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Dewetting of Polymer Films with Built-In Topographical Defects Binyang Du, Fengchao Xie, Yongjian Wang, Zhiyu Yang, and Ophelia K. C. Tsui* Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received May 30, 2002. In Final Form: August 12, 2002 Polymer coatings in actual use are subject to wear and tear. In this experiment, we look into the dewetting instability of more realistic polymer coatings wherein topographical fluctuations pre-existed. The topographical defects, produced by rubbing the film surface with a piled fabric, could be varied for the density by changing the number of rubbings, N. First, the dewetting mechanism was determined by comparing the dewetting morphology between the unrubbed and rubbed films. Nucleation dewetting was ascribed to samples wherein the characteristic wave vector, q*, of the final dewetted morphology increased with increasing N, whereas spinodal dewetting was ascribed to samples wherein q* was affected little. Second, the evolution of dewetting was compared between the unrubbed and rubbed films. Our result shows that perturbations from rubbing do not produce changes in the free energy of the films that will alter the prevailing dewetting mechanism or the characteristic wave vector in spinodal dewetting. Nonetheless, the rubbing-induced defects do affect the rupturing process, in manners depending on the dominating dewetting mechanisms.
Introduction Dewetting is a phenomenon in which liquid films on nonwetting substrate surfaces break up into liquid droplets. Because of the widespread usage of organic film coatings, a large amount of experimental and theoretical studies have been dedicated to the understanding of the dewetting phenomenon. Experimental investigations have researched a large variety of materials including simple molecular liquids,1 polymers,2 liquid metals,3 evaporating volatile liquids,4 and liquid crystals.5 But the majority of studies have focused on polymer films. According to these experiments, dewetting of liquid films proceeds via formation of holes in the films. These holes coarsen to form a polygon network that eventually breaks up into liquid droplets due to the Rayleigh instability.6 The latter steps, involving evolution of the holes, are governed by hydrodynamics of dewetting and are well understood.1,6,7 But no consensus has been reached on the physics that governs the important initial step, namely, the very cause of the instability in the first place. On a theoretical basis, two mechanisms are possible, according to whether the film is unstable or metastable.8,9 With unstable films, rupturing occurs spontaneously via a spinodal mechanism. In metastable films, rupturing starts from nucleation of domain bubbles, a process called heterogeneous nucleation. The distinction is thermo* To whom correspondence should be addressed. E-mail: phtsui@ ust.hk. (1) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715. (2) Reiter, G. Phys. Rev. Lett. 1992, 68, 75. (3) Bischof, J.; Scherer, D.; Herminghaus, S.; Leiderer, P. Phys. Rev. Lett. 1996, 77, 1536. (4) Thiele, U.; Mertig, M.; Pompe, W. Phys. Rev. Lett. 1998, 80, 2869. (5) Herminghaus, S.; Jacobs, K.; Mecke, K.; Bischof, J.; Fery, A.; Ibn-Elhaj, M.; Schlagowski, S. Science 1998, 282, 916. (6) Rayleigh, L. Proc. London Math. Soc. 1878, 10, 4. (7) Brochard-Wyart, F.; Daillant, J. Can. J. Phys. 1990, 68, 1084. (8) Seemann, R.; Herminghaus, S.; Jacobs, K. J. Phys.: Condens. Matter 2001, 13, 4925. (9) Seemann, R.; Herminghaus, S.; Jacobs, K. Phys. Rev. Lett. 2001, 86, 5534.
dynamic in character, determined by the sign of the curvature of the free energy, that is, G′′(h), where h is generally the order parameter. If G′′(h) is negative, the film is unstable. Otherwise, the film is either stable or metastable. Whether the boundary between unstable and metastable states can be accurately predicted depends on whether the correct form of the free energy, G(h), is known. For apolar polymer films on a substrate, the most widely adopted form assumes the nonretarded Lifshitz-van der Waals (vdW) interactions, namely, G(h) ) -A/12πh2,10 where A is the Hamaker constant and h (the order parameter) is the film thickness. However, this form of G(h) is valid only for a very small film thickness less than ∼80 nm. Otherwise, retardation effects have to be considered.11 In considering the spinodal stability of a system, one examines the change in free energy, ∆G, due to small fluctuations, ∆h(x), in the system order parameter. To a first-order approximation, ∆G is ∼(1/2)G′′(h)〈∆h2〉.12,13 If the sign of G′′(h) is negative, so will that of ∆G, and the system will accordingly be unstable against spontaneous growth in the fluctuations. With G(h) ) -A/12πh2, the condition for spinodal instability is fulfilled when the Hamaker constant is positive. Using this mean field approach and simplifying to linear calculations, Vrij12 and others7 have shown that the instability would drive the system into exponentially growing surface capillary waves, among which the fastest growing mode had wavelength λm ) (16π3γA)1/2h2 and growth rate Γm ) A2/48π2ηγh5, where γ and η are the liquid surface tension and viscosity, respectively. The theory also predicts that the instability should lead to the formation of correlated bicontinuous structures in a two-dimensional (2D) system12 bearing a characteristic wave vector equal to 2π/λm in the initial state that will, however, coarsen in later times as the (10) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. The form of G(h) written as -A/12πh2 is the unit area free energy. (11) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (12) Vrij, A.; Overbeek, J. Th. G. J. Am. Chem. Soc. 1968, 90, 3074. (13) Cahn, J. W. J. Chem. Phys. 1965, 42, 93.
10.1021/la020506q CCC: $22.00 © 2002 American Chemical Society Published on Web 10/03/2002
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enlarged amplitude of the surface waves renormalizes the free energy of the system. The distinction between spinodal dewetting and heterogeneous nucleation has mostly relied on comparisons of experimental dewetting patterns with the above theoretical results2-5,8,9,14-18 or with predictions from computer-simulated results from a presumed form of G(h).19,20 However, for cases in which only scattered holes were formed in the dewetting process,2,8,9,15,21 typically observed among polystyrene (PS) films of thickness > ∼10 nm, approaches of this kind have been proven ineffective. On one hand, such cases are unforeseen for spinodal rupturing since the linear theory12 only predicts the bicontinuous dewetting structures to form. On the other hand, they exhibited the h-2 dependence in the characteristic wave vector, qm (≡2π/λm),2,8,9,15 which is a wellrecognized characteristic of spinodal dewetting. More recently, by using the Minkowski functional analysis, Jacobs et al.21 found the holes to have no positional correlation, which argues against the holes being due to spinodal surface capillary waves. Furthermore, it was demonstrated that the h-4 dependence apparent in the measured density of holes could be easily mistaken from an exponential dependence in h, more appropriate evidence for heterogeneous nucleation. Nonetheless, threedimensional (3D) nonlinear simulations of Sharma et al.19 revealed that different morphologies (holes, bicontinuous ridges, droplets, etc.) and their combinations can be produced by the spinodal mechanism, with length scales predictable by the linear theory. On the other hand, Thiele et al. observed that spinodal dewetting and heterogeneous nucleation can coexist,4 adding complications to the controversy. In this experiment, we employ a somewhat different approach to distinguish between spinodal and nucleation dewetting. We have chosen the extensively studied PS/ SiO2/Si system for demonstration. Small height fluctuations (〈|∆h|〉/h < 10%) were introduced to the polymer films by mechanically rubbing the film surface with a rayon cloth before dewetting was initiated. Comparisons between rubbed and unrubbed films for the evolution of dewetting and the characteristic wave vectors showed that the rubbing-induced defects did not produce a significant change in the system’s free energy that might affect the dominating dewetting mechanism. When the density of introduced defects was increased, the characteristic wave vectors of those films dewetted by heterogeneous nucleation increased in magnitude while those of films dewetted by a spinodal mechanism remain unchanged. This simple protocol enables us to unambiguously determine that spinodal dewetting prevailed in thin films with h < 13.3 nm for our system whereas nucleation dewetting prevailed with h > 13.3 nm. From a practical point of view, the present results on the dewetting morphology and its evolution from rubbed polymer films may also shed light on the effect of wear and tear on the dewetting stability of a practical polymer coating. We discuss in detail how the rubbing-induced defects affected the dewetting mor(14) Reiter, G.; Sharma, A.; Casoli, A.; David, M.-O.; Khanna, R.; Auroy, P. Europhys. Lett. 1999, 46, 512. (15) Meredith, J. C.; Smith, A. P.; Karim, A.; Amis, E. J. Macromolecules 2000, 33, 9747. (16) Xie, R.; Karim, A.; Douglas, J. F.; Han, C. C.; Weiss, R. A. Phys. Rev. Lett. 1998, 81, 1251. (17) Reiter, G.; Khanna, R.; Sharma, A. Phys. Rev. Lett. 2000, 85, 1432. (18) Khanna, R.; Sharma, A.; Reiter, G. EP Jdirect 2000, E2, 1. (19) Sharma, A.; Khanna, R. Phys. Rev. Lett. 1998, 81, 3463. (20) Sharma, A.; Reiter, G. J. Colloid Interface Sci. 1996, 178, 383. (21) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Langmuir 1998, 14, 965.
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phology and the rate of rupturing observed in this experiment for spinodal and nucleation dewetting, respectively. Experiments Monodisperse PS (Mw ) 13 700 Da, Mw/Mn ) 1.1) was purchased from Scientific Polymer Products (Ontario, NY). The glass transition temperature of the polymer was measured to be 93 °C by differential scanning calorimetry (DSC). PS films with thicknesses ranging from 6.8 to 29.5 nm were prepared in a class 1000 clean room by spin-coating solutions of the polymer (0.2-1 wt % in toluene) onto cleaned silicon substrates covered with a 106 nm thick thermal oxide layer. The substrate cleaning procedure involves dipping the silicon wafers (unused before) into a mixture of H2SO4 and H2O2 (in 10:1 volume ratio) at 120 °C for 10 min, followed by thorough rinsing in deionized water. The coated polymer films were then baked inside a vacuum oven at 100 °C for 5 h to remove the residual solvent. No sign of dewetting was detectable in the polymer films after annealing. A variable angle spectroscopic ellipsometer by J. A. Woollam (Lincoln, NE) was used to determine the film thickness. To produce the artificial defects in the polymer films, the surfaces of the as-annealed samples were rubbed against a rayon cloth at a constant speed of 1 cm/s and a 10 g/cm2 normal pressure by using a home-built apparatus.22 The density of defects was changed by varying the number of rubbings from 0 to 10 times. Surface morphology was characterized by using a Seiko Instruments (Chiba, Japan) SPA-300HV atomic force microscope (AFM). Topographical images of the freshly rubbed films show that prominent grooves oriented parallel to the rubbing direction are produced (Figure 1), with their density showing a tendency to increase with increasing number of rubbings. Cross-sectional analysis shows that the grooves are typically ∼50 nm wide and ∼1 nm deep. To perform statistical averaging on the captured topography, we carried out 2D fast Fourier transformation (FFT) on the images of Figure 1, followed by radial averaging to obtain the Fourier spectra. The result is shown in Figure 2. As seen, the Fourier spectra due to different numbers of rubbings, N, look alike and are rather featureless. Moreover, the film roughness depends on N according to x(0.262 + 0.162N) (nm) (inset of Figure 2). This finding suggests that additional surface features caused by individual rubbings have the same average roughness of ∼0.16 nm and are independent of the pre-existing features produced by preceding rubbings. Hence, we deduce that the density of the introduced topographical features increases linearly with the number of rubbings. To perform the dewetting experiments, samples were heated at 180 °C either in a vacuum or in air. While results were found to be the same in either annealing environment, dewetting proceeded faster in the latter, as was previously noted.21 When annealed in air, only films with thicknesses greater than ∼20 nm needed to be heated longer than 30 min for complete dewetting to occur. The dewetting morphologies were determined either by using the AFM or a polarizing microscope (Olympus BX60) with Nomarski interference contrast. Studies on the morphological evolution of dewetting were ex situ; namely, the sample was repeatedly annealed at a lower temperature of 145 °C and then quenched to ambient for examination at various preselected cumulative annealing times. This allows images from several different areas to be taken. All results reported herein from ex situ measurements are representatives of data obtained from three to seven different spots on the sample. The annealing temperature has been chosen to enable easier monitoring of the dewetting process. No effect on the final dewetted morphology had been found by using different annealing temperatures.
Results and Discussion Distinguishing Dewetting Mechanism Using BuiltIn Topographical Defects. Shown in Figure 3a are the final dewetted patterns of the unrubbed PS films (h ) 6.8-30 nm). Between h ) 12.8 and 13.8 nm, one may (22) Tsang, O. C.; Tsui, O. K. C.; Yang, Z. Phys. Rev. E 2001, 63, 061603.
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Figure 1. AFM topographical images of freshly rubbed 20.3 nm thick PS films. The number of rubbings applied, N, is labeled at the lower left corner of each image. The white arrow inside the second image on the top row indicates a groove that is ∼50 nm wide and ∼1 nm deep.
Figure 2. (Main panel) Fourier spectra for the topography of the freshly rubbed films subject to different numbers of rubbings, N. (Inset) Roughness of the rubbed films plotted as a function of N. The solid line is a fit to y ) x(0.262 + 0.162N) (nm).
notice a drastic change in the dewetted morphology, which is remarkable for a mere 1 nm change in the film thickness. For h e 12.8 nm, the patterns contain uniformly dispersed small polymer droplets. But for h g 13.8 nm, the pattern displays a network of polygons composed of polymer beads. Both kinds of morphologies had been observed in previous studies.15,16 In Figure 3b, we show the final dewetted patterns of PS films of the same thickness rubbed 10 times. Compared to the dewetted patterns of the unrubbed samples, these patterns exhibit notable anisotropy. For the thinner films with h e 12.8 nm, the dewetted patterns are composed of uniformly distributed droplets oriented along the rubbing direction. But for the thicker samples (h g 13.8 nm), a combination of aligned droplets and polygon networks could be seen. Moreover, the density of droplets in the rubbed films with h < 13.3 nm appears to be similar to that of the unrubbed counterparts. On the other hand, the density of droplets or polygons in the rubbed films with h > 13.3 nm is notably higher than that in the corresponding unrubbed films. To better display the differences in dewetted morphology between rubbed and unrubbed films, we constructed Fourier spectra for each dewetted pattern displayed in
Figure 3, from which the characteristic wave vectors, q*, could be identified (see Figure 4a). Similar analysis was then repeated for dewetted films that had been subject to 3 and 5 times of rubbing. Figure 4b summarizes results of all dewetted films in plots of q* versus h. As seen, the data points are sharply divided between two regions about h ) 13.3 nm. Below 13.3 nm, q* is independent of N, but above, it increases with increasing N. This finding unambiguously evidences that spinodal dewetting dominated for h < 13.3 nm, but heterogeneous nucleation dominated for h > 13.3 nm. A time evolution study (data not shown) revealed that the abrupt drop in q* at the transition had come from a drastic reduction in the holenucleation rate and occurrence of coalescence of adjacent holes before droplet formation among the thicker films (h > 13 nm). The measurements are very reproducible. The very fact that the transition occurred at the same thickness (h ) 13.3 nm) for all four sets of data of different N is in itself evidence of excellent reproducibility. In the same graph is displayed another set of measurements for the unrubbed films, but from a different batch of samples (labeled “unrubbed(2)”). Good agreement between the two equivalent sets of data is immediately apparent in the thin film region (h < 13 nm). Conceivable discrepancy in the thick film region can be understood to result from difficulty in controlling the density of intrinsic defects governing heterogeneous nucleation. Another important point to note is the highly reproducible q*(h) data among different samples in the thin film region, which also provides a consistency check for the thin film regime to be dominated by spinodal dewetting since only for this mechanism should q*(h) be well-defined for a given h. While the present result confirms that only one mechanism dictated the final dewetted pattern, it is possible that both mechanisms had been operative in the rupturing process, as was previously noted.4 In fact, this is especially probable in thicker films wherein G′′(h) is small so that the spinodal rupturing rate, Γm(h), will also be small.12 Following conventional analysis, we model-fitted the q*(h) data of the unrubbed films (data labeled “unrubbed(1)” in Figure 4b) to the power law and found that they fit quite well to ∼h(-2.1(0.05) and ∼h(-2.5(0.1) for h below and above 13.3 nm, respectively (solid lines in Figure 4b). The
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Figure 3. Optical micrographs displaying final dewetted patterns of (a) unrubbed and (b) 10-time-rubbed PS films with different thicknesses from 6.8 to 29.5 nm.
fact that the latter is not notably different from the h-2 dependence could have been easily mistaken as evidence for the spinodal mechanism. We also model-fitted the same data to an exponential form, ∼exp(h/L), where L is a constant (dashed lines in Figure 4b). As seen, similarly good fits were also obtained. These findings are consistent with an earlier suggestion21 that the q* ∼ h-2 criterion is insufficient for the distinction between spinodal and nucleation dewetting. Another commonly used criterion for spinodal dewetting is the h dependence of the droplet diameter, Dd, namely,
Dd ∼ h1.5.2,20 We investigate its validity in our data. Shown in Figure 5 is the log-log plot of Dd versus h for the unrubbed films. Like the data of q*(h), the Dd(h) data are sharply divided between the two thickness regions about h ) 13.3 nm. By model-fitting data in each region to the power law (solid lines in Figure 5), we obtain fitted values of the exponents to be 1.4 ( 0.3 and 1.6 ( 0.2 for h below and above 13.3 nm, respectively. These values clearly demonstrate consistency with spinodal dewetting. On the other hand, we also find these data to fit well to the exponential form (dashed lines in Figure 5), which is a
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Figure 5. Double logarithmic plot of the average diameter of droplets, Dd, as a function of film thickness, h. Data were determined from the final dewetted patterns displayed in Figure 2a. Solid lines are fits to the power law; dashed lines are fits to an exponential function.
Figure 4. (a) Fourier spectra from the final dewetted pattern of the unrubbed films shown in Figure 3a. The arrows indicate the designated q* for each spectrum. (b) Characteristic wave vector of the final dewetted patterns, q*, as a function of the initial film thickness, h, for PS films rubbed different numbers of times as indicated. Solid lines are fits to the power law; dashed lines are fits to an exponential function defined in the text.
more appropriate signature for nucleation dewetting. The fact that the data of Dd(h) and q*(h) happen to fit well to both the power law and the exponential form may just reveal the general relation, Dd ∼ (q*)-3/4.2 That the two functional dependences are indistinguishable in either data set is a result of the narrow dynamic range that was employed in the data. While in principle this problem can be circumvented by making measurements over several orders of magnitude variation in h, the scaling relations expected of q*(h) and Dd(h) will subdue to retardation effects when the film thickness is too large. Therefore, it is our view that scaling relations should never be used alone as the guideline for distinguishing spinodal and nucleation dewetting. Initiation and Evolution of Dewetting in Thin Films with Imposed Rubbing-Induced Defects. We have seen from Figure 3 that the final dewetted patterns of rubbed films exhibit marked anisotropy as opposed to the isotropic patterns displayed by the unrubbed films. Furthermore, in the thicker films with h > 13.3 nm where nucleation dewetting prevailed, the characteristic wave
Figure 6. AFM topographical images of a 6.8 nm thick unrubbed PS film quenched from 145 °C to room temperature after different cumulative annealing times: (a) 10 s, (b) 300 s, (c) 420 s, and (d) 1400 s. The scale bars correspond to 4 µm.
vector could be increased by increasing the number of rubbings. In this section, we shall investigate how these unique dewetting behaviors of the rubbed films arose from the rubbing-induced defects. Two aspects will be focused upon, namely, how the initiation of dewetting in the rubbed films compares to that in the unrubbed films, and second, the way in which the imposed defects affect the propagation of the dewetting process. These questions will be addressed by comparing the evolution of dewetting morphologies of rubbed and unrubbed films, bearing in mind that the two different dewetting mechanisms need to be considered separately. We first look at samples of the thin film region where spinodal dewetting dominates. Shown in Figures 6 and 7 are the AFM topographical images obtained from, respectively, an unrubbed and a 10-time-rubbed PS film with a thickness of 6.8 nm upon annealing at 145 °C at different annealing times. In the unrubbed film, uniformly distributed circular holes appear after about 10 s (Figure 6a). Further annealing caused enlargement of the holes and appearance of more holes, which subsequently developed into a bicontinuous structure (Figure 6c). With
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Figure 7. AFM topographical images of a 6.8 nm thick 10-time-rubbed PS film quenched from 145 °C to room temperature after different cumulative annealing times: (a) 0 s, (b) 120 s, (c) 600 s, and (d) 900 s. The scale bars correspond to 4 µm.
subsequent annealing, the holes enlarged further until neighboring holes coalesced (Figure 6d) before the scattered polymer ribbons eventually broke up into separated liquid droplets. With the 10-time-rubbed film, on the other hand, the initial holes had a tendency to be elongated and align into straight lines parallel to the rubbing direction (Figure 7b). Upon further heating, bicontinuous structures, with an apparent orientation along the rubbing direction, are formed between long trenches that were formerly elongated holes (Figure 7c). The length scale of the features seems comparable to that found in the unrubbed film (cf. Figure 6c). Upon further annealing, holes in the bicontinuous structure grew in size and coalesced upon touching the neighboring holes to form distinctive arrays of ridges and droplets along the rubbing direction (Figure 7d). Next, we examine the thicker films wherein nucleation dewetting dominates. Displayed in Figures 8 and 9 are time sequences of AFM topographical images taken ex situ from, respectively, an unrubbed and a 10-time-rubbed PS film with a thickness of 20.3 nm annealed at 145 °C. In comparing the holes formed in the initial state, we notice that those holes formed in the unrubbed sample are randomly distributed and of different diameters ranging from 2 to 6.5 µm (Figure 8a). On the other hand, the holes formed in the rubbed film, though having a tendency to line up along straight lines parallel to the rubbing direction, are circular with a uniform diameter of ∼1.2 µm. They also display a notably higher areal density. These differences reveal that the defects in the rubbed and unrubbed films that had facilitated hole nucleation are of very different origins. It is reasonable to ascribe those in the unrubbed film to be intrinsic defects, whereas those in the rubbed film are ascribed to extrinsic defects. We will postpone discussing the possible origin of the latter until the next subsection. Since rubbed films must contain both kinds of defects, the notably higher density of holes found in the rubbed film indicates that the extrinsic defects markedly dominate the intrinsic ones in the 10-time-rubbed film. Upon further annealing, the
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Figure 8. Dewetting morphologies of a 20.3 nm thick unrubbed film after annealing at 145 °C for different cumulative times of (a) 5 min, (b) 35 min, (c) 60 min, and (d) 100 min. The image labeled as taken after 5 min is an AFM topographical micrograph. The other images are optical micrographs.
Figure 9. Dewetting morphologies of a 20.3 nm thick 10-timerubbed film after annealing at 145 °C for different cumulative times of (a) 3 min, (b) 22 min, (c) 60 min, and (d) 120 min. The image labeled as taken after 3 min is an AFM topographical micrograph. The other images are optical micrographs.
holes in both unrubbed and rubbed films grew in diameter (Figures 8b and 9b, respectively). As time increased, the diameter of the holes in the unrubbed film turned uniform in Figure 8b, indicating that the expansion of the holes at this point had overcome the initial spread in the hole sizes. We further note that the holes only grew bigger but remained uniform in size at yet later times (Figures 8c and 9c), suggesting that no new holes (which should have small sizes) were formed after the initial holes emerged. This picture is consistent with heterogeneous nucleation. Physical Origin for the Effects of Rubbing on Dewetting. When the surface of a polymer is rubbed by
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a piled fabric, not only is the topography modified but the configuration of the chains nearby is also changed. Previous dichroism measurements confirmed that rubbing induced anisotropy in polystyrene films supported on silicon.23,24 Moreover, the induced anisotropy extended by more than ∼50 nm from the free surface into the film.25 As the resultant optical dichroism was found to be orthogonal to24 and much too large to be accounted for22 by the form birefringence due to sample topography, it was inferred that the induced anisotropy had come from molecular alignment in the polymer. The strain associated with the molecular alignment should lead to an increase in the elastic energy and hence the total free energy, G(h), of the film. However, we do not expect this elastic energy, once engendered by rubbing, to alter with any subsequent variations in the surface topography of the film: A local dilation (or compression) in the film will lead to a decrease (or increase) in the local elastic energy density, but the integrated elastic energy should remain the same. The notion that the elastic energy from rubbing does not vary with h is supported by the data of Figure 4, showing q* (which is related to x-G′′(h)13) to be independent of the number of rubbings, which had been shown to have a strong effect on the molecular alignment and the strain in the polymer.22,25 Since the spinodal stability of a liquid film depends on whether spontaneous development of thickness undulations may lower the free energy, the rubbing-induced strain energy should not affect the physical nature of dewetting. Furthermore, previous temporal relaxation studies of rubbed PS films22,25 found that heating of the sample above Tg brought about complete relaxation of the anisotropy within seconds, which is of much shorter duration than the dewetting times of this experiment. Therefore, we eliminate the elastic energy associated with the rubbing-induced strain to play a significant role in the dewetting of the rubbed films. On the other hand, deformations from the act of rubbing can have an important effect on dewetting. In particular, the local stress from a fiber of the rubbing cloth can produce a region of plastic yield about the contact point wherein rearrangement of the local defects may take place. For example, it can lead to alignment of the defects with the strain field or coalescence of some small existing pores into bigger ones. The latter may explain the qualitatively different appearance found between holes formed in the unrubbed and rubbed films (cf. Figures 8a and 9a). Since the compressional stress produced by an indenter against a flat surface is local to the area in contact (n.b., the compressional stress distribution about an indenter, σ(r), is ∼x(a2 - r2), where a is the contact radius26), we expect any physical alteration due to rubbing to be local to the regions directly underneath the rubbinginduced surface indentations. Therefore, we maintain that the statistical result obtained earlier for the rubbinginduced topographical features (Figure 2) can still be used as a reasonable measure for the density of extrinsic defects from rubbing. In the following, we will sketch how most of the observed effects in the dewetting of rubbed films may be explained in terms of the topographical undulations induced and, where appropriate, the pores underneath them. (23) Liu, Y.; Russel, T. P.; Samant, M. G.; Stohr, J.; Brown, H. R.; Cossy-Favre, A.; Diaz, J. Macromolecules 1997, 30, 7768. (24) Schwab, A. D.; Agra, D. M. G.; Kim, J.-H.; Kumar, S.; Dhinojwala, A. Macromolecules 2000, 33, 4903. (25) Tsang, O. C.; Xie, F.; Tsui, O. K. C.; Yang, Z.; Zhang, J.; Shen, D.; Yang, X. J. Polym. Sci.: Polym. Phys. 2001, 39, 2906. (26) Tsui, O. K. C.; Wang, X. P.; Ho, J. Y. L.; Ng, T. K.; Xiao, X. Macromolecules 2000, 33, 4198.
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Higgins and Jones27 have studied spinodal dewetting of poly(methyl methacrylate) films on a rubbed glass substrate and observed anisotropy in the dewetting morphology. Likewise, simulations of Sharma and coworkers on liquid films dewetting from physically and/or chemically heterogeneous substrate surfaces also demonstrated regulated dewetting morphologies.28,29 As has been pointed out,27 spinodal instability is one in which any noise in the order parameter is amplified according to a dispersion relation, Γ(q). In the present problem, since the Fourier spectrum of the rubbing-induced fluctuations is rather featureless (Figure 2), the dewetting morphology of the rubbed films will be dictated by the Fourier components of the imposed fluctuations that maximize Γ(q). This point of view is consistent with observations made on the rubbed films undergoing spinodal dewetting (Figure 7). Anisotropy was readily seen in the initial stage of hole formation, which grew stronger over time as the Fourier component of the initial oriented fluctuations that peaked Γ(q) was selectively amplified. Formerly, Sharma and Ruckenstein30 had dealt with the problem of spinodal dewetting with built-in topographical fluctuations by using perturbation theories incorporated with a change of the base states to ones that constitute the starting topography. Their calculation showed that any finite amount of perturbations would cause both qm and Γm to increase. Using their results, if the amplitude of the perturbation is ∼10% of the initial film thickness, which is about the maximum height fluctuation we had introduced to our films, qm and Γm should increase by 1.11 and 1.54 times, respectively. The predicted order of change in the rate of dewetting is consistent with experiment based on visual comparison of the densities of holes in Figures 6 and 7. However, the predicted 11% change in the characteristic wave vector is not easily detectable owing to the broad Fourier spectra typically found for dewetting morphologies (Figure 4a). A more systematic comparison between experiment and this calculation of Sharma et al. will be a future study. In the thicker film regime (h > 13.3 nm) where dewetting by heterogeneous nucleation prevails, the rubbing-induced undulations interfere with the dewetting process in a different way. We adopt a paradigm based on the “porous film model” introduced by Jacobs et al.21 In essence, nucleation of holes occurs at points where successions of pores connect the surface region of the film (within ca. nanometers from the top) to its immediate bottom. Within this framework, local indentations will strive to form at the film surface, where these sites are, due to the dispersion forces that thin any dielectric layer between two like media.10 (In this case, the two like media are the pore just beneath the film surface and the air above.) The same dispersion forces also thin the polymer connections between any two adjacent pores. A through hole appears when all the polymer connections between neighboring pores and the surface indentation are drained. But when the succession of pores is too deeply buried, the polymer connecting between the topmost pore and the surface indentation cannot be drained away within experimental times. On the other hand, imposed surface indentations reaching within ca. nanometers to these buried defects can greatly shorten the nucleation times. As aforementioned, the topography added by each rubbing has an (27) Higgins, A. M.; Jones, R. A. L. Nature 2000, 404, 476. (28) Konnur, R.; Kargupta, K.; Sharma, A. Phys. Rev. Lett. 2000, 84, 931. (29) Kargupta, K.; Sharma, A. Langmuir 2002, 18, 1893. (30) Sharma, A.; Ruckenstein, E. J. Colloid Interface Sci. 1986, 113, 456.
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Conclusion
Figure 10. The characteristic wave vector, q*, versus the number of rubbings, N, for PS films of different thicknesses dewetted by heterogeneous nucleation. Solid lines are linear fits to the data.
average roughness of only 0.16 nm and is independent of the existing topography created by previous rubbings, so we envisage that only a small fraction of the indentations produced by rubbing are deep enough to reach the “nucleable” defects. As the number of rubbings is increased, the number of such indentations should increase in proportion. This scenario predicts that the density of nucleated holes should increase linearly with the number of rubbings. We examine the validity of the proposed interpretation by replotting the data of Figure 4b as q* versus N for thicknesses studied in the nucleation dewetting regime. The result is shown in Figure 10. As seen, the data demonstrate excellent agreement with linear relations. Deviation of the data point with N ) 10 and h ) 13.8 nm from the straight line extrapolated from the rest of the data may arise from the diminishing number of nucleable defects still remaining as N was increased toward 10. We also notice that the data of the thinner films exhibit larger slopes. The slope of the plots, dq*/dN, reveals the number of additional nucleated holes caused by a unit increment in the number of rubbings. With h decreased, the chance that the rubbing-induced indentations can reach such defects and assist them to form nucleated holes is improved. Essentially, rubbing affects nucleation dewetting through introduction of topographical indentations that can facilitate more buried defects to form nucleated holes.
In conclusion, dewetting of thin PS films imposed with small height fluctuations (〈|∆h|〉/h < 10%) has been investigated as a means to distinguish spinodal dewetting and heterogeneous nucleation and to determine the effects of pre-existing topographical fluctuations on film rupturing. By comparing the characteristic wave vectors of the final dewetted morphologies of thin films subject to different numbers of rubbings, we unequivocally demonstrated that samples with h below 13.3 nm rupture predominately by a spinodal mechanism whereas the thicker samples rupture primarily by heterogeneous nucleation. We also demonstrated that the perturbations presently introduced by rubbing the film surface with a piled fabric do not produce changes in the system’s free energy that will alter the dewetting mechanism to dominate. Nonetheless, substantial differences had been noted between dewetted morphologies of unrubbed and rubbed films. In particular, dewetted morphologies of the rubbed films exhibit strong anisotropy, which is not found in the unrubbed films. By comparing the evolution of dewetting morphologies in unrubbed and rubbed films, we investigated how the imposed topographical defects interacted with the spinodal and nucleation dewetting processes, respectively. Henceforth, paradigms were established to account for the observations. For spinodal dewetting, the wavelength selectivity of the spinodal mechanism causes the Fourier component of the imposed perturbation with q ) qm to dominate. For heterogeneous nucleation, on the other hand, the dewetting morphology is mostly shaped by the most far-reaching indentations that can facilitate nucleation of holes at some buried defects, which would otherwise not be achievable within experimental times by dispersion forces alone. Acknowledgment. We thank the Microelectronics Fabrication Facility of the Hong Kong University of Science and Technology (HKUST) for assistance with processing of the silicon substrates. We also thank the Materials Characterization & Preparation Facility of HKUST for allowing us to use their facilities. Support of F. Xie by the HKUST Postdoctoral Fellowship (PDF) Matching Fund is acknowledged. LA020506Q
