Langmuir 2001, 17, 6553-6559
6553
Dewetting Nucleation Centers at Soft Interfaces A. Martin, A. Buguin, and F. Brochard-Wyart*,† Laboratoire Physico-Chimie Curie, Institut Curie, UMR 168,11 Rue Pierre et Marie Curie, 75231 Paris Cedex 05, France Received April 4, 2001. In Final Form: June 19, 2001 We study the dewetting of a metastable liquid film, squeezed at a solid/rubber interface, induced by defects printed in the solid glass substrate. We have engraved both protruding (“Mesa”) and depression (“Vickers prints”) defects. For the Vickers prints,we find that a defect of size b dewets films of thickness e < e* ) xbh0, where h0 is a microscopic “elastic length” (≈100 Å, defined by the ratio of the liquid spreading parameter S by the elastic modulus E of the soft material). The same behavior is observed for thin Mesa. However, for thick Mesa, the dewetting is limited to the defect area and does not propagate. These results agrees with a theoretical model of nucleation at soft interfaces.
I. Introduction A prerequisite for the adherence of a soft material (a rubber “R”) on a wet substrate is the dewetting of the intercalated liquid film. We see this on a rainy day, when driving on a wet road: dry adhesive contacts of the tire on the pavement must be achieved in less than milliseconds to avoid skidding. The same sort of dewetting process also controls the outset of adhesion of immersed substrates, e.g. glues for boats or adhesion between living cells. The stability of the liquid film depends on the sign of the spreading parameter S
S ) γSR - (γSL + γ LR)
(1)
where the γij’s are the solid/rubber, solid/liquid, and liquid/ rubber interfacial tensions. If S > 0, the surface energy of the dry solid is higher, and a liquid film is always stable. If S < 0, the surface energy of the wet solid is higher, and the liquid dewets. Depending on the thickness of the film, two mechanisms of dewetting arise: (a) Nanoscopic films are unstable and dewet by amplification of thickness fluctuations.1,2 This regime is called “spinodal dewetting” by analogy with phase transitions. (b) Mesoscopic films (e > 20 nm) are metastable: the energy barrier to form a hole in a film is large compared to thermal activation energies, and an external action is necessary to initiate the dewetting. The films dewet by nucleation and growth of a dry patch.3 For a film exposed to air, holes in the film can easily be made by blowing air, by aspiration of the liquid with a pipet, or by touching the liquid with an hydrophobic needle or a fluorinated glass fiber of variable radius.4,5 If the hole is too small, it closes back. Only holes larger than a critical radius Rc grow. †
E-mail:
[email protected].
(1) Reiter, G. Science 1998, 282, 888. (2) Martin, A.; Rossier, O.; Buguin, A.; Auroy, P.; Brochard-Wyart, F. EPJE Soft Matter 2000, 3, 337. (3) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715. (4) Padday, J. F. Spec. Discuss. Faraday Soc. 1971, 1, 64. (5) Sykes, C.; Andrieu, C.; Detappe, V.; Deniau, S. J. Phys. III Fr. 1994, 4, 775.
Figure 1. Critical radius of an elastomer/solid bridge. For R > Rc, the contact grows. For R < Rc , the contact shrinks.
From experiments4-6 and theory7-9, one finds
Rc ≈
e sin θe
(2)
where θe is the equilibrium contact angle (it is related to the spreading coefficient S ) γ(cos θe - 1), where γ ) liquid surface tension). The free energy Fh to open a hole can be written (neglecting gravity)
Fh ) πSR2 + 2πRγ∆l
(3)
It describes the balance between the gain of surface energy of the dry patch and the excess of liquid/air surface energy at the periphery γ∆l ≈ γ[(1 - cos θe)/sin θe]e ≈ -(Se/sin θe). Fh reaches a maximal value for R ) Rc. The energy barrier Fh(Rc) ≈ |S|Rc2 ≈ γe2 is huge compared to thermal energy ((γe2/kT) ≈ (e2/a2), where a is a molecular length). This is why dust particles, or an external action, are always involved in the dewetting of metastable liquid films. We are interested here in the case of a film intercalated between a rubber and a solid substrate (Figure 1). We find two main difficulties: (i) One cannot act externally with a pipet or a needle to achieve a small dry contact. The only way to induce the dewetting is to print a defect on the elastomer surface or on the glass substrate. (6) Debregeas, G.; Brochard-Wyart, F. J. Colloid Interface Sci. 1997, 190, 134. (7) Taylor, G.; Michael, E. J. Fluid Mech. 1973, 58, 625. (8) Sharma, A.; Ruckenstein, E. J. Colloid Interface Sci. 1990, 137, 443. (9) Sykes, C. C. R. Acad. Sci., Ser. II 1991, 313, 607.
10.1021/la010503y CCC: $20.00 © 2001 American Chemical Society Published on Web 09/18/2001
6554
Langmuir, Vol. 17, No. 21, 2001
Martin et al.
(ii) When air is replaced by a soft medium, to make a hole in the film, one must also deform the rubber and the energy cost becomes huge for thick films. This is why one can remove only microscopic films. Our aim here is to study the optimal size and shape of the defects to induce the removal of intercalated films. The paper is organized as follows. We first describe the special features of the wetting at soft interfaces. We introduce the elastic length h0, which describes the competition between capillarity and elasticity in the rubber. We discuss the critical radius Rc of nucleation for the dewetting of intercalated films. In section III, we describe the “wet” JKR setup used to squeeze liquid films, and the reflection interference contrast microscopy (RICM) technique, used to observe the drying of R/S contacts. In the fourth part, we present the two shapes of defects engraved on the glass support: (i) inverse pyramid; (ii) mesa. Finally, we study the efficiency of the two types of nucleators. This is our guide to an experimental determination of Rc . II. Wetting at Soft Interfaces
Figure 2. Experimental setup to form and to observe thin liquid films sandwiched between a rigid plane solid (a silanized glass plate) and an elastomer lens.
What happens when air is replaced by a soft elastic material (Young’s modulus E)? The deformation of the medium surrounding liquid drops upset the classical laws of capillarity. One can define a characteristic length h0 ) |S|/E, where capillary and elastic energies become comparable. Typically, with E ) 106 Pa and |S|) 10 mN m-1,
Figure 3. Collapse of the liquid film in the case of spontaneous nucleation. The nucleation starts from several points at the periphery of the contact area, where the film thickness is smaller.
Dewetting Nucleation Centers at Soft Interfaces
Langmuir, Vol. 17, No. 21, 2001 6555
Figure 4. Geometry of (a) mesa nucleators and (b) Vickers prints. (c) Topography of a Vickers print obtained by atomic force microscopy. Its lateral size is b ) 9 µm. The depth of the crater is 1 µm, and the height of the surrounding protrusions is h ) 100 ( 10 nm. (d) View from above.
h0 ≈ 10 nm. The Young relation, which defines the contact angle at the triple line, will be valid only at scales less than this microscopic length h0, where anyway other forces (van der Waals) modify the drop’s profile.10 (a) Penny Shape of Drops. The shape of a sessile droplet, standing at a S/R interface, is a flat semiellipsoid,11 with thickness H related to the radius R by
6 H2 ) h0R π
(4)
By monitoring H and R, one can deduce the value of h0. This leads to a determination of S.12 (10) Pompe, J. T. Fery, A.; Herminghaus, S. Langmuir 1998, 14, 2585. (11) Sneddon L. N. Proc. R. Soc. London, A 1946, 187, 229. (12) Martin, P. Silberzan, P.; Brochard-Wyart, F. Langmuir 1997, 13, 4910.
Relation 4 can be understood by a simple scaling argument. The energy of the droplet Fd
H2 3 R R2
Fd = -SR2 + E
(5)
is the sum of a capillary energy for a flat drop and an elastic energy of the rubber for the deformation H/R spread over a region of size R3. The minimization of Fd with the constraint of constant volume (Ω ≈ HR2) leads to H2 ≈ h0R. (b) Critical Radius Rc. We return to the liquid film (thickness e) intercalated between the solid S and the rubber R. We have to evaluate the energy Fc required to make a bridge of radius R between the elastomer and the solid substrate (Figure 1). The deformation of the rubber around the contact extends over the “Griffith length” λ defined for an adhesive fracture λ ) e2/h0.11 The gain of
6556
Langmuir, Vol. 17, No. 21, 2001
Martin et al.
Figure 5. Nucleation by a Vickers print (b ) 1.5 µm). As the thickness e of the film squeezed at the R/S interface gets smaller than e*, a contact is nucleated on the Vickers print and propagates to the whole film.
surface energy to create a dry contact of radius R competes with the loss of elastic energy for a deformation e/λ extending in a volume 2πRλ2:
Fc = SR2 + E
(λe) Rλ 2
2
(6)
The maximum of Fc versus R defines the critical radius Rc. For R > Rc, a solid/rubber contact will expand
Rc ≈
e2 h0
(7)
Taking e ) 1 µm and ho ) 10 nm, one gets Rc ≈ 1 mm. To reach values of Rc in the range of micrometers, a typical size of aspirities, one thus needs to go down to film thickness e < 0.1 µm. Intercalated films are less fragile than films exposed to air: one can dewet only very thin films. In our experiments, we print in the solid support some nucleators of lateral size b. A film should dewet when it is thinner than a critical thickness e*, given by eq 7 with Rc ) b
e* ) xbh0
(8)
The elastomersPolyDiMethylSiloxanesis prepared from a commercial reaction mixture (two equal parts, Sylgard 170A&B, Dow Corning Corp.) from which undesirable reinforcing particles have been removed by centrifugation. Liquid droplets of the mixture are deposited on a nonwettable surface (a silanized glass slide). They form spherical caps. They are cured at 65 °C during 48 h; the cross-linking process is complete. We get elastomer lenses of radius of curvature R ) 1-3 mm, which are homogeneous and optically smooth. They behave like a pure elastic medium (Young modulus E ) 0.74 MPa). The solid substrate is a standard microscope glass slide, silanized with octadecyltrichlorosilane (OTS), using a standard procedure.13-14 The defects, printed on the glass before silanization, are described in the next section. The liquid is a fluorinated silicone oil (PFAS) used as received (Hu¨ls-Petrarch Corp). It is pure and immiscible with PDMS. We used two different molecular weights, Mw ) 2350 and Mw ) 4600. The respective viscosities, η ) 0.40 and 1.6 Pa s, are then about a thousand times larger than water viscosity. It slows down the dewetting which can be followed with a regular camera. The elastomer cap is attached to the arm of a micromanipulator (Narishige), which enables us to control its position with an accuracy of a fraction of a micrometer. We follow the normal approach of the lens along the axis of an objective (×20) of an inverted microscope (Zeiss, Axiovert 135) using RICM.15 When the elastomer is not in contact with the plate, we observe Newton rings corresponding to a spherical rubber lens. As we approach the lens toward the plate (with a speed of the order of 1 µm s-1) below a micrometer, the lens is deformed and a flat film of radius a ≈ 100 µm is formed (Figure 2). At this stage, we hold
III. Experimental Setup Intercalated films are formed by pressing an elastomer cap against a glass plate through a separating liquid drop. The experimental geometry is shown in Figure 2.
(13) Gun, J.; Sagiv, J. J. Colloid Interface Sci. 1986, 112, 457. (14) Brzoska, J. B.; Shahizadeh, N.; Rondelez, F. Nature 1992, 360, 24. (15) Ra¨dler, J.; Sackmann, E. J. Phys. II 1993, 3, 727.
Dewetting Nucleation Centers at Soft Interfaces
Langmuir, Vol. 17, No. 21, 2001 6557
the position of the rubber. The deformation of the elastic medium is = a/R = 10%. The total stress Ρ at the lubricated contact can be evaluated using Hooke’s law P = E ≈ 1 atm and is responsible for the drainage of the intercalated liquid film. Notice that the ploughing length of the rubber sphere, δ = a ) 10 µm, is much larger than the film thickness ( hc. We show in Figure 7 a sequence of dewetting for a “thick” mesa (b ) 21 µm, h ) 105 nm). The nucleation starts earlier on one point of the mesa, propagates to achieve a dry contact between the mesa surface and the rubber, and stops! We observe no propagation of the dewetting beyond the nucleator area. Instead, we observe finally the “collapse” coming from the border. The value of hc which separates the two regimes is hc = 30 ( 10 nm. VI. Discussion The values of e*(b) at which we observe nucleation and propagation of dewetting are plotted in Figure 8. The
The exponent 0.5 is determined with a limited accurracy, because b can vary only on 1 decade. The prefactor is on the order of unity. This dependence is compatible with the theoretical prediction for the radius of nucleation (eqs 7 and 8). The mesa nucleators are efficient only if their thickness h is less than a critical thickness hc. We can estimate the thickness hc by the following argument. We start from a bridge between the mesa and the rubber. To propagate the contact beyond, the elastomer must deform considerably to follow the step-shape profile of the mesa. The elastic energy required to step down along the glass surface is E(h/δ)2δ2b, where δ (on the order of h) is the size of the thin region where the rubber is deformed. The energy gain is the surface energy 2πbSh. The energy associated with the “step down” is ∆F ≈ (Εh2 + Sh)b . That is for ∆F e 0 we have h < hc, hc ) |S|/E ) h0. For our system, h0 ) 9 ( 1 nm is of the same order of magnitude as hc. On the other hand, if the step is smooth (tilting angle β), the gain of surface energy increases by a factor β-1, while the elastic energy remains the same. Therefore hc becomes much larger. This explains why the smooth relief around the inverse pyramid always propagates dry contacts. VII. Conclusion We have studied the controlled nucleation of an intercalated film using two kinds of nucleators: mesa and Vickers. With Vickers nucleators, dewetting is nucleated below a critical thickness e* and propagates to the whole of the contact. The relation between the critical thickness of the film and the lateral size of the nucleator agrees with the theory of nucleation at soft interfaces. With mesa nucleators on the other hand, two distinct behaviors are observed, depending on the size of the defect: (a) If h < hc , the contact is nucleated by the mesa relief and propagates to the whole film. (b) If h > hc, a dry patch forms on the top of the mesa relief but does not propagate beyond it.
Dewetting Nucleation Centers at Soft Interfaces
We have presented a model to interpret the two regimes and to evaluate the critical value hc. Experimental measurements are compatible with the predicted result (hc ≈ ho). In the real tire/wet road system, both of these behaviors are interesting: indentors of all scales and shapes are present on the road and are liable to start dewetting. The
Langmuir, Vol. 17, No. 21, 2001 6559
second case (h > hc) can also improve adherence significantly, even though dewetting does not propagate. Acknowledgment. We thank J. M. Vacherand, P. G. de Gennes, and E. Karatekin for stimulating discussion and O. Duroure for the AFM imaging. LA010503Y
