Thermally‐activated post‐growth dewetting of fullerene C60 on mica

Understanding and controlling the growth and stability of molecular thin films on solid surfaces is necessary to develop nanomaterials with well‐defined physical properties. As a prominent model system in organic electronics, we investigate the post‐growth dewetting kinetics of the fullerene C₆₀ on mica with real‐time and in situ X‐ray scattering. After layer‐by‐layer growth of C₆₀, we find a thermally‐activated post‐growth dewetting, where the smooth C₆₀‐layer breaks up into islands. This clearly shows that growth is kinetically limited before the system moves over an activation barrier into an energetically favored configuration. From the temperature‐dependent dewetting kinetics we find an effective activation barrier of 0.33 eV, which describes both the temperature‐dependent macroscopic changes in the surface morphology and the microscopic processes of inter‐ and intralayer diffusion during dewetting.

     

An improved boundary element method for the charge density of a thin electrified plate in ℝ3

A weakly singular integral equation of the first kind on a plane surface piece Γ is solved approximately via the Galerkin method. The determination of the solution of this integral equation (with the single-layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate Γ loaded with some given potential. Using piecewise constant or piecewise bilinear boundary elements we derive asymptotic estimates for the Galerkin error in the energy norm and analyse the effect of graded meshes. Estimates in lower order Sobolev norms are obtained via the Aubin–Nitsche trick. We describe in detail the numerical implementation of the Galerkin method with both piecewise-constant and piecewise-linear boundary elements. Numerical experiments show experimental rates of convergence that confirm our theoretical, asymptotic results.     

Freezing of polymer thin films and surfaces: The small molecular weight puzzle

Experimental observations (ellipsometry, scanning force microscopy, and nuclear magnetic recsonance (NMR)) of the freezing behavior of thin supported films as well as the free surface of atactic polystyrene are reported, taken at a particularly small molecular weight of 2 kg/mol. Remarkably, we find the same effect of reduction of the glass transition temperature, T_g, as observed earlier with much longer molecules. Furthermore, surface melting is observed by NMR, with the molten layer thickness similar to what has been observed with larger molecular weight. We conclude that molecular geometry effects cannot account for these observations, and that a consistent explanation must be presentable in a continuum picture. On the basis of the capillary mode spectrum of the free surface and of the supported films, we present such a model and find that it accounts very consistently with all observations made so far, at least with polystyrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2968–2979, 2006     

Proof of the local REM conjecture for number partitioning. I: Constant energy scales

In this article we consider the number partitioning problem (NPP ) in the following probabilistic version: Given n numbers X₁,…,X_n drawn i.i.d. from some distribution, one is asked to find the partition into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the numbers in the other set. In this probabilistic version, the NPP is equivalent to a mean‐field antiferromagnetic Ising spin glass, with spin configurations corresponding to partitions, and the energy of a spin configuration corresponding to the weight difference. Although the energy levels of this model are a priori highly correlated, a surprising recent conjecture of Bauke, Franz, and Mertens asserts that the energy spectrum of number partitioning is locally that of a random energy model (REM): the spacings between nearby energy levels are uncorrelated. More precisely, it was conjectured that the properly scaled energies converge to a Poisson process, and that the spin configurations corresponding to nearby energies are asymptotically uncorrelated. In this article, we prove these two claims, collectively known as the local REM conjecture. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Characterisation of light emitting diodes (LEDs) for application in digital holographic microscopy for inspection of micro and nanostructured surfaces

Partial coherent light sources open up prospects for phase noise reduction in digital holographically reconstructed phase distributions by suppressing multiple reflections in the experimental setup. Thus, light emitting diodes (LEDs) are investigated for application in digital holographic microscopy. First, the spectral properties and the resulting coherence length of an LED are characterised. In addition, an analysis of dispersion effects and their influence on the hologram formation is carried out. The coherence length of LEDs in the range of a few micrometers restricts the maximum interference fringe number in off-axis holography for spatial phase shifting. Thus, the application of temporal phase-shifting-based digital holographic reconstruction techniques is compared to spatial phase-shifting-based methods. It is demonstrated that LEDs are applicable for digital holographic microscopy in connection with both spatial and temporal phase-shifting-based techniques for reduction of noise in comparison to a laser-light-based experimental setup.