Monte Carlo studies of grain growth on curved surfaces

Self-formation of compositionally complex surface oxides on high entropy alloys observed by accelerated atom probe tomography: a route to sustainable catalysts

Sustainable catalysts rely on abundant elements which are prone to oxidation. A route to non-noble electrocatalysts is opened by directing the formation of unavoidable surface oxides towards creating a few atomic layers of an active and stable electrocatalyst, which is in direct contact with its metallic, conducting support. This is enabled by combining possibilities of compositionally complex solid solutions with accelerated atomic-scale surface characterization. Surface composition changes from the as-synthesized state to states after exposure to the oxygen evolution reaction (OER) are investigated using a Cantor-alloy-catalyst-coated tip array for atom probe tomography (APT): The film on top of the tip forms a nanoreactor which enables acquisition of intrinsic properties. The as-deposited film has an around 3 nm thick native oxide; short and prolonged OER exposures result in an oxygen-influenced surface layer with lower oxidation depth and altered metal composition. This shows that as-synthesized complex compositions can be used to obtain active and stable surface oxides under electrochemical load, while their surface evolution is observed by accelerated APT.

Curvature driven motion of a bubble in a toroidal Hele-Shaw cell

We investigate the equilibrium properties of a single area-minimizing bubble trapped between two narrowly separated parallel curved plates. We begin with the case of a bubble trapped between concentric spherical plates. We develop a model which shows that the surface energy of the bubble is lower when confined between spherical plates than between flat plates. We confirm our findings by comparing against Surface Evolver simulations. We then derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model, we consider a bubble trapped between concentric tori. In the toroidal case, we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature.

Stochastic phase segregation on surfaces

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.

Curvature-driven foam coarsening on a sphere: A computer simulation

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution and distribution of cells to the final stationary state.

Coarsening of a two-dimensional foam on a dome

In this paper we report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the narrow gap between two hemispheres. By contrast with coarsening in flat space, where six-sided bubbles neither grow nor shrink, we observe that six-sided bubbles grow with time at a rate that depends on their size. This result agrees with the modification to von Neumann's law predicted by J. E. Avron and D. Levine [Phys. Rev. Lett. 69, 208 (1992)]. For bubbles with a different number of sides, except possibly seven, there is too much noise in the growth rate data to demonstrate a difference with coarsening in flat space. In terms of the statistics of bubble topology, we find fewer three-, four-, and five-sided bubbles, and more bubbles with six or more sides, in comparison with the stationary distribution for coarsening in flat space. We also find good general agreement with the Aboav-Weaire law for the average number of sides of the neighbors of an n-sided bubble.

Influence of poly-l-lysine on the biomimetic growth of silica tubes in confined media

Pore channels of polycarbonate membranes were recently used as biomimetic models to study the effect of confinement on silicate condensation, leading to the formation of silica tubes exhibiting a core-shell structure. In this work, we preimmobilized poly-L-lysine on the membrane pores, leading to modification of the tube shell formation process and variation in core particle size. These data strengthen previous assumptions on the role of confinement on silica growth, i.e., interfacial interactions and perturbation of the diffusion coefficient. They also suggest that this approach is suitable to investigate in more detail the contribution of confinement effects on silica biomineralization.

Biomimetic growth of silica tubes in confined media

Polymer membranes were used as biomimetic environments to study the effect of confinement on silica formation. Within membrane pores, silica tubes were formed, consisting of a dense silica shell incorporating nanoparticle aggregates. The shell structure does not depend on the membrane pore size, suggesting that its formation proceeds via interfacial interactions with the pore surface. In contrast, the size of primary nanoparticles within core aggregates is influenced by pore dimensions, indicating an effect of confinement on the diffusion-limited growth of silica. A parallel can be drawn with reported roles of confinement in biomineralization processes, providing a basis for future developments in biosilicification mimetic approaches and biofunctional nanomaterials design.

Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.