Dynamics of Wetting: From Theory to Experiment - Springer Link

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INTERFACE SCIENCE 5, 129–139 (1997) c 1997 Kluwer Academic Publishers. Manufactured in The Netherlands. °

Dynamics of Wetting: From Theory to Experiment A.M. CAZABAT, S. GERDES, M.P. VALIGNAT AND S. VILLETTE College ` de France, CNRS URA 792, Physique de la Matiere ` Condens´ee, 11, Place Marcelin-Berthelot, 75231 Paris Cedex 05

Abstract. The main available theories for the dynamics of wetting are briefly summarized and discussed in reference to experiments. In partial wetting, hydrodynamic and molecular theories are equivalently efficient, even if the physical meaning of parameters is not so clear in the former ones. In complete wetting, hydrodynamic theories are the only ones valid at low angles, but some care has to be taken in the interpretation of the “slip length” introduced to remove the divergence of the dissipation at the contact line. The situation is less favourable at the molecular scale, where the theoretical description is still at its beginning, due to the multiplicity of behaviours. Keywords: wetting, thin films, slip length, contact angle

Wetting phenomena have been investigated for long, both from theoretical and experimental side [1–10]. Many theories have been proposed for wetting dynamics, based either on hydrodynamics [1–8] or on a molecular picture of the contact line [10]. Surprisingly enough, both approaches are equally efficient in most cases, although the working assumptions are at the opposite. Moreover, the physical meaning of the parameters in the equations is not always obvious. This introduction could have been written five years ago [11]. Since that time, great advances in computer simulation have taken place [12–15], new theories are born [16], and further experiments have been performed. However, many questions still remain unanswered. Let us first introduce the basic ingredients for wetting descriptions. Parameters Relevant in Dry Wetting Wetting refers to situations where a fluid 1 is put in contact with a solid in the presence of a fluid 2. We shall restrict the discussion to the case where 1 is a liquid and 2 a neutral gas, air for example, and to the so called “dry wetting”. This means that there is no equilibrium between the solid and the vapor of the liquid: the solid is initially “dry”, and the characteristic

time for evaporation-recondensation process of liquid molecules on the solid is much longer than the time scale of experiment. In this case, the relevant macroscopic parameter for wetting behaviour is the spreading parameter S, which is the difference between the excess free energies per unit surface of a solid-gas interface, and of a solidliquid-gas interface, where a thick film of liquid separates the solid and the gas phases. “Thick” means that the thickness of this film is larger than the range of the molecular interactions. S can be written as: S = γSG − γ − γSL

(1)

where the γi j are the interfacial tensions, with γ = γLG . S is positive or zero for complete dry wetting, negative for partial wetting, in which case the macroscopic equilibrium contact angle θe is given by: cos θe = 1 +

S γ

(2)

At the edge of the liquid, the thickness ζ becomes less than the range of “long range” interactions: the film is “thin”. Now, the free energy per unit surface of the solid-liquid-gas interface must be supplemented by a new contribution P(ζ ) accounting for the interaction between solid and gas through the liquid. Equivalently,

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an interaction force per unit surface can be introduced, this is the disjoining pressure 5(ζ ) [17]. One has: 5(ζ ) = −

dP dζ

Z

∞

S=

5(z) dz

(3)

0

Main Theories for the Dynamics of Dry Spreading We shall recall very briefly the main results of the theories, comprehensive reviews can be found in the literature [6, 18, 19]. The liquid is supposed to advance on the solid surface at constant velocity U as a macroscopic wedge with a dynamic contact angle θ differing from the equilibrium contact angle θe . At the very edge, the thickness of the film is molecular. If the contact angle is not too small (partial wetting, or complete wetting and non vanishing velocity), no significant crossover is expected to exist between the macroscopic wedge and the molecular part. On the contrary, in complete wetting and low velocity, a mesoscopic precursor film develops ahead of the macroscopic wedge, making the crossover to the molecular part (see Fig. 1). In this stationary situation, the excess capillary force (per unit length of contact line) Fc is compensated by the friction term Fv . Two classes of theories have been proposed to determine the relation between θ , θe and U , and differ in the way the friction is calculated. In hydrodynamic theories [1–8], Fv is assumed to be dominated by viscous dissipation in the macroscopic wedge and in the mesoscopic precursor, if any. In the molecular theory proposed by Blake [10, 19], the dissipation associated to molecules hopping at the molecular edge of the film is supposed to be the main contribution.

Note that, as viscous dissipation is not taken into account, the molecular theory is not expected to hold in complete wetting and small angles. Let us start with this theory [10, 19]. Wetting is described as an activated hopping process of molecules between adsorption sites. 3 is the distance between sites, K 0W the hopping frequency, which is related to the activation energy, kT the thermal energy. When the system is out of equilibrium, i.e., when the net resulting velocity U is non zero, the energy barriers in the forward and backward direction become different. A net dissipation is then associated to the motion, which compensates the unbalanced capillary force γ (cos θe − cos θ ). This gives: cos θe − cos θ =

2kT U arg sh γ 32 2K 0W 3

(4)

The hopping frequency is the result of two processes: the molecules have to reach the contact line before to be able to jump to adjacent places. The first process is also an activated process, where the viscosity η comes into play. One can write: K 0W = K 0S

h ηv0

(5)

where h is the Planck constant, and v0 the volume of matter performing the jump. For simple molecules, v0 is the volume of the molecule. For polymers, it can be a sub-ensemble, possibly a monomer. Now the equation is: cos θe − cos θ =

2kT ηU v0 arg sh 2 γ3 2K 0S 3h

(6)

Figure 1. Schematic profile of a liquid wedge advancing on a solid surface. The liquid wets the solid completely. θ is the dynamic contact angle. For low θ , a mesoscopic precursor film develops ahead of the wedge.

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Dynamics of Wetting

Another way to write it is: γ 32 (cos θe − cos θ) 2kT 2 h γ 3 (cos θe − cos θ ) sh = 2K 0S 3 ηv0 2kT

U = 2K 0W 3 sh

For one-directional jumps of frequency K 0W , the velocity would just be K 0W 3. Inside the hyperbolic sine, one clearly sees the ratio between the excess capillary energy for a surface 32 and the thermal energy kT . Although the theory mixes macroscopic and molecular parameters, these quantities have a physical meaning, which makes this approach very fruitful in the case of specific interactions between liquid and solid [19, 20]. Very often, adsorption sites and activation processes can be identified, and the values obtained for 3 and activation energies (which determine the value of K 0S ) are quite plausible. Let us discuss now hydrodynamic theories: Hydrodynamic theories deal with macroscopic and mesoscopic scale and assume no slip at the solid surface. This assumption has to be released at some distance from the contact line, to avoid the divergence of dissipation. The various approaches differ in the way this distance is introduced and in the range of angles treated. In all cases, the relevant parameter is the capillary number: Ca =

ηU γ

(7)

which is supposed to be small, and only first order terms in Ca are considered. The theory by Cox [7] treats the general problem of a fluid 1 displacing a fluid 2 on a solid surface for any viscosity ratio and contact angle. For non-vanishing angles, the hydrodynamic equations are solved to first order in Ca assuming that the macroscopic wedge with angle θ is terminated by a zone of molecular extension, where slip is allowed, the “microscopic contact angle” at the surface being θe . For very small angles, i.e., complete wetting and vanishing velocities, an intermediate mesoscopic zone must be introduced between this slip zone and the wedge. This accounts for the mesoscopic part of the precursor film. In this approach however, the number of parameters makes the comparison with experiment difficult, and we shall prefer the presentation by de Gennes, where the mesoscopic part of the precursor film is treated explicitly. Therefore, the physical

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meaning of lengths and angles, and also what a “small” angle is, becomes more clear. In the case where no “intermediate” zone has to be introduced in the Cox’ theory, the result can be written as some function of contact angle: · ¸ R g(θ ) = g(θe ) + Ca ln + Q e (8) λ R is a macroscopic length, in the range of millimeters, λ the slip length. The logarithm corresponds to the dissipation in the wedge, with R and λ as upper and lower cutoffs. Q e corresponds to the dissipation in the part of length λ. Q e is supposed to be small compared to the log term, in fact less than 1, and to vanish in complete wetting. In the simple case of a liquid displacing a gas, and for contact angles less than 3π/4, an approximate formula is [21]: · ¸ R θ 3 ≈ θe3 + 9Ca ln + Q e (9) λ In the case of complete wetting (and still assuming non vanishing angles), it becomes: θ 3 = 9Ca ln

R λ

(10)

Very similar results have been obtained for complete wetting, especially by Tanner [2], and a simple expression for them is often referred to as the “Tanner’s law”: as the log is supposed to vary slowly, being of the order of 14–16 (R is in the millimeter range and λ is a few ˚ one has: A), θ 3 ≈ K Ca

(11)

with K ≈ 100 being a constant. The “Tanner law” (11) has been reformulated by de Gennes [6] in the case of complete wetting for small and very small contact angles. Here, “small angles” means that the slope of the interface is low enough for the lubrication approximation to hold, and that the trigonometric functions will be taken to lowest order in θ. The mesoscopic precursor film is treated explicitely. The asymptotic solution of the Navier-Stokes equation supplemented by disjoining pressure terms, with a no-slip condition at the solid surface, gives the profile ζ (x) of the liquid, both in the macroscopic wedge and in the precursor. Here, x is the distance to the apparent contact line, defined as the extrapolation of the macroscopic wedge (see Fig. 2).

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Figure 2.

Symbols used in the approach by de Gennes.

In the macroscopic wedge, the disjoining pressure term can be neglected: · · ¸ ¸ d 2ζ d 2ζ d d ηU − γ 2 − 5(ζ ) ≈ −γ 2 3 2 = ζ dx dx dx dx (12) The profile can be asymptotically written as: · ¸ x 1/3 ζ (x) → x 9Ca ln x1

(13)

The cutoff length x1 is found by matching the solution in the wedge with the solution in the mesoscopic precursor, where the Navier-Stokes equation (with no slip at the solid surface) becomes: ¸ · d d d 2ζ ηU − γ 2 − 5(ζ ) ≈ [−5(ζ )] 3 2 = ζ dx dx dx (14) An explicit solution can be obtained if the disjoining pressure is known. For van der Waals gas-liquidsolid interactions with an effective Hamaker constant A(A < 0), one has: x1 = 2.5x0

with x0 = 3−1/16 aCa−2/3

where a is a molecular length: s −A a= 6πγ Finally, one can write: ¾¸1/3 · ½ 2 x ζ (x) → x 9Ca ln + ln Ca b 3 b ≈ 2a is also molecular.

(15)

(16)

(17)

The length of the precursor is: s a L≈ Ca

S γ

(18)

Although the various results look similar, the crossover length x1 in the theory does not correspond to a slip length: the no-slip condition is supposed to hold in the mesoscopic part of the precursor as well. Moreover, the local slope depends on the distance to the contact line: this reflects the difficulty to define an intrinsic contact angle in situations where the interface is distorted [22–24]. As a matter of fact, the approach by de Gennes makes a clear distinction between the distortion of the interface due to long range interactions, and the slip process. Except in the case of complete wetting and small angles, where the molecular theory does not hold (the capillary number is found to scale like θ 2 , instead of θ 3 ), the fits of experimental θ (U ) data using Cox or Blake theories are practically equivalent. As already said, the parameters in Blake’s theory account satisfactorily for the chemical specificity of the liquid-solid system. In contrast, the physical meaning of λ and Q e in Cox analysis is not always clear, and fitted Q e values are often much larger than 1, which means that the molecular dissipation is underestimated in the model [14, 25]. However, this approach is the more rigorous from the point of view of hydrodynamics. What must be understood now is when the mesoscopic part of the film becomes negligible. Then the Cox’ formula can be written in the simple form (10), and we expect Cox’ and de Gennes’ results to become equivalent. Moreover, this should make clear how experimental K values have to be interpreted in terms of slip length.

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We have addressed this problem on the experimental side, by studying the θ(U ) dependence for a large range of angles, between 50 and 20 degrees using goniometric techniques, and below 7 degrees with interferometry. Previous experiments by Garoff, Marsh and Dussan have been performed for somewhat larger angles [24]. The formula by de Gennes is: ¾¸1/3 · ½ 2 x ζ (x) → x 9Ca ln + ln Ca b 3

(19)

The “contact angle” θ(x) depends on the distance to the contact line. It is approximately given by: θ (x) ≈

· ½ ¾¸1/3 x 2 dζ (x) ≈ 9Ca ln + ln Ca (20) dx b 3

the derivative of the bracket being negligible with the orders of magnitude considered. For angles less than 7 degrees, with interferometry as the relevant technique, x corresponds to a few equalthickness interference fringes, tens of micrometers typically, sometimes less. The Ca values range from 10−4 to 10−6 and ln Ca from −9 to −14. Experimental data obtained by interferometry have been plotted, on Figs. 3 and 4, either as Ca1/3 versus θ , or as Ca versus θ 3 . They have been supplemented by

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goniometric measurements at larger Ca ≈ 10−3 [26]. The liquids are light silicone oils, the polydimethylsiloxanes, with trimethyl (PDMS) or hydroxyl (PDMSOH) ends. The solids are bare, oxidized silicon wafers. The viscosity of the oils is 0.1Po, the surface tension 21 · 10−3 Nm−1 . Complete wetting is achieved for both oils. For PDMS, measured values of K are around 17 for the lowest Ca(7 · 10−6 ) and 32 for the largest Ca(6 · 10−5 ). For Ca ≈ 10−3 , the goniometric technique [26] gives K ≈ 100. The formula by de Gennes ˚ over this whole range of Ca, with leads to b ≈ 2–9 A some tendency to find lower b values at larger Ca. For interferometric data, x is the distance to contact line over which fringes have been counted. For goniometric data, we took x = R ≈ mm. Note that b can be calculated from the Hamaker constant of the air˚ (a ≈ 2 A). ˚ The liquid-solid system and is around 4 A agreement is fairly good. The question now is, when (20) has to be replaced by the simple Cox formula (10) and how to interpret the corresponding length λ. ˚ Let us give some orders of magnitude. For b = 4 A, and assuming S ≈ γ , the length L of the precursor, the crossover x1 and the thickness ζ0 of the precursor at the crossover can be calculated. The condition for de Gennes’ analysis to be valid is x1 ¿ L, providing the thicknesses are in the mesoscopic range.

Figure 3. Plot of the experimental data Ca1/3 vs θ. In fact, U (t) and θ (t) are measured at the edge of spreading drops, and Ca1/3 is calculated as a function of θ at successive times. The maximum value on the θ-scale corresponds to 0.123 rd, i.e., 7 degrees. Upper curve, PDMS. Circles and crosses correspond to different drops. The upper part of the dotted straight line corresponds to K ≈ 32, the lower part to K ≈ 17. Lower curve, PDMS-OH. Squares and bow ties correspond to different drops. The upper part of the full straight line corresponds to K ≈ 85, the lower part to K ≈ 38.

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Figure 4. Same data as before, but for Ca vs θ 3 . The maximum value of Ca is 6 · 10−5 . The nonlinearity of the dependence is less visible, because closer to the origin.

Numerical values are as follows: ˚ For Ca = 7 · 10−6 , L ≈ 30 µm, x1 ≈ 5100 A, ˚ ζ0 ≈ 100 A ˚ For Ca = 6 · 10−5 , L ≈ 3.3 µm, x1 ≈ 1200 A, ˚ ζ0 ≈ 50 A ˚ For Ca = 10−3 , L ≈ 0.2 µm, x1 ≈ 180 A, ˚ ζ0 ≈ 20 A Therefore, the theory is expected to hold acceptably even for Ca = 10−3 . It would be meaningless to interpret b values in a too quantitative way, but at least orders of magnitude should be correct. If now (10) is used for Ca = 10−3 , i.e., angles around 40 degrees, where no “intermediate zone” was sup˚ (in fact, the posed to be needed, one finds λ ≈ 150 A. ˚ value of x1 for a ≈ 1.7 A). The contribution of the ln Ca term, ln Ca ≈ −7, is still not negligible. Therefore, the length λ must not be interpreted as a slip length. Measurements by Marsh et al. provided some evidence of a dependence of λ in the capillary number [24]. In conclusion, one can make de Gennes’ and Cox’ theories compatible, but λ is not a “slip length”. Low K values are not necessarily associated with slip, and any attempt to relate liquid-solid interaction to the θ (U ) data in complete wetting has to be done with care. The results obtained with the hydroxyl-terminated oil, which adsorbs by both ends on the surface [27], cannot be fitted by the hydrodynamic theories. K is

larger than for PDMS, which means larger friction, as expected. However, b values in (20) change by orders of magnitude with Ca, without in any case being plau˚ Here, the adsorption prosible (much less than A). cess interferes with spreading dynamics and makes the hydrodynamic analysis irrelevant. This behaviour of PDMS-OH is well known from experiments performed at the molecular scale [27, 28]. However, the link to macroscopic behaviour is still missing. Let us now see why, and which informations can be obtained from those experiments. One might expect that the study of the mesoscopic precursor film would allow a direct measurement of the parameters involved in the hydrodynamic analysis. This is unfortunately not so easy. Referring back to the previous experiment, we see that for Ca ≥ 10−5 , the mesoscopic precursor is too short to be observed by available techniques, especially if one remembers that it is driven by a moving wedge, which makes AFM irrelevant. For lower Ca, it is the assumption of stationarity which fails: the precursor is no longer the mesoscopic adiabatic film discussed above, the length L of which (18) is controlled by the macroscopic velocity U [6, 29]. It progressively becomes a “diffusive film”, with a short mesoscopic part followed by a much larger part of molecular thickness, with an overall length scaling like the square root of time t [30]. The formulae (15–20) loose their validity when this diffusive film becomes significant. With the air- PDMS-oxidized silicon wafer system, this was becoming the case for Ca = 7 · 10−6 .

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As a conclusion for this part, the various theories account satisfactorily for the dynamics of wetting in the non-wetting case. Although the molecular theory by Blake is somewhat empirical, it contains parameters with a clear physico-chemical meaning and is able to describe specific behaviours. The hydrodynamic theories are the only ones relevant for complete wetting and small angles. As a rule, they are more rigorous and contain parameters which are well defined for systems dominated by general long range interactions. Specific behaviours controlled by short range interactions can also be accounted for, but now with adjustable parameters. Up to now, there is still a missing link between macroscopic quantities like contact angles and microscopic parameters like slip lengths. Although microscopic films do not provide fitting parameters for macroscopic scale, they contain lot of information on short and long range interaction between liquid and solid. Let us give some examples. We shall restrict ourselves to diffusive films, the only one observable, growing ahead of quasi-static macroscopic wedges. Therefore, we shall not discuss the long-time spreading dynamics of small droplets, where the overall thickness is microscopic, and where volume conservation has to be taken into account [13, 15, 16, 31, 32].

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Diffusive Films and the Mesoscopic Scale Diffusive films are conveniently studied by spatially resolved ellipsometry [30, 33], among other techniques [32, 34]. In the mesoscopic range of thickness, the profile ζ (x, t) obeys a diffusion-like equation, with a thickness-dependent diffusion coefficient D(ζ ) [4, 17, 35]. One may write p x(ζ, t) ≈ D(ζ )t (21) with D(ζ ) =

ζ 3 d5(ζ ) 3η dζ

For van der Waals interactions: A D(ζ ) = − 6π ηζ

(22)

(23)

This formula can be compared with experimental measurements performed on various systems using spatially resolved ellipsometry, which is illustrated on the next figures. On Fig. 5 are plotted the results obtained with various PDMS on various substrates. The dotted lines are calculated from (23), taking into account the

Figure 5. Measured values of the “diffusion coefficient” D(ζ ) versus the film thickness ζ for PDMS microdroplets spreading spontaneously ˚ The light dotted on oxidized silicon wafers. Crosses: PDMS, viscosity 0.2 Po (fractionated oil). The thickness of the oxide (silica) is 20 A. ˚ line is the calculated value of D(ζ ) for this silica-silicon substrate assuming van der Waals interactions. The agreement is good for ζ ≥ 20 A. ˚ The heavy dotted line is the calculated value of D(ζ ). The agreement is good for Bow ties: same PDMS. The thickness of the silica is 100 A. ˚ Circles: PDMS, viscosity 1 Po (fractionated oil). The thickness of the silica is 20 A. ˚ A layer of trimethyl groups, typically 4 A ˚ thick, ζ ≥ 20 A. is grafted on the silica. The dash-dotted line is the calculated value of D for the silica-silicon substrate assuming van der Waals interactions, ˚ and neglecting the grafted layer. The agreement is good for ζ ≥ 60 A.

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Figure 6. Measured values of the thickness-dependent diffusion coefficient D(ζ ) versus the film thickness ζ for squalane microdroplets put ˚ Complete wetting is achieved at the macroscopic scale. The effective on oxidized silicon wafers. Crosses: the thickness of the silica is 20 A. ˚ Circles: the thickness of the silica is Hamaker constant is not known, but a straight line with slope-1 fits acceptably the data for ζ ≥ 30 A. ˚ Partial wetting is achieved at the macroscopic scale. The mesoscopic part of the drop is practically static. The molecular part spreads, 100 A. because the short range interactions are the same.

presence of the oxide layer on the silicon wafer, which makes A thickness-dependent [36, 37]. The agreement is quite good, but only in the mesoscopic part, as expected. On Fig. 6 are plotted results obtained with squalane, a saturated branched alkane C30 H62 , on wafers with different oxide layers. Squalane wets silicon (A < 0) but not silica (A > 0). The short range part does not change, but the long range part does indeed.

Diffusive Films and the Molecular Scale As we have reported experimental D(ζ ) values in the molecular range of ζ , let us now discuss the molecular scale. As a rule, D(ζ ) increases faster than ζ −1 at low thicknesses. The nonvolatile liquids we study can be volatile at two dimensions or not. If they are nonvolatile also at 2D, layering occurs in the thin part of the film which exhibit a step-like profile composed of superimposed monomolecular layers. This is the case at room temperature for PDMS oils with viscosity larger than 0.02 Po, and for a silicone derivative, the tetrakis(2-ethylhexoxy)silane (TK). This is also the case for squalane below 5◦ C.

If the liquid is volatile at 2D, the thickness profile is smooth. This is the case of squalane at room temperature or TK above 50◦ C. The square root of time law (21) is always very well obeyed in the molecular range of thicknesses as long as a reservoir is present and seems rather intuitive, being a sort of microscopic Washburn-like equation. Surprisingly enough, it has no general theoretical support at this scale. What is driving force and what is friction is not so obvious. Let us mention briefly the main models available. The model of stratified droplet developed by de Gennes [31], although it contains volume conservation, should in principle be used for droplets large enough for the center to act as a reservoir when only the very first layers are considered. Here, the thickness is microscopic and the film length macroscopic, thus mimiking the experimental situation in ellipsometric measurements. The driving term W is the change in chemical potential in the successive layers, while the friction force Fv is assumed to be viscous-like, i.e., proportional to the relative velocity 1v of the neighbouring layers, Fv ∝ ξ 1v. This is a logical assumption for a film with macroscopic extension. The t 0.5 law is found as an approximation when the successive layers grow at

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Figure 7a. Ellipsometric thickness profiles of a drop of tetrakis (2-ethylhexoxy)silane spreading on a bare, oxidized silicon wafer, at successive ˚ the diameter of the molecule. Relative humidity 40%, temperature 21◦ C. For this type of profile, times. The height of the steps is around 10 A, the radii of the successive layers scale like the square root of the time, and this is well accounted for by the model of de Gennes.

Figure 7b. Ellipsometric thickness profiles of drops of PDMS, viscosity 0.2 Po (fractionated oil), spreading on a bare, oxidized silicon wafer. The height of the layer is the transverse size of the chains, which are flat on the surface. The 4 profiles correspond to 4 drops with same initial size, at the same given time after deposition, for different relative humidity RH. RH is less than 20% for the inner (i.e., slowest) profile, then takes the values 80, 85, 90%. This is a case where W1 is large: only the first layer grows. Moreover, ξ1 decreases with increasing RH. For this type of profile, the radius of the first layer scales like the square root of the time, the other ones being roughly constant. The model of de Gennes cannot be used.

comparable rate. This is the case of the drop in Fig. 7a, and this seems to correspond to situations where the parameters W1 and ξ1 for the first layer do not differ too much from the ones in the upper layers.

For the first layer, D1 ≈ W1 /ξ1 . Large W1 and/or small ξ1 , i.e., large D1 values lead to profiles like the one in Fig. 7b. The first layer dominates the film. The model of de Gennes, which assumes

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well developed layering, cannot be used. For 2D nonvolatile liquids, only computer simulations are able to account for the experimental observation [12, 13, 15]. For liquids volatile at 2D, computer simulations still work, but an analytical model has been proposed recently [16], where now the driving term is the thermal energy kT . The liquid-liquid and solid-liquid interactions control the probability for a molecule first to pass from the reservoir to the film, and then to reach the edge by diffusing against the concentration gradient in the film. Preliminary studies of the temperature dependence of D1 have been performed with TK and squalane [38], but the comparison with the model is still to be done. Very large ξ1 values correspond to the case of PDMSOH, where irreversible adsorption takes place. At very short times, the growth of the first layer is observable. But rapidly this structure fades out and a shoulder dominates the profile, the thickness of which is the giration radius of the polymer chains. A network of chains adsorbed by both ends is building up [27]. The time needed for molecules of the reservoir to pass through this network becomes exponentially long and the spreading ultimately stops at the molecular scale. For compact instead of chain molecules, one might expect only the first layer to be irreversibly adsorb and the spreading to proceed further, but with a significantly thicker “first layer”. This is the caterpillar model proposed by Dussan [8]. For the moment, the studies of the molecular scale are more qualitative than quantitative. We know how to decrease ξ1 experimentally, either by surface grafting or by increasing the relative humidity, i.e., the amount of water adsorbed on the surface [28]. Surface-induced conformational changes have been observed in TK [28]. Studies of surface-induced melting and organization are under way in liquid crystals [39]. However, even basic questions remain unanswered: are there any equivalents of the activated processes proposed by Blake? Why does the molecular parameter D1 scale with the bulk parameter η−1 in PDMS when the chain length is changed? Is there any activated process there? How does the chain length play in W1 and ξ1 ? Where does the temperature dependence of D1 come from? [38] The tendency is to analyze it in terms of friction, i.e., ξ1 . But which is the role of the driving term? These questions can only by solved by combining theoretical methods—analytical models and computer simulations—and experimental studies, and as a joint

work between physicists and chemists. Such collaborations are under way. Acknowledgments Fruitful discussions with P.G. de Gennes are gratefully acknowledged. We thank S. Bardon for his kind help during the preparation of the manuscript. This work was partly supported by the Swedish Research Council for Engineering Sciences (TFR). References 1. F. Fairbrother and A. Stubbs, J. Chem. Soc. 1, 527 (1935); F.P. Bretherton, J. Fluid Mech. 10, 166 (1961). 2. L.H. Tanner, J. Phys. D 12, 1478 (1979). 3. C. Huh and L.E. Scriven, J. of Colloid Int. Sci. 35, 85 (1971). 4. B.V. Derjaguin and N.V. Churaev, Wetting Films (Nauka, Moscow, 1984). 5. V.M. Starov, Kolloidn. Zh. 45, 1154 (1983). 6. P.G. de Gennes, Rev. Mod. Physics 57, 827 (1985). 7. R.G. Cox, J. Fluid Mech. 168, 169 (1986). 8. E.B. Dussan V., Ann. Rev. Fluid Mech. 11, 371 (1979); E.B. Dussan V. and S. Davis, J. Fluid Mech. 65, 71 (1974). 9. R.L. Hoffmann, J. of Colloid Int. Sci. 94, 470 (1983). 10. T.D. Blake, How do wetting lines move? AIChE Spring Meeting (New Orleans, LA, 1988) Paper 1a; B.W. Cherry and C.M. Holmes, J. Colloid Int. Sci. 29, 174 (1969). 11. A.M. Cazabat, Adv. Coll. Int. Sci. 42, 65 (1992). 12. J. De Coninck, S. Hoorelbeke, M.P. Valignat, and A.M. Cazabat, Phys. Rev. E 48, 4549 (1993); J. De Coninck, N. Fraysse, M.P. Valignat, and A.M. Cazabat, Langmuir 9, 1906 (1993); J. De Coninck, U.D’ Ortona, J. Koplik, and J.R. Banavar, Phys. Rev. Lett. 74, 928 (1995); U.D’ Ortona, J. De Coninck, J. Koplik, and J.R. Banavar, Phys. Rev. E 53, 562 (1996). 13. L. Wagner, Phys. Rev. E 51, 499 (1995); S. Bekink, S. Karaborni, G. Verbist, and K. Esseling, Phys. Rev. Lett. 76, 3766 (1996). 14. M.O. Robbins and P.A. Thomson, Science 253, 916 (1991); M. Cieplak, E. Smith, and M.O. Robbins, Science 265, 1209 (1994). 15. A. Lukkarinen, D.B. Abraham, M. Karttunen, and K. Kaski, Phys. Rev. E 51, 2199, (1995); J. Nieminen, D. Abraham, M. Karttunen, and K. Kaski, Phys. Rev. Lett. 69, 124 (1992). 16. S.F. Burlatsky, G. Oshanin, A.M. Cazabat, and M. Moreau, Phys. Rev. Lett. 76, 86 (1995); S. Burlatsky, G. Oshanin, A.M. Cazabat, M. Moreau, and W.P. Reinhardt, Phys. Rev. E 54, 3832 (1996); G. Oshanin, J. De Coninck, A.M. Cazabat, and M. Moreau (submitted). 17. B.V. Derjaguin, N.V. Churaev, and V.M. Muller, Surface Forces, (Consultant Bureau, New-York, 1987); N.V. Churaev, Rev. Phys. Appl. 23, 975 (1988). 18. F. Brochard, P.G. de Gennes, and H. Hervet, Adv. Colloid Int. Sci. 34, 561 (1991); F. Brochard and P.G. de Gennes, Adv. Colloid Int. Sci. 39, 1 (1992). 19. T.D. Blake, Dynamic contact angles and wetting kinetics, in Wettability, edited by J.C. Berg, Surfactant Science Series (Marcel Dekker, N.Y., 1993), Vol. 49, p. 251.

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