Synthesis of Elusive Chloropnictenium Ions

This work describes the synthesis and full characterization of elusive chloropnictenium ion salts of the type [^RAr*N(SiMe)ECl][A] (^RAr*=2,6‐(CHPh₂)‐4‐R‐C₆H₂, R=Me, tBu; E=Sb, Bi; A^?=GaCl₄, Al(OCH(CF₃)₂)₄). In these species the cation is significantly stabilized by weak arene interactions to flanking phenyl groups of the ^RAr* moiety. In this context the bonding situation has been studied by computational means and the reactivity towards the Lewis base 4‐dimethylaminopyridine (dmap) was investigated.     

Gallai’s path decomposition conjecture for graphs of small maximum degree

Gallai’s path decomposition conjecture states that the edges of any connected graph on $n$ vertices can be decomposed into at most $\frac{n+1}{2}$ paths. We confirm that conjecture for all graphs with maximum degree at most five.     

Self-Assembly of C3 Symmetric Rigid Macrolactams into Very Polar and Porous Trigonal Crystals

Cyclohexane and cyclotri-β-alanyl have been used as scaffolds for the design of new C₃-symmetric rings incorporating conjugated alkenes and dienes. All three C₃-symmetric lactams share the same triangular shape and their crystal system is trigonal. They all belong to the R3 space group, R3m, R3 and R3c, for the increasingly large 12-, 18- and 24-membered rigid rings, respectively. All lactams stack on top of each other, through H-bonds and van der Waals noncovalent interactions, leading to endless supramolecular cylinders and tubes. The largest member of the family leads to tubes, the central pores of which is wide enough to let water in. A common feature of all the lactams is their very large dipole, of around 9 D, according to DFT calculations. Surprisingly, all the resulting cylinders and tubes pack side by side in the crystals, with all the dipoles pointing to the same direction. As a result, all three crystals are anisotropic and appear to be the first members of a new kind of highly polar crystals.     

On-Surface Synthesis and Characterization of Acene-Based Nanoribbons Incorporating Four-Membered Rings

A bottom up method for the synthesis of unique tetracene-based nanoribbons, which incorporate cyclobutadiene moieties as linkers between the acene segments, is reported. These structures were achieved through the formal [2+2] cycloaddition reaction of ortho-functionalized tetracene precursor monomers. The formation mechanism and the electronic and magnetic properties of these nanoribbons were comprehensively studied by means of a multitechnique approach. Ultra-high vacuum scanning tunneling microscopy showed the occurrence of metal-coordinated nanostructures at room temperature and their evolution into nanoribbons through formal [2+2] cycloaddition at 475 K. Frequency-shift non-contact atomic force microscopy images clearly proved the presence of bridging cyclobutadiene moieties upon covalent coupling of activated tetracene molecules. Insight into the electronic and vibrational properties of the so-formed ribbons was obtained by scanning tunneling microscopy, Raman spectroscopy, and theoretical calculations. Magnetic properties were addressed from a computational point of view, allowing us to propose promising candidates to magnetic acene-based ribbons incorporating four-membered rings. The reported findings will increase the understanding and availability of new graphene-based nanoribbons with high potential in future spintronics.     

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

Meccanica - This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent)...