Multi-fractal hierarchy of single-walled carbon nanotube hydrophobic coatings.A hierarchical structure is an assembly with a multi-scale morphology and with a large and accessible surface area.  Recent advances in nanomaterial science have made increasingly possible the design of hierarchical surfaces with specific and tunable properties.  Here, we report the fractal analysis of hierarchical single-walled carbon nanotube (SWCNT) films realized by a simple, rapid, reproducible, and inexpensive filtration process from an aqueous dispersion, then deposited by drytransfer printing method on several substrates, at room temperature.  Furthermore, by varying the thickness of carbon nanotube random networks, it is possible tailoring their wettability due to capillary phenomena in the porous films.  Moreover, in order to describe the wetting properties of such surfaces, we introduce a two-dimensional extension of the Wenzel-Cassie-Baxter theory.  The hierarchical surface roughness of SWCNT coatings coupled with their exceptional and tunable optical and electrical properties provide an ideal hydrophobic composite surface for a new class of optoelectronic and nanofluidic devices.
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