THE J O U R N A L OF
PH.YSICAIL C H E M I S T R Y Registared in U.S.Patent Office 0 Copyright, 1980, by the American Chemical Society
VOLUME 84, NUMBER 12
JUNE 12, 1980
Long-Range vs. Short-Range Forces. The Present State of Play 8. W. Ninham Department of Applied Mathematics, Research School of Physical Sciences, Institute of Advanced Studies, Australian National Unlversity, Canberra. A.C.T., Australia 2600 (Received August 27, 1979)
The successes of the DLVO theory of colloid stability have been so striking that long-range forces between molecules or surfaces--action at a distance mediated via a uniform continuum-has tended to dominate thinking in the subject. Earlier ideas typified by those of surface chemists like Langmuir (and indeed of Derjaguin), that solvent-mediated or structural forces passed on from molecule to molecule play an important role in colloid, especially biocolloid, stability were put to one side. Recent advances in liquid-state physics and now direct experiments have made it possible to describe and quantify these forces. At “large” distances they go over to the familiar van der Waals and double layer forces, but at distances less than typically around 10-15 molecular diameters they can have a totally different nature. Especially for systems of biological interest solvent-mediated forces can dominate interactions at small distances. An account will be given of the present state of our understanding of forces due to solvent structure. The emerging picture is that both the ideas of Langmuir and of DLVO were correct for the systems which mainly concerned them, the controversy between colloicl and surface scientists ending in an eminently satisfactory overall synthesis. 1. Introduction
I want to talk about recent developments in our ideas on forces due to liquid structure at interfaces, and to try to define what I have in mind, I want to quote to you the opening paragraph of an address by Clerk Maxwell1 on the subject “Action at a llistance” to the Royal Institution over 100 years ago. He began by saying:: “I have no new discovery to bring you this evening. I must ask you to go over very old ground and to turn your attention to a question which has been raised again and again ever since man began to think. The question is that of the transmission of force. We see that two bodies a t a distance from each other exert a mutual influence on each other’s motion. Does this mutual action depend on the existence of some third thing, some medium of communication occupying the space between the bodies, or do the bodies act on each other immediately without the intervention of anything else?” Maxwell was none too happy with force a t a distance. Nor was Newton. Indeed, in a letter1 to his friend Bentley, Newton went so far as to say: “That gravity should be innate, inherent and essential to matter, so that one body can act upon another at a distance, through a vacuum, 0022-3654/80/2084-1423$01 .OO/O
without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.” The whole thrust of the Maxwell-Faraday approach to electromagnetic phenomena was to underline the importance of material-like properties of the vacuum-of stresses and tensions mediating and propagating forces. But despite Maxwell’s ultimate triumph,2the earlier ideas of the German school3-Weber, Gauss, Riemann, Lorenz, and Neumann involving velocity-dependent action a t a distance-still tend to dominate our thinking as physicists in one way or another. We tend to regard an intervening medium as an annoying complication and by a process of sympathetic magic sweep the whole mess into an effective vacuum or uniform continuum wherein, in truth, sits all the interesting physics. However, in solution and colloid and surface chemistry the problem of transmission of force cannot be so tidily swept away. Here the physicists’ vacuum takes on reality and becomes the solvent medium. The question of‘ the nature and existence of the “aether” now takes on a com0 1980 American Chemical Society
1424
The Journal of Physical Chemistty, Vol. 84, No. 12, 1980
pletely new perspective. The solvent most certainly does exist. Because of the successes of the DLVO we do know, or think that we know, that in dealing with attractive and repulsive forces between colloidal particles, it is usually sufficient to replace the solvent by a continuum (or discrete medium of uniform density) which serves only through its macroscopic dielectric properties to modify those forces existing between two particles in a vacuum. But we are not completely sure. The older vague “hydration theories” and the more sophisticated ideas of Langmuir8 and of Onsagerg (that long-range attractive forces had little role to play in colloid stability) were put to one side. In Maxwell’s language: “the action between bodies at a distance may be accounted for by a series of actions between each successive pair of a series of bodies which occupy the intermediate space.” Langmuir’s experience with surfaces8 led him to the view that since the forces between molecules in a liquid were short ranged, dominated by molecular size, shape, and packing, the forces between two large particles were necessarily also short ranged, of the order of a few molecular diameters. He excluded, of course, electrostatic forces. We have then two very different points of view. Short-range correlations which exist in liquids can clearly give rise to some kind of “structural” forces between solute particles or surfaces a t distances at which the graininess of matter can no longer be ignored. But at what distances? Terms like “hydrophobic interactions”, “ionic hydration”, “Stern layers”, “specific ion adsorption”, “structured water”, and “anomalous swelling”,which have loomed large in the language of chemical physicists for half a century, have remained unquantified. In a very real sense these terms are only slightly more advanced mnemonics than the electric atmospheres and magnetic effluvia of Descartes and his contemporaries. This is unsatisfactory in the extreme. We would like to, we must, believe that some global principles can be established, that a synthesis of the two opposing views is possible-especially if we are ever to come to grips with biological questions. My assertion is that we are in sight of that synthesis. And to lay out the case I would ask you to bear with me if I remind you first of the situation concerning molecular forces between macroscopic bodies as it was up to a few years ago. 2. Forces in Colloid Science as They Were The potential between two particles large on a molecular scale is conceived of as comprising two p a r t ~ : ~the ~ *one l~ repulsive, the other attractive. Leaving aside those systems stabilized by polymers, a relatively new area where quite different mechanisms are involved (and where the first direct measurementsll have been reported only in 1978), we have: double layer forces, van der Waals forces, and a “third” or “effective” force due to the statistical mechanics of two phase equilibrium. The sins of omission in the difficult subject of doublelayer forced2 provide a litany of woes too numerous to bear recapitulation. Those sins will be visited on the third and fourth generations of those that follow. With no disrespect to the very fine experiments of people working on soap films and other systems, let us simply note that the most convincing direct measurements of double-layer forces which finally confirmed the nonlinear Poisson-Boltzmann theory over a large distance regime and at low salt concentration were carried out by Israelachvili et al.10213in 1976-77. On the one hand, these forces are par excellence an example of an indirect solvent-mediated force, the solvent being the dilute aqueous electrolyte. At a different
Ninham
level, that of the interacting ions of the electrolyte, the water medium is replaced by an inert continuum. There is no problem with this-except with the Stern layer. van der Waals forces across a solvent medium are theoretically understood at large distances’O and were measured directly, again13in 1976, for the first time. Together these forces have formed the basis for much of our thinking. The key assumption, that an intervening medium could be treated for most practical purposes as a passive uniform continuum, appeared to be vindicated.6 An apparent “third’ force (due to the competitive role of statistical mechanics and repulsive forces in determining long-range order and two-phase equilibria), which had plagued people concerned with suspensions of clays, latex spheres, and tobacco mosaic viruses, had been elucidated by Langmuir* and Onsagerg many years ago, forgotten, revived, and reluctantly accepted following work of our group14J6and others. The competitive role between clearly demarcated “long-range” vs. “short-range” (interfacial tension) forces and molecular geometry, and especially the importance of statistical mechanics in determining both the behavior of such many-body systems and in the selfassembly of amphiphilic molecules into structures like micelles, vesicles, and bilayers had been sorted out.16 No mysterious additional forces were required. Thus we could be reasonably content that our picture of forces was somewhere near correct. Even surface force energies could sometimes be “predicted” by assuming that Lifshitz or Hamaker theory held right down to contact.17J8 In retrospect our views were a little too facile. To see why, turn now to solution chemistry. 3. Indirect Evidence for Structural Forces Let us not recapitulate all the evidence. Recall that the strong ideality of solutions of large hydrophilic molecules like sucrose and glyceroPgand the contrasting nonideality of sim‘lar molecules which differ chemically only in minor respec s has remained a puzzle. Recall the problems of (abnormal) hydrophobic solutes.20 The swelling of lecithin and clay suspensions in water is curious. The apparent success of mean field theories of liquid crystal phase transitions is mysterious; they rely on some effective and still incomprehensible potential. Even for electrolytes the problem of what one means by hydration remains unquantified. T h e importance of “solvent structure”implying some mechanism f o r transmission of force, not simply hard core repulsion p l u s attraction or repulsive forces across a continuum-has to be recognized. It is too easy for the solution chemist to dismiss such thermodynamic observations as he has as due to specific molecular effects. To do so is a contribution a t the level of the “magnetic effluvia” of Descartes and his contemporaries. In fact, the germ of the ideas I now want to discuss goes back to 1763 when Ruder Boscovich, a famous Dalmatian philosopher and astronomer from the old republic of Ragussa (Dubrovnik), published his Theory of Natural Philosophy. He began his treatise with the following immodest introduction: “The following theory of mutual forces which I lit upon as far back as the year 1745 while I was studying various propositions arising from other well-known principles, and from which I have derived the very constitution of the simple elements of matter, presenh a system that is midway between that of Liebnitz and Newton. It has very much in common with both, and differs much from either, and as it is immensely more simple than either, it is undoubtedly suitable in a marvelous degree for deriving all the general properties of bodies, and certain of the special properties also, by means of the most rigorous demonstrations.” He then goes on
\
Long-Range vs. Short-Range Forces
The Journal of Physical Chemistty, Vol. 84,
No.
12, 1980
1425
corresponding to infinite repulsion for overlapping spheres, zero interaction outside the hard-core exclusion diameter. It follows that B2* = 16?ra3/3. The two expressions we have obtained for Bz* must be identical, whence pl0 = 3/32na3 N 1/32a3. This is absurd, because for a concentrated solvent of hard spheres corresponding (say) to a face-centered cubic array on average, we know that p? = 1/4(2)1/za3>> 1/32a3. What went wrong with the argument is the assumption that gz2(r)depends only on the direct hard-sphere interaction. In any hard-sphere liquid g22(r) will have damped oscillations which describe structure in the liquid over several particle diameters, and this damping Figure 1. The potential of mean force between “atom” according to reduces the magnitude of the integral over gz2(r). There Boscovich. is in total a hard-core repulsion p l u s an attractive tail in the potential of mean force, the tail arising because of the discrete and correlated nature of the solvent. This system illustrates the concept of an indirect (structural) force, but is a special and oversimplified case 25 atm. of the general problem. For the present model the solvent is, in fact, unperturbed by the solute molecules. When the solute molecule differs in its size or interaction properties from solvent molecules, the solvent distribution function, i.e., the structure of solvent, will be altered by the solute molecules. It is both the propagation of this distortion from bulk solvent properties and the bulk liquid structure together which are the source of the indirect interaction. [One further remark is that for various reasons most theoretical and simulation work on liquids (and hence the intuition regarding bulk solvent distribution functions) is Potential of Mean Force between atoms in a LJ fluid (1979) done at very high pressures (usually O(300 atm) or higher) where the role of the hard core is dominant. At lower Figure 2. Potential of mean force between two molecules of a Lenpressures, the attractive part of the potential is moire imnardJones fluid (after Yerlet**). portant and tends to smooth oscillations.] One could always attempt to model solution behavior to deduce (in effect) the forces between atoms in a medium (and colloidal systems) in terms of an “effective” hardillustrated in Figure 1, and to develop his unified field sphere model for solute and solvent molecules. This is an theory which embraced light, matter, gravitation, and inexercise in parameter fitting and patently absurd. To deed the whole universe. Note the oscillations in what we explain the temperature dependence of virial coefficients would now call the potential of mean force between two and the change in sign with temperature of B2* for, say, atoms. These trail off into a long-ranged tail. The conthe urea-water one has to suppose that the fidence of Boscovich was unbounded and provides a most “effective hard core” depends on temperature. To explain salutary and sober example of the dangers of theoreticians. the activity coefficients of cesium salts using the primitive In Figure 2 is plotted the corresponding modern Monte model, one has to suppose that hydrated ion radii are less Carlo simulation results for the same quantity for a Lenthan bare ionic radii, and for anions like NO3- and S042-, nard-Jones fluidaZ2The comparison is a bit mischievous, that their radii are negative!25 as Boscovich was concerned, we think, with vacuum interactions, but note how far we have come in 200 yearsThermodynamics is pretty crude and an insensitive test, the oscillations get damped a bit and the tail is shorter and while one can play the parameter-fitting game inranged! This form of bulk liquid distribution functions definitely, all one can really say is that some kind of extra is now understood insofar as these things can be, and the indirect interaction is implicated and the primitive model observation has an immediate illustrative con~equence.~~ is too crude. Unless we can come to grips with the solvent, Consider a dilute solution and imagine that both solute there is little hope of sorting out double-layer and specific and solvent molecules are made up of distinguishable hard ion effects. (Recall that even for the change in surface spheres of equal radii a. Suppose that the densities of tension of water due to electrolytes, a much simpler solute and solvent molecules are p2 and pl, respectively ( p l problem than the surface tension of water, or the vastly >> p2), and that the solution is incompressible (this apmore difficult double-layer problem, no theoretical work proximation leads to negligible error for hard-sphere lihas been done since the Onsager-Samarasz6 theory of quids). By construction the system is ideal, and for such 1934.) a system its osmotic pressure ?r is Very fortunately our liquid-state colleagues are making substantial progress, both experimentally and theoreti= kTpl0 In (1- P Z / P ~ O ) ppkT(1 + Yz/2p2/pIo) (1) call^.'^ The Debye-Huckel limiting law has finally been derived for an ion-dipole mixture,28asome progress has where pIo is the density of pure solvent. The second osbeen made in understanding the nature of the Born enmotic virial coefficient is Bz* = 1/2plo. But from the ergy,28band definite progress is in sight in computer simKirk~ood-Buff2~ theory of solutions which relates the ~ l a t i o nand ~ ~more from neutron-scattering experiment^.^^ correlation functions of statistical mechanics to thermodynamics, we have B 2 * = -l/zS[g22(r)- 11 d3r, where g22(r) Similar remarks apply to hydrophobic solutions, where is the solute-solute radial distribution function. If we we are well on the way toward an analytic p i c t ~ r ewhich ~,~~ ignore solvent structure, Le., use a primitive model, we captures the elusive essence of the intuition built up over should have g2&) = 1 ( r > 2a) or gzz(r)= 0 ( r < 2a), the years by Henry Frank and Felix Franks. I
P
;,I
1 T I I L O I Y or \+T \ L PII I O ~ O P I I Y
1426
The Journal of Physical Chemistry,
vQ/.84, NO. 72, 7980
4. S t r u c t u r a l Forces in Colloid Science If we accept that structural forces are important in understanding solutions, it is by no means obvious that they should be in colloid science. It is true that, while Lifshitz theory gives correctly the long-range temperature-dependent entropically driven van der W a a l ~ lforces ~ ? ~ ~in water, interaction free energies are hopelessly wrong at contact-likewise for the experiments of Laskowski and Kitchener on the boundary between hydrophobic and hydrophilic surfaces.33 But these could be argued away as structural effects (hydrogen-bond rearrangements) limited to the first one or two layers of water, and present theories would be unperturbed. On the other hand, the experiments of Derjaguin and C h ~ r a e vand ~ ~of Pashley and K i t ~ h e n e ron ~ ~thick water films on quartz point to some anomalous and large effects at the quartz-water interface. Again, we could dismiss this as a peculiarity of quartz, or the experimentalists, although this would be most unwise. Zettlemoyer’swork also poses diffi~ulties.~~ In the circumstanceswe do well to remember the lessons learned from the too confident Boscovich and appeal to direct experiment. In experiments which measure the forces acting between molecularly smooth mica in electrolyte solutions, Israelachvili and his colleagues find a strong repulsive exponential force with decay length around 5-10 A and dependent on salt concentration. These forces are clearly not double-layer forces and can dominate the interaction at distances below 30 A. It was at first thought that these could be exclusive to mica, but current work in progress with hydrophobic surfaces and adsorbed surfactant bilayers reveals that this is not so (see below). Similarly we cannot dismiss the earlier work of Rand, Le Neveu, and Parsegian3’ who measured exponentially decaying repulsive forces acting between lecithin bilayers (a hydrophilic colloid) by an extremely simple and clever osmotic method. These are independent of salt concentration. If van der Waals forces (as calculated by Lifshitz theory) are subtracted, what remains is a “hydration force”, a new repulsive force, apparently exponential with a decay length of 2 A, and very strong indeed. What is important to note is that these forces are sufficiently large to balance van der Waals forces (presumed to be given correctly by continuum theory) at distances around 30 8, and to dominate the interaction at smaller distances. This is precisely the sort of distance regime that colloid science has taught us to expect van der Waals forces (as calculated by continuum theory) to dominate. The first attempt to characterize these indirect solvent mediated forces was due to M a r ~ e l j a at ~ ~the ” ~ANU who had earlier developed a theory of lipid-mediated protein interactions in biological membra ne^.^^ His idea38was that the lecithin surface, being zwitterionic (dipolar), acts to order water dipoles at the surface. This order propagates through the system. Density variations are ignored. This surface-induced polarization causes a change in the bulk free energy density (see Figure 3). Assuming that the free energy density f varies slowly with distance, we borrow from physics and expand as
-[
f = 2X P2(x)+ 12(
5)*...I
- PEo
(2)
where Eo is the applied electric field, P(x) is the induced polarization, P = x E , D = EE,E = Eo - 47rP. The coefficient € 1 2 is~ obtained from buIk electrostatics and { is a correlation length. If we minimize the free-energy density subject to the boundary conditions P = &Poat the lecithin-water surface,
Ninham
+
&
d/2
-d/2
lecithin
water I-
rl I
lecithin
\--
t
P = - J Figure 3. Marcelja theory of structural forces.
take 4 (which has to be of the order of molecular dimensions) to be the measured value, and Po corresponding to full orientation of surface water molecules, we find a repulsive pressure
which agrees nicely with the experimental observations. This is a suggestive start which provides an entry point into the problem. It is an advance of which I think Langmuir would have thoroughly approved. The theory has many defects: (1) it is a continuum theory applied to distances of a few molecular diameters where matter is starting to appear discrete; ( 2 ) association of the order parameter with polarization is arbitrary (it could be hydrogen-bond orientation or density, say, or all three); (3) the forces are always monotonic, whether attractive or repulsive corresponding to like or unlike order at the respective surfaces; (4) the boundary condition is not well defined; (5) the Landau theory upon which the theory is based can be derived rigorously from statistical mechanics and holds strictly only in the limit of infinite correlation length (Here we are extrapolating down to the smallest possible distance ( 2 A # a)!). The theory is clearly outrageous. Nonetheless, it represents a distinct conceptual advance at the level of the Poisson-Boltzmann equation and is worth further exploration, for it captures the idea of propagation of force from molecule to molecule-as opposed to the older ideas where we arbitrarily demarcate an adjustable region of tight binding (hydration) from a region of bulk (uniform) solvent. To test these ideas further, we decided to push on, regardless, to a study of the thermodynamic properties of hydrophilic and hydrophobic solutes in ~ a t e r With . ~ ~ ~ ~ ~ a new order parameter identified as the solute-induced deviation of hydrogen-bond bending obtained through an extension of the Pople model of water, and again taking this to be 2 A, the theory appeared to account quite well for the properties of these solutions. While thermodynamics is a rather insensitive test, this was encouraging. However, before one can take mean field theory seriously (and obviously this would be an important advance), we must put the theory on a firmer basis. With that aim in mind, the author and colleagues launched on a program what can be deof studying, for simple model duced about forces at close separations from statistical mechanics. 5. Model Calculations
Consider, e.g., the system illustrated in Figure 4. This involves two attractive hard walls (2) separated by a model liquid (1)made up of molecules with a specified hard-core
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980 1427
Long-Range vs. Short-Range Forces
rd-i
Flgure 6. Free energy per unit area of hard walls interacting across a LennardJones fluid calculated via integral equation approaches (ref
43).
In other words, the corrections to the Hamaker force are already 30% at 100 molecular diameters! With these b. numbers, Hamaker (or Lifshitz) theory, which assumes that the liquid is a uniform continuum, would have broken Figure 4. Geometry for model calculations of the text. down totally around say 50 A. On the other hand, for systems of large Hamaker constants with which we have more confidence, AZl2 N O(A,,) N O(A,,) (for oil-water systems, Azlz “J All/lO), eq 4 would read I I I 1 I E ( x ) N I(*f; 47 + (7) 127rx2 The corrections to Hamaker theory would be expected to become significant (say 30%)at around 12 molecular diameters, say, 30-50 A. Of course, we cannot take these numbers too seriously (a two-body force description is hopelessly wrong to calculate Azlz and we must use Lifshitz). But we can deduce that Lifshitz-Hamaker theory must be going over to a quite different force law at close separations and that this breakdown will probably be much more dramatic for those systems with low Hamaker constants. Figure 5. Schematic representation of density profiles for liquid inIn retrospect, eq 4 is obvious (cf. Figure 5). For example, terfaces. two immiscible liquids will exhibit the density profiles diameter interacting via a two-body London p ~ t e n t i a l . ~ ~ illustrated schematically, with a separation 7 in their Gibbs dividing surface. The system is a triple film in which 7 One firm and rigorous result which emerges from detailed is a vacuum, and eq 4 is just the Lifshitz triple film calculations is the energy of interaction at large distances: All this is eminently satisfying: For “normal” systems (those with high Hamaker constant) we know that the -- 47 DLVO theory works well. The barrier to flocculation takes x3 its maximum typically at distances of the order of, or (4) greater than, 30 A, and all is right with the world. For “peculiar” systems (those with low Hamaker constants) where (cf. Figure 4) d is the distance of closest approach -biological systems, mesophases, emulsions-the indicaof wall and solute molecules tions have long been that some very different form laws may be operating. 7=d h2,’(y) dy (5) 0 If we go further to explore theoretically what happens with our model system at closer separations, we immediand the second term represents the absorption excess of ately run into the extremely difficult subject2’ which is the particles 1 against an attractive hard wall 2 (Figure 5). modern liquid-state physics. We have explored this region The evaluation of the absorption excess is difficult, and using integral equation approaches.@ The deficiencies of the distance d is clearly somewhat arbitrary, but typically these approaches are known43and are severe. Nonetlieless, we can take 1; hzl’(y) dy = -R1.Suppose we err on the of result which emerges (illustrated in Figure 6) the kind side of extreme caution and take 7 := R1, hopefully a severe should be somewhat close to the correct answer beyond underestimate. For oil across water we take All N 5.8 X two or three diameters. Note the overall smooth decay on erg, AZ2= 7.5 X erg, A12 N (AllA22)1/2.Then which are superimposed some oscillations. eq 4 reads Various other model calculations have been made. Especially illuminating are those on one-dimensional ~ y s t e m s , which 4 ~ ~ ~have ~ the advantage that the statistical mechanics can be done exactly. One can here examine the
2
2
jm
...)
1428
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980
Ninham
F/R (dyn/cm)
4
;
I
I
2-
Jump
25 4 .. .. .../;
I
I
O A
B
C
D
E
-2-
i
I
1
I
I //
I 5o _ / M C
.a 175 --b
//
. . . . ..>
>
Inaccessible
-10
-12 Figure 8. Measured force between mica surfaces separated by a nematic liquid crystal (5CB).
Flgure 7. Schematic illustration of structural forces.
interplay between several order parameters, one corresponding to dipolar ordering of the intervening fluid, and another due to density depletion at the interacting surfaces. Both order parameters, and others, must contribute to the actual situation existing in water. For some model systems44the structural forces are quite monotonic and indeed exponential as predicted by mean field theory. Whatever the overall story, though, it is clear that the picture of colloidal particle interactions based on a uniform continuum model for the solvent must be carefully revised. 6. S t r u c t u r a l Forces and Surface Energies How can a force law typified by Figure 6 be understood? Consider two perfect solids 2 interacting across an intervening (artificial) liquid 1 by London forces. This is illustrated schematically in Figure 7. Suppose that all have the same hard-core diameter, and choose the zero of energy to be infinite separation (2). The change in energy on contact is just A212/12~d2.At position B, particles 1 cannot squeeze between the plates which interact across a vacuum. The interaction energy is not screened. At position C, particles 1 can squeeze in and the Hamaker constant drops to Az12again. At position D, we cannot pack medium 1 properly. I t looks more “vacuum-like” than the bulk medium. At E we revert back to a completely screened interaction. For a liquid the force will exhibit some, but not all, oscillatory behavior exhibited by our artificial system, but we can understand the presence of oscillations in structural forces settling down to a long-range attractive tail. One remaining problem with our main thesis is the apparent success of the theories17 (based on pairwise summation) and of Israelachvilils (based on Lifshitz theory) to compute the surface energies of hydrocarbon liquids, where only dispersion forces operate. If we look carefully at these theories, we see that each involves two adjustable constants, the Hamaker or Lifshitz constant45and the surface-to-surface separation on contact. In addition, they involve the assumption that the density profile is uniform. If we suppose their correctness for hydrocarbons, they should be equally valid for a simple liquid-like argon. They are The Monte Carlo work of Barker and associa t e ~ gives ~ ’ out the correct result-the density profile is crucial to the proper calculation of surface energies.
Figure 9. Force between mica surfaces separated by a simple liquid (octamethylcyclotetrasiloxane).
7. Experiments on S t r u c t u r a l Forces Our ultimate test, given the unsatisfactory nature of liquid-state theories, must be appeal to direct experiment, and (before coming to grips with water a t interfaces) on as simple a system as possible. Several such experiments are being conducted in our laboratory by Horn and Israelachvili. With their permission I am happy to report their preliminary results.48 In the first experiment two molecularly smooth mica surfaces, made hydrophobic with a CTAB monolayer, are separated by a nematic liquid crystal whose molecules are oriented perpendicular to the surfaces. In the bulk this liquid crystal does not form layers, but near the surfaces it undergoes a transition to a layered phase. This system is reminiscent of a one-dimensional liquid between two hard wall^.^^^^^ The forces, shown in Figure 8, show clear structural effects: they oscillate, and the attractive wells occur at 25-A intervals and decay exponentially, as fsr mean field theory, with a decay length of about 20 A. Those oscillations might here just be due to squeezing out successive layers of a solid, hut in experiments with pure smectic liquids the oscillations do not decay at all. A transition from one order (nematic) to a higher order (smectic) is induced by the surfaces. A second aeries of experiment^^^ (Figure 9) is equally dramatic. We chose a simple liquid made up of large inert spherical moleculq of 10-A diameter (octamethylcyclo-
Long-Range
V!j.
Short-Range Forces
tetrasiloxane). The troughs and peaks appear at regular intervals of 10 A. However, the actual magnitude of the forces has SID far varied from experiment to experiment, which could be due to preferential adsorption of surfaceactive impurities in the liquid. Nevertheless, the 10-A periodicity of the oscillations strongly suggests that these are structural forces due to the siloxane liquid. These experiments will be reported in detail by Horn and Israela~hvili.~~ One consequence of their observations is that in interactions between colloid particles the forces may be different, on approach and on recession, and depend on the speed of collision, a point made by OverbeekaGAnother is that over the distances indicated these forces may be larger than the van der Waals forces so that structure can dominate, especially at small separations. For other liquids and surfaces structure may be more or less important. One further exciting consequence of the Horn experiments is that with different liquids (e.g., tetraphenylborate which has a strong dipole moment) we can hope to study the effect of different competing molecular effects on forces at interfaces (e.g., dipolar ordering, hard-sphere ordering, van der Wads attraction). Potentially we have a new kind of “microscope” to probe the Stern layer. I t would take me too far afield to report in too much detail on the equally dramatic effects found with surfactants by Pashley and Israelachvili.50 Suffice it to say that structural forces in water appear to have a decay length of around 3-4 A with hydrophilic surfaces (and dominate electrostatics) and are much weaker with hydrophobic surfaces. Quite extraordinary long-range effects are observed unless very special precautions are taken to clean up the water; the implications from this observation for force modelling in biological systems are clear. Although the (assumed exponential) decay length of hydration forces with hydrophilic surfactants obtained by Pashley and Israelachvili is about the same as those measured recently by Cowley et for charged multilayers, there are differences. In the former experiments a distinct primary minimum is observed, but not in the latter. The differences (of an order of magnitude less in the Pashley-Israelachvili experiments) assigned to the strength of structural forces are presumably due to the circumstance that in the former the surfactants are more or less anchored to mica, whereas in the latter they are more mobile. Difficulties in disentangling the data, e.g., subtraction of a van der Waals contribution calculated from continuum theory, and others, mean that we can look forward to some most interesting developmentsin the near future. 8. Conclusion I began with a quotation from Maxwell. Let me sum up the story as I see it with an0ther.l “If we leave out of account for the present the development of the ideas of science, and confine our attention to the extension of its boundaries, we shall see that it was most essential that Newton’s method should be extended to every branch of science to which it, was applicable-that we should investigate the forces with which bodies act on each other in the first place, before attempting to explain how that force is transmitted. No men could be better fitted to apply themselves to the first part of the problem than those who considered the second part unnecessary. Accordingly, Cavendish, Coulomb, and Poisson, the founders of the exact sciences of electricity and magnetism, paid no attention to those old notions of “magnetic effluvia” and “electric atmospheres”, which had been put forward in the previous century, but turned their undi-
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980
1429
vided attention to the determination of the law of force, according to which electrified and magnetized bodies attract and repel each other. In this way, the true laws of these actions were discovered, and this was done by men who never doubted that action took place at a distance, without the intervention of any medium, and who would have regarded the discovery of such a medium as complicating rather than explaining the undoubted phenomenon of attraction”. I want to put it to you that there is a parallel worth noting, however imprecise, with our own subject. In laying our foundations, those immortals of colloid science, Derjaguin, Landau, Verwey, and Overbeek, have correctly followed the path of Cavendish, Coulomb, and Poisson and the German school of electricity, and have ignored the medium. In colloid science the exponents of “hydration theories”, whom I have represented perhaps unfairly by Langmuir, are analogous to those who advocated “magnetic effluvia”. They were more concerned with the deep question of how force was transmitted, but could make no headway until the first part of the problem was done by DLVO. Both Maxwell and the German school were correct, But we know that the implications for physics of Maxwell’s discovery and radically different point of view-that the medium is the message-were profound. So too we can expect that our coming to grips with the solvent over the coming years will be revolutionary in colloid science, especially as it pertains to biology.
Acknowledgment. Acknowledgment is made to S. Levine, D. H. Everett, R. H. Ottewill, and B. A. Pethica who were insistent in posing the problem to the author; to theoretician colleagues D. Y. C. Chan, J. N. Israelachvili, S. Marcelja, D. J. Mitchell, and B. A. Pailthorpe, some of whom believed and some of whom did not, yet still worked; to R. G. Horn, R. M. Pashley, and J. N. Israelachvili who graciously allowed me to report their preliminary experiments prior to publication; and to T. W. Healy and R. J. Hunter who encouraged us all to continue.
References and Notes J. C. Maxwell, “The Scientlflc Papers of James Clerk Maxwell”, Vol. 2, W. D. Niven, Ed., Dover, New York, 1965, p 31 1 (Proceedings of the Royal Institution, Vol. VII). F. J. Dyson, BUN. Am. Math. Soc., 78,635 (1972). The two theories, Maxwell’s and those of the German school, were fundamentally opposed. That both arrived at the same prediction of the velocity of light in terms of electrical propertles posed a philosophicalconundrum resolved only much later. Dyson has lamented the loss to science due to the circumstance that Maxwell’srepeated low-key pleas to the mathematicians-that they should explore the consequences of his theory of the electromagneticfield-fell on deaf ears for more than a half-century. J. C. Maxwell, ref 1, p. 228; PresMentlaiAddress to the Mathematical and Physical Sections of the British Association, Liverpool, 1870; Nature (London), 2, 419 (1870). B. V. Derjaguin and L. Landau, Acta Pbys. Chim. USSR, 14, 633 (1941); more easily accessible In Landau’s Collected Works. E. J. W. Verwey and J. Th. G. Overbeek, “Theory of the Stability of Lyophobic Colloids”, Eisevier, Amsterdam, 1948. J. Th. G. Overbeek, J . Colloidhterface Sci., 58, 408 (1977); see also J. Lyklema, Croat. Cbem. Acta, 50, 77 (1977). H. Van Olphen, “An Introductbnto Clay Chemistry“, Wiley, New York, 1963, 1977, pp 52, 158 outline the conventionalvlews on the older “hydration” theorles of stability which are dismlssed. I. J. Langmuir, J. Chem. Pbys., 8 , 873 (1938). See also “The Collected Works of Irving Langmuir”, Voi. 6-9, C. Guy Suits, Ed., Pergamon, Oxford, 1961 (definltely required reading). Derjaguin had emphasized the Importance of structural forces even prior to the appearance of the Derjaguln-Landau theory of colloid stability. See references cited in Derjaguin et al., J . ColloM Sci., 19, 113 (1964). I am grateful to Professor DerJagulnfor reminding me. L. Onsager, Ann. N. Y . Acad. Sci., 51, 627 (1944). For further references on the status of Intermolecular forces in collokl science see: J. N. Israelachvlil and B. W. Ninham, J. ColbM Interface Sci., 58, 14 (1977); J. Mahanty and B. W. Ninham, ”Dispersion Forces”, Academic Press, London-New York, 1976; B. V. Derjaguln, Y. I. Rabinovlch, and N. V. Churaev, Nature(Loncbn),272, 313 (1978).
1430
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980
L. R. White, J. N. Israelachvili,and R. Tandon, Nature(London),277, 120 (1979); J. Lyklema and T. von Vliet, Faraday Discuss., 65, 25 (1978); F. W. Cain, R. H. Ottewill, and J. B. Smitham, ibid., 65, 33 (1978). These papers represent the first direct measurements of forces between surfaces due to polymers. The assertion might be considered unfair to those many authors who have tackled the double-layer problem over the years, especially to S.Levlne and his co-authors who have indeed addressed and delineated the difficulties in terms of specific models which do describe specific systems. In many respects these theories can be considered qulte adequate. However, unlike the situation for long-range van der Waals forces, all treatments of the double-layer are model dependent, because of difficulties with boundary conditions, and from the point of view of this paper there is a clear dlstinction between phenomenology and a (predictive) fundamental theory. It is worth recalling that the problem of dissociable surface groups was addressed only In 1970 [B. W. Ninham and V. A. Parsegian, J . Theor. Bioi., 31, 405 (1970)]; that the Poisson-Boltzmann equation gives no surface tension in the llmit of low salt and Is not rlgorously justlfied in statistical mechanics; that no consistent theory exists for the bulk properties of even the primitive model for electrolytes of unequal charge (e.g., CaCI,). For the real (nonprimitive) electrolyte, Le., one where the molecular nature of water is taken into account, the problems are even more massive. No theory yet exists to deal with the properties of even a simple bulk fluid model comprising dipoles embedded in hard spheres. However, progress in liquid-state physics has been rapid, and these problems are becoming less intractable with time than could possibly have been imagined 5 years ago. J. N. Israelachvili and G. Adams, Nature (London),262, 475 (1976); Faraday Discuss., 65, 20 (1978). See P. A. Forsyth, Jr., S.Marcelja, D. J. Mitchell, and B. W. Ninham, A&. CollokYInterfaceSci., 9, 37 (1978), for references to this subject and general treatment. S.Marcelja, D. J. Mitchell, and B. W. Ninham, Chem. Phys. Lett., 43, 353 (1976). J. N. Israelachvill, D. J. Mitchell, and B. W. Ninham, J. Chem. Soc., Faraday Trans. 2 , 72, 1525 (1976); Biochim. Biophys. Acta, 470, 185 (1977). F. M. Fowkes, Ind. Eng. Chem., 12, 40 (1964); J . CoiioidInferface Sci., 26, 493 (1968). Also R. J. Good in “Contact Angle, Wettability and Adhesion“, Adv. Chem. Ser., No. 43 (1964). J. N. Israelachvili, J. Chem. Soc., Farahy Trans. 2, 69, 1729 (1973). R. A. Robinson and R. H. Stokes, ”Electrolyte Solutions”, 2nd ed, Butterworths, London, 1968. D. Y. C. Chan, D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe in “Water: A Comprehensive Treatise”, Vol. 6, F. Franks, Ed., Plenum Press, New York, 1979. See also and especially: A. Gelger, A. Rahman, and F. H. Stillinger, J . Chem. Phys., 70, 263 (1979). R. J. Boscovlch, “A Theory of Natural Philosophy”, Latin-English ed. Open Court Publishing Co., Chicago-London, 1922. L. Verlet, Phys. Rev., 165, 201 (1968). S.Marcelja, D. J. Mitchell, B. W. Ninham, and M. J. Sculley, J. Chem. Soc., Faraday Trans. 2, 73, 630 (1977) (the observation is due to A. Ben-Naim). J. G. Kirkwood and F. P. Buff, J. Chem. Phys., 19, 774 (1951); see also H. L. Frledmann, J . Solution Chem., 1, 387, 413, 419 (1972). Unpublished manuscript of D. J. Mitchell and author. L. Onsager and N. T. Samaras, J . Chem, Phys., 2, 258 (1934). J. A. Barker and D. Henderson, Rev. Mod. Phys., 48, 587 (1976). (a) D. Y. C. Chan, D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe, J . Chem. Phys., 69, 691 (1978); J. S.HLye and G. Stell, ibid., 67, 1776 (1977); Faraday Discuss., 64, 16 (1977). (b) D. Y. C. Chan, D. J. Mitchell, and B. W. Ninham, J . Chem. Phys., 70, 2947 (1979). D. Marvin, private communication. I am grateful to Dr. Marvin for informino me of his work with Dr. Abraham In this area. See apGopriaie articles in the volume in ref 20. I D. Y. C. Chan, D. J. Mitchell, 8. W. Ninham, and B. A. Pailthorpe, J . Chem. Soc., Faraday Trans. 2, 74, 2050 (1978); 2. Elkoshi and A. Ben-Naim, J . Chem. Phys., 70, 1552 (1979). (32) V. A. Parsegian and B. W. Ninham, Biophys. J., 10, 684 (1970). Note, however, the difficulties of D. E. Brooks, Y. K. Levine, J. Requena, and D. A. Haydon, Proc. R . SOC.London, Ser. A, 347, 179 (1976), in reconcillng theory with their experiments. (33) J. Laskowski and J. A. Kitchener, J . Co//oidInterfaceSci., 29, 870 (1969).
Ninham (34) B. V. Derjaguin and N. V. Churaev, J . Colloa Interface Sci., 49, 249 (1974). (35) R. M. Pashley and J. A. Kitchener, J. Colloa Interface Sci., accepted for publication 1979. (36) K. Klier, J. H. Shen, and A. C. Zettlemoyer, J . Phys. Chem., 77, 1458 (1973); A. C. Zettlemoyer and E. McCatterty, Croat. Chem. Acta, 45, 173 (1973). (37) D. M. Le Neveu, R. P. Rand, and V. A. Parsegian, Nature (London), 259, 601 (1976); Biophys. J., 18, 209 (1977); A. C. Cowley, N. L. Fuller, R. P. Rand, and V. A. Parsegian, Biochemktry, 17,3163 (1978); D. Gingell, Science, 191, 399 (1975); and V. A. Parsegian, N. L. Fuller, and R. P. Rand, Proc. Natl. Acad. Sci. U.S.A., 76, 2750 (1979). (38) S.Marcelja, Croat. Chem. Acta, 49, 347 (1977); S.Marcelja and N. Radic, Chem. Phys. Lett., 42 129 (1976). (The mean field theory Ideas developed here for structural forces in thin films were anticipated by J. C. Maxwell, “Capillary Action” (1975) in “Encyclopaedia Brltannica”, 9th ed, updated by Lord Rayleigh in the 1 lth ed (191 l), building on ideas of Poisson and of van der Waals; see also J. S. Rowlinson, J. Stat. Phys., 20, 197 (1979). Although hls analysis is not correct, Maxwell does come up with 3 A as the range of structural forces in water.) (39) S.Marcella, Biochim. Biophys. Acta, 455, 1 (1976). (40) D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe, Chem. Phys. Lett., 51, 257 (1977); J . Chem. SOC.,Faraday Trans. 2, 74, 1098, 1116 (1978); J . ColloUInterface Sci., 64, 194 (1978); and D. Y. C. Chan, D. J. Mitchell, B. W. Ninham, and B. A. Paihorpe, ibM., 66, 462 (1979). See also refs. 43, 44, and 49. Earlier, S.G. Ash, D. H. Everett, and C. J. Radke, J . Chem. Soc., Faraday Trans 2, 69, 1256 (1973), had addressed the problem of solvent-mediated forces from a thermodynamic approach. (41) See second paper of ref 40. (42) B. W. Ninham and V. A. Parsegian, J. Chem. Phys.,52, 4578 (1970). (43) D. Y. C. Chan. D. J. Mitchell, B. W. Nlnham, and B. A. Pailthorpe, J. Chem. Soc.,Faraday Trans. 2, accepted for publication. Earlier calculations of last three authors in third reference in ref 40 are incorrect. (44) D. Y. C. Chan, D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe, Mol. Phys., 35, 1669 (1978); Chem. Phys. Lett., 56, 533 (1978); D. Ronis, E. Martina, and J. M. Deutch, Chem. Phys. Lett., 46, 53 (1977); see also ref 22. (45) It is, of course, absurd to claim that we can calculate Lifshitz free energles at very close separations, as Insufficient dielectric data are avallable. (46) Consider surface tension computed assuming the density profile as uniform up to an interface, and assume only dispersion forces operate. Now y = - ’ / z W , where W is the work of adhesion, and uslng Hamaker theory W = -1rp~A/12/~, where p is the density and /the closest approach of the surfaces on contact. A Is the London-van der Waals constant. Assume the liquid is close packed In a face centered cubic lattice. Then if R, is the intermolecular spacing from geometry, the distance of closest approach Is (2/3)”’ R, = 1. Hence y = ap2A/16R:. I f further we take the maximum density p = .\/2/R,3, then y = nA/8R: = 0.399A/R:. Compare this with the lattice sum and Include only nearest-neighbor interactions. Then y = 3”2A/R08 = 1.732h/R,8. The answers by the two methods (continuum or discrete) differ by a factor of 4.41 For argon we have R,, = 3.8 A, A/R: = 1.66 X lo-’‘ erg. Hence y(Hamaker) = 4.50 dyn/cm; y(lattice sum) = 20 dyn/cm. The correct answer Is 13.4 dynlcm at the triple point. To correct the two computed values to account for the fact that argon is less than close packed, we have to multiply by @R,3/.\/2)2 = 0.684. A continuum theory would give 3 dyn/cm, much too small. I f we recognize that Hamaker constants calculated by Lifshitz theory wlll be reduced from those calculated by Hamaker, we see that there is no way except by assuming a Miculously small distance of closest approach that continuum theories work. The structure of the interface is crucial, in general, even though curve-fltting works well in partlcular. (47) J. Myazahi, J. A. Baker, and G. M. Pound, J . Chem. Phys., 84,3364 (1976); Y. Singh and F. F. Abraham, \bid., 67, 537, 5960 (1977). (48) R. 0. Horn and J. N. Israelachvili, Chem. Phys. Lett., accepted for publlcation. (49) D. Y. C. Chan, D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe, J . Chem. Soc., Faraday Trans 2, 75, 556 (1979). (50) R. M. Pashley and J. N. Israebchvill, Collois and Surfaces, submltted for publication.
