Developing a General Interaction Potential for Hydrophobic and

Invited Feature Article pubs.acs.org/Langmuir

Developing a General Interaction Potential for Hydrophobic and Hydrophilic Interactions Stephen H. Donaldson, Jr.,† Anja Røyne,‡ Kai Kristiansen,† Michael V. Rapp,† Saurabh Das,† Matthew A. Gebbie,§ Dong Woog Lee,† Philipp Stock,∥ Markus Valtiner,∥ and Jacob Israelachvili*,†,§ †

Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080, United States Department of Physics, University of Oslo, 0316 Oslo, Norway § Materials Department, University of California, Santa Barbara, California 93106-5050, United States ∥ Interface Chemistry and Surface Engineering, Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany ‡

S Supporting Information *

ABSTRACT: We review direct force measurements on a broad class of hydrophobic and hydrophilic surfaces. These measurements have enabled the development of a general interaction potential per unit area, W(D) = −2γiHy exp(−D/DH) in terms of a nondimensional Hydra parameter, Hy, that applies to both hydrophobic and hydrophilic interactions between extended surfaces. This potential allows one to quantitatively account for additional attractions and repulsions not included in the wellknown combination of electrostatic double layer and van der Waals theories, the so-called Derjaguin−Landau−Verwey−Overbeek (DLVO) theory. The interaction energy is exponentially decaying with decay length DH ≈ 0.3−2 nm for both hydrophobic and hydrophilic interactions, with the exact value of DH depending on the precise system and conditions. The pre-exponential factor depends on the interfacial tension, γi, of the interacting surfaces and Hy. For Hy > 0, the interaction potential describes interactions between partially hydrophobic surfaces, with the maximum hydrophobic interaction (i.e., two fully hydrophobic surfaces) corresponding to Hy = 1. Hydrophobic interactions between hydrophobic monolayer surfaces measured with the surface forces apparatus (SFA) are shown to be well described by the proposed interaction potential. The potential becomes repulsive for Hy < 0, corresponding to partially hydrophilic (hydrated) interfaces. Hydrated surfaces such as mica, silica, and lipid bilayers are discussed and reviewed in the context of the values of Hy appropriate for each system. vapor−liquid-like interface.3,7 As two such hydrophobic interfaces approach each other, liquid water becomes metastable compared to the vapor and a drying transition induces evaporation between the two hydrophobic surfaces.8,9 A drying transition should occur between macroscopic hydrophobic interfaces at a separation distance of Dc ≈ 100 nm, according to the Kelvin equation.8−10 However, evaporation between two closely approaching static hydrophobic surfaces is generally not observed experimentally. A large energy barrier prevents evaporation even at nanoscopic distances of D ≈ 5−10 nm,11,12 and a strongly attractive surface interaction acts to pull the surfaces into contact at the same distances.13−16 Although a vapor bridge between the surfaces is the thermodynamic equilibrium state below Dc ≈ 100 nm, liquid water remains metastable throughout, so this attractive interaction occurs on a metastable branch of the freeenergy landscape. The attractive interaction between hydro-

1. INTRODUCTION Hydrophobic interactions are ubiquitous in water-based biological and technological systems and are directly implicated in everyday phenomena such as the separation of salad dressing, the gripping ability of surfers’ feet on a freshly waxed surfboard, and the cleaning action of shampoos and detergents. On the molecular level, biological membranes and proteins organize into highly specific structures that determine their functions, driven by the arrangement of hydrophobic units within the macromolecules. The self-assembly process of proteins, in which hydrophobic groups are buried within the macromolecular interior and hydrophilic groups are exposed to aqueous solution, was understood in simple terms in the 1950s and 1960s in seminal works by Kauzmann and Tanford.1,2 More recent theoretical work indicates that there is a general length-scale dependence for hydrophobic interactions: for small hydrophobes, the hydration free energy scales with volume, while for large hydrophobic surfaces, the hydration free energy scales with surface area, with the crossover occurring on a hydrophobic length scale of ∼1 nm.3−6 Therefore, near an extended hydrophobic surface, water cannot orient into the preferred hydrogen-bonding network, resulting in a fluctuating © XXXX American Chemical Society

Received: May 30, 2014 Revised: July 29, 2014

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dx.doi.org/10.1021/la502115g | Langmuir XXXX, XXX, XXX−XXX

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Invited Feature Article

Figure 1. (A) Approximate summary of previously measured repulsive forces between hydrophilic surfaces and attractive forces between hydrophobic surfaces. These forces can be monotonic or oscillatory as shown in the inset, with the approximate periodicity of the diameter of water molecules (0.3 nm). Oscillatory forces are observed only between rigid surfaces; these oscillations are often smeared out between real surfaces, resulting in the monotonic force envelope shown in gray in the inset. As shown schematically in (B), hydrophilic surfaces have one or more hydration layers that result in repulsive osmotic forces when two such surfaces approach and interact. At hydrophobic surfaces, as shown in (C), water cannot hydrogen bond, and thus the water molecules near both surfaces are highly fluctuating and close to a liquid−vapor phase transition. Thus, dewetting or attractive hydrophobic forces occur when two hydrophobic surfaces approach and interact. The measured interactions between such surfaces due to hydrophobicity/hydrophilicity can be described by eq 1 using the parameter values displayed in (A).

static forces rather than hydrophobic interactions.21−24 Alternatively, individual molecules can overturn, leading to a partially hydrophilic monolayer. Other longer-range (i.e., effective from D > 300 nm in some cases) attractive forces were shown to arise from bridging nanobubbles, revealing the importance of degassing the aqueous medium.18,25−27 The current understanding is that the effective range of the hydrophobic interaction that is inherently due to the hydrophobicity of the surfaces (i.e., the distance at which the purely hydrophobic force becomes measurable) is about 10−20 nm with decay length of about 1 nm.13 Adding further intrigue is that a shorter-ranged, attractive 0.3 nm exponential decay has been measured with dynamic SFA13,14 and very recent dynamic atomic force microscope (AFM) measurements17 between hydrophobic surfaces. Similar characteristic decay lengths, in fact, have also been measured between hydrophilic surfaces. Interestingly, around the same time as the original studies of the interactions between hydrophobic surfaces were being done, the interactions between hydrophilic surfaces were also under heavy investigation.28−33 Many of the early studies of interactions between hydrated surfaces were performed between rigid mica surfaces in aqueous salt solution and found an exponential repulsion with distance, with a decay length of about 1 nm.28−30 Further work between hydrophilic surfaces with thermally mobile groups (e.g., lipid bilayers) also showed an exponential repulsion, albeit with a significantly shorter decay length of about 0.3 nm.31,33 At the time, no qualitative or quantitative connection was made between the exponentially decaying forces that exhibited identical decay lengths albeit opposite signs (repulsive/attractive). These similar decay lengths, in the range of ∼0.3 to ∼1 nm for both hydrophobic and hydrophilic forces, indicate that perhaps there is a unifying mechanism for hydrophobic and hydrophilic interactions related to the degree of hydrogen bonding at a given interface. Indeed, some authors have referred to both attractive and repulsive hydration forces,34,35 but these interactions have not been fully unified theoretically, for example, in terms of a generalized potential function. The approximate ranges of previously measured forces as a function

phobic surfaces in water has become known as the hydrophobic interaction or hydrophobic force. The hydrophobic force is longer-ranged and stronger than van der Waals interactions, with an effective range of D ≤ 20 nm.13−15 Even for partially hydrophobic surfaces with contact angles smaller than 90°, a significant contribution from hydrophobicity is found. The exact physical mechanism of this force remains in question, although it should have some fundamental relationship to the physics of hydrophobicity discussed above, based on the loss of water’s hydrogen-bonding network at the mutually approaching hydrophobic interfaces. Since the first direct force measurements between two hydrophobic surfaces in 1982 using the surface forces apparatus (SFA),15 there have been many attempts to quantify the distance dependence of the attractive hydrophobic force.13−20 The original experimental study by Israelachvili and Pashley concluded that the hydrophobic attraction decayed approximately exponentially with a decay length of about 1 nm and an effective range of 10 nm.15 Subsequent studies provided wildly varying accounts of the range and magnitude of the hydrophobic attraction, with some work reporting an effective range of up to several micrometers.13 Within the past 10 years, Israelachvili and coworkers have shown that long-range artifacts can arise due to preparation techniques and experimental conditions,13,14,21 as discussed below, but pure hydrophobic interactions are found to be shorter-ranged and in fact are close to the interactions in the original study,15 with a decay length of ∼1 nm.13,14 The wide variation of reported data can be attributed to the inherent difficulty in studying hydrophobic interactions. This difficulty lies in the reproducible production of stable, impurity-free hydrophobic surfaces. In many of the early experiments, the surfaces were made hydrophobic by physically adsorbing a cationic surfactant or lipid monolayers on an anionic mica surface. It was later found that these monolayers can overturn with immersion time in aqueous solution, leaving behind a patchy surface of bilayer regions and bare mica regions.21,22 The interaction between two such surfaces is fully attractive, although due to the slow overturning of molecules, this attraction arises from electroB


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interaction potential. Perhaps they should not be considered to be separate but intimately related through the ability of water to hydrogen bond (or not) near a surface, which can induce corresponding and correlated changes in the density, orientation, and structure of water extending away from the surface and resulting in these physical interactions. The approximate range and magnitude of forces that have been directly measured between both hydrophobic and hydrophilic surfaces are shown schematically in Figure 1A. Equation 1 can be used to describe both the repulsive forces measured between two hydrophilic surfaces (Figure 1B) and the attractive forces measured between two hydrophobic surfaces (Figure 1C), with both the hydrophobic and hydrophilic forces discussed in detail below. This article describes the utility, development, and experimental testing of the interaction potential in eq 1, which was recently empirically derived.36−39 Important questions remain about the exact mechanisms for the hydrophobic and hydrophilic interactions under investigation, and hypotheses about the mechanisms and guidelines for future work from appropriate alternate techniques are provided toward the end of the article. However, important steps forward in understanding the range and magnitude of hydrophobic and hydrophilic interactions have now been completed, as detailed herewith. The article begins with a description of hydrophobic interactions in section 3, with subsections on interactions between silicone surfaces, hydrocarbon surfaces, and the effect of solvent quality. Section 4 covers hydrophilic interactions, both so-called primary and secondary hydration. Section 5 contains ideas and speculation on the origin of hydrophobic interactions, and section 6 is a summary section with suggestions for future experiments to resolve some of the many open questions, both experimental and theoretical, concerning hydrophobic and hydrophilic interactions.

of distance, between both hydrophobic and hydrophilic surfaces, are shown in Figure 1A. The attractive hydrophobic and repulsive hydrophilic forces tend to dominate typical van der Waals forces at most distances, for very hydrophobic surfaces and very hydrophilic surfaces, respectively. Oscillatory solvation forces that arise between smooth, crystalline surfaces with water layers in between also manifest an exponentially decaying (oscillatory) force with a periodicity of about 0.3 nm, as discussed later and shown in the inset of Figure 1A. This article reviews the current experimental situation for both hydrophobic and hydrophilic surface interactions that are generally monotonic, with a special focus on the recent development of an interaction potential that accounts for both the attractive hydrophobic and repulsive hydrophilic forces. The interaction potential is introduced fully below in eq 1. We recently derived an interaction potential to account for the hydrophobic attraction in surfactant membrane fusion36,37 and hydrophobic polymer coatings,38,39 shown in eq 1a, which can be used to calculate the interaction energy per unit area, WH, as a function of the separation distance, D, between two hydrophobic interfaces. The interaction potential depends on the hydrophobic−water interfacial tension γi (γi = 50 mJ/m2 for hydrocarbon interfaces in water), the Hydra parameter Hy, and the decay length DH ≈ 1 nm (but can be as small as 0.3 nm17). Hy ≡ 1 − a0/a, where a0 is the hydrophilic area and a is the hydrophobic area at a given interface. Defined in this way, Hy can be considered to be the effective fraction of hydrophobic area at a given interface or the fractional area covered by hydrophobic groups. For a ≫ a0, Hy = 1, which corresponds to the maximum hydrophobic interaction, while for 0 < Hy < 1, the surface is partially hydrophobic. This interaction potential also naturally accounts for repulsive interactions between hydrophilic surfaces, generally known as hydration forces, which exhibit decay lengths, DH, in the same range as hydrophobic interactions. When a0 > a, Hy < 0 (i.e., the interfacial surface coverage is dominated by hydrophilic groups) and the overall interaction potential becomes repulsive instead of attractive. Hydrophilic surfaces repel each other due to water’s ability to hydrogen bond and hydrate the surface, resulting in a repulsive osmotic pressure.40 Hydrophilic interactions are certainly ubiquitous in nature as well, providing stabilizing structural forces for self-assembled vesicles, micelles, and proteins. Equation 1a can be reformulated as shown in eq 1b, where γeff ≡ γiHy, reducing the number of unknown variables in situations where γi is not well defined, for example, in hydrophilic systems. A negative effective interfacial tension (i.e., Hy < 0 and γeff < 0) indicates that work needs to be done to bring the surfaces into contact. While there is a well-defined maximum for hydrophobic interactions (Hy = 1), there is no practical analog for an “ideal” or maximum hydrophilic interaction. The theoretical limit is perhaps γeff = −72 mJ/m2 (i.e., the surface tension of water) and describes in this case the interaction of two water films, but observed hydrophilic interactions are generally in the range of −0.5 to −15 mJ/m2 for the observed γeff. These issues will be discussed in more detail in the hydrophilic section below. WH = −2γiHye−D / DH

(1a)

WH = −2γeff e−D / DH

(1b)

2. EXPERIMENTAL SECTION Surface forces measurements described here utilized the SFA 2000 (Surforce LLC, Santa Barbara, CA), which has been described in detail elsewhere.41 The distance between back-silvered mica and gold interfaces was determined by multiple-beam interferometry by analyzing fringes of equal chromatic order (FECO). Before each experiment, clean mica and gold surfaces were brought into contact in air in order to calibrate D = 0. Hydrophobic surfaces attached to mica and gold surfaces were then mounted in the SFA in a cross-cylinder geometry. The SFA chamber was filled with aqueous solution (generally 1 mM NaCl, pH 3 unless stated otherwise), and force measurements were performed by approaching and separating the surfaces at a quasi-static rate of ∼2 nm/s. The force, F, was measured by a determination of the deflection, Δx of the force-measuring spring with spring constant k and simply applying Hooke’s law, F = kΔx. The radius of the surfaces, R, was also measured interferometrically to obtain the normalized force F/R which was plotted versus D in the force curves described in the text. All water used in the experiments was degassed by stirring with Teflon chips and pulling a weak vacuum for at least 1 h before the beginning of each experiment. Experiments performed with tetrahydrofuran (THF)/water mixtures were done by injecting a small volume of the THF/water mixture between the surfaces rather than filling the entire chamber with solution. PDMS films on gold were prepared as described previously.39 Briefly, a gold surface is initially functionalized with an amineterminated alkanethiol monolayer for 2 h in a 1 mM ethanolic solution of 11-amino-1-undecanethiol hydrochloride with 2 drops of triethylamine. Following monolayer attachment, the surface was rinsed for 30 s with ethanol, dried with a stream of N2, immediately immersed in pure monoglycidyl ether-terminated PDMS liquid (Mn = 5000 g/mol, Sigma-Aldrich, total contour length of SAM and PDMS is LC = 25 nm), and placed in an oven at 130 °C for 1 h, resulting in a covalently

With eq 1, these two apparently antithetical interactions (hydrophobic and hydrophilic) can be described by the same C


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poly(dimethylsiloxane) (PDMS) using click chemistry.39 A PDMS monolayer can also be attached to mica, using the same chemistry, as discussed in the Experimental Section. Here, we measured the interaction forces between these two PDMS monolayers in a 1 mM NaCl pH ∼3 aqueous solution using SFA. The SFA technique provides several advantages for measuring force−distance curves. The distance D is measured as the absolute separation distance at the point of interaction to ∼1 Å accuracy between two cross-cylinder surfaces while simultaneously measuring the force of interaction and the refractive index in the gap. The surface radius R, the distance D, and the shape of the interacting surfaces are measured through the optical technique known as FECO, which can be visualized as fringe wavelengths, λ, in a spectrometer. The measured force, F, is normalized by R in order to compare between different experiments and techniques since interaction forces generally scale with R, and the Derjaguin approximation can be applied to determine the interaction energy per unit area (i.e., W = F/ 2πR), and for the adhesion energy, Johnson−Kendall−Roberts (JKR) theory is used (i.e., Wad = 2Fad/3πR).42 The interaction between two chemisorbed hydrophobic PDMS layers in water is purely attractive during both approach and separation, as shown in Figure 2. During approach, the

attached layer of PDMS. For the surface force measurements described in this work, we also synthesized PDMS films on mica surfaces. The synthesis procedure on mica is very similar to that on gold with a few notable differences. The mica is first activated (i.e., the surface siloxane groups are converted to more reactive silanols) by placing the surface in a UV/ozone plasma oven (UVOCS Inc. model T10X10/OES, Montgomeryville, PA) for 30 min. The surface is then immediately immersed in a 1 vol % solution of (3-trimethoxysilylpropyl)diethylenetriamine (DETAS, Gelest Inc., Morrisville, PA) in methyl ethyl ketone (MEK, Sigma-Aldrich). Similar to the amine-thiol functionalization on gold, this step deposits a silane monolayer that exposes terminal amine groups. The silane is deposited for 2 h, at which point the surface is immediately rinsed with ethanol, blown dry with N2 gas, and then immediately placed in pure monoglycidyl ether-terminated PDMS liquid and placed in a vacuum oven at 80 °C for approximately 60 h. The vacuum oven is pumped down with argon to remove oxygen from the environment, with the main objective of this step to prevent the oxidation of the back-silvered mica. After the reaction, the PDMSfunctionalized mica surface is washed using the same procedure described previously,39 with much shorter sonication steps. One second of sonication is necessary (again with three sonication steps, see ref 39 for details) to remove physically bound PDMS molecules without damaging the underlying mica surface.

3. HYDROPHOBIC INTERACTIONS For Hy > 0 (and γeff > 0), eq 1 above describes hydrophobic interactions. Recent accounts indicate that DH ≈ 1 nm for supported hydrophobic interfaces,13,14 with more recent measurements using AFM between liquid fluorocarbon oil droplets finding DH ≈ 0.3 nm.17 The mechanisms for both decay lengths have not been fully elucidated, although the shorter decay is potentially due to shorter-ranged water correlations, with the longer decay due to longer-ranged dipolar, hydrogen bond network, or proton-hopping correlations. The physical mechanism will be discussed in more detail later in this article. As a historical example, we first examine the original direct measurement of hydrophobic interactions, which provided an empirical force−distance law for the hydrophobic interaction between two physisorbed cetyltrimethylammonium (CTAB) monolayers. Using the empirical force law provided by Israelachvili and Pashley15 of the form FH/R = (140 mN/m) exp(−D/1 nm) and converting to the form of eq 1 by the Derjaguin approximation WH = FH/2πR, a value of Hy = 0.2 was found. This value, much less than the maximum expected Hy = 1 for two fully hydrophobic surfaces, indicates that the CTAB layers were not fully hydrophobic in this case, likely due to the overturning of molecules. Importantly, recent work has shown that stable hydrophobic surfaces and a stable aqueous medium (i.e., degassed solutions) are crucial experimental considerations for consistent and reproducible fundamental studies of hydrophobic interactions.13,16 Many studies have used chemically attached silane hydrocarbon layers,14 but these are notoriously fickle and inconsistent to prepare. We developed a hydrophobic surface that is more consistent and simple to prepare, utilizing click chemistry for highly specific and consistent grafting of hydrophobic poly(dimethylsiloxane) (PDMS) on gold and mica surfaces.39 The following sections compare hydrophobic interactions between PDMS monolayers and more conventional hydrocarbon monolayers. 3.1. Hydrophobic Forces and Cavitation between Silicone and Hydrocarbon Monolayers. We recently described efforts to create a stable, chemically attached monolayer on gold with hydrophobic contact angle 110° of

Figure 2. Interaction between two PDMS thin films, with one film attached to mica and the other film attached to gold as shown. The data points shown are for the approach of the two PDMS films, exhibiting an exponentially decaying attractive force and eventually jump-in from DJ = 12.6 nm. The green curve is obtained from eq 1 using the parameters shown on the plot. Strong adhesion is measured during the retraction of the PDMS films as indicated, and the surfaces jump apart from the measured adhesive minimum at DJ = 1 nm.

surfaces jump-in to molecular contact due to a spring instability from jump distance DJ = 12.6 nm. This jump-in is much stronger than can be accounted for by the van der Waals force, as shown in Figure 2. During retraction, the PDMS films remain in adhesive contact until they jump-out at a measured adhesion energy of Wad = 2Fad/3πR = 94 ± 20 mJ/m2 (Hy = 1.07 ± 0.23), slightly larger on average than the expected thermodynamic adhesion of W0 = 2γi = 88 mJ/m2 for two PDMS films in water. Error margins are the standard deviation over the entire data set of 15 independent experiments. In each experiment the adhesion was measured for freshly made surfaces, and the variance arises from entirely different experimental setups. (The variance in adhesion is attributed to some degree of polymer entanglements and slight differences in film quality due to reagent quality.) The average decay length was also found to vary similarly, with the average decay length D


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being DH = 1.6 ± 0.4 nm over the full data set. The green curve is a representative fit to eq 1 with PDMS−water interfacial energy γ = 44 mJ/m2, Hy = 1, and DH = 1.7 nm, which quantitatively captures the measured data at all distances. It appears that a small degree of polymer entanglements and a slight bridging of PDMS chains occur across the water gap during the separation of the surfaces, as indicated by the jumpout distance of DJ = 1 to 2 nm (see also Figure 6B). The jumpout distance remained the same for an experiment performed an order of magnitude more slowly (i.e., closer to equilibrium by allowing each point to equilibrate for 30 s before measuring the force). Long-range bridging can be confidently ruled out, as PDMS segments extending significantly into aqueous solution would incur a huge energy penalty. However, short-range bridging or entanglements during the approach of the surfaces cannot be ruled out while the surfaces travel through the instability regime (Figure 2). It is possible that some PDMS chains are able to fluctuate, possibly leading to the slightly larger observed decay length of the hydrophobic force for the PDMS films, DH = 1.6 nm, as compared to hydrocarbon monolayers for which DH = 1 nm. These polymer monolayer surfaces appear to behave as ideal hydrophobic surfaces in aqueous solution, as the interaction is in quantitative agreement with the hydrophobic force law measured between two chemisorbed hydrocarbon surfaces (see below). 14 For further confirmation that these PDMS monolayers are a suitable model hydrophobic system, we also measured cavitation. As discussed above, evaporation is not usually observed in degassed solution during the approach of two hydrophobic plates. However, cavitation can be observed between fluorocarbon and hydrocarbon surfaces upon separating the surfaces.43 This is most likely caused by the combination of a large and immediate decrease in local pressure as the surfaces jump apart from adhesive contact and a lowered threshold for heterogeneous nucleation of a vapor cavity between the hydrophobic surfaces.43 By using a rigid steel beam instead of the usual cantilever spring in the SFA, the jump distance can be limited such that the vapor cavity that nucleates during the jump apart does not dissolve before the surfaces come to rest. Since the FECO are sensitive to changes in refractive index, the nucleated vapor cavity is easily observable. Figure 3 shows the FECO with PDMS surfaces in contact as well as immediately after separation. After separation, a discontinuity is observed in the FECO that corresponds to a vapor bridge with refractive index 1.0 (compared to the refractive index of water of 1.33). As shown in the Supporting Information (Figure S1), after the jump apart, the diameter of the nucleated vapor bridge remained constant as long as the surfaces are not disturbed. Upon separating the surfaces further, the vapor bridge diameter shrinks until the vapor disappears at D ≈ 500− 1700 nm in degassed aqueous solution. (If the solution is not degassed, vapor remains stable over a much longer distance.) As discussed in the Introduction, a vapor cavity can be stable between two parallel hydrophobic surfaces out to a separation of 100 nm or more.10 In order for a vapor cavity to be stable at thermodynamic equilibrium, it requires a surface of net zero curvature.44 In the process of separating the surfaces, this particular cavity shape is not continuously maintained, possibly due to pinning of the vapor−liquid−solid interface at small imperfections or asperities in the PDMS film. Stretching of the cavity therefore causes the pressure inside the cavity to become lower than that of the surrounding liquid, causing the cavity to

Figure 3. Schematic cartoons and corresponding FECO fringes immediately before (top panel) and after (bottom panel) the jump-out between two PDMS layers attached to mica. The n and n − 1 order FECO fringes are shown in the top panel. After the jump out, the n + 1 and n fringes are now within the viewing window, as indicated. The discontinuity observed in the bottom panel corresponds to a vapor bridge with a refractive index of 1.0. The observed faint bands in the FECO fringes in the contact region are optical defects or possibly small, angstrom-level asperities in the PDMS films.

shrink and disappear. However, it is notable that the vapor cavity disappears between 500 and 1700 nm, on the order of the same distance at which the Kelvin equation predicts the vapor to liquid metastability transition between hydrophobic surfaces.8,12 The hydrophobic forces between hydrocarbon monolayers behave similarly to the results shown for PDMS. As shown in Figure 4, between physisorbed dioctadecyldimethylammonium bromide (DODAB) monolayers on mica, the interactions are fully attractive. As discussed in the Introduction, artifacts can be

Figure 4. Interaction between monolayers of DODAB, a cationic double-chained surfactant in 10 mM KCl. Data points shown are for the approach of the two DODAB monolayers, and the red curve is obtained from eq 1 using the parameters shown on the plot. Strong adhesion is measured during the retraction of the monolayers as indicated. E


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Figure 5. Interaction forces between hydrophobic monolayers measured by AFM with a small radius tip (R ≈ 15 nm) approaching an extended gold surface. (A) Measured force−distance profiles show that the hydrophobic force is stronger than the van der Waals force for this system, and eq 1a can describe the data quantitatively with the parameter values shown on the plot. (B) Measured adhesion force between the hydrophobic layers decreases with increasing temperature, as shown in the histogram plot. Figure adapted from ref 45.

Figure 6. (A, B) Adhesion forces (left vertical axes) and energies (right vertical axes) between two PDMS films in water and water−THF mixtures and (C) schematic picture of water−PDMS−THF interfaces. In (A) the adhesion is shown as a function of THF concentration with an inset showing Hy as a function of THF concentration, while in (B) the force run (force vs distance curve) is shown during the separation of two PDMS films. On the basis of the experimental data, (C) shows a schematic of the PDMS film in pure water, in which the film is collapsed and water cannot hydrogen bond. In the presence of THF, water and THF can penetrate the PDMS layer, causing the chains to swell. THF molecules are slightly amphiphilic and adsorb to the interface, allowing water molecules to hydrogen bond at the THF/water/PDMS interfacial structure, thus eliminating the hydrophobic adhesion. Figure adapted from ref 46.

Introduction, recent AFM force measurements between hydrophobic oil droplets found a shorter decay length for the hydrophobic force, DH ≈ 0.3 nm,17 and still other AFM measurements with a colloidal probe between solid hydrocarbon layers found no measurable hydrophobic interaction at D > 6 nm.20 Very recent measurements reported in a forthcoming publication by two of us seek to resolve the apparent discrepancy between the SFA and AFM techniques. Stock et al. have used nanoscopic AFM tips (R ≈ 8−40 nm) approaching a molecularly smooth surface, both functionalized with a hydrocarbon self-assembled monolayer.45 The use of nanoscopic tips was shown to provide one significant advantage: the magnitude of the measured force is much smaller, allowing for accurate measurement to a closer distance before the jump-in due to spring instability. As shown in Figure 5A, a hydrophobic force is measured that is well described by eq 1 with Hy = 1, γi = 50 mJ/m2, and DH = 1 nm and with good agreement from large separations all the way to DJ ≈ 3 nm, even when extrapolating to the contact adhesion. The

observed when using physically adsorbed hydrophobic layers due to monolayer overturning. This overturning is observed in contact angle hysteresis on these surfaces, which are highly hydrophobic on advancing (110°) but much less so on receding (65°).21 Thus, we emphasize that these interactions must be measured during the first approach at a particular contact position and quickly after immersing in water because structural changes occur in the physisorbed monolayer both with time and after the loading/unloading cycle (e.g., overturning and molecule desorption). However, if prepared carefully, a shortrange attraction is observed, which is primarily due to the pure hydrophobic interaction. The observed hydrophobic attraction decays exponentially with a similar but slightly shorter decay length as compared to the above interactions for PDMS monolayers, DH ≈ 1.2 nm. The surfaces jump-in to molecular contact near DJ ≈ 10 nm, and the corresponding value for Hy is between 0.8 and 1. 3.2. Comparing SFA with AFM Measurements between Hydrophobic Monolayers. As mentioned in the F


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allows the mixed solvent to penetrate and solvate the PDMS chains, allowing hydrogen bonding to occur at the interface and effectively eliminating the strongly adhesive hydrophobic interaction, as shown schematically in Figure 6C. The inset of Figure 6A shows that Hy decreases roughly exponentially as a function of THF concentration. This leads to the general empirical exponential relation Hy(x) = Hy0e−bx, where x is the THF mole %, Hy0 = 1 is the value of Hy in pure water, and b = 0.16 is a parameter that describes how effectively the additive (THF in this case) causes a reduction in Hy. This empirical relation can possibly describe the behavior of Hy in the presence of different additive cosolvents. In that case, larger values of b would correspond to additives that effectively decrease the hydrophobic adhesion energy with smaller additive concentrations. The above results for both PDMS and hydrocarbon layers indicate that Hy is useful for describing the effective hydrophobicity and for quantifying the contribution of hydrophobicity to the interaction potential between hydrophobic surfaces in general. Furthermore, the degree of hydrophobicity and resulting Hy value can be tuned by varying the solvent composition as shown above by adding cosolvents. Other solvents should have similar effects, and the resulting Hy value should be some measure of the ability of water to hydrogen bond at a particular hydrophobic interface. Values of Hy ≈ 1 indicate that water is unable to hydrogen bond at the interface, corresponding to maximum hydrophobicity, while values near 0 indicate that water has little preference for the interface vs the bulk solution. For Hy < 0, the surface is hydrophilic and readily hydrated, as discussed in greater detail below.

hydrophobic force is stronger than the van der Waals forces for the system, as shown, and agrees quantitatively with the SFA results shown above. The improved resolution in the strongly attractive regime has shown that AFM and SFA agree reasonably well for nanoscopic (AFM, R ≈ 10 nm) to macroscopic (SFA, R ≈ 2 cm) size regimes. Surprisingly, the temperature dependence of hydrophobic interactions has not been extensively examined in direct force measurements, a topic that was also addressed in the recent work by Stock et al.45 Increasing the temperature is shown to significantly decrease the adhesion from about 600 mN/m at 23 °C to 450 mN/m at 60 °C, as shown in Figure 5B. This observation is consistent with theoretical predictions that describe the hydration of extended surfaces as enthalpic in origin3 and is also consistent with the typical behavior of the surface tension decreasing with increasing temperature. These important measurements demonstrate quantitatively that the hydrophobic interaction scales similarly for large surfaces (R ≈ 2 cm) and nanoscopic surfaces (R ≈ 10 nm). Increasing the temperature is shown to decrease the adhesion between hydrophobic surfaces, an effect that can also be induced by changing the solvent conditions, as discussed in the following section. 3.3. Solvent Quality Modulates the Effective Hydrophobicity. With the hydrophobic forces and cavitation behavior between the PDMS thin films in purely aqueous solutions established, the solvent conditions were altered to determine the effect on Hy. The apparent hydrophobicity and the resulting value for Hy can be modulated by mixing water with tetrahydrofuran (THF), which modifies the hydrogenbonding properties of the bulk liquid compared to those of purely aqueous solutions. Interestingly, THF is miscible with water and with PDMS; however, water and PDMS obviously are mostly insoluble. This makes THF an interesting additive to examine in hydrophobic interactions of PDMS, as it would be expected to decrease hydrophobic interactions between PDMS films. Another utility of eq 1 is that one needs only the contact value of the adhesion (i.e., the adhesion force or energy upon the jump-out from D = 0) in order to determine a unique value for Hy. The measured adhesion force Fad/R can be used to calculate the adhesion energy from JKR theory as Wad = 2Fad/ 3πR,42 and Hy can then be determined by Wad = 2γiHy. As expected, the addition of THF effectively decreases the hydrophobic interaction, as determined by Hy measured from the adhesion energy between two PDMS films with increasing THF concentration. The measured adhesion force decreases as the THF concentration increases, as shown in Figure 6A. The addition of THF also results in PDMS film swelling, and the bridging of PDMS segments between the two films is also observed at higher THF concentrations, as shown in Figure 6B. The force−distance profiles during the approach of the PDMS films in the presence of THF/water mixtures are similar across the concentration range examined, likely due to capillary bridging of THF/water vapor, as shown in Supporting Information (Figure S2). The addition of only 10 mol % THF decreases Hy from 1 (pure water) to 0.3, while 20 mol % THF results in Hy = 0.03 and 30 mol % THF results in Hy = 0.01 (Figure 6A, inset). The effective disappearance of hydrophobicity near 20−30 mol % THF corresponds to a minimum in the diffusion coefficient of water/THF binary mixtures,46 indicating that hydrogen bonding between water and THF is maximal at this same concentration. Hydrogen bonding between water and THF

4. HYDROPHILIC INTERACTIONS With negative values of Hy (and γeff < 0), eq 1 above describes repulsive hydration interactions. While questions remain about the exact theoretical origin of hydration forces,47−50 it is accepted that the perturbation of hydration layers leads to the observed forces, whether by the compression of thermally mobile groups or the dehydration of hydration layers. These hydration layers can be composed of hydrated ions, hydrated headgroups at lipid interfaces, or other hydrated moieties, as discussed below. To use eq 1a and Hy to quantitatively describe hydrophilic interactions, a value of γi is required. However, hydrophilic interactions are solely repulsive and thus do not have a well-defined interfacial energy. The reference value used here is γi = 50 mJ/m2, which is chosen for convenience and simply allows for quantitative comparison (i.e., the absolute magnitude of the interaction energy) among all of the different systems discussed, both hydrophobic and hydrophilic. Using eq 1b requires no reference value, and γeff < 0 values are reported in conjunction with the Hy values below. In fact, Hy < 0 (and γeff < 0) corresponds to a negative (repulsive) interfacial energythe interface would dissolve if possible but is held in place by attractive physical interactions or chemical bonds to substrates. Hydration interactions have been measured between lipid membranes,31,51 mica surfaces,28−30,52,53 silica surfaces,54,55 and polymer interfaces.33,39 While reviewing all of these examples is beyond the scope of this article, we will highlight notable examples from the literature in order to show the utility of Hy in describing these hydration interactions. The “pure” hydration force is structural in nature and therefore oscillatory with distance, arising from the layering of water molecules on G


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molecularly smooth, rigid surfaces.32 This oscillatory force− distance profile is superimposed on a repulsion for smooth, rigid surfaces. Most surfaces in nature are not atomically smooth, and the oscillatory layering is smeared out so that hydration forces are generally manifest as monotonically decaying repulsions. It is useful to distinguish hydration forces in terms of primary and secondary hydration.48,50 Primary hydration forces are short-ranged and are due to surface hydration layers of protruding surface moieties, while secondary hydration forces are slightly longer-ranged and are due to the hydration of solutes, such as counterions near charged surfaces. The physical mechanism is still not perfectly understood theoretically, but primary hydration forces likely arise from some combination of the entropic confinement of thermally mobile groups40 and the dehydration of hydrated surface moieties48 (e.g., lipid headgroups) at an interface. A large contribution from the entropic compression of hydrated surface moieties is expected because of the temperature dependence of such forces: increasing the temperature leads to an increase in the observed hydration force between bilayers.47 Regardless, these are generally found between thermally mobile surface groups and exhibit shorter decay lengths, with DH ≈ 0.3 nm. Secondary hydration forces, on the other hand, are found between nonmobile, rigid surfaces such as mica and clay surfaces/particles and were recently proposed to be due to ion−surface dispersion interactions50 and the dehydration of ions as they are pushed back onto the surfaces upon compression.49,52,53 For these reasons, secondary hydration forces are both co-ion- and counterion-specific and slightly longer-ranged with DH ≈ 1 nm due to the dehydration of both the underlying mica surface and the hydrated ions as the ions become further confined. The following sections will review several experimental systems, including both primary and secondary hydration, while highlighting both the utility and drawbacks of using Hy to describe such systems. 4.1. Secondary Hydration: Hydrophilic Interactions between Mica Surfaces. Hydration forces between mica surfaces arise from the energy required to dehydrate cations adsorbed at the anionic mica interface along with the dispersion interaction between the surface and the ion and are thus largely dependent on the ion-exchange properties of the surface.28−30,50 They also depend sensitively on the identity of the co-ion and counterion. Therefore, in the case of interaction forces between mica surfaces, Hy is determined by the identities and concentrations of the cations in aqueous salt solutions. For each cation there is a critical concentration above which hydration interactions are observed, depending on the degree of hydration of each specific ion.29,42 More highly hydrated ions correspond to larger values of Hy and larger decay lengths in general, as shown in Table 1. Many authors have previously reported the force law of steric hydration forces as F/R = C exp(−D/D0) mN/m, which is easily converted to the interaction energy W through the Derjaguin approximation by W = F/2πR; from this the Hy and γeff values can be found according to eq 1. Table 1 displays the force constant C and decay length D0 taken directly from the cited sources, the calculated Hy value, and the repulsive interaction energy W at a distance cutoff of D = 0.5 nm. For mica, the interaction energy is a more complete measure of the hydration than Hy because the interaction energy between two hydrated mica sheets with adsorbed ions can be used to deduce the repulsive energy between adsorbed cations on opposite surfaces.28 While Hy lies between −0.01 and −0.1 (γeff between

Table 1. Parameters for Modeling Hydrophilic Interactions for Mica and Silica Surfacesa C (mN/m) D0 (nm) Hy W(mJ/m2) γeff (mJ/m2)

Cs+

K+

Na+

Li+

Ca2+

Mg2+

silica

20 0.6 −0.03 1.4 −1.5

14 1.1 −0.02 1.4 −1

60 1 −0.1 5.8 −5

24 0.95 −0.04 2.2 −2

7 2 −0.01 0.86 −0.5

25 1.8 −0.04 3.0 −2

34 0.5 −0.05 2.0 −2.5

a Force constants C and decay lengths D0 from the literature29,30 for mica surfaces in the indicated cation salt solutions, with the final column for silica as noted. Hy and W(D = 0.5 nm) were calculated as described in the text and are rough indicators of the strength and range of hydrophilic interactions between such surfaces.

−0.5 and −5 mJ/m2) for the different cations studied, without a clear trend, the interaction energy W shows a rough trend, indicating that the strength and range of hydration forces increase with the hydration number of the cations: Mg2+ > Ca2+ > Li+ ≈ Na+ > K+ > Cs+.42 The strength of the hydration interaction is dependent on the exact surface coverage of cations. The outlying values for Na+ and Ca2+ that do not follow the above trend are likely due to differences in coverage rather than differences in hydration. For identical surface coverages of different ions, the magnitude of Hy combined with decay length D0 to calculate the interaction energy W provides an indicator of the ion-binding ability of mica surfaces for different cations in aqueous solution. More recent direct experimental work has further shown that specific ion effects are very important at higher concentrations (i.e., >50−100 mM) but do not necessarily follow the same trend described above for the hydration number. Ion correlation effects, such as confined networks of correlated ions, may lead to observed and sometimes unexpected effects, which include stronger adhesion than expected from purely van der Waals forces, longer decay lengths than expected from double-layer theory, and ion layering.52,53 There remains much to be learned about ion hydration, especially at higher ionic concentrations, but it is clear that ion hydration plays a major role in the measured secondary hydration forces between surfaces. 4.2. Primary Hydration: Hydrophilic Interactions between Silica Surfaces and Lipid Bilayers. Hydration interactions have also been measured between silica surfaces.54,55 In contrast to mica surfaces, for silica surfaces the hydration repulsion is insensitive to the ionic conditions. An empirical force relation was given by Grabbe and Horn,54 and the force constant was used to calculate Hy = −0.05 (Table 1), which is in the same range as the observed mica hydration forces. Unlike mica, which is crystalline and has specific ionexchange sites, the silica glass surface is amorphous with negatively charged silicic acid groups extending ∼5 Å from the surface. These silica “hairs” protrude from the surfaces and result in an extra repulsion that is intrinsic to the surfaces and partially steric in nature (between the overlapping hairs) rather than being influenced by changing the solution conditions.42 These forces can also be treated theoretically by including an extra shift in the distance of the outer Helmholtz plane where the double-layer forces begin, as shown by Vigil et al.,55 which eliminates the necessity of an extra steric hydration term in the overall interaction potential and allows the interactions to be described by standard DLVO theory. The shift in the hard-wall distance is equivalent to including an excluded volume term for H


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the finite size of the protruding groups in the van der Waals equation of state. A similar procedure was used to account for the extra repulsion observed between lipid membranes,31 for which hydration repulsion has recently been shown by molecular simulation to result from both the dehydration and depolarization of membrane headgroups,56 providing credence to the ideas introduced by Israelachvili and Wennerstrom.40 Both the Hy and shifting-out treatments are satisfactory as long as the zero distance is well defined, as will be discussed later in this section, but using Hy perhaps gives a better indication of the energy contribution to the overall interaction potential. For hydrophilic polymer interfaces, which can be highly hydrated in solution, larger values of Hy are found. Generally, polymer interfaces follow well-known brush or mushroom interactions in good solvents,42 but at higher compressions or in a bad solvent, a stronger and steeper repulsion, over and above the standard polymer or DLVO interaction, with DH ≈ 1 nm has been observed in several systems.39,57 Due to the similar decay length, magnitude, and clear change in slope (i.e., transition from standard polymer mushroom or DLVO to the steeper hydration repulsion), these forces were attributed to hydration forces. Again, excluded volume effects result in enhanced repulsion, over and above that obtained using pointsized segments as in the polymer brush and mushroom theories. A recent system we studied was the interaction of PEG-functionalized lipid bilayers with gold surfaces. While a polymeric mushroom force was observed as expected, at higher compression a steeper repulsion was measured, characteristic of a hydration repulsion. The magnitude of this repulsive force was found to vary with the functionalization on a PEGfunctionalized lipid bilayer. When the PEG lipids displayed an amine (NH3+) terminal group, the Hy value was −0.23 (γeff = −11.5 mJ/m2).57 For a simple CH3 termination, Hy decreased to −0.05 (γeff = −2.5 mJ/m2).57 A larger number of counterions and hydration water are present in the confined gap for the NH3+ termination, leading to the higher observed value for Hy. While the ultimate goal would be to use Hy as a parameter to describe the hydrophilicity in general of any set of interacting surfaces, one must take care in how it is applied. Hydrophobic surfaces have a well-defined zero distance (generally jumpingout from adhesive contact near or at the zero distance), but for many hydrophilic systems, especially soft matter systems such as hydrated lipids and polymers, it is difficult to define the exact “hard wall” or zero distance of the system. Given the short decay lengths of the hydrophilic interaction, lying somewhere between 0.3 and 1.5 nm, even a shift of only a few angstroms in the hard wall distance results in a large change in the magnitude of Hy. Provided the hard wall is well defined, systems can be compared to divulge and compare characteristic hydrophilicity. According to the Hy values determined here, mica and silica surfaces have similar degrees of hydration, and hydrophilic polymeric surfaces are more highly hydrated. The higher degree of hydration for polymers might be expected because of their larger excluded volume, which provides a higher degree of configurational entropy loss upon confinement. These excluded volume effects also result in a further increase in the force at small separations in the osmotic limit. To summarize, Hy provides a simple measure of the strength and range of hydration interactions. The straightforward aspect is simultaneously advantageous and a drawback: advantageous for its simplicity and ease of application but lacking in its ability to describe some of the essential physics. Especially in the case

of lipid bilayers, for example, there are complex forces including headgroup overlap, protrusion, and undulation forces47 that can occur in concert with the excluded volume effects due to the actual hydration layers of the lipid headgroups. Investigations are currently underway to resolve these different contributions and isolate the hydration component. Keeping in mind the differences between primary and secondary hydration42,48−50 as well as the complex interactions (solvent−solvent, solvent− surface, solute−solvent, solute−surface, and solute−solute) that are not fully treated in the Hy description,50 it can still be an effective descriptor of the characteristic hydration forces in a given system. For primary hydration, Hy should provide some measure of the strength of hydration water binding and/or the size and coverage of protruding molecular groups and is thus a measure of water−surface interactions. On the other hand, using Hy to describe secondary hydration is somewhat conceptually different in that it now describes ion−water interactions. Hy provides a measure of ion-specific hydration interactions in the case of secondary hydration, specifically through the dehydration of surface-bound ions; therefore, secondary hydration can be thought of as part of the electric double layer interaction (i.e., inner Helmholtz layer overlap). With similar decay lengths that appear to decay universally exponentially and a well-defined value of the repulsive energy through Hy or γeff but with continued formidable questions from the theoretical perspective,48 we find that Hy is suitable as an empirical treatment for hydration interactions. However, the exponential of eq 1 with Hy is not valid for all distances because the force increases more quickly in the last few angstroms near contact, as van der Waals forces at contact generally do not dominate in such systems.

5. SPECULATING ON THE ORIGIN OF HYDROPHOBIC INTERACTIONS The important question remains: what is the physical mechanism of emergent hydrophobic interactions? Is it due to depletion attraction, an attractive structural force arising from a small density depletion layer near a hydrophobic surface? The answer to this question appears to be no. Even when a decay length of 0.3 nm (i.e., the approximate size of a water molecule) was found in recent AFM experiments between hydrophobic droplets, the hydrophobic force was measurable at a separation of D ≈ 3 nm, which is at least 10 water layers.17 While the 0.3 nm decay may also be present in SFA experiments,14 clearly an additional longer-ranged component is present in these and other SFA experiments with a decay length of around 1 nm. Molecular simulations show that there is no depleted density immediately adjacent to a hydrophobic interface3 and recent X-ray reflectivity measurements indicate only a molecular-scale density depletion (maximum depletion gap ∼5 Å),58−60 so a short-range number density depletion force can be ruled out as the mechanism. Longer-ranged effects are implicated, and these are hypothesized to be entropic effects, which could be related to longerranged density depletion, water molecule orientation, correlations in the hydrogen-bonding network, or proton hopping. All of these may contribute to the overall hydrophobic interaction, as discussed below. Density depletion forces are implicated in very recent highly precise refractive index measurements with SFA measurements between hydrophobic surfaces in water performed in the Kuhl laboratory at UC Davis. These measurements indicate that the average refractive index in the gap begins to decrease near D ≈ I


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20 nm, approximately the same distance as the onset of the hydrophobic force with DH ≈ 1 nm, potentially indicating that correlated water depletion layers provide a major contribution to the measured hydrophobic force.61 These measurements will be fully detailed in a forthcoming publication.61 Longer-ranged orientational correlations resulting in stronger polarization than expected from conventional van der Waals forces may also be responsible for some part of the hydrophobic interaction. In fact, dipolar correlations have already been predicted as the mechanism of long-range hydrophobic forces.62,63 Recent theoretical work suggests that dipolar correlations or longrange angular correlations due to fluctuating hydrogen bonds between water molecules can extend up to 10 nm from a single water molecule in the bulk liquid.63,64 These predictions were corroborated by second-harmonic light-scattering experiments, which found long-range orientation correlations in water, nitrobenzene, and several other polar liquids out to ∼100 molecular diamaters.65,66 Such dipolar correlations were shown to lead to an exponentially decaying force of attraction in simulations between hydrophobic surfaces with a decay length of 1.2 nm using a very large simulation box,63 in agreement with the decay lengths measured by SFA in this work. Large dipoles may also be formed by long-range proton hopping,67,68 which was recently shown to occur in bulk liquid water. To test the hypothesis that the hydrophobic interaction builds up through dipolar correlations, we performed the force measurement between PDMS surfaces while rapidly oscillating one of the surfaces. We hypothesized that rapid oscillatory motions should frustrate correlations that may be present. However, as shown in the Supporting Information, an oscillatory approach with a frequency of 1−8 kHz and an amplitude of 10 nm has no apparent effect on the decay length or range of hydrophobic interactions (Figure S3). Thus, any correlations that possibly exist between hydrophobic surfaces occur at a frequency greater than 8 kHz. This is perhaps unsurprising, since proton transfers and rotational correlation times are on the time scale of picoseconds in bulk solution.67 Nonetheless, several important observations were made during the oscillatory approach force measurements. First, the fast oscillations (vibrations) generate large elastohydrodynamic repulsive (compressive) and attractive (tensile) regimes that are highly sensitive to the amplitude and frequency of oscillations. The repulsive interaction dominates, and in a control experiment between bare mica surfaces under the same solution conditions, it was observed to occur with a similar frequency dependence and range of repulsion, as shown in the Supporting Information (Figures S4 and S5). Interestingly, the magnitude of the repulsion at any given separation was much smaller between two mica surfaces than between two PDMS surfaces, indicating that both the viscoelasticity of the PDMS film and likely the glue beneath the underlying mica and gold substrates contribute to the long-range elastohydrodynamic repulsion. One very important observation was made during the oscillatory approach, exclusively with the hydrophobic PDMS surfaces. As the surfaces were driven toward each other with a 5 kHz vibration, it was observed that the cavitation of a vapor bridge occurred when the surfaces were still at a large separation distance (D ≈ 100 nm), a clear manifestation of the metastable liquid water converting to water vapor (a vapor cavity or bridge) as discussed in the Introduction. As shown in Figure 7, as the surfaces approach each other, a vapor bridge nucleates at a separation distance of about D ≈ 100 nm. The

Figure 7. Schematic diagrams and corresponding FECO fringes immediately before (left) and after (right) the nucleation of a vapor cavity during the dynamic approach of two PDMS films. The white shaded bands indicate the fringe positions of the PDMS surfaces when in flat adhesive contact (corresponding to D = 0). The vapor nucleates at a distance of D ≈ 100 nm.

vibrations place the intervening liquid under dynamic tension, inducing stress fluctuations, potentially a capillary wave fluctuation9 or negative pressure, decreasing the magnitude of the energy barrier and allowing the stable free-energy pathway to be observed. Nucleation was not always observed at all contact positions, indicating that the energy barrier was also possibly lowered even further in this case by nanoscale topological defects on the PDMS surface. Nanoscale roughness could allow for the possibility of capillary condensed vapor in tiny cavities in the PDMS, leading to a lower energy barrier for macroscopic cavity formation. Upon separating the surfaces, the vapor is stable until it disappears at D ≈ 1500 nm, similar to the above case when vapor is nucleated upon separation of the PDMS surfaces. Therefore, the vapor is not stable on isolated hydrophobic surfaces, as expected thermodynamically. This is perhaps the first observation of a spontaneous liquidto-vapor transition during the approach of two hydrophobic interfaces. Cavitation was previously observed between polystyrene films, but pre-existing bridging nanobubbles were potentially implicated;18 we observed no sign of pre-existing nanobubbles in these experiments. This is an important observation, as it demonstrates that cavitation between macroscopic hydrophobic surfaces is accessible experimentally at large separation distances (D ≈ 100 nm) simply by applying high-frequency vibrations. In the same experiment, both the lowest-energy state (bridging vapor) and metastable state (hydrophobic force) could be observed by modulating the frequency of oscillations, which has the effect of decreasing the dewetting free-energy barrier. It is beyond the scope of this work to fully analyze all of the important implications of these observations. Dynamic control of cavitation, strong repulsive forces, and controllably decreasing the adhesion between surfaces in general are important aspects that will be discussed fully in a follow-up work.

6. SUMMARY AND FUTURE DIRECTIONS Questions remain, as ever, both experimentally and theoretically. However, the interaction potential in eq 1 has now been shown to describe both hydrophobic and hydrophilic interactions, with decay lengths DH of between 0.3 and 2.0 nm for both cases, with the exact value of DH dependent on the chemical and morphological identity of the surfaces and the J


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Nonetheless, without robust first-principles theories predicting the exponential forces that are routinely observed between hydrophobic or hydrophilic surfaces, the interaction potential of eq 1 provides a useful tool that extends from the well-known DLVO theory to quantitatively account for more complex interactions involving hydrophobic and hydrophilic surfaces in a unified way. The potential has been shown to apply to a variety of length scales, from extended surfaces (R ≈ 2 cm) all the way to nanoparticles and nanoscopic AFM tips (R ≈ 10 nm). It remains to be seen if eq 1 applies to smaller hydrophobes (molecular scale, R ≈ 1−5 nm), in which case Hy would likely be dependent on both the orientation and other surrounding molecular groups. Given the complexity of experimental systems thus far examined, we anticipate that the potential can capture more complicated aggregation and self-assembly phenomena, such as protein aggregation and adhesion, biomembrane interactions, and other systems in which hydrophobic and hydrophilic forces play a determining role.

solution conditions. The mechanism for hydrophilic interactions, while perhaps not perfectly understood, generally appears due to the confinement of hydrated ions or thermally mobile protrusions and the dehydration of such moieties, with the decay length and/or Hy magnitude being positively correlated with the size and coverage of the ions or protrusions. The physical mechanism for the hydrophobic interaction remains less clear, although we hypothesize that the longerranged nature of the force is due to long-range correlations from dipolar, angular, or proton-hopping correlations among water molecules confined between hydrophobic surfaces. This hypothesis is supported by recent theoretical calculations that show a similar functional form for the hydrophobic interaction.63 With this in mind, angular correlations should be determined, if possible, near hydrophobic interfaces or colloids using second-harmonic light scattering. Measuring hydration water dynamics near hydrophobic and hydrophilic interfaces with dynamic nuclear polarization techniques could also prove illuminating and provide a molecular-level measure of hydrophobicity or hydrophilicity.69 An especially revealing experiment would be coupling the SFA with spectroscopic tools to allow for measurements of water orientation, the hydrogen bonding network, or the proton distribution as a function of the distance between surfaces, but an extension to the SFA that allows the coupled measurement of force and water’s structural features is still in the early stages of development. Additionally, further work should be done on elucidating the nature of the transition from hydrophobic to hydrophilic (Hy > 0 to Hy < 0) by the careful synthesis of monolayers that have a controlled surface density of hydrophobic/hydrophilic groups. The discrepancy in the measured decay lengths in recent AFM measurements between hydrophobic oil droplets17 (DH ≈ 0.3 nm) and SFA measurements between supported hydrophobic layers (DH ≈ 1 nm) is another aspect that requires further investigation. An analogy to the hydrophilic forces is perhaps appropriate here. The difference in decay lengths may arise from the difference between a fluctuating, liquid hydrophobic interface and a rigid supported one, similar to the hydrophilic case. The range of the experimentally observed hydrophobic force (even for DH ≈ 0.3 nm, measured at D ≈ 3 nm) remains larger than the capability for detailed molecular simulations. As calculations and water models become more accurate and efficient, some of these questions could be probed with larger simulation boxes using water models that include water autoionization, in order to investigate possible contributions from long-range angular correlations or proton hopping during the interaction of hydrophobic particles. However, we would expect a correlation between the experimentally determined Hy and the degree of fluctuations near a hydrophobic interface calculated from molecular dynamics simulations. In summary, the interaction potential of eq 1 has proven useful for describing quantitatively the interactions between both hydrophobic (Hy > 0) and hydrophilic (Hy < 0) surfaces. While the precise physical mechanisms for both interactions are not fully understood, specifying Hy for a given system allows for easy estimation of the interaction energy due to hydrophobicity/hydrophilicity. For the decay length, 0.3 nm < DH < 2 nm appears to be the proper range for both hydrophilic and hydrophobic interactions, with the exact value of DH depending on the precise system. We recognize that the simplicity of the model cannot capture all of the relevant complex physics near hydrophobic and hydrophilic interfaces.

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ASSOCIATED CONTENT

S Supporting Information *

Vapor bridge dissolution, force−distance profiles during the approach of PDMS surfaces in mixed water/tetrahydrofuran solutions, hydrophobic forces during oscillatory approach, frequency-modulated forces between PDMS surfaces, and frequency-modulated forces between mica surfaces. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. Biographies Stephen H. Donaldson Jr. received his B.S. in chemical engineering from Virginia Tech in 2008. He received his Ph.D. in chemical engineering in 2014 from UC Santa Barbara, working with Prof. Jacob Israelachvili and Prof. Bradley Chmelka. His doctoral research focused on direct measurements of hydrophobic and hydration interactions in self-assembling systems. He is now a postdoctoral scholar working with Prof. Israelachvili, focusing on developing SFA instrumentation, biomembrane interactions, and wet adhesion studies. Anja Røyne received her B.Sc. in 2003 from the Norwegian University of Life Sciences and her M.Sc. in physics in 2005 from the University of Sydney. In 2011, she received her Ph.D. from the University of Oslo on the study of mechanochemical interface processes in the context of rock weathering. She currently holds a postdoctoral grant from the Norwegian Research Council to study interfacial forces in geological systems and has spent time as a visiting researcher in the group of Prof. Israelachvili. Kai Kristiansen received his Doctor Scientiarum (Dr. Scient.) in physics in 2005 from the University of Oslo, Norway. Currently, he is an associate project scientist in the field of interfacial science and condensed matter physics (including biophysics, electrochemistry, geophysics, colloidal science, tribology, and nanoscience) at the University of California, Santa Barbara, working with Prof. Jacob Israelachvili. He also develops new research instrumentation for studying surface forces and other interfacial phenomena. Michael V. Rapp received his B.S. in chemical engineering from Virginia Tech in 2011. He is currently a Ph.D. student at the University of California, Santa Barbara and an NSF graduate research K


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National Science Foundation under grant number CHE1059108 and by the Procter & Gamble Company. M.V. acknowledges financial support through a Marie Curie International Outgoing Fellowship within the Seventh European Community Framework Programme (project no. IOF253079). A.R. acknowledges support from the Norwegian Research Council. M.V.R. acknowledges support from an NSF graduate research fellowship.

fellow in Prof. Jacob Israelachvili’s group. In his research, Michael primarily uses the surface forces apparatus to study the behavior of amphiphilic polymers, proteins, and small biomolecules at both hydrophobic and hydrophilic interfaces. Saurabh Das received his B.S. in chemical engineering from University Institute of Chemical Technology, Mumbai, in 2009. He is currently a fourth year Ph.D. student in the Department of Chemical Engineering at UC Santa Barbara under Prof. Israelachvili. He works on the adhesive and tribological properties of wet and dry interfaces with a focus on biolubrication (conferred by proteins and polysaccharides), mussel protein adhesives, and gecko mimetic structures.

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REFERENCES

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Matthew A. Gebbie received his B.S. in chemical engineering from NC State University in 2010, where he engaged in research on the physical properties of ionic liquids in the laboratory of Prof. Wesley Henderson. He is currently a fifth year Ph.D. candidate in materials science at UC Santa Barbara and a member of Prof. Israelachvili’s interfacial sciences research group. His thesis research focuses on elucidating the interplay of colloidal interactions in complex, confined soft matter systems, including ionic liquids, hydrophobic interfaces, and surface-active peptides. Dong Woog Lee received his B.S. in chemical and biomolecular engineering from KAIST, South Korea in 2008. He received his Ph.D. in chemical engineering at UC Santa Barbara under Prof. Israelachvili, and currently he is working as a postdoctoral researcher in the same group. His research focuses on studying various interaction forces in bioadhesion (membrane, proteins, and biomimetic polymers) and biolubrication (articular joints and model surfaces) using the surface forces apparatus (SFA). Philipp Stock received his Ph.D. in bioinorganic chemistry at the Technical University in Berlin in 2012. Since then he has been a postdoctoral researcher with Dr. Markus Valtiner at the Max-PlanckInstitut für Eisenforschung GmbH. He is interested in single-molecule force spectroscopy, XPS spectroscopy, and hydrophobic forces in protein materials. Markus Valtiner was a postdoctoral and Marie Curie international outgoing fellow working with Prof. Israelachvili at UC Santa Barbara. Currently he is a group leader at the Max-Planck-Institut für Eisenforschung GmbH working on chemistry and forces at electrochemical interfaces, single-molecule force spectroscopy, and protein materials. Jacob Israelachvili received his B.A. and M.A. in (experimental) physics from the University of Cambridge, England, and also carried out graduate and postgraduate research work there in the Surface Physics Department of the Cavendish Laboratory. He received his Ph.D. in 1972. After a 2 year EMBO research fellowship at the University of Stockholm, he left for Australia, where from 1974 to 1986 he led an experimental research group devoted to measuring the forces between surfaces. In 1986, he joined the faculty at UCSB, where he holds joint appointments as professor in the Chemical Engineering Department, the Materials Department, and the BioMolecular Science and Engineering Program. Israelachvili’s research interests are in the general area of intermolecular and intersurface forces in biological, complex fluid, and materials systems. He uses the surface forces apparatus for directly measuring the static and dynamic forces between surfaces in liquids and vapors and for studying other interfacial phenomena on the molecular level.

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ACKNOWLEDGMENTS We thank Daniel Kienle and Tonya Kuhl for sharing unpublished work. This work was supported by the U.S. L


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Developing a General Interaction Potential for Hydrophobic and

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