Contact Angle and Adhesion Dynamics and Hysteresis on

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Contact angle and adhesion dynamics and hysteresis on molecularly smooth chemically homogeneous surfaces Szu-Ying Chen, Yair Kaufman, Alex M Schrader, Dongjin Seo, Dong Woog Lee, Steven H Page, Peter H. Koenig, Sandra Isaacs, Yonas Gizaw, and Jacob N. Israelachvili Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02075 • Publication Date (Web): 26 Jul 2017 Downloaded from http://pubs.acs.org on July 30, 2017

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Contact angle and adhesion dynamics and hysteresis on molecularly smooth chemically homogeneous surfaces Szu-Ying Chena, Yair Kaufmanb, Alex M. Schradera, Dongjin Seoa, Dong Woog Leec, Steven H. Paged, Peter H. Koenige, Sandra Isaacsd, Yonas Gizawd, and Jacob N. Israelachvilia,f,* a Department of Chemical Engineering, University of California at Santa Barbara (UCSB), Santa

Barbara, California 93106. b Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben

Gurion University of the Negev, Sede Boqer Campus 84990, Midreshet Ben-Gurion, Israel. c School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology

(UNIST), UNIST-gil 50, Ulsan 689-798, Republic of Korea. d The Procter & Gamble Co., Winton Hill Business Center, 6210 Center Hill Avenue, Cincinnati, Ohio

45224. e The Procter & Gamble Co., Beckett Ridge Technical Center, Union Centre Boulevard, West Chester

Township, Ohio 45069. f Materials Department, University of California at Santa Barbara (UCSB), Santa Barbara, California

93106. * To whom correspondences should be addressed. Email: [email protected]

Abstract Measuring truly equilibrium adhesion energies or contact angles to obtain the thermodynamic values are experimentally difficult because they require loading/unloading or advancing/receding boundaries to be measured at rates that can be slower than 1 nm/s. We have measured advancing-receding contact angles and loading-unloading energies for various systems and geometries involving molecularly smooth and chemically homogeneous surfaces moving at different but steady velocities in both directions, ±V, focusing on the thermodynamic limit of ±V à 0. We have used the Bell Theory (1978) to derive expressions for the dynamic (velocity-dependent) adhesion energies and contact angles suitable for both (i) dynamic adhesion measurements using the classic Johnson-Kendall-Roberts (JKR, 1971) theory of ‘contact mechanics’, and (ii) dynamic contact angle hysteresis measurements of both rolling droplets and syringe-controlled (sessile) droplets on various surfaces. We present our results for systems that exhibited both steady and varying velocities from V~10 mm/s to 0.1 nm/s, where in all cases, but one, the advancing (V > 0) and receding (V < 0) adhesion energies and/or contact angles converged towards the same theoretical (thermodynamic) values as V à 0. Our equations for the dynamic contact angles are similar to the classic equations of Blake & Haynes (1969) and fitted the experimental adhesion data equally well over the range of velocities studied, although with somewhat different fitting parameters for the characteristic molecular length/dimension or area, and characteristic bond formation/rapture lifetime or velocity. Our theoretical and experimental methods and results unify previous kinetic theories of adhesion and contact angle hysteresis, and offer new 1

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experimental methods for testing kinetic models in the thermodynamic, quasi-static, limit. Our analyses are limited to kinetic effects only, and we conclude that hydrodynamic, i.e., viscous, and inertial effects do not play a role at the interfacial velocities of our experiments, i.e., V < (1-10) mm/s (for water and hexadecane, but for viscous polymers it may be different), consistent with previously reported studies. 1. Introduction There have been two main approaches to theoretically analyze or model moving droplets on surfaces, including the so-called ‘static’, advancing, and receding contact angles as functions of the advancing/receding velocity of the ‘three-phase boundary’, TPB (also known as the three-phase contact-line – TPL, and three-phase zone – TPZ). These are the hydrodynamic and kinetic or molecular models/theories1, where the first depends on the bulk fluid viscosity and slip conditions at the bulk liquid-solid interface, and the second – pioneered by Blake & Haynes2 (and here referred to as the Blake Kinetic Model or Theory) – on the kinetics of molecular adsorption (binding, association) and desorption (unbinding, dissociation) at the front and back (trailing) ends of a moving droplet, or – in the case of sessile droplet or captive bubble experiments – on the advancing and receding angles as the droplet volume is increased or decreased (usually via a syringe). In the latter type of experiments (see Figure 1C) there is total control of the velocity of the TPB, while in experiments with droplets rolling down an inclined plane (Figure 1B) the velocities at the front and back cannot be controlled, and are often different, with the front moving faster than the back, which ‘creeps’ or is ‘pinned’ before it starts to move. The theoretical and experimental literature of liquid-on-solid adhesion and contact angle hysteresis goes back to the 1950s2,3 and is quite voluminous (see recent review by Eral et al.1) and we do not intend to review it all here. Nevertheless, some examples of different experimental techniques that have been used to measure liquid-on-solid works of adhesion include: Kuna et al.4 and Voïtchovsky et al.5, who measured works of adhesion using Atomic Force Microscopy (AFM), and Tadmor et al.6, who measured ‘works of separation’ from the forces and shapes of detaching liquid droplets from solid surfaces. Here, in this article, we present a new ‘kinetic’ model for such systems based on the Bell Theory7-9 – here referred to as the Bell Kinetic Model or Theory – which we also generalize to include the loadingunloading dynamics of adhering/detaching surfaces. We measured dynamic adhesion energies and hysteresis both via contact angle and adhesion force measurements on a number of different systems. We then compared our results with the predictions of both the earlier (Blake) and our (Bell) kinetic models. We first develop a theoretical framework for quantitatively analyzing the various wetting and adhesion systems based on the Bell Theory of the dynamic (kinetic) forces and energies associated with molecular adsorption/desorption (binding/unbinding) processes. Our analysis is restricted to molecularly smooth, rigid (non-deformable), and chemically

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homogeneous surfaces (e.g., mica, silica, etc.), and does not include hydrodynamic forces or effects due to pinning of the TPB. In the Bell theory, and in this analysis, the liquid molecules at the surface of the droplet are assumed to be moving in a ‘tank track’ rolling motion, i.e., coming down onto the surface only at the (advancing) front, and pulled up from the surface only at the back (receding end), as illustrated in Figure S3 in Supporting Information Section 2. Thus, we assume a ‘no-slip’ condition at the liquid-solid interface. Following our derivations, we compare our equations with both previous theories, as well as previously measured and new experiments with water, hydrocarbon, and polymer liquids in the 4 types of liquid-solid and thin film configurations depicted in Figure 1 B-E. 1.1. The ‘friction’ of moving droplets (liquid fronts) Before proceeding to consider dynamic effects, we review the ‘friction forces’ on a liquid droplet, and how these forces are related to the droplet geometry and the advancing and receding adhesion energies, W, and corresponding contact angles, q. Figure 1 shows how the processes occurring at two shearing solid surfaces or ‘solid-on-solid’ sliding (Figure 1A) are different from those occurring at the contact interface of a liquid moving or, more strictly, rolling or peeling, across a solid surface (Figure 1 B-D, and Figure S3), where the ‘dynamic’ Young-Dupré equation is different at the advancing and receding fronts, and given by at the advancing front: gLV (1 + cos qA ) = WA ,

(1)

at the receding front: gLV (1 + cos q R ) = WR .

(2)

In the thermodynamic limit, as V à 0, which is generally referred to as the static or quasistatic condition, there is no contact angle hysteresis as elaborated below, and Equations (1) and (2) both reduce to the thermodynamic Young-Dupré equation, Equation (7):

gLV (1 + cos q0 ) = W0 . Similar effects occur at other liquid-solid interfaces that peel onto or away from each other, for example, as illustrated in Figure 1E, involving two solid (elastic or viscoelastic) surfaces with ‘fluid-like’ but surface-bound surfactant monolayers or liquid polymer films that – as we show in Section 2.4 – are also analyzable using the Bell Kinetic Theory. 3


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Figure 1. (A) Solid-on-solid sliding: conventional friction geometry of a smooth solid surface of area A sliding on another solid surface where d is the molecular or asperity size (strictly, the lateral distance between adhesion energy minima – see Figure S1 in Supporting Information Section 1), and 𝛥𝑊 = (𝑊% − 𝑊' ) is the adhesion energy (or work of adhesion) hysteresis in terms of the energies on loading (approaching or advancing), 𝑊' , and unloading (retracting or receding), 𝑊% , giving the friction force, F, of Equations (3a,b). While the terms loading and unloading usually refer to surfaces approaching (advancing) or separating (receding) in the ‘normal’ direction, the same concepts apply at the molecular level when considering the energy changes associated with the lateral (shearing) motion during frictional sliding, where the two surfaces first have to separate (dilate) by ~0.1-1.0 Å before they can move laterally. See Supporting Information Section 1 and Chapter 18 of Israelachvili9 for details. (B–E) Analogous situations for (B) ‘Roll-off experiments’: droplets rolling down an inclined plane, (C) syringe injections of macroscopic liquid droplets, (D) a squeezed macroscopic (>microns) capillary bridge, and (E) loading/unloading (JKR cycles) of thin fluid films adhering (on compression) or peeling away (on separation). All of these situations give rise to ‘adhesion hysteresis’ described by Equations (5a,b). More detailed analyses of these systems are given in Sections 1.2 and 2, and the Supporting Information. 1.1.1. Advancing and receding droplets, and droplets rolling down inclined planes As mentioned above, the main difference between solid-on-solid friction and liquid-onsolid friction is that in the former, all the molecules of the top surface are moving together relative to the bottom surface, while in the latter, under the usual ‘no-slip’ boundary conditions, they are stationary with respect to the lower surface. This is also true for the case of Figure 1E, where the two surfaces ‘peel’ away on separating without shearing or ‘slipping’. Indeed, for a liquid to move across a solid surface, it is not necessary that slip or partial slip has to occur at any point of the liquid-solid interface/contact region – adsorption and desorption of the molecules at the front and end (essentially peeling or ‘tank-track-like’ 4


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rolling, as illustrated in Figure S3) is all that is required, which is also implicit in most kinetic models2,3. We start with the equation for solid-on-solid friction of Figure 1A, derived in Figure S1 in Supporting Information Section 1, and rewritten in the form:

𝐹∥ = 𝐴 𝜀% 𝑊% − 𝜀' 𝑊' /𝛿

(3a)

where A is the ‘frictional interaction surface area’, 𝛿 is the lateral distance between adhesion energy minima (see Figures 1A, 2, S3 and S4), eR and eA are the fractions (£1.0) of the kinetic energies transferred to the solid surfaces at the advancing (adsorbing) front, and to the liquid at the receding (desorbing) end during molecular collisions (see Figure S3). In the limiting cases where there is complete, or nearly complete, energy transfer for both the adsorbing and desorbing molecules, then eR » eA » e » 1, and Equation (3a) simplifies to Equation (3b) which, in the limit of e = 1, may be called the ‘ideal condition’: 𝐹∥ = 𝜀𝐴 𝑊% − 𝑊' /𝛿 = 𝐴 𝑊% − 𝑊' /𝛿 . (3b) To proceed further, we require the expression for the ‘frictional interaction surface area’, A, for a liquid droplet moving on a solid surface at the advancing and receding fronts. This is done in Figure 2. Figure 2. Derivation of Equations (4a,b). Schematic of the main features of an asymmetric droplet moving at velocity V across a flat homogeneous surface by an incremental displacement, d, showing the surface interaction areas in red in the upper, SIDE VIEW panel, and the light blue shaded regions in the lower, TOP VIEW panel. From simple geometry, the change in the interaction area, A, at the front and back are equal to that of a rectangle of width d and height 2𝑟1 (note that d has molecular dimensions, i.e., 𝑟1 » 𝛿 ). Thus, A = Width of base × Height = 2𝛿𝑟1 . Note that A is independent of the advancing and receding radii, rA and rR, as well as the vertical height, H, and lateral length, L, of the droplet, but depends only on the lateral displacement, d, and the (maximum) width of the droplet that is in contact with the surface, 2𝑟1 . Figure 2 shows that, to a good approximation, the detailed shape of the droplet does not matter – or is of secondary importance – the (constant) molecular dimension, d, and the

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maximum width of the droplet, 2𝑟1 , being the only relevant length parameters. Inserting

A = 2d r^ in Equation (3a) we obtain:

𝐹∥ = 2𝐴 𝜀% 𝛾% − 𝜀' 𝛾' /𝛿 = 2 2𝛿𝑟1 𝜀% 𝛾% − 𝜀' 𝛾' /𝛿

(4a)

𝐹∥ = 2𝑟1 𝜀% 𝑊% − 𝜀' 𝑊' = 2𝑟1 𝜀% cos 𝜃% − 𝜀' cos 𝜃' 𝛾DE .

(4b)

It is important to note that even when the front and back move at different velocities, i.e., VA ¹ VR, the above equations still hold because at each end the ratio A /d is the same and given by A/d = 2d r^/d = 2 r^ . This is because, independently of the velocities at each end, it is still the lateral molecular-scale distance/dimension, d, where the liquid molecules desorb (detach, move up) at the receding end, and adsorb (bind, or come down) at the advancing front, as illustrated in Figure S1. These are the only places where the analogy with solid-onsolid sliding holds. Everywhere else, the liquid molecules remain in contact with the surface, i.e., do not move relative to the solid surface as the droplet moves, as would be the case with solid-on-solid sliding. Thus, when V is not constant, or when VA ¹ VR, while the above equations still hold, the parameters, e A , e R , and r^ , which are expected to be velocity dependent, may change during non-steady or asymmetric sliding. In many cases, e R » e A = e » 1, when Equation (3a) reduces to Equation (3b), and Equations (4a) and (4b) become 𝐹∥ = 2𝜀𝑟1 𝑊% − 𝑊' = 2𝜀𝑟1 cos 𝜃% − cos 𝜃' 𝛾DE ,

(4c)

where the case of e = 1 may be considered as the ‘ideal condition’. Finally, as V à0, we must have 𝐹∥ à 0, and therefore e R = e A = e = 1, so that in this limit:

𝐹∥ → 2𝑟1 𝑊% − 𝑊' ≈ 2𝑟1 cos 𝜃% − cos 𝜃' 𝛾DE → 0.

(4d)

One form of Equations (4b) and (4c) specific for the case of ε = 1 was first introduced by Furmidge10, and then derived using hydrodynamic theory by Dussan11. Various other versions of these equations have also appeared in the literature, as reviewed by Wolfram & Faust12 and Extrand & Kumagai13. In these analyses it is implicitly assumed that eA= eR, so that only equations having the form of Equation (4c) are considered. In these analyses the factor 2e r^

( )

( )

p of Equation (4c) appears in various forms, such as p R , 2 R , and p4 R (corresponding to e =

1.57, 0.79, and 0.64, respectively), where R is not necessarily the half-width r^ of the droplet. Most of these analyses focus on the effects of droplet shape rather than the effects of the velocities of the advancing and receding fronts on these shapes and, in turn, the contact angles and friction forces. More recently, Semprebon & Brinkmann14 carried out a comprehensive computational investigation of transient rather than steady-state motions, including the ‘static’ advancing and receding angles at the ‘onset of motion’, as well as pinning and depinning 6


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transitions. Other ‘onset of motion’ approaches15-17 have also analyzed the forces associated with droplets sliding/rolling on superhydrophobic surfaces18 and systems in which there is no pinning19. The way the advancing and receding velocities, VA and VR, determine the effective surface energies, works of adhesion, boundary radii, contact angles and other relevant measurable parameters of the systems of Figure 1 B-E are analyzed in the experimental section (Section 2) after we first consider the dynamic (velocity- and/or rate-dependent) interactions within a general framework in the following Section 1.2. 1.2. Dynamic/kinetic molecular interactions of moving droplets Referring to Figure 1C, at the advancing edge we expect (cf. Figures S3 and S4) the adhesion energy initially or at first contact, WA, to be lower than the (final) thermodynamically equilibrium value, W0. This is because at thermodynamic equilibrium, the liquid molecules have reordered from their initial configurations at first contact to maximize their (attractive adhesion, by convention negative – see Footnote 1 in Supporting Information Section 1) interaction energy with the surface atoms or molecules. The faster the advancing front moves, the larger we expect this difference – i.e., the hysteresis – to be (see Chapters 9 and 22 of Israelachvili9), while for an infinitely slow advance (as V à 0) we expect WA àW0. Our model is based on the Bell Theory7, which has previously been applied almost exclusively to single molecule or bond rapture forces. Here, in Supporting Information Section 2, we apply this model to multiple bond making-and-breaking between macroscopic surfaces, and obtain the following expressions for the velocity-dependent advancing and receding energies: For advancing: WA = W0 -

V+v V+v kT kT ln ( v A ), or (cos q A - cos q 0 ) = - g ln ( v A ) , (5a) a0 A A LV a0

For receding: WR = W0 +

V+v V+v kT kT ln ( v R ), or (cos q R - cos q0 ) = + g ln ( v R ) . (5b) a0 R R LV a0

where vA=s/tA and vR=s/tR are the characteristic ‘relaxation’ velocities associated with the characteristic dimensions: molecular lengths scales s » d , area a0 » s 2 » d 2 , and times tA and

tR, of the molecular interactions at the advancing (adsorption) and receding (desorption) fronts (See Equations (A3) and (A4) in Supporting Information Section 2). (Note that by convention, the adhesion energy or work of adhesion, W, like the surface energy or tension, g, is positive because the reference state, i.e., zero adhesion energy, is when the surfaces are in adhesive contact, while when the reference state is the separated state, as in plots of interaction potentials, it is negative.)

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The above equations can be applied to both liquid motion on macroscopic surfaces (Sections 2.1 and 2.2), and, in particular, to loading-unloading adhesion and ‘contact mechanics’ measurements (Sections 2.3 and 2.4) where separation can occur via simple “Mode I” or peeling detachment (also fracture, failure). We may also note that unlike singlemolecule AFM experiments that probe small number of molecules or a protein molecule with a number of unravelling domains to which the Bell theory has been successfully applied20,21, we here have a situation where many bonds (essentially ~ r^ /d bonds) are broken each time the front moves by even d =1 nm. Equations (5a,b) show that as the droplet moves infinitely slowly (i.e., for V « n or as V à 0), the system approaches thermodynamic equilibrium as: For advancing:

(cosθ A − cosθ 0 ) = − γ

V+v V ≪ vA kT kT kTV ln ( v A )= − γ ln (1+ vV ) ⎯V→0 ⎯⎯→ − 3 γ a a A A LV 0 LV 0 LV σ τA

, (6a)

For receding:

(cosθ R − cosθ 0 ) = + γ

V+v V ≪vR kT kT kTV ln ( v R )= + γ ln (1+ vV ) ⎯V→0 ⎯⎯→ + γ LV σ 3τ R R R LV a0 LV a0

. (6b)

Thus, as V à 0 the advancing and receding energies, Equations (5a,b), and contact angles, Equations (6a,b), converge: i.e., WA = WR = W0, and qA = qR = q 0, which are now related by the thermodynamic Young-Dupré equation:

gLV (1 + cos q0 ) = W0 .

(7)

There is now no contact angle hysteresis, and zero friction forces, Equation (4d), as expected for an infinitely slow ‘dynamic’ process at quasi-thermodynamic equilibrium. Our equations also provide a means for identifying the molecular relaxation/reordering times and binding/unbinding (adsorption/desorption) energies of advancing and receding fronts at different droplet velocities or adhering contact radii, and the velocity, v0, below which a TPB is expected to be reversible. When the velocity is very small, we have ‘creep’, and as all the velocities approach zero there should be no contact angle hysteresis, i.e., as V à 0, 𝐹∥ à 0. Strictly, according to the laws of adhesion and friction (see Chapter 18 of Israelachvili9), at any finite temperature the droplet (or any body, liquid or solid) should move – whether by detachment from adhesion or by frictional sliding – at the slightest applied force, e.g., slope angle of the tilted surface, although as already discussed the speed could be «1 Å/s, and therefore difficult to observe/detect or measure accurately.

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Equations (6a,b) have certain similarities to the classic equations previously derived by Blake & Haynes2,22 – here referred to as the Blake-kinetic theory – and used ever since for analyzing kinetic (dynamic) contact angle hysteresis1,2,22,23: (cosθA/R − cosθ 0 ) = −

⎛ ±V ⎞

2kT kTV V ≪ 2 λκ −1 →∓ V→0 γ LV λ 2 sinh ⎜⎝ 2λκ ⎟⎠ ⎯⎯⎯⎯ γ LV λ 3κ

,

(8)

where l is a characteristic length having molecular dimensions, also variously referred to as the ‘molecular width or length’, ‘molecular displacement’, or ‘distance between adsorption sites’1,2,22,23. l is essentially the same as s in the Bell Theory analysis – and estimated to be in the range from 0.4 to 1.8 nm for different liquids22. k is a characteristic rate constant or frequency of the adsorption-desorption processes (in units of s-1) – essentially analogous to t0 in the Bell Theory, and estimated to be in the range ns to 1 s depending on the binding energies and possibly local viscosity3,22. However, as illustrated in Supporting Information Section 2 and Figures S3 and S4, in the Bell model, t0A and t0R are the times the molecules take to respectively adsorb and desorb, which includes their reorganization times on the surfaces, where these times (and therefore the frequencies k) can be very different, and also likely to be cooperative. In general, we expect t0R > t0A, so that vA > vR. Thus, we find that the above two theories or approaches give essentially identical equations in the thermodynamic limit. We also conclude that ‘static’ contact angle hysteresis (as in Figure 1 of Blake22 or Figure 2 of Eral et al.1), even for smooth surfaces, should not exist if the waiting time before reversing the direction of motion (R « A) is long enough, i.e., if V is truly quasi-static, which, as we shall see, may require V to be much less than 1 Å/s or vA and V > vR, so long as the interactions are dominated by molecular interactions and not by inertial or hydrodynamic forces. A detailed analysis and comparison of hydrodynamic, molecular/kinetic and combined models for various liquids23 suggests that hydrodynamic effects are more important at low contact angles, i.e., at the receding ends of droplets, and at velocities V > 1 cm/s (cf. Figures 1 and 2 in Schneemilch et al.23 for advancing and receding data on OMCTS). It is worth stressing once again that in the Bell theory, and in this analysis, the liquid molecules are assumed to be coming down onto the surfaces on approach (adsorption, advancing front) and are pulled up from the surfaces on separation (desorption, receding front), as shown in Figure S3. Thus, interfacial ‘slip’ is not the mechanism by which the liquid molecules are assumed to move, even in the first layer. Their motion during friction and adhesion is more akin to ‘rolling friction’ [see Section 18.8 of Israelachvili9], and pictorially like a rolling ‘tank track’ as in Figure S3, as well as to the so-called “Mode I fracture” in the tensile testing of materials (see Figure S1), and ‘peeling’ adhesion during loading and/or unloading in JKR experiments (Section 2.4). In the following Section, we compare the above theories and equations with the results of various dynamic experiments with liquid droplets and adhering/retracting fluid monolayer surfaces at velocities well below 1 cm/s, where hydrodynamic effects are not expected to be significant. 2. Experimental Section: Applying the above equations to some old, and some new, experimental data In this Section we describe the results of the 4 different geometries depicted in Figure 1 BE, starting with the ‘rolling droplet’ geometry (Figure 1B). Unlike the other three geometries, the rolling droplet geometry is ‘asymmetrical’ in the sense that the advancing and receding fronts can move semi-independently of each other, i.e., the advancing front velocity VA can be different from the receding front (tail end) velocity, VR; while the other three geometries are closer to being ‘symmetrical’ (minimal or no asymmetric change in shape change) in the sense that, at any time, all fronts have the same radius and are either advancing or receding at the 10


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same velocity, VA or VR, that can therefore be measured independently. However, in the case of Figure 1D with a liquid bridge between the two surfaces, or Figure 1E with adsorbed monolayers/films on the surfaces, the systems become ‘asymmetric’ if the two surfaces or adsorbed films are different. But the advancing/loading and receding/unloading velocities can be independently and accurately controlled and measured. 2.1. Rolling droplet experiments (geometry of Figure 1B) Rolling droplet experiments are essentially a test of Equation (4b) which can be written in the form: 𝐹∥ = 2𝑟1 𝜀% cos 𝜃% − 𝜀' cos 𝜃' 𝛾DE ,

(11)

which, for e R = e A = e , becomes 𝐹∥ = 2𝜀𝑟1 cos 𝜃% − cos 𝜃' 𝛾DE .

(12)

Figure 3 shows some early results obtained for near-circular drops of water on 7 polymer surfaces, where the data is well fitted by Equation (12), viz, for e R = e A = e = 1.

Figure 3. Measured friction forces as a function of advancing and receding angles for nearcircular drops of water (geometry of Figure 1B) on 7 polymer surfaces: paraffin, polystyrene, polyethylene, PMMA (poly(methyl methacrylate)), polycarbonate, Teflon (polytetrafluoroethylene), and polypropylene. The red line is for a prefactor of 2gLV (e = 1) as in Equation (12), instead of pgLV (black line of original article). [Drawn from numerical values given by Wolfram & Faust12, Table II, p. 222; see also Extrand & Gent24]. Most experiments have found good fits to Equation (12) for slopes corresponding to e less than 1.0, for example, e = 2/p = 0.64 24, but usually under non-steady-state sliding conditions, 11


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for example, at the onset of sliding, or when there is pinning of the receding edge, stick-slip, accelerating droplet, etc. Under such conditions, using the Bell Model, we need to apply Equation (11) where the parameters eR and eA are likely to depend on the two contact angles as well as on VR and VA (since we require e R®1 and e A ® 1 in the thermodynamic limit when cosqR = cosqA and 𝐹∥ = 0 at V® 0 ). If under such ‘non-ideal’ conditions there is a trailing film at the back (cf. Figure S3), then e R < 1, while if there is a precursor film at the front (less common for moving droplets, especially at high V) e A < 1. Thus, it is not unreasonable to expect that, in most cases, eR < eA, which would make the slope correspond to an effective e < 1 in Equation (12), and for the data points to fall below the ‘ideal’ line for e = 1. Figure 4 shows our measurements of water droplets on 9 different surfaces at the onset of motion, where the average value for e was between 0.87 and 1.05 depending on whether the line was made to pass through the origin or not. In addition, the data points fall slightly below the line for e = 1, suggesting that eR < eA in Equation (12). The velocities of the TPB were not measured in these experiments, where the data correspond to the ‘onset of sliding from rest’ of either the front or back of the droplet, so that a more detailed quantitative analysis of the data, requiring a knowledge of VR and VA and how they affect the advancing and receding energies (cf. green circle in Figure 5, left side), is not possible at this stage.

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Figure 4. Roll-off contact angle experiments (configuration of Figure 1B) for droplets of water (Millipore purified, volumes: 10, 20, 30 and 40 µl) about to roll down inclined planes of 9 materials: polyethylene, nylon, copper, tungsten carbide, Teflon (polytetrafluoroethylene), a silica wafer, Lexan (polycarbonate), Plexiglas (poly(methyl methacrylate)), and polyvinyl acetate. The contact angles were measured for the so-called ‘resting’ or ‘onset of motion’ state, i.e., immediately prior to motion defined as the first visible displacement of the advancing or receding ends of the droplet. Some droplets exhibited pinning or stick-slip motion. For each material, a total of twenty experiments were carried out. The highest (average) advancing angle measured was 125°, and the lowest receding angle measured was 11°. The black line is the prediction of Equation (12) for e = 1.0. The 9 data points are fitted by (1) the green line passing through the origin (slope corresponding to e = 0.87), and (2) the red line fitted to the data points only (slope of e = 1.05). The dotted red line extending from the solid red line suggests the (unmeasured) behavior as 𝐹∥ → 0 when qR® qA. In addition, the data points all fall below the e = 1 line, indicating, that eR < eA (see text). 2.2. Syringe injection-retraction experiments (geometry of Figure 1C) In these, and the subsequent experimental geometry tested, the systems are radially symmetrical, so that at any time the liquid front is either advancing or receding, which allows for the independent testing of Equations (5a,b) at well-controlled advancing or receding velocities. We carried out syringe injection-retraction (advancing-receding) experiments with 13


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liquid hexadecane and water at constant contact-line velocities, V, on monolayers of OTS (~0.5 nm thick) coated on rigid, smooth silica. Experiments with water on solid PDMS surfaces were also done. The results for hexadecane (θ0 < 90°) and water (θ0 > 90°) are shown in Figures 5 and 6, respectively.

Figure 5. Left side: Fit of Equations (5a,b) (red and blue curves) to syringe injectionretraction experimental data of the advancing (red) and receding (blue) contact angles (and, equivalently, advancing and receding works of adhesion) as a function of contact-line (TPB) velocity of droplets of hexadecane on a monolayer of OTS (~0.5 nm thick) chemisorbed on a smooth, rigid silica surface (θ0 < 90°). Note that the Young-Dupré equation predicts Cos θ > 1 above a certain W, implying θ < 0°, which is unphysical. This condition results in a wetting film of finite thickness (see Figures 13.7 and 17.6 of Israelachvili9); the measured contact angle remains at 0°. The green lines in the green circle show the effects of different advancing and receding velocities (VA and VR, respectively) on the works of adhesion and, in turn, the contact angles. The vertical line corresponds to a droplet moving everywhere at the same velocity, i.e., VA = VR. The slanted line is when VA ≠ VR (in this case, VA > VR), which is discussed at the end of the paragraph following Equations (4a) and (4b). Right side: Snapshot images of hexadecane (A) receding and (B) advancing on the OTS monolayer at a constant contactline velocity of V ~ 2 μm/s. At this relatively low velocity, the CAH is small, with an advancing contact angle of θA = 28° and a receding contact angle of θR = 25°. As shown in Figure 5, only at V < 1 µm/s is the wetting behavior effectively reversible, with no CAH and with θ exhibiting the ‘thermodynamic equilibrium value’, θ0. Only for velocities V above ~5 μm/s does the CAH noticeably increase as the two contact angles begin to diverge, and the experimental data is well-fitted by Equations (5a,b). Note that the vertical CAH arrow in Figure 5 is proportional to the friction force, F, at the same advancing and 14


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receding velocities, discussed in Section 2.1. The exact value of W0 for this self-assembled monolayer system is unknown but expected to be close to W0~55 mJ/m2, corresponding to a surface tension of ~55/2 = ~27.5 mN/m – the value for hexadecane.

Figure 6. Advancing (red) and receding (blue) contact angles (and corresponding advancing and receding works of adhesion) as a function of contact-line (TPB) velocity of droplets of water on a hydrophobic monolayer of OTS (~0.5 nm thick) chemisorbed on a smooth silica surface (θ0 > 90°) from syringe injection-retraction experiments. The colored solid circles are the experimental data points, and the colored solid lines correspond to each respective average. Inset: Snapshot images of water (A) advancing and (B) receding on the OTS monolayer at a constant TPB velocity of V~20 μm/s, at which velocity there is near reversibility, with an advancing contact angle of θA = 113° and a receding contact angle of θR = 108°. Very similar results and trends (very small CAH) are found for water on a hydrophobic PDMS surface of RMS roughness 0.4 nm (not shown). Unlike the results of Figure 5 for hexadecane on OTS, those of Figure 6 for water on OTS do not appear to be converging at low V. In general, it is possible for there to be more than one relaxation process in any wetting hysteresis phenomenon. For example, in addition to the ‘kinetic’ nano-scale molecular adsorption/desorption processes, one also expects there to be nano- to micro-scale bulging of the elastic (or viscoelastic) surfaces at the TPB due to the normal stress component of the liquid-vapor interface, γLVsinq, which for water would be quite high. This ‘line-tension-induced deformation’ of surfaces is a well-known effect1517,25-28, but so far there is no theory for analyzing the rate-dependent deformations and dynamic contact angles associated with this phenomenon, and these line-tension effects are beyond the scope of this manuscript. 2.3. Detaching capillary bridge experiments (geometry of Figure 1D) We now test the Bell-kinetic theory Equations (5a,b) on some previously reported results on the loading and unloading forces and energies of two curved elastic surfaces with liquid droplets (capillary bridges) or adsorbed films between them (corresponding to the 15


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geometries of Figure 1D and 1E) which were not previously analyzed/interpreted in terms of any model. We also compare the results with fits to the Blake-kinetic theory. In these experiments the two surfaces were identical so that these systems belong to the ‘symmetrical’ geometry, discussed above. Figure 7 shows the works of adhesion as measured from the pull-off (adhesion) forces, Fad, of a liquid bridge of polystyrene (PS), MW 580 Da, at +23°C (well above the Tg of -45°C) where PS is a liquid, between two surfaces (configuration of Figure 1D) in a Surface Forces Apparatus (SFA)29. In Figure 7A the orange and blue curves were each fitted independently to the Blake- and Bell-kinetic equations, Equations (5b) and (8), respectively. The corresponding values for the fitted parameters in each case are given in the plots. It is readily apparent that both theories describe the results equally well, giving the same value for W0 » 68 mJ/m2, in agreement with the thermodynamic value of 66-70 mJ/m2, and with similar and physically reasonable fitted parameters that are within a factor of ~2 of each other when these are compared as in Equation (10), viz. l2 compared to a0, and k compared to n/l . A direct comparison of these values would require detailed analyses of the different experiments to which the two equations were fitted. Thus, λ2 may not be the same as the area a0 that each polymer molecule occupies; for example, a low or high value for a0 may reflect complex polymer loops, trains or interpenetrations at or across the contact interface (as in the original Bell theory), which would then not be simply related to the segment length or cross-sectional area of the molecules.

Figure 7. Fits of the Bell- and Blake-kinetic theories to SFA experimental data of the work of adhesion versus separation rate (configuration of Figure 1D) for liquid PS 580 at T = 23°C (T » Tg = -45°C, viscosity h » 20 Pa-s) between two mica surfaces in inert air or dry nitrogen vapor atmosphere (experimental data adapted from Zeng et al.29). (A) Independent best fit curves to the Bell- and Blake-kinetic equations (blue and orange curves, respectively), giving the same good agreement with the experimental data, but for different fitting parameters for the characteristic lengths, areas, rates and/or relaxation times. (B) Comparison of WR as predicted by the Bell-kinetic model (blue curve) and Blake-kinetic model (orange curve). It is 16


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interesting to note that when the fitting parameters are chosen to fit the two equations, we see in (B) that the two very different-looking equations actually agree to within ~10 % as the velocity changes by 12 orders of magnitude! Higher MW PS melts were also studied, up to 2,000,000 Da with Tg values above room temperature for MW > 1,200. These were also studied at T » Tg. Again, the Bell- and Blakekinetic equations appear to predict the right trends in WA. For example, for PS 1,300 at 51°C (see Figure 8) where V » vA, a logarithmic curve was found to fit the data much better than a linear or other function.

Figure 8. Measured unloading adhesion energy WR vs. the unloading velocity V for PS 1,300 at 51°C (Tg = +34°C, η ~ 20 mPa·s) where V » vA and therefore WR » W0 and where the plot is almost perfectly logarithmic. 2.4 JKR dynamic loading-unloading adhesion plots (geometry of Figure 1E) Here we consider the configuration of Figure 1E involving a Johnson-Kendall-Roberts (JKR)-type measurement9,30 of both loading and unloading (advancing and receding) of two negatively charged mica surfaces coated with a monolayer of the positively-charged (cationic) surfactant hexadecyl-trimethyl-ammonium-bromide (CTAB), with their 16carbon fluid hydrocarbon chains exposed, in the SFA. As shown in Figure 9A, the loading and unloading paths are farther away from the equilibrium path (middle of the shaded area) the higher the loading and unloading rates, da/dt, more or less symmetrically. Equations (5a,b) and 6(a,b) should apply to this type of ‘peeling’ adhesion, and Figure 9B shows how the loading and unloading energies vary with the velocity, defined by V = d(contact radius)/dt = da/dt. The extrapolated data show that only at velocities below ~0.1 nm/s, will the loading/unloading paths be reversible.

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Figure 9. (A) Conventional JKR a3-F plots of the cube of the contact radius a versus normal load, L or 𝐹1 , for a fluid CTAB self-assembled surfactant monolayer on mica (CTAB is positively charged, mica is negatively charged) at 25°C at different loading (advancing/approaching) and unloading (receding/retracting) velocities, V = da/dt. The results show that WA < W0 while WR > W0, as expected. The solid lines are fits to the data points using the JKR Equation9,30 which gave: for the fast loops (average V = 2.7x10-2 µm/s), WA = 40 mJ/m2 and WR = 100 mJ/m2, while for the slow loops (average V = 3.6x10-3 µm/s), WA = 47.4 mJ/m2 and WR = 89.0 mJ/m2. (B) Fits of the data using Equations (5a,b), for the deviations of WA and WR from W0 = 68 mJ/m2 with increasing V. [Schematics and data adapted from Chen et al.31]. 3. Analysis, discussion and conclusions We present a model based on the Bell Theory that is similar to previous molecular/kinetic models (e.g., the Blake Kinetic Model), with similar equations and physical assumptions, but with some difference in the values needed to fit experimental result to the equations of new Bell Kinetic Model. We demonstrate that the model is also applicable to adhesion, peeling, JKR loading-unloading cycles (adhesion hysteresis), and adhesion/contact mechanics involving Mode I fracture/failure mechanisms of viscous and viscoelastic surfaces or adsorbed surface layers, such as fluid surfactant or lipid monolayers. In addition, by measuring dynamic contact angles at different advancing and receding velocities, the proposed model allows for extrapolating the thermodynamically stable contact angle (i.e., adhesion energy) on atomically smooth and rigid surfaces, q0, which cannot be easily measured. Furthermore, the extrapolated contact angle, q0, can then be used to predict the metastable and the thermodynamically stable contact angles on textured/patterned surfaces by using other models, e.g., the “wetting model” that was proposed by Kaufman et al.32. As in the case of previous kinetic theories, the equations we derived are in terms of the equilibrium values of the contact angle q0 and adhesion energy W0 as well as a molecular 18


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dimension, s » d, or area, a0 » s 2 » d 2 , and relaxation time, t ; or relaxation velocity, v = s/t, below which the systems can be considered to be truly ‘quasi-static’, i.e., effectively manifesting their thermodynamic properties during motion. In these thermodynamic limits (where V < vA and V < vR): WA à WR à W0, qA à qR à q0, and there is no more ‘adhesion hysteresis’ or ‘contact angle hysteresis’. For the low to quite high viscosity fluids and films studied or considered here (η ~ 2 mPa-s to ~20 Pa-s, i.e., 4 decades) the relaxation velocities, v, were found to vary from ~0.1 nm/s to ~10 mm/s (8 decades). At higher sliding velocities, typically V > 10 mm/s, other factors come into play, such as hydrodynamic/viscous and inertial forces, which are discussed but not considered here. However, it is clear that many adhesion experiments using different samples and techniques will often measure adhesion forces (as well as ‘static’ contact angles after stopping after an advance) that are much higher than the ‘true’, i.e., equilibrium thermodynamic, values. The very low, and often experimentally unattainable, velocities of «1 Å/s, required to attain reversible conditions, suggest that there is probably no such thing as a true “zero rate fracture strength”, “yield stress”, or “static contact angle hysteresis” at V = 0. It may appear surprising or unexpected that the molecular relation times that we find, here referred to as the ‘adsorption’ and ‘desorption’ times, can be so long – ms or even seconds (but very similar to what was already noted 60 years ago by Hansen & Miotto3). However, these times also include the times to overcome any energy barriers associated with the molecular reorientations on the surfaces that define the complete adsorption and desorption processes (stage IV in Figure S4). Thus, these times are not determined by the diffusion rate of the molecules reaching the surfaces, but the time it takes for them to reorganize once they are at the surface – involving adjusting their position and orientation in synergy with the surface and neighboring liquid molecules. Thus, for s = 1 nm and t 0 = 0.1

ms – 1.0 s 3, we obtain characteristic or critical relaxation velocities in the range 1 nm/s – 10 µm/s, which nicely falls within the range of measured values reported here and in the literature. The systems studied here involve molecularly smooth, rigid (non-deformable), and chemically homogeneous surfaces where neither ‘static’ (intrinsic, fixed) nor ‘dynamic’ roughness (i.e., roughness induced by the high stresses at the TPB on a soft elastic or viscoelastic surface) arise; these effects are often inferred to be the cause of contact angle hysteresis, but our results suggest that contact angle hysteresis can arise even on molecularly smooth, rigid, and chemically homogenous surfaces, and that the origins of this type of contact angle hysteresis can only be unambiguously established by performing measurements at different, and especially ultra-low, rates. Moreover, surface roughness is not necessarily the reason for high contact angle hysteresis, as evidenced by the high hysteresis observed on smooth OTS surfaces as shown in Figure 5. In the case of rough Teflon or PDMS surfaces, the low hysteresis is likely to be due to the low binding energy and high mobility of the water molecules at the hydrophobic surfaces, resulting in high values for vA 19


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and vR, that allow for the near equilibrium contact angles to be manifest already at high velocities even though these surfaces are generally very rough. Our results also suggest that moving or rolling liquids do not necessarily have to ‘slip’ at any point, and instead provide insights into alternative (adsorption and desorption) mechanisms occurring at the advancing and receding ends of liquids moving (or rolling) across smooth surfaces, and especially the molecular reorganizations occurring on adhesion (coming on) and detachment (separation). Further experiments and theoretical analyses would require simultaneous measurements of the instantaneous advancing and receding front velocities, as well as the changing droplet shapes, to establish how these velocities, as well as other rate effects such as pinning and stick-slip motion, determine or are related to the parameters e A , e R and, in turn, the contact angles and other relevant system parameters. Extension of the models to rough and patterned, including chemically heterogeneous and ‘adaptable’ or ‘responsive’ surfaces (where physical or chemical deformations and changes are produced by the high stresses at the TPB) would also be a natural next step for understanding the complex and subtle effects of the wetting and adhesion behavior of more common everyday systems. Acknowledgments This work was supported by a grant from the Procter & Gamble Company. Dong Woog Lee was supported by grants from the National Research Foundation of Korea funded by the Korean Government (NRF-2016R1C1B2014294). The contact angle measurements were performed using the DataPhysics OCA 15Pro instrument. We thank the Saudi Arabian Oil Company (Saudi Aramco) for funding the purchase of the contact angle measurement instrument. We also thank Keetanart Rattananan for fruitful discussions and assistance with some data analysis. Supporting Information. Adhesion energy contributions to solid-on-solid friction; Dynamics of adhering and detaching molecules.

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Eral, H. B.; Oh, J. M.; t Mannetje, D. J. C. M. Contact Angle Hysteresis: A Review of Fundamentals and Applications. Colloid Polym. Sci. 2013, 291, 247–260. Blake, T. D.; Haynes, J. M. Kinetics of Liquid/Liquid Dispacement. J. Colloid Interface Sci. 1969, 30 (3), 421–423. Hansen, R. S.; Miotto, M. Relaxation Phenomena and Contact Angle Hysteresis. J. Am. Chem. Soc. 1957, 79 (7), 1765. Kuna, J. J.; Voïtchovsky, K.; Singh, C.; Jiang, H.; Mwenifumbo, S.; Ghorai, P. K.; Stevens, M. M.; Glotzer, S. C.; Stellacci, F. The Effect of Nanometre-Scale Structure on Interfacial Energy. Nat. Mater. 2009, 8 (10), 837–842. Voïtchovsky, K.; Kuna, J. J.; Contera, S. A.; Tosatti, E.; Stellacci, F. Direct Mapping of the Solid-Liquid Adhesion Energy with Subnanometre Resolution. Nat. Nanotechnol. 2010, 5(6), 401–405. Tadmor, R.; Das, R.; Gulec, S.; Liu, J.; N'guessan, H. E.; Shah, M.; Wasnik, P. S.; Yadav, S. B. Solid–Liquid Work of Adhesion. Langmuir 2017, 33, 3594–3600. Bell, G. I. Models for the Specific Adhesion of Cells to Cells. Science 1978, 200 (4342), 618–627. Evans, E.; Ritchie, K. Dynamic Strength of Molecular Adhesion Bonds. Biophys. J. 1997, 72 (4), 1541–1555. Israelachvili, J. N. Intermolecular and Surface Forces, 3rd Edition; Academic Press: London, 2011, 2014. Furmidge, C. Studies at Phase Interfaces. I. the Sliding of Liquid Drops on Solid Surfaces and a Theory for Spray Retention. J. Colloid Sci. 1962, 17 (4), 309–324. Dussan V., E. B. On the Ability of Drops or Bubbles to Stick to Non-Horizontal Surfaces of Solids. Part 2. Small Drops or Bubbles Having Contact Angles of Arbitrary Size. J. Fluid Mech. 1985, 151, 1–20. Wolfram, E.; Faust, R. Wetting, Spreading, and Adhesion; Padday, J. F., Ed.; Academic Press: New York, 1978; pp 213–222. Extrand, C. W.; Kumagai, Y. Liquid Drops on an Inclined Plane: The Relation Between Contact Angles, Drop Shape, and Retentive Force. J. Colloid Interface Sci. 1995, 170 (2), 515–521. Semprebon, C.; Brinkmann, M. On the Onset of Motion of Sliding Drops. Soft Matter 2014, 10, 3325–3334. Tadmor, R.; Bahadur, P.; Leh, A.; N’guessan, H. E.; Jaini, R.; Dang, L. Measurement of Lateral Adhesion Forces at the Interface Between a Liquid Drop and a Substrate. Phys. Rev. Lett. 2009, 103 (26), 266101–4. Tadmor, R. Approaches in Wetting Phenomena. Soft Matter 2011, 7, 1577–1580. N’guessan, H. E.; Leh, A.; Cox, P.; Bahadur, P.; Tadmor, R.; Patra, P.; Vajtai, R.; Ajayan, P. M.; Wasnik, P. S. Water Tribology on Graphene. Nat. Comm. 2012, 3 (1242), 1–5. Vahabi, H.; Wang, W.; Popat, K. C.; Kwon, G.; Holland, T. B.; Kota, A. K. Metallic Superhydrophobic Surfaces via Thermal Sensitization. Appl. Phys. Lett. 2017, 110 (25), 251602–5. Xu, W.; Xu, J.; Li, X.; Tian, Y.; Choi, C.-H.; Yang, E.-H. Lateral Actuation of an Organic Droplet on Conjugated Polymer Electrodes via Imbalanced Interfacial Tensions. Soft Matter 2016, 12, 6902–6909. 21


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Friddle, R. W.; Noy, A.; De Yoreo, J. J. Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 13573– 13578. Alsteens, D.; Pfreundschuh, M.; Zhang, C.; Spoerri, P. M.; Coughlin, S. R.; Kobilka, B. K.; Müller, D. J. Imaging G Protein-Coupled Receptors While Quantifying Their Ligand-Binding Free-Energy Landscape. Nat. Methods 2015, 12 (9), 845–853. Blake, T. D. The Physics of Moving Wetting Lines. J. Colloid Interface Sci. 2006, 299, 1–13. Schneemilch, M.; Hayes, R. A.; Petrov, J. G.; Ralston, J. Dynamic Wetting and Dewetting of a Low-Energy Surface by Pure Liquids. Langmuir 1998, 14 (24), 7047–7051. Extrand, C. W.; Gent, A. N. Retention of Liquid Drops by Solid Surfaces. J. Colloid Interface Sci. 1990, 138 (2), 431–442. Jerison, E. R.; Xu, Y.; Wilen, L. A.; Dufresne, E. R. Deformation of an Elastic Substrate by a Three-Phase Contact Line. Phys. Rev. Lett. 2011, 106 (186103), 1–4. White, L. R. The Contact Angle on an Elastic Substrate. 1. The Role of Disjoining Pressure in the Surface Mechanics. J. Colloid Interface Sci. 2003, 258, 82–96. Shanahan, M. E. R.; de Gennes, P. G. The Ridge Produced by a Liquid Near the Triple Line Solid Liquid Fluid. Comptes Rendus Acad. Sci. Serie II 1986, 302, 517–521. Carré, A.; Gastel, J. C.; Shanahan, M. E. R. Viscoelastic Effects in the Spreading of Liquids. Nature 1996, 379, 432–434. Zeng, H.; Maeda, N.; Chen, N.; Tirrell, M.; Israelachvili, J. Adhesion and Friction of Polystyrene Surfaces Around Tg. Macromolecules 2006, 39 (6), 2350–2363. Johnson, K. L.; Kendall, K.; Roberts, A. D. Surface Energy and the Contact of Elastic Solids. Proc. R. Soc. London, Ser. A 1971, 324 (1558), 301–313. Chen, Y. L.; Helm, C. A.; Israelachvili, J. N. Molecular Mechanisms Associated with Adhesion and Contact Angle Hysteresis of Monolayer Surfaces. J. Phys. Chem. 1991, 95 (26), 10736–10747. Kaufman, Y.; Chen, S.-Y.; Mishra, H.; Schrader, A. M.; Lee, D. W.; Das, S.; Donaldson, S. H., Jr.; Israelachvili, J. N. Simple-to-Apply Wetting Model to Predict Thermodynamically Stable and Metastable Contact Angles on Textured/Rough/Patterned Surfaces. J. Phys. Chem. C 2017, 121 (10), 5642–5656.

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Table of Contents Graphic Contact angle and adhesion dynamics and hysteresis on molecularly smooth chemically homogeneous surfaces Szu-Ying Chena, Yair Kaufmanb, Alex M. Schradera, Dongjin Seoa, Dong Woog Leec, Steven H. Paged, Peter H. Koenige, Sandra Isaacsd, Yonas Gizawd, and Jacob N. Israelachvilia,f,* a Department of Chemical Engineering, University of California at Santa Barbara (UCSB), Santa

Barbara, California 93106. b Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben

Gurion University of the Negev, Sede Boqer Campus 84990, Midreshet Ben-Gurion, Israel. c School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology

(UNIST), UNIST-gil 50, Ulsan 689-798, Republic of Korea. d The Procter & Gamble Co., Winton Hill Business Center, 6210 Center Hill Avenue, Cincinnati, Ohio

45224. e The Procter & Gamble Co., Beckett Ridge Technical Center, Union Centre Boulevard, West Chester

Township, Ohio 45069. f Materials Department, University of California at Santa Barbara (UCSB), Santa Barbara, California

93106. * To whom correspondences should be addressed. Email: [email protected]

For Table of Contents Only

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