Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.Comment: 37 pages, LaTeX, 12 figures, minor changes (published version

Structure and macroscopic tackiness of ultra-thin pressure sensitive adhesive films

Ultrathin layers of the statistical copolymer P(nBA-stat-MA) with a majority of n-butyl acrylate (nBA) and a minority of methyl acrylate (MA) are characterized with respect to the film morphology and the mechanical response in a probe tack test. The probed copolymer can be regarded as a model system of a pressure sensitive adhesive (PSA). The films are prepared by spin-coating which enables an easy thickness control via the polymer concentration of the solution. The film thickness is determined with x-ray reflectivity (XRR) and white light interferometry (WLI). Grazing incidence small angle x-ray scattering (GISAXS) provides detailed and statistically significant information about the film morphology. Two types of lateral structures are identified and no strong correlation of these structures with the PSA film thickness is observed. In contrast, prominent parameters of the probe tack test, such as the stress maximum and the tack energy, exhibit an exponential dependence on the film thickness

Multiple-scaled polymer surfaces investigated with micro-focus grazing-incidence small-angle X-ray scattering

We show that a position-sensitive sample surface information of multiple-scaled polymer films is successfully addressed with micro-focus grazing-incidence small-angle X-ray scattering (μ-GISAXS). From the analysis of the diffuse scattering without further model assumptions the length scale of the heterogeneous structures is determinable. The method is illustrated by an example of two-step dewetted polystyrene (PS) films exhibiting droplets on a nano scale in coexistence with mesoscopic drops. The results are compared to scanning force microscopy measurements. As compared to the conventional transmission geometry using the same micro-focus optics the resolvable length scale is increased by one order of magnitude

Influence of film thickness on the phase separation mechanism in ultra-thin conducting polymer blend films

The film morphology of thin polymer blend films based on poly[(1-methoxy)-4-(2-ethylhexyloxy)-p-phenylenevinylene] (MEH-PPV) and poly(N-vinylcarbazole) (PVK) is probed as a function of film thickness. Blend films are prepared with spin-coating of polymer solutions with different concentrations on top of solid supports. The blending ratio of both conducting polymers is kept constant. The film and surface morphology is probed with grazing incidence ultrasmall-angle X-ray scattering (GIUSAXS) and atomic force microscopy (AFM). A linear dependence between the film thickness and the averaged phase separation is found. In addition, X-ray reflectivity measurements show an enrichment of PVK at the substrate interface. UV/vis spectroscopy measurements indicate a linearly increasing amount of both homopolymers in the blend films for increasing film thicknesses. The generalized knowledge about the influence of the film thickness on the phase separation behavior in conducting polymer blend films is finally used to describe the phase separation formation during the spin-coating process, and the results are discussed in the framework of an adapted Flory-Huggins theory for rodlike polymers