Front propagation into unstable metal nanowires

Abstract

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled, and forms a coherent pattern behind it. It is well described by a linear marginal stability analysis of front propagation into an unstable state. In some cases, nonlinearities of the wire dynamics are found to trigger an invasive mode that pushes the front. Experimental procedures that could lead to the observation of this phenomenon are suggested. Front propagation into unstable states occurs in many areas of physics, chemistry, and biology (see Ref.[1] for a recent review), and is often related to pattern formation mechanisms. In this paper, I show that metal nanowires, whose dynamics can be described by a continuum model, the nanoscale free-electron model (NFEM) [2,3,4], exhibit such front propagation into unstable cylinders.Recent transmission electron microscopy experiments [5,6,7,8] have observed gold and silver nanowires to form long cylinders, with diameters of order one nanometer, that are stable for seconds at a time at room temperature. A theoretical description within the NFEM shows [3,9] that such self-assembly is natural if conditions are such that the atom mobility allows the wire to explore its configuration space and reach its equilibrium shape, as is the case at room temperature for these metals.Due to the high number of surface atoms-with low coordination numbers-in such nanowires, surface effects are particularly important, and favor wire breakup due to the Rayleigh instability [10,11]. It has been shown, using the NFEM [4,12], that the quantum confinement of electrons in the cross-section of the wire provide electron-shell effects-similar to those well-known in cluster physics [13]-that compete with surface effects, and stabilize cylindrical wires for a finite range around magic radii [11,12], as well as a number of number of wires with broken axial symmetry [14,15].The NFEM [2,3,4] is a continuum model where the atomic structure is replaced by a uniform, positively charged background, and the emphasis is put on the electronic structure. An extension of the model [3] includes ionic dynamics through surface self-diffusion, which is expected to dominate the structural dynamics in such thin wires. One of its important predictions is that a random wire naturally evolves into a universal equilibrium shape consisting of a perfect cylinder of a magic radius, connected to thicker leads [3,9]. Recently, the rich kink dy- * Electronic address: buerki@physics.arizona.edu namics of the NFEM has been described [16], and shown to be qualitatively similar to the thinning mechanism of gold nanowires ...