Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants

Abstract

Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an unstable fashion, developing a typical motif that resembles the familiar surface of a cauliflower plant. Through experiments on CVD production of amorphous hydrogenated carbon films leading to cauliflower-like fronts, we provide a quantitative assessment of a continuum description of CVD interface growth. As a result, we identify non-locality, non-conservation and randomness as the main general mechanisms controlling the formation of these ubiquitous shapes. We also show that the surfaces of actual cauliflower plants and combustion fronts obey the same scaling laws, proving the validity of the theory 6 2 over seven orders of magnitude in length scales. Thus, a theoretical justification is provided, which had remained elusive so far, for the remarkable similarity between the textures of surfaces found for systems that differ widely in physical nature and typical scales. Contents

Synthesis of graphene-like transparent conductive films on dielectric substrates using a modified filtered vacuum arc system

“…The STM measurements reveal a rough and disordered carbon coating characterized by a fractal cauliflower-shape structure with an average roughness of 3.0 nm comparable to that published in Ref. 18. On the same sample, a TEM characterization shown in Figure 4(b) has been carried out.…”

Fabrication of broadband omnidirectional non-reflective gold surfaces by electrodeposition

“…6, the electrodeposition time has a significant effect on the morphology of the gold deposits grown at 21.2 V versus Ag/AgCl. As already observed for the production of amorphous hydrogenated carbon films by chemical vapor deposition, 21 a granular structure appears at short times with a characteristic length scale that grows in a disorderly fashion with further deposition. Figure 6 also shows that the electrodeposition time has also a significant effect on the appearance of the gold deposits grown at 21.2 V. They become darker with time, which corresponds to the fractal growth of the romanesco broccoli-like microstructures.…”

Pattern-Wavelength Coarsening from Topological Dynamics in Silicon Nanofoams

“…In turn, the dynamical study of the topological properties of the cellular structure allows us to derive the value of the coarsening exponent. Thus, while a number of assumptions remain to be understood from a more fundamental or rigorous point of view, our Letter puts forward the use of topological characterizations to classify pattern dynamics far from equilibrium, in particular, for classes of systems that remain not completely understood, such as the KS and related systems [43]. An additional benefit of the approach, to be explored further, is its applicability to higher dimensional foams [29,44,45].…”