Host-Guest Chemistry of Truncated Tetrahedral Imine Cages with Ammonium Ions

Three shape-persistent [4+4] imine cages with truncated tetrahedral geometry with different window sizes were studied as hosts for the encapsulation of tetra-n-alkylammonium salts of various bulkiness. In various solvents the cages behave differently. For instance, in dichloromethane the cage with smallest window size takes up NEt₄⁺ but not NMe₄ ^{+ ,} which is in contrast to the two cages with larger windows hosting both ions. To find out the reason for this, kinetic experiments were carried out to determine the velocity of uptake but also to deduce the activation barriers for these processes. To support the experimental results, calculations for the guest uptakes have been performed by molecular mechanics’ simulations. Finally, the complexation of pharmaceutical interested compounds, such as acetylcholine, muscarine or denatonium have been determined by NMR experiments.     

Templated‐Assembly of CsPbBr3 Perovskite Nanocrystals into 2D Photonic Supercrystals with Amplified Spontaneous Emission

Perovskite nanocrystals (NCs) have revolutionized optoelectronic devices because of their versatile optical properties. However, controlling and extending these functionalities often requires a light‐management strategy involving additional processing steps. Herein, we introduce a simple approach to shape perovskite nanocrystals (NC) into photonic architectures that provide light management by directly shaping the active material. Pre‐patterned polydimethylsiloxane (PDMS) templates are used for the template‐induced self‐assembly of 10 nm CsPbBr₃ perovskite NC colloids into large area (1 cm²) 2D photonic crystals with tunable lattice spacing, ranging from 400 nm up to several microns. The photonic crystal arrangement facilitates efficient light coupling to the nanocrystal layer, thereby increasing the electric field intensity within the perovskite film. As a result, CsPbBr₃ 2D photonic crystals show amplified spontaneous emission (ASE) under lower optical excitation fluences in the near‐IR, in contrast to equivalent flat NC films prepared using the same colloidal ink. This improvement is attributed to the enhanced multi‐photon absorption caused by light trapping in the photonic crystal.     

Considerations to Rayleigh’s hypothesis

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.     

Numerical Simulation of Decaying Turbulence in an Adaptive Wavelet Basis

The present note is concerned with the numerical simulation of two-dimensional homogeneous decaying turbulence. We employ a Galerkin-type discretization in an adaptive basis of orthogonal wavelets. Therewith the solution is represented by means of a reduced basis being adapted at each time step. This is one of the first times that wavelet decomposition of a turbulent flow field has been used not only for a posteriori analysis but directly for the computation of the flow in a reduced basis. A classical Fourier method furnishesa suitable reference solution.