Langmuir 1999, 15, 2551-2558
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Thin Film Instability Induced by Long-Range Forces Gu¨nter Reiter,*,† Ashutosh Sharma,‡ Alain Casoli,† Marie-Odile David,† Rajesh Khanna,† and Philippe Auroy§ Institut de Chimie des Surfaces et Interfaces - CNRS, 15, rue Jean Starcky, B.P. 2488, 68057 Mulhouse Cedex, France, Department of Chemical Engineering, Indian Institute of Technology, Kanpur, U.P. 208016, India, and Institut Curie, Section de Physique et Chimie, URA 448 du CNRS, 11, rue Pierre et Marie Curie, 75231 Paris Cedex 05, France Received October 20, 1998. In Final Form: December 22, 1998 Dispersion forces are present everywhere. Their importance, however, is largely neglected because directly at a surface or at an interface they are mostly weak compared with specific interaction of short range. Here, we show that these forces are nonetheless extremely relevant and may have drastic consequences on the stability of thin films. We demonstrate that a force (per unit area) of 0, SP < 0); type II systems, where a longrange attraction (A > 0) combines with a shorter-range repulsion (SP > 0); and, type IV systems where a longrange repulsion (A < 0) combines with a shorter-range attraction (SP < 0). Type III systems (both, long- and shortrange interactions are repulsive) are stable. It is well-known from colloid science that two particles, named 1 and 2, immersed in a fluid, designated as 3, may either attract or repel each other, even over distances (h) of many tens of nanometers (see Figure 1). Such longrange interaction may be due to apolar van der Waals forces that can be described by a product of two terms.1-10,97,98 The first term is accounting for the energetic properties of the different materials, expressed by an effective Hamaker constant A132. The second term de(94) Leibler, L.; Ajdari, A.; Mourran, A.; Coulon, G.; Chatenay, D. In Ordering in Macromolecular Systems; Teramoto, A.; Kobayashi, M.; Norisuje, T., Eds.; Springer-Verlag: Berlin, 1994; pp 301-311. (95) Shull., K. Faraday Discuss. 1994, 98, 203. (96) Martin, J. I.; Wang, Z.-G.; Schick, M. Langmuir 1996, 12, 2 and 4950. (97) Hamaker, H. C. Physica 1937, 4, 1058. (98) Visser, J. Adv. Coll. Interface Sci. 1972, 3, 331.
xγD3 )(xγD2 - xγD3 )
(2)
The term δo is an atomic cutoff distance (0.158 nm9) arising from the short-range Born repulsion. Assuming now that particles 1 and 2 are infinitely large, one ends up with a thin film of medium 3 separating media 1 and 2. Such a change in geometry does not affect A132. The total excess free energy ∆G due only to van der Waals interactions in a thin film system is given by (see e.g., refs 5 and 9; in some publications, e.g., refs 8 and 23 the definition of ∆G is slightly different: eq 3 does not contain a negative sign)
∆G ) -A132/12πh2
(3)
Assuming a typical value of 10-20 J for A132, we obtain at h ) 100 nm a force (per unit area) of 1 Pa acting on the film surface. The interaction between the two bodies 1 and 2 across the medium 3 becomes extremely small for h of the order of micrometers. If A132 is negative, 1 and 2 repel each other, seeking to make the film infinitely thick. A positive effective Hamaker constant represents attraction between 1 and 2, trying to remove the film completely. Positive A132 also means that a thin film is unstable. By thinning the film locally, one reduces the free energy more than it costs, due to mass conservation, to increase the film thickness some place else. Mathematically this means that the second derivative of ∆G with respect to h has to be negative for the film to be unstable. Such attraction then can lead to “roughening” of the film. The interfacial tension γ32, however, will create a Laplace pressure (see e.g., refs 8-14) that will smoothen out undulations, preferentially the ones with a small local radius of curvature. The competition between attractive long-range forces and Laplace pressure thus determines a critical wavelength beyond which fluctuations will grow increasingly more rapidly. In an approximative theory, the early stages of growth can be described by an exponential function. However, it has to be noted that the force acting on the film varies with film thickness and cannot be represented by the value at the mean thickness if the thickness variations get large. The growth of depressions will accelerate much more the deeper the depressions get. Eventually, the depressions hit the substrate and, on nonwettable substrates, rupture the film which, in turn, will initiate a dewetting process. Because of such nonlinear behavior caused by the strongly increasing attraction as the thickness gets smaller, before rupture sets in, most of the time is needed to create depressions of a few percent of the film thickness. Systematic experiments on the influence of antagonistic short- and long-range forces on film stability have not yet been performed. Such systems have only recently been studied theoretically by 2- and 3-dimensional computer simulations.11,26,34 3. Experimental Section 3.1. Why Polymers? Our main goal in choosing a suitable experimental system was to have the best possible knowledge and control over the forces acting in the thin film system. Entropic
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Figure 2. Detailed schematic presentation of the system used; that is, bimodal PDMS brushes covered with a film of free PDMS molecules. The connectors are well intermixed with the free molecules. The thickness h is the thickness of the whole PDMS layer, including grafted and free molecules. effects of polymers provide a possibility to model and control interfacial interactions.94-96 Such effects allow one to create repulsive and attractive surfaces. This may lead to the, at first, surprising fact that polymers even may dewet a layer of identical but grafted molecules () polymer brush).53,61 However, if one adds long but otherwise identical polymers to this brush (i.e., creates a bimodal brush), one can reestablish wettability.62 The polymer will spread out on such a bimodal brush surface. The long molecules will act as connectors across the nonwettable interface. Already a rather low number of connectors (the thickness of the washed and dried brush system increases only by a few Angstroms, meaning that the connector molecules do not touch each other) may prevent dewetting. The dense brush of short polymers underneath the connectors serves also to avoid contacts between the chemically different silicon substrate and free polymers. The effective substrate-film interface is now between the surface of the brush and the free molecules.96 Such bimodal brushes have the advantage that they allow one to modify short-range interactions at the substrate-film interface without introducing chemical differences between substrate and film. Consequently, A132 is not altered. We note, and will prove it by the subsequent experiments, that a wettable bimodal brush surface does not necessarily imply that such a thin film is stable because A132 may still be positive. 3.2. Brush Preparation. We decided to use bimodal poly(dimethylsiloxane) (PDMS) brushes supported by silicon wafers and coated by thin films of PDMS. In Figure 2 we present a schematic drawing of the samples used. This system has the advantages that we can perform experiments at room temperature and that we can put liquids like water or ethylene glycol (extremely bad solvents for PDMS) on top of the polymer. Endfunctionalized PDMS molecules, allowing chemical bonds to the wafer, of two different molecular weights were synthesized anionically by one of us (P. A.) and grafted sequentially onto the wafers. The procedure is described next and shown schematically in Figure 3. First, monomodal dense brushes were made from SiH monofunctionalized poly(dimethylsiloxane) (PDMS, liquid at room temperature) chains of uniform length (molecular weight, Mw ) 8800 g/mol; polydispersity, I < 1.1). Prior to grafting, the silicon wafer (cleaned by UV ozone) was treated with chlorodimethylvinylsilane (CDMVS) to suppress adsorption of a PDMS and to functionalize the surface with vinyl groups. The SiH-PDMS, diluted in heptane containing a platinum catalyst, was spincoated onto the wafer. The resulting films were annealed at 120 °C, allowing a chemical reaction hydrosilation between the SiHend groups and the vinyl groups at the substrate. The samples were put into a bath of heptane to wash off all nongrafted molecules. From the dry thickness (d), determined by ellipsometry, the grafting density (υ) of the brush chains [υ ) d/(Na3)62] could be deduced, with N being the number of monomers per grafted chain and a (∼5 Å) being the statistical segment length.99 Because of the high grafting density (υ ) 0.44 chains/nm2), the (99) Le´ger, L.; Hervet, H.; Massey, G.; Durliat, E. J. Phys.: Condens. Matter 1997, 9, 7719.
Figure 3. Schematic drawing representing the way the bimodal polymer brushes have been prepared.
Figure 4. Variations of the excess free energy per unit area (∆G) with film thickness (h) for the investigated system. The full and dash-dotted line represent the case when the surrounding medium are water and air (positive and negative A132), respectively. Because of the grafted PDMS molecules, a layer proportional to the size of these molecules has to remain on the substrate. This phenomenon is indicated by a positive spreading coefficient () ∆G (h ) 0)) and positive values of ∆G at small thicknesses. As a consequence, we obtain a minimum at a distance of about the size of the grafted molecules. chains were preferentially oriented and stretched in the direction normal to the silicon surface. This procedure caused an autophobic behavior, indicating only little interpenetration (about 1 nm) between network and brush.61,62,94,95 Bimodal brushes resulted from a monomodal brush onto which we grafted a few much longer PDMS chains (Mw ) 121 800 g/mol, I < 1.1), which acted as connectors.62 This grafting was done by spin-coating a thin (about 50 nm) film of reactive long PDMS molecules onto the already existing brush of short PDMS molecules. After annealing for about 2 h at 120 °C, a few molecules were able to penetrate the brush of short PDMS molecules and graft onto the silicon wafer. The nongrafted molecules were washed off in a bath of heptane. The number of connectors (per unit area) was deduced from the difference between the thicknesses of the dry monomodal and bimodal brushes. The bimodal brush was coated with a PDMS film (Mw ) 28 kg/mol, viscosity ) 1000 cSt) of variable thickness. To initiate the instability, we replaced the surrounding medium air by some liquid (mostly bidistilled water). Other liquids, such as ethylene glycol or salt and surfactant solutions showed qualitatively the same behavior. Quantitative differences are due to differences in the interfacial tensions. The evolution of the instability was followed at room temperature and in real time by optical microscopy. Removing water resulted in re-spreading of PDMS (vide infra).
Thin Film Instability
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Figure 5. Optical micrographs from a 41-nm thick PDMS film. Pictures are taken at (A) t ) 39 s, (B) t ) 88 s, (C) t ) 211 s, (D) t ) 395 s, (E) t ) 656 s, and (F) t ) 680 s. A millimeter thick layer of water was added at time t ) 0. The size of each micrograph is 200 × 200 µm2. The shades of gray correspond to thicknesses from zero (white) to about 100 nm (black). This interference scheme is repeated for larger thicknesses. Removing the water layer after 650 s inverted the sign of the Hamaker constant again. The droplets became unstable and re-spreading was observed. We want to emphasize that PDMS films on bimodal brushes were stable in air. No signs of dewetting or characteristic patterns were observed. This result has to be contrasted to films on monomodal brushes, where one could initiate dewetting by defects. Putting such films under water also led to dewetting. However, when water was removed, dewetting continued and absolutely no re-spreading was observed. 3.3. Hamaker Constants. PDMS has a lower Hamaker constant than silicon.98 The bounding medium air has a Hamaker constant equal to zero. Consequently, A132 is negative, and a thin film of PDMS (in air) is stable (upper broken line in Figure 4). The situation changes dramatically if medium 2 is a liquid that has a higher Hamaker constant than PDMS. We replaced air by putting water on top of the PDMS film and thereby changed the sign of A132 (Figure 4, lower broken line, continued as a full line D for large values of h). The value of γwater is 21.8 mJ/m2 5,6 100 for PDMS. Water compared with γD of about 20.7 mJ/m PDMS does not wet PDMS and is also an extremely bad solvent for PDMS. The interfacial tensions between water and grafted or free PDMS molecules, respectively, are the same (about 39 mJ/ m2 101). The increased interfacial tension of PDMS/water with respect to that of PDMS/air tends to smoothen the film. However, long-range forces can destabilize the film. For the present system, the final state is expected to be droplets on a thin wetting film. In theoretical treatments, this situation has been call pseudopartial wetting,8 and the process to arrive there was termed “morphological phase separation”.9-11 It is evident that a layer of PDMS has to remain because we have attached PDMS molecules chemically to the silicon wafer. In addition, because of the connector molecules, this brush is wettable by PDMS, which is expressed by a positive spreading coefficient S ) ∆G(h ) 0). This situation is indicated by the full line in Figure 4, which exhibits a minimum at a finite value of h. The main advantage of the model system investigated here is that we have control over the substrate interactions by controlling the grafting density and also over the long-range van der Waals interactions by varying the bounding medium, allowing even the sign of the effective Hamaker constant to be changed. (100) Sauer, B. B.; Dee, G. T. Macromolecules 1991, 24, 2124. (101) Bergeron, V.; Langevin, D. Macromolecules 1996, 29, 306.
4. Results and Discussion 4.1. Morphology. The typical spatial and temporal evolution of a thin PDMS film covered with water as a function of time is shown in Figures 5-7 for different film thicknesses. Comparable results have been obtained with other bounding media like ethylene glycol or surfactant solutions. As we were observing the evolution of a nanoscopic film across a millimeter thick water layer, the contrast (indicating thickness and, in particular, thickness variations) is not very good primarily because of a reduction of the refractive index contrast. Thus, the quality of the pictures is poor, especially for thickness modulations of
