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Mesoscopic Patterning in Evaporated Polymer Solutions: New Experimental Data and Physical Mechanisms Edward Bormashenko,*,† Roman Pogreb,† Oleg Stanevsky,† Yelena Bormashenko,† Tamir Stein,† and Oleg Gengelman‡ The Research Institute, The College of Judea and Samaria, 44837, Ariel, Israel, and Faculty of Mechanical Engineering, Technion, Technion City, 32000, Haifa, Israel Received July 8, 2005. In Final Form: August 4, 2005 Mesoscopically ordered patterns were obtained when polymer solutions were applied to tilted substrates and evaporated immediately under ambient conditions in a slow air current. The patterns were studied with optical, scanning electron, and atomic force microscopy. Shadowgraph visualization of the patterning was carried out, and visualization of the flow with an ink tracer was performed. Restrained and nonrestrained flows of the polymer solution gave rise to very similar patterning. The formation of the patterns on different solid substrates, including substrates wetted with silicon oil, was investigated. The concentration of the polymer solutions exerted an influence on the characteristic dimension of mesoscaled cells. A physical mechanism of the patterning is proposed. The mechanism is based on the mass transport instability occurring under the intensive evaporation of the solvent. The model satisfactorily explains the experimental findings.
1. Introduction Patterning in evaporated polymer solutions has been studied intensively during the past decade. It has been shown that, under particular conditions, ordered patterns emerge under evaporation on a length scale that significantly exceeds molecular dimensions.1-10 Evaporationinduced regular mesoscopic patterns demonstrate a potential for various optical applications, including optical waveguide arrays, diffraction gratings, and photonic band gap materials.11 However, the physical mechanism of mesoscaled structuring in polymer solutions remains a mystery. The formation of mesoscaled patterns is usually attributed to surface-tension-driven Marangoni instability, on the basis of the assumption that small random motions at the mobile surface must be amplified when the motive force that depends on the concentration or temperature gradients is stronger than the viscous frictional force.2-10,12-16 On the other hand, De Gennes related mesoscopic self-organization to another kind of instability.17-18 He showed that in an evaporating film, a * E-mail:
[email protected]. † The College of Judea and Samaria. ‡ Technion. (1) Ma, X.; Xia, Y.; Chen, E.-Q.; Mi, Y.; Wang, X.; Shi, A.-Ch. Langmuir 2004, 20, 9520. (2) Mitov, Z.; Kumacheva, E. Phys. Rev. Lett. 1998, 81 (16), 3427. (3) Kumacheva, E.; Li, L.; Winnik, M. A.; Shinozaki, D. M.; Cheng, P. C. Langmuir 1997, 13, 2483. (4) Li, M.; Xu, Sh.; Kumacheva, E. Macromolecules 2000, 33, 4972. (5) Weh, L.; Ventur, A. J. Colloidal Interface Sci. 2004, 271, 407. (6) Weh, L. J. Colloidal Interface Sci. 2001, 235, 210. (7) Weh, L.; Venthur A. Macromol. Mater. Eng. 2004, 289, 227. (8) Merkt, D.; Bestehorn, M. Physica D 2003, 185, 196. (9) Karthaus, O.; Grasjo, L.; Maruyama, N.; Shimomura, M. Thin Solid Films 1998, 327, 829. (10) Maruyama, N.; Koito, T.; Nishida, J.; Sawadaishi, T.; Cieren, X.; Ijiro, O.; Karthaus, O.; Shimomura, M. Thin Solid Films 1998, 327, 854. (11) Yabu, K.; Shimomura, M. Adv. Funct. Mater. 2005, 15 (4), 575. (12) Colinet, P.; Legros, J. C.; Velarde, M. G. Nonlinear Dynamics of Surface-Tension-Driven Instabilities; Wiley: Berlin, 2001. (13) Reichenbach, J.; Linde, H. J. Colloidal Interface Sci. 1981, 84 (20), 433. (14) Linde, H.; Velarde, M. G.; Wierschem, A.; Waldhelm, W.; Loeschke, K.; Rednikov, A. Y. J. Colloidal Interface Sci. 1997, 188, 16.
Figure 1. Sketch of the experimental unit.
“plume” of solvent-rich fluid induces a local depression in surface tension, and the surface forces tend to strengthen the plume. His calculations led to the conclusion that this kind of instability should dominate over the classic Be´nard-Marangoni instabilities. In our recent work, we showed that one more kind of diffusion instability may occur.19-20 This instability is due to the formation of a polymer-rich layer under the intensive evaporation of a polymer solution. Additionally, it was shown recently that the processes of phase separation and nucleation may play a decisive role in the patterning processes when the solution is essentially far from thermodynamic equilibrium.21-24 Thus, it could be con(15) Oron, A.; Nepomnyashchy, A. A. Phys. Rev. E 2004, 69, 016313. (16) Regnier, V. C.; Dauby, P. C.; Lebon, G. Phys. Fluids 2000, 12 (11), 2787. (17) De Gennes, P. G. Eur. Phys. J. E 2001, 6, 421. (18) De Gennes, P. G. Eur. Phys. J. E 2002, 7, 31. (19) Bormashenko, E.; Pogreb, R.; Stanevsky, O.; Bormashenko, Y.; Stein, T.; Gaisin, V.-Z. Macromol. Mater. Eng. 2005, 290, 114. (20) Bormashenko, E.; Pogreb, R.; Stanevsky, O.; Bormashenko, Y.; Stein, T.; Cohen, R.; Nunberg, M.; Vladimir-Zeev Gaisin, V.-Z.; Gorelik, M. Mater. Lett. 2005, 59, 2461. (21) Rabani, E.; Reichman, D. R.; Geissler, Ph. L.; Brus, L. E. Nature 2003, 426, 271.
10.1021/la0518492 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/16/2005
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Figure 2. Channel used for the study of the restrained flow of the polymer solution.
cluded that the processes of mesoscopic patterning in evaporated polymer solutions are far from being completely understood. Our investigation can shed light on the physical mechanisms responsible for the mesoscopic structuring in thin polymer films. 2. Experimental Section Polycarbonate (PC), Lexan 141 (supplied by GE Plastics), was dissolved in dichloromethane (supplied by Karlo Erba Reagenti), and the concentration of the solution was varied in the range of 1-10 wt %. The solution was dripped on the tilted solid substrates, as depicted in Figure 1, and dried immediately in an air stream under ambient conditions. The humidity was 30-45% RH, and
Langmuir, Vol. 21, No. 21, 2005 9605 the air current velocity was v ) 0.1-0.2 m/s. Air current velocity and humidity were measured with a precise hygro-thermoanemometer from Extech Instruments 407412. The temperature in the evaporated layer was measured with a noncontact pyrometer (Extech 42 500). The slope of the substrate was varied in the range of R ) 30-45°. To visualize the solution flow, tiny black ink drops (∼500 µm in diameter) were applied to the substrate surface (Figure 1.). The ink was carried along the substrate by the polymer solution, leaving distinct black traces, which were distinguishable with an optical microscope. We studied polymer solution flow in two cases: restrained transversally and nonrestrained. Restrained flow on the tilted substrates was studied with a specially prepared limiting channel (framework), which is depicted in Figure 2. The height of the channel was 3 mm, D1 ) 14 mm, and D2 ) 4 mm. The channel was imposed tightly on the tilted substrate. The solution flow is sketched in Figure 2. Quartz glass, polypropylene (PP), and gold-coated quartz glass were used as substrates. The substrates were cleaned thoroughly with acetone and ethyl alcohol and rinsed with a large amount of distilled water. The influence of wetting on the patterning was studied using quartz glass substrates lubricated with silicon oil (Si-50, supplied by Dow Corning Co.). Blotting paper was used to wet the quartz glass plates with silicon oil, and the plates were then kept in an oven for 30 min at 50 °C. Shadowgraph visualization of the process was achieved using an experimental technique described in detail by Weh and Kumacheva.2,7 The structure of the dry film was studied by optical, scanning electron (SEM), and atomic force (AFM) (Park Scientific Instruments M5) microscopy.
3. Results and Discussion 3.1. Influence of Polymer Solution Concentration on Mesoscaled Patterning. Mesoscaled patterns were observed on each type of substratesquartz glass, PP, and gold-coated quartz glasssunder a broad range of concentrations (1-10 wt %) and under all inclination angles. Humidity did not exert an influence on the patterning. Temperature measurements showed that the process of evaporation was practically isothermic. The optical mi-
Figure 3. (a) Increases in the characteristic dimensions of the cells with the concentration of the polymer (PC) solution: (A) c ) 1 wt %, (B) c ) 7 wt %, (C) c ) 10 wt %; substrate: PP; slope: R ) 30°. (b) Increases in the characteristic dimensions of the cells with the concentration of the polymer (PC) solution: (A) c ) 1 wt %, (B) c ) 7 wt %, (C) c ) 10 wt %; substrate: quartz glass; slope: R ) 30°.
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Figure 4. SEM images of the mesoscaled patterns: c ) 7 wt %; substrate: PP; slope: R ) 30°.
Figure 5. AFM images of thin (A) and broad (B) boundaries separating mesoscopic cells: c ) 7 wt %; substrate: PP; slope: R ) 30°.
croscopy images of the patterns displayed in Figure 3 are similar to those already reported by our group. Mesoscaled cells are oriented lengthwise (parallel to the x axis, Figure 1). Closer SEM inspection of the patterns revealed mesoscopic cells separated by porous boundaries (Figure 4). The three-dimensional (3D) structure of the boundaries and their profile, measured along the boundary, were established with AFM microscopy (displayed in Figure 5). An AFM study of the mesoscaled structure allowed for an estimation of the film thickness, which was established as 2-6 µm and increased with the concentration of polymer solution. AFM demonstrated that there is no significant variation in the film height across the pattern (the mesoscopic cell is practically flat). We established that the concentration of the solution exerts a dramatic influence on the mesoscopic patterning. Higher concentrations promoted the formation of larger mesoscaled cells. The tendency of the cells to grow with the polymer concentration is illustrated by Figure 3. Another type of self-assembly is depicted in Figure 6. Distinct concentric structures built from micrometric pores could be recognized. The mechanism of the formation of these structures will be discussed below. (22) Mu¨ller-Buschbaum, P.; Bauer, E.; Wunnicke, O.; Stamm, M. J. Phys.: Condens. Matter 2005, 17, S363-S368. (23) Sharma, A. Langmuir 1998, 14, 4915. (24) Kargupta, K.; Konnur, R.; Sharma, A. Langmuir 2001, 17, 1294.
Figure 6. SEM image of the mesoscopic cell: c ) 7 wt %; substrate: PP; slope: R ) 30°.
3.2. Patterns Formed on the Substrates Lubricated with Silicon Oil. Patterning behavior changed dramatically when tilted substrates wetted with silicon oil were coated under the same conditions. Mesoscaled cells disappeared, and linear “strings” composed of mi-
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Figure 8. Shadowgraph visualization of the flow: (A) formation of the mesoscopic network, (B) bubble migration toward the network, and (C) formation of the eventual mesoscopic structure.
Figure 7. (A) SEM images of “strings” composed of the micrometrically scaled pores that formed on the substrates wetted with the silicon oil. (B) Self-assembled honeycomb pattern formed within the string. Slope: R ) 30°; substrate: PP; c ) 5 wt %.
crometric pores were formed, such as those depicted in Figure 7A. In specific areas of these strings, close-packed hexagonal honeycomb patterns were observed (Figure 7B), similar to the structures already reported by our group.20 3.3. Shadowgraph Visualization of the Mesoscaled Patterning. The shadowgraph technique allowed for effective visualization of the mesoscopic self-assembly dynamics. Several distinct stages of the self-assembling process were observed. At the first stage, a network built from thin (∼1 µm thickness) boundaries was formed on each type of substrate, with the exception of lubricated plates (Figure 8A). The boundaries were formed almost immediately and existed over the first 5 s of the drying process. The dimensions of the network cells were close to those of mesoscopic cells. We relate the formation of these boundaries to evaporation-induced instability, the nature of which will be discussed below. At the second stage, the intensive formation of solvent vapor bubbles was observed. The low boiling temperature of the solvent (39 °C) should be mentioned. The bubbles migrated toward the boundaries of the network cells (Figure 8B). The migration promotes the formation of cylindrically symmetric patterns, which are sketched in Figure 8C and depicted in detail in Figure 6. The total time span of the process is ∼10 s. We emphasize that no mesoscopic
network was observed when substrates wetted with silicon oil were coated. 3.4. Ink Tracer Visualization of the Polymer Solution Flow. A black ink tracer, carried by the polymer solution along the tilted substrate (Figure 1), allowed for effective visualization of the flow. We established that the character of patterning did not change in the presence of the ink drop (compare Figures 3aC and 9). Optical microscopy images (presented in Figure 9) bear witness to the fact that only longitudinal displacement of the tracer occurs. The black ink tracer forms a straight line parallel to the x axis (Figure 1); it is oriented lengthwise along with the mesoscopic cells. It is important that there is no experimental evidence of the transversal spreading of the tracer (Figure 9). 3.5. Restrained Flow of the Evaporated Solution. The flow of the solution restrained with the channel described in the experimental section gave rise to the mesoscaled structures seen under nonrestrained conditions and discussed previously. Mesoscopic patterning occurred both in the “broad” and in the “narrow” segments of the channel (Figure 10). It is noteworthy that the characteristic dimension of the mesoscopic cell is unaffected by the channel’s width. 3.6. Discussion. The shadowgraph visualization illustrated in Figure 8 supplies a picture that is typical for evaporation-induced instabilities.12-19 We will try to answer the question, What kind of instability occurs: surface-tension-induced Marangoni-like instability12-16 or mass transport instability?17-19 The characteristic dimensionless Marangoni numbers of the Marangoni instability are given by
MaC ) -
2 dσ d (dc/dz) dc ηD
(1)
when surface tension depends on the concentration c, in which σ is surface tension, η is the dynamic viscosity, D is the diffusion coefficient, z is the coordinate perpendicular to the surface, and d is the layer thickness, and by
MaT ) -
2 dσ d (dT/dz) dT ηλ
(2)
when surface tension σ depends on the temperature, in which λ is the thermal diffusivity. It should be emphasized that Marangoni numbers depend on the surface tension gradients only and not on the surface tension. Apparently, Marangoni instability (governed by MaT) could hardly be responsible for the mesoscopic self-assembly. The thickness of the film established by AFM is 2-6 µm (Figure 5); hence, the evaporation takes place under practically isothermal conditions.19 However, one more possibility of
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Figure 9. Traces formed by black ink drops (optical microscopy image). Substrate: PP; c ) 5 wt %; slope: R ) 30°.
Figure 10. Polymer solution flow restrained by the channel (optical microscopy image). Substrate: PP; c ) 5 wt %; slope: R ) 30°.
surface-tension-induced instability remains, which is governed by MaC. We have already proposed an alternative physical mechanism involving diffusion instability. This is based on the observation that, under intensive evaporation, a polymer-rich boundary layer of thickness s is formed almost immediately.25 The local perturbation of the thickness of such a layer, forming a trough from outside the evaporated boundary layer, has a tendency to grow as the reduced thickness facilitates the diffusion of the solvent in that place.19 Consequently, a local crest outside the boundary layer tends to grow as it suppresses the diffusion. Small-wavelength perturbations of this sort are suppressed by surface tension; therefore, there is a critical scale for the development of the layer instabilities. For this kind of instability, we obtained the characteristic dimension b of the mesoscopic cell estimation, given by19 3
b ) 2π
x
s4σ (D∆c)2F
(3)
in which s is the boundary layer thickness, and ∆c is the dimensionless concentration jump of solvent at the (25) Krantz, W. B.; Ray, R. J.; Sani, R. L. J. Membr. Sci. 1986, 29, 11.
boundary layer. For the sake of numeric evaluation, we estimate s ≈ 70 nm; this estimation for the thickness of the boundary layer was obtained by De Gennes and the physical parameters of the solvents that were established experimentally.18,26 Our estimation resulted in b ≈ 10 µm. This figure (at least) qualitatively coincides with experimental findings. It should be noted that eq 3, in contrast to the Marangoni number, depends on the surface tension directly and does not depend on the surface tension gradient. It is instructive to estimate the characteristic time associated with the suggested model of network formation. The characteristic time of diffusion may be estimated as t ≈ x2/D, in which x is characteristic film thickness, and D is the diffusion coefficient. In the very beginning of the process, the diffusion coefficient may be equal to that of pure solvent: D ≈ 4 × 10-9 m2/s. For the initial film thickness, x ≈ 20 µm, and the characteristic time is ∼10-1 s. This value correlates with the observed time for the formation of the mesoscopic network (panel A in Figure 8). The total time span of the process, which is ∼10 s, is defined by the relatively slow migration of the solvent vapor bubbles toward the boundaries of the network cells (panel B in Figure 8). We believe that eq 3 explains the tendency of the cells to grow with the polymer concentration, as illustrated in Figure 3. Waggoner showed experimentally that the diffusion coefficients of the chlorinated solvents are reduced as the polymer concentration c in the solution grows.27 Hence, according to eq 3, b grows with c. We suppose that the diffusion instability model explains (at least qualitatively) the experimental findings displayed in Figure 3. We draw special attention the fact that there is no evidence of the transversal flow of the solution within mesoscopic cells (see Figure 9), whereas Marangoni instability promotes the formation of such transversal flows.12 Particular emphasis should be placed on the fact that the restrained flow of the solution did not exert an influence on the mesoscopic cell dimensions, whereas patterns generated by Marangoni instability are extremely sensitive to boundary conditions.5-7,12-14 Influence exerted by the substrate on the patterning process calls for special treatment. Quartz glass, PP, and gold-coated substrates promoted the formation of very similar patterns. Hence, it could be concluded that surface tension σs at the solid substrate/air interface does not have an effect on the mesoscaled patterning in a very broad range of σs (∼30-150 mN/m).28-29 However, the situation (26) Prielmeier, F. X.; Lu¨demann, H.-D. Mol. Phys. 1986, 58 (3), 593. (27) Waggoner, R. A.; Blum, F. D.; Macelroy, J. M. D. Macromolecules 1993, 26, 6841. (28) De Gennes, P. G.; Brochard-Wyart, F.; Que¨re¨, D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003.
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changed dramatically when the substrate was lubricated with silicon oil. We believe that small quantities of silicon oil were mixed with the polymer solution under the flow, and it is well-recognized that even minor quantities of poly(dimethylsiloxane) essentially decrease the surface tension of polymer solutions.30 Thus, according to eq 3, the characteristic dimension of the cell is decreased drastically, and when it becomes smaller than the characteristic dimension of the solvent vapor bubble, the pattern is totally changed (Figure 7). Last but not least, there is no Marangoni instability when the liquid layer is heated from above.12,15 We observed patterns very similar to those presented in the paper when the polymer solution was heated intensively from above.19,20 Thus, we finally conclude that Marangoni instability could not be responsible for the mesoscopic patterning in our case, and mass-transport-induced instability, as developed in our previous works, provides a much better explanation for the experimental findings. Conclusions Patterning in evaporated polymer solutions was investigated when polymer solutions were deposited on tilted substrates. Self-assembled mesoscaled patterns were observed. The AFM study of the mesoscopic cells is (29) Van Krevelen, D. W. Properties of Polymers; Elsevier: New York, 1997. (30) Mann, E. K.; Langevin, D. Langmuir 1991, 7, 1112.
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reported first. The impact of the substrate on the formation of the pattern was studied: various solid substrates promoted the formation of very similar patterns, whereas substrates lubricated with silicon oil gave rise to submicrometrically ordered patterns. The concentration of polymer solution exerts a decisive influence on the characteristic dimension of the mesoscopic cell. The visualization of the flow, performed with an ink tracer, demonstrated the absence of transversal flow within mesoscopic cells. The restrained (with a specially prepared channel) and nonrestrained flows of the polymer solution gave rise to very similar patterns. All experimental findings could be explained on the basis of the assumption that patterning is due to mass transport instability, which is rather different from surface-tension-induced Marangoni instability; moreover, the traditional Marangoni instability mechanism does not satisfactorily explain the collection of experimental results presented in the paper. Acknowledgment. The authors are grateful to M. Zinigrad for his continuous support of our research activity. The authors are thankful to De Gennes, A. Nepomnyashchy, A. Voronel, A. Sheshnev, and G. Whyman for fruitful discussions. We thank N. Litvak, Al. Shulzinger, G. Leibovitch, and Z. Barkay for SEM and AFM imaging of the samples. The work has been supported by the Israel Ministry of Absorption. O.V.G. is grateful to the Taub and Shalom Foundations for their financial support. LA0518492
