Dynamics of Dewetting at the Nanoscale Using Molecular Dynamics

Mar 1, 2007 - Molecular dynamics of dewetting of ultra-thin water films on solid substrate. Ai-jin Xu , Zhe-wei Zhou , Guo-hui Hu. Applied Mathematics...
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Langmuir 2007, 23, 3774-3785

Dynamics of Dewetting at the Nanoscale Using Molecular Dynamics E. Bertrand,* T. D. Blake, V. Ledauphin, G. Ogonowski, and J. De Coninck Centre for Research in Molecular Modelling, UniVersity of Mons-Hainaut, Parc Initialis, AV. Copernic 1, 7000 Mons, Belgium

D. Fornasiero and J. Ralston Ian Wark Research Institute, UniVersity of South Australia, Mawson Lakes, South Australia 5095, Australia ReceiVed October 5, 2006. In Final Form: January 15, 2007 Large-scale molecular dynamics simulations are used to model the dewetting of solid surfaces by partially wetting thin liquid films. Two levels of solid-liquid interaction are considered that give rise to large equilibrium contact angles. The initial length and thickness of the films are varied over a wide range at the nanoscale. Spontaneous dewetting is initiated by removing a band of molecules either from each end of the film or from its center. As observed experimentally and in previous simulations, the films recede at an initially constant speed, creating a growing rim of liquid with a constant receding dynamic contact angle. Consistent with the current understanding of wetting dynamics, film recession is faster on the more poorly wetted surface to an extent that cannot be explained solely by the increase in the surface tension driving force. In addition, the rates of recession of the thinnest films are found to increase with decreasing film thickness. These new results imply not only that the mobility of the liquid molecules adjacent to the solid increases with decreasing solid-liquid interactions, but also that the mobility adjacent to the free surface of the film is higher than in the bulk, so that the effective viscosity of the film decreases with thickness.

1. Introduction Many industrial and material processing operations require a liquid to be spread on a solid. Examples include coating, printing, plant protection, adhesives, oil recovery, and lubrication. The liquid may take many forms ranging from a simple solution to a more complex emulsion or dispersion; the solid may have a continuous surface or be finely divided, as in the case of porous media or a fiber mat. The continued development of such applications requires an understanding of the dynamics of the wetting process. In particular, it is often of interest to know how fast the liquid can be made to wet the solid surface. A key parameter characterizing wetting is the contact angle, the angle formed by the liquid meniscus with the solid surface at the three-phase contact line, i.e., the wetting line. The static value of this angle characterizes the intrinsic wettability of the solid for the liquid. Under dynamic conditions, the contact angle is disturbed from its equilibrium value, increasing steadily with speed during wetting and decreasing during dewetting. Experimental studies of wetting dynamics have shown that the displacement of a liquid meniscus across a solid surface involves one or more channels of energy dissipation: specifically viscous dissipation and dissipation in the immediate vicinity of the wetting line.1 The latter has been termed wetting-line friction.2 To explain the observed behavior and, in particular, the behavior of the dynamic contact angle, hydrodynamic,1,3-7 molecular kinetic,8,9 * To whom correspondence [email protected].

should

be

addressed.

E-mail:

(1) Voinov, O. V. Fluid Dyn. 1976, 11, 714. (2) De Ruijter, M. J.; Blake, T. D.; De Coninck, J. Langmuir 1999, 15, 7836. (3) Huh, C.; Scriven, L. E. J. Colloid Interface Sci. 1971, 35, 85. (4) Dussan, V, E. B. J. Fluid Mech. 1976, 77, 665. (5) de Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827. (6) Cox, R. G. J. Fluid Mech. 1986, 168, 169. (7) Shikhmurzaev, Y. D. J. Fluid Mech. 1997, 334, 211. (8) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421. (9) Blake, T. D. In Wettability; Berg J. C., Ed.; Marcel Dekker: New York, 1993; p 251.

and combined10-12 models have been devised. These models have been recently reviewed against evidence drawn from experiment and molecular dynamics simulations.13 Over the last 10 years or so, molecular dynamics has been used to study wetting dynamics in considerable detail. By considering very large systems, the influence of solid-liquid interactions has been investigated for various substrate geometries, including flat surfaces,2,14-18 fibers,19,20 and pores.21,22 In this way, it has been shown how microscopic parameters such as the mobility of the liquid molecules near the solid surface can be controlled and measured. At the same time, relevant macroscopic characteristics, such as the dynamic contact angle and the flow field, have been calculated from the simulations. The results, when combined, strongly support the microscopic validity of the molecular kinetic model of dynamic wetting.2,15,20 The dewetting of solids by liquid films also plays an important role in many high-value processes. One example is froth flotation, in which solid particlesstypically mineralssare captured and extracted from an aqueous bath by rising bubbles of air. The (10) Petrov, P. G.; Petrov, J. G. Langmuir 1992, 8, 1762. (11) Brochard-Wyart, F.; de Gennes, P. G. AdV. Colloid Interface Sci. 1992, 39, 1. (12) De Ruijter, M. J.; De Coninck, J.; Oshanin, G. Langmuir 1999, 15, 22092216. (13) Blake, T. D. J. Colloid Interface Sci. 2006, 299, 1. (14) De Coninck, J.; D’Ortona, U.; Koplik, J.; Banavar, J. R. Phys. ReV. E 1996, 53, 562. (15) Blake, T. D.; Clarke, A.; De Coninck, J.; de Ruijter, M. J. Langmuir 1997, 13, 2164. (16) Heine, D. R.; Grest, G. S.; Webb, E. B., III. Phys. ReV. E 2003, 68, 061603-1. (17) Heine, D. R.; Grest, G. S.; Webb, E. B., III. Phys. ReV. E 2003, 70, 011606-1. (18) Bertrand, E.; Blake, T. D.; De Coninck, J. Langmuir 2005, 21, 6628. (19) Seveno, D.; De Coninck, J. Langmuir 2004, 20, 737. (20) Seveno, D.; Ogonowski, G.; De Coninck, J. Langmuir 2004, 20, 8385. (21) Martic, G.; Gentner, F.; Seveno, D.; Coulon, D.; De Coninck, J.; Blake, T. D. Langmuir 2002, 18, 7971. (22) Martic, G.; Gentner, F.; Seveno, D.; De Coninck, J.; Blake, T. D. J. Colloid Interface Sci. 2004, 270, 171.

10.1021/la062920m CCC: $37.00 © 2007 American Chemical Society Published on Web 03/01/2007

Dynamics of Dewetting at the Nanoscale

Langmuir, Vol. 23, No. 7, 2007 3775 Table 1. Sizes of the Free Liquid Films and Their Corresponding Film Tensions γL

Figure 1. Evolution of the instantaneous film tension γL versus time for the system comprising 100 × 100 × 1 eight-atom chains. The line shows the average value of the film tension once equilibrium has been attained.

dewetting of a mineral surface, which takes place when the intervening, aqueous film ruptures between an approaching air bubble and a hydrophobic mineral surface, has long been of interest to physical scientists, dating from the early studies of Wark23 and Gaudin,24 and continuing to the present day.25 Under the turbulent conditions found in a flotation pulp, the motion of the three-phase contact line over the solid surface may occur as a result of spontaneous dewetting, leading to a particle being captured by a bubble, or forced rewetting, during subsequent detachment. Certainly, the kinetics of expansion of the contact line has been of interest for many years to flotation scientists, with perhaps the most elegant early descriptions to be found in the work of Scheludko and co-workers (see, e.g., refs 26 and 27). In the latter studies, the kinetics was found to depend strongly upon the radius of contact, as well as on solution variables such as pH. Experimental studies of the dewetting of thin (10-50 µm) films of simple organic liquids, such as alkanes and silicone oils on silicon wafers treated to make them oleophobic,28 have shown that as the liquid retracts from the surface it accumulates in a rim at the receding edge of the film. For a given system, the wetting line recedes at a constant velocity, inversely proportional to the viscosity of the liquid. Linear behavior with time t is predicted theoretically on the basis of analysis of the energy dissipation at the leading and trailing edges of the growing rim.29-31 Studies of spontaneous rupture and dewetting by thin films of viscous polymers have also confirmed that the rims grow evenly in size with the growth of holes, without altering the overall rim profile.32 However, due to slip at the solid(23) Wark, I. W. J. Phys. Chem. 1933, 37, 623. (24) Gaudin, A. M.; Decker, F. G. J. Colloid Interface Sci. 1967, 24, 151. (25) Ralston, J.; Dukhin, S. S.; Mishchuk, N. A. AdV. Colloid Interface Sci. 2002, 95, 145. (26) Scheludko, A.; Tschaljowska, S.; Fabricant, A. Spec. Disc. Faraday Soc. 1970, 1, 112. (27) Scheludko, A.; Toshev, B. V.; Bojadjiev, D. T. J. Chem. Soc., Faraday Trans. 1 1976, 12, 2815. (28) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. ReV. Lett. 1991, 66, 715. (29) Brochard-Wyart, F.; de Meglio, J. M.; Que´re´, D. C. R. Acad. Sci. (Paris) 1987, 304, 553. (30) Brochard-Wyart, F.; Daillant, J. Can. J. Phys. 1989, 68, 1084. (31) Brochard-Wyart, F.; Debregeas, G.; Fondecave, R.; Martin, P. Macromolecules 1997, 30, 1211. (32) Seemann, R.; Herminghaus, S.; Neto, C.; Schlagowski, S.; Podzimek, D.; Konrad, R.; Mantz, H.; Jacobs, K. J. Phys.: Condens. Matter 2005, 17, S267.

size (chains)

no. of atoms

thickness (Å)

γL (10-3 N/m)

100 × 100 × 1 100 × 100 × 2 100 × 100 × 3 100 × 100 × 4

80 000 160 000 240 000 320 000

∼22 ∼50 ∼78 ∼105

2.49 ( 0.41 2.50 ( 0.59 2.48 ( 0.73 2.50 ( 0.85

polymer interface beneath the growing rim, the radius of the growing hole may follow t2/3.31-33 For aqueous systems of relevance to mineral flotation, the details of the rim profile during spontaneous dewetting have yet to be studied.34 On the other hand, forced wetting and dewetting of aqueous systems has been probed by a number of experimental methods such as the Wilhelmy technique.35 In all cases, a combined molecular kinetic and hydrodynamic approach successfully describes the observed dependence of the dynamic contact angle on velocity. In comparison with these experimental studies, much less attention has been paid to dewetting from the perspective of molecular dynamics simulations. However, notable pioneering studies have been carried out by Hwang et al.,36 Liu et al.,37 and Koplik and Banavar.38 The latter study demonstrated film instability leading to spinodal dewetting, the growth of dry spots, and the formation of a liquid rim at the receding edge of the film. In addition, it was confirmed that dewetting proceeded at a constant velocity with a constant (though fluctuating) receding contact angle distinctly smaller than the static angle. The main objectives of the current work are to extend these studies to learn more about the associated dynamics and, in particular, to take a detailed look at the influence of solid-liquid interaction and film thickness. Except in the manner of forming the initial films, the methods employed are similar to those used by Koplik and Banavar38 and build on those developed in our previous studies of the dynamics of wetting. The paper is organized as follows. Section 2 is devoted to the presentation of the model. In section 3, we describe the way in which the films are formed on the solid surface, providing the initial conditions for our dewetting simulations. Our results are presented and discussed in section 4. Concluding remarks are given in section 5.

2. Model The model used in our simulations of dewetting comprises a thin film of liquid on a flat solid substrate. The liquid molecules are eight-atom chains, denoted “L”. By considering chains rather than single atoms, we increase the viscosity of the liquid to more realistic values and considerably reduce evaporation into the surrounding vacuum. This strategy is consistent with previous work in related areas, such as droplet spreading.2,14-17 The molecules of the liquid interact not only with each other, but also with the atoms of the solid, denoted “S”. For simplicity, we assume that this interaction is via a pairwise Lennard-Jones potential: (33) Brochard-Wyart, F.; de Gennes, P. G; Hervert, H.; Redon, C. Langmuir 1994, 10, 1566. (34) Phan, C. M.; Nguyen, A.; Evans, G. M. J. Colloid Interface Sci. 2006, 296, 669. (35) Hayes, R. A.; Ralston, J. J. Colloid Interface Sci. 1993, 159, 429. (36) Hwang, C.-C.; Hsieh, J.-Y.; Chang, K.-H.; Liao, J.-J. Physica (Amsterdam) 1998, 256A, 333. (37) Liu, H.; Bhattacharya, A.; Chakrabarti, A. J. Chem. Phys. 1998, 109, 8607. (38) Koplik, J.; Banavar, J. R. Phys. ReV. Lett. 2000, 84, 4401.

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( ( )

Uab ) 4ab Cab

σab rij

12

- Dab

Bertrand et al.

( )) σab rij

6

(1)

where, for a given pair of atoms a and b, the coefficients ab and σab are related in the usual way to the depth of the potential well and the effective molecular diameter, respectively, and rij is the distance of separation.39 For convenience the same values of ab ) 33.33 K (4.6 × 10-22 J) and σab ) 3.5 Å were used for the different types of interaction: L-L, S-S, and L-S. This procedure is arbitrary, but allows us to set the values systematically21 and also ensures that the L-S interactions are consistent with the Berthelot rule:

σab ) 0.5(σaa + σbb)

(2)

ab ) (aabb)0.5

(3)

The constants Cab and Dab that appear in eq 1 permit us to selectively increase or decrease the repulsive (Cab) or attractive (Dab) part of the potential and so specify the coupling between different types of atoms. This enables us to modify the solidliquid interactions and so study the influence of the wettability of the solid surface with respect to the liquid film. The Lennard-Jones potentials provide the essential framework for the molecular interactions in our system, but it is necessary to add some other elements based on realistic physical models. The range of the Lennard-Jones potential is theoretically infinite, so in principle, one should consider the interactions between all possible pairs of atoms in the system. Fortunately, however, the potential decreases very steeply with interatomic distance, so to a good approximation, we can truncate the potential at a relatively small cutoff radius, usually 2.5σ. This substantially reduces the number of computations. To maintain a constant distance between any two adjacent atoms within a given liquid molecule, we have incorporated a confining potential between nearest neighbors i and j:

Vconf(rij) ) Arij6

(4)

The power 6 is chosen for computational convenience.15 The constant A is derived from the Lennard-Jones parameters and is defined as A ) LL/(σLL)6. Vconf and LL are expressed in the same units of energy and rij and σLL in the same units of distance. The solid substrate is a square planar lattice with periodic boundary conditions, comprising three atomic layers. This thickness is sufficient bearing in mind the spherical cutoff for the Lennard-Jones potential. Each solid atom is placed at a lattice node 3.93 Å from its four nearest neighbors, corresponding to 21/6σSS. The atoms of the solid vibrate thermally around their initial equilibrium position according to a harmonic potential of the form

VH ) B(ri - rio)2

(5)

with ri the instantaneous position of a solid atom and rio its equilibrium position.15,18 The constant B is also derived from the Lennard-Jones parameters and is defined as B ) 2.5(SS(σSS)2). While very simple, this specification provides a realistic solid surface. To define a time scale for our simulations, it is necessary to assign masses to the atoms. For all the atoms (L and S) we used mL ) mS ) 12 g mol-1, i.e., the molar mass of carbon. Once (39) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Clarendon Press: Oxford, 1987.

Figure 2. Density profile of the four free films constructed.

Figure 3. Evolution of the contact angle versus time for the two couplings considered: (a) CSL ) DSL ) 0.3; (b) CSL ) DSL ) 0.6. The horizontal lines show the value of the equilibrium contact angle in each case.

again, this choice is arbitrary, but does not affect our results qualitatively and allows us to compare them with other relevant studies. The time step between computational iterations was 0.005 ps, and all the simulations were carried out at a temperature of 33.33 K. In summary, we consider liquid films of varied thicknesses, formed of chainlike molecules of eight atoms, on the surface of a solid substrate built of three atomic layers.

3. Construction of Liquid Films on the Solid Surface To study the process of dewetting, it is necessary to form a uniform film of liquid on a solid surface with which it does not have a great affinity. If sufficiently thin (typically less than about 1 mm),28 such a film will spontaneously dewet the solid once a source of instability is created. The construction of the liquid film and initiation of dewetting is conveniently divided into three stages: creating a uniform free film, transferring it to the solid surface, and initiating instability. Film Creation. Here, the aim is to produce uniform free liquid films of several thicknesses. Each film has two surfaces in contact with the vapor phase, which is essentially a vacuum for the eight-atom molecules. We use periodic boundary conditions in the x and y directions (i.e., the plane of the film), which allow the film to equilibrate and form a square planar structure of dimensions 391.1 Å × 391.1 Å. Within the comparatively short

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Langmuir, Vol. 23, No. 7, 2007 3777

Figure 5. View of an equilibrated liquid film of 100 × 100 × 1 eight-atom chains, deposited in the center of the solid substrate and confined by an upper repulsive solid layer, with CLS ) 1.0, DLS ) 0.6 (substrate) and CLS ) 1.0, DLS ) 0 (confining layer). A total of 66 000 atoms are used for the substrate and 22 000 atoms for the confining layer (not shown in the top image). The 3-dimensional images shown here and in subsequent figures were generated using VMD software.44 Figure 4. Profile of the drop at equilibrium on the solid substrate, with CSL ) DSL ) 0.6. The upper and lower surfaces of the solid substrate are represented by the two horizontal dashed lines. The first two layers of liquid in contact with the solid are not shown. Black triangles delineate the edge of each layer, and white circles show the fitted circular profile. Table 2. Equilibrium Contact Angles Obtained for a Drop Spreading on a Solid Substrate with the Two Couplings Considereda coupling

equilibrium contact angle θeq (deg)

CSL ) DSL ) 0.3 CSL ) DSL ) 0.6

143.8 ( 2.8 101.6 ( 1.5

a The quoted errors are the standard deviations of the angles once equilibrium is attained.

time scale of our simulations, free films of such small lateral dimensions are stable against the capillary fluctuations that destabilize macroscopic films. This has been confirmed by calculating the wavelength and time constant of the fastest growing perturbation in each case.40 During equilibration, which lasts 106 iterations, we keep the temperature constant at 33.33 K and compute the film tension at each iteration using the formula41,42

γL )

1 A

〈∑∑ ( ) 〉 1

i>j j

2

rij -

3zij2 dU(rij) rij

drij

(6)

where A is the area of the liquid film in the x-y plane, rij the distance between atoms i and j, zij the distance between these two atoms in the z direction, and U(rij) the potential energy. As there are two liquid-vapor interfaces, the result must be halved to obtain the surface tension. The evolution of the film tension for a system of 100 × 100 × 1 eight-atom molecular chains is shown in Figure 1. Evidently, 106 iterations are more than sufficient to reach an equilibrium state with this system. The sizes of each of the four free liquid films created are listed in Table 1 together with their film tensions γL. Also shown are their equilibrium thicknesses. These were determined by computing the density profile of the films in the z direction, as illustrated in Figure 2. All the films have the same, uniform central density. The upper and lower surfaces of the films are taken to be at the z position where the density is approximately 85% of the bulk density, which is a procedure commonly used to locate a liquid/vapor interface. As can be seen from the table, (40) Vrij, A. Discuss. Faraday Soc. 1966, 42, 23. (41) Kirkwood, J. G.; Buff, F. P. J. Chem. Phys. 1949, 17, 338. (42) Salomons, E.; Mareschal, M. J. Phys.: Condens. Matter 1991, 3, 3645.

Figure 6. Top and side views of a type I simulation with the system from Figure 5 (simulation 7, Table 3). Removal of a 50 Å band of molecules in the center of the film initiates rectilinear dewetting in the x direction, as shown by the arrows. The system contains 69 824 liquid atoms and 66 000 solid atoms, with CSL ) DSL ) 0.6.

the film tensions are sensibly constant and independent of film thickness over the range investigated. These procedures enable us to obtain stable, homogeneous liquid films, which we can use as the starting point for building liquid films of varied size and thickness on the solid surface. Film Deposition. Once the free films have been equilibrated, we deposit them centrally on the solid substrate. Depending on the thickness of the film chosen for the dewetting simulation, we either place the entire film on the substrate or take a slice within the plane of the film around its center of mass. This allows us to study films of intermediate thicknesses. We are also interested in the influence of the length of the film. We therefore build films 2, 3, or 4 times longer in the x direction (i.e., that in which dewetting will be initiated) by replicating a basic film as necessary and retaining the periodic boundary condition in the y direction only, with the width of the film maintained at 391.1 Å. Before proceeding, however, the coupling constants CSL and DSL appearing in eq 1 need to be adjusted to give the moderate liquid-solid affinity required for partial wetting, which is characterized by a relatively large equilibrium contact angle. To determine the values of CSL and DSL necessary to produce the desired wettability conditions, we studied the spreading of an initially spherical drop of 5000 molecules (40 000 atoms) of radius 77.7 Å placed at the center of a circular solid substrate comprising 66 102 atoms, arranged in three atomic layers as described above. The radius of the solid was 4 times larger than that of the drops. The drops were formed by first equilibrating

3778 Langmuir, Vol. 23, No. 7, 2007

Figure 7. Top and side views of type II simulation with the system from Figure 5 (simulation 25, Table 4). Removal of 60 Å bands of molecules from each end of this film initiates rectilinear dewetting in the x direction as shown by the arrows. The system contains 64 472 liquid atoms and 66 000 solid atoms.

a large cube of 27 040 molecules (216 320 atoms) and then extracting the required drop from the center of the cube, retaining only those molecules whose center of mass was inside a sphere of the selected radius. On the basis of previous studies, we considered two cases: CSL ) DSL ) 0.6 and CSL ) DSL ) 0.3, with other parameters identical to those used for the films (same values of , σ, and T). Next we allowed the drop and the solid to equilibrate independently for 105 iterations at constant temperature, with the drop placed in the vacuum above the substrate at a distance of 100 Å. The drop was then moved into contact with the solid and spreading commenced. From this moment, only the temperature of the solid was controlled. The position of each atom of the liquid was measured every 103 iterations, allowing us to extract the contact angle from each snapshot. Details of the method have been given in previous publications.2,15 In brief, we divided the drop into horizontal layers 3 Å in thickness (small enough to give sufficient layers while retaining a uniform density within each layer). By symmetry, we determined the center of these layers and calculated the density of atoms as a function of the radial distance from the center. The radius of each layer was then given as the distance from the center at which the density fell below a selected cutoff value, taken to be about 85% of the central density, as before. We confirmed that our results did not depend on our choice of this cutoff value. This technique enabled us to build the complete profile of the drop and to study its evolution with time in a way that mimics real experiments. To determine the contact angle at any instant, we found the best circular fit to the measured profile. The first two layers in contact with the solid were omitted from the fit, since this part of the drop deviates from the otherwise spherical form.43 Figure 3 gives the evolution of the contact angle θ versus time for the two couplings investigated. The profile of the drop at equilibrium for CSL ) DSL ) 0.6 is given in Figure 4. We note that for both CSL ) DSL ) 0.6 and CSL ) DSL ) 0.3 we have the partial wetting conditions favorable for observing dewetting. These two couplings were therefore selected for further study (Table 2). Having identified the couplings required to specify the solidliquid interaction, we can proceed to deposit the films on the solid substrate. However, this is not straightforward. Because the S-L couplings give rise to partial wetting, the liquid film does not spread spontaneously. One approach to circumvent this would have been to deposit the film under conditions of complete (43) De Coninck, J.; Dunlop, F.; Menu, F. Phys. ReV. E 1993, 47, 1820.

Bertrand et al.

Figure 8. Profile of the liquid film during type I dewetting with CSL ) DSL ) 0.6 at iteration 2.89 × 105 (simulation 10, Table 3). The system comprises a total of 297 552 liquid atoms divided into two half-systems (RH and LH) of lengths 687 and 689 Å along x, respectively, on a solid of 180 000 atoms. The film had an initial thickness of 30.3 Å. The horizontal dashed line represents the upper surface of the solid substrate. For clarity, the liquid atoms are not shown.

Figure 9. Superimposed sequence of snapshots of the left edge of the LH half of the film in Figure 8 at (a) iteration 0, (b) iteration 105, and (c) iteration 2 × 105. The upper surface of the solid is represented by the horizontal dashed line.

wetting (CSL ) DSL ) 1) and then adjust the coupling constants to those required for partial wetting. This is the method used by Koplik and Banavar.38 However, after several trials the following alternative method was adopted to avoid introducing artifacts due to increased layering near a completely wetted surface and to give greater control over the initial thickness of the partially wetting film. A previously created free film is positioned at the center of the rectangular solid and confined there by placing a single atomic layer of purely repulsive solid above it. The confining layer interacts via the Lennard-Jones potential, but with the attractive part set equal to zero. The layer constrains the liquid to remain as a uniform flat film on the lower substrate and enables us to compress the film to the required final thickness and length in a continuous manner. Compression is achieved by raising the lower substrate at a rate of 2 × 10-4 Å per iteration. The time required varies from 0.9 × 105 to 1.75 × 105 iterations depending on the final thickness. This is followed by a period of equilibration

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Langmuir, Vol. 23, No. 7, 2007 3779

Figure 10. Sequence of snapshots of the system from Figure 8 (simulation 10, Table 3), with CSL ) DSL ) 0.6, 297 552 liquid atoms, an initial thickness of 30.3 Å, and a length of 687-689 Å. Table 3. Characteristics of Type I Dewetting Simulations coupling 1 CSL ) DSL ) 0.6 2 3 4 5 6 7 8 9 10 11 12 13 CSL ) DSL ) 0.3 14 15 16 17 18 19 20

no. of no. of S atoms L atoms 66 000 66 000 180 000 66 000 66 000 180 000 66 000 180 000 180 000 180 000 180 000 180 000 66 000 66 000 66 000 66 000 180 000 66 000 180 000 180 000

23 992 29 088 158 568 36 264 48 944 212 672 69 824 301 648 248 528 297 552 170 200 217 416 24 392 29 216 36 968 50 560 158 872 72 048 213 152 301 712

length (Å)

thickness (Å)

196-198 214-221 865-867 205-202 224-222 907-912 254-254 951-954 630-633 687-689 316-315 375-377 226-227 229-226 246-248 316-316 932-931 403-410 1003-1001 1078-1078

10.0 ( 1.0 10.9 ( 1.0 13.4 ( 0.7 13.9 ( 0.9 16.5 ( 0.7 17.2 ( 0.7 20.9 ( 1.5 23.1 ( 0.7 28.5 ( 0.9 30.3 ( 1.0 41.0 ( 0.8 43.2 ( 0.9 10.1 ( 1.0 11.1 ( 1.2 13.0 ( 1.2 13.2 ( 0.8 14.1 ( 0.9 17.4 ( 1.2 17.6 ( 1.3 21.7 ( 1.0

lasting between 3.2 × 105 and 106 iterations, during which the substrate and the confining layer are held stationary and the temperature of the system is held constant at 33.33 K. Periodic boundary conditions are retained in the y direction only, allowing the liquid molecules to relax and reach equilibrium between the two solid surfaces. Equilibrium is confirmed when the energy of the system remains constant and the free edges of the film are stationary over time. To avoid the liquid atoms penetrating the solid surfaces, we set CLS ) 1.0 at this stage, with DSL ) 0.6 or 0.3 for the lower surface and zero for the confining surface. Subsequent dewetting simulations are carried out after CSL ) DSL ) 0.6 or 0.3 is reset. The width of the films in the y direction is always 391.1 Å, while that in the x direction varies with the simulation. The solid extends sufficiently in the x direction to allow space for the films to equilibrate. A total of 20 simulations were prepared in this way. Figure 5 gives a typical view of a system at this point. Initiating Dewetting. Here we describe the procedure for withdrawing the upper surface and initiating dewetting. We begin at the end of the preceding stage, where we have a film of liquid

Table 4. Characteristics of Type II Dewetting Simulations coupling 21 22 23 24 25 26 27 28 29 30 31 32

CSL ) DSL ) 0.6

CSL ) DSL ) 0.3

no. of S atoms

no. of L atoms

length (Å)

thickness (Å)

66 000 66 000 66 000 66 000 66 000 180 000 180 000 66 000 66 000 66 000 66 000 66 000

20 608 25 104 30 816 42 888 64 472 158 584 206 320 21 352 25 328 32 496 46 272 51 864

327 367 339 378 439 560 684 382 384 423 566 479

9.3 ( 0.6 9.7 ( 0.5 13.4 ( 0.6 16.9 ( 0.5 21.8 ( 0.5 40.3 ( 0.7 42.0 ( 0.8 10.3 ( 0.6 11.1 ( 0.5 12.4 ( 0.4 13.7 ( 0.4 16.2 ( 0.5

sandwiched between two solid layers and forced to spread on the lower one with which it has only moderate affinity. Two types of dewetting simulations are considered. In the first, which we call type I, we remove a band of liquid molecules of width 50 Å from the center of the film to initiate dewetting along two rectilinear fronts. Note that once the film is released by removing the upper confining layer and resetting CSL ) DSL ) 0.6 or 0.3, dewetting also starts at the two ends of the film, but along more ragged fronts. An example of this first type of simulation is illustrated in Figure 6. Type I simulations give us two useful dewetting fronts, but have the disadvantage of halving the length of the films and thus decreasing the duration of the dewetting process. We therefore also use a second type of dewetting simulation, type II, where we remove bands of molecules, of width 60 Å, from each end of the film. This technique has the advantage of maintaining the length of the system, while still creating two useful rectilinear dewetting fronts. An example of a type II simulation is illustrated in Figure 7. During dewetting runs with these two types of simulation, we maintain the temperature of only the solid constant. In the absence of instabilities causing spontaneous film rupture (see below), the geometry chosen for the films, together with the periodic boundary conditions in the y direction, preserves the rectilinear dewetting fronts, which eventually retract to leave cylindrical rivulets of liquid.

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Figure 11. Thickness of the liquid film at its center versus time. (Left) Simulations with CSL ) DSL ) 0.6: (a) simulation 24 (type II), with 42 888 liquid atoms; (b) the RH half of simulation 9 (type I), with 248 528 liquid atoms. (Right) Simulations with CSL ) DSL ) 0.3: (c) simulation 32 (type II), with 51 864 liquid atoms; (d) the RH half of simulation 20 (type I), with 301 712 liquid atoms. The horizontal dashed lines show the initial thickness of each film.

Figure 12. Side view of the RH half-system of simulation 12 (type I) dewetting with CSL ) DSL ) 0.6 at iteration 1.3 × 105. The upper surface of the solid is represented by the dashed horizontal line. For clarity, the liquid atoms are omitted. Open circles delineate the envelope of the film. Filled circles show the circular fit to the rim obtained by fitting 55 points.

In all, we carried out 32 simulations of both types, with liquid films having various initial lengths and thicknesses and coupling CSL ) DSL ) 0.6 or 0.3.

4. Results and Discussion Evolution of the Film. To obtain useful data, we must determine the profile of the liquid film on the solid substrate at frequent intervals during dewetting, just as we did for the spreading drop in the preceding section. As before, the positions of the atoms in the film are recorded every 103 iterations, but since we no longer have circular symmetry, the technique used to obtain the profile must be modified and adapted to the rectangular geometry of the film and the presence of any rim. For the dewetting simulations, we found it more useful to section the film into 1 Å thick vertical slices taken perpendicular to the x axis along which the film recedes. The base of each slice is given by the upper surface of the solid substrate. The position of the upper surface of the film is given by the height above the base at which the density falls below some cutoff value. As in

the case of the spreading drop, this is taken to be equal to ∼85% of the bulk density. A typical profile is illustrated in Figure 8 for one of the type I simulations at iteration 2.89 × 105. This method enables us to study the evolution of the film with time as dewetting proceeds and so determine important quantities such as the central thickness of the film, the rate of recession of the dewetting fronts, and the contact angle. As an example, Figure 9 shows the superposition of three partial profiles, determined at the start and at two later intervals for the system of Figure 8. Here, we can already discern the growth of a rim of liquid at the dewetting front. A rim is predicted theoretically and has been observed in many experimental studies, as has the constant thickness of the film between the two rims, corresponding to the zone not yet disturbed by dewetting.5,11,28-33,45-47 A sequence of snapshots of the system is given in Figure 10, where we see the progressive retraction of the dewetting fronts and the growth of the rims. From profiles such as these, we can determine the initial length of each film, as given by the difference in the x coordinate of the extremities of the profile at time t ) 0. The values, together with the other initial characteristics of the films used in the simulations (couplings, number of atoms, and film thicknesses), are listed in Table 3 for type I dewetting (showing the lengths of both halves of the film) and in Table 4 for type II dewetting. To determine the thickness of the films as they evolve, we start from the center of the film (type II) or from the center of each half-system (type I) and take the average of the height at points on either side. As can be seen from Figure 9, the central region of the film is not immediately affected by the rims, which form at the edges and retract toward the center. Typical results are shown graphically in Figure 11 for four representative simulations of different thicknesses, two each of type I and type II with CSL ) DSL ) 0.6 and CSL ) DSL ) 0.3. The initial thicknesses shown in Tables 3 and 4 were obtained by averaging the thicknesses during the period when the center is undisturbed. The quoted errors are the standard deviations. For type I simulations, we average the values for the two halfsystems. (44) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33, http://www.ks.uiuc.edu/Research/vmd/. (45) Reiter, G. Science 1998, 282, 888. (46) Reiter, G. Phys. ReV. Lett. 2001, 87, 186101. (47) Damman, P.; Baudelet, N.; Reiter, G. Phys. ReV. Lett. 2003, 91, 216101.

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Figure 13. Receding contact angle versus time computed for the four thickest liquid films with CSL ) DSL ) 0.6: (a) left edge of the RH half-system of simulation 11 (type I), thickness 41.0 Å; (b) left edge of the RH half-system of simulation 12 (type I), thickness 43.2 Å; (c) left edge of simulation 26 (type II), thickness 40.3 Å; (d) left edge of simulation 27 (type II), thickness 42.0 Å. The error bars show the standard deviations found using from 45 to 65 points in the fitting procedure. The horizontal lines represent the average value of the contact angle during the constant angle period for each system.

Dynamic Contact Angle. Another important quantity is the dynamic contact angle at the receding solid-liquid-vapor contact line. The method used to determine this angle is analogous to that used with the spreading drops. For dewetting, we consider only that part of the envelope corresponding to the rim and fit it to a circular arc. The contact angle is then calculated from the slope of the arc at the contact line. The number of points taken into account in the fit is arbitrary and variable, but we have tested the fitting procedure by varying the number between 20 and 65 and checking how well the fit matched the profile of the rim by measuring the error on a frame-by-frame basis as the film evolved. This showed that the best fits were obtained using between 45 and 65 points. An example of one such fit is given in Figure 12. To investigate how the contact angle varies during dewetting, we compute the contact angle every 103 iterations along the two rectilinear fronts using 45, 46, 47, ..., 65 points for the circular fit and average the result for a given profile. This is done only for the thickest films (40.3-43.2 Å) with coupling CSL ) DSL ) 0.6, for which this technique is usable and seems to give reliable results (simulations 11 and 12 from Table 3 and simulations 26 and 27 from Table 4). Figure 13 shows that, for these four simulations, the receding contact angle fluctuates with time around a more-or-less constant value of about 90°, which is significantly less than the equilibrium angle of 101.6° ( 1.5°

(Table 2). This result is in qualitative agreement with experiment28 and with previous molecular dynamics simulations38 where a value of about 90° was also observed with a coupling of CSL ) 0.75. The error bars shown in Figure 13 are the standard deviations. Dewetting Dynamics. The technique used to measure the dynamic contact angle also enables us to determine the position of the receding edge of the film as a function of time and thus characterize the dynamics of dewetting. Consistent behavior was observed with all the simulations. Figure 14 gives the results for the same four simulations as in Figure 11. Evidently, the film initially dewets the solid at a constant speed as observed in experiments with simple liquids28,48 and in previous molecular dynamics simulations38 and also predicted theoretically.11,28-31 Figure 14 shows that, in terms of the overall time scale of the simulated process, the linear, constant-speed regime extends over a comparatively long period, which depends on the initial length and thickness of the film, as well as the coupling constants CSL and DSL. For simulation 24, with 42 888 atoms, a thickness of 16.9 Å, and a length of 378 Å, the speed is constant for 1 ns or 2 × 105 iterations; for simulation 9, with a total of 248 528 atoms, a thickness of 28.5 Å, and a half-system length of 633 Å, it is constant for more than 3.5 ns or 7 × 105 iterations. (48) Blake, T. D.; Ruschak, K. J. Nature 1979, 282, 489.

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Figure 14. Position of the dewetting front versus time for the same four systems as in Figure 11: (a) left edge of simulation 24 (type II) with CSL ) DSL ) 0.6 and thickness 16.9 Å; (b) left edge of the RH half-system of simulation 9 (type I) with CSL ) DSL ) 0.6 and thickness 28.5 Å; (c) left edge of simulation 32 (type II) with CSL ) DSL ) 0.3 and thickness 16.2 Å; (d) left edge of the RH half-system of simulation 20 (type I) with CSL ) DSL ) 0.3 and thickness 21.7 Å. The linear fits indicate the constant-speed periods.

For the thickest films, the linear regime ends when the rims merge and begin to form a cylindrical rivulet. However, for the thinnest films, the linear regime is prematurely curtailed because holes (i.e., dry patches) appear in the film, which eventually breaks up into droplets. As concluded by Koplik and Banavar,38 since there is no source of heterogeneous nucleation, hole formation is presumably due to fluctuations in the thickness of the intrinsically metastable films, leading to growth of unstable modes,40,49 and is therefore equivalent to the spinodal dewetting observed for thin polymer films on poorly wetted surfaces.32 The final patterns obtained and the overall behavior are also very similar to those observed when aqueous films are disrupted on hydrophobic surfaces,50,51 but here heterogeneous nucleation is the more likely trigger. In the present simulations, for both CSL ) DSL ) 0.6 and 0.3, the films show instabilities below the same thickness of about 17 Å. Theoretical considerations lead one to expect the onset of breakup due to random disturbances to depend on both thickness and the intermolecular coupling (i.e., the wettability).32,49 Calculations have confirmed that the wavelength of the fastest (49) Ruckenstein, E.; Jain, R. K., J. Chem. Soc., Faraday Trans. 2 1974, 70, 132. (50) Schulze, H. J. Physicochemical Elementary Processes in Flotation; Elsevier: Amsterdam, 1983; Chapter 4. (51) Stoeckelhuber, K. W.; Radoev, B.; Wenger, W.; Schulze, H. J. Langmuir 2004, 20, 164.

growing perturbation is indeed commensurate with the size of our films in those cases where breakup is observed. A typical sequence of events is illustrated in Figure 15, where we see nucleation and growth of dry patches along with progressive retraction of the film toward the center (despite the periodic boundary conditions imposed in the y direction). This sequence is from simulation 21, with CSL ) DSL ) 0.6, an initial thickness of 9.3 Å, and a length of 327 Å. Note that not all nucleated dry patches grow as the film recedes: some disappear; others coalesce. This appears to be similar to the nucleation process reported by Liu et al.37 in which dry patches smaller than some critical size were found to heal. In the more recent study by Koplik and Banavar,38 holes larger than a few atomic diameters invariably continued to grow. The latter authors attributed the difference in behavior to the use by Liu et al. of a purely repulsive and unstructured substrate. Since the solid in our simulations was similar to the more realistic substrate used by Koplik and Banavar, the source of this difference in behavior remains of interest and worthy of further study. In addition to their influence on the duration of the constantspeed dewetting regime, the solid-liquid coupling parameters also affect the dewetting speed, with weaker couplings tending to accelerate dewetting. The dewetting speeds of the rectilinear fronts in our simulations are listed in Table 5 for CSL ) DSL ) 0.6 and in Table 6 for CSL ) DSL ) 0.3. For both type I and type

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Figure 15. Sequence of snapshots from simulation 21 with CSL ) DSL ) 0.6, an initial thickness of 9.3 Å, and a length of 327 Å. Snapshots taken at (a) iteration 0, (b) iteration 5 × 104, (c) iteration 105, and (d) iteration 1.5 × 105. The growth of dry patches inside the liquid film is evident. Table 5. Dewetting Speeds of the Fronts Created by the Withdrawal of a Band of Molecules for Both Type I and Type II Simulations with CSL ) DSL ) 0.6a type 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23 24 25 26 27 a

I

II

thickness (Å)

speed (m/s)

R2

10.0 ( 1.0 10.9 ( 1.0 13.4 ( 0.7 13.9 ( 0.9 16.5 ( 0.7 17.2 ( 0.7 20.9 ( 1.5 23.1 ( 0.7 28.5 ( 0.9 30.3 ( 1.0 41.0 ( 0.8 43.2 ( 0.9 9.3 ( 0.6 9.7 ( 0.5 13.4 ( 0.6 16.9 ( 0.5 21.8 ( 0.5 40.3 ( 0.7 42.0 ( 0.8

12.53 ( 0.11 8.25 ( 0.05 7.38 ( 0.31 6.63 ( 0.01 6.91 ( 0.44 6.60 ( 0.49 5.67 ( 0.09 5.74 ( 0.02 4.51 ( 0.03 4.69 ( 0.05 4.99 ( 0.29 4.33 ( 0.12 12.05 ( 0.66 9.53 ( 0.67 9.50 ( 0.48 7.75 ( 0.28 7.27 ( 0.50 5.52 ( 0.02 5.24 ( 0.08

0.960 0.970 0.977 0.976 0.984 0.993 0.990 0.998 0.997 0.996 0.987 0.992 0.967 0.979 0.987 0.995 0.993 0.996 0.994

The values of R2 indicate the quality of the linear fits to the data.

II simulations we compute the speed as the average speed of the two fronts created by the removal of the bands of molecules. The quoted error is the standard deviation of the two speeds obtained

Table 6. Dewetting Speeds of the Fronts Created by the Withdrawal of a Band of Molecules for Both Type I and Type II Simulations with CSL ) DSL ) 0.3a type 13 14 15 16 17 18 19 20 28 29 30 31 32 a

I

II

thickness (Å)

speed (m/s)

R2

10.1 ( 1.0 11.1 ( 1.2 13.0 ( 1.2 13.2 ( 0.8 14.1 ( 0.9 17.4 ( 1.2 17.6 ( 1.3 21.7 ( 1.0 10.3 ( 0.6 11.1 ( 0.5 12.4 ( 0.4 13.7 ( 0.4 16.2 ( 0.5

44.66 ( 0.90 54.53 ( 3.97 51.72 ( 0.76 49.20 ( 0.03 45.64 ( 0.57 42.69 ( 1.09 37.76 ( 0.87 26.28 ( 0.38 54.29 ( 2.21 45.05 ( 2.91 50.91 ( 1.12 48.52 ( 0.58 42.37 ( 0.47

0.983 0.994 0.994 0.995 0.993 0.996 0.997 0.998 0.990 0.981 0.995 0.992 0.997

The values of R2 indicate the quality of the linear fit to the data.

for a given simulation. The value of R2 is an average of the values for the two linear fits to the position of the dewetting fronts versus time. Comparing the values in the two tables, we see that the coupling CSL ) DSL ) 0.3 gives rise to dewetting speeds that are up to 10 times greater than those found with CSL ) DSL ) 0.6. This increase is partially understandable in terms of the increased driving force for dewetting as the equilibrium contact angle is increased, but this cannot be the whole story or even the principal

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Figure 16. Dewetting speeds as a function of film thickness for CSL ) DSL ) 0.6 from Table 5.

Figure 17. Dewetting speeds as a function of film thickness for CSL ) DSL ) 0.3 from Table 6.

explanation. The driving force for dewetting is the reduction in surface free energy that occurs as the areas of the solid-liquid and liquid-vapor interfaces are reduced and that of the solidvapor interface is increased. For unit displacement of unit length of the wetting line, this free energy change is given by the spreading coefficient

For example, in the regime where the radius of the growing hole follows t2/3, the velocity appears to follow h-1/2, where h is the film thickness.31 This dependence is compatible with that shown in Figures 16 and 17. In other dewetting experiments with thin films of entangled polystyrene melts in the linear growth regime,58 the observed behavior could be reconciled with theory only if the viscosity of the melts were a decreasing function of thickness below 50 nm or so. In addition, even short-chain polymer melts have been found to exhibit a significant reduction in the glass transition temperature as the film thickness is reduced below 100 nm.32 For the present simulations with simple liquids, there also seems to be good evidence that the increase in dewetting rates with decreasing film thickness is due to an increase in molecular mobility, i.e., a reduction in the effective viscosity of the film. Table 1 shows that the surface tension of the film is independent of thickness, at least for the thicker films, so this means that the driving force S is sensibly constant for a given coupling. Since the central part of the film is undisturbed, S must be dissipated within the receding rim, presumably by some combination of wetting-line friction and viscous flow. However, in contrast to the constant driving force, dewetting speeds increase by at least a factor of 3 as the film thickness is reduced. It therefore follows that the dissipation due to viscous flow or interactions with the substrate must be decreasing with thickness. It is not clear how the increasing proximity of the free liquid surface might significantly increase the mobility of molecules adjacent to the solid wall, so the logical conclusion is that, for a given coupling, the increase in the overall mobility within the film is due to the increasing proportion of molecules that are adjacent to the free liquid surface and that the mobility near this surface is greater than in the bulk. Taken together, our results confirm that the dewetting process for nanometer thick films is a rich area for investigation by molecular dynamics. The observed behavior reproduces much of what is seen in macroscopic experiments and previous molecular dynamics simulations, such as a constant dewetting velocity with a constant contact angle, the development of a rim that collects the liquid as it recedes, and the apparently spinodal breakup of the thinnest films. However, in addition, the quantitative behavior is more complex. In particular, the precise rate of film recession turns out to be a function not only of the wettability of the film on the substrate, which may be expected

S ) γS - γSL - γL ) γL(cos θeq - 1)

(7)

where γL is the surface tension of the liquid and θeq is the equilibrium contact angle. From the values of the equilibrium contact angles given in Table 2, the increase in S on reducing CSL ) DSL ) 0.6 to 0.3 is only about 50% and, therefore, cannot explain a 10-fold increase in dewetting speed. However, another probable cause is the predicted increase in molecular mobility near more poorly wetted solid surfaces,52,53 with weaker couplings giving rise to higher mobility and, therefore, potentially higher dewetting speeds. Recently, it has been argued that whereas the rate of wetting depends in a complex way on the equilibrium contact angle, the rate of dewetting always increases with decreasing wettability, not only because the driving force increases, but also because of a corresponding reduction in wetting-line friction.54 Furthermore, while there is much debate about the magnitude of the effect, there is increasing evidence, both from experiment and from molecular dynamics simulations55,56 that slip between a liquid and a solid surface is greater for poorly wetted solids than for more wettable ones.57 Just as significantly, at both couplings, the simulations show that the initial thickness of the film has a profound effect on the dewetting speed. This can be seen clearly in Figures 16 and 17, where the results from Tables 5 and 6 are collated for both types of simulation. Evidently, there is an inverse relationship between dewetting speed and film thickness over the range investigated. In the case of viscous polymers, which exhibit slip at the solid-polymer interface, there is experimental and theoretical evidence that the dewetting velocity depends on the film thickness. (52) Tolstoi, D. M. Dokl. Akad. Nauk SSSR 1953, 85, 1089. (53) Blake, T. D. Colloids Surf. 1990, 47, 135. (54) Blake, T. D.; De Coninck, J. AdV. Colloid Interface Sci. 2002, 96, 21. (55) Barrat, J.-L.; Bocquet, L. Phys. ReV. Lett. 1999, 82, 4671. (56) Cieplak, M.; Koplik, J.; Banavar, J. R. Phys. ReV. Lett. 2001, 86, 803. (57) Lauga, E.; Brenner, M. P.; Stone, H. A. In Handbook of Experimental Fluid Dynamics; Foss, A., Tropea, C., Yarin, A., Eds.; Springer: New York, 2006; in press, http://web.mit.edu/lauga/www/publications.html.

(58) Masson, J,-L.; Green, P. F. Phys. ReV. E 2002, 65, 031806.

Dynamics of Dewetting at the Nanoscale

on the basis of current theories of wetting and dewetting, but also of film thickness. Moreover, the rate of recession would appear not to reach its asymptotic (i.e., bulk) value until the films are at least several tens of nanometers thick, which is beyond the range of action of the intermolecular forces included in the simulation.

5. Conclusions Large-scale molecular dynamics simulations have been successfully applied to model the dewetting dynamics of thin liquid films on a partially wetted solid surface at the nanoscale. Two levels of solid-liquid interaction have been considered that give rise to large equilibrium contact angles. The initial length and thickness of the films have been varied over a wide range. Spontaneous dewetting was initiated by removing a band of molecules either from each end of the film or from its center. The qualitative behaviors observed with both levels of solidliquid interaction are similar and in agreement both with experiment and with previous molecular dynamics studies.36-38 In particular, the films show an initially constant rate of recession and the development of a thickening rim of liquid at the receding front, while the central part of the film remains undisturbed. For the thicker films (∼40 Å), where it is possible to measure the dynamic receding angle with sufficient precision, this angle also remains constant as observed experimentally. Consistent with the increase in the driving force for dewetting, the rates of recession seen on the more poorly wetted surface are greater

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than those found for the more wettable surface. However, the increase is much greater than can be explained by the increase in driving force alone, and it is proposed that the main cause is an increase in liquid mobility near the less wettable surface. In addition to the above, the rates of recession on both surfaces have been found to depend inversely on the film thickness. These results seem to imply not only that the mobility of the liquid molecules adjacent to the solid decreases with solid-liquid interactions, but also that the mobility adjacent to the free surface of the film is higher than in the bulk, so that the average viscosity of the film decreases with thickness. This dependency is currently under detailed investigation and will be the subject of later publications. The effect clearly has important repercussions for our understanding of hydrodynamic slip between a liquid and a solid and in such practical areas as microfluidics and lubrication. Another topic for further investigation is the separate influence of solid-liquid interactions, film thickness, and film viscosity on the apparently spinodal breakup and dewetting seen with the thinnest films. Acknowledgment. E.B. thanks Elie Raphae¨l, David Seveno, and Gre´gory Martic for fruitful discussions concerning dewetting and molecular dynamics. The partial financial support for this work by the FNRS, the Re´gion Wallonne, and the Australian Research Council Special Research Centre Scheme is also acknowledged. LA062920M