The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions

We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide some applications of this regularity result, especially in the calculus of variations for the area functional. © 2020 Wiley Periodicals LLC     

CaCuMn<Subscript>6</Subscript>O<Subscript>12</Subscript> vs. CaCu<Subscript>2</Subscript>Mn<Subscript>5</Subscript>O<Subscript>12</Subscript>: A comparative study

The ferrimagnetic compounds Ca(Cu_xMn_3?x)Mn₄O₁₂ of the double distorted perovskites AC₃B₄O₁₂ family exhibit a rapid increase of the ferromagnetic component in magnetization at partial substitution of square coordinated (Mn³⁺)_C for (Cu²⁺)_C. In the transport properties, this is seen as a change of the semiconducting type of resistivity for the metallic one. The evolution of magnetic properties of Ca(Cu_xMn_3?x)Mn₄O₁₂ is driven by strong antiferromagnetic exchange interaction of (Cu²⁺)_C with (Mn³⁺/Mn⁴⁺)_B coordinated octahedra. The competing interactions of (Mn³⁺)_C with (Mn³⁺/Mn⁴⁺)_B lead to the formation of noncollinear magnetic structures that can be aligned by magnetic fields.     

A step forward in metal nitride and carbide synthesis: from pure nanopowders to nanocomposites

Transition metal nitrides and carbides (MN/MC) are intriguing materials due to their combination of properties that place them between high-performance ceramics and pure metals. Recent progress in easier synthetic routes toward their production as bulk or nanostructured materials explains the current surge in sustained attention such progress has been receiving. After progressing toward easier syntheses of MN/MC nanosystems as pure phases, coupling MN/MC with a second phase for the production of hybrids and nanocomposites is considered a next important step in the development of these nanosystems. The coupled phase can simply be a different nitride or carbide; it also can be a polymer, a poly(ionic liquid) or a carbon phase, just to give a few examples. The combination of these phases with MN/MC nanoparticles could lead to multifunctional materials. The aim of the present review is to show how far the research concerning the production of MN/MC-based nanocomposites has progressed, especially in terms of controlled composition, morphology and properties. We discuss the most intensely investigated systems and related motivations, as well as partially unexplored yet appealing alternative materials.     

Nanopatterns of molecular spoked wheels as giant homologues of benzene tricarboxylic acids

Molecular spoked wheels with D_3h and C_s symmetry are synthesized by Vollhardt trimerization of C_2v-symmetric dumbbell structures with central acetylene units and subsequent intramolecular ring closure. Scanning tunneling microscopy of the D_3h-symmetric species at the solid/liquid interface on graphite reveals triporous chiral honeycomb nanopatterns in which the alkoxy side chains dominate the packing over the carboxylic acid groups, which remain unpaired. In contrast, C_s-symmetric isomers partially allow for pairing of the carboxylic acids, which therefore act as a probe for the reduced alkoxy chain nanopattern stabilization. This observation also reflects the adsorbate substrate symmetry mismatch, which leads to an increase of nanopattern complexity and unexpected templating of alkoxy side chains along the graphite armchair directions. State-of-the-art GFN-FF calculations confirm the overall structure of this packing and attribute the unusual side-chain orientation to a steric constraint in a confined environment. These calculations go far beyond conventional simple space-filling models and are therefore particularly suitable for this special case of molecular packing.

Scanning tunneling microscopy investigations of phenylene-based molecular spoked wheels with D_3h and C_s symmetries on graphite show the competitive or complementary effects of carboxylic acid groups and alkoxy chains on the nanopattern formation.     

Control of Excited‐State Conformations in B,N‐Acenes

We present a new concept to control the conformations of molecules in the excited state through harvesting negative hyperconjugation. The strategy was realized with the 2,3,1,4‐benzodiazadiborinane scaffold, which was prepared by a new synthetic procedure. Photochemical studies identified dual light emission, which was assigned to well‐defined conformers. The emission at longer wavelength can be switched off by restricting the rotational degrees of freedom in the solid state as well as by controlling the energy levels of the excited states through adjusting the solvent polarity.     

Topochemical Reactions in Langmuir-Blodgett Multilayers

Abstract

The topochemical polymerization of diacetylenes and.the dimerization of cinnamic acid derivatives have been studied in Langmuir-Blodgett-multilayers. The resulting polymer films are of controlled thickness and morphology and exhibit excellent stability. Structure, morphology and phase changes occuring in monomer and polymer films have been investigated using spectroscopic methods, electron and x-ray diffraction. Possible applications of the polymer films are discussed.