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Adsorption Forces between Hydrophobic Monolayers V. V. Yaminsky,*,†,‡ B. W. Ninham,‡ H. K. Christenson,‡ and R. M. Pashley§ Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Institute of Advanced Studies, and Department of Chemistry, The Australian National University, Canberra, A.C.T. 0200, Australia Received September 8, 1995. In Final Form: December 15, 1995X Thermodynamic analysis of energy vs distance plots for the interaction of silica and mica surfaces in solutions of CTAB (cetyltrimethylammonium bromide) and similar surfactants at different concentrations shows that the long range attraction observed around the point of zero charge (pzc) is a charge regulation effect enchanced by the cooperativity of the cationic surfactant adsorption at anionic hydrophilic surfaces. The application of the Gibbs adsorption equation to experimental data shows that in the low concentration regime the adsorption increases with decreasing separation. This is due to an electrostatic contribution to the free energy of adsorption which increases as surfaces approach. An additional adsorption energy gain arises from association of hydrophobic tails when a sufficiently large adsorption density is reached and two-dimensional micellization is enhanced in the gap. A small increase of the electrochemical potential with decreasing separation gives rise to a large increase of adsorption. The double-layer repulsion at long distances corresponds to the ordinary DLVO result as long as changes in adsorption with separation remain small. At smaller separations the potential falls below its initial value because of the cooperative adsorption of the potential-determining ion, which results in the shift of the pzc to lower concentrations at close separations. The interaction is more attractive than would be expected from the constant potential approximation. The interaction pattern determined by equilibrium surfactant adsorption is different from that for nonpolar surfaces in pure water. An enhancement of adsorption in confined geometries is typical of condensation phenomena. A similar mechanism occurs for deposited monolayers of insoluble surfactants.
Introduction Force measurements on many systems1-4 have confirmed the existence of a predicted5 very long range attraction between hydrophobic surfaces. The forces are much stronger than van der Waals forces, they vary from system to system and no agreed theoretical explanation has yet emerged. We here extend earlier work6-8 to show that application of the Gibbs adsorption equation to surface force and wetting tension data can provide an insight into mechanisms. Hydrophobic interactions have been discussed previously in terms of contact angle, surface and water structure, solute, and electrostatic effects (see e.g. ref 9). For our thermodynamic analysis we make a distinction between intrinsically hydrophobic surfaces and those rendered hydrophobic due to surfactant adsorption. The first kind includes interfaces of water with nonpolar solids and liquids or air and polar solids with chemisorbed nonpolar speciesslike silylated glass. The second kind includes surfaces of mica and silica in solutions of cationic * Author to whom all correspondence should be addressed. Telephone: (06) 249 4693. FAX: (06) 249 0732. E-mail: vvy110@ rsphysse.anu.edu.au. † On leave from the Institute of Physical Chemistry, The Russian (USSR) Academy of Sciences, Moscow. ‡ Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Institute of Advanced Studies, The Australian National University. § Department of Chemistry, The Australian National University. X Abstract published in Advance ACS Abstracts, April 1, 1996. (1) Israelachvili, J. N.; Pashley, R. M. Nature 1982, 300, 341. (2) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W. Science 1985, 229, 1088. (3) Rabinovich, Ya. I.; Derjaguin, B. V. Colloids Surf. 1988, 30, 243. (4) Christenson, H. K. In Modern Approaches to Wettability: Theory and Applications; Schrader, M. E., Loeb, G., Eds.; Plenum Press: New York, 1992; p 29. (5) Pchelin, V. A. Vestn. Mosk. Univ. 1972, No. 2, 131; 1973, No. 2, 131 (in Russian). (6) Yaminsky, V. V. Langmuir 1994, 10, 2710. (7) Yaminsky, V. V.; Yaminskaya, K. B. Langmuir 1995, 11, 936. (8) Yaminsky, V. V.; Christenson, H. K. J. Phys. Chem. 1995, 99, 5176. (9) Yaminsky, V. V.; Ninham, B. W. Langmuir 1993, 9, 3618.
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surfactants. For these systems surfactant adsorption is reversible. At each bulk surfactant concentration the adsorption in a gap between two such surfaces is uniquely defined and varies with separation. To discuss these different categories of systems, we use the Gibbs equation
Γi ) -∂γ/∂µi; -dγ )
∑Γi dµi
(1)
which relates adsorption Γ to the surface tension γ via the values of the chemical potential µi ) µi° + kT ln ai. For an ideal solution the activity ai of a component i can be taken to be its concentration ci. Adsorption in a gap between two surfaces a distance D apart is
Γi(D) )
∫0D[ci(z) - ci,bulk] dz
(2)
where c(z) is the concentration profile and cbulk the bulk concentration. We take Γ(D)∞) ) 2Γ∞ to define adsorption at isolated interfaces. Then the interaction free energy per unit area defined as
E(D) ) γ(D) - 2γ∞
(3)
follows from the measured force F between two spheres of radius R via the Derjaguin expression E ) πRF, a rigorous result for hard core bodies. It follows that
-∂E(D)/∂µi ) Γi(D) - 2Γi∞
(4)
This equation is fundamental to our analysis. It shows how adsorption changes with separation are connected to force measurements and vice versa
E - Eref )
∑i ∫µ
µi i,ref
[Γi - 2Γi∞] dµi
(4a)
The reference potential can be for interaction in vacuum, pure solvent, etc. © 1996 American Chemical Society
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The Gibbs adsorption equation is a route to exact thermodynamic consideration of interfacial phenomena including long range electric double-layer forces,10 oscillatory solvation forces,8 and capillary phase transitions. The first two of the following examples cover intrinsically hydrophobic surfaces in water (1) and surfactant solutions (2), and the last three, adsorbed (3) and deposited (5) monolayers and salt effects (4). 1. Nonpolar Surfaces in Water For nonpolar, intrinsically hydrophobic surfaces (category 1) the simplest case is when the medium is water alone. Ideally, there are no dissociable groups. Indeed, silylated surfaces in water11 are effectively uncharged. The basic equation (eq 4) is still valid for a monocomponent medium. In practice, however, with surface force experiments the chemical potential of a monocomponent liquid cannot be varied. (For a bulk pure liquid at a fixed temperature only the application of high pressure can induce a substantial change in chemical potential. It can be changed if forces are measured across a condensate in equilibrium with the vapor of a liquid. However,12 such experiments involve other specific complications and there are currently no available data with hydrophobic surfaces.) Because of the lack of relevant data eq 4 cannot here be applied directly to experimental results. Equation 4a suggests an alternative theoretical approach. However, in this case also the construction of an exact adsorption model which must be sensitive to structural parameters of the liquid and of the surfaces themselves is in general difficult. This is because such a model has to account for molecular aspects of wetting hysteresis in particular. Nevertheless, important qualitative conclusions follow from simple dimensional considerations.9,13 The existence of a long range attractive force implies that the adsorption difference that occurs in eqs 4 and 4a is negative. This means that the density of a nonwetting liquid must decrease when the distance between surfaces decreases. This follows also from the thermodynamic theory of phase transitions. This subcritical effect is not necessarily accompanied by macroscopic cavitation. It arises for contact angles less than 90° when capillary vapor condensates are thermodynamically unstable. The density deficiency extends to large distances and leads to a long range attraction which can indeed be much larger than van-der-Waals forces. The effect is due to an enhancement of molecular density fluctuations in a lateral direction induced by decreased boundary attraction.9,13 The real situation is complicated by the fact that the experimental results embrace further uncertainties. Thus in practice water contains dissolved air. And the control of these further components whose adsorption behavior could interfere with the force is usually poor or nonexistent.14 It is therefore not surprising that results for seemingly similar systems can vary substantially. This observation only confirms that fine structural and environmental details to which so far little attention has been paid are important. We note here only general trends. When the equilibrium macroscopic contact angle is larger than 90° the probability of a critical fluctuation becomes large at a distance of at least several molecular dimensions. However, due to (10) Everett, D. H.; Radke, C. J. In Adsorption at Interfaces; Mittal, K. L., Ed.; ACS Symposium Series 8; American Chemical Society: Washington, D.C., 1975; p 1. (11) Yaminsky, V. V.; Ninham, B. W.; Stewart, A. M. Langmuir 1996, 12, 831. (12) Christenson, H. K.; Yaminsky, V. V. Langmuir 1993, 9, 2448. (13) Yaminsky, V. V.; Ninham, B. W. Langmuir, submitted. (14) Meagher, L.; Craig, V. S. J. Langmuir 1994, 10, 2736.
contact angle hysteresis, macroscopic cavitation may be suppressed unless the dynamic receding angle is also larger than 90°. In this case rupture of a metastable aqueous film between hydrophobic surfaces may be triggered at much larger distances. At these distances the excess internal stress in the film 2τr/D (τr ) γL cos θr is the receding wetting tension) becomes comparable to the strength of a liquid. As for solids, this can be much less than the ideal strength. Noncontact cavitation in a system with an obtuse receding contact angle has indeed been observed,15 through a discontinuity in the force from several hundreds of angstroms. This discontinuity corresponds to an abrupt change of density from the liquid to the vapor phase, and the distance at which this capillary-phase transition occurs (typically 500 Å) agrees with the rupture stress estimate. For this system no measurable force at longer distances was detected within the accuracy of surface force apparatus experiments. The capillary force which exhibits hysteretic behavior increases down to a separation on the order of 100 Å. At this point, below which the force gradient exceeds the stiffness of the measuring spring of the surface force apparatus, mechanical stability is lost and surfaces jump into contact. In the less hydrophobic system studied in ref 11, with a negative equilibrium wetting tension and an advancing tension close to zero, jump into contact also occurred from distances of 100 Å. But no attractive or repulsive forces were discernible before jump into contact occurs. Similar behavior with a large jump-in distance has been observed with surfaces of hydrophobic polymer.14 In several reported cases attraction before the jump-in was not pronounced,11,14 although one of the first measurements of a very long range attraction was also for methylated silica.3 2. Nonpolar Surfaces in Ionic Surfactant Solutions Adsorption of ionic surfactants such as CTAB onto initially uncharged hydrophobic surfaces like methylated glass induces a repulsion at long distances and reduces the jump-in distance11 (Figure 1). The charge of the surface increases with adsorption, which increases with surfactant concentration. The repulsive double-layer effect agrees with classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory at large distances and with expectations from surface energy considerations at shorter distances and down to contact. We analyze this example in detail before proceeding to surfaces made hydrophobic by surfactant. The general equation comprises a sum of adsorption differences for all components:
-dE )
∑i [Γi(D) - 2Γi∞] dµi
(4b)
Here the components include water molecules, protons, hydroxide ions, surfactant cations CTA+, and counterions Br-, with further trace ion contaminants in distilled water. They include further dissolved components from the atmosphere, like nitrogen, oxygen, carbon dioxide, and products of its dissociation. Both adsorption terms ΓH2O(D) and 2ΓH2O∞ for pure water between hydrophobic surfaces could be finite and negative, and their difference Γ(D) - 2Γ∞ is negative. Both will also change due to surfactant adsorption. However, as long as surfactant concentration in submicellar solutions remains low (cmc ∼ 10-3 M for cetyltrimethylammonium bromide (CTAB)), the chemical potential of water is (15) Parker, J. L.; Claesson, P. M.; Attard, P. J. Phys. Chem. 1994, 98, 8468.
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-dE/2 dµ ) Γ - 2Γ∞
Figure 1. Interaction between uncharged nonpolar surfaces in pure water (0) and ionic surfactant solutions with increasing (1, 2, 3) concentration (schematically). For methylated glass in aqueous CTAB and similar systems, (∂E/∂µ)D ≈ ∆E/∆µ > 0 and also d(-∂E/∂µ)/dD > 0 at all µ and all D. The adsorption of the surfactant at any given concentration always decreases with decreasing separation in the whole range of distances from infinity to zero. The scales are chosen arbitrarily to give an idea of the orders of magnitude of the forces and distances involved, see e.g. experimental data in ref 11.
practically unchanged when surfactant is added. The corresponding solvent term does not contribute directly to a change in the interaction energy under such conditions. The same is true for the cosolutes present. Even if their adsorption is significant, their chemical potentials are constant to a first approximation and the corresponding terms in the sum in eq 4b vanish. The only two components which matter are the cation and the anion of the surfactant. We have therefore
-dE ) ∆Γ + dµ+ + ∆Γ- dµwhere + now refers to CTA+ and - refers to Br- and ∆Γ ) Γ(D) - 2Γ∞. We have already noted that for this system the condition of zero charge is satisfied in pure water. Under such conditions each surfactant cation adsorbs with its anion to maintain electroneutrality. Exchange with ionic species from distilled water is possible. But this is insignificant because the concentrations of such species are much smaller than the CTAB concentration. To this approximation then, Γ+ ) Γ-. Note also that concentrations of spurious ions are not changed when surfactant is added. Their chemical potential remains constant. In any event their contribution to the interaction energy is negligible. While the only ions which are at a significant concentration are those from the surfactant, concentrations are low and the Debye-Huckel approximation holds for activity coefficients. Under such conditions dµ+ ) dµbecause the concentrations of both ions are equal and the activity coefficients which depend only on the overall ionic strengths are equal. Then because CTAB is a strong electrolyte, Γ+ ) Γ- ) Γ. Here Γ denotes the adsorption of CTAB as a neutral compound consisting of a pair of ions. Also dµ+ ) dµ- ) dµ, where µ denotes the mean ion activity. With these assumptions eq 4b reduces further to
-dE ) 2(Γ - 2Γ∞) dµ and we finally arrive at
(5)
The problem of considering the separate activities of the two ions is thereby circumvented. The last equation can be applied immediately to experimental data. Because concentrations are sufficiently low, corrections for nonideality can be neglected. For practical purposes one can assume dµ ) kT d ln c and take for c the analytical concentration of CTAB. At all distances the energy of interaction rises with increasing surfactant concentration, as shown in Figure 1. Adsorption at isolated interfaces increases with concentration and levels off at a maximum value when the monolayer is condensed prior to the cmc. While at a given surfactant concentration adsorption at a single surface is constant, it decreases when two surfaces approach each other. At each concentration in the whole range of distances (-dE/2 dµ) is negative. It increases in absolute value with decreasing separation. This shows that adsorption is a monotonically decreasing function of separation, for all concentrations and for all distances. CTAB is desorbed as the surfaces approach each other. The desorption of the surfactant cation is identical with the desorption of the counterion. At large distances the repulsive force is given by the DLVO expressions. The latter indeed follow from the Gibbs thermodynamic equation applied to the PoissonBoltzmann adsorption model.10 It appears that for this particular system both the potential-determining ions, here CTA+, and the counterions within the double layer are always desorbed to the same extent and together give equal contributions to the overall double-layer repulsive force. The physical meaning of the effect is clear. The electrostatic interaction is transmitted between the charged planes formed by ionic head groups of surfactant monolayers. This repulsion, which increases with decreasing separation, drives the adsorbed surfactant cations within the monolayers apart to the surface outside the interaction zone and away from the surfaces into the bulk solution. The anions within the overlapping diffuse double layers are depleted to the same extent. The resulting effect is accounted for thermodynamically in the integral osmotic terms of the Gibbs adsorption equation. As long as the charged monolayers are far apart and concentrations are low, the point charge Poisson-Boltzmann adsorption model is valid. The effects can be addressed in terms from chemical thermodynamics, like chemical potential, adsorption, and surface tension, or else their electrochemical counterparts, electrochemical potential, surface charge, and electric potential. If the separation is decreased in a step fast enough compared to characteristic times of adsorption reequilibration, surface charge remains unchanged and electric potential rises. But adsorbed layers of typical micellar surfactants like CTAB at interfaces of water with air or nonpolar liquids and solids are laterally mobile, and molecular exchange with solution is also rapid. Desorption occurs. This reduces the potential to its original value, which depends only on concentration, and the process is accompanied by a relaxation of the force. To put it differently, the electrochemical potential of adsorbed surfactant ions rises when surfaces come together at constant charge and at constant chemical potential in the bulk. Effectively this means that the free energy of adsorption within the monolayer in a gap of a finite width becomes less negative (smaller in absolute magnitude) than for isolated surfaces. The monolayers respond by decreasing adsorption density until equilib-
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rium with the bulk is reestablished. At this point the (electro)chemical potential of adsorbed surfactant ions within the monolayer is restored to the value of the chemical potential in the bulk. When separations are small enough and local concentrations are high, the electrochemical approximation breaks down. Hydrophobic association forces between surfactant tails and hard core/excluded volume effects which determine the monolayer adsorption of the surfactant become involved explicitly and change with separation. All these interactions including reorientation effects contribute to the overall energy of the final expulsion of the monolayers from the contact. We note that for this system all “additional” contributions are effectively repulsive. This is true a fortiori for the hydrophobic interactions responsible for the surfactant adsorption. This hydrophobic energy is released when surfactant adsorbs at the free interface, but equally it has to be taken back in order to squeeze the adsorbed molecules away from the gap and into the solution when the surfaces come together. As a result, the net repulsion at short separations can be larger than the DLVO result. This is the thermodynamic origin of the short range “non-DLVO” repulsive forces. The extra “hydration” repulsion can dominate down to zero separation if it is not counterbalanced by an even stronger attraction at close distances. The constant potential assumption is no longer valid in this regime. The electric potential falls to zero after all adsorbed components are squeezed away, as it does for the final coalescence stage of rupture of a “black” (Newtonian) soap film. It is clear from this last example that no residual potential remains because no interface is left. At zero separation, adsorption for all components is zero according to eq 2. From eq 4a it follows that the repulsive contribution to the energy of interaction which results from surfactant desorption at zero separation is twice the surface pressure of the surfactant layers at isolated surfaces,
γ∞ref - γ∞ )
∫µµ ≈-∞ Γ∞ dµ ref
) [E(D)0) - Eref(D)0)]/2 The reference state here is for pure water. The change of surface energy due to surfactant adsorption (for the isolated interfaces) can be measured independently of surface forces via wetting and/or adsorption techniques.7 For methylated surfaces the surface pressure even in micellar solutions remains lower than Eref/2sthe value of adhesion in pure water. The difference accounts for the finite values of adhesion over the whole range of concentrations observed in these systems.11 For the present system the absolute minimum of the interaction potential in surfactant solutions is indeed attained at zero separation when all Γi ) 0 for all components including surfactant and water as well. This follows also from eq 4a and the experimental fact that adhesion in solution equals adhesion in air minus the wetting tension (the values of surface pressure at the nonpolar solid-vapor interface are negligible). Contact thermodynamics has been considered experimentally in detail elsewhere.6,11,16 Submonolayer contact effects which cannot be resolved via direct distance measurements follow from a comparison of adhesion and surface energy parameters. (16) Yaminsky, V. V.; Pchelin, V. A.; Amelina, E. A.; Shchukin, E. D. Coagulation Contacts in Disperse Systems; Chimia: Moscow, 1982; p 185 (in Russian).
It is clear, however, that the monolayers are expelled from nonzero distances. At high surfactant concentrations when contact angles are below 90° so that cavitation is prevented, the jump-in distance is about 40 Å. This is twice the monolayer thickness. Monolayers are in a condensed state at such concentrations. Adsorption falls dramatically from the monolayer value to zero over a range of smaller distances. The variation of the height of the barrier with electrolyte clearly follows surface pressure trends rather than DLVO fits. At low concentrations when the equilibrium contact angle is above 90° and the jump-in distances are long, the final monolayer collapse still may occur at smaller “monolayer” distances. However, if noncontact cavitation occurs, adsorption for surfactant and also for water falls immediately at the cavitation distance to the negative value of -cbD because all the molecules are expelled. The adsorption then increases linearly with distance to zero at contact, at D ) 0. 3. Anionic Surfaces in Cationic Surfactant Solutions The first experimental observations of the hydrophobic force1,2 and many subsequent works have been made on mica and silica rendered hydrophobic by cationic surfactants. They are different from those considered in the previous section. Both mica and silica are hydrophilic and negatively charged. The contact angle is close to zero for mica and hydroxylated silica. For dehydroxylated silica it can be larger. We first remark on the similarities and differences between the two surfaces. Mica is strongly charged in pure water. The surface charge for silica is an order of magnitude smaller but is still quite substantial and rises with pH. Unlike intrinsically hydrophobic surfaces which adhere in water even more strongly than in air, adhesion is low for hydrophilic surfaces in water. For mica, adhesion in water is lower than in air by an order of magnitude but remains finite. For silica in water, adhesion is reduced to zero. The above thermodynamic considerations show that the energy of interaction at zero separation equals the energy of adhesion in a dry atmosphere plus the wetting tension plus the surface pressure of adsorbed water vapor. For small contact angles the wetting tension, i.e. the difference between the solid-vapor and solid-liquid surface tensions, is close to the surface tension of water at its interface with air, that is about 70 mN/m. The surface pressure which is negligible for low-energy nonpolar surfaces has large and similar magnitudes for silica and mica. Coincidentally, these are close to the surface tension of water. For freshly cleaved mica in an inert atmosphere (dry nitrogen) adhesion has a negative value which is larger in absolute magnitude than the positive medium contribution resulting from wetting and adsorption.17 The overall sum is negative, and this accounts for the small but finite adhesion in water. On the other hand, for silica the initial adhesion in air is apparently somewhat lower and its sum with wetting tension and surface pressure, which gives the energy of interaction at zero separation, is positive. Under such conditions water adsorption must generate a repulsion. Thermodynamic considerations lead to the conclusion that such a hydrophilic repulsion, unlike the hydrophobic attraction, is inevitably short ranged.9 However, in the case of silica the situation is complicated further by the possibility of surface hydrolysis, which can result in a polymeric silica gel. The repulsive effects due to the latter (17) Christenson, H. K. J. Phys. Chem. 1993, 97, 12034.
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can propagate to substantial distances.18 At still larger separations the repulsion reverts to the DLVO form and is due to the surface charge. Consider now what happens at an interface with water when surfactants are added. Adsorption of cationic surfactants proceeds at negative surface sites of the solid. At very low CTAB concentrations (less than e.g. the concentration of ions in purified water) adsorption densities are low. Indeed, as long as adsorption is driven by electrostatic forces alone, the free energy of adsorption of a surfactant cation should not be different from that for a monovalent inorganic cation. Adsorption rises cooperatively on approaching the point of zero charge (pzc). At this point anionic sites dissociated in pure water are mostly taken up with surfactant cations. Because the initial charge density is high, the resulting adsorption density is high enough to allow surfactant tails to associate in hydrophobic patches. At some concentration, before the pzc, a critical density is reached above which a substantial degree of tail association becomes possible. This is a two-dimensional analogue of micellization. The free energy of adsorption within such surface micelles contains hydrophobic and electrostatic contributions. Both are attractive. The energy gain is thus far larger than for single isolated molecules. It is also larger than for adsorption at air-water or water-hydrocarbon (methylated glass) interfaces. The latter is driven by hydrophobic attraction, but electrostatic contributions to the free energy of adsorption are in this case repulsive. At concentrations for which the pzc is reached, adsorption densities at the interface with air are indeed negligibly small. In agreement with this mechanism (as discussed in detail in ref 6) the point of zero charge is attained at a lower concentration for more strongly charged mica (pzc about 5 × 10-6 M) and at a higher concentration for less strongly charged silica (pzc about 5 × 10-5 M). A larger adsorbed density results in a larger hydrophobic contribution to the free energy of adsorption. Unlike bulk micelles and condensed layers adsorbed from micellar solutions, these “flat” micelles formed at much lower concentrations are essentially hydrophobic. However, also at the point of zero charge, the surface on average remains overall hydrophilic. This is because only a limited fraction of the originally hydrophilic surface is covered by hydrophobic tails. Indeed, for silica the initial charge density, about 700 Å2 per charge in pure water, corresponds to a limiting adsorption density of about 700 Å2 per CTA+ ion at the pzc. The cross section of a CTA+ ion is about 100 Å2. Only 10-15% of the area is covered, or even less, since the tails tend to aggregate in patches. Contact angles are surprisingly high for such low coverages. For silica glass the contact angle increases from zero with pure water to an equilibrium value of about 70° at the pzc. But macroscopic angles are here due to the much higher adsorption at the vapor side of the threephase line. The free energy of adsorption at the solidvapor interface is larger because the hydrophobic contribution is larger. The entire surfactant tail escapes contact with water on the air side. A condensed monolayer with an area per molecule around 100 Å2 forms at the pzc at the silica-air interface. The equilibrium wetting tension/adsorption difference isotherms for cationic surfactant on silica and mica have been considered in detail elsewhere.7 Surface force effects of cationic surfactant adsorption at such surfaces at low concentrations are in a sense (18) Vigil, G.; Xu, Zh.; Steinberg, S.; Israelachvili, J. N. J. Colloid Interface Sci. 1994, 165, 367.
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Figure 2. Interaction between anionic polar surfaces in pure water (0) and cationic surfactant solutions with increasing (1, 2, 3) concentration (schematically). For silica and mica in aqueous CTAB, (∂E/∂µ)D ≈ ∆E/∆µ < 0 and also d(-∂E/∂µ)/dD < 0 at all µ and all D. The adsorption of the surfactant at any given concentration always increases with decreasing separation at separations from infinity to contact. Note that in surfactant-free hydrophobic systems adsorption of water itself decreases with separation. The scales are chosen arbitrarily to give an idea of the orders of magnitude of the forces and distances involved, see e.g. experimental data in ref 23.
opposite to those considered in the previous section. For example the double-layer repulsion, initially strong in pure water, decreases with an increase of concentration and eventually vanishes at the pzc. In the same concentration intervals the free energy of adhesion increases. Adhesion is zero in water for silica, and E/2 ≈ 10 mN/m at the pzc. For mica adhesion values at the pzc are as high as 30 mN/m, compared to about 3 mN/m in pure water. At all concentrations (below the p.z.c.) and at all distances (above the monolayer contact) the free energy of interaction decreases with surfactant concentration. This is exactly opposite to the surface force trend considered in the previous section (cf. Figures 1 and 2). Only at higher concentrations above the pzc and on approaching the cmc, when an outer hydrophilic layer is adsorbed on the top of the inner, hydrophobic, layer, is that trend reversed. Unlike hydrophilic layers adsorbed at neutral hydrophobic interfaces by a molecular ion pair mechanism, hydrophilic surfaces of silica or mica in pure water are initially charged and the hydrophobic layer builds up at lower concentrations through ion exchange. Because the surface is initially charged and because the pzc, around which the main effect takes place, may be comparable to the concentration of residual electrolyte in pure water, the justification for neglect of corresponding Γ dµ terms is not so straightforward. However, to a first approximation the number of deprotonized surface groups is independent of the concentration of CTAB. This follows from the fact that CTA+ adsorption density at the pzc for an isolated surface equals the initial surface charge.6 Negative adsorption of coions is small in absolute magnitude, and even though additional Br- ions are introduced with CTAB, anionic contributions to a change in interaction energy are small. This is evident through the fact that hardly any effects are caused by adding inorganic 1:1 electrolyte at such concentrations apart from a slight decrease of the Debye length. When CTAB is adsorbed, a counterion is desorbed, but the latter is at constant chemical potential. Under such conditions CTA+ remains the only thermodynamically active component. The basic equation then takes the form
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-dE ) (Γ - 2Γ∞) dµ
(6)
where Γ now refers to CTA+ and dµ ) kT d ln cCTAB to a good approximation. From the fact that the energy of interaction at all distances increases with increasing concentration (Figure 2) it follows that adsorption increases as separation decreases. This is true over the whole range of distances from infinity down to adhesive contact at all concentrations below the pzc. Only on approaching the cmc does adhesion fall again and doublelayer repulsion rise. The latter effect associated with a desorption of the outer layer (assigned in ref 19 as a reason for hydrophobic attraction) is qualitatively similar to the effect of CTAB adsorption on the interaction between methylated surfaces, as considered in the previous section. We shall concentrate, however, on the lower concentration ranges. At large separations CTAB exhibits the ordinary DLVO behavior which is expected for a potential-determining ion. The double-layer repulsion is reduced by surfactant because the surface charge is reduced. The thermodynamic result showing that adsorption increases with decreasing separation has the following interpretation. In the absence of adsorption equilibration, approach under constant charge conditions increases the surface potential (in absolute value). Adsorption reequilibration brings it down to the original value by attracting more surfactant into the gap. This is in contrast to the situation for surfactant layers at initially uncharged hydrophobic interfaces for which surfactant cation together with bromide anion have both to be desorbed to lower the potential. In the present case with initially charged hydrophilic surfaces the same effect is achieved by an increased adsorption of surfactant cation at the anionic surface sites responsible for the charge. A similar effect would be induced by a strongly adsorbing inorganic anion as well, such as Cr3+ for example. However, for inorganic ions the interaction remains repulsive down to shorter separations, in qualitative agreement with conventional DLVO theory. At close separations the repulsive effect can even exceed DLVO expectation. For example, for mica surfaces adhesive in pure water the adhesion falls to zero above some critical electrolyte concentration and the interaction becomes repulsive at short range.20 By contrast, adhesion rises in the presence of cationic surfactants. The contact effects of CTAB and similar surfactants with silica and mica as compared to those of inorganic electrolytes are explored in detail in an earlier publication.6 While at large distances the increase of adsorption with separation is small, the effect at contact is dramatic. For silica, for example, contact adsorption at concentrations around the pzc is several times larger than that at isolated interfaces. The area per molecule in contact is about 100 Å2 compared with the corresponding value of about 700 Å2 for a single surface. In this case too the effect has a clear physical meaning. For adsorption in a narrow gap of molecular thicknesses the hydrophobic contribution to the adsorption free energy is much larger because hydrocarbon tails can totally escape the aqueous environment in the narrow slit. The adsorbed layer is condensed in contact while it remains rarefied at isolated surfaces where the tails are exposed to water. A similar condensation, and for a similar reason, occurs at the silicaair interface, for which adsorption is also several times (19) Podgornik, R.; Parsegian, V. A. J. Phys. Chem. 1995, 99, 9491. (20) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531.
larger than the maximum pzc adsorption at the silicawater interface. If considered thermodynamically, experimental results which have caused the most confusion over the past decade show that adsorption begins to deviate from the constant potential DLVO trend at much larger separations. The barrier distance below which the interaction becomes attractive is large at concentrations several times lower than the pzc, and the interaction is purely attractive at all distances when all charge is apparently neutralized. This presents a paradox: there is no such attraction in the absence of CTAB! This can easily be verified by adding NaCl up to 10-1 M to suppress the double layer. There is no interaction at long range apart from a very weak van-der-Waals attraction noticeable prior to a steep “hard wall” repulsion at short distances.21,22 Experimental data presented earlier23 show that at c ≈ 9 × 10-6 M the repulsion peaks at a value E/2 ≈ 0.01 mN/m at D ≈ 20 nm. At c ≈ 4.5 × 10-5 M (≈pzc) the interaction energy is zero or slightly negative at the same distance of 20 nm. On bringing the surfaces from infinity to this separation, adsorption increases according to eq 6 by 1.6 × 1011 molecules/cm2 or by ≈1% of its initial amount Γ∞ ≈ 1.4 × 1013 molecules/cm2 for isolated surfaces. On going further down from 20 nm to contact, adsorption is further increased by 300-400%. An enhanced rise of adsorption from separations of hundreds of angstroms can hardly be explained by extending the contact argument. It cannot be explained either by extrapolating electrostatic arguments alone to shorter distances. In view of the mechanism of adsorption a combination of the two provides the key to the mystery: The long range attraction begins to show up at concentrations several times smaller than the pzc. The system is here just below the point from which cooperative adsorption, which leads to charge neutralization at isolated interfaces, is poised to proceed. The ordinary constant potential approximation assumes that the long range electrostatic repulsion which enhances adsorption of a potential-determining ion is the only factor responsible for charge regulation. However, because of the cooperative nature of the adsorption a small increase in the free energy of adsorption due to an equivalent increase of electrochemical potential gives rise to a large increase of adsorption with decreasing intersurface separation. After a critical adsorption density is reached, sufficient to allow the hydrophobic tails to associate, adsorption is in no way in proportion to the change in electrochemical potential as might be expected from a mass action law with fixed equilibrium constant. Rather, adsorption increases much faster. A similar cooperative increase of adsorption with increasing chemical potential in the bulk solution happens at a slightly higher concentration at an isolated interface. Effectively, this means that the point of zero charge is shifted to lower concentrations at shorter separations. Because of this electrochemical potential effect on adsorption densities, adsorption at finite separations can also be larger than the maximum pzc adsorption values at isolated interfaces. Further, while the surfaces on the average are electrically neutral, they represent effectively a mosaic of positive and negative ions. And because of the lateral attraction between hydrocarbon tails they have a tendency to segregate in patches. (21) Horn, R. G.; Smith, D. T.; Haller, W. Chem. Phys. Lett. 1989, 162, 404. (22) Rabinovich, Ya. I.; Derjaguin, B. V.; Churaev, N. V. Adv. Colloid Interface Sci. 1982, 16, 63. (23) Parker, J. L.; Yaminsky, V. V.; Claesson, P. M. J. Phys. Chem. 1993, 97, 7706.
1942 Langmuir, Vol. 12, No. 8, 1996
In spite of a high free energy of adsorption which makes desorption a relatively slow process, the adsorbed CTA+ cations retain high lateral mobility, as is evidenced by a number of surface force and wetting tension effects.6,7 Fluctuating (macro)dipole interactions have been suggested as a factor in additional attraction. Water density fluctuations responsible for “ordinary” hydrophobic interactions can be one more factor which enables transmission of adsorption effects to longer distances. It might be noted also that CTAB concentrations are comparable with or even larger than the concentration of residual ions in water. Before all the charge is neutralized, at a larger concentration or a shorter distance, the hydrophobic CTA+ cation may be the main counterion in the double layer. Macrocavitation as a possible source of the long range attraction seems here to be a less likely proposition. Equilibrium contact angles at least for CTAB on silica are less than 90° though the advancing angles are substantially higher than the equilibrium values. Also the actual hydrophobic area at isolated surfaces is much lower than what could be expected for such angles if hydrophobic species were irreversibly chemisorbed. No evidence which could confirm a capillary liquid-vapor phase transition for CTAB solutions so far exists. However, vapor capillary condensation cannot be excluded as a contributing mechanism for more hydrophobic monolayers formed from for example double-chain cationic surfactants. Microcavitation between adsorbed patches which in fact can be extremely hydrophobic is not ruled out. An increase of adsorption with decreasing intersurface separation can be considered as a step toward a capillary phase separation for the adsorbed component itself. The effect is well-known for vapors of wetting liquids on solid substrates.24 Below saturation, even if the contact angle is zero, the thickness of adsorbed layers at single surfaces is finite. Adsorption (thickness) increases with decreasing separation under the effect of van-der-Waals forces. From a critical distance the film grows spontaneously and the gap is filled with condensate. The condensate is stable up to a larger distance, which follows from the Kelvin equation. Capillary phase separation similarly occurs in a solvent phase for a partly miscible wetting solute. The critical condensation distance decreases with decreasing concentration (vapor pressure) and is smaller when contact angles are larger. At sufficiently low concentrations the hysteresis vanishes and adsorption becomes a unique function of separation for all distances. In the case of silica or mica in aqueous CTAB the attractive van der Waals effect is substituted for electrostatic attraction between surfactant cations and negatively charged surfaces enhanced by their proximity. Because the electrostatic double-layer interaction effectively extends to larger distances than van-der-Waals forces, the increase of surfactant adsorption driven by electrostatic and hydrophobic interaction is significant from larger separations and the resulting subcritical attraction is stronger than that for van-der-Waals solutes. In the latter case the effect could be resolved only in thicknesses not in forces.24 For surfactant layers there is no critical phase transition in spite of the fact that the layers, rarefied at free interfaces, are condensed when in contact. The hydrophobic interaction is apparently hysteresis free. This is not surprising because the only bulk phase transition is micellization. Acting concentrations are by orders of (24) Christenson, H. K. Phys. Rev. Lett. 1994, 73, 1821.
Letters
magnitude smaller than the cmc. And micellization, unlike ordinary phase separation, proceeds without activation. More detailed discrimination of molecular mechanisms behind the experimentally observed enhancement of adsorption from long distances will become possible only through detailed theoretical consideration of ionic adsorption and from experimental data sufficiently extensive to admit of quantitative thermodynamic analysis. From the existing data one can deduce unambiguously only that there is a continuous transition in the vicinity of the pzc from a slow increase of adsorption with decreasing separation at long separation to the very high contact values which occur at the intermediate distance ranges. Some additional light on the mechanisms may be shed by electrolyte experiments briefly treated in the next section. Of course, by choosing a sufficiently high Hamaker constant, the attraction can formally be fitted to the dispersion potential, as has been done in ref 19. But by no means does this remove the inconsistency. For example, there is no such attraction between methylated surfaces in ethanol. One still has to assume that Hamaker constants are several orders of magnitude higher for water than for wetting liquids. It is worth mentioning that the interaction changes from repulsive to attractive in the range of distances where the constant potential result begins to deviate from the constant charge result. For the weakly charged silica surfaces (about 25 mV) this indeed happens from distances below 20 nm. The “extra” repulsive energy of the constant charge approximation is effectively converted into an “extra” attractive (hydrophobic) energy. (The experimental interaction potential looks much like a mirror reflection of the constant charge in the constant potential energydistance curve.) 4. Salt Effects with Adsorbed Hydrophobic Monolayers It has been recently reported25 in accordance with some earlier observations that simple electrolytes reduce the range of attraction at the pzc, with a screening length half the Debye length. Such a screening effect could be expected from what now is called the zero frequency ion pair charge fluctuation approximation of contact limit vander-Waals nonlinear Poisson-Boltzmann theory.26,27 The results were fitted to an empirical equation
E ) -RkT(Lce-2κD)/(2κD) where L is a length parameter (Bjerrum length) and R is on the order of 103. NaCl is present up to much higher concentration than CTAB, and as long as the pzc assumption holds, both Na+ and Cl- ions should be adsorbed to the same extent. Application of the relevant thermodynamic equation (eq 5) leads to
Γ - 2Γ∞ ≈ -R(Lce-2κD)/2 The adsorption difference is negative, since the energy increases by addition of salt. Ions are expelled when surfaces approach each other. If charge fluctuations in the planes of the surfaces generate a long range force, a diffuse electrically neutral atmosphere of positive and negative ions might be expected. The equation bears a (25) Kekicheff, P.; Spalla, O. Phys. Rev. Lett. 1995, 75, 1851. (26) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: New York, 1976; Chapter 7. (27) Spalla, O.; Belloni, L. Phys. Rev. Lett. 1995, 74, 2515.
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Langmuir, Vol. 12, No. 8, 1996 1943
superficial resemblance to the Poisson-Boltzmann adsorption isotherm in the Debye-Huckel approximation for counterions at a charged surface in the zero charge limit. The preexponential factor is in fact on the order of the surface charge of silica in pure water ≈ adsorption density at the pzc. Whether the effect could be attributed to surfactant desorption from a silica gel layer has to be seen. 5. Nonequilibrium Layers The longest range for attractive forces has been observed typically for monolayers of water insoluble surfactants formed on mica by e.g. Blodgett deposition.4 If such monolayers were to be perfectly stable, as is suggested by the traditional term “insoluble”, they could be expected to behave in force measurements similarly to chemisorbed silane layers. This is not the case, and even if desorption into the bulk was totally prevented, the lateral mobility remains similar to that for adsorbed layers of shorter chain surfactants. Unlike covalently bonded chemisorbed species the lateral diffusion of physiosorbed surfactants is not hindered. If the maximum molecular density of a close packed monolayer is not reached, the layer retains a capacity to respond to changes of intersurface forces by changing adsorption density. The role of the bulk reservoir in this self-regulating system is played by the surface outside the interaction area. As long as the monolayer is allowed to readjust itself in response to changing conditions and an equilibrium density profile in the lateral direction is maintained during a force run, the Gibbs equation is applicable as for monolayers on a Langmuir trough when the adsorption is changed reversibly by changing the position of the barrier. This does not yet explain, however, why the attraction between such layers often extends to larger distances than for soluble surfactants and is often retained at higher salt concentrations when the Debye length is short. It has been shown in the previous sections that for soluble surfactants adsorption is not restricted to a monolayer. The adsorbed layer is apparently diffuse and extends to significant distances away from the surface where the solution still remains enriched with the surfactant. While the rate of the diffusion into the bulk for deposited layers of less soluble surfactants can be indeed low (but it is still finite, as is suggested by capillarographic measurements28 ), a low solubility does not imply that a rearrangement of the layer cannot occur. It is known that the rates of desorption of LB-deposited monolayers are much higher from the three-phase line than from the solid-liquid interface.28 The transfer of the deposited layer back onto the air-water interface is much more favorable than for desorption into the bulk. The additional free energy gain is the free energy of adsorption from the bulk onto the interface with air. The latter is particularly high for longer chain surfactants. The layer displays a similar tendency to become more condensed at the vapor side and more rarefied at the liquid side of the three-phase line in the plane of the solid.7 There is a similar energy gain for molecular transport into the gap between two surfaces, for both soluble and insoluble surfactants.6 Deposited layers are essentially nonequilibrium and are easily damaged on contact in essentially the same way as they are damaged at the three(28) Yaminsky, V. V.; Claesson, P. M.; Eriksson, J. C. J. Colloid Interface Sci. 1993, 161, 91.
phase line. This is a move toward a thermodynamically more favorable state. No such changes occur with chemisorbed silane layers which are stable not only in water but also in organic solvents, both at the solid-liquid interface and at the three-phase line,28 as well as on contact between the two surfaces. Deposited LB monolayers unlike silane layers are rapidly desorbed by polar organic liquids like ethanol. A swollen (e.g. liquid crystalline)/desorbed/detached material in whichever form is even more mobile than the original monolayer and can lead to a further enhancement of adsorption, as for soluble surfactants. It is interesting to note that interaction in a bulk liquid crystalline phase often shows a very long range attractive component.29 The only apparent limit for the range of such a force is that for a capillary force. While the range of the attraction determined by such nonequilibrium condensates is essentially unlimited, the functional forms of the attraction can be variable. The surfactant material outside the original monolayer is in a random state and has diffuse boundaries of an e.g. liquid crystalline soft (lyophilic gel-like) phase. Its properties are dependent on ionic composition but are not necessarily correlated to the Debye length. When the system is not at equilibrium and the chemical potentials are not defined, its behavior cannot be analyzed thermodynamically in a straightforward way as for soluble surfactants. Qualitatively, experimental observations on such systems are consistent with the general concept of a capillary type precondensation phenomenon. A similar attraction of an even longer range is observed for freshly molten silica glass surfaces in water vapor. Hydrophilic ionic components of commercial glasses are segregated at the surface during melting and form swollen condensates in the vapor. A more detailed experimental account of the capillary effects relevant to “polywater” will be presented separately. In summary, our analysis shows that at least for “hydrophobic” interactions induced by ionic surfactants in dilute electrolyte an understanding of the long range forces follows from the application of the Le Chatelier principle to ion exchange surfactant adsorption. General considerations along the same lines as this paper have been made by Pethica.30 We remark finally that an exact formal treatment of the surfactant-electrolyte-charged interface interactions problem including attractive lateral interaction is implicit in ref 31, and relevant charge regulation ideas were extended lately.32 A full analytic consideration will be presented by us subsequently. Acknowledgment. One of the authors (V.V.Y.) wishes to thank David Antelmi for attracting his attention to his work on the phenomenon of a long range monotonically attractive component of the oscillatory force in liquid crystalline capillary phases. Note Added in Proof. New experimental results which support these mechanisms are presented in a separate publication.33 LA950740Z (29) Antelmi, D. A.; Kekicheff, P.; Richetti, P. J. Phys. II 1995, 5, 103. (30) Pethica, B. A. Colloids Surf., in press. (31) Ninham, B. W.; Parsegian, V. A. J. Theor. Biol. 1971, 31, 405. (32) Hall, D. G. J. Colloid Interface Sci. 1985, 108, 411. (33) Yaminsky, V.; Jones, C.; Yaminsky, F.; Ninham, B. W. Langmuir, submitted.
