Analyzing diffuse scattering with supercomputers

Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341–359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super- or grid computer. The faulted layer stacking in single crystals of trigonal three-pointedstar- shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

From supramolecular sheets to fibers and back: establishing the critical parameters that govern the morphology of pyrene-based self-assembled materials

The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.

From supramolecular sheets to fibers and back: establishing the critical parameters that govern the morphology of pyrene-based self-assembled materials

The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.