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On the surface tension of solid substances
Physica III. no 10
December 1936
ON THE SURFACE TENSION OF SOLID SUBSTANCES by R.?\.]. SAAL and]. F. T. BLOTT I. Introduction, In numerous scientific and technical problems the interface of a solid against a liquid or a gas plays an important part. For this reason we have made a critical study of the various methods proposed for the determination of the surface tension of solids. Investigations concerning the phenomena at such interfaces are frequently directed towards adsorption phenomena. Furthermore. in those cases where a solid substance is brought into contact with two liquids, or with a liquid and a gas, a study of the"wetting" properties of the material can be made, which is done by determining the angle of contact. But unlike in the case of two liquids, or of aliquid and a gas, it is impossible to make direct measurements of the interfacial tension between a solid and a liquid or a gas, as the determination of interfacial tensions is based on the observation of a certain shape of equilibrium of the interface, which is, of course, impracticable in view of the small forces in question, owing to the great rigidity of the solid. Consequently, indirect methods onlyhave been proposed, the study of which will be the subject of this paper. When determining the angle of contact a distinction must be made between cases in which the surface tension of a solid against its vapour phase is measured and such in which there is a second component in the system. In the latter case the surface betwcer, the solid and the gas phase will have undergone a change through adsorption, as a result of which in general the surface tension will have altered too. The same holds good for the interface between a solid and a liquid, in such cases where a second liquid phase is added. We 'will from now on indicate this changed interfacial tension by o", bclng o used for denoting the interfacial tension under the initial conditions. \Ve will revert later to the important difference between a and a': - 1099-
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Therefore, in a system of a solid with a liquid and a gas phase (or with two liquids) only the surface tension of the liquid against the gas phase (or the second liquid) and the angle of contact can be measured, whereas we should like to know three interfacial tensions. Seeing that the relation (see fig. 1) a;3 - a;2 = a23 cos (( (1) exists, a third factor is missing, viz. either the interfacial tension of the solid against the liquid or that against the gas phase. It must be kept in mind that it may be very difficult to measure this angle of contact, whilst, moreover, it is a' that is found from the formula, whereas a is often desired. A number of methods of finding this third factor have been proposed; as already stated, these will be critically reviewed in the following pages, and their results compared.
Qa~(3)~
Gi3'
~ Uj~' 50 lid (1J
Fig. I. Interfacial tensions in a system of solid-liquid-gas.
II. Methods. 1. Be r g g r en's met hod 1). As a matter of fact, this method has not been devised for solids, but for highly viscous liquids. A thread of the material is suspended vertically; the surface tension will tend to shorten the thread, whereas its weight will tend to lengthen it. The surface tension of the liquid can be calculated by determining the exact length at which no elongation or contraction occurs. B erg g r e n found for pitch about 50 dynes/em at 30°C; by linear extrapolation from capillary height determination at 105155°C. a value of about 35 dynes/em is found. M a c k 2) made similar determinations in respect of asphaltic bitumens and found about 30 dynes/em at room temperature. This is the same order of magnitude as found by extrapolation from determinations at high temperatures. For solids, however, which sometimes at high temperatures con tract noticeably in the same manner 3), this method does not apply, as a constant viscosity must be presupposed in the calculation. B e r gg r e n himself observes that upon applying his method to liquids
ON THE SURFACE TENSION OF SOLID SUBSTAKCES
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with elastic after-effect (e.g. molten copal), serious disturbances occur. 2. M. e tho d s bas e don the sol ubi lit Y 0 ron the v a p 0 u r ten s ion 0 f min ute par tic I e s. On thermodynamic principes it can be reasoned that the vapour tension (or the solubility) of drops of liquid distributed in a gas (or in a second liquid) is higher according as the drop is smaller. This increase in vapour tension is related to the curvature of the particles according to the formula 4) D.p = 2cr • r PI in which a is the surface tension and Pg and PI stand for the density of the gas phase and of the liquid phase respectively and r for the radius of the drop. Conversely, in principle surface tensions can be determined with the aid of this phenomenon. This method has also been applied to solid particles 5). It must be remembered, however, that in this case the process of evaporation takes place in quite a different way. In the case of liquids the evaporation of a small part of the drop is accompanied by a sort of displacement of the liquid through the whole drop, so that, more or less, the whole drop is concerned in this process. But, on the other hand, in a crystal there is of course no such displacement, so that the evaporation must be considered as alocal process. Since in the thermodynamic treatment for liquids the behaviour of the whole drop is considered, the same reasoning cannot be applied to solids. K 0 ssci 6) has treated this question extensively and for brevity's sake we would refer the reader to his work. In this connection we would only remark that a small crystal is assumed to have the same geometrical shape as a large one '); in which case, fi-om a kinetic point of view, an influence of the size of the particle on the vapour tension is theoretically conceivable only for particles of the magnitude of the attraction sphere. There is no reason to assume that there is any difference between the vapour tension of a molecule in a crystal plane of a :small particle (appreciably larger than the attraction sphere) and that of a large particle, as the circumstances are exactly the same in both cases. In our opinion, it is therefore impossible to measure the surface or interfacial tension of solids in this manner. Any slight effects observed may just as well have to be ascribed to a change in the condition of
.rr,
) 102
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the small crystal, for instance due to. the mechanical treatment in pulverization 8). On the other hand, a small crystal docs possess a higher energy content per unit of weight, which can be demonstrated by calorific tests: evaporation heat, heat of solution, melting heat, etc. 9). This does not contradict the above reasoning that there is no difference in vapour tension etc. between large and small crystals. In ~act, one may consider- a mass of crystals as a mixture of two components of different energy content, namely the molecules that are present in a crystal plane and those inside the crystals, but which are in equilibrium with each other. The difference between a great number of small crystals and onelargecrystal is only a difference in "mixture ratio". In the latter case we leave the crystal edge and crystal corners out of consideration, because they contribute only a minute part to the total energy of the crystal as compared with the surface. By calorific methods it is therefore possible in principle to determine the total surface energy of a solid. The relation between total surface energy (E s ) and free surface energy a is given by the formula
ti,
=
dcr cr-T dT'
(2)
but it is obvious that there is no simple method of deducing the free surface energy from the total surface energy by means of this equation. Consequently, there is no method based on the difference between the properties of small crystals and those of large ones, for determining the surface tension of solid materials. 3. C a I cuI a t ion a c cor din g t 0 B 0 r n's met hod. Calculations based on the lattice structure of crystals have been evolved by B 0 r nand S t ern 10). However, these calculations can only be regarded as approximate. Actually, the total surface energy is calculated for the absolute zero temperature. As is shown by formula (2), the total surface energy at this temperature is equal to the free surface energy, so that B 0 r nand S t ern's values apply at the same time to the surface tension. For comparison with other data it is of course a drawback that no figures can be given for other temperatures. 4. Ant 0 now's met hod. Ant 0110 W 11) found that pastes
OX THE SURFACE TEXSIOX OF SOLID SUBSTAXCES
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composed of an oil and carbon black may show at a certain mixing ratio an angle on contact of 90° with a solid substance, and he assumed that in such cases the surface tension of the solid against the gas phase was equal to the surface tension of the paste. However, Ant 0 now's theoretical deduction is wrong, because according.to formula (I) an angle of contact of 90° means that the interfacial tension between solid and liquid phase becomes equal to that between solid and gas phase, whilst the surface tension of the liquid is no longer of any account. Moreover, such pastes arc probably rigid, so that an accurate measurement of the angle of contact and of the surface tension is impossible. 5. Lorn a nan d Z w i k k e r's Met hod. Recently N e Ilen s t e y nand Roo den bur g 12) and L 0 man and Z w i k k e r 13) proposed a method which at first sight looked very attractive, but which, in our opinion, does not bear thorough criticism U). In view of the rather complicated theoretical deduction involved and the extensive experimental work done, we will consider this method in more detail. The method is based upon a relation found by Ant 0 now 15) between the interfacial tension between two liquids and the surface tension of the two liquid phases of such systems, measured against the corresponding vapour phase. Denoting the surface tension of substance 1 by VI 2 byv2 .. phase 1 by VI " 2 by v; and the interfacial tension between phases I and 2 by Vl2 Ant
0
n
0
w's rule runs as follows: (3)
Te symbol I J means that invariably the absolute value of v; must be taken. In table 1 we give some values showing how well the figures may tally. However, marked deviations from this rule will be found in some records 16), particularly in cases where orientation of molecules in the interface takes place.
VI -
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TABLE I Examples of Ant Liquid I = water Liquid 2 = benzene Liquid 2 = ether
I I
al 73 73
0
I
a,
I
a'i
I
29 17
I
63.2 28.1
n
0
w's rule.
I
a',
I
28.8 17.5
I I
au 34.4 10.6
I I
0'1-0"1
34.4 dynes/em 10.6 dynes/em
If the rule is to hold good, therefore, it is essential to take the surface tensions of the phases; conversely, it will never be possible to deduce anything from Ant 0 now's rule but the surface tension of the phase and not that of the pure substance, which, in view especially of the example of ether/water, may make an enormous difference. When a~ is taken instead of al the values found for the surface tension of water are 63 dynes/em and 28 dynes/em respectively, instead of 73 dynes/em. The discrepancy is also considerable with other substances; thus, from measurements applied to benzene/ mercury, about 390 dnyes/crn is found for the surface tension of the mercury phase, instead of 475 dynes/em. As this example shows, these great differences cannot be the result of a change in the liquid as a consequence of solubility, but can only be ascribed to adsorption. Ant 0 now's rule has now also been applied by analogy to a solid in contact with a liquid by Nell ens t e y nand R 0 0den bur g (loc. cit.) and by Lorn a nand Z w i k k e r (loc. cit.). These investigators combined the rule with formula (1). This produces what was referred to in the introduction as the "third factor" and gives us the equations: crl2 = I cr~3 - cr;3 I crl2 = cr~3 - cr;3 cos 9.
(4a) (4b) A drawback of this treatment is that from this formula the interfacial tension of the solid against the gas phase will be obtained as cr', but never as cr itself. If this difference is ignored, erroneous conclusions are obtained. As the symbol in the first equation will have to be negative if the angle of contact is larger than 0°, the following relation can be derived: 2 cr~3 = (cos 9 1) cr;3' (5) If now the accents are omitted, it would follow that: 1. incomplete wetting only occurs if the surface tension of the liquid is greater than that of the solid substance;
+
OX THE SURFACE TEXSIOX OF SOLID sunSTAXCES
1105
2. the angle of contact of different liquids against one and the same solid is only determined by the surface tension of the liquid. This last conclusion would preclude the existence of any difference between hydrophilic and hydrophobic liquids, which is counter to all experience. Bar t e 11 1 7 ) , for instance, carefully recorded the correlation occurring in this field, so we may conclude that it is not permissible, in the case of solid materials, to disregard the difference between v and o': Now it must be observed that Lorn a nand Z w i k k e r do not bear this difference in mind, and they regard it as only natural that the same value can be taken for the surface tension of a solid against the gas phase in the case of one and the same solid with different liquids. As we have shown above, this is not correct, so that conclusionsmay not be drawn, for example, regarding the adhesion of asphaltic bitumens to a solid substance, if the "surface tension" of that solid substance has been deduced with the aid of water or mercury (loc. cit. page 1195). We would point out that a similar objection may be raised to Bar tell's theoretical interpretation of his measurements 18). There too, it is assumed that the inte'rfacial tension of a solid substance against a phase is equal to the interfacial tension against the constituent which forms the principal component of the phase. But even if we disregard this difference, there are still objections to the deductions of L 0 man and Z w i k k e r. These investigators (Ioc. cit.) believe that their deduction supports the correctness of Ant 0 now's rule. For instance, from formulae 4a and 4b, for one and the same solid against two liquids 1 and 2, they derive the formula
cos~ 91 = l/~'
(6) V2 cos e 92 in which VI and V2 are the surface tensions of the liquids and 91 and 92 the corresponding angles of contact. And this equation indeed does hold good in their experimen ts for wa tel' and mercury on various solids. But its derivation is not quite correct all the same, as appears from the following calculation. To facilitate comparison we retain L 0 man and Z w i k k e r's notation (x = interfacial tension solid/gasphase, y = interfacial tension solidfliquid phase). We start from the formula : x = VI cos '?I t)'1 = V2 cos 92 +)'2, Physica III
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so that generally cos ?i = 2 cos- {- ?i 1
_
cos 2 ?i -
1-
-J/Gi + X -
X-Yi a, )'i
2Gj'
from which it follows that: COSt?1 =
1Ii;
.IIGI +X-YI.
cos 2 ?2 GI G2 +x - Y2 Hence, as long as crl x - 1'1 = G2 X - )'2' it will invariably be found that Lam a nan d Z w i k k e r's formula applies. This may also be written in another way:
+
GI -
1'1 = G2 -
+
1'2 = constant =
k,
and k in that csae is indeed a material constant of the solid, but it need not necessarily represent the surface tension of the solid, as implied by Ant a now's rule cr-1' = x. In other words: if L 0 man and Z wi k k e r's formula (6) does apply, it has been proved that cr - l' is independent of the liquid used, but this magnitude is not necessarily equal to the surface tension of the material, so that the validity of Ant a now's rule has not been proved. It may be asked what value can then be attached to Lam a n and Z w i k k e r's figures for the surface tension of solids. They deduce the formula rrcos2 t 9 = x, from which x is calculated. If we assume o - l' = k = x - c, in which c is another material constant of the solid (at least as long as formula (6) applies), it may be proved that in general c must be positive. For we may write x-1' x-1' COS? = -cr- = x l' - c
+
If for a given solid c should be negative, there could never be any liquid which would give complete wetting, as x and l' are essentially positive. Such a case is only imaginable by way of exception. As a rule any solid will be completely "wettable" by at least one liquid, so that c = 0 or > 0 must apply for the solid. If c = 0, in other words if Ant a now's rule applied, the solid can only be completely wetted for the exceptional case l' = 0, so that x = cr. But in the
OX THE SURFACETENSIOX OF SOLID SUBSTANCES
1107
general case of complete wetting y will be positive, so that it must be concluded that as long as formula (6) applies, c will as a rule have a positive value. Now it can easily be calculated that rr cos? } 9, is equal to lJ-j'
2
+x =
x-
~-c.
Therefore the values for a cos? -} 9 (which, according to L 0 man and Z w i k k e r, equals the surface tension of the solid) prove to be smaller than the surface tension of the solid. To what extent they are smaller cannot be deduced, however, from the measurements. Hence, if the difference between rrand cr' had not been disregarded beforehand, L 0 man and Z wi k k er's figures would at least show a minimum limit. But now this is not the case either.
III. Comparison oj the results [ound by the various methods dealt with above. From the above critical review it appears that there is really no single reliable method for measuring the surface tension of solid substances. We shall therefore not make a thorough systematic comparison between all the results obtained by the various methods proposed, but simply demonstrate from a few cases that there is no proper agreement between them, and that it is also impossible to correlate the results of these methods with theoretical expectations. Before doing so, however; we should like to deal with a general difficulty that presents itself in such measurements. The surface of a solid will frequently be soiled through adsorption; the method of cleaning is therefore of prime importance. In this connection we refer to L 0 man and Z wi k k e r's article (loc.cit. page 1197); where it is stated that the method of cleaning is a very influential factor. Thus, to be able to compare the determinations, it is necessary that the method of cleaning should be carefully described. This, however, is often forgotten. We shall illustrate this by means of the measurements of L om a nand Z wi k k e r (loc. cit.). In ouropinion, the approximately equal values for the surface tensions of various stones (see Table Ia of their paper) may, if no special precautions were taken with regard to cleaning. be due to the fact that the measurements were invariably made against one and the same substance, in this case a greasy film on the insufficiently cleaned material; the statement that the angle of contact sometimes alters fairly quickly is in keeping with this
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supposition (loc. cit. page 1186). Further, to explain the influence of cleaning they assume a special change in the surface of. the solid substance, e.g. in the case of mercury on glass, where the angle of contact is altered very much by heating the glass previously to about 400°C. On the other hand the same behaviour in the case of quartz, in which a chemical change of this kind is not possible, is explained by the removal of organic contaminations (loc. cit. page 1199). In our opinion such explanations are rather dangerous. But even if the surface has been well cleaned, complications may occur. For instance, the time during which the solid is in contact with the liquid may also be of influence. To show this we shall quote some experiments made by H. E i I e r s (unpublished) with regard to the wetting of bitumen by water. A drop of water (0.60 gr) placed on a Mexican asphaltic bitumen (pen. 40/50) had a diameter of 17.2 mm : 0,2. The same asphaltic bitumen, after being poured out and cooled for two days under water and then dried, gave a diameter of I drop (0.60 gr.) of 19.0 ~ 0.2 mm. Therefore, the wetting by water is increased by prolonged immersion in water, notwithstanding the fact that the bitumen had in the meantime been thoroughly dried. We explain this phenomenon by a change in the orientation or the distribution of the molecules in the interface. Whereas, when the bitumen is kept dry, it is mainly saturated groups which protrude upon its being subjected to prolonged contact with water a change will occur and the more unsaturated groups will mainly form the surface layer. The same behaviour is shown by stearic acid which has been crystallized in contact with water or in contact with air. In the first case the surface is easily wettable, whilst in the second case the wetting is very bad. Prolonged immersion of the latter surface in water makes it again wettable as a result of the reorientation of the molecules. We will now show by some examples the poor agreement between the experimental data. a. S a Its. In table II we give the values calculated by B 0 r n 10) for the solid salt, and at the same time measurements by J a eg e r 19) for the molten state. These latter measurements have been linearly extrapolated to -273°C, so as to enable us to compare them with B 0 r n's figures; these values are of course only rough approximations.
ON THE SURFACE TENSION OF SOLID SUBSTANCES
1109
TAI3LE II Surface tension of salts in dynes/em.
Salt
KCl KI3r KI NaCl "aUr KaI
Calculation crt at -273°C by I3 0 r n
107 92 74 150 119 96
!llelted salt Determinations by J a e g e r
ar, 95.8 85.7 75.2 113.8 105.8 85.6
I
T, 800 775 737 803 761 706
I
cr, 69.6 75.4 66.5 88.0 78.0 77.6
I
T. 1167 920 873 1172 1166 861
I
~
Extrapolated -~73°C. (cr:l
crt
170 160 140 190 180 135
1.6 1.7 1.9 1.3 1.5 1.4
It is at all events evident that the figures are of the same order of magnitude. On the other hand, Lip set t, J 0 h n son and :\1 a ass 9) give 400 dynes/em for NaCl; this figure was derived from measurements of the heat of solution of finely dispersed salt. b. Asp hal tic bit u me n ..Ashaltic bitumen is a very suitable material for comparing various methods of determining the surface tension of solid substances. Essentially it is a liquid substance which makes it possible to extrapolate measurements at high temperatures to normal temperatures with sufficient accuracy. (The break found by Nell ens t e y n 20) in the (J - T curve of asphaltic bitumens has nothing to do with surface tension, but is caused by some disturbing factor during the determination 21)). At the same time the viscosity at ordinary temperatures may be high enough for the application of the methods proposed for solid substances. Now the result found by extrapolation from high temperatures is, say, (J = 35 dynes/em. The same order of magnitude is found by 1\1 a c k 2) with Be r g g r en's method. On the other hand, Lorn a nand Z w i kk e r (loc. cit.) give 6 l , a value which is certainly too high. c. G 1ass. Glass gives the same possibility for comparing the methods for liquid and for solid materials. But here we encounter the difficulty that the materials may have been different. In the literature on the subject a value of (J = 150 dynes/em at 12001450°C is given 22). If the value 135 dynes/em at room temperature found by Nell ens t e y nand H. 0 0 den bur g (loc. cit.) or by Lorn a nan d Z w i k k e r (loc. cit.) can be compared with this figure, their result seems to be open to some doubt. d. 1\1 eta 1s. Liquid metals generally show a high surface tension
1110
O~ THE SURFACE TENSIOX OF SOLID SUBSTAKCES
(e.g. 500 dynes/em) 21). There is some reason to expect no great difference (for instance, not by a factor as high as 10) between the surface tension of liquids and that of solids. In this connection the low values found by Lorn a nand Z w i k k e r (abt 50 dynes/em) are doubtful. Against these measurements it may be argued further that no complete wetting of, for instance, steel by water is found, whereas it is known that after having been freed from grease by brushing with lime and chalk, this metal as a rule can be completely wetted by water. From the few examples given above it is clear that no proper agreement between the different methods exists. IV. Conclusion. A critical description is given of the various methods proposed for the determination of the surface tension of solid substances. It is shown that none of these methods can give a reliable determination of this property. Received October 2, 1936.
REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)
ncr g g r e n, Ann. Physik (4) "'1, 61,1914. :\1 a e k, Ind. Eng. Chern. 27, 1500,1935. C hap rn a n & I' 0 r t c r, Proc, roy. Soc. London (A) 83, 65, 1909. Tho rn son, Phil. :\Iag. (4) "'2, 448,1871. W. 0 s twa I d, Z. physik. Chern. :.1'0, 503, 1900. K 0 sse I, Ann. Physik (5) 21, 457,1934. E h r e n f e s t, Ann. Physik (4) "'8, 360,1915. Dun don & :\1 a e k, J. arner, chern. Soc. 1:>, 2479, 1924. Lipsett, Johnson & :\Iaass, J.arner.chern.Soc.... !J,925,1927. e.g. S.-B. Akad. Wiss, Berlin 901, 1919. All ton 0 w, Phil. :\Iag. (7) 1, 1258, 1926;"',792,1927. Chern. Wcekbl. au, 189, 1933. Physica I, 1182, 1934. Also sec Phys. Z. 311, 603, 1935. J. Chim. phys, s, 372, 1907. Sec for instance F u c h s, Koll, Z. ii2, 262, 1930. J. amer, chem, Soc. ;;11, 2205,1934. Coli. Syrup. s, 112, 1928. Z. anorg. allg. Chern. 101, I, 1917. Koll. chem, Beih. 31, 434,1930. S a a I, 0 e I un d K 0 hie 2,367,1934; Chern. \\'eekbl. :12, 486,1935. Was h bur n, Phys. Rev. (2) 20, 94, 1920; Rec. Trav, chirn. .'\2, 686, 1923. La 11 dol t B 6 r n s t c i n, Physikal. chem, Tabellen 1923, p,: 1931.
December 1936
ON THE SURFACE TENSION OF SOLID SUBSTANCES by R.?\.]. SAAL and]. F. T. BLOTT I. Introduction, In numerous scientific and technical problems the interface of a solid against a liquid or a gas plays an important part. For this reason we have made a critical study of the various methods proposed for the determination of the surface tension of solids. Investigations concerning the phenomena at such interfaces are frequently directed towards adsorption phenomena. Furthermore. in those cases where a solid substance is brought into contact with two liquids, or with a liquid and a gas, a study of the"wetting" properties of the material can be made, which is done by determining the angle of contact. But unlike in the case of two liquids, or of aliquid and a gas, it is impossible to make direct measurements of the interfacial tension between a solid and a liquid or a gas, as the determination of interfacial tensions is based on the observation of a certain shape of equilibrium of the interface, which is, of course, impracticable in view of the small forces in question, owing to the great rigidity of the solid. Consequently, indirect methods onlyhave been proposed, the study of which will be the subject of this paper. When determining the angle of contact a distinction must be made between cases in which the surface tension of a solid against its vapour phase is measured and such in which there is a second component in the system. In the latter case the surface betwcer, the solid and the gas phase will have undergone a change through adsorption, as a result of which in general the surface tension will have altered too. The same holds good for the interface between a solid and a liquid, in such cases where a second liquid phase is added. We 'will from now on indicate this changed interfacial tension by o", bclng o used for denoting the interfacial tension under the initial conditions. \Ve will revert later to the important difference between a and a': - 1099-
1100
R.
x, J.
SAAL AND
J.
F. T. BLaTT
Therefore, in a system of a solid with a liquid and a gas phase (or with two liquids) only the surface tension of the liquid against the gas phase (or the second liquid) and the angle of contact can be measured, whereas we should like to know three interfacial tensions. Seeing that the relation (see fig. 1) a;3 - a;2 = a23 cos (( (1) exists, a third factor is missing, viz. either the interfacial tension of the solid against the liquid or that against the gas phase. It must be kept in mind that it may be very difficult to measure this angle of contact, whilst, moreover, it is a' that is found from the formula, whereas a is often desired. A number of methods of finding this third factor have been proposed; as already stated, these will be critically reviewed in the following pages, and their results compared.
Qa~(3)~
Gi3'
~ Uj~' 50 lid (1J
Fig. I. Interfacial tensions in a system of solid-liquid-gas.
II. Methods. 1. Be r g g r en's met hod 1). As a matter of fact, this method has not been devised for solids, but for highly viscous liquids. A thread of the material is suspended vertically; the surface tension will tend to shorten the thread, whereas its weight will tend to lengthen it. The surface tension of the liquid can be calculated by determining the exact length at which no elongation or contraction occurs. B erg g r e n found for pitch about 50 dynes/em at 30°C; by linear extrapolation from capillary height determination at 105155°C. a value of about 35 dynes/em is found. M a c k 2) made similar determinations in respect of asphaltic bitumens and found about 30 dynes/em at room temperature. This is the same order of magnitude as found by extrapolation from determinations at high temperatures. For solids, however, which sometimes at high temperatures con tract noticeably in the same manner 3), this method does not apply, as a constant viscosity must be presupposed in the calculation. B e r gg r e n himself observes that upon applying his method to liquids
ON THE SURFACE TENSION OF SOLID SUBSTAKCES
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with elastic after-effect (e.g. molten copal), serious disturbances occur. 2. M. e tho d s bas e don the sol ubi lit Y 0 ron the v a p 0 u r ten s ion 0 f min ute par tic I e s. On thermodynamic principes it can be reasoned that the vapour tension (or the solubility) of drops of liquid distributed in a gas (or in a second liquid) is higher according as the drop is smaller. This increase in vapour tension is related to the curvature of the particles according to the formula 4) D.p = 2cr • r PI in which a is the surface tension and Pg and PI stand for the density of the gas phase and of the liquid phase respectively and r for the radius of the drop. Conversely, in principle surface tensions can be determined with the aid of this phenomenon. This method has also been applied to solid particles 5). It must be remembered, however, that in this case the process of evaporation takes place in quite a different way. In the case of liquids the evaporation of a small part of the drop is accompanied by a sort of displacement of the liquid through the whole drop, so that, more or less, the whole drop is concerned in this process. But, on the other hand, in a crystal there is of course no such displacement, so that the evaporation must be considered as alocal process. Since in the thermodynamic treatment for liquids the behaviour of the whole drop is considered, the same reasoning cannot be applied to solids. K 0 ssci 6) has treated this question extensively and for brevity's sake we would refer the reader to his work. In this connection we would only remark that a small crystal is assumed to have the same geometrical shape as a large one '); in which case, fi-om a kinetic point of view, an influence of the size of the particle on the vapour tension is theoretically conceivable only for particles of the magnitude of the attraction sphere. There is no reason to assume that there is any difference between the vapour tension of a molecule in a crystal plane of a :small particle (appreciably larger than the attraction sphere) and that of a large particle, as the circumstances are exactly the same in both cases. In our opinion, it is therefore impossible to measure the surface or interfacial tension of solids in this manner. Any slight effects observed may just as well have to be ascribed to a change in the condition of
.rr,
) 102
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the small crystal, for instance due to. the mechanical treatment in pulverization 8). On the other hand, a small crystal docs possess a higher energy content per unit of weight, which can be demonstrated by calorific tests: evaporation heat, heat of solution, melting heat, etc. 9). This does not contradict the above reasoning that there is no difference in vapour tension etc. between large and small crystals. In ~act, one may consider- a mass of crystals as a mixture of two components of different energy content, namely the molecules that are present in a crystal plane and those inside the crystals, but which are in equilibrium with each other. The difference between a great number of small crystals and onelargecrystal is only a difference in "mixture ratio". In the latter case we leave the crystal edge and crystal corners out of consideration, because they contribute only a minute part to the total energy of the crystal as compared with the surface. By calorific methods it is therefore possible in principle to determine the total surface energy of a solid. The relation between total surface energy (E s ) and free surface energy a is given by the formula
ti,
=
dcr cr-T dT'
(2)
but it is obvious that there is no simple method of deducing the free surface energy from the total surface energy by means of this equation. Consequently, there is no method based on the difference between the properties of small crystals and those of large ones, for determining the surface tension of solid materials. 3. C a I cuI a t ion a c cor din g t 0 B 0 r n's met hod. Calculations based on the lattice structure of crystals have been evolved by B 0 r nand S t ern 10). However, these calculations can only be regarded as approximate. Actually, the total surface energy is calculated for the absolute zero temperature. As is shown by formula (2), the total surface energy at this temperature is equal to the free surface energy, so that B 0 r nand S t ern's values apply at the same time to the surface tension. For comparison with other data it is of course a drawback that no figures can be given for other temperatures. 4. Ant 0 now's met hod. Ant 0110 W 11) found that pastes
OX THE SURFACE TEXSIOX OF SOLID SUBSTAXCES
1103
composed of an oil and carbon black may show at a certain mixing ratio an angle on contact of 90° with a solid substance, and he assumed that in such cases the surface tension of the solid against the gas phase was equal to the surface tension of the paste. However, Ant 0 now's theoretical deduction is wrong, because according.to formula (I) an angle of contact of 90° means that the interfacial tension between solid and liquid phase becomes equal to that between solid and gas phase, whilst the surface tension of the liquid is no longer of any account. Moreover, such pastes arc probably rigid, so that an accurate measurement of the angle of contact and of the surface tension is impossible. 5. Lorn a nan d Z w i k k e r's Met hod. Recently N e Ilen s t e y nand Roo den bur g 12) and L 0 man and Z w i k k e r 13) proposed a method which at first sight looked very attractive, but which, in our opinion, does not bear thorough criticism U). In view of the rather complicated theoretical deduction involved and the extensive experimental work done, we will consider this method in more detail. The method is based upon a relation found by Ant 0 now 15) between the interfacial tension between two liquids and the surface tension of the two liquid phases of such systems, measured against the corresponding vapour phase. Denoting the surface tension of substance 1 by VI 2 byv2 .. phase 1 by VI " 2 by v; and the interfacial tension between phases I and 2 by Vl2 Ant
0
n
0
w's rule runs as follows: (3)
Te symbol I J means that invariably the absolute value of v; must be taken. In table 1 we give some values showing how well the figures may tally. However, marked deviations from this rule will be found in some records 16), particularly in cases where orientation of molecules in the interface takes place.
VI -
1104
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J.
F. T. BLOTT
TABLE I Examples of Ant Liquid I = water Liquid 2 = benzene Liquid 2 = ether
I I
al 73 73
0
I
a,
I
a'i
I
29 17
I
63.2 28.1
n
0
w's rule.
I
a',
I
28.8 17.5
I I
au 34.4 10.6
I I
0'1-0"1
34.4 dynes/em 10.6 dynes/em
If the rule is to hold good, therefore, it is essential to take the surface tensions of the phases; conversely, it will never be possible to deduce anything from Ant 0 now's rule but the surface tension of the phase and not that of the pure substance, which, in view especially of the example of ether/water, may make an enormous difference. When a~ is taken instead of al the values found for the surface tension of water are 63 dynes/em and 28 dynes/em respectively, instead of 73 dynes/em. The discrepancy is also considerable with other substances; thus, from measurements applied to benzene/ mercury, about 390 dnyes/crn is found for the surface tension of the mercury phase, instead of 475 dynes/em. As this example shows, these great differences cannot be the result of a change in the liquid as a consequence of solubility, but can only be ascribed to adsorption. Ant 0 now's rule has now also been applied by analogy to a solid in contact with a liquid by Nell ens t e y nand R 0 0den bur g (loc. cit.) and by Lorn a nand Z w i k k e r (loc. cit.). These investigators combined the rule with formula (1). This produces what was referred to in the introduction as the "third factor" and gives us the equations: crl2 = I cr~3 - cr;3 I crl2 = cr~3 - cr;3 cos 9.
(4a) (4b) A drawback of this treatment is that from this formula the interfacial tension of the solid against the gas phase will be obtained as cr', but never as cr itself. If this difference is ignored, erroneous conclusions are obtained. As the symbol in the first equation will have to be negative if the angle of contact is larger than 0°, the following relation can be derived: 2 cr~3 = (cos 9 1) cr;3' (5) If now the accents are omitted, it would follow that: 1. incomplete wetting only occurs if the surface tension of the liquid is greater than that of the solid substance;
+
OX THE SURFACE TEXSIOX OF SOLID sunSTAXCES
1105
2. the angle of contact of different liquids against one and the same solid is only determined by the surface tension of the liquid. This last conclusion would preclude the existence of any difference between hydrophilic and hydrophobic liquids, which is counter to all experience. Bar t e 11 1 7 ) , for instance, carefully recorded the correlation occurring in this field, so we may conclude that it is not permissible, in the case of solid materials, to disregard the difference between v and o': Now it must be observed that Lorn a nand Z w i k k e r do not bear this difference in mind, and they regard it as only natural that the same value can be taken for the surface tension of a solid against the gas phase in the case of one and the same solid with different liquids. As we have shown above, this is not correct, so that conclusionsmay not be drawn, for example, regarding the adhesion of asphaltic bitumens to a solid substance, if the "surface tension" of that solid substance has been deduced with the aid of water or mercury (loc. cit. page 1195). We would point out that a similar objection may be raised to Bar tell's theoretical interpretation of his measurements 18). There too, it is assumed that the inte'rfacial tension of a solid substance against a phase is equal to the interfacial tension against the constituent which forms the principal component of the phase. But even if we disregard this difference, there are still objections to the deductions of L 0 man and Z w i k k e r. These investigators (Ioc. cit.) believe that their deduction supports the correctness of Ant 0 now's rule. For instance, from formulae 4a and 4b, for one and the same solid against two liquids 1 and 2, they derive the formula
cos~ 91 = l/~'
(6) V2 cos e 92 in which VI and V2 are the surface tensions of the liquids and 91 and 92 the corresponding angles of contact. And this equation indeed does hold good in their experimen ts for wa tel' and mercury on various solids. But its derivation is not quite correct all the same, as appears from the following calculation. To facilitate comparison we retain L 0 man and Z w i k k e r's notation (x = interfacial tension solid/gasphase, y = interfacial tension solidfliquid phase). We start from the formula : x = VI cos '?I t)'1 = V2 cos 92 +)'2, Physica III
70
1106
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J.
SAAL AXD
J.
F. T. BLOTT
so that generally cos ?i = 2 cos- {- ?i 1
_
cos 2 ?i -
1-
-J/Gi + X -
X-Yi a, )'i
2Gj'
from which it follows that: COSt?1 =
1Ii;
.IIGI +X-YI.
cos 2 ?2 GI G2 +x - Y2 Hence, as long as crl x - 1'1 = G2 X - )'2' it will invariably be found that Lam a nan d Z w i k k e r's formula applies. This may also be written in another way:
+
GI -
1'1 = G2 -
+
1'2 = constant =
k,
and k in that csae is indeed a material constant of the solid, but it need not necessarily represent the surface tension of the solid, as implied by Ant a now's rule cr-1' = x. In other words: if L 0 man and Z wi k k e r's formula (6) does apply, it has been proved that cr - l' is independent of the liquid used, but this magnitude is not necessarily equal to the surface tension of the material, so that the validity of Ant a now's rule has not been proved. It may be asked what value can then be attached to Lam a n and Z w i k k e r's figures for the surface tension of solids. They deduce the formula rrcos2 t 9 = x, from which x is calculated. If we assume o - l' = k = x - c, in which c is another material constant of the solid (at least as long as formula (6) applies), it may be proved that in general c must be positive. For we may write x-1' x-1' COS? = -cr- = x l' - c
+
If for a given solid c should be negative, there could never be any liquid which would give complete wetting, as x and l' are essentially positive. Such a case is only imaginable by way of exception. As a rule any solid will be completely "wettable" by at least one liquid, so that c = 0 or > 0 must apply for the solid. If c = 0, in other words if Ant a now's rule applied, the solid can only be completely wetted for the exceptional case l' = 0, so that x = cr. But in the
OX THE SURFACETENSIOX OF SOLID SUBSTANCES
1107
general case of complete wetting y will be positive, so that it must be concluded that as long as formula (6) applies, c will as a rule have a positive value. Now it can easily be calculated that rr cos? } 9, is equal to lJ-j'
2
+x =
x-
~-c.
Therefore the values for a cos? -} 9 (which, according to L 0 man and Z w i k k e r, equals the surface tension of the solid) prove to be smaller than the surface tension of the solid. To what extent they are smaller cannot be deduced, however, from the measurements. Hence, if the difference between rrand cr' had not been disregarded beforehand, L 0 man and Z wi k k er's figures would at least show a minimum limit. But now this is not the case either.
III. Comparison oj the results [ound by the various methods dealt with above. From the above critical review it appears that there is really no single reliable method for measuring the surface tension of solid substances. We shall therefore not make a thorough systematic comparison between all the results obtained by the various methods proposed, but simply demonstrate from a few cases that there is no proper agreement between them, and that it is also impossible to correlate the results of these methods with theoretical expectations. Before doing so, however; we should like to deal with a general difficulty that presents itself in such measurements. The surface of a solid will frequently be soiled through adsorption; the method of cleaning is therefore of prime importance. In this connection we refer to L 0 man and Z wi k k e r's article (loc.cit. page 1197); where it is stated that the method of cleaning is a very influential factor. Thus, to be able to compare the determinations, it is necessary that the method of cleaning should be carefully described. This, however, is often forgotten. We shall illustrate this by means of the measurements of L om a nand Z wi k k e r (loc. cit.). In ouropinion, the approximately equal values for the surface tensions of various stones (see Table Ia of their paper) may, if no special precautions were taken with regard to cleaning. be due to the fact that the measurements were invariably made against one and the same substance, in this case a greasy film on the insufficiently cleaned material; the statement that the angle of contact sometimes alters fairly quickly is in keeping with this
1108
R. N.
J.
SAAL AND
J.
F. T. BLOTT
supposition (loc. cit. page 1186). Further, to explain the influence of cleaning they assume a special change in the surface of. the solid substance, e.g. in the case of mercury on glass, where the angle of contact is altered very much by heating the glass previously to about 400°C. On the other hand the same behaviour in the case of quartz, in which a chemical change of this kind is not possible, is explained by the removal of organic contaminations (loc. cit. page 1199). In our opinion such explanations are rather dangerous. But even if the surface has been well cleaned, complications may occur. For instance, the time during which the solid is in contact with the liquid may also be of influence. To show this we shall quote some experiments made by H. E i I e r s (unpublished) with regard to the wetting of bitumen by water. A drop of water (0.60 gr) placed on a Mexican asphaltic bitumen (pen. 40/50) had a diameter of 17.2 mm : 0,2. The same asphaltic bitumen, after being poured out and cooled for two days under water and then dried, gave a diameter of I drop (0.60 gr.) of 19.0 ~ 0.2 mm. Therefore, the wetting by water is increased by prolonged immersion in water, notwithstanding the fact that the bitumen had in the meantime been thoroughly dried. We explain this phenomenon by a change in the orientation or the distribution of the molecules in the interface. Whereas, when the bitumen is kept dry, it is mainly saturated groups which protrude upon its being subjected to prolonged contact with water a change will occur and the more unsaturated groups will mainly form the surface layer. The same behaviour is shown by stearic acid which has been crystallized in contact with water or in contact with air. In the first case the surface is easily wettable, whilst in the second case the wetting is very bad. Prolonged immersion of the latter surface in water makes it again wettable as a result of the reorientation of the molecules. We will now show by some examples the poor agreement between the experimental data. a. S a Its. In table II we give the values calculated by B 0 r n 10) for the solid salt, and at the same time measurements by J a eg e r 19) for the molten state. These latter measurements have been linearly extrapolated to -273°C, so as to enable us to compare them with B 0 r n's figures; these values are of course only rough approximations.
ON THE SURFACE TENSION OF SOLID SUBSTANCES
1109
TAI3LE II Surface tension of salts in dynes/em.
Salt
KCl KI3r KI NaCl "aUr KaI
Calculation crt at -273°C by I3 0 r n
107 92 74 150 119 96
!llelted salt Determinations by J a e g e r
ar, 95.8 85.7 75.2 113.8 105.8 85.6
I
T, 800 775 737 803 761 706
I
cr, 69.6 75.4 66.5 88.0 78.0 77.6
I
T. 1167 920 873 1172 1166 861
I
~
Extrapolated -~73°C. (cr:l
crt
170 160 140 190 180 135
1.6 1.7 1.9 1.3 1.5 1.4
It is at all events evident that the figures are of the same order of magnitude. On the other hand, Lip set t, J 0 h n son and :\1 a ass 9) give 400 dynes/em for NaCl; this figure was derived from measurements of the heat of solution of finely dispersed salt. b. Asp hal tic bit u me n ..Ashaltic bitumen is a very suitable material for comparing various methods of determining the surface tension of solid substances. Essentially it is a liquid substance which makes it possible to extrapolate measurements at high temperatures to normal temperatures with sufficient accuracy. (The break found by Nell ens t e y n 20) in the (J - T curve of asphaltic bitumens has nothing to do with surface tension, but is caused by some disturbing factor during the determination 21)). At the same time the viscosity at ordinary temperatures may be high enough for the application of the methods proposed for solid substances. Now the result found by extrapolation from high temperatures is, say, (J = 35 dynes/em. The same order of magnitude is found by 1\1 a c k 2) with Be r g g r en's method. On the other hand, Lorn a nand Z w i kk e r (loc. cit.) give 6 l , a value which is certainly too high. c. G 1ass. Glass gives the same possibility for comparing the methods for liquid and for solid materials. But here we encounter the difficulty that the materials may have been different. In the literature on the subject a value of (J = 150 dynes/em at 12001450°C is given 22). If the value 135 dynes/em at room temperature found by Nell ens t e y nand H. 0 0 den bur g (loc. cit.) or by Lorn a nan d Z w i k k e r (loc. cit.) can be compared with this figure, their result seems to be open to some doubt. d. 1\1 eta 1s. Liquid metals generally show a high surface tension
1110
O~ THE SURFACE TENSIOX OF SOLID SUBSTAKCES
(e.g. 500 dynes/em) 21). There is some reason to expect no great difference (for instance, not by a factor as high as 10) between the surface tension of liquids and that of solids. In this connection the low values found by Lorn a nand Z w i k k e r (abt 50 dynes/em) are doubtful. Against these measurements it may be argued further that no complete wetting of, for instance, steel by water is found, whereas it is known that after having been freed from grease by brushing with lime and chalk, this metal as a rule can be completely wetted by water. From the few examples given above it is clear that no proper agreement between the different methods exists. IV. Conclusion. A critical description is given of the various methods proposed for the determination of the surface tension of solid substances. It is shown that none of these methods can give a reliable determination of this property. Received October 2, 1936.
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ncr g g r e n, Ann. Physik (4) "'1, 61,1914. :\1 a e k, Ind. Eng. Chern. 27, 1500,1935. C hap rn a n & I' 0 r t c r, Proc, roy. Soc. London (A) 83, 65, 1909. Tho rn son, Phil. :\Iag. (4) "'2, 448,1871. W. 0 s twa I d, Z. physik. Chern. :.1'0, 503, 1900. K 0 sse I, Ann. Physik (5) 21, 457,1934. E h r e n f e s t, Ann. Physik (4) "'8, 360,1915. Dun don & :\1 a e k, J. arner, chern. Soc. 1:>, 2479, 1924. Lipsett, Johnson & :\Iaass, J.arner.chern.Soc.... !J,925,1927. e.g. S.-B. Akad. Wiss, Berlin 901, 1919. All ton 0 w, Phil. :\Iag. (7) 1, 1258, 1926;"',792,1927. Chern. Wcekbl. au, 189, 1933. Physica I, 1182, 1934. Also sec Phys. Z. 311, 603, 1935. J. Chim. phys, s, 372, 1907. Sec for instance F u c h s, Koll, Z. ii2, 262, 1930. J. amer, chem, Soc. ;;11, 2205,1934. Coli. Syrup. s, 112, 1928. Z. anorg. allg. Chern. 101, I, 1917. Koll. chem, Beih. 31, 434,1930. S a a I, 0 e I un d K 0 hie 2,367,1934; Chern. \\'eekbl. :12, 486,1935. Was h bur n, Phys. Rev. (2) 20, 94, 1920; Rec. Trav, chirn. .'\2, 686, 1923. La 11 dol t B 6 r n s t c i n, Physikal. chem, Tabellen 1923, p,: 1931.