Various types of micro- and nanoarchitectures can be spontaneously fabricated using chemical reactions initiated by wet stamping (WETS) and propelled by diffusive transport of participating reagents. Desired small-scale structures emerge as a result of complex sequences of reaction-diffusion events. These events are encoded in the chemical kinetics and transport properties of the system's components, and in the system's geometry. With various types of chemistries and initial conditions imposed by WETS, it is possible to ‘program’ different fabrication tasks and make technologically useful structures, such as microlens arrays, microfluidic systems, diffractive elements, and supports for cell studies.

Article Outline

Delineating initial conditions by wet stamping

One-step reactions: fabrication of microlens arrays

Sequential reactions: fabrication of multilevel microfluidic architectures

Periodic reactions: ‘wavy’ substrates

Parallel reactions: multitasking

Hard substrates

The third dimension

Outlook

References

Despite enormous progress in materials’ structuring, many types of technologically useful, small-scale patterns and surface topographies remain challenging targets for currently used methods. This is especially true for multilevel or curvilinear surface reliefs, which are sought after in microfluidic devices¹ and micro-total-analysis (μTAS) systems², as stamps for simultaneous patterning of more than one type of biomolecule³, in microsensors and actuators⁴, and in a variety of optical elements^{5 and 6}. Typically, fabrication of such structures requires either several rounds of photolithography and precise registration^{7 and 8} or the use of serial techniques, such as localized electrodeposition methods⁹, reactive-ion etching¹⁰, proton and ion beam machining^{11 and 12}, laser ablation¹³, powder blasting¹⁴, or electrochemical micromachining¹⁵. These procedures are usually laborious, often expensive, and are especially difficult when dealing with hard/brittle materials and features of submicrometer dimensions.

Conceptually, all these methods share the common assumption that in order to make smaller architectures, one must first increase the resolution of the ‘parent’ fabrication tool – be it a stamp, writing beam, or milling microchisel. Although this ‘what you print/ablate/drill/mill is what you get’ philosophy appears very logical and quite intuitive, it is interesting to note that nature – the ultimate builder – uses it only rarely to make surface patterns and structures (Fig. 1). Indeed, skin patterns in fish¹⁶, zebras, and tigers¹⁷, compositional zones in seashells¹⁸ and agates¹⁹, or the fantastic three-dimensional shells of radiolarians²⁰ and diatoms²¹ are not meticulously ‘imprinted’ by some underlying template or a writing tool, but rather emerge spontaneously from a self-organization process carried out by the organism as a whole. On the most abstract (and simplistic) level, such processes can be viewed as a chemical ‘program’ comprising the details of the chemical reactions involved (e.g. rate constants of mineralization of diatoms’ siliceous skeletons), information about the migration/delivery of different substrates (e.g. diffusion constants and concentrations of silica to be mineralized), and the initial/boundary conditions of the process (e.g. positions of silica deposition vesicles). The execution of these ‘instructions’ is synonymous with the task of fabrication.

In this review, we illustrate how the idea of ‘chemical programming’ can be extended to the fabrication of some technologically relevant micro- and nanostructures. The ‘programs’ we execute are all based on simple inorganic reactions and diffusive transport of the participating chemicals through the supporting ‘soft’ medium. The desired structures emerge via complex sequences of reaction and diffusion (RD)²² events coupled to the medium's elastic properties. The architectures built in this way have spatial resolution down to the submicrometer level and have applications in micro-optical and microfluidic devices, optical gratings, and supports for controlled cell spreading. Once made, they can be replicated faithfully into elastomers, polymers, and – using another RD processing step – into hard materials, including glasses, crystals, and semiconductors.

Delineating initial conditions by wet stamping

Over the past two years, our group^{22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 and 37} has developed an experimental technique that allows the initiation and precise control of RD processes in complex microgeometries. In its simplest variation, our method – called wet stamping, or WETS – uses micropatterned hydrogel stamps to deliver a solution of one or more³⁵ reactants into dry gel or polymer films doped with chemical(s) that react with those delivered from the stamp (see Fig. 2a).

In a typical experiment, a patterned agarose stamp is prepared^{23, 30 and 38} by casting hot agarose against an appropriately micropatterned photolithographic master, soaking the solidified gel in a desired reagent, and placing it onto a dry gel substrate. Upon contact, reagents flow from the stamp's microfeatures into the film and initiate an RD process therein. Importantly, the difference in hydration of the stamp and the dry substrate ensures not only directional but also purely diffusive transport of chemicals (see elsewhere³⁸ for details). This property eliminates hydrodynamic/backflow effects²³ and enables the resolution of micro- and even nanoscopic³⁷ RD patterns. Overall, this straightforward technique enables one to impose well-defined initial and boundary conditions determined by the geometry of the stamp's features, and to control RD processes down to the nanoscale^{30 and 37}.

One-step reactions: fabrication of microlens arrays

To translate an RD process into a surface topography, it is necessary to couple it to the elastic properties of the supporting medium. Gel substrates used in WETS permit such coupling with a variety of inorganic reactions that cause gel swelling^{39 and 40} with a magnitude proportional to the reaction's extent at a given location.

As an example, consider a reaction of silver nitrate delivered from the stamp with potassium hexacyanoferrate uniformly dispersed in a thin layer of dry gelatin. To make microlenses²⁹, RD is initiated from stamps patterned with an array of depressions in bas relief (Fig. 2a). The precipitation reaction between Ag⁺ cations (diffusing inward from the contours of the depressions into gelatin) and [Fe(CN)₆]⁴⁻ anions contained therein, 4Ag⁺ + [Fe(CN)₆]⁴⁻ → Ag₄[Fe(CN)₆] (↓), results in a pronounced expansion of the gel. Importantly, the degree of this expansion is: (i) proportional to the amount of precipitate formed at a given location, and (ii) monotonically decreases with the distance from the features’ edges. The latter is a result of the fact that, as the Ag⁺/precipitation front propagates inwards from the feature's edge, the unreacted [Fe(CN)₆]⁴⁻ experiences a sharp concentration gradient at this front and diffuses in its direction (i.e. outwards). By the time Ag⁺ cations reach the center of the patterned region, almost all the [Fe(CN)₆]⁴⁻ anions have diffused away, and the degree of swelling is smaller at the center than near the feature's edge. Ultimately, when the RD process comes to a halt, the surface of the gel is patterned with curvilinear depressions. Depending on the applied pattern, these depressions can be sections of a sphere (when RD is initiated from circles) or pyramidal (when initiated from polygonal contours). In both cases, the heights and curvatures of the microstructures can be controlled by the concentrations of the chemicals used and/or by the dimensions of the patterned features. Importantly, the depressions can be replicated easily into optically transparent polymers (Fig. 2b) to give large (up to 3 cm × 3 cm) arrays of regular microlenses with excellent focusing properties.

Sequential reactions: fabrication of multilevel microfluidic architectures

The reaction between Ag⁺ and [Fe(CN)₆]⁴⁻ can produce complex multilevel surface reliefs when applied to processes initiated from disjoint features³¹. As in the previous example, regions directly below the stamped features swell to the highest degree and are connected by curvilinear valleys. Remarkably, however, these valleys are now bisected by midlevel buckles running perpendicular to the direction of reaction-front propagation. To explain the formation of these buckles (Fig. 3), we first note that, unlike in the case of microlenses where the diffusion of [Fe(CN)₆]⁴⁻ toward the incoming reaction fronts was approximately radial, the hexacyanoferrate ions in the present system move in response to more complex gradients. In particular, because various portions of the nearby features are at different distances, [Fe(CN)₆]⁴⁻ concentration gradients also exist in the direction perpendicular to the reaction-front propagation. These gradients cause slow, ‘secondary’ flows of [Fe(CN)₆]⁴⁻ (red arrows in Fig. 3a). The key step in transforming these flows into buckles is that, as time passes, the Ag₄[Fe(CN)₆] precipitate reacts with water and decomposes into immobile Ag₂O and regenerated [Fe(CN)₆]⁴⁻. Importantly, Ag₂O collects in the buckle regions, causes their swelling, and hinders further migration of [Fe(CN)₆]⁴⁻ ions. While the locations and relative heights of the buckles can be determined precisely by modeling⁴¹, the rule of thumb to guide device fabrication is that the buckles connect the closest and most ‘spiked’ regions of the nearby features and their heights can be varied between 15-50% of the valley depth.

Fig. 4 illustrates how these heuristic rules can be used in the design of passive microfluidic mixers. Here, the initial conditions for the RD process (as before, determined by the geometry of the stamp) are given by contours of the channel from which Ag⁺ cations migrate ‘inwards’ into the dry gel. Because the stamped regions (‘the background’) swell uniformly, the channels are depressions in an otherwise flat surface. The ridges in the channels are obtained by using stamps in which the sidewalls of the stamped patterns have either small, spiked protrusions (Fig. 4a) or small features between these walls (e.g. circles in Fig. 4b). The first type of design gives channels with perpendicular, regularly spaced ridges – channels of very similar topographies have been shown to be excellent micromixers⁴². In the second design, the arrangement of ridges is more complex and is inspired by the caterpillar flow mixer developed by Ehrfeld and coworkers⁴³. In both cases, the architectures developed in the gelatin film can be replicated easily in polydimethylsiloxane (PDMS), demonstrating that they can be used as masters for actual devices.

Periodic reactions: ‘wavy’ substrates

So far, we have discussed reactions that can generate only one (e.g. a lens) or a few (e.g. buckles) distinct microstructures for every stamped feature. Ideally, we would like to have chemical ‘instructions’ in our repertoire that can generate multiple structures from one feature^{23, 28 and 37}. The so-called periodic precipitation (PP) reactions^{44 and 45} are ideal candidates for this task. These reactions involve select pairs of inorganic salts that – while diffusing through a gel matrix – not only precipitate upon reaching the solubility product, but also collect the precipitate into discrete bands (Fig. 5a). Importantly, the positions x_n of the consecutive bands increase regularly according to Jablczynski's law⁴⁶, x_n+1 / x_n = 1 + p, where p stands for the spacing coefficient. We have recently shown²³ that, for PP processes initiated by WETS in thin films, the values of p can be adjusted by both the concentrations of salts used and the geometry/dimensions of the wet-stamped initial conditions. In addition, many PP reactions (notably, 2AgNO₃ + K₂Cr₂O₇ → Ag₂Cr₂O₇ (↓) + 2KNO₃) cause buckling of the substrate in the regions of the precipitation bands, and the heights of the buckles can be controlled and adjusted with nanometer precision³⁷ by changing various system parameters. Together, these findings allow for very flexible schemes of surface structuring.

Figs. 5b-d illustrate application of this method to the fabrication of arrays of parallel surface wrinkles with heights that increase approximately linearly from tens of nanometers to several microns³⁷. The generation of these otherwise hard-to-make reliefs^{47, 48, 49 and 50} follows from the fact that the forming bands collect all the precipitate from between each other, and that the amount of precipitate collected by band number n (counting in the direction of front propagation) is proportional to its distance from the source x_n. In addition, deformation of the surface is proportional to the local concentration of the precipitate. By varying either the concentration of the co-precipitating salts and/or the physical properties of the gel layer (which affect diffusivities of ions), it is then possible to modulate not only band spacing but also the overall slopes of the patterns. Fig. 5d shows the use of one such pattern to orient cancer cells. In contrast to surface reliefs having binary topographies, the ‘wavy’ supports of varying heights allow for parallel (i.e. simultaneous) monitoring of cellular responses to a continuum of surface topographies. This ability has proven useful in our research on the quantitative aspects of cell spreading and motility in response to physical obstacles (a topic related to cancer metastasis⁵¹). Interestingly, the same types of reliefs are efficient microparticle sorters: when a solution of microparticles of different sizes is dewetted from the surface, smaller particles are selectively trapped by shallow waves while larger ones are captured in deeper grooves³⁷.

Finally, with proper adjustment of the boundary and initial conditions, PP reactions can be used to build diffractive elements of complicated geometries. For example, by propagating the AgNO₃/K₂Cr₂O₇ reaction in photopatterned gel films³⁷, it is possible to vary local band spacings and curvature, or even stop band formation in certain regions (Fig. 6a). The same reaction propagating inwards from a circular boundary of radius R produces concentric rings²⁸ with radii r_n that scale as ln(R - r_n) (N n), where n is the ring number counted from the center outwards (Fig. 6b, left). These rings can focus light similar to the well-known Fresnel zone plates⁵². Remarkably, when the three-dimensional topography of these rings is replicated into optically transparent polymers or elastomers (Fig. 6c), the resultant structures (Fig. 6b, right) focus light more efficiently than Fresnel lenses of comparable dimensions having more bands (Fig. 6d).

Parallel reactions: multitasking

A good program should be able to execute more than one procedure. Translating this requirement into the language of our chemical instructions, it is desirable to execute several different fabrication reactions in parallel. Technically, this task appears straightforward as both the substrate and the stamp can be loaded with more than one reagent. The difficulty lies in finding chemicals that will react selectively without interference of cross-precipitation (‘chemical orthogonality’) and lead to independent surface deformations (‘mechanical orthogonality’).

Fulfilling the first condition has proven relatively easy, and we have used this strategy to create several types of chemically patterned surfaces, such as the multicolor and gradient patterns³⁵. For surface fabrication, however, the added mechanical orthogonality condition is hard to fulfill, as the salts that swell thin films usually co-precipitate indiscriminately. To overcome this limitation, we have used a different strategy in which films are composed of multiple layers with each layer supporting a different fabrication process. A simple illustration of this approach in a two-layer system is shown in Fig. 7. Here, AgNO₃ delivered from the stamp reacts (i) with Ag₄[Fe(CN)₆] contained in the bottom layer to cause gel swelling, and (ii) with K₂Cr₂O₇ contained in the top layer to produce PP bands. The sum of these processes gives deep curvilinear features (like the ones in lenses or microfluidic circuits) decorated with smaller PP undulations. Architectures of this type are potentially interesting in the context of microfluidic optical detection, where substances flowing through deep channels could be analyzed by light diffracting from the smaller-scale reliefs embossed on the channel's wall(s)^{53 and 54}.

Of course, these are only preliminary examples, and generalization to other types of structures will require systematic identification of suitable orthogonal chemistries. A possibly simpler route might be first to perform the reactions to distribute the appropriate chemicals within the substrate, and only then develop the three-dimensional microstructure by using an auxiliary swelling reaction. Work in this direction is now in progress in our laboratory.

Hard substrates

The RD approach can be extended to structuring hard materials. Although in this case RD processes cannot be propagated through the material itself, structuring can be achieved by interfacial reactions. In the simplest variation^{32 and 36} – with no real programming yet – an agarose stamp soaked with a chemical that etches/dissolves the desired hard material is simply placed in contact with the substrate. Localized structuring relies on diffusive transport of chemicals within the stamp such that the stamp's bulk acts as a two-way chemical ‘pump’, simultaneously supplying fresh etchant (e.g. HF for glass) and removing reaction products (SiF₆²⁻) from the gel/substrate interface (Fig. 8a, left).These processes allow the gel to literally cut into the substrate – importantly, with full retention of the stamp's topography. Fig. 8 illustrates the use of this method for etching arrays of microlenses in glass (Fig. 8a), complex reliefs in a water-soluble crystal (Fig. 8b), and a nanopattern in Si (Fig. 8c).

The method can be rendered programmable by including reagents in the stamps that react with the products of etching, and can thus autonomously direct reaction fluxes in the system. Fig. 8e provides one example⁵⁵, in which an agarose stamp structuring a K₃[Fe(CN)₆] crystal carries Fe²⁺ ions. These ions react with the dissolved [Fe(CN)₆]³⁻ and give a Prussian blue precipitate that is impermeable to ion diffusion and also hardens the agarose matrix³⁶. The precipitate initially forms mostly near the centers of the stamp's features, and depletes Fe²⁺ from near the features’ walls. Etching is gradually redirected toward the walls and, as it progresses, more and more precipitate forms near the features’ centers. (This somewhat counterintuitive statement is based on both experiment and modeling of the diffusive fluxes in the system.) The growing difference in Prussian blue content between the central and the peripheral regions causes the latter to sag, and leads to even more etching near the walls. Overall, the process etches wells with raised regions near their centers. This primitive form of diffusional ‘feedback’ mechanism can be applied in other geometries and with other chemistries to yield nonbinary reliefs from binary stamp patterns.

The third dimension

Extension of any scientific approach – either experimental or theoretical – from two to three dimensions is usually a nontrivial but rewarding enterprise. Fabrication by RD is no exception. The difficult part is to control the flow of chemicals in small, three-dimensional spaces; the reward could be an entirely new class of materials with underlying three-dimensional micro- or nanostructures. One possible approach – similar to WETS in two dimensions – is to develop methods that deliver the reagents to their initial locations on three-dimensional manifolds. This strategy, however, would almost certainly require complicated delivery systems and thus lose much of the charm of spontaneous fabrication. An alternative approach is to perform three-dimensional fabrication on simple components and then use the power of self-assembly⁵⁶ to build larger structures.

To illustrate this point, consider fabrication of an open lattice crystal, in which metallic microspheres are distributed periodically within a transparent, supporting medium (Fig. 9). Could RD assist in building such a structure? On the whole, probably not since it would be rather hard to find a chemical reaction that goes through the material and deposits metallic spheres periodically in three-dimensional space. With the assistance of self-assembly, however, the problem becomes tractable if one uses three-dimensional RD only to create the unit cell domains. This is illustrated in Fig. 9a, where an easy-to-make silicate microcube is first uniformly loaded with colloidal Cu particles. An etching reaction is then initiated at the cube's boundary (by simply immersing the cube in an HCl solution)⁵⁷. As the reaction front propagates inwards, it removes the metal and ultimately gives a sphere centered perfectly at the cube's center. When many such cubes are used and then self-assembled, they give the desired open-lattice crystal (Fig. 9b). Of course, with more complex shapes for the unit cell elements, this fabrication scheme could generate objects other than spherical and crystal symmetries other than cubic. Such RD/self-assembly mediated transformations in three dimensions, however, are largely an uncharted territory. They certainly present some fantastic opportunities for future work and one day, may even allow us to fabricate in three dimensions as skillfully as radiolarians do.

Outlook

In summary, programmable chemical reactions provide a conceptually novel method of micro- and nanofabrication. Since only a few systems have been demonstrated so far, more work is needed to test suitable reactions and substrate materials. This effort should ultimately enable classification of reactions/substrate combinations according to their mutual ‘orthogonality’, the tasks they can perform, and application of these combinations to fabricate structures of arbitrary topographies. While for some desired structures the choice of fabrication reactions and initial conditions should be straightforward, others might require nontrivial back-engineering. In this context, development of computational algorithms^{28, 29, 30 and 31} to accompany experimental studies presents fascinating challenges and opportunities for modeling of micro- and nanoscale RD processes. From a practical perspective, the choice of materials for reagent delivery should be improved, and more sturdy alternatives to agarose should be sought. Finally, extension of the method to three dimensions and its synergy with self-assembly can lead to new types of micro- and nanostructured materials. While this is certainly an ambitious goal, its pursuit is motivated by nature's elegant examples of chemical reactions performing complex fabrication tasks in three-dimensional cellular environments.