Langmuir 1991, 7, 1229-1234
1229
Oriented Dipoles at Interfaces: Calculation of Surface Potential and Surface Tension Wendy C. Duncan-Hewitt Faculty of Pharmacy, University of Toronto, 19 Russell Street, Toronto, Ontario M5S 1A1, Canada Received June 18,1990.I n Final Form: December 3, 1990 A simple method is introduced that estimates the surface free energy of pure, polar liquids. For longchain amphiphiles, the calculation is almost intuitive. In addition to the refractive index spectrum and dielectric permittivites used to calculatethe van der Waals component from the Lifshitz theory, knowledge of the partial charge distribution in the dipolar molecule, the molecular conformation, and a model of the molecular packing at the liquid/vapor interface is required. For smaller, highly polar molecules, the molecular packing at the interface is not as easily predicted intuitively so that knowledge of the surface potential jump, x, is also required. This parameter is not experimentally accessible and the models used presently to calculate it from the surface potential, $, are inadequate. In response to this need, a new model has been developed which predicts the surface potential jump from experimental data. Finally, the surface free energies of water, methanol, and several other polar liquids are calculated as the sum of a van der Waals contribution arising from the interactions between randomly oriented molecules and an electrostatic, orientational term calculated from the partial charge distribution in the molecules.
Introduction Macroscopicobservations of interfacial phenomena such as wetting and adhesion are often interpreted in terms of the van der Waals interaction which, in fact, consists of three distinct interactions, all possessing the same rd distance dependence: (1) the Keesom (orientation) component gives the angle-averagedinteraction between a large number of dipoles whose kinetic energy is sufficient to allow them to rotate freely; (2) the Debye (induction) component gives angle-averaged interaction between a nonpolar molecule and a dipole, and (3) the London (dispersion) component gives the interaction between two nonpolar molecules. The dispersion component is ubiquitous and it often predominates. The behavior of nonpolar and weakly polar materials is described well by theories that consider van der Waals forces alone. For example, using Hamaker constants calculated from the Lifshitz theory of van der Waals interactions, Israelachvili calculated the surface free energy of a number of liquids as follows’
where Yvdw is the van der Waals surface free energy, A is the Hamaker constant, the DOis the separation between two planar surfaces at contact. By use of a “universal” interfacial contact separation of 0.165 nm, the surface free energies of nonpolar liquids were predicted with remarkable accuracy. The predictions become increasingly poor, however, the more polar the liquid is. The surface free energy of water a t 25 “C was predicted to be 18 mJ m-2, which is much less than the experimental value of 72.5 mJ m-2. The discrepancy is usually attributed to “polar” or “orientational” effects, although the exact nature of these effects is not usually specified. An inspection of the assumptions inherent in theories of van der Waals forces is illuminating. For example, the van der Waals interaction between two molecules separated by a few molecular diameters may be calculated in (1) Israelachvili, J. N. Intermolecular and Surface Forces with Applications to Colloidal and Biological Systems; Academic Press: New York, 1989; p 28.
0743-7463/91/2407-1229$02.50/0
a straightforward manner as a sum of the three components. But as the molecules are brought closer together, some of the work will be expended in orienting the molecules to maximizetheir interaction. When a preferred orientation is adopted, the angle-averaged values for the van der Waals interactions are no longer appropriate. If a third molecule is then added to the system, its behavior will be influenced by the two original molecules and it will also introduce another component into the field which will modify the interaction between the first two molecules. The field that results is not a simple sum of the individual fields, and as further molecules are added to the system, the problem becomes exceedingly complex. Theories of van der Waals forces such as that developed by Lifshitz2 avoid these problems by ignoring molecular structure altogether. The interactions between large bodies are calculated in terms of the volume densities of bulk properties such as dielectric constants and indices of refraction. This continuum approximation cannot be used to predict the behavior of a system if its structure a t the location of interest is very different from that in the bulk. Surfaces are problematic in this sense, since the molecular densities, bonding, and entropy often change dramatically within the few molecular layers that make up an interface. Problems generally arise a t short distances, for example when solvation effects, hydrophobicity, adhesion at contact, and surface free energies are considered. This paper considers the consequences of the discrete nature of liquids at the macroscopic level. Van der WaalsLifshitz calculations give only the contribution of angleaveraged forces to macroscopicinterfacial parameters such as the surface free energy and do not address the effect of oriented dipoles. The orientational effect is difficult to quantitate within the conventional thermodynamic framework because it consists of two components: (1) Reorientation occurs to maximize the molecular interactions. In particular, if the material is able to hydrogen bond with itself, the reorientation minimizes the number of “dangling” hydrogen bonds. This component is favorable energetically. (2) Lifshitz, E. M. Sou. Phys.-JETP (Engl. Transl.) 1966,2, 73.
0 1991 American Chemical Society
Duncan- Hewitt
1230 Langmuir, Vol. 7,No. 6,1991 H
H
H
H
I 'V
hqmd phase
In this orientation, very few hydroxyl groups will come into contact with the vapor phase, which is sensible, since hydrogen bonding is maximized in this way. But then it is erroneous to incorporate the energetics of hydroxyl group interactions into the calculation of van der Waals forces, which would occur automatically if the bulk properties for the aliphatic alcohol were used in eq 2. Therefore it is more appropriate to use the bulk properties of 1-octane in the Lifshitz calculation. The remaining orientational effech may be taken into account in the following way. The surface free energy of a liquid gives the work required to expand the surface by a unit area and this is achieved by moving a molecule from the bulk into the surface. No net electrostatic work will be required to move either a nonpolar molecule or a randomly oriented dipole into the surface. But extra work will be required to move an oriented dipole against the surface dipolar potential given by the Helmholtz equation (eq 3) into an interface consisting of oriented dipoles
x = p sin (4)/2e
dipole
ultCrfac,dplane
Figure 1. Configuration of the molecules at the 1-octanol/vapor interface. The dipole orientation is fixed by the van der Waals
packing of the aliphatic chains.
(2)Reorientation decreases the number of configurations available to the molecules at the interface and is entropically unfavorable. To determine the contribution of preferential interfacial orientation to surface free energies nominally calculated from macroscopic parameters such as refractive indices, it would seem that one requires independent estimates of these two contributions; but for polar molecules an alternate approach exists.
Surface Free Energy Calculation for Large Amphiphilic Molecules For example, consider the manner in which the surface free energy of 1-octanol might be calculated. If the dielectric constant and refractive index are known, an estimate of the van der Waals contribution to the surface free energy may be calculated by using eq 2 (estimate of the Hamaker constant') and eq 1(estimate of surface free energy using the Hamaker constant) A
N
0.75 kT ([el - e3]/[e1
+ e3])' +
0.13 hv,(n,'
- n32)2/(n12 + n32)1.5(2)
where t i is the dielectric constant of material i, nj its index of refraction, ue is the electronic absorption frequency, k is the Boltzmann constant, and h is Planck's constant. For interactions under vacuum, t3 and n3 are equal to one. More exact equations may be used for media with more than one absorption frequency or materials with different absorption frequencies.3~~ The most probable configuration of the molecules in the 1-octanol liquid/vapor interface is shown in Figure 1. The geometry of the molecular assembly at the interface essentially is controlled by the van der Waals packing of the hydrocarbon chains. Incidentally, this packing also constrains the orientation of the hydroxyl group dipole and should give rise to a surface potential jump across the interface, since it is not parallel to the interfacial plane. ~
~~~~~~~~
(3) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. (4) Hough, D. B.; White, L. R. Adu. Colloid Interface Sci. 1980,14,3.
(3)
where p is the dipole density in the interface, 6 is the angle that the dipoles makes with the interface, and e is the dielectric ~ o n s t a n t . The ~ dipolar contribution to the surface free energy is then calculated as the work per unit area required to move all the partial oriented dipolar charges on the molecule into position in the interface (it is assumed that the molecular density in the interface is approximately the same as that in the bulk) Yd
=
qp
XIa
(4)
where Yd is the dipolar (partial charge) contribution to the surface free energy, C qp is the sum of the absolute values of the partial charges within the dipole, x is the surface potential jump associated with the layer of oriented dipoles, and a is the molecular area at the interface. This approach was used successfully to calculate the surface free energy of 1-pentanol and 1-octanol (Table I). Consider next the case of aliphatic carboxylic acids. Their dipole momenta are large yet their surface free energies are smaller than might be expected (Table I). This observation is explained by noting that carboxylic acids associate strongly in the liquid state; in fact only 2-3 %I of the molecules exist in monomeric form.' The net dipole moment of a dimeric carboxylic acid is zero. Taking this fact into account, the surface potential jump is calculated as a sum of two contributions: that of the dimers (zero potential) and that of the monomers, the relative number densities of the two being given by the equilibrium ratio in the bulk. The correct surface free energy values may then be calculated (Table I). In summary, the surface free energy of a liquid consisting of long-chain amphiphiles is assumed to be the sum of an orientation-independent component and an oriented dipolar component. The dipolar component is calculated by (1) determining the orientation of the molecular dipole relative to the interface by assuming that the molecules pack as shown in Figure 1, (2) calculating the surface potential jump from the Helmholtz equation for oriented dipoles, and (3) calculating the work per unit required to move the partial dipolar charges into position in the an( 5 ) Thompson, M.; Wong, H. E.; Dorn, A. W. Anal. Chim. Acta 1987, 200, 319.
(6) Hodgman, C. D., Weaet, R. C., Shankland, R. S., Selby, S. M., MS. CRCHandbook OjChemistryandPhysics; CRC Publications: Cleveland,
OH, 1963.
(7) Pimentel, G. C., McClellan, A. L., EMS. Hydrogen Bonding, W. H. Freeman and Co.: San Franscisco, CA, 1960; p 229.
Langmuir, Val. 7, No. 6, 1991 1231
Oriented Dipoles at Interfaces
Table I. Parameters Used To Calculate the Dipolar and van der Waals Components of the Surface Free Energy of Various Liauids. ~~
~
material
density, g/mL
~ 1 0 - 1 9ma
dipole moment, D
dielectric constant
partial dipolar charge (from am1 calcn)
dipole orientation, deg (from surface plane)
acetonitrile hexanoic acid methanol 1-octanol 1-pentanol octanoic acid water
0.783 0.945 0.793 0.825 0.817 0.910 1.OOO
6.9 2.1 2.8 2.5 2.1 2.2 0.73
2.89 1.87 1.70 1.51 1.53 1.87 1.84
38.8 2.6 32.2 10.3 13.9 2.4 72.8
0.330 0.684 0.399 0.329 0.329 0.684 0.480
21 29.2 6.7 6.6 8.3 29.7 25.2
material acetonitrile hexanoic acid methanol 1-octanol 1-pentanol octanoic acid water
area,
fraction monomers 0.0272
0.0225
surface potential jump, V
dipole component .surface tension, mJ/m2
Liftahitz component surface tension, mJ/m2
total predicted surface tension, mJ/m2
true surface tension, mJ/m2
0.0231 0.3210 0.0066 0.0128 0.0146 0.3330 0.0259
11.3 9.3 4.8
18.0 18.0 18.0 22.0 18.3 22.0 18.0
29.3 27.3 22.8 27.5 25.8 29.4 72.6
29.0 27.3 23.0 27.5 25.7 29.2 72.5
5.5 7.5 7.4 54.6
a The predicted and experimental values for the total surface free energy are also shown. The projected area is calculated from the surface orientation and am1 calculations.
simulation method electrostatic Monte Carlo Monte Carlo molecular dynamic molecular dynamic molecular dynamic a
Table 11. Comparison of Some Simulations of Liquid Interfaces. molecular model surface potential surface dielectric constant (no. of molecules) jump, mV tension, mJ/m2 used in calculations pt dipole/pt quadrupole 29 72.8 water ST2 (256) 97 f 6 water ST2 (116) 80 water Tip4P (342) 100 132 water CC (1OOO) 160 30 1 water 25.6 1to 78.2 14.5 -30 TIPS (1OOO) 1 methanol -6 to -9 1to 32.2
density, g/mL 1
ref 12 13
1.5
14
1
15
0.85
16
0.69
17
The water dipole points toward the liquid phase.
isotropic interface (the dipolar component of the surface free energy).
Surface Free Energy Calculation for Small Polar Molecules The idea that large, amphiphilic, molecules adopt a preferred orientation at surfaces is highly accepted but has been disputed in the case of smaller, more symmetrical molecules where it is argued that orientational effects will be averaged out by thermal agitation. However, H a r d 9 and Harkinsgsuggested that all polar molecules will orient themselves, giving the most gradual change in properties as the interface is traversed and maximizing the mutual interaction energy. Evidence that small, highly polar molecules do indeed adopt a preferred orientation at the liquid/vapor interface may be found in the results of computer simulation studies and the experimental measurement of surface entropies,1° second harmonic generation,” and surface potentials. Some important results of a variety of computer simulations of the water interface and one simulation of the methanol interface are shown in Table 11. As was
discussed above, if dipoles adopt a preferred orientation at an interface, there should be a surface potential jump, x,associated with the interface. It can been seen that the simulations do in fact predict a preferred dipole orientation at the liquid/vapor interface. A positive value indicates that on average the dipoles are oriented preferentially toward the liquid phase. Unfortunately, the surface potential jump and surface free energy values predicted by simulation studies vary over a large range. Only Stillinger and Ben Naim12considered the effect of the surrounding molecules on the electrostatic field by using the bulk permittivity rather than the dielectric permittivity of free space (e,- = 8.854 X 10-l2C2J-l m-l 9. In one instancels sufficient experimental information was presented to permit the surface potential of water to be recalculated by using the more realistic assumption that the dielectric constant changes abruptly from 1 to the bulk value (78.2) at the Gibbs dividing surface. The surface potential jump calculated in this way was 25.6 mV, which agrees with that calculated by Stillinger and Ben Naim12 using their electrostatic approach (and also that derived
(13) Lee, C. Y.; Scott, H. L. J. Chem. Phys. 1980, 73, 4591. (14) Christou, N. I.; Whitehouse, J.; Nicholson, D.; Parsonage, N. G. Mol. Phys. 1985, 55, 39. (15) Wilson. M. A.: Pohorille.. A.:. Pratt. L. R. J. Chem. Phvs. 1987.91, (8)Hardy, W. B. h o c . R. SOC.London, A 1913,88,303. . . (9) Harkins, W. D. Z . Phys. Chem. 1928, 139,647. 48f3. (10) Good, R. J. J.Phys. Chem. 1967, 61, 810. (16) Matsumoto, M.; Kataoka, Y.J. Chem. Phys. 1988,88, 3233. (11)Goh,M.C.;Hicks,J.M.;Kemnitz,K.;Pinto,G.R.;Bhattecharyya, (17) Matsumoto, M.; Kataoka, Y. J. Chem. Phys. 1989,5U, 2398. (18) Gabler, R. Electrical Interactions in Molecular Biophysics, An K.; Einsenthal, K. B. J. Phys. Chem. 1988,92, 6074. Introduction; Academic Press: New York, 1978; p 79. (12) Stillinger, F. H.; Ben Naim, A. J. Chem. Phys. 1967, 47, 4431.
1232 Langmuir, Vol. 7, No. 6,1991
from the results of the surface potential experiments described below). Although the same authors also simulated themethanol/ vapor interface in another paper, less experimental data were presented for this material (dielectric constant = 32.2). The surface potential jump for methanol was recalculated to be approximately -6 to -9 mV by interpolating from contour maps of orientational angle probability at two temperatures and by assuming that the properties vary continuously and monotonically (the authors stated in their text that this was the case). The surface potential jump provides the required orientational information in the absence of an intuitive model of molecular orientation at the interface (see eq 3). If x could be determined experimentally and if the partial charge distributions on a given moleculewere known (using am1 calculations, for examplelg), the dipolar contribution to the surface free energy could be calculate as described in the preceding section (eq 4) and the total surface free energy could then be calculated from the sum of the dipolar and van der Waals contributions. Unfortunately x , is not subject to experimental measurement because it involves solely the work required to bring an isolated charge across an interfacea20Real charges are always associated with a particle, and it is impossible to separate the chemical and electrical parts of the work required to bring the particle across the interface. The surface potential jump must be estimated by interpreting the results of surface potential measurements using a model of the interface.
Estimation of the Surface Potential Jump from Surface Potential Measurements The experimental technique usually employed to investigate x actually measures the Volta potential difference between the surface under investigation and that of a metal probe: it is defined as e-l times the difference in the work required to bring a charge from infinity to a point just outside the surfaces. The measured experimental value is called the surface potential, # (a nomenclature that can give rise to many interpretive difficulties if the literature is not read with care!). The surface potential jump for water has been calculated from $by using a variety of theoretical models, and values ranging from 30 to 130 mV21p22have been reported in the literature. The range is similar to that associated with simulational approaches. Borazio, McTigue, and co-workers used voltaic cells to measure the variation with concentration of the surface potentials of several dilute aqueous solutions and a dilute methanolic KC1 s o l ~ t i o n Since . ~ ~ ~the ~ ~surface potential jump is not measurable, they used a model developed by Madden et a1.26(Figure 2a) in which it is assumed that the potential decays exponentially from the surface into the solution with a decay length of X. The second derivative of this expression, which gives the charge concentration, is combined with the Poisson/Boltzmann equation, then (19) Stewart,J. J. P.; Seiler,F. J. MOPAC Version4.0;QCPE Bloomington, IN. (20) Adamson, A. W. Physical Chemistry of Surfaces, 2nd ed.; Interscience Publishers: New York, 1967. (21) Phillips, M. C. In Water: A Comprehensive Treatise;Franks, F., Ed.; Plenum: New York, 1975; Vol. 5, p 133. (22) Randles, J. E. B.; Schiffrin,D. J. J. Electroanal. Chem. 1965, I O , 480.
(23) Barraclough, C. G.; Borazio, A,; McTigue, P. T. J. Electroanal. Chem. Interfacial Electrochem. 1988,243, 353. (24) Borazio, A.; Farrell, J. R.; McTigue, P. J. Electroanal. Chem. Interfacial Electrochem. 1985, 193, 103. (25) Madden, W. G.; Gomer, R.; Mandell, M. J. Phys. Chem. 1977,81, 2652.
0
0
O
0 w8
Z
0
W
0 O K w
0
Q
O
c w Q
: \
Figure 2. Models of the liquid/vapor interface used to predict the surface potentialjump. In the Madden et al. modelm(Figure 2a), the ions are not assumed to be hydrated and penetrate the surface layer. In the present model (Figure 2b), the ions are hydrated and do not penetrate the interface. the composite equation is linearized and integrated to give the following relationship: X, - Xo
= -KXXo(l
+ KX)
(5)
where xmis the surface potential of the solution, xo is the surface potential of the pure liquid, and K is the inverse Debye length. This derivation is problematic, since the surface potential and surface potential jump are not differentiated. Nevertheless, when Borazio et al.23applied this model, they predicted that the surface potential of water was 25 mV with a decay length of several angstroms. Their procedure did not fit the experimental data for methanol, although the authors conjectured that a minimum value for the surface potential should be about 90 mV. The model is inadequate for the following reasons: (1) I t is unlikely that ions will penetrate the surface in the manner assumed by the authors. They will be strongly hydrated, so that it will be the hydration spheres, and not the naked ions, that will penetrate the interface. (2) The potential must die off much more rapidly than is assumed in the model since it arises from a layer of partially oriented dipoles (Figure 3). The simplest approximation of this configuration is a sheet of oriented dipoles, for which the difference of two exponentials, one associated with the partial negative charge and one associated with the partial positive charge, should be calculated. The manner in which the potential varies with distance from these surfaces can be calculated by using the discrete lattice approach26 (Figure 4a). Given a lattice oEdiscrete (26) Lennard-Jone, J. E.; Dent, B. M. Trans. Faraday SOC.1928,24, 92.
Oriented Dipoles at Interfaces ,0254
0"Grahame' model . .
.
.
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Langmuir, VoZ. 7, No. 6,1991 1233 *"Madden" model
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.
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I
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A
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> E
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0
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e
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t
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00s
61
ois
62
ois
d3
concentration o f KCl, M
Figure 6. Surface potential vs ionic concentration for solutions of KC1 in methanol. The predicted values are derived by using a surface potential jump value of -6 mV. The experimental values are taken from Barraclough et aL23
(1)The surface charge density is due to a monolayer of oriented dipoles. The magnitude of the charge "seen" by a solute ion is calculated the same way as the relative magnitude of a charge is calculated for the Helmholtz equation for the surface potential of smeared-out dipoles. That is, it is the total charge density times the sine of the angle between the dipole and the surface. (2) The measured surface potential, $0, is then given by the Grahame equati0n.l For a 1:l electrolyte this is
0
0 0 0
0
0
O0O0 0 0 0
0
-300.
-605
charge
0
0
014
- I40f - 160.
*; Q
p a r t i a l charge
0
012
-280.
0
0
0n e g a t i v e p a r t i a l
a
01
Q)
0
0
0
0
0
0
0
0
0
0
e
008
n e x p e r im e n t a l
Y
0 positive
006
Figure 5. Surface potential vs ionic concentration for solutions of KC1 in water. The predicted values are derived by using a surface potential jump value of 25 mV. The experimental values are taken from Borazio et al.24
z
I o
004
concentration, M
Figure 3. Potential vs distance from the liquid/vapor interface. The potential dies off much more rapidly for the model in Figure 2b, which assumes that the surface potential jump arises from a monolayer of oriented dipoles which is not penetrated by ions.
0
002
a2 = 2000eeokTNo(saltconcentration,
b
Figure 4. Discrete lattice model. The potential for the discrete lattice of ions shown in part a is given by eq 6. The manner is which a monolayer of dipoles may be represented by the discrete lattice model is shown in part b.
charges separated from each other by a fixed distance, d, the field (E,) is given by
E, = a/2eeo[l + (2(COS (2ax/d) + cos (27ry/d)) x exp(-2~z/d)+ . .I (6) where (T is the surface charge density and z is the distance from the surface. The effect of a sheet of dipoles can be modeled by two infinite lattices of discrete charges oriented spatially to simulate a layer of oriented dipoles (Figure 4b). The potential for this configuration dies to almost zero within 2 A for the simple sheet of oriented dipoles (Figure 3). An alternate model, which is similar to that associated with the Grahame equation,l that differentiates between the surface potential and surface potential jump has been adopted in this paper. It has the following properties (Figure 2b):
M) X (sinh ($o/kT) - 2) (7) where a is the surface charge density, e is the dielectric constant of the medium, T is the temperature in K, NOis Avogadro's number, and k is the Boltzmann constant. This equation may be fitted to the experimental values for $ reported by Borazio, M ~ T i g u e , ~ and 3 , ~ ~co-workers for solutions of various electrolytes at varying concentrations to give a constant surface charge density, t ~ . When this parameter is related to an Helmholtz model of oriented surface dipoles, the associated value for x can be calculated by using eq 3. A value of 25 mV was calculated in this way for water and approximately -6 mV for methanol (Figures 5 and 6). These values are identical with those calculated from the molecular distributions predicted from molecular dynamics simulations (to within the experimental error of the molecular dynamic method) if one considers the effect of the relatively high molecular density on the electrostatic field.12 When these values were used in eq 4 to give the dipolar contribution to the surface free energy and these free energy values were added to the van der Waals contribution, the surface free energies of methanol and water were predicted within experimental error (Table I).
1234 Langmuir, Vol. 7, No.6,1991 74
721
N
-
oexperimenfal
Xcalculated
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Duncan-Hewitt
,
k
t
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$ 66. 64: Y
al 6 2 * 60.
x
L
. 290
300
, 310
,
.
, 320
, 330
,
,
.
340
, 350
,
, 360
.
, 370
,
380
temperature, K
Figure 7. Surface tension vs temperature for pure water. The experimental values are taken from Hodgman et al.; and the predicted values are calculated from the sum of the van der Waals contribution*(taking the variation of the dielectric constant and refractive index into account) and the dipolar contribution. The values for the dipolar contribution are calculated from the simulation data of Matsumoto and Kataoka,16 assuming the dielectric constant assumes its bulk value at the Gibbs surface (95% confidence intervals shown).
The surface free energy, surface entropy, dielectric constant, index of refraction, x, and density vary with temperature. The variation of the dielectric constant opposes the effect of the other variables with respect to prediction of the surface free energy. Nevertheless, the temperature dependence of the surface free energy6 is predicted from the surface potential jump approach to within experimental error (Figure 7). The calculation can also be performed for acetonitrile, although its surface potential jump has not been estimated accurately (100 f 60 mVZ7). Using an am1 model of the molecule, with the molecular parameters shown in Table I and an estimated van der Waals contribution of 18 mJ (27) Case, B.;Hush, N.S.Parsons, R. J. Electroanal. Chem. 1965,10, 360.
m-2 to the total surface free energy, the surface potential jump should actually be about 23 mV, with the dipole oriented at about 21" from the surface to give the correct surface free energy of 29.3 mJ m-z at 20 "C. This prediction awaits experimental verification. This paper does not describe the first attempt to predict liquid surface free energies from microscopic considerations. Davis28 used a statistical mechanical approach to assesses the contribution of dipolar forces to the surface free energy. These calculations were later modified by Sullivan29 and Fulton.so Unfortunately the calculation requires an estimate of R,, a cutoff distance for anisotropic interactions (i.e., dipole effects) which is unknown. Their final conclusion, that 39 mJ m-2 of the surface free energy can be attributed to anisotropic (orientational) effects, is uncertain as a result. These very simple calculations yield unequivocal predictions, provide some new and intuitively pleasing insight into the nature of the surface free energy of pure liquids, and provide some compelling evidence that surface dipole orientation effects should be considered seriously. It might behoove us to reconsider our evaluation of the relative importance of short-range forces in interfacial phenomena. Finally, it may be feasible to extend this type of calculation to predict the surface free energies of solids which are intrinsically immeasurable. Acknowledgment. I thank Professor Michael Thompson and Walter Dorn from the Department of Chemistry, University of Toronto, for many useful discussions. Financial support from the Faculty of Pharmacy, University of Toronto, and the Medical Research Council of Canada is gratefully acknowledged. Registry No. HzO, 7732-18-5; MeOH, 67-56-1; KC1, 744740-7;acetonitrile,75-05-8;hexanoicacid, 142-62-1;1-octanol,11187-5; 1-pentanol, 71-41-0; octanoic acid, 124-07-2. (28) Davis, H.T.J. Chem. Phys. 1975,62,412. (29) Sullivan, D.J. Chem. Phys. 1975,63,3684. (30)Fulton, R. L. J . Chem. Phys. 1976,64,1857.
