An ellipsometric study of layered droplets

Thin Solid Films, 234 (1993) 475-477

475

An ellipsometric study of layered droplets M . P. V a l i g n a t , N . F r a y s s e , A . M . C a z a b a t , F. H e s l o t a n d P. L e v i n s o n Coll~ge de France, Physique de la Matibre Condens~e, 11 place Marcelin Berthelot, 75231 Paris C~dex 05 (France)

Abstract The thickness profiles of microdroplets of non-volatile liquids spreading on smooth solid surfaces have been studied by spatially resolved ellipsometric measurements. Our set-up is a polarization-modulated, single-wavelength ellipsometer working at the Brewster angle. The lateral resolution is 25 lam, the thickness resolution is 0.2 A with a time constant of 100 ms in the detection electronics. This allows one to record the drops' profiles as a function of time. The "thick" part of these profiles (typically between 20 and 300/~) is smooth. The "thin" part exhibits distinct molecular steps. Information on interactions and rheology at the microscopic scale can be extracted.

1. Introduction Thin liquid films play an important role in industrial processes dealing with coating and adhesion: the performance of adhesive joints and the quality of coatings is often controlled by the first molecular liquid layers in contact with the solid surface. The static and rheological properties of these thin films are still largely unknown, but they can be conveniently investigated by recording the thickness profiles of spreading microdroplets at increasing times. Only non-volatile liquids with a low contact angle on the solid surface can be studied in this way, but they are also the most widely used for practical applications: silicone derivatives are well-known examples.

2. Experimental set-up Spreading microdroplets are molecularly thin, and extend over millimetres. Therefore, thickness and lateral resolution are needed for a detailed study of their shape and of its time evolution. The ellipsometer works at the Brewster angle, with allows us to focus the light beam to an elliptic spot of small axis 25 ~tm (the fight source is an H e - N e laser). The solid substrates are silicon wafers, which provide a large index contrast between the underlying silicon and the layers on top of it: these layers are the natural oxide SiO2, in some cases a hydrophobic grafted layer, and the spreading liquid film. All these layers are measured as a whole, and the film thickness is deduced by comparison of the measurements before and after drop deposition. The thickness resolution is good, typically 0.1/~ for each measurement, i.e. 0.2 A for the difference. This is due to the large index contrast, but is also characteristic of

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polarization-modulated set-ups [1-4]. Our photoelastic modulator works at 50 kHz, which makes the detection extremely fast: this is convenient for dynamic systems such as spreading droplets.

3. Liquid droplets Non-volatile liquids with low equilibrium contact angle 0e on silica or grafted hydrophobic layers are mainly silicone oils, such as polydimethylsiloxanes (PDMS), widely used as a base for adhesive compounds. Shorter silanes and siloxanes are also good candidates, an example being tetrakis(2-ethylhexoxy)silane (TK). PDMS is a worm-like flexible linear molecule, with a transverse size of 7 A and various chain lengths. T K is a compact, roughly spherical molecule, 10/~ in diameter, with a central silicon atom and four branched arms. At the macroscopic scale, the difference between complete wetting (0e = 0°), and partial wetting (0e # 0 °) is clear. For 0e = 0 °, the drop spreads completely. For 0, # 0 °, an equilibrium is reached, with the finite contact angle 0e at the edge of the drop. This is not so at the microscopic scale. In fact, a non-wetting droplet has to be in equilibrium with a thin film, the thickness of which depends on the 0~ value. For low contact angles (a few degrees) this thickness is a few molecular layers. Only for higher contact angles is the equilibrium film negligible at the molecular scale. As the spreading of microscopic droplets is an evolution towards equilibrium, there is no basic difference in the growth of the first monolayers for PDMS (0, = 0 °) and T K (0, ~ 2°). Moreover, the spreading is so slow that the system is always far from equilibrium within the experimental time scales. In most cases, only a

© 1993 -- Elsevier Sequoia. All fights reserved

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M. P. Valignat et al. / Ellipsometry of layered droplets

detailed analysis of the "thick" part of the profile could reveal a difference between low and zero contact angle.

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4. Theoretical analyses Thin liquid films are not bulk phases: the chemical potential #(z) of a molecule depends on the film thickness z and differs from its bulk value #b = #(m). A widely used parameter is the disjoining pressure H(z) = [~b - #(z)]/Vo, where v0 is the molecular volume [5]. For van der Waals fluids and thicknesses larger than 20-50 A, l-l(z) can be written as ll(z) = A/6nz 3, A being the effective Hamaker constant for the g a s liquid-solid system [6, 7]. For thinner films, an oscillatory behaviour of II(z) is often observed in atomic force measurements [6], owing to steric interactions in the vicinity of the solid surface. No theory is available in this range. The disjoining pressure has been defined for flat films at equilibrium. In fact, it can be used also for spreading droplets because the surface slope is low (see the experimental profiles in the following), and the spreading very slow. Theoretical models are available in two cases. (i) At short times, the maximum height of the drop is "large", of the order of 500/~ or more. The centre of the drop acts as a reservoir for the thin film. The change AR(z, t) in the radius at height z with time t can be written as [8, 9] AR(z, t ) = [D(z)t] 1/2, where D(z) is some "thickness-dependent diffusion coefficient". For z > 20/~ typically, the flow in the film is a Poiseuille flow, and D ( z ) = (z3/3~/)dII/dz, where r/ is the bulk liquid viscosity [8]. In the case of van der Waals fluids, the simple relation D(z) = A/6mlz results. For thinner films, D(z) is still proportional to dll[dz, but now the flow contains unknown molecular parameters [9]. (ii) At long times, the drop has flattened out, and no reservoir is available any longer. The upper layers slow down, recede and finally disappear into the lower layers. No model can a priori be written. Experiments are needed to provide bases for a theoretical analysis.

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Fig. l. Ellipsometric profiles of a T K droplet after spreading on a silicon wafer with 38 A of silica on top of the silicon (molecule size, 10]~): curve a, 2 0 h after deposition; curve b, 4 4 h ; curve c, l15h; curve d, 211 h.

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Fig. 2. Ellipsometric profiles of a T K droplet spreading on a silicon wafer bearing a pre-existing monomolecular layer ( 10/~) of the same liquid (silica layer, 20 A): curve a, 5.5 h after deposition; curve b, 30 h; curve c, 48 h; curve d, 127 h. The monomoleeular layer is built by first putting a small drop of T K in a "swimming pool", Le. inside a little circle drawn on the wafer with an ink pen, the ink being strongly non-wettable by TK. The "walls" of the "swimming pool" are visible at both edges of the profiles. The investigated droplet has been put on top of this film, after complete coverage of the available surface has been obtained. With some care and patience, it is possible to adjust the size of the first deposited drop to reach the desired coverage.

5. Experimental results A typical series of thickness profiles is shown in Fig. 1 for a T K drop. As already mentioned, the thicker part of the drop is smooth. In the thinner part, steps are observable, corresponding to successive molecular layers. The experiment can be repeated on a pre-existing static monolayer of the same liquid: this is illustrated in Fig. 2. In Fig. 3, the radii of the two first molecular steps of the previous drop (Fig. 2) have been plotted vs. the

square root of the time. Nice straight lines are obtained at short times, in good agreement with the theoretical predictions. In Fig. 4, the "diffusion coefficient" D(z) measured for a large drop of PDMS is satisfactorily compared with the calculated value of a van der Waals fluid and z/> 20 ]k. The shape of the corresponding D(z) curve for T K looks similar at low thickness (z ~< 30/~, i.e. three molecular layers), but decreases more steeply for thicker films, the effective Hamaker constant A being

M. P. Valignat et al. / Ellipsometry of layered droplets

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Fig. 3. Radius of the two first molecular layers of the previous drop (Fig. 2) as a function of the square root of the time. The "diffusion coefficients" D(z) are 10-1°m2s -1 and 6 × 10 T M m2s -1 for the first ( + ) and second ( O ) layers respectively.

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Figures 1, curves c and d, and 2, curve d, provide the basis for the analysis of flattened droplets: the most obvious features are the strong layering of the liquid and steep edges of the molecular layers. This suggests a model of an incompressible, layered droplet [10], where the molecular layers are assumed to be compact, with thickness a, the size of the molecule. The molecular parameters are the values of the disjoining pressure in the successive layers (i.e. W , = - I I ( n a ) for the nth layer), and the friction coefficients ( . . . . 1 between layers. This model captures the main observed features of the drop evolution [11, 12]. However, only combinations of the molecular parameters can be calculated at the moment. A systematic study with comparison of spreading rates on bare surfaces and on surfaces covered by a pre-existing layer (such as that in Fig. 2) is underway, in order to reduce the number of unknowns without introducing additional assumptions.

References ....

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Fig. 4. Log-log plot of D(z) (m2s -I) vs. z (m) for PDMS ( A ) on a silicon wafer with a silica layer of thickness 20 A. - - - , calculated value assuming van der Waals interactions for the four-layer system air/PDMS/Si02/Si. The following Hamaker constants for the threelayer systems have been used: A(air[PDMS/Si02)= 1.5 x 10-2°J; A(aJr/PDMS/Si) = 6 x 10- ~ J. The PDMS viscosity r / = 200 cP. D(z) values for TK spreading on the same wafer have been also reported on the figure ( + ) . To allow comparisons, the D values have been first corrected for the viscosity difference (t/= 6.8 cP for TK). In fact, D(z) = 1.6 x 10-mm2s -1 for the first monolayer and 1.2 x 10 -1° m 2 s -t for the second, dose to the value for the first layer on the pre-existing static monolayer. The curves look rather similar for z < 25 A, and then the TK curve decreases more rapidly.

negative for this non-wetting liquid. Only the very first molecular layers (typically five) actually spread.

1 S. N. Jaspcrson and S. E. Schnatterly, Rev. Sci. Instrum., 40 (1969) 761. 2 B. Drrvillon, J. Perrin, R. Marbot and A. Violet, Rev. Sci. Instrum., 53 (1982) p. 969. 3 D. Bcaglehole, Physica B, 100(1980) 163. 4 J. Meunier, Thin Solid Films, 234 (1993) 471. 5 B. Derjaguin, J. Colloids USSR, 17(1955) 191. 6 J. Israelachvili, Intermolecular and Surface Forces, Academic Press, New York, 1985. 7 P. G. de Genncs, Rev. Mod. Phys., 57 (1985) 827. 8 J. F. Joanny and P. G. de Gcnnes, J. Phys. (Paris), 47 (1986) 121. 9 A. M. Cazabat, N. Fraysse and F. Heslot, Colloids Surf, 52 (1991) 1. 10 P. G. de Genncs and A. M. Cazabat, C.R. Acad. Sci. Paris, Sdr. II, 310(1990) 1601. 11 N. Fraysse, M. Cazabat and A. M. Cazabat, C.R. Acad. Sci. Paris, S$r. II, 314 (1992) 1025. 12 M. P. Valignat, N. Fraysse, A. M. Cazabat, P. Lcvinson, F. Heslot and M. Cazabat, submitted to Colloids Surf