Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Comprehensive Characterization of Shredded Lithium-Ion Battery Recycling Material

Herein we report on an analytical study of dry-shredded lithium-ion battery (LIB) materials with unknown composition. Samples from an industrial recycling process were analyzed concerning the elemental composition and (organic) compound speciation. Deep understanding of the base material for LIB recycling was obtained by identification and analysis of transition metal stoichiometry, current collector metals, base electrolyte and electrolyte additive residues, aging marker molecules and polymer binder fingerprints. For reversed engineering purposes, the main electrode and electrolyte chemistries were traced back to pristine materials. Furthermore, possible lifetime application and accompanied aging was evaluated based on target analysis on characteristic molecules described in literature. With this, the reported analytics provided precious information for value estimation of the undefined spent batteries and enabled tailored recycling process deliberations. The comprehensive feedstock characterization shown in this work paves the way for targeted process control in LIB recycling processes.     

TEAD–YAP Interaction Inhibitors and MDM2 Binders from DNA-Encoded Indole-Focused Ugi Peptidomimetics

DNA-encoded combinatorial synthesis provides efficient and dense coverage of chemical space around privileged molecular structures. The indole side chain of tryptophan plays a prominent role in key, or “hot spot”, regions of protein–protein interactions. A DNA-encoded combinatorial peptoid library was designed based on the Ugi four-component reaction by employing tryptophan-mimetic indole side chains to probe the surface of target proteins. Several peptoids were synthesized on a chemically stable hexathymidine adapter oligonucleotide “hexT”, encoded by DNA sequences, and substituted by azide-alkyne cycloaddition to yield a library of 8112 molecules. Selection experiments for the tumor-relevant proteins MDM2 and TEAD4 yielded MDM2 binders and a novel class of TEAD-YAP interaction inhibitors that perturbed the expression of a gene under the control of these Hippo pathway effectors.     

Eu(O2C-C≡C-CO2): An EuII Containing Anhydrous Coordination Polymer with High Stability and Negative Thermal Expansion

Anhydrous Eu^II–acetylenedicarboxylate (EuADC; ADC²⁻ = ⁻O₂C-C≡C-CO₂⁻) was synthesized by reaction of EuBr₂ with K₂ADC or H₂ADC in degassed water under oxygen-free conditions. EuADC crystallizes in the SrADC type structure (I4₁/amd, Z=4) forming a 3D coordination polymer with a diamond-like arrangement of Eu²⁺ nodes (msw topology including the connecting ADC²⁻ linkers). Deep orange coloured EuADC is stable in air and starts decomposing upon heating in an argon atmosphere only at 440 °C. Measurements of the magnetic susceptibilities (μ_eff=7.76 μ_B) and ¹⁵¹Eu Mössbauer spectra (δ=−13.25 mm s⁻¹ at 78 K) confirm the existence of Eu²⁺ cations. Diffuse reflectance spectra indicate a direct optical band gap of E_g=2.64 eV (470 nm), which is in accordance with the orange colour of the material. Surprisingly, EuADC does not show any photoluminescence under irradiation with UV light of different wavelengths. Similar to SrADC, EuADC exhibits a negative thermal volume expansion below room temperature with a volume expansion coefficient α_V=−9.4(12)×10⁻⁶ K⁻¹.     

Nanoscale Organolanthanum Clusters: Nuclearity-Directing Role of Cyclopentadienyl and Halogenido Ligands

Tetramethylaluminato/halogenido(X) ligand exchange reactions in half-sandwich complexes [Cp^RLa(AlMe₄)₂] are feasible in non-coordinating solvents and provide access to large coordination clusters of the type [Cp^RLaX₂]_x. Incomplete exchange reactions generate the hexalanthanum clusters [Cp^R₆La₆X₈(AlMe₄)₄] (Cp^R=Cp*=C₅Me₅, X=I; Cp^R=Cp′=C₅H₄SiMe₃, X=Br, I). Treatment of [Cp*La(AlMe₄)₂] with two equivalents Me₃SiI gave the nonalanthanum cluster [Cp*LaI₂]₉, while the exhaustive reaction of [Cp′La(AlMe₄)₂] with the halogenido transfer reagents Me₃GeX and Me₃SiX (X=I, Br, Cl) produced a series of monocyclopentadienyl rare-earth-metal clusters with distinct nuclearity. Depending on the halogenido ion size the homometallic clusters [Cp′LaCl₂]₁₀ and [Cp′LaX₂]₁₂ (X=Br, I) could be isolated, whereas different crystallization techniques led to the aggregation of clusters of distinct structural motifs, including the desilylated cyclopentadienyl-bridged cluster [(μ-Cp)₂Cp′₈La₈I₁₄] and the heteroaluminato derivative [Cp′₁₀La₁₀Br₁₈(AlBr₂Me₂)₂]. The use of the Cp′ ancillary ligand facilitates cluster characterization by means of NMR spectroscopy.     

Scanning tunneling microscopy with atomic resolution on ReS2 single crystals grown by vapor phase transport

Atomic resolution images of layered transition metal-dichalcogenide ReS₂ single-crystals (n-type semiconductor) were obtained using a scanning tunneling microscope with a positive tip. In most cases only unresolved clusters of four rhenium atoms could be seen. Occasional images with higher resolution showed that these bright structures consist of four separated atoms. The symmetry of the imaged atoms is identical to that of the rhenium sublattice but not to that of the sulfur atoms. We conclude therefore that the main contribution to the tunneling current is due to the rhenium atoms, although the sulfur atoms are placed by about 0.15 nm closer to the tip. Thus for our positive bias of the tip the tunneling electrons originate from occupied rhenium states in the valence band of the semiconductor.