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This and the next image are from:
Derek Breid (University of Massachusetts, Amherst),
“Controlling morphology in swelling-induced wrinkled surfaces”, Ph.D dissertation, Polymer Science and Engineering, University of Massachusetts – Amherst, February 2012
PARTIAL ABSTRACT: Wrinkles represent a pathway towards the spontaneous generation of ordered surface microstructure for applications in numerous fields. Examples of highly complex ordered wrinkle structures abound in Nature, but the ability to harness this potential for advanced material applications remains limited. This work focuses on understanding the relationship between the patterns on a wrinkled surface and the experimental conditions under which they form. Because wrinkles form in response to applied stresses, particular attention is given to the nature of the stresses in a wrinkling surface. The fundamental insight gained was then utilized to account for observed wrinkle formation phenomena within more complex geometric and kinetic settings.
In order to carefully control and measure the applied stresses on a wrinkling film, a swelling-based system was developed using poly(dimethylsiloxane) (PDMS), surface-oxidized with a UV- ozone treatment. The swelling of the oxidized surface upon exposure to an ethanol vapor atmosphere was characterized using beam-bending experiments, allowing quantitative measurements of the applied stress. The wrinkle morphologies were characterized as a function of the overstress, defined as the ratio of the applied swelling stress to the critical buckling stress of the material. A transition in the dominant morphology of the wrinkled surfaces from dimple patterns to ridge patterns was observed at an overstress value of ~2. The pattern dependence of wrinkles on the ratio of the principal stresses was examined by fabricating samples with a gradient prestress. When swollen, these samples exhibited a smooth morphological transition from non-equibiaxial to equibiaxial patterns, with prestrains as low as 2.5% exhibiting non-equibiaxial characteristics. This transition was seen both in samples with low and high overstresses. To explore the impact of these stress states in more complex geometries, wrinkling hemispherical surfaces with radii of curvature ranging from 50-1000 m were fabricated using the same material system. Upon wrinkling, the hemispheres formed complex hierarchical assemblies reminiscent of naturally occurring structures. The curvature of a surface exhibited a correlation with its critical buckling stress, independent of other factors. This enables the surface curvature to be used as an independent control over the dimple-to-ridge transition which occurs as a function of overstress. As in the flat buckling surfaces, this transition was shown to occur at an overstress value of ~2. Surface curvature was also shown to improve the observed hexagonal ordering of the dimple arrays, resulting in the formation of regular "golf ball" structures. Geometric effects in finite flat plates were also examined. Using circular masks during the oxidation process, plates with radii ranging from 0.4-8.6 mm were created. Upon wrinkling, a dimple-to-ridge transition was observed with increasing plate size, with the morphological switch occurring at a radius of ~2 mm. This observed transition was not found to be due to the inherent mechanics of plates of different size
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