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Langmuir 1997, 13, 4910-4914
Sessile Droplets at a Solid/Elastomer Interface P. Martin, P. Silberzan, and F. Brochard-Wyart* P. C. C, Institut Curie, section de recherche, 11, rue Pierre et Marie Curie, 75231 Paris cedex 05, France Received March 25, 1997. In Final Form: June 12, 1997X The spreading parameter S is the fundamental parameter controlling the stability of thin liquid films intercalated between a hydrophobic solid and a soft elastomer (Young modulus E): S ) γSR - (γSL + γLR), where γSR, γSL, and γLR are respectively the solid/elastomer, solid/liquid, and liquid/elastomer interfacial tensions. We describe here a simple experimental method to determine S. We monitor by interferometry the profile of liquid droplets squeezed at the solid/elastomer interface. S is negative and the droplets do not spread. We find that (i) an intercalated droplet is a very flat semiellipsoid with a macroscopic contact angle of 90° and (ii) the radius R of the wet area scales like R ∝ H2/h0, where H is the thickness at the center and h0 ) |S|/E is a characteristic length in the range of 100 Å. From the shape analysis we extract h0 and as a consequence the spreading parameter S. This measurement was performed for different liquids sandwiched between a cross-linked silicone polymer and chemically modified glass slides. Liquid droplets trapped at the solid/elastomer interface give similar results except that we get ellipsoid instead of semi-ellipsoid. In this particular case the spreading parameter is simply given by S ) -2γLR and compares well with an independent measurement of γLR.
1. Introduction The lubrication properties of water (or other liquids) films squeezed between a solid and a rubber have been studied over the last 4 decades.1 It is related to specific problems such as smear associated with windscreen wiper blades, lacrymal film stability between cornea and contact lenses, or water lubrication of rubber bearings. The stability of liquid films intercalated between a rigid solid substrate and a rubber (Young modulus E) is controlled by the spreading coefficient
S ) γSR - (γSL + γLR)
(1)
where γSR, γSL, and γLR are the solid/rubber, solid/liquid, and liquid/rubber interfacial tensions. If S < 0, the system gains energy by squeezing the intercalated liquid away to create an intimate contact between the solid and the rubber: the film is metastable and dewets by nucleation and growth of dry patches. We can estimate the critical radius Rc of nucleation for such a film (Figure 1). We derive Rc by balancing the surface energy we gain by forming a bridge between the rubber and the solid substrate with the elastic energy of deformation we have to pay to form such a bridge:
( )
-S Rc2 ∝ E
e 2Rc3 Rc
(2)
where e is the film thickness. This leads to
Rc ∝ e2/h0
(3)
where h0 ) |S|/E is a characteristic length. However, individual interfacial tensions are difficult to measure and therefore S is often hard to work out without making crude approximations.2,3 One could think of using a JKR technique to deduce S, since -S also measures the Dupre´ work of adhesion at the solid/liquid interface. The JKR model4 predicts the radius “a” of contact deformation when a rubber sphere is brought in contact with a rigid solid plate under an external load P X
Abstract published in Advance ACS Abstracts, August 1, 1997.
(1) Roberts, A. D. Tribology 1977, 10 (2), 115-22. (2) Girifalco, L. A.; Good, R. J. J. Phys. Chem. 1957, 61, 904. (3) Good, R. J.; Girifalco, L. A. J. Phys. Chem. 1960, 64, 561.
S0743-7463(97)00315-6 CCC: $14.00
Figure 1. Sketch of a rubber bridge (radius R) formed in a liquid film (thickness e) intercalated between a solid substrate and an elastomer. If the rubber/solid contact radius R is lower than Rc, the critical radius, the dry contact will shrink, otherwise it will expand and the liquid will be removed.
a3 )
9 C {P + 3π|S|C + [6π|S|CP + (3π|S|C)2]0.5} 16 E (4)
()
where C is the radius of curvature of the sphere. The JKR test has been widely used when done in air and the a3 versus P (at fixed C) curve gives the work of adhesion of the sphere.5-7 Nevertheless, such an experiment is difficult to perform in our case since it involves a force measurement in a liquid medium. Even a simple experiment at zero external load is not trivial since buoyancy forces have to be taken into account. Furthermore, if the liquid is denser than the rubber (as in our case), the buoyancy forces can overcome the pull-out force and we will not get a contact between the solid and the sphere without applying an external load. For the more usual case of a liquid film exposed to air,8 the spreading parameter Sair (Sair ) γSO - (γSL + γ), where γSO, γSL, and γ are respectively the solid/gas, solid/liquid, and liquid/gas interfacial tensions, is easily derived from (4) Johnson, K. L.; Kendall, K.; Roberts, A. D.Proc. R. Soc. London, Ser. A 1971, 324, 301-313. (5) Barquins, M. Wear 1992, 158, 87. (6) Horn, R. G.; Israelachvili, J. N.; Pribac, F. J. Colloid. Sci. 1986, 115 (2), 480. (7) Chaudury, M. K.; Whitesides, G. M. Langmuir 1991, 7, 10131025. (8) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715.
© 1997 American Chemical Society
Sessile Droplets at a Solid/Elastomer Interface
Langmuir, Vol. 13, No. 18, 1997 4911
In our experiments we always inject droplets with R(∼100 µm) >> h0. Therefore they should be very flat: H/R ≈ (h0/R)1/2
