxford University Press, New York, 1950.
280
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:
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15. BOWDEN, F. P., Endeavaur , January, 1957, p. 5. : 16. WEYL, W. A., J. Colloid:Sci 6, 389 (1951). 17. NAKAYA, U., AND 1V[ATSUMOT0,, U . S. Army Snow Ice and Permafrost Research Establishment Corps of Engineers, Research Paper 4. 18. ,~ENSEN, D. C., On t h e Cohesion of Ice, M. S. thesis, Pennsylvania State University. : : ~ ,' 19. HoRI, T., TEION KAZAKU, BUTSURIHEN (Low Temperature Science Laboratory), Ser. A, 15, 34 (1956) ; S,!PRE Translation 62. 20. DEBRuYNE, N. A., ANDHOUWINK,R., "Adhesion and Adhesives," p: 66. Elsevier, Amsterdam, 1951. ,
i,:
i
!
14, 268-280 (1959)
A D H E S I V E P R O P E R T I E S OF ICE H. H. G. JeUinek 1 U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Wilmette, Illinois Received January 9, I959 INTRODUCTION
The adhesive properties of ice have scarcely been studied experimentally from a fundamental point of view. There are numerous papers in the literature on ice-releasing substances, which have been investigated especially with regard to airplane de-icing, but all this work has been done from the applied point of view. Some fundamental experimental work on tensile properties of ice sandwiched between metal plugs and some theoretical work using heat of immersion and adsorption data have been carried out (1, 2). Attempts have also been made to calculate adhesive strength (3). However, these approaches, though of intrinsic value, consider only some of the problems concerned with adhesion. It is generally true that substances with which water forms a large contact angle adhere less to ice than those which show a small contact angle. But the contact angle can be considered only as a guide. It is well known that ice and indeed all solid substances have imperfections statistically distributed throughout their mass. Thus, the actual cohesive strength of ice is many magnitudes smaller than the one expected from theory (1). The same is true for the adhesive strength. Moreover, the plastic-elastic properties of the substances involved will also play an important role for the adhesive strength. Another complication is caused by adsorption of gases at the interfaces. U~fless extreme precautions are taken, adhesion between two substances does not take place between two clean surfaces but between surfaces which have gases adsorbed. Another complication arises owing to slight solubilities in each other of the substances involved. Last, the surface roughness down to molecular dimensions also plays a role. Thus, it is seen that adhesive studies deal with a complex situation. A realistic approach to adhesion will have to start with a systematic collection of experimental data, obtained under rigid experimental conditions. In the present work, a beginning has been made in the study of the ad1 Presented at the 134th Meeting of the American Chemical Society, Chicago, September 8, 1958. 268
ADHESIVE PROPERTIES OF ICE
269
hesive properties of ice with respect to stainless steel, polystyrene, and polymethylmethacrylate as a function of cross-sectional area and thickness of the ice specimen and also of temperature. Experiments were carried out by applying forces in shear and in tension. EXPERIMENTAL
Materials
Stainless steel was grade 304/A with polished surface; the finishing polish was obtained with Lapping Compound No. 38-900 A, U. S. Products Company. Cast polystyrene and polymethylmethacrylate (Lucite) sheets were selected such that no unevenness could be detected by visual inspection. Distilled water was passed through exchange resin and boiled out continuously; the procedure will be described subsequently. Snow-ice was prepared as described previously (4). All cleaning fluids such as methanol and benzene were of reagent grade. Apparatus
The tensile apparatus and the corresponding mounting device were the same as described in a previous paper (1). The shear apparatus was similar to the tensile apparatus except that the mounting apparatus and the shear apparatus were combined. (For details see ref. 5.) The ice was sandwiched between two metal disks or between a metal disk and a plastic disk. One of the disks had a hook which was constructed in such a way that the force was acting in line with the disk-ice interface. PROCEDURE
Tensile Experiments
The mounting, carried out at -10°C., was critical and had to be standardized rigidly. The polystyrene, polymethylmethacrylate, and metal disks were cleaned carefully with methanol before each test. That this cleaning procedure is satisfactory was shown by contact angle measurements (6). Thus, polymethylmethacrylate and polystyrene gave--using similar cleaning procedures--initial contact angles of 87 ° and 90 °, respectively. A metal disk was fixed into the steel rod of the vertical mounting device (see reference 1, Fig. 1) and the plastic disk was fixed into the lower part. A flask with water boiling on a hot plate was always ready next to the mounting apparatus and water was squeezed out directly (wash bottle fashion) on to the plastic disk, forming a large drop which covered the whole surface. The drop was left to cool for a standardized time, which had to be found by trial for each cross-sectional area. Then the water at the edge of the plastic surface was touched with a pointed ice crystal; if the conditions were right,
270
JELLINEK
the water froze so t h a t the crystals traveled first across the plastic-water interface, driving residual air from the interface. As quickly as possible, the stainless steel rod carrying the metal disk was lowered to a predetermined distance; the whole a s s e m b l y was left for at least 20 minutes and subsequently transferred to the tensile strength apparatus. I t was noticed t h a t the surface of the plastic disks became crazed and cloudy after a number of tests; thus, not more than three tests were carried out with each plastic disk.
Shear Experiments With stainless steel disks, only snow-ice was used. Cylinders were turned on a lathe at - 1 0 ° C . and frozen to one of the steel disks. The snow-ice cylinder was then cut to the desired height and mounted (for details see reference 5). In the case of a plastic disk, the seeding procedure as described in the previous section was used (see reference 5). EXPERIMENTAL
RESULTS
Shear Experiments Shear experiments for snow-ice (density ca. 0.886 g./cm, s) sandwiched between polished steel plates were carried out as a function of cross-sectional area at - 5 ° C . (Table I ) and as a function of temperature for constant cross section (Fig. 1, for details see reference 5). As can be seen from Table I, the adhesive strength of ice/stainless steel is independent of the cross-sectional area of the specimens and of the thickness of the ice. The adhesive strength of ice/stainless steel as a function of t e m p e r a t u r e rises linearly with decreasing temperature as is apparent from Fig. 1. I t shows a very a b r u p t change from adhesive breaks to cohesive breaks in the TABLE I Adhesive Strength of Snow Ice~Stainless Steel Obtained from shear experiments as a function of cross-sectional area at -5°C. All breaks were purely adhesive. Thickness of ice layer 0.2 to 0.4 cm. Adhesive strength
(kg./cm?)
Cross section
(em'~) 1.54 3.14 4.91 6.61
Mean
Standard deviation
5.44 5.50 5.32 5.41
d= 0.40 =t= 0.72 =t= 1.14 =h 0.49
Standard error of mean 2=0.12 ±0.19 -+-0.32 ±0.15
Time of load application (sec.) 14 23 28 41
ADHESIVE
PROPERTIES
OF
271
ICE
17 -®__
16 15 14
13 12
c~
II ~0 9 8
z w
7 6 5 ,4 3 2 I
0
/ r
I
r
q
L ~
-I0
i
h
,
,
-20
I
i
i
i
i
i
-50
TEMPERATURE (~C)
Fie. 1. Strength as a function of temperature for snow-ice, sandwiched between stainless steel disks, obtained by shear. Cross-sectional area 1.54 cm. 2, height 0.2 to 0.4 cm. Adhesive breaks only down to -13°C.; cohesive breaks only below -13°C. Each point represents the average of at least 12 tests. neighborhood of - 1 3 ° C . Below this temperature, practically all breaks are cohesive and show only a very slight decrease with temperature. The adhesive branch of the curve in Fig. 1 can be represented by the equation: S~ = - 1.24t -- 0.18 kg./cm. 2,
[1]
where S~ is the average adhesive strength and t the temperature in degrees centigrade. The magnitude of the cohesive strength is similar to that of the cohesive breaks by tension, reported in a previous paper (1). For instance, the tensile strength of snow-ice of height 0.5 cm. was found at - 4 . 5 ° C . to be 15.5 kg./cm. 2 at a stress rate of 0.64 kg./cm.2-sec., which is of slightly smaller magnitude than the cohesive strength values found by shear. The average stress rate for the shear experiments at --14, --20, and - 3 4 . 3 ° C . was 0.52 kg./cm.2-sec. The cohesive breaks are actually of similar shape to the most frequent type obtained previously under tension (see reference 1, Fig. 4A). Shear experiments were MSO carried out with ice frozen to polystyrene disks (for detailed data, see reference 5). The cross-sectionM areas in the range from 3.14 to 9.6 cm. ~ have no influence on the adhesive strength. The shear data on the adhesive strength of ice/polystyrene as a function
272
JELLINEK
/
0.50
0.40 (,9 .,,r
0.30
/
Z hi Q: t'-
co 0.20 IM o') w
:c a
0.10
0
-20
-I0
TEMPERATURE (°C)
FIG. 2. A d h e s i v e s t r e n g t h of i c e / p o l y s t y r e n e as a f u n c t i o n of t e m p e r a t u r e , o b t a i n e d b y s h e a r . C r o s s - s e c t i o n a l a r e a 9.61 c m ? , h e i g h t 7.6 × 10 -2 c m . E a c h p o i n t r e p r e s e n t s t h e a v e r a g e of a t l e a s t 12 t e s t s . TABLE
II
Adhesive Strength of Ice/Polystyrene O b t a i n e d f r o m t e n s i l e e x p e r i m e n t s , (a) a t - 5 ° C . for t w o c r o s s - s e c t i o n a l a r e a s ; (b) as a f u n c t i o n of r a t e of s t r e s s a p p l i c a t i o n a t a r e a 1.54 c m . ~ T h i c k n e s s 0.1 c m . Adhesive strength (kg./cm2.) (a) Cross section (em.~)
1.54 3.14
Type of break
--
]
__
I
Standard error of mean
I
3.3 2.1
~-2.4 4-0.16
~-0.7 ~-0.05
1.9 2.1
4-0.34 ±0.50
4-0.10 ±0.16
All a d h e s i v e
! i ! i
(b) a Rate Of Stress application kg/vm.~Sec. 0.3 1.0
Standard deviation
M an t t 1 ]Mean, adhesive e , oa breaks only
3.7
All a d h e s i v e ~ 10 a d h e s i v e [ 2 cohesive
F o r r a t e 0.55 kg./cm.2/sec., see u n d e r (a).
of temperature at constant cross section are plotted in Fig. 2 and can be expressed by the equation: Sa = - 2 . 8 X 10-2t kg./cm. 2.
[2]
These experiments also had an approximately constant rate of stress application (see reference 5).
ADHESIVE
PROPERTIES
OF
273
ICE
/-
6.0 5.0 o ~D
4.0 "1" Q9 Z bO~
3.0
W
>
2.0
w
1.0
I
o
i
I
I
I
t
I
1
-IO
I
I
I
I,
-2o
TEMPERATURE (°C)
FIG. 3. Adhesive strength of ice/polystyrene as a function of temperature, obtained by tension. Cross-sectional area 1.54 cm3, height 0.1 cm. Each point represents the average of at least 12 tests. Atmospheric pressure should be subtracted from strength values.
Tensile Experiments Tensile experiments were carried out with ice frozen to polystyrene and polymethylmethaerylate (Lucite). The data for two different cross-sectional areas for polystyrene obtained at - 5 ° C . are shown in Table I I (a). Apparently, the cross-sectional areas have little influence in this range of areas. The strength was also investigated as a function of temperature keeping the cross section constant. The m e a n adhesive values are plotted against temperature in Fig. 3 and can be represented b y SA = - 0 . 1 7 3 t ~- 1.81 kg./cm. 2.
[3]
For the tensile experiments also, the rate of stress application was found to be approximately constant. (For details, see reference 5). A number of experiments on the system ice/polystyrene were carried out at different rates of stress application (different speeds of motor). The results, listed in Table I I (b), show t h a t the rate of stress application in the range investigated has no effect on the adhesive strength. A number of experiments were also carried out on adhesion of ice to polymethylmethacrylate (Lucite) at - 5 ° C . For a cross-sectional area of 0.785 cm. 2, thickness 0.1 cm. and rate of stress application of ca. 1.1 k g . / cm.2/see, a mean adhesive strength of 4.4 k g . / c m J was found (standard d e ~ a t i o n ± 2 . 9 , standard error of mean 4-0.7). There were 19 adhesive
274
JELLINEK
breaks and 4 borderline cases. These data indicate that the adhesive strength of ice/polymethylmethacrylateis larger than the adhesive strength of ice/polystyrene. DISCUSSION The shear experiments where snow-ice was sandwiched between two stainless steel plates will be discussed first. These experiments bring out three remarkable characteristics: First, the adhesive strength is independent of cross-sectional area; second, the adhesive strength is independent of the thickness of the ice layer (only a small range has been investigated); and third, adhesive strength is a linear function of the temperature until it becomes larger than the cohesive strength of ice at about -13°C., where a very sharp transition from adhesive to cohesive breaks takes place. The only experiments by other authors which are of interest in this connection are those by Itunsaker et al. (7). Their experiments on the adhesive strength of ice/brass as a function of temperature show a striking similarity to the results obtained here with stainless steel. The transition point from adhesive to cohesive breaks was found by these investigators to be about -12°C. whereas the one found in the present work lies at about - 13°C. Similarly, as in the case of tensile strength (cohesive strength) of ice (1), the experimental adhesive strength is several magnitudes smaller than expected from theory. Czyzak (3) has calculated the adhesive strength of water adhering to iron by a classical and a quantum-mechanical method. The classical adhesive strength at 300°K. was calculated as 13050 kg./cm. ~ and the quantum-mechanical one as 6770 kg./cm. 2. Moreover, this strength should be almost independent of temperature. The experimental adhesive strength at 268°K. was found in the present work to be about 6 kg./cm. 2. In a previous paper (1), the present author accounted for this discrepancy by the assumption of imperfections randomly distributed in the ice; these imperfections were assumed to have a definite strength distribution. It was found that the tensile strength increases very rapidly as the height of the ice disks decreases. Two theoretical cases can be distinguished. First: as soon as the strength of the weakest imperfection of the specimen is reached, rupture of the specimen takes place. For such a case, the average tensile strength should be a function of the volume of the specimens only. Second, when the strength of the weakest imperfection in the specimen is reached, a crack of definite average length is produced, then the next weakest imperfection opens up until in cascade fashion the specimen is ruptured. In this second case, the average tensile strength will depend not only on the volume but also on the cross-sectional area. Similar assumptions can be made in the case of adhesion. If adhesive rupture takes place when the strength of the weakest imperfection is reached, the adhesive strength--using a Weibull distribution (1)--is given by
A D H E S I V E P R O P E R T I E S OF ICE
S.~ = k l A -1I~ + C
275
[4]
where SA is the average adhesive strength, ~, kl, and C are constants, and A is the cross-sectional area of the specimen. In the second case, where rupture takes place in cascade fashion (for derivations, see references 1 and 5), the adhesive strength is independent of cross-sectionM area, in agreement with the experimental results. .Mthough the assumption of imperfections in or near the interface explains the low experimental adhesive strength as compared with the theoretically expected one, it fails completely to account for the marked difference found in the behavior of the ice disks in tension and in shear. If the ice is assumed to adhere directly to the stainless steel, there is no apparent reason at all why the adhesive bond should be so small in the case of shear and so large in tension. The adhesive strength at -5°C. was about 6 kg./cm. 2 in shear; in tension, if the ice disk was thin enough, 70 kg./cm. 2 could be applied without obtaining an adhesive break, and there is no reason why a larger stress could not be applied if the disk could be made still thinner. As a matter of fact, the bulk tensile strength of snow-ice is of similar magnitude as the bulk shear strength and also as that of the torsional shear strength (8), and they are only slightly dependent on the temperature. The ]arge temperature dependence of the adhesive strength is indicative rather of a viscous process in a liquid than of shear strength of polycrystalline solids. This contradictory behavior under shear and tension can, however, be reconciled if the assumption is made that a liquidlike layer, an amorphous layer, with properties somewhere intermediate between ice and water is situated in the interface. The suggestion that a liquidlike layer exists on ice in the neighborhood of the melting point is not new. Faraday (9) suggested such a theory in 1859 to explain the phenomenon of regelation. Tyndall (10) supported Faraday's idea (see also Dorsey (11)), but J. Thomson (12) and W. Thomson (Lord Kelvin) (13) argued against it and put forward the idea of pressure melting. However, very large pressures are needed to depress the melting point of ice (e.g., under 590 atm. the melting point of ice is - 5 ° C . ) , and this theory does not seem to be tenable. In this connection, Bowden's and Tabor's (14) discussion of a liquid layer on ice produced by friction is of interest (see also Bowden (15)). More recently, Weyl (16) assumed a liquidlike layer on ice for energetic reasons. Nakaya and Matsumoto (17) carried out experiments on the cohesion of ice spheres and found quite frequently that the spheres rotated before separating, which is a good indication of liquid layers on the ice spheres. Similar experiments in a more quantitative way were carried out by Jensen (18) supporting the conclusions of the Japanese workers. Hori (19) performed interesting experiments on the freezing and evaporation of thin water films. Observations
276
JELL:[NEK
indicated, though not with certainty, that very thin supercooled water films (ca. 1 u thick) did not crystallize even when seeded. On the basis of these observations, it is not unreasonable to assume that ice has a liquidlike layer on its surface not only when in contact with air but also when it is in contact with other substances, such as steel and polymers. The properties of such a film would be influenced by the nature of the solid surface. Thus, it is not to be expected that the liquidlike layer is of the same consistency and thickness when in contact with metal as when in contact with various polymers. The consequence for shear and tensile experiments of assuming a liquidlike layer in the interface will now be considered. Such a discussion must be semiquantitative at best, as practically nothing is known quantitatively of the viscosity, thickness, and other properties of such films. In the case of shear, the liquidlike layer will be assumed to be a Newtonian liquid as a first approximation. For a film between two parallel plates of which one is stationary and the other moves with a velocity vt at time t, a relationship is valid as follows: zt
~v~ L
-
[5]
'
where zt is the shear stress at time t; v the effective viscosity coefficient and L the thickness of the liquidlike layer; and vt the velocity of the metal plate at time t. As the adhesive strength was found to be independent of the cross-sectional area, boundary effects do not seem to be important. In Eq. [5] 7, L, and vt are not known experimentally; only the breaking stress and total deformation velocity are known; the latter is given by the movement of the threaded steel rod. In the present instance, the total deformation rate was always 9 X 10-3 cm./sec. However, this total deformation velocity is shared between the test sample and the chain connecting the sample to the load ceil. It was shown in a previous paper (1) t h a t practically all the deformation takes place in the chain. Thus, the system can be considered to be composed of a dashpot and spring in series (Maxwell unit), whose total rate of deformation is constant; hence __ F t L
c
12
wR ~ + E =
dFt
d--t'
[6]
where c is the constant total deformation rate; Ft is the load at time t, ~ the viscosity coefficient and L the thickness of the liquidlike layer; 12the length and E Young's modulus of the chain and R the radius of the specimen. Equation [6] can be written as: dt
-
12
c
~rR2/.
[7]
ADHESIVE PROPERTIES OF ICE
277
Actually, the rate of stress application WaS f0urid to be nearly constant. This means that the second term in the parentheses of Eq. [7] should be small compared with the first one. An upper limit of L/v can thus be estimated. At - 5 ° C . , for instance, the adhesive strength for ice/steel was found to be 5.5 kg./cm. 2 = 5.5 X 106 dynes/cm. 2 and c = 9 X 10-3 cm./sec.; hence
Ft L wR 2
(~t L -
v~
iS]
should not be larger than about 1 X 10-3 cm./sec. This gives:
L/V = 1.8 X 10-1° cm.3/dyne-sec. According to Weyl (16) the liquidlike layer should be several hundred molecules thick. If one puts L = 10-6 cm., then ~ = 5 X 10~ poises. Such a viscosity coefficient can be considered an effective viscosity only over the whole layer and will be appreciably influenced by surface irregularities of the confining solids. I t may be remarked that the viscosity of supercooled water at - 5 ° C . is 2.1 X 10-2 poise and that of crystalline ice is about 1014 poises (4). The large difference in the adhesive strength for the tensile and shear experiments can now be accounted for readily by assuming a liquidlike layer between the ice and the stainless steel plates. Surface tension forces will be considered first. The situation is shown in Fig. 4. The two solid phases are bound together by surface tension forces. In the present case the contact angles between ice, steel, and the liquidlike layer are assumed to be zero 2 and the pressure difference Ap is given b y Ap = 2~/L, where is the surface tension of the liquid and L the layer thickness. An upper estimate of the thickness of L can be obtained easily. It was found previously (1), when the cohesive strength of ice was investigated as a function of ice thickness, that the thinnest ice specimen, 2.5 X 10-2 cm. thick, showed a purely cohesive break with strength of 70 kg./cm. 2 at - 5 ° C . Hence, the adhesive strength under tension must be at least 70 kg./cm. 2, probably appreciably higher. Taking Ap = 7 X 107 dynes/cm. 2 and ~ = 76.4 dynes/ cm., which is the surface tension of water at - 5 ° C . , one obtains an upper estimate for L of 2 X 10-6 cm. Hence, an ice cylinder of several millimeters height as used in these experiments will break in cohesion long before the surface tension forces are overcome. Even if the surface tension forces were small, the viscosity would play 2 In a recent paper by L. E. R a r a t y and D. Tabor [Proc. Roy. Soc. (London) A245, 184 (1958)] it is s t a t e d t h a t electrolytically degreased stainless steel has a zero contact angle, whereas stainless steel refluxed in benzene has an advancing contact angle of 55 ° and a receding angle of 30 °, which would reduce Ap by half if the ice/liquid and steel/liquid contact angles are b o t h taken as 60 ° (cos 60 ° = ~ ) .
278
JELLINEK
I I
ICE !{ LIQUIDLIKLAYER E STEEL
FIG. 4. Liquidlike layer between ice and solid material.
an important role when the two plates are pulled apart over time intervals of 10 to 20 seconds. The force F t holding the plates together, assuming the liquid to be Newtonian, is given b y (20) Ft -
3~TrR~ 8tL ~
where n is the viscosity, L the thickness of the liquidlike layer, t the time of complete separation of the plates, and R the initial radius of the liquid specimen. For ,1 = 5 X 103 poises, L = 10-6 era., t = 10 to 20 see., the ice will break in cohesion long before the separation of the plates is effected. The experimental results obtained with polystyrene and polymethylmethacrylate can also be accounted for on the basis of a liquidlike layer in the interface. In the ease of the shear experiments with polystyrene, an adhesive strength of about 0.13 kg./cm. 2 was found at - 5 ° C . Again using vt - 1 X 10-3 cm./sec., the ratio L / n becomes 7.7 X 10-9 cm.3/dyne-sec. Taking again n = 5 X 103 poises, which is probably not permissible, L becomes 3.9 X 10-5 cm. The ease of tension is more complicated because of the finite contact angle. Though only a qualitative picture of the processes involved has been given here, it is believed that the assumption of a liquidlike layer is necessary for an understanding of the experimental results. ACKNOWLEDGMENTS It is the author's pleasure to thank Mr. G. M. Walker and Mr. R. D. Setzer for the competent performance of the tensile and shear experiments, respectively, tte also thanks Dr. J. K. Landauer for helpful discussions, Mr. B. L. Hansen for advice in the construction of the apparatus, and Dr. H. Bader and Fir. J. A. Bender for their interest in this work. SUMMARY
An apparatus has been constructed for the investigation of the adhesive strength of ice by shear experiments.
ADHESIVE PROPERTIES OF ICE
279
For the system snow-ice/stainless steel, shear experiments yielded pure adhesive breaks down to a temperature of about - 1 3 ° C . , where a sharp transition to cohesive breaks took place. The adhesive strength for this system is a linear function of the temperature, and is independent of the cross-sectional area and height of specimens in the ranges investigated. The system ice/polystyrene gave pure adhesive breaks on shear. The adhesive strength was found to be a linear function of temperature down to a temperature of - 15°C. and independent of cross-sectional area. Tensile experiments on the system ice/polystyrene yielded a linear relationship between adhesive strength and temperature in a range from - 2 to - 2 5 . 5 ° C . Cross-sectional area and rate of stress application had no effect on the adhesive strength in the ranges investigated. The system ice/polymethylmethacrylate showed a larger adhesive strength than the system ice/polystyrene. The experimental results are explained by the assumption of a liquidlike layer between ice and the solid interface. The thickness and consistency of this liquidlike layer are a function of temperature and the nature of the solid interface. The surface tension forces and frictional forces operative in the liquidlike layer are discussed. REFERENCES 1. JELLINEK, ]-~. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 23; also JELLINEK, H. H. G., Proc. Phys. Soc. (London) 71,797 (1958). 2. BERGHAUSEN, P. E., GOOD, R. J., KRAus, G., PODOLSKY, B., AND SOLLER, W., WADC Technical Report 53-461, (1953) and WADC Technical Report 55-44, (1955). 3. CZYSAK,S. J., in "Adhesion and Adhesives, Fundamentals and Practice, Society of Chemical Industry," p. 16. Wiley, New York, 1954. 4. JELLINEK, I~. ~-L G., AND BRILL, R., J. Appl. Phys. 27, 1198 (1956). 5. JELLINEK, H. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 38 (1957). 6. JELLINEK, H. H. G., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Report 36 (1957). 7. HUNSAKER,J. C., KEYES, F. G., HOUGHTON,H. G., JOHNSON, C. A., AND DOTSON, J. V., Progress Report to National Academy of Sciences, M.I.T., Report No. 1 (1940). 8. BUTKOVICH,W. R., U. S. Army Snow Ice and Permafrost Research Establishment, Corps of Engineers, Research Paper 11 (1954). 9. FARADAY, M., Phil. Mag. [4] 17, 162 (1859); also Proc. Roy. Soc. (London) 10, 440 (1860). 10. TYNDALL,J., Proc. Roy. Soc. (London) Ag, 141 (1858). 11. ]:)ORSEY, N. E., Properties of Ordinary Water Substance, p. 412. Reinhold, New York, 1926. 12. THOMSON,J., Proc. Roy. Soc. (London) A10,152 (1859) ; ibid. A l l , 198, 473 (1861). 13. THOMSON,W., Proc. Roy. Soc. (London) Ag, 761 (1858). 14. BOWDEN, F. P., AND TABOR, D., "The Friction and Lubrication of Solids," p. 65 and Chapter 15. Oxford University Press, New York, 1950.
280
: '
:
JELLINEK
15. BOWDEN, F. P., Endeavaur , January, 1957, p. 5. : 16. WEYL, W. A., J. Colloid:Sci 6, 389 (1951). 17. NAKAYA, U., AND 1V[ATSUMOT0,, U . S. Army Snow Ice and Permafrost Research Establishment Corps of Engineers, Research Paper 4. 18. ,~ENSEN, D. C., On t h e Cohesion of Ice, M. S. thesis, Pennsylvania State University. : : ~ ,' 19. HoRI, T., TEION KAZAKU, BUTSURIHEN (Low Temperature Science Laboratory), Ser. A, 15, 34 (1956) ; S,!PRE Translation 62. 20. DEBRuYNE, N. A., ANDHOUWINK,R., "Adhesion and Adhesives," p: 66. Elsevier, Amsterdam, 1951. ,
i,:
i
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