Mesoscopic Reaction-Diffusion Fronts Control Biomorph Growth

Abstract

Biomorphs are inorganic assemblies of crystalline nanorods that form noncrystalline microshapes such as helices, funnels, and leaf-shaped sheets. This nanoscale-to-microscale self-organization occurs from simple reactants in aqueous solution and suggests new engineering methods as well as insights into biomineralization; to date, however, the underlying mechanisms are not understood. Here we describe a reaction-diffusion model for sheet growth that reproduces the experimentally observed biomorph shapes. The sheet edges are logarithmic spirals caused by the propagation failure of the crystallization front. The resulting defect motion is dynamically related to nonlinear wave dynamics in subexcitable media such as the photoinhibited Belousov-Zhabotinsky reaction. An expanded model includes a nematic-like director field that sets the average nanorod orientation irreversibly during crystallization. The growth front of worm-like biomorph helices also obeys logarithmic spirals, suggesting future applications of reaction-diffusion models for the simulation of three-dimensional biomorphs.