FREDERICK 11. FOWKES
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Vol. 67
ADDITIVITY OF INTERMOLECULAR FORCES AT INTERFACES. I. DETERMINATION OF THE CONTRIBUTION TO SURFACE AND INTERFACIAL TENSIONS OF DISPERSION FORCES IN VARIOUS LIQUIDS’ BY FREDERICK M. FOWKES~ Shell Development Company, Emeryvzlle, Culijornza Received February 18, 1963
The tension in the surface of liquids ( y ) is a direct measure of interrnolecular forces, for saturated hydroc:irbons the surface tension measures only the dispersion forces, but for coinplex liquids such as water the surface tension is the sum of the contributions of dipole interactions and hydrogen-bonding ( 7 ” )and dispersion forces ( 7 “ ) . The tension a t liquid-liquid interfaces is the sun1 of tensions in the two adjacent interfacial layers. I n the interfacial monolayer of liquid 1, the tension is deternlined by the difference in the tensions resulting frorn 1-1 interactions and 1-3 interactions; this equals ( 7 1 - G G d ) if 1-2 interactions involve ()Illy dispersion forms. For example, at the interface between water 1 and saturntcd hydrorarbons 2, m hcw only dispersion forres interact
ICvnluation of y l d with y 1 and y I 2values a t “lo with saturated hydrocxrboris givcs Y H , O ~ = 2 I .8 & 0.7 dynes/ mi. and y1zsd = 200 f 7 dyncs/cm. Knowledge of these values allows evnluittion of the magnitude of other types of interrnoledar forves. Furtherniore, these two valurs rnay be used to cal(date the interfacial tension between water arid rncwury (c:ilculated v:tlue -k25 dynes/crn. ; expeririirnttll value 4 2 1 i 1 2 i ) .
Introduction Surface tension has long ago been recognized as a direct measure of intermolecular forces, but a reinterpretation using our present knowledge of the various typcs of intermolecular forccs shows that surface and interfacial tensions are valuable tools for determining the magnitude of the various types of intermolecular forccs. Tension in Surface Layers.-The tension in surface layers is the result of thc attraction of the bulk liquid for the surface layer. ~Iolcculcsarc pulled into the bulk liquid from the surface layer and the resulting increase in intermolecular distance results in a twodimensional tension. The intermolecular forces in saturated hydrocarbons are only the van der Waals or London dispersion forces which result from the attraction between fluctuating dipoles (resulting from the rapid fluctuation of the location of electrons in molecules) and the dipoles induced in other molecules by these dipoles. Such interactions occur between all kinds of molecules and atoms. Since the relatively weak intermolecular attractions between hydrocarbons are the best known example of purc dispcrsion force interaction, it has been assumed by many that dispersion force interactions are always weak ; it will be shown that this assumption is somctimes far from the truth. In polar or metallic liquids the intermolecular forccs involve hydrogen bonds, dipole interactions, and metallic bonds in addition to the dispcrsion forces. The tension in surface layers depends on the sum of the attraction forces bearing on the surface molecules, and the value of the dispersion force contribution is largcly independent of the other forces. Consequently, it is proposed that we represent the surface tension y as the sum of the polar or metallic force contributions and the dispersion force contribution. For mercury Yrlg =
7rrc
111
3-
YElg
(I
(1)
( 1 ) I’reaented a t tho 1 4 l s t National Meeting of tho .\merictm C l i o i ~ i i c ~ l Socii,ty, Washington, 11. C., hIarc11, 1RG2. (2) Sprague Electric Co., North Adams, Rlasa.
whcre 7”’is the contribution of the metallic forces arid yd the contribution of dispersion forces. Similarly for water 71i*o = yrr,oll
+
Y*i*O(’
(2)
where the first term is the polar intcraction term (mostly hydrogen-bonding) . The Nature of Interfacial Tension.-At t he interface between two liquids, the adjacent layers of dissimilar molecules are in force fields very different from those existing in the bulk liquids. These two layers have diffcrent intermolecular distances, different pressures, and different chemical potentials from the bulk, and might well be considered as separate phases. Thus, a t a liquid-liquid interface there really arc two distinct iiitcrfacial monolayers, cach of which has a tension (or pressure) different from that of the bulk phase, and the measured interfacial tension is the sum of thc tensions in the two monolayers. It must be recognized that while most of the interfacial forces are confined to the adjacent molecular laycrs, they also bear to some dcgrcc on molecules somewhat further from the interface. Thus, the tension really is distributed to a small degree over a greater depth than a monolayer. This fact is rccognizrd and accounted for though riot rcpcated throughout the following argument. Figurc 1 is a simplified diagram of a liquid-liquid intcrface, showing the adjacent interfacial monolayers of each phase. Both monolayers are in tension and the measured interfacial tension is the sum of the two tensions. I n the interfacial monolayer of phasc 1, attraction by the bulk phase tends to producc a tension equal to the surface tension (TI), but this effect is opposed 1 ) ~ attraction from the unlike liquid. I t is proposed that the surface tension term resulting from the intermolecular attraction of the dissimilar liquids is tl1c geometric mean of thc interacting tcnsion contributions of the two liquids, providing these interact by dispersion forces. If liquids 1 and 2 intcract only by dispersion forces, and have dispersion force contributions to surface tcil(3) F. &I. Fowkes, J . I’hys. Chen., 66, 1863 (lV62).
ADDITIVITYOP INTERMOLECULAR FORCES AT INTERFACES
Dec., 1963
sion yld and ,y2dJ then the tension term due to the attraction of phase 2 for the interfacial monolayer of phase 1 -will be dyldyzd. The calculation of the intermolecular attraction between dissimilar molecules as the geometric mean of the dispersion forces of the two sets of like molecules comeB directly, from the original predictions of London4(providing intermolecular distances are equal) and is confirmed for a wide variety of dissimilar molecules by the studies of “regular” solution^.^ The sum of the tensions in the interfacial monolayer of phase 1 is y1 - d y l d y 2 d and in the interfacial monolayer of phase 2 is ’yz - Vyldyzd. Therefore, the sum of the tensions in the interface (ylZ)is YlZ
= Y1
+ Yz - 2dy,dY*d
d
Yi
=
(Yi f Yz - Yiz)’/4Yzd
.iquid I
.iquid 2
t
vqq-
(4)
and then assume yzd = y2 for hydrocarbons. The result, 200 dynes/cm., is reasonably independent of which hydrocarbon is used; the standard deviation is only 7 dynes/cm. This shows mercury atoms develop very strong dispersion forces; the 200 ergs/cm.2 corresponds to a surface free energy of 2.4 kcal./g.-atom resulting from dispersion fdrces. The metallic bond accounts for the 284 dynes/cm. difference between the surface tension (484 dynes/cm.) and 7 ~thus~metal~ ; lic bonds account for only 60% of the interatomic forces in mercury a t 20”. I n the interfacial monolayer of mercury next to the hydrocarbon, the tension is the result of the attraction of the bulk phase of mercury (YE%)lessened by the opposing attraction of the hydrocarbon ( d g d ) . With benzene (using y~~~ = 200 dynes/cm.) this amounts to 484 - 76 = 408 dynes/cm. However, in (4) See J. H. Hildebrand and R L. Scott, “Regular Solutions.” PrenticeHzll Publishing Co , Enrlewood Cliffs, N. J , 1982, pp. 79-80 ( 5 ) J. I I Hildebrand and R. L. Scott, ”Solubility of Nonelectrolrtes,” 3rd E d , Reinhold Publishing Co , New York, N Y . , 1950 (6) Reference 4, pp. 29 -3 1. (7) L A. Girifalco and R J Good, J . P h y s Chem., 61, 004 (1957). ( 8 ) R J. Good, “Theon*=,for the Estimation of Surface and Inteifa‘ial Enermes I V . Interfacial Tension betneen Pure Organic Liquids and Water, ’ presented before the Division of Colloid and Surface Chemistry, 142nd National Meeting of the American Chemical Society, Sept., 1962.
c Y2
Y12 = YI t Y e- 2 2 / ; d1 y b2
(3)
According to London’s equations, the geometric mean is correct only for dissimilar molecules of equal size. However, studies of regular solutions show that differences in molecular volume m great as 10: 1 make no deviation in applying this rule.6 Good and Girifalco7 have also used the geometric mean of surface free energies to predict the magnitude of interfacial free energies ; however, they have included a correction term for disparity in molecular volumes. Originally they did not separate the tension into a sum of contributions resulting from different types of intermolecular forces; Good’s recent work now includes this feature.* Mercury-Hydrocarbon Interfaces.-1CIercury-hydrocarbon interfaces a re good examples of the interaction of dissimilar liquids by dispersion forces only. Hydrocarbons have only dispersion force interactions while mercury has the nietallic bond in addition to dispersion forces. The metallic bond cannot be expected to interact with hydrocarbons. Table I shows some values of y H e d calculated from surface and interfacial tensions with ten different hydrocarbons a t 20°, using eq. 3 in the form
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Toluene o-Xylene m-Xylene
28.5 30 1 28.9
389 359 357
208 200 211
200 i 7
FREDERICK M. FOWKES
2640
Vol. 67
s = yTv - ( y o +
TOW)
(3
This equation gives the surface free energy change associated with spreading; positive values indicate spreading will occur. It should now be obvious that y 0 T Y is determined by yo for any pure saturated hydrocarbon, so that on applying eq. 3 to eq. 5 for these systems
Fig. Z.-Relation of spreading coefficient to surface tension of oils. Circles, pure hydrocarbons; squares, refined oils. Results of Sawyer (S),16 Langmuir (L),16 and Zisman ( Z ) . I 7
%-Decanea n-Tetradecanea Cy clohexane" Decalin'
23.9 25.6 25.5 29.9
51.2 52.2 50.2 51.4
21.6 ' 21.8f0.7 20.8 22.7 22.0
If one uses this value of ~ H to~ calculate o ~ by eq. 3 the interfacial tensions against water of aromatic hydrocarbons having surface tensions of 28-30 dynes/cni. (assuming the aromatics have only dispersion force interactions with water), the calculated values are all close to 51 dynes/cm. Since the experimental values are from 35 to 39 dynes/cm., there is a discrepancy of 13-16 dynes/cm. resulting presumably from the existence of forces across the interface other than dispersion forces (perhaps 7bonds). The surface free energy of these bonds amounts to 1kcal./mole of the aromatic hydrocarbons. Spreading of Hydrocarbons on Water.-The tendency for an organic liquid (0)to spread on water (W) is often expressed in terms of the X-IarkinslZ spreading coefficient. (11) W. M. Sawyer m d 11'.h l . li'owkou, .7. ~ 7 Chem.. ~ 60, ~ 1235 ~ (1966). . (12) W. 11. Harkins, "Physical Chemistly of Surface I'ilms," Reinhold Puhlisliing Co., New Pork, K . Y., 1952, pp. 41-49.
This equation reduces to zero when yo = y ~which ~ is , 21.8 dynes/cm. at 20". Thus, hydrocarbons with surface tensions less than 21.8 dynes/cm. (heptane, hexane, etc.) should spread on water, and the saturated hydrocarbons with surface tensions above 21.8 dynes/cm. (n-nonane, n-decane, etc.) should not spread on water; this has been verified. The critical value of 21.8 dynes/ em. for saturated hydrocarbons to spread on water is like Zisman's "critical surface tension (yc) for spreading" on solid ~urfaces,~3~4 and will be shown to be an identical concept.9 Zisman has found yo values for crystalline waxes and for Teflon to be close to 21.8; thus, these substances have about identical wettability (by saturated hydrocarbons) as water. The relation of X to yo given in eq. 6 is the nearly straight line shown in Fig. 2 ; actually the slope of S us. yo becomes increasingly negative (-1.10 when yo = 27 dynes/cm. and -1.17 when yo = 32 dynes/cm.). The experimental ralues for pure saturated liydrocarbons (circles) are seen to fall right on the line, but refined oils (squares) are not on the line. The reason is that in the refined mixtures the value of yo is determined preferentially by the lighter fractions, while yo17 is determined primarily by the heavier fractions; this leads to higher than predicted values. On the other hand, if the oil is less highly extracted of its aromatic components, yow is lower than predicted from yo and the resulting values of 8 tend to fall below the line. The experimental results shown in the figure were taken from the work of Sawyer,?V16Langmuir, and Zisman." Spreading of Hydrocarbons on Mercury.-The spreading of hydrocarbons on mercury must follow the predictions of an equation analogous to (6) in which ywd is replaced by 7 ~ Since ~ y~~~ ~ .is 200 dynes/cm., then all hydrocarbons with yo less than 200 dynes/cm. must spread on mercury; obviously this includes all hydrocarbons. The formation of a duplex film with hydrocarbon surface and hydrocarbon-mercury interface reduces the surface tension by the value of the spreading coefficient 8, as discussed in the previous section (eq. 5 and 6). However, the numerical values are much larger than observed with aqueous substrates. For hexane, hexadecane, benzene, and tetralin (tetrahydronaphthalene) the spreading coefficients on mercury are +84.5, +94, +94.5, and +98 dynes/cm. The equilibrium spreading pressure r0 of monolayers of these hydrocarbons on mercury is almost the same as these values of X.18 Because of the ease with which hydrocarbons and their derivatives spread on mercury, (13) 1%. W.Fox and W. -4. Zisman, ,l.C e I b i d Scz., 6, 014 (1950). (14) E. G. Shafrin and W.A. Zisman, J . Phys. Chem., 64, 619 (1960). (16) W. M. Sa:.ryer, unpublished results. (IF) I. Langmuir, J. Chem. Phys., 1, 766 (1933). (17) W. A. Zisman, %bid.,9, 534 (1941). (18) C. Kemball and E. IC. Rideal, Pioe. R o y . SOC.( L O I I ~ O I 187A, I), 53 (1946).
Dec., 1963
CARBOX-CATALYZED HYDROGEN-DEUTERICM EXCHAXGE REACTIOK
film balance studies of such monolayers can be made.19 These show that long n-alkyl chains lie flat on the surface (at low film pressures), a behavior never observed on aqueous substrates. The reason is now obvious; the values of the spreading coefficients illustrate this point. For example with n-hexadecane, XN,O = -6.5 ~ +94 dynes/cm. dynes/cm. and S H== Since spreading coefficients are equal to the adhesional forces ( 2 6 9 minus the coliesional forces of the spreading liquid (2y2),this means that the adhesion of hexadecane to water is weaker than its internal cohesion, whereas its adhesion to mercury is far stronger than its internal cohesion. The Mercury-Water Interface.-The metallic bond of mercury and the hydrogen bond of water are not expected to interact a t the mercury-water interface; however, there is the possibility of a xvater dipole inducing an “image” dipole in the mercury. This effect is not expected to be appreciable, and as will be shown later these effects are immeasurably small for a number of polar organic inolecules.20 Consequently, it is reasonable to expect that the interfacial tension between water and mercury can be calculated from the known values of yHgd and yHzOd (200 and 21.8 dynes/ cm., respectively) iusiiig eq. 3. The result, 424.8 dynes/cm., is close to values obtained by the most careful measurements: 426.7 by GouylZ1427 by Henry and Jackson,22 and 426 2 dynes/cm. by Smolders.23 If dipole-image forces were active a t this interface in addition to dispersion forces, one would expect the experimental measurements to be lower than the calculated value; since this is not the case, one can dismiss dipole-image forces as negligible in this system. The spreading coefiicieiit of water on mercury is - 12 dynes/cm. and, consequently, water should not spread on mercury, as has been observed by hark in^.^^ This is in considerable contrast to the spreading of hydrocarbons. It is of interest to consider the possibility of hydro(19) (20) faces. (21) (22) (23) (24)
A. H. Ellison, J . Phys. Chem., 66, 1867 (1962). F. M. Foukes, “Additivity of Intermolecular Forces at InterIV,” to be published
M. Gouy, Ann. phys., 6 , 5 (1916). D. C. Henry a n d J. J. Jackson, Nature, 142, 616 (1938). C. A. Smolders, Rec. trav. chim., 80, 635 (1961). W. D. Harkins, ref. 12, p. 47.
2541
carbons (3) spreading at the mercury (l)/water (2) interface to substitute a hydrocarbon/water interface (723) and a hydrocarbon/mercury interface ( y ~ for ) the mercury water interface (ylz). Such spreading should y13 < y12. The tendency of pure occur when 7 2 3 saturated hydrocarbons to spread (at this interface) can then be given by the sign of
+
When
y3 = y2d,the above expression is zero, but when y3 > yzd the result is positive and the hydrocarbon will
spread. Thus, a t 20°, hydrocarbons with surface tensions in excess of 21.8 dynes/cm. will spontaneously spread a t the mercury-water interface. Thus, very small traces of hydrocarbons in a system can lead to incorrectly low interfacial tensions for the water-mercury interface. I n the case of benzene, where the benzene-water interfacial tension is quite low (35 dynes/ cm.) because of an additional interaction, one would expect traces of benzene to lower the mater-mercury interfacial tension from 426 dynes/cni. to 396 dynes/cm. 35). Butlerz6has observed exactly 396 dynes/ (361 cm. when using benzene-saturated water. With better understanding of the situation let us now examine the adsorption of water-soluble organic compounds a t the water-mercury interface, such as the example described by Blomgren.10 I n this work it was shown that for a variety of derivatives with butyl and phenyl radicals, the latter had an average free energy of adsorption 2.5 kcal./mole greater than the former. We might not expect the butyl groups to displace water from the interface, but m7e would expect the phenyl groups to do so, lowering the interfacial free energy by 30 ergs/cm.2 (426-396). The measured concentration of phenyl groups was 3.7 X 10-lO moles/cm.2 and, consequently, the surface free energy of the adsorption amounts to 2 kcal./mole. Thus, most of the observed effect can be attributed to the stronger dispersion forces operating between mercury and phenyl groups than those operating between mercury and butyl groups.
+
(23) E. B. Butler, 142nd National Meeting of t h e American Che~nical Society, Stlantic City, N. J., Sept., 1962.
THE CARBON-CATALYZED HYDROGEN-DEUTERIURI EXCHANGE REACTION BY 14. J. ROSSITER,R. NELSOXSMITH,AND JAMES R. LUDDES Department of Chemistrg, Ponwna College, Claremont, California Received February 25, 1965
It is found that, contrary to previously published results, the Ht-Dz exchange reaction is not catalyzed by “pure” carbon surfaces in the temperature range 50 to 540”. This conclusion is based on experiments with a variety of ash-free sugar charcoals whicll were prepared a t temperatures ranging from 600 to 1000” and which varied in hydrogen content from 0.42 to 2.5% and in oxygen content from 0.44 to 3.7%. A charcoal sample containing 0.15% Fe showed moderate catalytic activity toward H2-Dz exchange a t 50”. It is concluded that the catalytic activity described in previous accounts was caused by impurities and not by the carbon surfaces per se.
The work described in this paper was initiated becausc of the report by Turkevich and Larochel that (1) J. Turkuvicli :tnd J. Liuoclie, 2. physik. Cizern. (l’rankfurt), 16, 3‘39 (1958).
carbon surfaces can catalyze the hydrogen-deuterium exchange reaction at 50’. They showed that sugar charcoals increased in thcir ability to catalyze this cxchange as the temperature of their preparation in-
