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Center for Nonlinear Studies |
Wavefronts associated with reaction diffusion and self-assembly processes are ubiquitous in the natural world. For example, the frontal polymerization of actin and tubulin is largely responsible for cellular movement and the separation of chromosomes in cellular mitosis, respectively, and such fronts play a large role in the movement of cells and particulates at larger scales within the tissue of animals and even in the competitive social interactions and population dynamics of animals at larger scales. Mathematically similar self-assembly fronts also arise in azoic phenomena such as crystallization and diverse other types of ordering fronts involving thermodynamic transitions. While it often claimed that this type of self-sustaining or /autocatalytic/ front propagation is well described by mean field ‘reaction diffusion’ or ‘phase field’ ordering models, it has recently become appreciated from simulations that /fluctuation effects/ in lower spatial dimensions can lead to appreciable deviations from the classical mean field theory (MFT) of this type of front propagation. The present work directly addresses the existence of these fluctuation effects in a real physical system through a high resolution study of this type of frontal growth process in two dimensions where fluctuation effects are expected based on previous simulations. In particular, we consider the frontal ordering of the organosilane molecules deposited on the silica-coated surfaces, a system of technological interest in its own right. By following the progress of this self-organization process via near-edge x-ray absorption fine structure spectroscopy (NEXAFS), we find that the self-assembled monolayer (SAM) of organosilane molecules organize from the edge of the wafer as a propagating planar wavefront with a well-defined velocity, /c/. In accordance with two-dimensional simulations of this type of front propagation that include fluctuation effects, we find that the interfacial width w(t) of these SAM self-assembly fronts exhibits a power-law broadening in time, w(t) ~ t^b , rather than the constant width predicted by mean field theory. Moreover, the observed exponent values accord rather well with previous simulation estimates. This is the first experimental evidence of fluctuation-induced interfacial broadening in autocatalytic front propagation. These observations have significant implications for diverse other near two-dimensional ordering fronts occurring in a biological or materials processing context.
Host: Turab Lookman