The long-range attraction between hydrophobic macroscopic surfaces

Highlights

• In the absence of nanobubbles, all hydrophobic surfaces interact similarly

• Interaction is A exp.(−2κD)/2κD at large separations with A scaling as ionic strength

• Microstructuration of the hydrophobic layer, overall charge-neutral, is essential

• Electrostatic mechanism through correlations and charge fluctuations around zero

• A single master curve explains the strength of the attraction for all the systems

Abstract

Direct measurements of the long-range strongly attractive force observed between macroscopic hydrophobic surfaces across aqueous solutions are reexamined in light of recent experiments and theoretical developments. The focus is on systems in the absence of submicroscopic bubbles (preexistent or induced) to avoid capillary bridging forces. Other possible interferences to the measurements are also eliminated. The force-distance profiles are obtained directly (no contributions from electrical double layer or hydrodynamics) between symmetric identical hydrophobic surfaces, overall charge-neutral, at the thermodynamic equilibrium and in a quenched state. Therefore in the well-defined geometry of crossed-cylinders, sphere-flat, or sphere-sphere, there is no additional interaction to be considered except the ever-present dispersion forces, negligible at large separations. For the three main categories of substrates rendered hydrophobic, namely surfaces obtained with surfactant monolayers physically adsorbed from solution to deposited ones, and substrates coated with a hydrophobizing agent bonded chemically onto the surface, the interaction energy scales as A exp (−2κD)/2κD at large separations, with measured decay lengths in accord with theoretical predictions, simply being half the Debye screening length, κ⁻¹/2, at least in non vanishing electrolyte. Taken together with the prefactor A scaling as the ionic strength, the interaction energy is demonstrated to have an electrostatic origin in all the systems. Thanks to our recent SFAX coupling force measurements with x-ray solution scattering under controlled nano-confinement, the microstructuration of the adsorbed film emerges as an essential feature in the molecular mechanism for explaining the observed attraction of larger magnitude than dispersion forces. The adsorption of pairs of positive and negative ions on small islands along the interface, the fluctuation of the surface charge density around a zero mean-value with desorption into or adsorption from the electrolyte solution, the correlations in the local surface ion concentrations along the surfaces, the redistribution of counterions upon intersurface variation, all contribute and are tuned finely by the inhomogeneities and defects present in the hydrophobic layers. It appears that the magnitude of the interacting energy can be described by a single master curve encompassing all the systems.

Introduction

Attractive hydrophobic forces play an important role in nature and industrial technological processes [[1], [2], [3]]. Examples include self-assembly of micelles, vesicles, and membranes [[4], [5], [6], [7]], folding of proteins [8], wetting phenomena [9], microfluidic transport, emulsion flocculation, destabilization of aqueous colloidal suspensions in mineral froth flotation separation process [10,11] where one of the colliding partner is a coarser air bubble and the hydrophobic particle will attach onto the bubble resulting in heterocoagulation. The hydrophobic force results from the underlying unfavorable solvation free energy of nonpolar solutes in aqueous or polar solutions. This so-called hydrophobic effect [4] manifests itself in many ways at the nano, meso, and macroscopic scales: hydrophobic moieties aggregate or cluster, oil separate from water, phase separation occurs, apolar/polar interfaces build up and arrange to create a large variety of structures (lyotropic liquid crystals), hydrophobic surfaces adhere strongly, water films dewet hydrophobic substrates resulting in a droplet with a large contact angle, etc. It was evidenced 50 years ago that two macroscopic hydrophobic surfaces may interact over large separations [12,13]. Since then, despite an extensive investigation, the experimental body of work on the range and magnitude of the hydrophobic force does not converge: recent overviews [[14], [15], [16], [17]] summarize the measurements of the hydrophobic force between a large variety of substrates, the effect of solution conditions (Temperature, salt addition, gas dissolution…), and some of the artifacts that may have occurred. Even when these artifacts are circumvented, it has been concluded that the experimental results are themselves often contradictory. As pointed out by all the reviews the discrepancies are attributed to the fact that different experimental force-distance measuring techniques and different methods of hydrophobization result in different measured range and magnitude of the interaction, highlighting possible interferences to the measurements [[14], [15], [16], [17]].

The hydrophobic surfaces that have been employed to investigate the hydrophobic attraction experimentally can be classified into three main categories: (i) inherently hydrophobic surfaces such as bulk polymer surfaces; (ii) substrates coated with a hydrophobizing agent bonded chemically onto the surface; (iii) surfaces obtained with surfactant monolayers physically adsorbed from solution to deposited ones.

Among the inherently hydrophobic substrates (system i), solid polymer surfaces and soft hydrophobic systems such as oil drops in water and gas bubbles have been investigated. With any aqueous solution, an interface invariably carries or develops a surface charge [1,2,18]. This gives rise to an electrostatic repulsion due to the overlap of electrical double layers at such surfaces, explaining why, for instance, aqueous dispersions of polytetrafluoroethylene (PTFE, Teflon) particles [19] may remain stable despite the particles being hydrophobic. In aqueous solutions an electrical double layer repulsion also operates between oil droplets [20] and between gas bubbles [21]. The deformable interfaces of the soft hydrophobic systems add to the complexity of the overall interaction: as recently elegantly demonstrated, the local properties of the bubble surface vary during its interaction with another surface, and there is dynamic coupling between thin film flow and double-layer structure [22]. Therefore, inferring what are the strength and the distance dependence of the intrinsic hydrophobic attraction in soft hydrophobic systems is not an easy task despite efforts for suppressing as far as possible all the other interactions that contribute to the overall interaction [17,20]. Similar difficulties are met when the interaction between solid polymer surfaces is investigated. The development of surface charge leads to a double-layer electric repulsion that masks the attractive hydrophobic contribution as shown for polydimethylsiloxane films [23] and polystyrene surfaces [24]. In addition, solid polymer substrates usually present interfaces that are not atomically smooth, with a variation in the physicochemical and structural surface properties. Both the physical heterogeneity (above all roughness) of the solid surfaces and their chemical heterogeneity have consequences not only for the range and magnitude of the attraction, but also for its variation with distance. The force-distance profile depends not only on solution conditions, but also on the history of previous contacts between the surfaces [25]. The appearance of step discontinuities in the profiles suggests that submicroscopic bubbles or cavities can be formed as soon as opposite surfaces had come into contact. These nanoscopic bubbles, which usually take place in roughness cavities, can coalesce and form gas bridges at the approach of surfaces. The formation of nanobubbles on solid surfaces requires a minimum of hydrophobicity as well as roughness and increases with further increase of the hydrophobicity, roughness, physical and chemical heterogeneities. Thus, when present, the long-range attraction between polymer surfaces (such as polystyrene [[25], [26], [27]] and teflon [28,29]) is usually consistent with a gas bridging (nanobubble) mechanism as observed in many systems of the second class (ii).

Indeed, for surfaces coated with a hydrophobizing agent bonded chemically onto the surface (such as silica surfaces coated with silane coupling reagents [[30], [31], [32], [33], [34], [35], [36], [37], [38]]), the origin of the forces measured for system (ii) has achieved the widest consensus. These chemisorbed hydrophobic substrates usually give a very high surface contact angle. On such surfaces, very small bubbles can attach stably when the substrates are in contact with an aqueous solution due to the incompatibility between the apolar surface and the polar medium. As suggested in the mid-1990s [32], these nanobubbles coalesce and form a gas bridge when two opposite hydrophobic substrates approach close to each other, inducing a discontinuous attraction profile with the separation. The existence of cap-shaped nanobubbles was experimentally confirmed later by atomic force microscopy (AFM) [39,40]; it has also been noted that large pancakes can form sometimes with large lateral expansion over several hundreds of nanometers and a height of a few nanometers [41,42]. What is attractive about bridging bubbles or cavities for these long-ranged forces is that the range of the force is related to their physical size. However, one conceptual difficulty with the small bubbles proposal is that, one would expect a lifetime of the order of microseconds, due to the high Laplace pressure inside the nanobubbles that drives the gas into the liquid. Since the pioneering works, the last two decades have seen a wealth of research on the nanobubbles and the resulting capillary force. A large focus has been on the direct imaging of nanobubbles using AFM and in-depth discussions to explain the existence and stability (> hours) of the surface nanobubbles (for recent reviews see refs. 43,44). It is now clear that in nearly all the systems (ii), what was thought to be a hydrophobic force was actually a capillary force resulting from the gaseous bridge formed from the coalescence of nanobubbles at the liquid-hydrophobic interface [14,45]. Thus, the so-called “hydrophobic” force measured in such cases appears to be a misleading term [14,43,45].

On the other hand, it has been suggested that the origin of the force is different for the surfaces with physically adsorbed surfactants. Understanding the behavior in this third class (iii) of systems is also important for industrial applications and processes, ranging from detergency, dispersants or stabilization of suspensions [46], paint and coating technology, surface conditioning (hair care formulations, sunscreens, make-up products, fabrics, dyeing, etc.) [47], filtration [48], nanoparticle synthesis [49,50], lubrication [51] to ore flotation [11]. The way the surfactant molecules interact with the substrate whether due to electrostatic attraction, hydrogen or covalent bonding, or hydrophobic forces, will determine the structure and morphology of the adsorbed film, and thereby how the surface properties of the substrate are modified when it gets coated. At a hydrophilic surface surfactant adsorption is highly cooperative and is in the form of surface aggregates (hemimicelles, admicelles, monolayered-like and bilayered-like patches) [46]. For ionic surfactants adsorbed onto oppositely charged substrates, the cooperative nature of the adsorption is reinforced by electrostatic attraction. Determining the force-distance profile between two opposite surfaces with adsorbed surfactants is of importance. It so happened the first indications of a hydrophobic attraction profile with separation were obtained with mica surfaces (negatively charged in water [[52], [53], [54]]) immersed in solutions of oppositely charged surfactant — the cationic cetyltrimethylammonium bromide C₁₆TAB [55]. Since then there have been many published accounts of hydrophobic forces measured between adsorbed layers of cationic surfactants with mica and silica substrates (for a review, see Ref. [15]). However, accurate determination of the force law has been prevented by intrinsic difficulties in the techniques used. Among many, the main limitation is due to the fact that, in most cases, the net attraction has been inferred by subtraction from a measured force that is overall repulsive (due to either hydrodynamic or electrical double layers). This procedure leads to considerable uncertainty, not only in cases where the hydrophobic attraction is long-range, but also when it is short-range. Indeed, except a few investigations detailed below, most of the measurements of the force between hydrophobic surfaces have been carried out with charged surfaces (for reviews, see refs. 14–17). The repulsive double-layer interaction present in such cases has to be subtracted from the measured force. But the assumed electrostatic repulsion has been calculated within the DLVO theory [56,57], a too simplified framework as it does not take into account, beyond many, the structure of the water liquid close to the surface and the correlations between the ions. Therefore the resulting attraction deduced when so many free parameters are chosen to fit experimental data using a theory, that is anyway, clearly inapplicable [[58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71]] has confused the literature. In particular, these limitations explain why the effects of dissolved electrolyte on the measured interaction have resulted in a number of observations that appear to be contradictory, as it was already pointed out 25 years ago [72] and repeatedly underlined since then.

Actually, for charged surfactants adsorbing to oppositely charged surfaces from solution, there is a limited range of concentration for which the surfactant-coated substrate is overall electrically neutral, as it was demonstrated for the cationic C₁₆TAB adsorbed on negatively charged substrates such as mica [73], glass [74,75] and silica [75]. Close to the point-of-zero charge (around 1/100 cmc (critical micellar concentration), the exact value depends on the surface charge of the substrate and hence the pH), there appears a long-range attraction, which is much larger than any possible van der Waals force [73]. Outside these narrow concentrations ranges, the surfactant-coated substrates carry invariably a surface charge. This interference inhibits a pure appraisal of the hydrophobic interaction for extended surfaces that are no longer globally electrically neutral. Indeed, measuring a total force that appears attractive does not mean that there are no repulsive double-layer forces but only that the attractive component is stronger at all surface separations. Thus, caution must be taken with previous works being hampered by electrical neutrality and stability-related issues, particularly as surfaces which were stable were not necessarily electrically neutral. This remark also applies for substrates rendered hydrophobic by chemical adsorption: see for instance the measured interactions between silanated mica surfaces that are actually not charge neutral [76,77].

Additional complexity arises also when the thermodynamic equilibrium has not been achieved. This is well illustrated for non quenched systems such as surfaces with physically adsorbed surfactants for which exists a possible variation of surfactant adsorption upon change in the surface separation. The ability of the molecules to move around on a dynamic time scale upon changes in the water gap thickness between the two confining surfactant-coated substrates induces an adsorption instability [78,79]. This is particularly exacerbated for surfactant layers weakly anchored as observed for mica surfaces covered by ethoxylated amine surfactant [80]. This driven adsorption instability is also favored when the surfactant coated-substrates are not at the thermodynamic adsorption equilibrium [81]. Note also that insufficient equilibration time for surfactant adsorption may create film morphometries at solid / liquid interfaces that are not representative of the structural organization at the thermodynamic equilibrium [82]. It should be emphasized that the interplay between intersurface and intrasurface energetics generally implies that the desorption of the charged surfactant species is collective and occurs at a rather well-defined surface separation [79] (as opposed to a gradual charge regulation process such as ordinary double-layer interactions [83]). This suggests that such a collective desorption will be more likely if the charged species form surface aggregates that will desorb as an entity [80]. Whatever the mechanism is, the importance of being at the thermodynamic equilibrium is fundamental: as pointed out by Pethica, unless adsorption equilibrium is ensured, the Derjaguin approximation [84] is strictly invalid, and the calculated work of approach may not give the free energy [78]. As a consequence any measured force – distance profile between such opposite substrates cannot be utilized to infer the hydrophobic interaction potential of extended surfaces.

Although the existence of a long-range attractive interaction between extended hydrophobic surfaces is by now well documented, the variety of results suggest strongly that there is no single mechanism that can account for the diversity of behavior observed with differently prepared hydrophobic surfaces. According to the range of the interaction measured the results can be classified into three main categories: (i) an attraction of variable strength and range, often discontinuous with discernible steps on approach; (ii) a strong and short-range attraction between very stable surfaces; (iii) a long-range attraction with exponential decay [[14], [15], [16], [17]]. The forces of type (i) are now well interpreted as resulting from the presence of small bubbles on one or both surfaces. Whatever the stabilizing factor for their existence is (surface-active materials originating from the preparation of the hydrophobic substrate (such as in the silylation procedure); sub-microscopic cracks and defects in the surfaces providing sites where bubbles may lodge, etc.), the interaction is a capillary-like force induced by the gaseous bridge formed from the coalescence of these nanobubbles at the liquid-hydrophobic interface. Therefore this interaction is not the focus of our present work. We will also leave the case (ii) out of the scope of the present article. Indeed, there are insufficient data to give an accurate functional form of these strong attractive interactions of short-range observed typically for gap widths smaller than a dozen of nanometers. This limitation arises from the sensitivity to details of the surface morphology and chemistry. Thus the variability in factors such as roughness, the precise nature of the chemical groups involved (such as –CH₂ or –CH₃), orientational effects and non-equilibrium, was pointed out as playing a significant role [15]. Rather, in the present article, we will deal with the attraction at long-range that has been reported in a variety of systems. These include substrates rendered hydrophobic with surfactant monolayers physically adsorbed from solution to deposited ones (dip-coating, Langmuir-Blodgett films), and self-assembling monolayers (SAMs) chemically adsorbed on surfaces (such as silane films).

The very long range strongly attractive force observed between macroscopic hydrophobic surfaces in aqueous solution is intriguing. The discrepancy between the results appears puzzling and a number of questions remain unanswered. However, these forces have been measured up to surface separations of 100 nm with magnitude that are 1–2 orders larger than those predicted by continuum theory (dispersions forces from Lifshitz theory [85]). It is a debated issue whether this deviation from continuum behavior should be attributed to molecular properties of the liquid, of the surface, or to surface interactions. Several theoretical explanations have been attempted and will be discussed in § 4: ordering of the liquid layers adjacent to the surface [86], anomalous polarization due to local enhancement of the permittivity [87], local fluctuation of adsorbed charges [88,89], in-plane polarized domains with lateral dipole interactions [90], cavitation instability [91,92], ionic exchange coupled with ion-ion correlations [[93], [94], [95]], dynamic structure in the confined liquid with collective vibrational motions [96,97].

Before proceeding it is appropriate to summarize the scope of this article. We narrow our focus to the long-range attraction (even asymptotic) operating between a pair of hydrophobic macroscopic surfaces. We restrict our description to systems that meet the following six criteria: (i) The opposite extended surfaces interact through a well-defined geometry (crossed cylinders, sphere-plane, sphere-sphere) with a local radius of curvature (typically in the range from 0.01 to 20 mm) several orders of magnitude larger than the surface separation range (0–0.2 μm). (ii) No submicroscopic bubbles are present at the liquid-hydrophobic interface or are induced when the opposite surfaces have come into contact. (iii) The surfaces are made of identical material: not only the underlying solid substrates are strictly identical in terms of homogeneity, smoothness, and physicochemical properties (such as wetting), but also their hydrophobic coating (physically adsorbed surfactant monolayer-like, chemisorbed silanized film) is prepared and achieved by means of the same procedure. (iv) They are surface-stable entities in aqueous electrolyte solutions. Long-term durability is here understood twofold. First coating integrity must be achieved for effectiveness preventing the absence of damage or local structural modification (at all the spatial and time scales) by means of the investigating technique. This means that the morphometry of the hydrophobic film is quenched, at the thermodynamic equilibrium. Secondly, the substrate / film assembly must be mechanically stable overcoming the often encountered limitation of ultimate film delamination or detachment of some coated parts from the substrate immersed in liquids. (v) The hydrophobic surfaces are electrically neutral in aqueous electrolyte solutions and hence there is no electrical double layer interaction contributing to the measured surface forces. (vi) the attractive force-distance profile is obtained directly from the force measuring technique in a quasi-static manner or when the hydrodynamic contribution is negligible. Since it is not obscured by any other repulsive forces (electrical double layer, hydrodynamic, presence of nanobubbles), the long-range attraction between extended hydrophobic surfaces is nothing else than the gross attractive profile measured directly. Only the ubiquitous dispersion interaction remains but it is negligible at large separations.

Three systems fulfilling all these six criteria have been selected in our presentation. Optimum conditions in the preparation of the hydrophobic substrates have been privileged. There were monolayers of single-chain cationic water soluble surfactants (cetyltrimethylammonium bromide, C₁₆TAB) adsorbed on mica or glass surface, monolayers of highly insoluble double-chained cationic surfactant (dioctadecylammonium, DODA, with either the acetate (DODAA) or bromide (DODABr) counterions) deposited on mica by dip-coating or by Langmuir-Blodgett, and glass surfaces hydrophobized by silanization.

In terms of experimental techniques, we start by review the four main devices and methods that have been used for measuring the force-distance profiles in these systems. We give a brief summary of facts necessary for the appreciation of the different experiments. In particular we emphasize the advantages and the limitations of each procedure (§ 2). Then the experimental data obtained both by other groups and by us are presented for the three aforementioned systems (§ 3). The fact that the long-range attraction profile in aqueous solutions obeys the same law for so different systems suggests that a similar mechanism is at play. Taking advantage of the electrostatic mechanism proposed for electrically neutral hydrophobic surfaces immersed in aqueous surfactant solutions [94,98], we generalize this interpretation for the other systems (§ 4): only the inhomogeneities along the interface need to be recognized.