Langmuir 1990,6, 873-876
873
Hydration or Steric Forces between Amphiphilic Surfaces? Jacob N. Israelachvili**+and Hdkan Wennerstromt Department of Chemical & Nuclear Engineering, Materials Department, and Institute of Theoretical Physics, University of California, Santa Barbara, California 93106 Received December 14, 1989 The strongly repulsive short-range force between amphiphilicsurfaces has, since Langmuir, been associated with how these surfaces modify the local water structure. We consider the results of both old and new experiments and conclude that these so-called "hydration" forces are not due to water structure. Instead, they originate from the entropic (osmotic) repulsion of molecular groups that are thermally excited to protrude from these fluid-like surfaces. Genuine hydration effects play a minor role, mainly in determining the hydrated size of the protruding groups. Our conclusions resolve many inconsistencies and observations that were not reconcilable with the hydration model.
Introduction
For many years now, strongly repulsive short-range forces have been measured between bilayer and other amphiphilic surfaces in water.'" The forces have a typical range of 1-3 nm, below which they can dominate over the van der Waals and electrostatic double-layer forces. These forces do not appear to have a simple electrostatic origin since they also occur between uncharged bilayers. The most accurate measurements of these forces have been done between lecithin and various other uncharged bilayers in aqueous solutions,z~7where the repulsion is found to decay exponentially with distance, D, according to
F = +Ce-D/X per unit area (1) where the decay length, A, is close to 0.2 nm-a value that appears to be strikingly close to the size of a water molecule. This fact, fortified with some early theoretical considerations? gave support to the idea that this force is due to water structure, and it is now commonly referred to as the "hydration" force.g Hydration forces were originally proposed by Langmuir and others" to account for the repulsion and swelling of amphiphilic and colloidal surfaces even when there is no electrostatic repulsion between them. These forces are believed to arise whenever surfaces have a strong affinity for water (i.e., are hydrophilic), which is in turn related to the way surfaces induce order in or alter the structure of the adjacent water molecules. Department of Chemical & Nuclear Engineering. Institute of Theoretical Physics. Permanent addrees: Div. Physical Chemistry 1, Chemical Center, P.O. Box 124, 5-22100 Lund, Sweden. (1) Clunie, J. S.;Goodman, J. F.; Symons, P. C. Nature 1967, 216, t
1203. (2) LeNeveu, D. M.; Rand, R. P.; Parsegian, V. A. Nature 1976,259, 601. Pamegian, V. A.; Fuller, N.; Rand, R. P. R o c . Natl. Acad. Sci. U.S.A. 1979, 76,2750. (3) Lis, L. J.; McAlister, M.; Fuller, N.; Rand, R. P.; Parsegian, V. A. Biophys. J . 1982, 37, 657. (4) Marra, J.; Israelachvili, J. N. Biochemistry 1986,24, 4608. (5) Israelachvili, J. N. Chem. Scripta 1986,25,7. (6) McIntosh, T. J.; Simon, S.A. Biochemistry 1986,25,4058. (7) Rand, R. P.; Paraegian, V. A. Biochim. Biophys. Acta 1989,988, 351. (8)Marcelja, S.;Radic, N. Chem. Phys. Lett. 1976, 42, 129. Cruen, D. W. R.; Marcelja, S.J. Chem. SOC.,Faraday Tram 2 1983, 79,225. (9) Some authors prefer other terms,such as 'structural" or 'solva-
tion" force. (10) Langmuir, I. J. Chem. Phys. 1938,6, 873. Jordine, E. St. A. J. Colloid Interface Sci. 1973, 45, 435.
Earl theoretical work on the subject by Marcelja' and othersrl tended to confirm the existence of an exponentially repulsive force arising from the electric "polarization" of water molecules by surfaces. The decay length was some correlation length characteristic for water. I t was not easy to derive theoretically and had to be assumed or fitted, though it seemed conceivable that it could be close to the size of water molecules, viz., about 0.2 nm, as had been measured. Unfortunately, a more rigorous theoretical analysis using molecular dynamics simulations" failed to predict the expected monotonicallydecaying force. Instead, with surfaces modeled on lecithin and mica, only decaying oscillatory profiles were obtained. "Oscillatory" forces had previously been predicted to arise from solvent structuring effects between any two solid surfaces,l' and they have been extensively measured between smooth, rigid surfaces across water and other liquids." These oscillatory solvation forces are well-understoodtheoretically both for simple liquids and water." Could the monotonically repulsive hydration force between bilayers be a smearedout oscillatory force, due to the thermal motion and "roughness" of the mobile head-groups?'*' After all, in the computer simulation the lecithin head-groups were kept immobilized, whereas those of real surfaces are highly mobile. So far there has been no definitive answer to this, and the origin of these exponentially repulsive forces has remained a mystery. Experimentally, too, the rapidly accumulating data are producing a far from simple picture. Experiments with different surfactant and lipid bilayers in water have yielded values for X varying from less than 0.1 nm to above 0.3 nm.' With such a large range, X no longer appears to correlate with the size of the water molecule or with some obvious characteristic property of water.
Relation between Hydration Forces and Solvent Structure It was recently rep~rted'"'~that the forces between (11) Schiby, D.; Ruckenstein, E. Chem. Phys. Lett. 1983, 95, 435. Attard, P.; Batchelor, M. T. Chem. Phys. Lett. 1988,149,206. (12) Kjellander, R.; Marcelja, S. Chem. Scripta 1986, 25, 73. Kjellander, R.; Marcelja, S. Chem. Phys. Lett. 1985,120,393. (13) van Megen, W.; Snook, I. K. J. Chem. SOC.,Faraday Tram 2 1979, 75,1095; J. Chem. Phys. 1981, 74,1409. (14) Israelachvili,J. N.; McCuiggan, P. M. Science 1988,241, 795. (15) Henderson, D.; Lozada-Caeeou, M. J. Colloid Interface Sci. 1986,114,180. (16) Persson, P. K. T.; Bergenstihl, B. A. Biophys. J. 1986,47, 743.
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Letters
814 L a n g m u i r , Vol. 6, No. 4, 1990
lecithin bilayers in a variety of nonaqueous solvents are very similar to those measured in water, viz., exponentially repulsive with similar magnitudes and decay lengths. These results show that these -hvdration" forces should not be considered as being unique to water and question whether thev should even be considered as a solvation force. Other recent data do not appear to support the modified solvent-structure origin of these forces: (1) Recent measurements" of the forces between partially hydrophobic (thinned) bilayers have shown that attractive 'hydrophobic" forces and repulsive 'hydration" forces can exist simultaneously, each one dominating over a different distance regime. If, as is believed, each of these forces arises from water structure, it is difficult to imagine the simultaneous existence of both. The results suggest that at least one of these forces is not a true solvation force. (2) Much weaker or no hydration forces are seen between highly charged bilayer surface^'^ even though these might be expected to have equally strong or even stronger effects on water molecules than uncharged surfaces (such as lecithin). (3) Compressibility measurements of lecithin bilayers suggest that their thickness must be undergoing very large thermal fluctuations." These results exclude the possibility that the interhilayer forces act across pure water and suggest that a steric type of thermal fluctuation force must also exist.'.5 This is discussed more fully below. (4) The preexponential factor C in eq 1varies strongly (by 1-2 orders of magnitude) for surfaces that are chemically very similar, for example, lecithins and phosphatidylethanolamines in the gel, liquid-crystalline, and L, states!.7 This is in marked contrast to NMR measurements" of hydration and water structure, which reveal only minor differences. (5) Many surfactant bilayers in water do not swell a t all when in the solid-crystalline state" but do swell in the liquid-crystalline state. No good reason has ever been given to explain why more solvent structure develops in the less ordered liquid-crystalline state than in the more ordered one. LoneWavelength Thermal Fluctuation Forces: T h e Undulation Force Some insight into an alternative explanation for these forces comes from the "undulation" force theory of All elastic sheets, including fluid bilayers, have Helfri~h.2~ thermal undulations whose amplitude and density increase with increasing temperature, T,and decreasing bilayer bendine modulus.. K,." Helfrich showed that the force per u n s area between two such bilayers at a mean distance D apart (Figure 1, top) is repulsive and given by F
(kn2/KbD3. (17) McIntosh. T. J.; Magid, A. D.;Simon, S. A. Biochemistry 1989, 28,7904. (18) Helm. C. A,; Israelsehvili, J. N.; McGuiggan, P. M. Science 1989,246,919. (19)Marra, J. Biophys. J . 1986,50, 815: J. Phys. Chem. 1986. 90, 2145: l986.50,815. Cowley, A. C.; Fuller, N. L.; Rand, R. P.;Parser ian, V. A. Biochemistry 1978, 17, 3163 (contrary to what was claimed by the authors, the force between pure, negatively charged, phosphatidylglyeerol bilayers is quantitatively accounted for by the PoissonBoltzmann equation down to 1 nm, the smallest distance measured). (20) Lis. L. J.; MeAlister, M.;Fuller. N.; Rand. R. P.; Psrsegian, V. A. Biophys. J. 1982,37,667. (21) Seelig. J. Q. Re". Biophya. 1977. 10, 353. Lindblam, G.; Wennerstrom, H.:Arvidson, G. Int. J. Qumtum Chem. 1977,XII, Suppl. 0 161 _,
(22) Tiddy, G . J. T. Phys. Rep. 1980,57,1.
(23)Helfrich. W. 2.Naturforseh. 1978,330,305. Helfrich, W.;SerR. M. I1 Nuoua Cimento 1984,3D,137.
YUBS.
Figure 1. Schematic illustration of two types of thermal flue tuations associated with flexible, fluid interfaces or membranes such as bilayers and monolayers. (Top)Thermallyexcited undulations of membranes. These are long-wavelength waves describable in terms of continuum elasticity throry; they give rise to long-range undulotion forces. (Bottom) Thermally excited molecular protrusions (for example, a head-group attached to a hydrocarbon chain or even an isolated chain). These are molec ular-size surface fluctuations that must he described in terms of molecular theories; they give rise to short-rangesteric o r p r o trusion forces.
For a while it appeared that the repulsive undulation force might be the hydration force. However, the distance dependence was wrong, and the calculated force was too weak except for very flexible bila~ers.2~ In some cases, the undulation force dominates at large separations (>1.5-2.5 nm) but is usually negligible at small distances, where the interaction is dominated by the exponential repulsion. The undulation force is essentially an entropic force arising from the confinement of thermally excited waves (undulations) into a smaller region of space as two membranes approach each other. Although most apparent for the undulation force, a careful analysis reveals that for all established mechanisms of repulsions between similar surfaces in a (bulk) incompressible system the source of the repulsion is due to entropic confinement. By combining the observations on experimental results of "hydration forces" and theoretical considerations on the nature of the repulsions arising from constraints of surface molecular motions imposed by an approaching second surface, we now show that the most likely source of the hydration force is also due to entropic confinement?' Molecular-Scale Thermal Fluctuation Forces: Steric Protrusion Forces The molecular-scale motions occurring a t the nonpolar-polar interfaces of surfactant and lipid structures cannot be described within the continuum picture as can the long-wavelength undulations. These local motions will typically have smaller amplitudes but will be more numerous than the undulations (Figure 1, lower part). The inevitable confinement of these motions as two surfaces approach each other provides an additional repulsive component to the fluctuation force. What is the expected magnitude and distance dependence of this force? To answer this question, we adopt a simple model (Figure 1) where each surface has local thermal protrusions of lateral dimension u, extending a distance z, into the solution. Let there be n sites per unit area (n ii: 1 / d (24)Evans. A. E.; Pamedan, V. A. Pmc. Notl. Acad. Sei. U.S.A. 1986. 83,7132. Safinya, C. R.; b u x . D.;Smith, G. S.; Sinha, S. K.; Dimon, P.; Clark. N. A,; Belloeq. A. M. Phys. Rev. Lett. 1986,57,2718. (25) Wennerstrbm, H.; Jbnsson. B. J. Phys. (LaUlis, R.) 1988.49, 1033.
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Letters with one protrusion degree of freedom per site, and let u(zi) be the protrusion energy. For two surfaces facing each other, whose protrusions are not allowed to overlap, the configurational integral Z of the 2n degrees of freedom factorizes into n identical "two-particle" configurational integrals z
z = 2"
(2)
z = ~ d z 2 ~ Dexp(-u12/kT) - ' p dz,
(3)
D (nm) 0
0.5
1.0
1.5
2.0
2.5
I
I
I
I
I
1
where u12 contains the one-particle potentials u ( z l ) + ~(2,). We ignore nearest-neighbor interactions and infrasurface correlations. To obtain an explicit expression for the force, we need to specify the protrusion potential u(zi), which in a first approximation would be expected to increase linearly with the protrusion length zi: u(zJ = azi
(4)
There are good experimental and theoretical reasons for using eq 4. Aniansson" analyzed the protrusions of surfactants from micellar surfaces in terms of the free energy of molecular hydrocarbon-water contactz7and arrived at a value for the "interaction parameter" of a = 3 X lo-" J/m. Theoretically, the unfavorable energy of a fingerlike protrusion (Figure 1) is given by the excess area it exposes, m z , multiplied by the interfacial energy, y. That is a = 7ruy (5) Inserting typical values such as u = 0.3-0.5 nm (for a hydrocarbon chain) andz7 y = 20 mJ/m2, we obtain a similar value of a (2-3) X J/m. With u12 = u(z,) 42,) = a(zl + z2), as defined by eq 4, the integral of eq 3 is easily solved to give
Normalized Distance ( D / h )
Figure 2. (Left-hand ordinate and lower axis) Heavy dashed line shows the theoretically predicted steric protrusion interaction plotted in dimensionless units of normalized force (per unit area) against normalized distance, as given by eq 8. For surface separations between 1 and 15 decay lengths (1 C D / h C 15), the force varies roughly exponentially (solid line) and is adequately given by F / n a = 2.7e-D/X. At very small separa0, the force tends to the intuitively tions (D/X < 1) as D obvious osmotic limit of F = 2nkT/D. (Right-hand ordinate and upper axis) Heavy dashed line now corresponds to the force (pressure) for an interaction parameter of CY = 2.5 X lo-" J/m and a surface density of n = 2 X 10l8 m-', at T = 25 "C. Thin dashed lines are experimental force curves for egg lecithin as measured by different groups: upper line (refs 3 , 7 ) , lower line (refs 6, 17).
-
the case when there is only one type of protruding mode. In reality, surface groups will generally have several conformational degrees of freedom which will become candidates for additional protrusion modes. Nevertheless, z = (kT/a)2[1- (1 + Da/kT)e-dD/kT] (6) this simple model yields decay lengths and reexponential factors typical of those normally measured,518~~*~~ though which immediately gives the force per unit area (or preswe may note that the "measured" values themselves (see sure) as Figure 2) depend on how the measurements are made (na2D/ k T ) and how one defines D = 0. For example, for egg leciF = t3G/dD = k T t3 In Z / d D = [ l - (1 ~ x D / k T ) e - " ~ / ~ ~ ]thin, values for X range from 0.17 to 0.26 nm while values for C range from 4 X lo' to 4 X lo9 N/m2, depend(7) ing on how the experimental data are interpreted.6*7"7 In view of the good agreement between experiment and or the first-order theory presented here, we suggest that the F / n a = (D/X)e-D/A/[l - (1 + D/X)e-D/A] (8) entropic repulsion of protruding molecular groups is the real origin of these short-range forces, which may convewhere X = k T f a . niently be referred to as "steric" force^^*^^ or "protruFigure 2 shows a plot of normalized force, F / n a , against sion* forces if we wish to distinguish them from the steric normalized distance, D/X. We see that in contrast to forces normally associated with the interactions between the undulation force the steric protrusion effect yields polymer-covered surfaces. an essentially exponential force: F = Ce-D/Xwith a decay length of Discussion and Conclusions X = k T / a = k T / w s y for D > X (94 The above quantitative analysis shows that between and a weakly distance dependent preexponential factor fluid amphiphilic surfaces there must always be an exponentially decaying entropic repulsion whose decay length C = 2.7na 6%) depends on the amphiphile-solvent interaction and not Insertin typical values for a ( ~ ( 2 - 3 )X lo-" J/m) and on some characteristic property of the solvent. This force n (=l/> 2 X 10l6 m-2) at T = 25 OC,we obtain X = is therefore more akin to the "steric" force between poly0.13-0.20 nm and C = 1.4 X lo8 N/m2 (see Figure 2). mer-covered surfaces" than to any solvation force. GenThe above derivation is only a first approximation for uine solvation (hydration) effects are still there, but they play an indirect role, mainly in determining the solvated (hydrated) size of the protruding head-groups and the (26) Aniansson, G. A. E. J. Phys. Chem. 1978,82,2805. interactions between them. In other words, hydration (27) JBmon, B.; Wenneretxtjm, H. J . Colloid Interface Sci. 1981,80,
+
+
-
482. Parsegian, V. A. Trans. Faraday SOC.1966,62,848. (28) Dolan, A. K.; Edwards, S. F. R o c . R. SOC.London 1974, A337,
509. Ieraelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, New York, 1985.
(29) McIntosh, T. J.; Magid, A. D.; Simon, S. A. Biochemistry 1988, 26, 7325.
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effects modulate the thermal forces rather than the other way round.24 For amphiphiles in the "gel" phase, one would still expect there to be a protrusion force, including contributions from the mobile head-groups. In the light of the above, we can rationalize many hitherto unexplained phenomena, including those listed earlier. Thus, we can understand why exponentially repulsive forces between lecithin also occur in nonaqueous solvent^'^*'^ and why-as we go from water to formamide to propanediol-the decay lengths progressively increase (from 0.17 to 0.26 nm) as the interfacial tensions de~rease.'~Experimentally, one also finds that low decay lengths are enerally associated with high preexponential factors;'' this too is predicted by eq 9, which shows the opposite dependencies of X and C on a (at the same 79. Another issue that is immediately resolved concerns the large thickness fluctuations and apparent overlap of opposin head-groups even in fully hydrated systems?'.' It had previously been recognizedm*'-' that at sufficiently small separations the hydration interaction should become replaced by the steric repulsion of overlapping head-groups; yet the measured forces never showed any break in the smoothly exponential line down to mean surface separations of 0.3-0.5 nm.2.3i6*7*29 With the present interpretation this paradox disappears: viz., the socalled steric force was always there right from the start. Note, too, the predicted steep upturn of the force at very small D (Figure 2), as has also been ~bserved.~' It is likely that, in a first approximation, the protrusion force is additive with other forces such as double-
layer, van der Waals, undulation, hydration, and hydrophobic forces. However, in some cases these forces may be coupled; e.g., the protrusion force may be supressed between charged surfaces, as is the undulation force.30 Clearly, more rigorous experimental and theoretical analyses are needed than given here to explore the full nature and implications of this type of interaction. Thus, computer simulations should include any motional degrees of freedom of molecular groups a t interfaces, headgroup tilting, etc., while experiments should consider which surface-bound groups are mobile and which are immobile. Finally, on the conceptual level, our findings imply that more careful thought must be given before using terms such as "structured water", "hydration layer", "headgroup hydration", "water binding", etc. For example, it is no longer obvious that the amount of water uptake per head-group during the swelling of a lamellar phase can be directly associated with the "structured water" or "hydration" of that group. Acknowledgment. We are grateful to Wolfgang Helfrich, Stjepan Marcelja, Sol Gruner, Phil Pincus, and Christiane Helm for their insightful comments. J.N.I. was supported by ONR Grant N0014-87-K-0013 and H.W. by NSF Grant PHY82-17853 supplemented by funds from NASA. (30) Pincus, P.; Joanny, J.-F.; Andelman, D. Europhys. Lett. Submitted.
The Origin of Static Friction in Ultrathin Liquid Films John Van Alsten and Steve Granick' Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801 Received November 21, 1989 We study the solid-like shear response (the static friction) of liquid films of both compact and chain geometry, whose thickness approaches molecular dimensions. The nonpolar liquids were confined between parallel plates (step-free single crystals) of muscovite mica. The finite shear stress required to produce sliding increased with measurement time over intervals from minutes to hours, at temperatures above the bulk melting temperature or the bulk glass transition temperature. This loss of fluidity may reflect a vitrified state imposed by the liquid's confinement.
Introduction The physical behavior of confined fluids can differ remarkably from that in the unconstrained bulk. This has implications in many areas, from biology to tribology. Much progress has been made in understanding static equilibrium, and it has become well-established that packing requirements near a solid boundary impose order on the fluid near this solid boundary-the local density shows decaying oscillations normal to the surface with a period of about one particle diameter.' However, little is known about relaxation and diffusion within such interfacial regions. In earlier ~ t u d i e s , ~we - ~performed measure(1) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1985; Chapter 13 and references therein. (2) Van Alsten, J.; Granick, S. Phys. Rev. Lett. 1988,61, 2570.
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ments to explore the dynamic shear response of nonpolar fluids confined as a sandwich between ultrasmooth parallel surfaces that were close together (a discrete number of molecular layers) but not quite touching. Two varieties of mechanical response were found: liquid-like, but with a rate of viscous energy dissipation enhanced by orders of magnitude over that for the isotropic liquids, and solid-like, meaning that sliding did not occur unless a certain shear stress (or "yield stress") was attained. At a given film thickness, liquid-like behavior degraded into solid-like behavior with increasing net normal pressure. Such yield stress behavior is familiar but not understood. It is the well-known fact of life, static friction. (3) Van Aleten, J.; Granick, S. Tribology Trans. 1989,32, 246. (4) Van Alsten, J.; Granick, S. Mot. Res. Soc. h o c . 1989, 140, 125.
0 1990 American Chemical Society
