Pattern Formation

Inversion of Pattern Anisotropy During CO Oxidation on Pt(110) Correlated with Appearance of Subsurface Oxygen

by Christian Punckt

P. Sadeghi, K. Dunphy, C. Punckt. H. H. Rotermund
J. Phys. Chem. C 116 (2012) 4686

Spatiotemporal patterns occurring during the catalytic oxidation of carbon monoxide on Pt(110) show a strong... more Spatiotemporal patterns occurring during the catalytic oxidation of carbon monoxide on Pt(110) show a strong anisotropy due to differences in the diffusion coefficients along the two major crystallographic axes of the catalyst: Reaction waves propagating parallel to the missing rows of the reconstructed Pt surface are much faster than reaction waves propagating in the perpendicular direction. In this Article, we report on the observation that, as a function of the exposure to reactant gases, the propagation velocities on the Pt surface change drastically, resulting in a complete reversal of the anisotropy. This observation is correlated with the appearance of subsurface oxygen in photoemission electron microscopic images of the reaction patterns.

Amplitude equations for reaction-diffusion systems with cross diffusion

by Evgeny Zemskov

Theoretical Model for Faraday Waves With Multiple-Frequency Forcing

by Ron Lifshitz

R. Lifshitz and D. M. Petrich. Phys. Rev. Lett.79 (1997) 1261-1264.

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern- forming dynamics of a... more A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern- forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with 2-, 4-, 6-, and 12-fold symmetric patterns, similar to the periodic and quasiperiodic patterns observed in recent experiments.

Buckle-driven delamination in thin polymer films.

by Ratna Kumar Annabattula

Co-authored with P. R. Onck, Published in Proceedings of the Third International conference on Multiscale Materials Modelling, 18-22 Sep 2006, Freiburg, Germany. ISBN 978-3-8167-7206-4

The formation of blisters as a result of delamination and buckling of thin films under compressive stresses is a well... more The formation of blisters as a result of delamination and buckling of thin films under compressive stresses is a well known (but, unwanted) phenomenon. Although unwanted during service, it can be exploited in design to fabricate well-controlled sub-micron patterns in thin films. The shape of the buckled film depends on the interface properties, thickness of the film and the internal film stresses. A finite element model with geometric nonlinear effects and cohesive elements (to simulate the interface between film and substrate) is being developed to understand the buckle-driven delamination and re-adhesion of compressed polymer films. The 2D model will be used as a basis for the subsequent development of a 3D model to understand various film patterns observed in experiments.

Micron-scale pattern formation in pre-stressed polygonal films

by Ratna Kumar Annabattula

Co-authored with P. R. Onck, accepted for publication in Journal of Applied Physics, 109, 033517, (2011).

In this paper we explore the spontaneous formation of micropatterns in thin pre-stressed polygonal films using finite... more In this paper we explore the spontaneous formation of micropatterns in thin pre-stressed polygonal films using finite element simulations. We study films with different size, thickness and shape, including square, rectangular, pentagonal and hexagonal films. Patterns form when the films release the internal eigenstrain by buckling-up, after which the films bond-back to the substrate. After an initial symmetric evolution of the buckling pro le, the symmetry of the deflection pattern breaks when the wavelength of wriggles near the film edges decreases. During bond back the deflection morphology converges to a four-fold, five-fold and six-fold ridging pattern for the square, pentagonal and hexagonal fi lms, respectively, showing a close resemblance with experimental film systems of similar size and shape. Rectangular fi lms of large length to width ratio go through a transition in buckling shapes from the initial Euler mode, through the varicose mode into the anti-symmetric telephone-cord mode. For all the fi lm shapes, the ratio of the film height to the effective film width scales with the squareroot of eigenstrain and is independent of thickness. The bond-back mechanism determines the final wrinkle morphology and is governed by the eigenstrain value at the end of the buckling-up stage and a dimensionless parameter that relates the interface energy to the strain energy in the film.

Searching for Spatial Patterns in a Pollinator–-Plant-–Herbivore Mathematical Model

by Víctor F. Breña-Medina

Published in Bulletin of Mathematical Biology, 2010.

This paper deals with the spatio-temporal dynamics of a pollinator–plant–herbivore mathematical model. The full model... more This paper deals with the spatio-temporal dynamics of a pollinator–plant–herbivore mathematical model. The full model consists of three nonlinear reaction–diffusion–advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases. The first one is a model for a mutualistic interaction (pollinator–plant), later on a sort of predator–prey (plant–herbivore) interaction model is studied. In both cases, the interaction term is described by a Holling response of type II. Finally, by considering that the plant population is the unique feeding source for the herbivores, a mathematical model for the three interacting populations is considered. By incorporating a constant diffusion term into the equations for the pollinators and herbivores, we numerically study the spatiotemporal dynamics of the first two mentioned models. For the full model, a constant diffusion and advection terms are included in the equation for the pollinators. For the resulting model, we sketch the proof of the existence, positiveness, and boundedness of solution for an initial and boundary values problem. In order to see the separated effect of the diffusion and advection terms on the final population distributions, a set of numerical simulations are included. We used homogeneous Dirichlet and Neumann boundary conditions.

Morphological Phase Separation in Unstable Thin Films: Pattern Formation and Growth

by Prabhat Jaiswal

Phys. Chem. Chem. Phys. 13, 13598 (2011) [6 pages]
DOI: 10.1039/C0CP03013A, Communication

http://pubs.rsc.org/en/Content/ArticleLanding/2011/CP/c0cp03013a

Patterning by Ion-Beam Sputtering

by Minwoong Joe

We review and study pattern formations arising in a sputter-eroded surface. The patterns include nanodots, holes,... more We review and study pattern formations arising in a sputter-eroded surface. The patterns include nanodots, holes, ripples, and so on. Our study is focused on the theoretical aspect. Several kinetic equations are reviewed first, and then a linearly superposed Kuramoto-Sivashinsky (KS) equation is derived explicitly. The latter equation was introduced for the purpose of illustrating dual ion-beam sputtering (DIBS), where two ion beams are simultaneously projected onto the surface at a grazing angle and cross perpendicular in azimuth. The numerical values of the coefficients of the superposed KS equation are obtained by using the transport of ions in matter (TRIM) algorithm. This shows no linear instability for growing patterns as observed in a recent DIBS experiment. Nanopatterning through the DIBS process is thus beyond the scope of the kinetics under the standard KS equation.

Nanopatterning by multiple-ion-beam sputtering

by Minwoong Joe

We conducted a systematic study on nanopatterning by multiple-ion-beam sputtering, focusing on the superposition of... more We conducted a systematic study on nanopatterning by multiple-ion-beam sputtering, focusing on the superposition of the simple patterns formed by individual ion beams. When Au(001) is simultaneously sputtered by two ion beams at grazing incidence, both nanodot and nanohole patterns are obtained. If a rippled surface is subsequently sputtered at normal incidence, a nanobead pattern is obtained. All of the obtained patterns consist of the nanopatterns formed by individual ion beams; however, the superposition of nanopatterns is not realized in its ideal form. We also discuss the microscopic mechanism of pattern formation by multiple-ion-beam sputtering, and consider the questions and possibilities remaining to be explored.

Nanopatterning by dual-ion-beam sputtering

by Minwoong Joe

We studied the development of ordered nanopatterns during dual-ion-beam sputtering (DIBS) of Au(001) in which two ion... more We studied the development of ordered nanopatterns during dual-ion-beam sputtering (DIBS) of Au(001) in which two ion beams that cross perpendicular to each other at their azimuth are incident on the surface at a grazing angle. In the erosion (diffusion) regime, a square-symmetric two-dimensional (2D) pattern of nanodots (holes) is formed. The 2D pattern is achieved only when the two beams are balanced in the erosion regime. In the diffusion regime, no such condition is required. The observations cannot be explained by the Kuramoto-Sivashinsky (KS) equation derived from Sigmund theory with two ion beams.

Suppression of spatiotemporal chaos in the oscillatory CO oxidation on Pt(110) by focused laser light

by Christian Punckt

C. Punckt, M. Stich, C. Beta, H. H. Rotermund