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Kinetics of Autophobic Dewetting of Polymer Films Gu¨nter Reiter* and Rajesh Khanna Institut de Chimie des Surfaces et Interfaces, CNRS, 15, rue Jean Starcky, B.P. 2488, 68057 Mulhouse Cedex, France Received January 24, 2000. In Final Form: May 2, 2000 We experimentally investigated the retraction of poly(dimethylsiloxane) films of variable thickness on layers of chemically identical molecules, end-grafted onto a silicon substrate (autophobic dewetting of a melt-on-brush system). Measuring simultaneously the dewetted distance (d) and the width (w) of the rim formed by the collection of the retracted liquid, we were able to determine in situ and in real time (t) the contact angle, the velocity of retraction, and the energy dissipation mechanism at the melt-brush interface. The dewetting velocity decreased linearly with the width of the rim. Together with the characteristic thickness dependence and an exponent R of 2/3 for the power-law behavior of d ∼ tR, we concluded that the melt is slipping on the brush. The slippage length was on the order of 10 µm, indicating little interpenetration between melt and brush. We demonstrate that dewetting experiments represent a valuable tool for the characterization of static and kinetic properties of polymer-polymer interfaces.
1. Introduction 1-7
involved in the In recent years, the basic processes retraction of a liquid from a nonwettable surface it was forced to cover have been the focus of various dewetting experiments,3,6,8-32 many of them using thin polymer films. The phenomenon of dewetting occurs frequently in our (1) De Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (2) Brochard-Wyart, F.; Daillant, J. Can. J. Phys. 1990, 68, 1084. (3) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715. (4) Brochard-Wyart, F.; Martin, P.; Redon, C. Langmuir 1993, 9, 3682. (5) Brochard-Wyart, F.; de Gennes, P.-G.; Hervert, H.; Redon, C. Langmuir 1994, 10, 1566. (6) Redon, C.; Brzoska, J. B.; Brochard-Wyart, F. Macromolecules 1994, 27, 468. (7) Brochard-Wyart, F.; Debre´geas, G.; Fondecave, R.; Martin, P. Macromolecules 1997, 30, 1211. (8) Reiter, G. Phys. Rev. Lett. 1992, 68, 75. (9) Shull, K. R.; Karis, T. E. Langmuir 1994, 10, 334. (10) Yerushalmi-Rozen, R.; Klein, J. Langmuir 1995, 11, 2806. (11) Lambooy, P.; Phelan, K. C.; Haugg, O.; Krausch, G. Phys. Rev. Lett. 1996, 76, 1110. (12) Krausch, G. J. Phys.: Condens. Matter 1997, 9, 7741. (13) Pan, Q.; Winey, K. I.; Hu, H. H.; Composto, R. J. Langmuir 1997, 13, 1758. (14) Segalman, R. A.; Green, P. F. Macromolecules 1999, 32, 801. (15) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Langmuir 1998, 14, 965. (16) Stange, T. G.; Evans, D. F.; Hendrickson, W. A. Langmuir 1997, 13, 4459. (17) Zhao, W.; et al. Phys. Rev. Lett. 1993, 70, 1453. (18) Lipson, S. G. Phys. Scr. 1996, T67, 63. (19) Yerushalmi-Rozen, R.; Kerle, T.; Klein, J. Science 1999, 285, 1254. (20) Martin, P.; Brochard-Wyart, F. Phys. Rev. Lett. 1998, 80, 3296. (21) Buiguin, A.; Vovelle, L.; Brochard-Wyart, F. Phys. Rev. Lett. 1999, 83, 1183. (22) Martin, P.; Brochard-Wyart, F. Phys. Rev. Lett. 1998, 80, 3296. (23) Debre´geas, G.; Martin, P,; Brochard-Wyart, F. Phys. Rev. Lett. 1995, 75, 3886. (24) Debre´geas, G.; de Gennes, P.-G.; Brochardt-Wyart, F. Science 1998, 279, 1704. (25) Liu, Y.; et al. Phys. Rev. Lett. 1994, 73, 440. (26) Reiter, G.; Auroy, P.; Auvray, L. Macromolecules 1996, 29, 2150. (27) Reiter, G.; Schultz, J.; Auroy, P.; Auvray, L. Europhys. Lett. 1996, 33, 29. (28) Henn, G.; Bucknall, D. G.; Stamm, M.; Vanhoorne, P.; Je´roˆme, R. Macromolecules 1996, 29, 4305. (29) Sheiko, S.; Lermann, E.; Mo¨ller, M. Langmuir 1996, 12, 4015. (30) Kerle, T.; Yerushalmi-Rozen, R.; Klein, J. Europhys. Lett. 1997, 38, 207. (31) Van der Wielen, M. W. J.; Cohen Stuart, M. A.; Fleer, G. J. Langmuir 1998, 14, 7065.
everyday life and for a variety of systems. For example, everybody has already observed how a water film on a windscreen dries up or the retraction of paint from an oily (dirty) wall on which it does not want to stay. Certainly, it is necessary to understand the underlying fundamental processes first. On the basis of such knowledge, studying dewetting can then allow us to determine interfacial properties and their changes in real time and in situ. Theoretical predictions, in particular by Franc¸ oise Brochard,2-7 have been valuable guides for the design of appropriate experiments. However, theory is by far more advanced than experiments. This is especially true for the case where a polymer slips33-37 on a nonwettable substrate. The static interaction between materials and wettability of materials are to a large extent characterized by the interfacial tensions. In 1805, Thomas Young stated38 that contact angle measurements present a simple and surprisingly accurate way to assess such molecular interactions by considering macroscopic phenomena. However, it is difficult to investigate kinetic effects such as friction (energy dissipation) at such an interface by contact angle measurements alone. Such velocity-dependent information can be obtained from dewetting experiments. Dewetting is governed by static and dynamic molecular interfacial properties. Thus, simple dewetting experiments by eye, or using an optical microscope for better resolution, allow us to obtain time-resolved information on a molecular scale. Here, we use dewetting to investigate the properties of a polymer melt slipping on a layer of chemically identical molecules, end-grafted to a silicon substrate (polymer brush). The entropy difference between grafted and free polymers results in autophobic behavior of the brush.39,40 (32) Jacobs, K.; Seemann, R.; Schatz, G.; Herminghaus, S. Langmuir 1998, 14, 4961. (33) Brochard, F.; de Gennes, P. G. Langmuir 1992, 8, 3033. (34) Brochard-Wyart, F.; Gay, C.; de Gennes, P. G. Macromolecules 1996, 29, 377. (35) Thompson, P. A.; Troian, S. M. Nature 1997, 389, 360. (36) Migler, K.; Hervet, H.; Le´ger, L. Phys. Rev. Lett. 1993, 70, 287 (37) Durliat, E.; Hervet, H.; Le´ger, L. Europhys. Lett. 1997, 38, 383. (38) Young, T. Philos. Trans. R. Soc., London 1805, 95, 65. (39) 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; p 301.
10.1021/la000088u CCC: $19.00 © 2000 American Chemical Society Published on Web 06/23/2000
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We relate the displacement of a contact line to kinetic effects at a polymer-polymer interface. As the capillary driving forces and energy dissipation at the interface are intrinsic properties controlled by molecular interactions, our system is self-adjusting at all stages of the process to any variations of experimental conditions. We are interested in the following questions. How does a polymer move or flow on its own monolayer, or more generally, how do macromolecules slide past each other? What are the consequences of the autophobic behavior between grafted and free polymers for dewetting? What is the value of the friction coefficient at such polymerpolymer interfaces? After a brief description of our experimental conditions, we present what existing theory predicts for our system. We then proceed by presenting the experimental results which we discuss in light of theory described above. Finally, we show what we can learn about changes of the system during dewetting and conclude by re-emphasizing the most important observations on the molecular parameters controlling interfacial properties. 2. Experiments Samples. For our experiments, we used thin (20-850 nm) poly(dimethylsiloxane) (PDMS) films (liquid at room temperature), prepared by spin-coating, supported by silicon wafers which were coated with a layer of end-grafted PDMS molecules. Grafting polymers by one end at a high areal density onto a solid substrate leads to a reduction of the entropy of the grafted with respect to free molecules. This may lead to autophobic behavior,39,40 i.e., the free molecules will dewet the grafted layer.25-31 Dewetting was followed in real time by optical microscopy. Brush Preparation. First, the silicon wafers (cleaned by UV ozone) were treated chemically with chlorodimethylvinylsilane (CDMVS) to avoid adsorption of PDMS and to functionalize the surface with vinyl groups. For the brush, we used end-functionalized PDMS molecules (SiH-monofunctionalized, molecular weight Mw ) 8800 g/mol, polydispersity I < 1.1) synthesized anionically by Philippe Auroy (Institut Curie, Paris, France). SiH-PDMS, diluted in heptane containing a platinum catalyst, was spin-coated onto the wafer. The resulting films were annealed at 120 °C, allowing a chemical reaction (hydrosilation) between the SiH end 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 (e), determined by ellipsometry, the grafting density (υ) of the brush chains [υ ) e/(Na3)] could be deduced, with N being the number of monomers per grafted chain and a being ∼0.5 nm, the statistical segment length.37 Due to the high grafting density (υ was between 0.4 and 0.5 chain/nm2, corresponding to an e between 6 and 7.4 nm), the chains were preferentially oriented and stretched in the direction normal to the silicon surface, causing a large entropy loss of the grafted polymers. The thickness (varying between 20 and 850 nm) of the film of free polymers [in most cases, we used a high molecular weight (Mw) of 308 000 g/mol] on top of the brush was determined by ellipsometry. Optical Microscopy. Thermal treatment was performed directly under the microscope. The samples were placed onto an enclosed hot stage (LINKAM THMS600), purged with nitrogen, under a Leitz-Metallux 3 optical microscope. No polarization or phase contrast was used. Contrast is due to the interference of the reflected white light at the substrate-film and film-air interfaces, resulting in well-defined interference colors which can be calibrated with a resolution of about 10 nm. We have followed the retraction of the three-phase contact line and the growth of the rim in real time by capturing the images with a CCD camera. All data were stored with a VCR for later analysis.
3. Theory (Based on the Work by F. Brochard et al.3-6) In a typical dewetting experiment, the driving capillary forces (uncompensated Young force) are balanced by (40) Shull, K. Faraday Discuss. 1994, 98, 203.
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viscous forces (forces per unit length of the three-phase contact line): Fd ) Fv. In a good approximation, Fd is determined by the contact angle (θ) and the surface tension (γ) of the liquid: Fd ) 0.5γθ2. Fv depends on the hydrodynamics of liquid retraction on top of the substrate. For nonslipping films, the energy is dissipated in a small volume located at the contact line. Then, Fv is simply proportional to the viscosity (η) and the velocity (V). In such dewetting experiments, V has to be constant in time.3 However, long polymers on a nonadsorbing substrate have been found to slip. In such cases, the energy is dissipated over the whole moving part of the film characterized by the width w of the rim collecting the liquid from the dewetted region. There, Fv ) (3ηVw)/b. The parameter b is called the slippage length.
Fd ) 0.5γθ2 ) (3ηVw)/b ) Fv
(1)
For nonvolatile liquids such as polymers, w is related to the dewetted distance (d) by mass conservation. For a films of thickness h, we obtain
dh ) Cw2θ
(2)
The constant C accounts for the asymmetric shape of the rim.5 It has been found5 to be approximately 0.1. We want to point out that eq 2 allows us to determine the contact angle at any stage of the dewetting experiment. However, for almost all our samples, θ(t) turned out to be constant (see Figure 4) or only slightly (about 10%) decreasing in time. Equations 1 and 2 allow us to obtain for the time (t) dependence of d, w, and V the following equations:
d(t) ) Pt2/3 w(t) ) Qt1/3 V(t) ) 2/3Pt-1/3
(3)
with the prefactors P and Q, assumed to be timeindependent, being
P ) (0.25γC1/2)2/3θ5/3b2/3η-2/3h-1/3
(4a)
Q ) (0.25γC-1)1/3θ1/3b1/3η-1/3h1/3
(4b)
Measuring the width of the rim at time ti and determining the velocity from the temporal increase of d [V(ti) ) [d(ti) - d(ti-1)]/(ti - ti-1)], we can obtain b directly without any fitting (i.e., without the use of eq 3) for any time interval (ti - ti-1). (This allows us to check for possible temporal changes in b.) In particular, we do not have to assume any exponent for a power-law relation between d and t.
b(ti) ) 3ηV(ti)w(ti)/Fd(ti)
(5a)
Using P and Q obtained from fits (based on eq 3) to the curves of d and w as a function of time, respectively (i.e., assuming that b and θ do not depend on time) we can obtain b also:
b ) 2ηPQ/Fd
(5b)
4. Results We measured the displacement of the front (F) and the rear (R) position of the rim as a function of time (Figure 1) using optical microscopy. The starting point of zero distance (O) was set by breaking the silicon substrate
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Figure 1. Typical result for dewetting of a PDMS film (92 nm, Mw ) 308 000 g/mol) on top of a densely grafted brush of endfunctionalized PDMS molecules (6.3 nm, Mw ) 8800 g/mol). The temperature was 50 °C. The front (F) and rear (R) positions of the rim as a function of time are shown by the squares and circles, respectively. The position of the origin (O) has been set to zero. The width (w) of the rim (w ) R - F) is given by open diamonds. The unbroken lines are best fits to the data using the following equation: Y ) A(t - to)R, where Y stands for F, R, and w, A is a constant prefactor, and to is the time offset. Results for the exponent R are given in the inset.
Figure 3. Typical image of the rim created by dewetting of a 95 nm thick film (conditions as described in the legend of Figure 1) measured with an optical microscope (A; size, 100 µm × 200 µm) at 50 °C, or by AFM (B and C) at room temperature, using a Nanoscope IIIa/Dimension 3000 apparatus (Digital Instruments) in the tapping mode at ambient conditions. Note that the spacing between successive interference fringes in panel A is smaller on the left side, indicating a steeper slope. This is confirmed by the cross section of AFM image B shown in panel C. The contact angle determined directly by AFM or obtained from the spacing of the interference fringes agrees nicely with the values obtained from eq 2. Figure 2. Dewetted distance (d) as a function of time on doublelogarithmic scales for the same conditions as described in the legend of Figure 1 but for different film thicknesses as indicated in the inset. The straight lines are best fits to the data using the following equation: d ) P(t - to)R. We obtained R ) 0.65 ( 0.05. Note that two independent measurements using the same sample give the same results (filled and open triangles). Note further that films with similar thicknesses (47 and 52 nm) show rather different prefactors P.
along a crystallographic axis in two parts. By breaking the sample, we created a three-phase contact line between the substrate, the film, and the surrounding environment (mostly air purged with nitrogen). Consequently, we thereby initiated dewetting. The dewetted distance (d) is given by d(t) ) F(t) - O, and the width of the rim (w) is given by w(t) ) R(t) - F(t). From these measures, we obtained the dewetting velocity (V) by taking differences: V(ti) ) [d(ti) - d(ti-1)]/(ti - ti-1). For all our experiments at low temperatures around 50 °C, we obtained (within the error bar of about 0.05) exponents R ) 2/3 and β ) 1/3 for the temporal increase of d and w, respectively. The results from films of different thicknesses clearly showed that thinner films dewetted faster (Figure 2). For
the conditions of the measurements shown in Figure 2, we obtained d ∼ tR, with R varying between 0.63 and 0.71. These values are close to the theoretically expected value of 2/3 and corroborate previous polymer dewetting experiments of (at least partially) slipping films.6,26,31,32 It should be noted that the two repeated measurements on a single sample (h ) 92 nm) give very similar results, for both the prefactor P and the value of the exponent. On the contrary, two independent samples with rather similar thicknesses (h ) 47 nm and h ) 52 nm) can exhibit significantly different prefactors. Theory predicted5 that for slipping films the shape of the rim, which is built up in the course of a dewetting experiment, has to be asymmetric. We have confirmed this by optical microscopy (Figure 3A) and atomic force microscopy (AFM) (Figure 3B,C). The distance between consecutive interference fringes in Figure 3A is inversely proportional to the slope of the rim, as can be seen clearly in the corresponding cross section (Figure 3C) obtained by AFM. The dotted symmetric profile representing a section of a circle indicates what is expected for the nonslipping case. The deviations are clearly visible.
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Figure 4. Contact angles as determined from eq 2 for various films dewetting the underlying PDMS brush at 50 °C as a function of time. The films have the following thicknesses: 47 nm (triangles), 49 nm (squares), 92 nm (circles), and 135 nm (diamonds). The dotted lines represent guides to the eye.
Figure 5. Contact angles as determined from eq 2, averaged over the whole time range of the experiment, as a function of film thickness on double-logarithmic scales. Data were obtained at 50 °C (open squares) and 130 °C (filled circles).
Measuring the dewetted distance and the width of the rim simultaneously allowed us to determine the contact angle in situ and in real time based on the assumption of mass conservation (see eq 2). Typical results are shown in Figure 4. It should be noted that due to small differences in the brush properties the value of the contact angle differed between samples but it was rather constant in time. Nevertheless, most samples exhibited values within a narrow band from 6 to 10°. There is no systematic relation between film thickness and contact angle (see Figure 5). A slight decrease of the contact angle with film thickness might be suggested by the data but cannot be confirmed due to the large variation of the contact angle between samples of the same thickness. Additional experiments are needed to clarify this matter. We could determine the dewetting velocity, the width of the rim, and the driving force (i.e., the contact angle) independently. This allowed us to use both eqs 5a and 5b to determine the slippage length for our system. Both methods yielded very similar results. The results at 130 °C are shown in Figure 6. It should be noted that our
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Figure 6. Slippage length as determined from eq 5a, averaged over the whole time range of the experiment (open circles), and deduced from the prefactors P and Q (filled squares) using eq 5b as a function of film thickness on double-logarithmic scales. Data were obtained at 130 °C.
Figure 7. Prefactors P (filled symbols) and Q (open symbols) as a function of film thickness (h) on double-logarithmic scales. Data were obtained from eq 3 under the assumption that the contact angle and the slippage length were the same for all samples. Fitting power-law relations P ∼ hβ and Q ∼ hγ (straight lines) to these data yields the exponents β and γ indicated in the figure. Data were obtained at 50 °C (circles) and 130 °C (squares).
samples did not allow us to find a clear relation between contact angle and slippage length (see Discussion). If we assume that we can characterize all our samples by a single mean value for θ and a single mean value for b around which the observed values scatter only statistically, we expect to obtain the thickness dependence of the prefactors P and Q as given in eq 4. In Figure 7, we show the results based on such an assumption. First of all, it has to be noted that the data points scatter widely. Leastsquares fits on double-logarithmic scales yielded the slopes indicated in the figure. These values, in particular for P, are deviating from the theoretically predicted ones. The two series of experiments at 50 °C and at 130 °C show similar trends and almost superpose if the viscosity is normalized to a reference temperature.41 If we, however, normalize the prefactor P, which essentially is determined by three variable parameters (the viscosity and the surface tension are the same for all
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Figure 9. Normalized dewetting velocity [VN ) V/(Fdb)] as a function of the width (w) of the rim on double-logarithmic scales for films of various thicknesses and for various temperatures as given in the legend. All data fall nicely onto a master curve with a slope of -1 (VN ∼ 1/w).
Figure 8. Appropriately normalized prefactor P (on doublelogarithmic scales) as a function of (A) film thickness (Ph), (B) contact angle (Pθ), and (C) slip length (Pb) at 50 °C (filled squares) and 130 °C (open circles), respectively. The straight lines act as guides to the eye indicated by the slopes given in the figure. Ph ) P/(0.25γC1/2)2/3θ5/3b2/3η-2/3. Pθ ) (Ph1/3η2/3)/b2/3. Pb ) Ph1/3η2/3/ (0.25γC1/2)2/3θ5/3. The best power-law fits (of the type Px ∼ yR) give Ph ∼ h-0.29(0.03 (Ph ∼ h-0.33(0.03), Pθ ∼ θ1.54(0.12 (Pθ ∼ θ1.71(0.10), and Pb ∼ b-0.67(0.05 (Pb ∼ b-0.59(0.05) at 130 °C. The results for 50 °C are in brackets.
samples), with two of these parameters we can find the predicted power-law dependences (see Figure 8). The accumulation of experimental uncertainties of the individual measurements leads to quite large error bars. Nonetheless, the scatter seems to be acceptable. The large number of about 50 individual experiments and the large parameter ranges allowed a meaningful determination of exponents. The resulting values agreed with theoretical predictions. This clearly indicates that the theoretical description includes all relevant parameters (otherwise, such an agreement cannot be expected) and furthermore demonstrates that the way we determined b and θ is correct. Note that calculating b from eq 5b does not directly imply a thickness dependence of P. One does not even have to know the film thickness if the contact angle is determined directly like in Figure 3. The dewetting velocity normalized by the time-independent values of the driving force Fd and b (giving a parameter in units of meters per Newton seconds) as a function of the width of the rim is presented in Figure 9. (41) The viscosity is normalized with respect to a reference temperature (chosen to be 25 °C) using the shift factor aT given by the WLF equation (Ferry, J. D. Viscoelastic Properties of polymers, 3rd ed.; Wiley: New York, 1980): log aT ) [-C1(T - 25)]/[C2 + (T - 25)] with C1 ) 1.9 and C2 ) 222.
Figure 10. Slippage length (obtained from eq 5a) as a function of dewetting velocity on-double logarithmic scales for films of various thicknesses at 50 °C. Note that the velocity decreased in the course of an experiment.
It was possible to superpose results from different temperatures (adjusting for the temperature dependence of the viscosity41) and different thicknesses on a single master curve. It can be clearly seen that the normalized velocity (and also the velocity for individual measurements) decreased linearly with the width of the rim. As the dewetting velocity varied with time, we could establish a velocity dependence of the slippage length (Figure 10). Within the error bars, b did not vary with V. However, due to the experimental errors involved in determining θ, V, and w, the data scatter widely. The influence of temperature is shown in Figure 11. As expected, the dewetting velocity increased with temperature. The contact angle (Figure 11B) indicates an increase with temperature (a detailed study is in progress) but was independent of time. The slippage length was about constant (Figure 11C). At the highest temperatures, however, b seems to decrease with decreasing V. We attribute this to a decrease of b with time caused by trapping or adsorbing very few polymers from the film within the brush.42 Free polymers may be (temporarily) (42) Reiter, G.; Khanna, R. To be published.
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Figure 11. Influence of temperature: (A) dewetted distance vs time (double-logarithmic scales), (B) contact angle vs time (linear scales), and (C) slippage length vs dewetting velocity (double-logarithmic scales). The temperature was 35 °C (squares), 50 °C (circles), 100 °C (diamonds), and 150 °C (triangles).
anchored at “defects” within the brush. This led to the observed “apparent” velocity dependence of b as the velocity also decreased with time (the width of the rim grew and thus slowed dewetting). It has to be noted that even if b is independent of velocity, b may change with time (and thus with velocity) if the interfacial properties change in the course of the experiment. Our experiments show that the parameter b is a very sensitive measure of interface modifications. 5. Discussion To be as close as possible to the assumptions made by theory, in particular a nonadsorbing interface, we have chosen a polymer system which avoided specific interactions between different chemical species. Polymers provide such a possibility of a “neutral” interface as they allow us to model and to control interactions at an interface based on entropic effects.39,40 Such effects may lead to autophobic behavior induced by the differences in the entropy of endgrafted and free polymers. The effective substrate-film interface at which dewetting occurred in our experiments was between the surface of the layer of end-grafted
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molecules and the free polymers, i.e., between chemically identical polymers. We want to emphasize that we have determined and varied all relevant parameters independently. η was varied by taking different monodisperse polymer fractions or by performing experiments at different temperatures, and the values of γ are tabulated43 and do not vary much for the molecular weights of the chosen polymers; θ was determined from mass conservation (eq 2) and b from the balance of viscous and capillary forces (see eq 1). Consequently, our macroscopic dewetting experiments allowed us to obtain time-resolved information about interfacial properties such as the slippage length or the dynamic contact angle. In addition, all other relations between the above parameters can be found, e.g., the velocity dependence of b or the relation between the friction coefficient k ()η/b) and θ. We note that in contrast to most other dewetting experiments we were measuring the dewetted distance and the width of the rim simultaneously. This allowed us (1) to test theory and (2) to determine the contact angle and slippage length, even without any fitting or the “guess” of additional parameters. Therefore, we are not forced to use only the value of the exponent R (from d ∼ tR) to decide between no-slip or slip at the brush-melt interface. This is the more crucial as the precise values of exponents are difficult to determine in general and may deviate from the above-mentioned theoretically expected ones.5,32,42 In some cases, the slowing down of dewetting may have been induced by other factors, e.g., surface modifications in the course of the experiment. Consequently, if the slippage length varies with time, the exact value of the exponent deviates from 2/3. In such cases, a power-law analysis becomes questionable. Different slopes (on a doublelogarithmic presentation) may be observed at different times. In some experiments on less perfect brushes or at high temperatures, we found values around 1/2. Thus, we believe that more convincing proof for slippage is the dependence on film thickness as given by eq 4 and shown in Figure 2. We have clear evidence for slippage based on several arguments predicted by theory: the time dependence of the dewetted distance and the width of the rim, the thickness dependence of the dewetting velocity, the asymmetric shape of the rim, and the reciprocal dependence of the dewetting velocity on the width of the rim. All our observations are in close agreement with theory. In particular, the dewetting velocity (for a given dewetted distance) was faster as the films became thinner. (Note that for nonslipping films the film thickness has no influence on the dewetting velocity.) From Figure 9, we can deduce that energy is dissipated over the whole interface between the moving rim and the substrate. The viscous force is proportional to the width of the rim which, in turn, depends on the initial thickness of the film. Consequently, our experiments clearly showed that the melt of long chains slipped on a brush of end-grafted chemically identical molecules. Dewetting experiments of polymer films (nonvolatile liquids) allow the in situ and real time determination of contact angles. The absolute precision is the best for the smallest contact angles (the relative precision being more or less constant) as it depends only on the measures of two distances. Large widths of the rim at comparatively short dewetted distances give small contact angles (see eq 2). The precision of the individual values is determined by the accuracy of the measures of d and w which is on (43) Sauer, B. B.; Dee, G. T. Macromolecules 1991, 24, 2124.
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the order of 1 µm. This is in contrast to contact angle measurements using AFM or goniometers which allow us to determine an absolute precision of the order of a few tenths of a degree, largely independent of the actual value of the contact angle. Moreover, it is rather difficult to measure the contact angle during dewetting using a goniometer. Such high precision is necessary for determining (small) temperature effects. The contact angle of individual samples increased with temperature.42 Our data (see Figure 5), however, do not allow us to extract a clear temperature effect as the differences between individual samples were too large. We want to draw attention to the fact that the observed slippage length was quite large (on the order of 10 µm). b is related to the friction coefficient k (per area a2 of a monomer) by k ) η/b. Comparing a typical value obtained for k to the value of the monomeric friction coefficient44 ko ) 3.7 × 107 Pa s-1 m-1 shows that only a few (x) frictional contacts (per unit interfacial area) contributed to the measured friction (k ) xko). This implies that the free molecules could penetrate only slightly into the densely grafted brush.44 Less perfect brushes with slightly lower grafting densities showed lower θ and much lower b values, i.e., deeper interpenetration. In addition, such brushes did not show the expected d ∼ t2/3 behavior. We also want to add a word of caution which at the same time shows the high sensitivity of our approach. Although we prepared rather excellent polymer brushes (a necessary prerequisite for the autophobic behavior in the first place; “bad”, i.e., brushes of low or heterogeneous grafting density, did not show dewetting at all!), our samples nonetheless differed somewhat, expressed by different contact angles and slippage lengths. Without knowing the exact values of θ and b, one cannot determine the correct thickness dependence of the prefactors P and Q and may erroneously question theory. Consequently, one has to determine these two parameters if one wants to compare the behavior of different samples, even if these samples have been prepared exactly the same way and even if the thickness of the grafted layer was constant within the resolution of ellipsometry (0.2 nm). The difference in dewetting behavior between samples does not result from inaccurate measurements as demonstrated by repeated measurements on the same sample which give the same results (see Figure 2, 92 nm thick film). (44) Brown, H. R. Science 1994, 263, 1411.
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The parameters θ and b characterize static and kinetic interfacial properties, respectively. These two parameters can vary independently. Samples with the same contact angle may exhibit rather different values of b. It has been found previously that adding a few connector molecules (the same as the brush molecules but with a higher molecular weight) to a polymer brush can significantly slow (or even stop) dewetting.27 However, as long as the number of these connector molecules is low, no measurable change in the contact angle could be detected. Our experiments (see Figure 11) also show that the contact angle stayed constant although the slippage length decreased (see the high-temperature runs). 6. Conclusions From the results presented above, we can clearly and unambiguously conclude that polymers can not only dewet but also slip on their own brush as a consequence of autophobicity. Moreover, our polymer system is ideally suited for testing theoretical predictions of the consequences of slippage in dewetting. From measures of the dewetted distance and the width of the rim collecting the retracted liquid, we determine in a straightforward way the “incompatibility” between free and grafted identical molecules, expressed by the contact angle, and the interfacial friction characterized by a slippage length. The theoretically predicted relations between velocity, energy dissipation, capillary driving force, viscosity and film thickness have been successfully verified. On the basis of these relations, we have access to an interpretation of the changes in interfacial properties in the course of the experiment, impossible for any other technique of such simplicity. Thus, dewetting experiments provide a practical and fast means for interfacial characterization, both static and dynamic. Acknowledgment. We are indebted to Philippe Auroy for providing us with the end-functionalized PDMS molecules. Fruitful discussions with Alain Casoli, Philippe Auroy, Ashutosh Sharma, and Franc¸ oise Brochard are gratefully acknowledged. This work was supported by the Indo-French Centre for the Promotion of Advanced Research/Centre Franco-Indien Pour la Promotion de la Recherche. LA000088U
