6.4.2.1 Solvent
Varying experimental parameters can lead to changes in the relative magnitude of the film’s folding diameter and folding time. The folding diameter is a measure of the diameter of the cylinder that forms upon exposure of these PDMS/SU-8 films to nonpolar solvent. Solvents were selected based upon their ability to swell native PDMS. Five solvents (pentane, toluene, 2- butanone, ethyl acetate, dioxane) were selected with literature reported PDMS solvent swelling ratios ranging from 1.16 (dioxane) to 1.44 (pentane)9. It was determined that as the PDMS swelling ratio increases, both time required for the material to fold and the folding diameter will decrease (Figure 6.3). This experimental result can be viewed in the same manner that increasing the lattice mismatch of a semiconductor bilayer or thermal expansion mismatch of a bimetallic film causes the films to coil tighter and more quickly. In our case a large volumetric change leads to a greater internal strain, driving self-assembly. Bending curvature of bilayers are typically analyzed by the classical Timoshenko formula 12. Our system follows the same general principals but is complicated because it lacks a defined boundary between the two materials. The gradient of crosslinked SU-8 50 fades gradually from the UV-exposed surface region until the material has no crosslinked photoresist. An additional complication is the significant changes in the film thickness and Young’s modulus that occur during swelling. We hope to address these issues and present a quantitative view in future work; currently we limit the scope of this work to a qualitative understanding of the variables within the system.
6.4.2.2 Degree of SU-8 Crosslinking
Another variable that affects the folding dynamics of this film is the post-bake curing temperature that follows UV patterning. Samples consisting of 50 wt % PDMS/SU-8 (120 m
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thick) were photoexposed and the post-bake temperature was varied (50-200oC). These samples were then cut into identical sizes (32mm x 32mm square) and immersed in toluene. Toluene was selected as the solvent because it was previously determined (See Figure 6.3) to allow for rapid folding. Samples heated at 50oC and 200oC did not spontaneously fold. The Tg of SU-8
monomer (uncross-linked) is 55oC. At curing temperatures below the Tg, the SU-8 does not
significantly cross-link and therefore the system is not constrained by the densely cross-linked SU-8. The 50oC-cured samples are also tackier than other samples and undergo greater plastic deformation upon delamination from the support, further indicating that the SU-8 has not been cross-linked. The opposite heating extreme, 200oC, is approaching the Tg of a fully cross-linked
SU-8 film. At this processing temperature, uncontrolled cross-linking occurs evenly throughout the film. The material yellows and hardens, becoming brittle and therefore difficult to remove from the processing support. These samples did not fold because there was no decreasing gradient of crosslinked SU-8 to create the different swelling rates between SU-8 and PDMS upon exposure to nonpolar solvent. The ideal postbake curing temperature range was determined to be between 90-150oC. At these temperatures, the cross-linking of the SU-8 component remains localized and allows for a gradient of decreasing degree of cross-linking density to be formed, which minimizes both the folding time and folding diameter(See Figure 6.4).
6.4.2.3 PDMS/SU-8 Composition Ratio
Another variable that affects the folding properties is the mass ratios of PDMS to SU-8 in the pre-polymer solution. An increase in mass percent PDMS will decrease the degree of cross- linking of the SU-8 because of the increased average separation between SU-8 monomer units due to lower relative concentration. This will result in smaller, cross-linked SU-8 portions that are more elastic and susceptible to solvent infiltration (the mechanical behavior will more closely
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resemble bulk PDMS). The patterned line samples will fold into cylinders but with a larger radius of curvature (relative to samples with a lower mass % PDMS) and therefore smaller folding diameter. The variation in the mass % PDMS was found to have a processing window between 50-75wt % PDMS. At PDMS mass percent below 50%, the mixture becomes extremely viscous and cannot spin coat. When the mass percent of PDMS exceeds 75% the polymer film becomes too thin and difficult to handle.
6.4.2.4 Film Thickness
The thickness of the film can affect its folding dynamics, and the film thickness is controlled by the speed (rpm) of the spin coating. A plot of the film thickness versus spin speed is presented in Figure 6.5 for sample compositions of 50% and 75% weight PDMS. Using these two PDMS mass ratios, the average inner folding diameter in toluene was determined as a function of film thickness (Figure 6.6). It was found that thicker samples (samples spun at a slower rate) for a given composition had larger folding diameters. Within the spin speed range studied (500 up to 2500 rpm, 30 seconds), all samples successfully folded, indicating formation of an SU-8 cross-linking gradient for all thicknesses explored. The thickest samples (spun at 500 rpm) showed the greatest variation in folding diameter between 50% and 75% PDMS by mass, which was partly attributed to reproducibility problems of the film thickness at low very spin speeds. Also, these samples did not fold into a complete cylinder, so the diameters had to be extrapolated from the radius of curvature. Even thinner layers (spin coated at 3500 rpm) were tested, yielding a more complex folding geometry that will be discussed later.
The growth of the folding diameter with increasing thickness is once again similar in trend to what is observed with the rolling of thin bi- and multilayer films13 analyzed using variations of the classical Timoshenko formula.14 In our system, the depth of the patterned,
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cross-linked, SU-8 gradient is constant (between each particular sample composition) and the thickness of the PDMS layer increases with decreasing spin speed. The PDMS to a first approximation can be viewed as the strained substrate and the SU-8 as the film layer (though not continuous) in a bilayer system. Experiments with the rolling of strained semiconductor films13 have demonstrated that the folding diameter tends to increase with increasing substrate thickness, this is identical to what is observed in our system (Figure 6.6). We also observe that with increasing sample thickness the differences in the folding diameter for the two compositions (50 and 75 wt % PDMS) increases. This is attributed to less SU-8 cross-linking as the PDMS component is increased; demonstrating that sample composition greatly affects the folding.
6.4.2.5 Sample Size
The sample size also affects the folding time and folding diameter. Squares and rectangles of different side lengths were investigated to learn more about the relationship of size to folding dynamics. For the rectangle, only the length of the side parallel to the patterned lines was varied. In both instances it was determined that the average folding time is inversely proportional to the size of the sample (see Figure 6.7). This is attributed to the fact that the diffusion rate of the toluene into the sample is constant (1.32E-6 cm2/s for toluene in 100% PDMS15). As the sample becomes larger, more toluene will diffuse into the film per unit time. More PDMS swells, driving the sample to fold more rapidly. When folding is complete, the system has reached equilibrium, and relatively constant diameter is obtained (Figure 6.8). This is in agreement with the classical Timoshenko formula14 which has no length dependence only thickness dependence at equilibrium. Even though more film has to fold in the longer samples, this extra folding was determined to be negligible in relation to folding time. The lengths of the lines appear to more strongly control the folding time than the total number of cross-linked SU-8
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lines in the sample. This is explained by comparing the folding time for the 25mm x 25mm square (30 ± 7 sec, Figure 6.7a) to the rectangle (length = 25 mm, width = 12.5 mm, 28 ± 6 sec, Figure 6.7b) with half the total area. The rectangular geometry has roughly half the number of lines but an identical folding time. In the opposite case, where the rectangle (length = 25 mm, width = 50 mm, 28 ± 6 sec, Figure 6.7b) has twice the area (square 13 mm, 51 ± 11 sec, Figure 6.7a), the folding time is shorter. The rectangle with length 13 mm and width 25 mm (48 ± 3 sec, Supplemental Figure 6.7b) in contrast has a similar folding time to square (3 mm, 51 ± 11 sec, Supplemental Figure 6.7a).