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One-Step Multilevel Microfabrication by Reaction-Diffusion Christopher J. Campbell, Rafal Klajn, Marcin Fialkowski, and Bartosz A. Grzybowski* Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208 Received May 18, 2004. In Final Form: July 12, 2004
A new experimental technique is described that uses reaction-diffusion phenomena as a means of one-step microfabrication of complex, multilevel surface reliefs. Thin films of dry gelatin doped with potassium hexacyanoferrate are chemically micropatterned with a solution of silver nitrate delivered from an agarose stamp. Precipitation reaction between the two salts causes the surface to deform. The mechanism of surface deformation is shown to involve a sequence of reactions, diffusion, and gel swelling/contraction. This mechanism is established experimentally and provides a basis of a theoretical lattice-gas model that allows prediction surface topographies emerging from arbitrary geometries of the stamped features. The usefulness of the technique is demonstrated by using it to rapidly prepare two types of mold for passive microfluidic mixers.
Introduction Surfaces with multilevel, nonbinary surface reliefs are sought in microfluidic devices1 and µTAS systems,2 as stamps for simultaneous patterning of more than one type of biomolecules,3 and in a variety of optical elements.4,5 Microfabrication of multilevel surfaces involves either several rounds of photolithography and precise registration6,7 or the use of serial techniques, such as two-photon lithography,8 synchrotron radiation etching,9,10 proton and ion beam machining,11,12 or localized electrodeposition methods.13 Given the laborious nature and/or high cost of these methods, it would be desirable to develop multilevel patterning techniques that are both parallel and one-step; in this context, we considered the reaction-diffusion (RD) phenomena.14,15 Although RD systems have long been known to spontaneously generate intricate spatial patterns,16,17 they have not been considered useful in modern * Author to whom correspondence should be addressed. E-mail:
[email protected]. Fax (847) 491-3728. (1) Stroock, A. D.; Dertinger, S. K. W.; Ajdari, A.; Mezic, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647. (2) Ehrfeld, W.; Hessel, V.; Lehr, H. Top. Curr. Chem. 1998, 194, 233. (3) Tien, J.; Nelson, C. M.; Chen, C. S. Proc. Nat. Acad. Sci. 2002, 99, 1758. (4) Daschner, W.; Long, P.; Stein, R.; Wu, C.; Lee, S. H. Appl. Opt. 1997, 36, 4675. (5) Fu, Y. Q.; Bryan, N. K. A.; Shing, O. N. Rev. Sci. Instrum. 2000, 71, 1009. (6) Boche, B. Microel. Microeng. 1994, 26, 63. (7) Walsby, E. D.; Wang, S.; Xu, J.; Yuan, T.; Blaikie, R.; Durbin, S. M.; Zhang, X. C.; Cumming, D. R. S. J. Vac. Sci. Technol. B 2002, 20, 2780. (8) Yu, T.; Ober, C. K.; Kuebler, S. M.; Zhou, W.; Marder, S. R.; Perry, J. W. Adv. Mater. 2003, 15, 517 (9) Katoh, T.; Nishi, N.; Fukagawa, M.; Ueno, H.; Sugiyama, S. Sens. Actuators, A 2001, 89, 10. (10) Tolfree, D. W. L. Rep. Prog. Phys. 1998, 61, 313. (11) Watt, F.; van Kan, J. A.; Osipowicz, T. MRS Bull. 2000, 25, 33. (12) Fu, Y. Q.; Kok, N.; Bryan, A.; Hung, N. P.; Shing, O. N. Rev. Sci. Instrum. 2000, 71, 1006. (13) Madden, J. D.; Hunter, I. W. J. Microelectromech. Sys. 1996, 5, 24. (14) Turing, A. M. Phil Trans. R. Soc. 1952, 237, 37. (15) Nicolis, G.; Prigogine, I. Self-orgnaization in nonequilibrium systemssfrom dissipative structures to order through fluctuations; Wiley: New York, 1977.
microfabrication and microtechnology, mainly because of the inability to control the RD patterns at the microscale and to translate the gradients of participating chemicals into surface deformations. Here, we describe an RD system that overcomes both of these limitations and provides a basis for a reliable and flexible method of macrofabricating surfaces with useful multilevel reliefs. This system uses agarose stamps patterned in bas-relief to locally deliver a solution of silver nitrate, AgNO3, onto a surface of dry gelatin doped with potassium hexacyanoferrate, K4Fe(CN)6. A precipitation reaction between silver cations diffusing into gelatin and hexacyanoferrate anions therein results in a pronounced expansion (swelling) of the gel that is proportional to the amount of precipitate formed at a given location. Regions directly below the stamped features swell to the highest degree and are connected by mid-level ridges (buckles)18-20 bisecting low-level grooves. Remarkably, the buckles are approximately perpendicular to the directions of propagation of the reaction fronts originating from the patterned features. This directionalitysuncommon to RD systems, in which structures usually form along the reaction frontssis a consequence of a complex sequence of reaction, diffusion, swelling, and gel contraction. In the following, we describe the experiments that allow qualitative understanding of this sequence, use the results of these experiments to construct a theoretical model to calculate surface topographies emerging from arbitrary geometries of the stamped patterns, and apply our method to fabricate two types of molds for passive microfluidic mixers.1,21 (16) Campbell, C. J.; Fialkowski, M.; Klajn, R.; Bensemann, I. T.; Grzybowski, B. A. Adv. Mater. 2004, in press. (17) (a) Ouyang, Q.; Swinney, H. L. Nature 1991, 352, 610. (b) Lengyel, I.; Epstein, I. R. Science 1991, 251, 650. (18) Bowden, N.; Brittain, S.; Evans, A. G.; Hutchinson, J. W.; Whitesides, G. M. Nature 1998, 393, 146. (19) Sharp, J. S.; Jones, R. A. L. Adv. Mater. 2002, 14, 799. (20) Yoo, P. J.; Park, S. Y.; Kwon, S. J.; Suh, K. Y.; Lee, H. H. Appl. Phys. Lett. 2003, 83, 4444. (21) Campbell, C. J.; Grzybowski, B. A. Philos. Trans. R. Soc. London A 2004, 362, 1069.
10.1021/la0487747 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/24/2004
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Langmuir, Vol. 21, No. 1, 2005 419 (T ≈ 25 °C, RH ≈ 20-40%). Replicas of the micropatterned gelatin were made by casting PDMS and curing it at 30 °C overnight.
Results and Discussion
Figure 1. (a) The upper picture illustrates the experimental setup for patterning AgNO3 onto thin films of dry gelatin doped with K4Fe(CN)6 and defines pertinent dimensions: d ) 50 µm, Ls ) 25-300 µm, Lf ) 50-500 µm, hs ) 0.5-1 cm, hf ) 50-75 µm, w ) 1 cm. (b) The graph gives the dependence of the gel swelling (after 15 min of contact) on the concentration of silver nitrate solution in the stamp. The line is the least-squares fit to the data. (c) The pictures show a sideshot of a stamp soaked in 1.04 M AgNO3 and placed onto gelatin (50 µm thick, 1% w/w K4Fe(CN)6) at times t ) 0 (upper picture) and t ) 20 min. (lower picture). Scale bar is 200 µm. (d) Optical micrograph of a nonuniformly swollen gelatin surface 30 s after stamping with an array of circles (Ls ) 100 µm, Lf ) 100 µm, 1 M AgNO3). (e) An SEM picture of a UV-cured Norland Optical Adhesive replica of a swollen gel shown in (d). Note that the pattern has no buckles between the features.
Experimental Section Figure 1a outlines the experimental procedure. A hot, degassed 8% w/w solution of agarose (OmniPur Agarose, Darmstadt, Germany) in deionized water was cast against an oxidized poly(dimethyl siloxane) (PDMS, Sylgard 184, Dow Corning) master having an array of depressions (25-750 µm) embossed on its surface. After gelation, the agarose layer was gently peeled off and cut into ∼ 2 cm × 2 cm rectangular blocks (stamps) patterned with an array of raised features in bas-relief. The stamps were soaked in a solution of AgNO3 (typically, 0.65-1.50 M) for 12 h. Immediately prior to use, each stamp was dried on a tissue paper for 120 s and applied onto a dry, thin (d0 ≈ 50 µm) film of saltdoped gelatin. Gelatin films were prepared from deionized water solution containing 10% w/w gelatin (Gelatin B, 225 bloom, Sigma-Aldrich) and 1% w/w of K4Fe(CN)6; this solution was heated at 75 °C for 30 min, spin-coated onto a flat glass surface, allowed to gelate under ambient conditions, and thoroughly dried under vacuum for 48 h. Stamps were removed from the surface of gelatin approximately t ) 20 min after their application, and the surface was left to dry for 6-7 h under ambient conditions
1. Mechanism of Surface Deformation. Once in conformal contact, water from the stamp rapidly wets the surface of dry gelatin and slowly diffuses into its bulk. Wetting of the surface is driven by capillarity and occurs at a rate of ∼1.5 µm/sec; the transport of water into the bulk of the gel is a diffusive process against the osmotic pressure due to the immobilized K4Fe(CN)6 and is characterized by the diffusion coefficient22 Dw ≈ 10-7 cm2/ s. When silver cations carried by water enter the gel, they are instantaneously precipitated in reaction with Fe(CN)64to give Ag4Fe(CN)6 (subsequently, this precipitate slowly reacts with water to give silver oxide and hexacyanoferrate anions; vide supra). Local concentration of Ag+ is replenished by the diffusion from the stamp, but the precipitation front does not propagate until all Fe(CN)64- at a given location is used. As a result, the wetting front moves faster than the precipitation frontsin other words, precipitation occurs in an already wetted gel. Both the water uptake and the formation of precipitate contribute to the pronounced swelling of the gelatin film (Figure 1b,c). To quantify this swelling, we performed a series of experiments in which either pure water or solutions of AgNO3 (0.12-1.5 M) were delivered to the gelatin surface from unpatterned stamps (i.e., from rectangular agarose blocks). We found that pure water swells the 50 µm gel by 90 µm and that for silver nitrate solutions the degree of swelling increases linearly with concentration: d - d0 ) R[AgNO3] + β, where d is the thickness of the swollen gel, d0 is that of a dry gel, R ) 112 µm/M of AgNO3, and β ) 90 µm. We note that the coefficient of expansion, R, was much smaller (approximately by an order of magnitude) for solutions of other common inorganic salts we tested (e.g., FeCl3, CoCl2, and CuCl2). We do not attempt to explain here the peculiar effect of Ag4Fe(CN)6 on the structure of the gel but only mention that various inorganic salts can cause either gel swelling or its contractionsthe magnitudes of these effects are hard to predict and rationalize and their origin(s) is not completely understood.23,24 When stamps patterned in bas-relief and soaked in pure water were applied onto the gelatin film, the surface swelled uniformly. In contrast, identical stamps soaked in a solution of AgNO3 gave nonuniform swelling (Figure 1d,e) and later developed multilevel structure reliefs (cf. Figures 2-4). These observations suggest that the formation of multilevel structures is related to the formation of the Ag4Fe(CN)6 precipitate in the gelatin matrix. To understand this relationship, we performed a set of experiments in whichsusing a combination of chemical testing and SEM imagingswe monitored local concentrations of the chemicals participating in the RD processes at various times after stamping. These chemicals were silver cations delivered from the agarose stamp, hexacyannoferrate anions originally in the gelatin matrix, silver hexacyanoferrate precipitate that formed when these ions reacted, and silver oxide particles and hexacyanoferrate ions into which Ag4Fe(CN)6 slowly decomposed (Figure 2a). To visualize the concentrations of either unused or regenerated Fe(CN)64-, we stained the gelatin with FeCl3s (22) Fialkowski, M.; Campbell, C. J.; Bensemann, I. T.; Grzybowski, B. A. Langmuir 2004, 20, 3513. (23) Wu, C.; Yan, C. Y. Macromolecules 1994, 27, 4516. (24) English, A. E.; Mafe, S.; Manzanares, J. A.; Yu, X.; Grosberg, A. Y.; Tanaka, T. J. Chem. Phys. 1996, 104, 8713.
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Figure 2. The reaction-diffusion phenomena underlying formation of surface deformations. (a) Chemical reactions taking place in the wetted gelatin: silver cations react with hexacyanoferrate anions, instantaneously forming Ag4Fe(CN)6 precipitate. Over time, the silver hexacyanoferrate complex decomposes into silver oxide and hexacyanoferrate anions.18 Local concentrations of Fe(CN)64- can be monitored by staining with iron (III) chloride; in the schemes in pictures (b)-(d) these local concentrations are approximately color-coded in the shades of gray. Similarly, regions where Ag2O forms are indicated by grainy patterns. (b) Swelling and RD at early times. The upper right picture is an optical micrograph of the gelatin surface 1 min after stamping. The schemes in the left and central columns give the local concentrations of the reagents, and the directions in which they diffuse. Symbol C/B means that C is present close to the gelatin’s surface, whereas unconsumed B resides beneath, in the bulk of the gel. Pictures in the right column are the optical micrographs of surfaces stained with FeCl3: the upper picture shows a flooded surface; the lower one shows a surface that was contact-stamped. (c) The arrows illustrate the directions of diffusion at times ∼1 min < t < ∼20 min. In the scheme in the central column, regions where the mutually perpendicular arrows meet correspond to precipitation zones (buckles); these regions are also shown in the lower-left scheme. The optical micrograph in the right column shows the surface flooded with FeCl3sthe pale blue color reflects the precipitation of hexacyanoferrate ions. (d) When the gel dries buckles, distinct surface buckles appear. Pictures in the right column illustrate the regeneration of Fe(CN)64- and production of Ag2O particles resulting from the slow decomposition of C. (e) Profilograms of the buckled surfaces: over the stamped features (left) and over the buckles (center and right). The buckles are more pronounced when more concentrated AgNO3 solutions are used. (f) Dependence of the separation between the buckles on the spacing between stamped squares, Ls, for two different ratios Lf/Ls, where Lf is the size of a square in the array.
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Figure 3. The first two columns from the left show optical micrographs of regular arrays of surface deformations forming from arrays of features of different geometries: the left column has the large-area photographs, and the right column corresponds to close-ups. (a) buckling in a square array of circles (Ls ) 150 µm, Lf ) 75 µm) gives eight buckles per circle circle, with two from each side of the square unit cell surrounding the circle. (b) Buckling from an array of triangles, with eight buckles per each triangle. (c) An array of crosses forms 12 buckles extending from each feature. (d) An array of teeth gives buckles extending from the edges of every tooth. (e) Stamped array of wavy lines gives buckles in the regions of close proximity between the lines. (f) Transverse buckling does not occur in geometries such as, for example, concentric circles. In all experimental pictures, the scale bars correspond to 200 µm. In all pictures, the regions below the stamped features are the most elevated ones. The rightmost column shows the patterns predicted by the lattice gas model; locations of the buckles are indicated by red lines. The values of parameters used to generate these patterns were: A(n ) 0) ) 4, B ) 100, λ ) 2, DA/DB ) 0.3, c ) 4; Wo was used as a fitting parameter.
when Fe3+ cations reacted with Fe(CN)64-, they produced a dark Prussian Blue precipitate. Particles of Ag2O produced by the decomposition of Ag4Fe(CN)6 were imaged by SEM. The results of our experimentssillustrated here for a stamped square array of squaresssupport the mechanism of surface deformation that can be qualitatively described as a succession of the steps (Figures 2be): (i) RD at Early Times (t < ∼1 min; Figure 2b) Silver cations diffuse from the stamp into the gelatin matrix and precipitate Fe(CN)64-. Since most precipitation occurs
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Figure 4. RD microfabrication of molds for passive microfluidic mixers. (a, i) A scheme of a microfluidic channel with two inlets, a mixing region (snaking lines) and one outlet; typical channel width, w ≈ 100-250 µm. Red circle indicates the area whose the close-ups are shown in (b)-(d). (ii) The left picture illustrates a stamp geometry in which channel edges are decorated with small triangles. The right picture shows the topography of the gelatin surface, which a stamp of this geometry is expected to produce. Modeling predicts the formation of pronounced ridges connecting the tips of nearby triangles on opposite channel walls. (iii) Same as in (ii) but for a channel with small circles inside; right picture shows the results of modeling. This stamped geometry is expected to produce a channel having a criss-cross pattern of surface ridges. (b) Experimental profilograms along (I) and across (II) the channels described in (b, ii) and (b, iii), respectively. (c,d) Large-area optical micrographs and an SEM image (lower right) of the two types of molds for microfluidic mixers. The insert in (c) shows the mold illuminated from the bottom to visualize distinct surface depressions separated by buckles. All scale bars correspond to 300 µm.
below the stamped features, these features swell to the highest degree and are connected by shallow valleys (Figure 2b, pictures on the left); at this stage, there are no buckles connecting the nearby squares. The unreacted hexacyanoferrate anions between the features experience sharp concentration gradients at the precipitation fronts and diffuse in their directionsthat is, toward the features. For an array shown in Figure 2b, the regions between the neighboring squares are cleared of Fe(CN)64- first and appear transparent when stained with FeCl3. Under the stamped features themselves, hexacyanoferrate ions near the surface are fully converted to Ag4Fe(CN)6 but are present deeper into the layer, where they are supplied by the diffusion from between the squares. This is confirmed by two experiments: (1) when the surface is flooded with a solution of FeCl3 which is allowed to penetrate deep into the gelatin, the squares turn blue (Figure 2b, upper right picture); (2) in contrast, when the surface is touched for a brief period of time (“contact-stamped”) by an agarose
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block soaked in FeCl3, water penetrates to a smaller depth, and the features stain to a pale blue color (lower left picture). (ii) RD at Intermediate Times (∼1 min < t < ∼30 min; Figure 2c). The “unused” Fe(CN)64- ions remaining in the central region between the four squares (white circle in the middle scheme in Figure 2c) diffuse not only in the directions of the incoming reaction fronts but also “horizontally” and “vertically” toward the clear lines between the neighboring squares. Since these lines are depleted of Fe(CN)64-, diffusion toward them is driven by the concentration gradient of Fe(CN)64-. Hexacyannoferrate ions diffusing in the “horizontal” and “vertical” direction are “intersected” by the Ag+ ions diffusing from the edges of the squares. As a result, precipitation occurs approximately along the line joining the nearest vertexes of neighboring squares (indicated as light gray bands in the lower-left scheme in Figure 2c). Diffusion of chemicals and water in the gel continues until, after ∼20 min, the free energy gain due to wetting is offset by the increase in the elastic potential energy due to the deformation of the surface.22 At that time, the local concentrations of chemicals are set: the regions between the neighboring squares and the central region contain neither the precipitate nor Fe(CN)64- and appear transparent upon flooding with FeCl3 (Figure 2c, upper right picture); the regions below the squares and along the precipitation zones connecting the squares contain mostly Ag4Fe(CN)6 and residual amounts of unconsumed Fe(CN)64- (these regions stain pale blue). We note that the intensity of the blue color below the stamped features is lower than in Figure 2b, indicating that even the Fe(CN)64- deep in the bulk of the gel got consumed. (iii) Gel Drying After Stamp Removal (t ≈ 6 h; Figure 2d). When the stamp is removed from the surface, two processes occur simultaneously: water slowly evaporates from the gelatin and Ag4Fe(CN)6 decomposes to silver oxide and Fe(CN)64-. Evaporation is accompanied by sagging of the gel, predominantly in the regions devoid of Ag4Fe(CN)6. Because these regions are diffusionally separated by precipitation zones,25 they sag independently. Gelatin settles down on both sides of each precipitation zone, while the zones themselves remain elevatedsthese elevated regions are the surface microbuckles that become pronounced roughly 6 h after the removal of the stamp (Figure 2d, picture on the left). Decomposition of Ag4Fe(CN)6 is evidenced by the formation of Ag2O particles (cf. the SEM image in the lower right picture in Figure 2d) and by the features and the precipitation zones turning dark blue upon FeCl3 staining (Figure 2d, upper right picture). 2. Surface Topography. General Characteristics. In the gelatin patterned with a square array of squares, the central point between the four squares is the nadir of the surface and lies ∼20-40 µm below the flat tops of the stamped features. The crests of the buckles rise ca. ∼1015 µm above the nadir and have heights, hB, measured from the crest of a buckle to a nadir between two neighboring buckles, of 2-7 µm. Precise dimensions depend on the concentration of AgNO3 in the stamp and on the periodicity of the stamped array. For a given (25) Formation of precipitates in salt/K4Fe(CN)6-gelatin systems such as the one we studied causes a dramatic decrease of the diffusion coefficients of ions and/or water moving through the precipitation zones (see ref 16). Importantly, in the array of squares discussed in the text, precipitation along the horizontal and vertical lines (buckles) obstructs diffusion between the central and clear-line regions. This effect was verified experimentally by applying dye solutions into the swollen gel: while the dye diffused rapidly in the regions between the buckles, its diffusion through the buckles was much slower.
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geometry of the array, the heights of the buckles increase roughly linearly with increasing concentration of silver nitrate solution (Figure 2e) up to 15% w/w. More concentrated solutions are impractical to use as they destroy the gelatin matrix. For a given concentration of the stamping solution and for Ls < 2Lf′, hB increases with increasing spacing between the features up to Ls ≈ 150 µm. When Ls > 2Lf, no buckles appear, reflecting the fact that not all of the wide space between the squares is wetted and swollen, and the precipitation zones responsible for the formation of buckles do not form. Spacing between the nearest, parallel buckles increases linearly with Ls and does not depend on the ratio Lf/Ls for values up to ∼1.5 (Figure 2f). We note that buckles form from features as small as Lf ) 50 µm and separated by Ls ) 25 µm. For different geometries of stamped features, the emerging surface topographies are often complex. While a square array of circles (Figure 3a) gives an easily predictable buckling pattern similar to that of a square array of squares, the locations of buckles emerging from the arrays of triangles (Figure 3b), crosses (Figure 3c), teethed-lines (Figure 3d), or wavy lines (Figure 3e) are hard to foretell a priori. The qualitative predictions that can be made are that (i) regions below the features always swell the most, (ii) the mid-level buckles form approximately between the pointed edges of nearby features, (iii) no ridges form in patterns in which there is no diffusion in the direction perpendicular to the line joining the nearby points on nearby features (e.g., in arrays of parallel lines or concentric circles, Figure 3f), and (iv) most pronounced relative swelling (i.e., ratio of buckle height to absolute depth of the relief) is maximal for spacing between the features ∼150-200 µm and for [AgNO3] ) 15%. Modeling. Although the reaction/diffusion/swelling equations governing the evolution of the surface are too complicated to solve analytically, surface topographies can be faithfully modeled using numerical methods. To this end, we implemented a lattice-gas model with a reaction term algorithm.26 In this model, the reactants diffused and reacted in a gel matrix represented as a union of square cells. Initially, each cell had the same concentration of hexacyanoferrate ions (denoted here as A). Silver cations (B) and water (W) were delivered to the cells that corresponded to the features of the stamp. On the basis of our earlier work on wetting of thin films of ionically doped dry gelatin,22 we assumed that the rate of delivery of both B and W decayed exponentially with time (here, with simulation step number, n): B˙ ) B0 exp(-λn) and W ˙ ) W0 exp(-λn), where λ is a constant. In each simulation step, (i) B and W were added to the gel, (ii) A and B were allowed to perform m diffusion steps on the square lattice (relative diffusion coefficients DA/DB ) 0.3 were taken from experiment; parameter m related speeds of diffusion and delivery), and (iii) in cells where A and B were present in sufficient quantities, they reacted according to 4A + B f A4B V. The energy of the system was then calculated as a sum of swelling and wetting energies. We assumed that swelling energy was proportional to the sum of squares of the vertical deformations of the gel over all cells,27,28 ES ∼ ∑ij(∆hij)2. Because, as evidenced by experiment, these deformations were proportional to the amount of precipitate, swelling energy could be written out as ES ) c∑ij[A4B] 2ij where c is the energetic cost of swelling per unit concentration of A4B and the summation is over all cells (26) Doolen, G. D., Ed.; Addison-Wesley: New York, 1990. (27) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Weinheim, 1953; Chapter 13. (28) Rivlin, R. S. In Rheology, Theory and Applications; Eirich, F., Ed.; Academic Press: New York, 1956; pp 351-384.
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(i, j). The wetting energy was favorablesthat is, it lowered the energy of the systemsand was linearly proportional (with the proportionality constant set equal to -1) to the amount of water transferred into the gel, EW ) -W0(1 exp(-λn))/λ; we note that, because of this linear proportionality, water molecules did not have to be explicitly accounted for in the simulations. The system was allowed to evolve as long as its total energy remained negative: simulation was halted when the cost of deforming the gel exceeded the energetic gain of wetting. Local concentrations of precipitate at that time were then plotted to visualize the buckled surface. As shown in the right column of Figure 3, the predictions of the model were in excellent agreement with experiment. A graphically interfaced executable of the program to predict surface topographies emerging from an arbitrary stamped pattern is available in the supplemental information.29 3. Microfabrication of Multilevel Molds for Microfluidic Mixers. While the ribbed surfaces obtained from arrays of isolated features might have interesting mechanical (especially, bending moduli) and optical properties (e.g., nonbinary diffraction gratings), we expect our RD patterning method to be most immediately applicable to the fabrication of multilevel microfluidic circuits (usually, a very laborious process involving multiple rounds of photolithography1,21,30). To demonstrate this capability, we prepared two types of surface molds for passive microfluidic mixers (Figure 4). Passive mixers have no moving parts and achieve mixing by virtue of channel topography alone. In the most common type of design, the bottom of the channel is patterned with an array of surface ridges.1,31 When laminarly flowing liquids are passed through such a patterned channel, the ridges cause the liquids to advect and “fold onto themselves”. This so-called chaotic advection32,33 increases the interfacial area between the fluids and facilitates mixing. In our designs, the channels were delineated by the portions of the surface that were not stamped. The stamped regions swelled uniformly so that the channels were depressions in an otherwise flat surface. The ridges in the channels were obtained by using stamps in which the sidewalls of the channels had either small protrusions (triangles in Figure 4a, ii) or features inside of the channels (circles in Figure 4a, iii). The first type of design gave channels with regularly spaced ridges running across the channel (Figure 4b,c; left column) and of heights ca. 16% of the channel’s depthschannels of very similar topographies have been shown to be excellent micromixers.34 In the second design (Figure 4b,c; right column), the arrangement of ridges was more complex and was inspired by the caterpillar flow mixer developed by Ehrfeld and co-workers.35 In both cases, the design of the stamps was aided by the modeling software we developed, and the modeled surface topographies were in excellent agreement with those observed in experiments. Also, both gelatin molds were successfully replicated in PDMS, demonstrat(29) The executable program can be found in the supplemental information. (30) Ehrfeld, W.; Lowe, H.; Hessel, V. Microreactors: new technology for modern chemistry, 1st ed.; Wiley-VCH: Weinheim, 2000. (31) Stroock, A. D.; Dertinger, S. K. W.; Whitesides, G. M.; Adjari, A. Anal. Chem. 2002, 74, 5306. (32) Aref, H. J. Fluid Mech. 1984, 143, 1. (33) Ottino, J. M. The kinematics of mixing: stretching, chaos, and transport.; Cambridge University Press: Cambridge, 1989. (34) Stroock, A. D.; McGraw, G. J. Philos. Trans. R. Soc. London A 2004, 362, 971. (35) Ehrfeld, W.; Hartmass, J.; Hessel, V.; Kiesewalter, S.; Lowe, H. In Proc. Micro Total Analysis Systems Symp. 2000; van den Berg, A.; Olthuis, W.; Bergveld, P., Eds.; Kluwer: Dordrecht, 2000; pp 33-40.
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ing that they can be used as masters for actual devices. We are currently developing more-sophisticated designs that will use multilevel topographies not only for mixing but also for fluid redirection and optical detection of analytes. Conclusions In summary, we have developed a novel, flexible experimental technique that significantly simplifies microfabrication of multilevel surface reliefs. This work demonstrates, for the first time, that reaction-diffusion phenomena can provide a viable alternative to established microfabrication methods. Since a large number of substances are known that cause gels to swell or contract to different degrees and with different rates,23,24 our method can be used with many types of chemistries and can produce other types of surface reliefs (e.g., periodic ridges through Liesegang-like precipitation36). In this context, stamps or gel supports containing more than one reactive substance might be especially interesting and might not only yield intricate surface topographies but also present (36) Muller, S. C.; Ross, J. J. Phys. Chem. A. 2003, 107, 7997.
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a range of interesting theoretical questions about RD phenomena with several competing processes. Since the regions of surface deformations can be selectively chemically modified/colored (cf. Figure 2), the method can be used for fabrication of optical elements (e.g., diffraction gratings or arrays of planar waveguides), in which the surface ridges would have different values of the index of refraction and/or optical absorptivity than the remaining portions of the surface. Acknowledgment. B.G. gratefully acknowledges financial support from Northwestern University start-up funds and from the Camille and Henry Dreyfus New Faculty Awards Program. C.C. was supported in part by the NSF-IGERT program “Dynamics of Complex Systems in Science and Engineering” (DGE-9987577). M.F. was supported by the NATO Scientific Fellowship. Supporting Information Available: Program to predict surface topographies emerging from an arbitrary stamped pattern. This material is available free of charge via the Internet at http://pubs.acs.org. LA0487747
