Limits of size scalability of diffusion and growth: Atoms versus molecules versus colloids.

Understanding fundamental growth processes is key to the control of nonequilibrium structure formation for a wide range of materials on all length scales, from atomic to molecular and even colloidal systems. While atomic systems are relatively well studied, molecular and colloidal growth are currently moving more into the focus. This poses the question to what extent growth laws are size scalable between different material systems. We study this question by analyzing the potential energy landscape and performing kinetic Monte Carlo simulations for three representative systems. While submonolayer (island) growth is found to be essentially scalable, we find marked differences when moving into the third (vertical) dimension.

Unravelling the multilayer growth of the fullerene C60 in real time.

Molecular semiconductors are increasingly used in devices, but understanding of elementary nanoscopic processes in molecular film growth is in its infancy. Here we use real-time in situ specular and diffuse X-ray scattering in combination with kinetic Monte Carlo simulations to study C60 nucleation and multilayer growth. We determine a self-consistent set of energy parameters describing both intra- and interlayer diffusion processes in C60 growth. This approach yields an effective Ehrlich-Schwoebel barrier of EES=110 meV, diffusion barrier of ED=540 meV and binding energy of EB=130 meV. Analysing the particle-resolved dynamics, we find that the lateral diffusion is similar to colloids, but characterized by an atom-like Schwoebel barrier. Our results contribute to a fundamental understanding of molecular growth processes in a system, which forms an important intermediate case between atoms and colloids.

Minkowski tensor shape analysis of cellular, granular and porous structures.

Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure-property relationships for tensor-valued or orientation-dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor-valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear-time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co-polymer films by an electric field imaged by surface force microscopy; (b) local cell anisotropy of spherical bead pack models for granular matter and of closed-cell liquid foam models; (c) surface orientation in open-cell solid foams studied by X-ray tomography; and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.