van der Waals forces in oil/water systems

van der Waals Forces in Oil/Water Systems

~[. REQUENA, 1 D. E. BROOKS, 2 AND D. A. HAYDON

Physiological Laboratory, Downing Street, Cambridge, United Kingdom

Received June 1, 1976; accepted July 21, 1976

Free energies of formation of "black" lipid films have been determined from their contact angles. In these films the repulsive forces are of such short range that i t is possible to estimate relatively accurately that par t of the free-energy change that originates from the van der Waals forces. I t is shown that if the van der Waals free energies are interpreted on the assumption that the films are isotropic layers of hydrocarbon bounded by semi-infinite aqueous phases, the Hamaker coefficients vary considerably from one film to another, contrary to the predictions of the Lifshitz theory. If, on the other hand, it is recognized that the hydrocarbon region of a film is, in fact, a layered structure and that there are differences, albeit small, between the dielectric properties of the chains of the lipid stabilizer and the alkane solvent (some of which is retained in the film), the conflict between theory and experiment is largely removed. Thus, Hamaker coefficients calculated from the Lifshitz theory for multilayered systems agree well in nearly all instances with the corresponding experimental coefficients.

INTRODUCTION

The direct measurement of van der Waals forces in liquid/liquid systems presents con- siderable technical difficulties. The methods so successfully developed by Derjaguin, Abriko- sova, and Lifshitz (1) and others (2-5) to study the interaction between solids in gases may perhaps be used for solids in liquids, but it is less obvious that they will succeed in purely liquid systems. For the present, therefore, it is of interest to consider less direct approaches, such as the examination of thin liquid films. A fundamental objection to this kind of approach is that it is usually very difficult to make adequate allowance for the influence of forces other than those of van der Waals. There are nevertheless certain types of systems in which these additional forces are of such short range relative to the van der Waals forces that they do not need to be known with any great accuracy. One such system is the

1Present address: Centro de Biofisica, Insfituto Venezolano de Investigaciones Cientificas, Caracas, Venezuela.

2 Present address: Department of Pathology, Uni- versity of British Columbia, Vancouver 8, Canada.

thin lipid film formed in aqueous solution (6). In this instance it has been shown that the contribution of the electrodynamic forces to the free energy of formation of the film may be estimated to within ca. 10% (7, 8).

The lipid films which have been investigated were formed from monoglycerides or phospholipids in alkane solution. Their drainage (under aqueous solutions) is .comparable to that of aqueous soap films and consists of the flow of a dilute solution of the lipid in the alkane from between monolayers of the lipid adsorbed (or spread) at oil/water interfaces (6). The thinning process ceases when the chains of the juxtaposed adsorbed monolayers interact. The final equilibrium films have thicknesses of the order of twice the chain length of the lipid used, the precise thickness depending on the alkane solvent (6).

The change, ~XA*, in the Helmholtz free energy accompanying the thinning of unit area of a film is given by (6, 9, 10)

AA* = (¢ -- 27), El3

where ~ is the tension of the film and 7 the

26

Journal of Colloid and Interface Science, Vol. 58, No. 1, January 1977 Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

VAN DER WAALS FORCES 27

tension of the adjacent bulk phase interfaces. To a good approximation, Eq. [1] may be rewritten in terms of the contact angle 0, where 0 is defined by

2"r(cos 0 -- 1) = ~ -- 2% [-2]

Equation [1] thus becomes

AA* = 2~(cos 0 -- 1). [-3]

Implicit in the use of this equation is the assumption that the van der Waals and other forces acting across the thin film cease abruptly at a (hypothetical) contact line between the film and the bulk lipid solution. That there is, in fact, a transition region and that this, in principle, affects the validity of Eq. [3] is well recognized (10). I t will be sho~m in a

later section, however, that the resulting error in ~A* is, in the present systems, negligible.

The only components of AA* which seem at all likely to be important are those arising from the van der Waals (2~Avw), electrical double layer (zXAo), and steric (~XA~) interaction free energies.

Thus

AA* = 2~Avw + AAo + 2~A~. [4]

I t will be argued below that zXAo and &A~ are small compared with zXAvw.

EXPERIMENTAL DATA

For the calculation of the free energy of thinning of the films it is necessary to know the film area, the interfacial tension of the bulk oil

TABLE I

The Film Thickness, Interfacial Tension, Contact Angle, and Free Energy of Thinning for Some Black Lipid Film Systems at 20°C ~

System Thickness of Interfacial cos 0 Free energy of forma- hydrocarbon tension, "r tion per unit area,

region, (dyn cm 1) AA* X l0 S (ergs cm-~) h ((X) ~- 2%)

Monoolein q- n-heptane 47.1 4.70 Monoolein q- n-octane 47.8 4.38 Monoolein -]- n-decane 48.1 3.84 Monoolein q- n-dodecane 45.3 3.45 Monoolein + n-tetradecane 40.7 3.04 Monoolein q- n-pentadecane 36.6 2.88 Monoolein -k n-hexadecane 32.7 2.51 Monoolein -}- cis-5-decene 40.5 12.75 Monomyristolein q- n-decane 44.4 1.68 Monopalmitolein + n-decane 46.3 2.70 Monoeicosenoin q- n-decane 53.1 4.26 Monoerucin q- n-decane 57.0 11.2 4- 1.0 Mononervonin q- n-decane 64.6 12.6 ± 1.0

Monolinolein -k n-decane 48.5 3.30 Monolinolenin -k n-decane 35.9 2.86 Monolinolein + n-hexadecane 30.2 2.36 Monooleyl glyceryl ether

+ n-hexadecane 35.4 3.74 Monooleyl glyceryl ether

+ n-decane 48.9 4.89 1,2 dioleyl phosphatidyl choline

+ n-decane 48.3 3.18 Brain phosphatidyl serine

+ n-decane 50.2 2.03

0.999256 ±0.000007 --6.994-0.14 0.999377 ±0.000005 - -5 .46±0 .10 0.999415 ±0.000004 --4.49-4-0.09 0.99940(1) 4-0.00002 - -4 .13±0 .19 0.99913(6) 4-0.00002 - -5 .25±0 .20 0.99855(2) 4-0.00002 - -8 .34±0 .26 0.995503 ±0.000053 --22.574-0.72 0.999712 4-0.000006 - -7 .34±0 .18 0.998632 4-0,000026 - -4 .60±0.22 0.999193 ±0.000018 - -4 .36±0 .18 0.999586 +0.000004 --3.534-0.07 0.999832 4.0.000005 - -3 .76±0 .45 0,999902 ±0.000002 - -2 .46±0 .32

0.999207 ::t:0.000006 - -5 .23±0 .05 0.996402 ±0.000065 --10.004-0.75 0.991079 4-0.000050 --14.48±0.61

0.997869 4-0.000025 --15.944-0.40

0.999521 4-0.000006 --4.684-0.11

0.999228 4-0.00001 - -4 .90±0 .30

0.999036 4-0.000045 - -3 .91±0 .36

, The aqueous solution was 0.1 M NaC1.

Journal of Colloid and fnterface Science, Vol. 58, No. i, January 1977

28 REQUENA, BR00KS AND HAYDON

I f 19 J J ic

hc

I f

I ql I

W W q t

~ T

I I I I t 9 I I

w

Models i Gnd ~ Model II--[

FIG. 1. Models for the black lipid film. In Model I the film is assumed to be simply a layer of liquid hydrocarbon (hc) sandwiched between two aqueous phases (w). Model II takes account of the fact that there are polar groups (g) (glyceryl esters in the present systems) between the hydrocarbon and the aqueous regions. Model III is similar to Model II except in that the hydrocarbon layer is assumed to be stratified into lipid chain (1) and solvent (s) regions. In Models I and II the whole of the hydrocarbon layer is regarded as displaceab]e whereas in Model III only the central solvent layer can vary in thickness.

and aqueous phases with which the film is in equilibrium, and the contact angle. In order to compare the free energies with those predicted theoretically, it is also necessary to know the thickness of the films. The determination of the film area was a trivial matter and the measurement of the tension was achieved by two independent methods, all orthodox drop- volume technique (11) and by the application of the Lippmann equation (12). For systems in which both methods were used the agreement between the two results was to within the experimental error (12). The determination of the contact angle and the film thickness require more detailed description.

The contact angle. On viewing either the Plateau-Gibbs border, or a lens of the lipid phase trapped in the black film in reflected monochromatic light, fringes can be seen from which the contours of the interfaces may be calculated (7, 8). For both the border and the lens it is possible, to extrapolate to the hypothetical contact llne and so obtain the contact angle. The two methods give the same angle in spite of the difference in pressure between the lens and the border. Estimates of the pressure difference and of the van der Waals forces, however, show that this was to be expected. The question also arises as to whether the extrapolated angle can legitimately be used in Eqs. [-2-] and [-3-]. This can be answered particularly easily in the case of the lens. The

interference fringes show that to within 1 ~m of their edges the lenses, which are some 100 #m in diameter, consist very precisely of two identical segments of a sphere, one on either side of the plane of the black film. At 1 ~m from the edge, the angle of the surface with the plane of the film is within 2% of O, the angle obtained by extrapolation to the contact line. At the same point, the lens is between 500 and t000 A in thickness and the van der Waals forces should be negligibly small. The error in zXA* through using Eq. [3-] should therefore be, at most, about 4%.

The film thickness. For lipid films in aqueous media the film thickness is, in most instances, more readily and accurately accessible from electrical capacitance than from optical reflec- tance measurements (6). The electrical method yields the thickness of the hydrocarbon region only, however, and that of the polar group layers has to be estimated from the consideration of molecular models. Fortunately, the nature and dimensions of the polar group seem, from experiment, to be of only slight importance in the interpretation of the free energies (see below). Furthermore, since only alkyl chain molecules are involved, the dielectric constant, which is needed to calculate the thickness from the capacitance, is very insensitive as to which lipid and alkane solvent are used to form the film. Confirmation of the validity of the electrical method of thickness

Journal of Colloid and Interface Science, Vol. 58, No. i, January 1977


measurement has come from the examination of "solventless" phospholipid membranes, where capacitance data, and X-ray diffraction studies of the stacked membranes in liquid crystalline material, have given very similar results (13, 14).

Experimental data are displayed in Table I. The film capacitances and compositions from which the thicknesses were calculated have been given elsewhere (8, 15).

D I S C U S S I O N

The Calculation of the van der Waals Component of the Free Energy of Thinning

In order to determine AA~w from Eq. [-4~ it is necessary either to know AA~ and AA~ or to be able to show that these quantities may be neglected. There are several reasons for thinking that AAo is very small, one being that neither the adsorption of ions to the film, nor large variations in the ionic composition of the aqueous solutions appear to have appreciable effects on AA* (8, 15). A more useful demon- stration of the likely magnitudes of AAo and AA~ comes from the recognition that they are both "repulsive" terms and can be studied by

compressing the films under applied electrical potentials. A detailed description of such experiments and their interpretation is too long to be included here, but the outcome for the two systems that were fully examined (monoolein -}- n-decane and monoolein -t- n- hexadecane) was that AAo-t-AA~ amounted to approximately 9% of AA* (8). The compressibility, and other properties, of the remaining systems were largely intermediate to those mentioned above and it has been assumed that a similar relationship between the repulsive and total free energy exists also in these instances. Except in Fig. 3, the difference between AAvw and AA* will be ignored, so that it should be borne in mind that, elsewhere, the absolute values of the experimental Hamaker coefficients could be a few percent low.

Three models were explored in interpreting the free energies.

The Three-Layer Model

The experimental Hamaker coefficients. The essential features of the three-layer model are shown in Fig. 1. The film is considered to be

9 × I O - - c

u

5 -

30 40 50 60 70 Hydrocarbon thickness (~)

FIG. 2. Hamaker coefficients as a function of the hydrocarbon thickness of the lipid film. The experimental values are indicated by the points and were calculated from the free energies using Eq. [-5-]. No correction for the repulsive forces has been attempted, so that the true experimental values should be ca. 9% higher. The theoretical Hamaker coefficients were calculated assuming Model I (Fig. 1) and all fell within the range indicated by the dashed lines. If Model II had been used, the values would have been fairly consistently ca. 10% lower.

J o u r n a l o f Co l lo id a n d In l e r face Sc ience , Vol. 58, No. 1, January 1977

30 REQUENA, BROOKS AND HAYDON

simply a layer of liquid hydrocarbon between two semi-infinite aqueous phases. The polar groups of the lipids are disregarded because they constitute a layer which is thin relative to the hydrocarbon layer and because they are interspersed by and, in their dielectric properties, similar to water. No distinction is made between the chains of the hydrocarbon and of the alkane solvent which remains in the film, and hence the formation of the film amounts merely to the drainage of a layer of bulk aliphatic hydrocarbon from between the two aqueous solutions. The van der Waals free energy may then be written (16),

AA* ~ A,w - --A/12~rh ~, E5]

where A is tile Hamaker coefficient. In this equation the Hamaker coefficient should be independent of the film thickness, h. However, a plot of the data (Fig. 2) shows that this is not so. Although A appears to approach a constant value at large h, it rises increasingly rapidly as h decreases and reaches some four times this value in the thinnest film. The explanation of the nonconstancy of A will be considered below, but first it is of interest to compare the present data with Hamaker coefficients calculated from Lifshitz theory.

The theoretical Hamaker coe ficients. As has been pointed out by Ninham and Parsegian (17), the van der Waals forces in the present systems are unlikely to be appreciably re- tarded. For the three-layer model (Fig. 1), Ninham and Parsegian (17) give the following expression for the Hamaker coefficient:

"f0" A = --~kT Y'/ x in (1 -- &~-w2e-~)dx, n = 0

[6] where

~o(i~.) - ~ ( i ~ )

~o(~.) + ~,~(~~) and

~,~ = (27rkT/h)n. [-8-]

In these expressions ~, and eho are the dielectric permeabilities of water and hydrocarbon, respectively, and both are functions of the

Journal of Colloid and Interface Science, Vol. 58, No. 1, January

imaginary frequency o~ ( = i ~ ) . 27rh is Planck's constant and n is an integer. In the summation in Eq. E6-] the prime indicates that the term for n = 0 should be multiplied by ½.

The dielectric permeabilities may be written in the form

Cm~ Ci~

1 + ~/~mw 1 + (~/~i~) 2

C u r + ~ . [9]

+ (~ /~)~

The assignment of values to the constants for hydrocarbon/water systems has been discussed generally by Ninham and Parsegian (17) and Gingell and Parsegian (18) and, for the present thin film systems by Brooks et al. (19).

The calculated Hamaker coefficients vary slightly over the range of systems in Table I because the composition of the hydrocarbon in the film varies. But this effect is very small and since, from tile nature of the model, the theoretical A cannot be a function of h, the results all lie in a narrow band, as shown in Fig. 2. I t is notable that there is excellent agreement between the theoretical Hamaker coefficients and the experimental values for the thicker films. In absolute magnitude, the coefficients are not much greater than tile zero frequency term in Eq. F6~, i.e., approximately 3kT/4. I t is for this reason, and because the films are relatively thin, that retardation can be disregarded.

Despite the apparent success of the theory as applied to the thicker films, there is no way of accounting for the variation in A with h, and it is necessary to examine more carefully the validity of the simple three-layer model. An obvious deficiency is the neglect of the polar groups of the lipids. I t is possible that tile interactions of these groups with similar groups, and with water, on the far side of the film is significant and, that as the films become thinner, these interactions become dominant. With this in mind, films were examined in which the head groups differed. The last three sets of data in Table I are for phospholipids

1977


and a glyceryI ether. As can be seen, however,

the flee energies for these films are very

similar to those for monoglyceride films of comparable thickness. Further evidence for the unimportance of the polar groups may be found in the results for monoglyceride films formed in glycerol (15). In such systems the distinction between the polar groups and the solvent was largely removed, but the Hamaker coefficient still increased markedly as the film thickness decreased. Finally, calculations of the theoretical Hamaker coefficient were carried out on the basis of Model II of Fig. 1, in which the polar groups are considered to constitute two additional homogeneous layers. The equations appropriate to this model have been derived by Ninham and Parsegian (20) and are

A = - - a k T ~ ' x ln 1 n=3 d 0

F &'~-~ + zX~ -~'e-~/h 7 2 l . . . . . . e - x L1 + j,t., ElO]

where

and

aho_: = [ 1 1 ] ~hc(/#n) -J- eg(i~n )

~ - ~ = . 1-12] ~=(~) + ~w(#~)

In these expressions h and c are the thicknesses of the hydrocarbon and polar group layers, respectively, and eg is the dielectric permeability of the polar groups. The polar group layer was assumed to be made up of pure glycerol and the spectroscopic data were estimated as described in an earlier paper (19). The resulting Hamaker coefficients were ca. 10% smaller than those for the three-layer model (I) but showed a very similar lack of variation with film thickness. They were also insensitive to uncertainties in the spectroscopic data for glycerol.

I t must be concluded that the major part of the variation of the Hamaker coefficient with

film thickness is unlikely to originate from the

presence of the polar groups of the lipids. The

three-layer model could, however, be more seriously inadequate in the way in which it depicts the hydrocarbon region. Notwith- standing the fact that this region consists of two distinct species, lipid chains and alkane solvent, Model I presupposes a homogeneous layer of the appropriate average composition. There are reasons, discussed in the next section, for thinking that this model is too simple.

The Seven-Layer Model

I t has been shown elsewhere (21) from consideration of the compressibility of the lipid films, that the lipid chains and the solvent are almost certainly not perfectly mixed. In- stead, the lipid chains appear to be concen- trated at the edges and the solvent in the middle of the films. The precise state of affairs seems to depend strongly on the chain length of the alkane used. Consider the lipid mono- otein. In decane and shorter chain alkanes the film thicknesses are close to twice the extended length of the glyceride chains. The relatively high compressibility of these films is, however, consistent with the idea that only a very small proportion of the glyceride chains reach the middle of the film at any one time (21). The large majority of the chains thus appear to spend most of their time packed close to the sides while the central region of the film consists largely of alkane solvent. In other words, the decane does not penetrate completely into the glyceride chain region. When hexadecane is used, this lack of penetration is still more pronounced, to the extent that in this instance the tendency of the lipid chains to be fully extended is so slight that the film thickness is well under its maximum value, and the amount of solvent retained in the film is proportion- ately reduced.

From the above consideration it seems that it would be reasonable to consider a model in which the films thin through the drainage of the bulk lipid solution from between two close-

Journal of Colloid and Interface Science, Vol. 58, No. 1, January 1977


packed arrays of lipid chains. This model is the opposite extreme of the three-layer model (I) in that it assumes no mixing of the solvent with the lipid chains, while Model I assumes complete mixing. Obviously a layer of nearly pure solvent in the middle of the film is not consistent with the notion that the film is stabilized by the interaction of the lipid chains but, as an approximation to the internal structure of the film, this model is not obviously less satisfactory than Model I. In the calculation of the effective Hamaker coefficient from Eq. [-5] the distance variable is now a (Fig. 1, Model III). This may be found from the composition of the film (8, 15). Thus the value of a is proportional to the volume fraction of alkane solvent present. If ~ is the volume fraction of the lipid chains,

and

2b = ~h [131

a = h - - 2 b . [14]

The parameter b is the thickness of the close- packed lipid chains (Fig. 1) and is found from a knowledge of the adsorption of the lipid and an assumption as to the partial molar volumes

of the lipid chains in the film. Values of ¢ and a for some of the Systems of Table I are shown in Table 1I.

The experimental t tamaker coefficients. As can be seen from Table II, the magnitudes of the Hamaker coefficients according to Model III are considerably less than those for Model I. This is merely because the distance a is always less than h. Thus

A m oxp = A~ii~°XP(aVh2). B5~

Physically, the smaller A arises from a change in the reference energy state, i.e., in the in- finitely thick film. Instead of being directly in contact with the displaceable hydrocarbon, as in Models I or II, the polar phases are now always screened by the layers of close-packed lipid chains. For comparable changes in the distance variable, therefore, the changes in the van der Waals interactions as the two polar phases approach each other are less in Model III than in Models I or II.

The theoretical Hamaker coej~cienls. The appropriate Lifshitz equations for the seven- layer model (III) may be derived from a relativistic expression given by Parsegian and

TABLE II

Theoretical and Experimental Hamaker Coefficients for the Seven-Layer Model (III)

Volume fraction q~ a A "xp X 10~ A ~he°r X 101~ of lipid chains (~_) (ergs) (ergs)

Monoolein q- n-heptane Monoolein q- n-octane Monoolein q- n-decane Monoolein q- n-dodecane Monoolein q- n-tetradecane Monoolein -}- n-pentadecane Monoolein q- n-hexadecane Monoolein -I- cis-5-decene

Monomyristolein q- n-decane Monopalmitolein -]- n-decane Monolinolein q- n-decane Monolinolein q- n-hexadecane Monolinolenin -}- n-decane Monoeicosenoin q- n-decane Monoerucin q- n-decane Mononervonin -[- n-decane

0.52 22.6 13.5 9.8 0.51 23.4 10.9 9.7 0.51 23.6 9.4 9.5 0.54 21.0 6.9 8.5 0.60 16.0 5.1 6.9 0.67 12.0 4.5 5.2 0.74 8.5 6.2 3.7 0.60 16.2 7.3 7.0 0.42 25.8 11.5 12.8 0.47 24.5 9.9 10.9 0.49 24.7 12.0 10.5 0.79 6.3 6.4 3.1 0.65 12.6 12.3 7.1 0.51 26.0 9.0 9.5 0.52 27.4 10.6 9.2 0.51 31.7 9.3 9.5

Journal of Colloid and Interface Science, Vol. 58, No. 1. January 1977


15

O_ ×

IO ._u

:E 5

09

0

0 5 I0 15 I I I

I I I 5 I0 15 ~5

Experimental Harnokercoef f i c ien tx lO (erq)

20 I

I 20

Fie.. 3. A comparison of experimental and theoretical Hamaker coefficients according to Model III (Fig. 1). The full and dashed lines represent the equality of the theoretical coefficients with, respectively, the experimental values without (lower scale) and with (upper scale) a 9% correction for repulsion.

Ninham (22). The Hamaker coemcient is then

A = - - a k T ~7_,' x l n 1 n~0 a 0

where

- - ~ Z~s--I 3E Ae--xb/a]2 e z}

Al_g -~- Ag_we -~d'~

[16]

A = [17-1 1 + Al_gAg_~,e -x~/~ '

and As-1 and Al_g are given by relationships similar to those of Eqs. [7-1, [-11-], and El2]. The differences between the dielectric permeabilities of the lipid chain and solvent layers are obviously very small but may be estimated as shown previously (15, 19). The Hamaker coefficients are listed in Table II. They still originate largely from the zero frequency terms, but they now vary from one system to another considerably more than did the theoretical values for Model I. For complete- ness, the contributions of the polar group layers have been included but, as for Models I and II, they affect the results by at most a few percent.

The experimental and theoretical Hamaker coefficients for Model I I [ are compared graphically in Fig. 3. I t is immediately obvious that this model is more successful than I or II in that the thinner films no longer appear to be anomalous. In fact, for more than half of the systems examined the agreement is to within 20% and in no instance is there a discrepancy of more than about a factor of 2. Moreover, such discrepancies as do remain may be qualitatively accounted for by recognizing that the true condition of the fihns will be intermediate between that assumed in the Models I (or II) and III, i.e., there will be some intermixing of lipid chains and solvent. This point is illustrated in Fig. 4 where, in the monoolein-heptane system, results are shown for various degrees of intermixing. In order to obtain these curves it has been sup- posed that given amounts of the solvent from the central region have been transferred successively to the lipid chain regions, the homogeneity of the latter being preserved and the overall dimensions and composition of the film remaining constant. The experimental Hamaker coefficient decreases simply because, as the solvent layer is made thinner (at con-

Journal of Colloid and Interface Science, VoL 58, No. 1, January 1977


15-

i '° ~s

C 0-1 0-2 03 04 Volume fraction of solvent (s) in lipid chain region

I 05

FIO. 4. The effect of intermixing solvent and lipid chains on the Hamaker coefficients according to Model n I . The film is of monoolein and n-heptane, and the abscissa indicates the amount of solvent assumed to be present in the chain region. The values of A at zero mixing are thus as given in Table n . The arrow indicates the point at which all the solvent has been inter- mixed and the distance a reduced to zero. O, experimental; and e , theoretical Hamaker coefficients.

stant free energy) the distance variable a decreases. The theoretical Hamaker coefficient changes because the transfer of the solvent alters the thickness and dielectric permeability of the screening layer of lipid chains. The fact that the two curves intersect is encouraging in that it suggests that with a more detailed knowledge of the film structure it should be possible to improve still further the agreement between the experimental and theoretical Hamaker coefficients.

CONCLUSIONS

Two of the more interesting findings which have emerged from the above investigation are

(1) that despite the very close similarity of the chains of the stabilizing lipids to the alkane solvent, the partial segregation of the two species in a thin film can be of crucial

importance for the calculation of the van der Waals forces; and

(2) that the agreement between the theoretical (Lifshitz) and experimental Hamaker coefficients is exceedingly good.

Taken together these two conclusions sug- gest that in the thicker lipid films, the interactions are predominantly those of the aqueous phases across an effectively homogeneous layer of aliphatic hydrocarbon whereas, in the thinner films, it is the interaction of the screening layers of lipid chains across the solvent layer which becomes predominant. This last ob- servation has obvious implications for the understanding of thin liquid films generally.

REFERENCES

1. DERJAOUIN, B. V., ABRIKOSOVA, I. I., AND LIFSHITZ, E. M., Quart. Rev. Chem. Sac. 10, 295 (1956).

2. KITCHENER, .[. A., AND PROSSER, A. P., Proc. Roy. Sac. London Ser. A 242, 403 (1957).

3. BLACK, W., DE JONOit, J. G. V., OVERBEEK, J. TI~I. G., AND SPARNAAY, M. ]., Trans. Faraday Sac. 56, 1597 (1960).

4. ROUWELER, G. C. J., AND OVERBEEK, ]. TH. G., Trans. Faraday Sac. 67, 2117 (1971).

5. ISRAELACHVILI, J. N., AND TABOR, D., Proc. Roy. Sac. London Ser. A 331, 19 (1972).

6. FETTIPLACE, R., GORDON, L. G. M., HLADKY, S. B., REQUENA, J., ZINGSIIEIM, H. P., AND HAYDON~ D. A., in "Methods in Membrane Biology" (E. D. Korn, Ed.), Vol. 4, p. 1. Plenum Press, New York, 1974.

7. HAYDON, D. A., AND TAYLOR, J. L., Nature (Lon- don) 217, 739 (1968).

8. REQUENA, J., BILLETY, D. F., AND HAYDON, D. A., Proc. Roy. Sac. London Ser. A 34"/, 141 (1975).

9. SC~IELUI)I,:O, A., Advan. Colloid Interface Sci. 1, 391 (1976).

10. DE FEIJTER, J. A., AND VRIJ, A., J. Electroanat. Chem. 37, 9 (1972).

11. AVEYARD, R., AND HAYDON, D. A., Trans. Faraday Sac. 61, 2255 (1965).

12. REQUENA, J., AND HAYDON, D. A., J. Colloid Inter- face Sci. 51, 315 (1975).

13. HAYDON, D. A., Ann, N. Y. Acad. Sci. 264, 1 (1975). 14. BENZ, R., FROHLICH, O., L•UOER, P., AND MONTAL,

M., Biochim. Biophys. Acta 394, 323 (1975). 15. REQUENA, J., AND I{AYDON, D. A., Proc. ROy. Sac.

London Set. A. 347, 161 (1975). 16. PARSEOIAN, V. A., Ann. Rev. Biophys. Bioeng. 2,

221 (1973).

Journal of Colloid and Interface Science, Vol. 58, No. I, January 1977


17. NINHAM, B. W., AND PARSEGIAN, V. A., Biophys. Y. 10, 646 (1970).

18. GINGELL, D., AND PARSEGIAN*, V. A., J. Theor. Biol. 36, 41 (1972).

19. BROOKS, D. E., LEVINE, x~. K., REQUENA, J., AND HAYDON, D. A., Proc. Roy. Soc. London Ser. A 347, 179 (1975).

20. NINtIAM, B. W., AND PARSEGIAN, V. A., Y. Chem. Phys. 52, 4578 (1970).

21. ANDREWS, D. M., MANEV, E. D., AND HAYDON, D. A., Spec. Discuss. Faraday Soc. No. 1, 46 (1970).

22. PARSEGIAN, V. A., AND ~INItA]~, B. W., J. Theor. Biol. 38, 101 (1973).

Journal of Colloid and Interface Science, Vol. 58, No, 1, January !977

van der Waals forces in oil/water systems

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