Arrays of microlenses of complex shapes prepared by reaction-diffusion in thin films of ionically doped gels
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(a) Top picture is the scheme of the experimental setup. Middle picture shows an agarose stamp (denoted with hatched lines) placed in contact with gelatin at . The arrows indicate the directions of diffusion of cations (black arrows) and anions (gray arrows). Bottom: After the stamp is taken off , and gelatin is allowed to dry , the regions between the stamped features appear as curvilinear depressions on the gelatin’s surface. The dimensions of these depressions, and , depend on the size of the stamped features, and on the concentrations of the salts used. The graph on the right shows qualitative trends observed with increasing salt concentrations. As or are increased (from dashed to solid to dotted lines), the degree of gel swelling in the regions below and around the features increases; at the same time, the reaction fronts propagate more and more inwards lifting the central portion of the circle. Above certain concentration (here, above that corresponding to the solid line), the dimensions of the depressions—that is, and —start decreasing. (b) Optical micrograph of an array of circularly symmetric depressions (, , , ] in the gelatin master (left), and a SEM image of the corresponding array of microlenses on the surface of a PDMS replica. The scale bars correspond to . The geometries of microlenses in this and other arrays—with exception of large circles and/or low salt concentrations—were well-approximated by the sections of a sphere, and their focal lengths agreed with those calculated using the spherical approximation. For the array shown here replicated in PDMS —Refs. 18 and 19, the focal length was measured at compared to the calculated value of .
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(a) Experimental dependence of the depth, , of circularly symmetric depressions on feature size, , for varying concentrations of in gelatin [ 0.25%, 0.5%, 0.75%, 1.0%] and for a constant concentration of in the stamp (10%). Inset shows the same data plotted against for different values of [ , , , ]. (b) as a function of for and for varying from 5% to 20% [ 5%, 10%, 15%, 20%]. Inset shows the same data plotted against for different values of [ , , , ]. Graphs in (a) and (b) were created based on profilometric measurements of the gelatin masters. Standard deviations are reported for the depths of the microlenses, and were collected from at least three independent stampings with two profilometric scans (averaged over ten times each) spanning two to five features for each stamping. For lenses with , the standard deviations for the depths and widths of the microlenses were less than 1%. (c) Experimental (left) and modeled (right) surface profiles for circular depressions (solid line) and (dashed line) for varying concentrations of silver nitrate and for in gelatin. (d) Theoretical dependence of on (both in arbitrary units) for varying concentrations of in gelatin [ 0.75, 1.5, 2.25, 3] and with constant in the stamp. (e) Theoretical dependence of on for varying concentrations of in the stamp [ 25, 50, 75, 100] and for (arbitrary units). Each data point in (d) and (e) is an average of 50 simulation runs performed with , , ; . In all simulations, the concentrations were in arbitrary units that, however, were linearly proportional to the experimental concentrations. The 10% experimental concentration of was assigned a numerical value of 50 in the simulations, and concentration of potassium hexacyanoferrate corresponded to 3.
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Microlenses of complex base shapes: (a) triangular, (b) square, (c) hexagonal, and (d) pentagonal stars. The left column shows the optical micrographs (, ), while the right one has the results of the numerical simulations performed with , , , , ; . The insert to (a) illustrates a long-range order in the stamped array of triangles. Insets to (b) and (c) are the images of the focal plane of the corresponding lens arrays. Scale bars in the primary pictures in (a)–(d) correspond to ; those in the inserts are 1 mm in (a) and in (b) and (c).
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