Stress-Induced Acceleration and Ordering in Solid-State Dewetting.

We report on the influence of elastic strain on solid-state dewetting. Using continuum modeling, we first study the consequences of elastic stress on the pinching of the film away from the triple line during dewetting. We find that elastic stress in the solid film decreases both the time and the distance at which the film pinches in such a way that the dewetting front is accelerated. In addition, the spatial organization of islands emerging from the dewetting process is affected by strain. As an example, we demonstrate that ordered arrays of quantum dots can be achieved from solid-state dewetting of a square island in the presence of elastic stress.

Gauging Nanoswimmer Dynamics via the Motion of Large Bodies.

Nanoswimmers are ubiquitous in biotechnology and nanotechnology but are extremely challenging to measure due to their minute size and driving forces. A simple method is proposed for detecting the elusive physical features of nanoswimmers by observing how they affect the motion of much larger, easily traceable particles. Modeling the swimmers as hydrodynamic force dipoles, we find direct, easy-to-calibrate relations between the observable power spectrum and diffusivity of the tracers and the dynamic characteristics of the swimmers-their force dipole moment and correlation times.

Disjoining-pressure-induced acceleration of mass shedding in solid-state dewetting.

Surface-diffusion mediated solid-state dewetting has been observed and studied in a number of different systems during the past two decades. This process can be accompanied by the pinching of the film at a finite distance from the retracting triple line. The repetition of this pinching is often referred to as periodic mass shedding. We show that the disjoining pressure of the film can accelerate mass shedding by orders of magnitude in ultrathin films with nanometric thickness. In the presence of power-law disjoining pressures induced by van der Waals forces, the mass shedding time exhibits an approximate power-law dependence on film thickness t_{ms}∼h[over ¯]^{ν}, with ν≈6. Exponentially decaying disjoining forces also give rise to a strong acceleration of mass shedding. However, due to the finite range of the exponential potential, the mass shedding time does not exhibit a simple power-law dependence on the thickness, and is controlled by a cutoff thickness. In addition, two-dimensional simulations indicate that, within the range of thicknesses that we have studied and for isotropic dynamics, the transversal instability of a straight front does not lead to fingering, and mass shedding is the dominant instability of the dewetting front. Finally, we also show that no significant difference is observed in the dewetting dynamics between simulations based on a model with a wetting potential integrated over the film surface area, or over the projected substrate area.

Coarsening dynamics in the Swift-Hohenberg equation with an external field.

We study the Swift-Hohenberg equation (SHE) in the presence of an external field. The application of the field leads to a phase diagram with three phases, i.e., stripe, hexagon, and uniform. We focus on coarsening after a quench from the uniform to stripe or hexagon regions. For stripe patterns, we find that the length scale associated with the order-parameter structure factor has the same growth exponent (≃1/4) as for the SHE with zero field. The growth process is slower in the case of hexagonal patterns, with the effective growth exponent varying between 1/6 and 1/9, depending on the quench parameters. For deep quenches in the hexagonal phase, the growth process stops at late stages when defect boundaries become pinned.

Triple-line kinetics for solid films.

We present a derivation of the triple-line kinetic boundary conditions for a solid film in contact with a solid substrate for both nonconserved (evaporation-condensation) and conserved (surface diffusion) dynamics. The result is obtained via a matched asymptotic expansion from a mesoscopic model with a thickness-dependent wetting potential (or disjoining pressure) and mobility. In the nonconserved case, we obtain a single boundary condition, which relates the triple-line velocity with the deviation of the contact angle from its equilibrium value. In the conserved case, two kinetic boundary conditions are needed. They relate the velocity and mass flux at the triple line to the contact angle deviation and discontinuity of the chemical potential. These linear relations are described by three kinetic coefficients. The conditions under which the kinetic coefficients remain finite are obtained. We find, for example, that some kinetic coefficients diverge within the conserved model in the presence of van der Waals interaction.

Coarsening of stripe patterns: variations with quench depth and scaling.

The coarsening of stripe patterns when the system is evolved from random initial states is studied by varying the quench depth ε, which is a measure of distance from the transition point of the stripe phase. The dynamics of the growth of stripe order, which is characterized by two length scales, depends on the quench depth. The growth exponents of the two length scales vary continuously with ε. The decay exponents for free energy, stripe curvature, and densities of defects like grain boundaries and dislocations also show similar variation. This implies a breakdown of the standard picture of nonequilibrium dynamical scaling. In order to understand the variations with ε we propose an additional scaling with a length scale dependent on ε. The main contribution to this length scale comes from the "pinning potential," which is unique to systems where the order parameter is spatially periodic. The periodic order parameter gives rise to an ε-dependent potential, which can pin defects like grain boundaries, dislocations, etc. This additional scaling provides a compact description of variations of growth exponents with quench depth in terms of just one exponent for each of the length scales. The relaxation of free energy, stripe curvature, and the defect densities have also been related to these length scales. The study is done at zero temperature using Swift-Hohenberg equation in two dimensions.

Stripe patterns: role of initial state and boundary conditions.

This paper presents results on stripe patterns by numerical solution of the Swift-Hohenberg equation. The focus is on the role of initial state and boundary conditions. We choose initial states which generate simple defect configurations and study their evolution. Various classes of defects are identified and their motion and relaxation is studied numerically. We first study the dynamics of a straight front and present a comparison of numerical results with some analytical results. We then study the domain-wall dynamics in configurations containing two and three domains and identify some mechanisms of their relaxation. Rates of domain-wall relaxation depend on several features like incommensuration, dislocations and orientations in neighboring domains, in addition to the curvature of the walls. For a generic class of domain walls the relaxation process has an intrinsic frustration which leads to generation of dislocations. This process also generates stripe curvature thereby making relaxation nonmonotonic. We have also generated some other topological defects and studied their evolution and the effect of boundary conditions on their stability.

Velocity correlations and mobility in single-file diffusion.

We study the velocity correlations of a tagged particle in an infinite assembly of interacting particles with a given density in one dimension. The assembly is in contact with a heat bath, and the particles interact via a hard-core repulsion with each other. We evaluate the two-time velocity correlation function exactly as function of time when an ensemble average is taken over initial conditions. This correlation function decays rapidly with time and becomes negative, with the rate of decay increasing with the density. This is followed by a slow decay toward zero through a power-law behavior of the form -t(-3/2) at large times for all densities. We also consider mobility of the assembly in the presence of a constant force acting on the particles, as well as the mobility of a tagged particle when only the tagged particle is driven by the force. The power spectrum of velocity fluctuations is also presented.