Doctor of Philosophy (PhD)
A liquid thread of radius R will break up into drops if the axial wavelength of the surface perturbation L > 2πR. If L < 2πR, the thread is stable and will remain intact. This is Rayleigh’s stability criterion based on a continuum model. We use molecular dynamics to simulate the evolution of Lennard-Jones liquid threads with equilibrium radius R = 2.3-6.6, where R has been non-dimensionalized by the distance at which the Lennard-Jones potential equals zero. We find that if R is fixed, the wavelength L is bounded by Lmin and Lmax. For L > Lmax the thread always breaks up and stays as drops, and for L < Lmin the thread remains intact. However, for Lmin < L < Lmax, the thread oscillates continuously among several shapes. The appearance of various shapes can be explained by the energy fluctuation of the system.
We also simulate the evolution of Lennard-Jones nanowires with equilibrium radius R = 1.57, 2.58, 3.59, and 4.60 by molecular dynamics. The wires are evolved at temperatures slightly below the melting temperatures, which are found by computing the bond-length fluctuation. Rayleigh’s criterion is obeyed with the critical wavelength slightly smaller than 2πR.
We then introduce a marker-particle method for the computation of three-dimensional solid surface morphologies evolving by surface diffusion. We demonstrate the method by computing the evolution of perturbed cylindrical wires on a substrate. Furthermore, when the marker particles are redistributed periodically to maintain even spacing, the method can follow breakup of the wire.
Modeling equilibrium crystal shapes is necessary to numerically study the stability and evolution of crystals. We model the surface stiffness of crystals instead of surface energy. And a facet is represented by Dirac delta function. Our approach is demonstrated by modeling two-dimensional axially symmetric crystals and three-dimensional axisymmetric crystals.
We finally perform a linear stability analysis of three-dimensional finite axisymmetric wires with anisotropic surface energy. We arrive at an eigenvalue problem with the eigenvaule representing the growth rate of a perturbation. We find that wires are stable with length-to-radius ratio greater than 2π, which is in contrast to previous theoretical predictions.
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Du, Ping, "The Effect of Anisotropic Surface Energy on the Stability of Micro and Nano Wires" (2010). LSU Doctoral Dissertations. 3082.