Elastic Instabilities: A new route to design complex patterns

Pattern formation, i.e. the outcome of self-organization, has fascinated scientists for centuries. A large effort was devoted to understand the formation of regular patterns in dissipative structures. More recently, it appears that self-organized structures could also be achieved near equilibrium. There is a great variety of physical and chemical systems that, near equilibrium, exhibit periodic patterns. For instance, stripes or bubbles could be observed in thin films of magnetic garnet, superconducting materials, block copolymers, liquid crystals, phospholipids, and ferrofluids. Wrinkling instability of compressed rigid membranes on soft elastic substrates leads also to the formation of periodic patterns near equilibrium. Since the seminal paper of Bowden et al. (Nature 1998), various systems were proposed to generate nano- and micrometric wrinkles via the application of compressive stresses to multilayers. In addition to its purely fundamental interest, these instabilities also offer a new route to build in a simple, cost-effective, and well-defined way nano- and microstructured surfaces without the use of the traditional, robust techniques developed in the microelectronics industry. In this thesis, we develop a new system, metal-polymer-substrate trilayers, that exhibit wrinkling when heated above the glass transition temperature of the polymer. We explain in detail the mechanism at the origin of wrinkling and expand existing models to obtain a complete description of the relevant parameters that govern both the amplitude and the wavelength of the obtained pattern. In light of this, we show that by playing with the rheological properties of the polymer we are able to control precisely the geometry of the wrinkles. Furthermore, to generate surfaces with a tailor-made buckling pattern, we develop an original variant of the experiments. We tune the boundary conditions at the polymer-substrate interface by chemically patterning the substrates with regions of high and low adhesion. In this way, we obtain patterns with wrinkles being oriented differently above the sticky and the slippery regions. This last result is very surprising since it seems, at first sight, unrealistic to imagine that the chemical nature of the substrate could affect the elastic instability of the skin through a micron-thick polymer film. To explore wrinkled patterns with complex morphologies, we couple the wrinkling instability with solvent diffusion. Molecular diffusion in the polymer layer triggers the transition from an unwrinkled to a wrinkled state, provided that stimuloresponsive mutlilayers are used. The wrinkled pattern obtained is determined by the geometry of the diffusion process. To understand this surprising observation, we explain in detail how the scalar field related to the solvent concentration affects so strongly the elastic instabilities usually determined by the tensorial stress field. This mechanism allows us thus to grant exotic stress distributions which lead to very intriguing patterns (e.g. parallel or radial folds, herringbones). Interestingly, we find that under specific conditions, a hierarchical wrinkled morphology, i.e. pattern of wrinkles branching into generations of ever-higher folds, develops. We study other manifestations of hierarchical structures existing around us. In this frame, we derive a general concept that a plate constrained at one edge (with a fixed wavelength) but free at the opposite one evolves naturally to larger wavelengths to minimize its bending energy. We show theoretically that the evolution results from a compromise between the gain in bending energy and the energetic penalties related to the change of wavelength. We demonstrate the universality of these concepts by showing that our commonplace suspended curtain behaves like nanometer-thick polystyrene films deposited on water and further compressed. We close this thesis by making a short review of the main applications related to wrinkling that are already described in literature and develop in detail one of them, the use of wrinkling to investigate cell contact guidance.Doctorat en science