Pattern Formation by Rim Instability in Dewetting Polymer Thin Films


the materials removed from the dry regions are stored into the rims of the wet region. In particular on a highly non-wettable or slippery substrate, d...
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Chapter 15

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Pattern Formation by Rim Instability in Dewetting Polymer Thin Films 1

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Yuji Asano , Akitaka Hoshino , Hideki Miyaji , Yoshihisa Miyamoto , and Koji Fukao 2

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Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Department of Fundamental Science, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606—8501, Japan Department of Polymer Science and Engineering, Kyoto Institute of Technology, Kyoto 606-8585, Japan 2

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The dewetting process of thin polystyrene films from 5 to 50nm in thickness on a silicon substrate is investigated. A spreading dry patch formed on dewetting is surrounded with a circular rim, which stores the liquid matter expelled from the dewetted region. When the diameter of the patch exceeds a thickness-dependent critical value, the rim is deformed by morphological instability; the instability gives rise to the diversity of self-organization processes of liquid ridges or droplets formed eventually on partially wettable substrates. A morphological phase diagram of the deformed rim is given in the diameter of dry patch and the initial film thickness. In the final stage of dewetting, liquid droplets arrange to form a "polygon network" in thick films and "polygons with random droplets" in thin films. The origin of the instability is discussed in terms of surfacefreeenergy.

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© 2004 American Chemical Society

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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The growing technological importance of dewetting rangesfromcoating of nano-scale devices to industrial lubricants, where homogeneity of liquidfilmsis usually demanded for practical applications. Furthermore, self-organization of liquid droplets via dewetting processes nowadays attracts many researchers' interests because of the diversity of patterns formed via complicated dissipative processes coupling with each other. When the thickness of a liquid film on a non-wettable substrate is thinner than that in equilibrium (usually -mm), the film ruptures with cylindrical holes and shrinksfromthe contact line, on which three phases (liquid, substrate and air) meet. For relatively thickerfilms,initial holes are nucleated by dust particles and defects on the substrates. In the case of sub-micron thickfilms,another origin of spinodal decomposition dominates for the formation of initial holes, and hence the density distribution of the holes depends on the initial film thickness (/). Once the cylindrical holes are created on the film, dewetting proceeds and the materials removedfromthe dry regions are stored into therimsof the wet region. In particular on a highly non-wettable or slippery substrate, deformation of rims by the morphological instability has been reported (2, 3). The rim instability is expected to control the dewetting dynamics involving dewetting velocity and pattern formation process in partially wetting region. In this paper, we investigate the rim instability and its effects on the arrangement of droplets formed in thefinaldewetting process. Film Rupturing Induced by Spinodal Instability

Brochard and Dalliant have indicated that liquid films on non-wettable substrates are spinodally unstable against thicknessfluctuationif the thickness e is thinner than lOOnm (i). Their model of linearized capillary wave instability predicts that the thickness fluctuation with a characteristic wave vector qu is amplified most rapidly to nucleate initial dry spots separated by 2π/# fromeach other. Their result is Μ

(1)

where a is the molecular length defined by α =\Α\Ιβτϋγ, A = A L - A L is the difference between the solid-liquid and liquid-liquid Hamaker constants, and /is the interfacial energy of the liquid-air. Reiter has examined the rupturing properties of thinfilmsof polymers with relatively high molecular weight and observed that the number density of holes, 2

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In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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JVp, depends upon initial film thickness as N ~e , agreeing with eq (1) (2). By using a 2D fast Fourier transform of A F M topographical images of surface undulations, Xie et al. have observed more directly the properties of spinodal instability in dewetting; the thicknessfluctuationswith wave vector qq are suppressed with time (4), p

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Experimental The molecular weight of atactic polystyrene used in this study is M =36,000 (MyM =1.06). The glass transition temperature T is 90°C. Polystyrene thin films were prepared by spin coating of toluene solutions on native-oxidized silicon wafers. In order to remove the solvent from the films, these films were dried at 100°C (just above Tg) in a vacuum oven for 24 hrs. The film thickness was measured by atomic force microscopy (AFM, SHMADZU SPM-9500J) at room temperature to be from 5 to 50nm. By AFM the contact angle in equilibrium, which is a measure of wettability, was determined: ft=23°±l°. After holding the samples in the vacuum oven at a dewetting temperature of 180°C for appropriate time, we quenched the dewetting films at room temperature. For optical microscopy, we used monochromatic light of 546nm in wavelength. Small undulations of the deformed rims were thereby recognized as the contrast of interference fringes. We also used a hot stage (MettlerFP800) for in situ observation of the dewetting process at 180°C. w

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Results Node creation by rim instability Figure 1 shows a series of time evolution of a dry patch with a circular rim in a 29nm thick film at 180°C. Node-like deformations are observed in the rim with increasing diameter, and the developed nodes were slowed down to give rise tofinger-likepatterns. Reiter has suggested that thefingeringpatterns are due to interfacial slippage of the polymer films on the substrates (5) since the dewetting velocity dependent on the width of the rims, which is responsible for retardation of thicker parts of rims, is characteristic of slippingrims(6).

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Figure 1. O p t i c a l micrographs of time evolution of deformed circular rims with nodes. The growing nodes form afingeringpattern. Scale bar is 10pm.

In order to investigate the dependence of the morphological instability on the initial film thickness, we observed the rims of dry patches at a given diameter for various film thickness: a uniformrimon a relatively thick film (Figure 2 A), a slightly deformed one with "nodes" (B), a rim with large nodes which do not catch up with the whole retreat of therimto cause "fingering" (C) and the ensemble of droplets distributed after thefingering(D). Since the diameters of the patches are almost the same, the morphological difference is attributed to the difference in thickness of thefilms.We note two important aspects. Firstly not only the width of therimsbut also the distance between the nodes increased withfilmthickness. The dependence of the wavelength of the undulations on the width of therimreminds us of morphological instability of clamped doughnut geometry (7). Secondly, the critical diameter of the patch, at

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Figure 2. Optical micrographs of a dry patch in a thinfilmwith various thicknesses. (A) 45nm, β) 23nm, (C) 18nm, (D) 6nm. The size ofmicrograph is 40pm χ40μη.

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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191 which the nodes become observable, also increases with film thickness. We will show later that the critical diameter and the distribution of initial holes couple with each other and determine the final dewetting patterns formed by the droplets. Figure 3 shows the node density, which is the number of nodes per unit length of arim,as a function of diameter of a dry patch for an 18nm thick film. The broken curve is a hyperbola corresponding to the number of nodes fixed at 6. For diameters of dry patch less than about 15pm, the number of nodes was observed to be nearly constant during the growth of the patch; for small diameter of the dry patch the node density decreases in proportion to the inverse of the diameter of the patch. When the diameter of the patch increased, new nodes appeared between neighboring nodes so that the node density remained constant. The average number of initial nodes and the constant node density are 6 and 0.12/μπι, respectively for the 18nm thick film as shown in Figure 3. Both the values decreased with increasing initial film thickness (Figure 4).

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Diameter of Dry Patch (μτπ)

Figure 5. Node density vs. diameter of a dry patch of an 18nm thickfilm. The horizontal dash-dotted line is constant node density offt12/pm for the large diameter of dry patches.

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Node Density (1/jim)

Figure 4. Density of nodes in the circular rims around the dry patches. Uniform rims without node were observedfor small dry patches of relatively thickfilms.

Final droplet pattern formed by rim instability The left side of Figure 5 (regions (a)-(c)) is a morphological phase diagram of rims in the phase space of the initial thickness of the film and the dry patch diameter; three characteristic morphologies of the dewetting rims are drawn: uniform rims (region (a) in Figure 5), deformed rims with nodes (region (b)) and rims deformed severely with the fingering (region (c)). The lateral axis (diameter of dry patch) corresponds to the time elapsed during dewetting. In the right side of the diagram (regions (d) and (e)), the final droplet patterns (see Figure 6) are drawn schematically. These patterns are formed when neighboring rims merge to be broken into droplets arranged in a pattern similar to the Voronoi polygons. For example, a dry patch in a 20nm thick film had a uniform rim with a small diameter at first, and proceeded laterally on black region in Figure 5. When the diameter of the patch reached about ΙΟμιη, the node-like deformation on the rim became observable. After that, the patch with nodes developed and eventually met neighboring patches at the diameter of ΙΟΟμιη. As a result, a polygon network of liquid droplets appeared in region (d). On the other hand, no uniform

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

193 rim is observed in 6nm thick film. Accordingly the dry patch grew with nodes even in the early stage of dewetting. In this case,fingeringpattern occurred at 6μπι in diameter, and the neighboring fingering rims met each other at the diameter of 25μπι. Elongated fingers were broken into several small droplets, which were enclosed by each polygon as drawn in region (e) of Figure 5. Obviously, the averaged diameter of the polygon, D , at a given film thickness in regions (d) and (e), is determined by the value at the corresponding boundary between region (b) or (c) and region (d) or (e). D has been reported to be proportional to the square of the film thickness, e which agrees with the result predicted on the basis of the spinodal instability: eq (1) (2). We confirmed this relation in the narrow region of film thickness from 11 to 21nm; the slope of the boundary line between region (c) and region (d) or (e) for 1 lnm