Lithium Insertion Mechanism in Iron-Based Oxyfluorides with Anionic Vacancies Probed by PDF Analysis

The mechanism of lithium insertion that occurs in an iron oxyfluoride sample with a hexagonal–tungsten–bronze (HTB)-type structure was investigated by the pair distribution function. This study reveals that upon lithiation, the HTB framework collapses to yield disordered rutile and rock salt phases followed by a conversion reaction of the fluoride phase toward lithium fluoride and nanometer-sized metallic iron. The occurrence of anionic vacancies in the pristine framework was shown to strongly impact the electrochemical activity, that is, the reversible capacity scales with the content of anionic vacancies. Similar to FeOF-type electrodes, upon de-lithiation, a disordered rutile phase forms, showing that the anionic chemistry dictates the atomic arrangement of the re-oxidized phase. Finally, it was shown that the nanoscaling and structural rearrangement induced by the conversion reaction allow the in situ formation of new electrode materials with enhanced electrochemical properties.     

Atomic-Scale Insights into Electrode Surface Dynamics by High-Speed Scanning Probe Microscopy

Atomic-scale processes at electrode surfaces in liquid electrolytes are central elemental steps of electrochemical reactions. Detailed insights into the structure of these interfaces can be obtained with in situ scanning tunnelling and atomic force microscopy. By increasing the time resolution of these methods into the millisecond range, highly dynamic processes at electrode surfaces become directly observable. This review gives an overview of in situ studies with video-rate scanning probe microscopy techniques. Firstly, quantitative investigations into the dynamic behaviour of individual adsorbed atoms and molecules are described. These reveal a complex dependence of adsorbate surface diffusion on potential and co-adsorbed species and provide data on adsorbate–adsorbate and adsorbate–substrate interactions in a liquid environment. Secondly, results on collective dynamic phenomena are discussed, such as molecular self-assembly, the dynamics of nanoscale structures, nucleation and growth, and surface restructuring due to phase-formation processes.     

1,2,4,5-Tetrakis(tetramethylguanidino)-3,6-diethynyl-benzenes: Fluorescent Probes,Redox-Active Ligands and Strong Organic Electron Donors

In this work, the change of reactivity induced by the introduction of two para-ethynyl substituents (CCSi(iPr)₃ or CCH) to the organic electron-donor 1,2,4,5-tetrakis(tetramethylguanidino)-benzene is evaluated. The redox-properties and redox-state dependent fluorescence are evaluated, and dinuclear Cu^I and Cu^II complexes synthesized. The Lewis-acidic B(C₆F₅)₃ substitutes the proton of the ethynyl −CCH groups to give new anionic −CCB(C₆F₅)₃⁻ substituents, leading eventually to a novel dianionic strong electron donor in its diprotonated form. Its two-electron oxidation with dioxygen in the presence of a copper catalyst yields the first redox-active guanidine that is neutral (instead of cationic) in its oxidized form.     

Analysis of a new drug of abuse: Cathinone derivative 1‐(3,4‐dimethoxyphenyl)‐2‐(ethylamino)pentan‐1‐one

Recently, novel psychoactive drugs for human abuse such as amphetamines, phenethylamines, benzofuries, and tryptamines, cathinones have gained high popularity. These designer drugs are mainly sold via online stores as “bath salts” and are labeled “not for human consumption.” Due to the novelty of the compounds, only a little information about pharmacology, toxicology, and the long‐term damage they may cause is available. Moreover, there are only few analytical methods for their identification and analysis. Among new cathinone derivatives, 1‐(3,4‐dimethoxyphenyl)‐2‐(ethylamino)pentan‐1‐one (DL‐4662), became available via an internet shop. A sample of this compound was purchased and investigated. The first aim of our study was an identity check by NMR spectroscopy and gas chromatography with mass spectrometry. As many of the recreational drugs are chiral and are mainly sold as racemates, a further goal of our research was enantioseparation by gas chromatography with mass spectrometry and high‐performance liquid chromatography with UV detection, to prove whether DL‐4662 was traded enantiomerically pure or as racemic mixture. Both chiral separation methods showed the presence of a racemate.     

Two Novel Characterizations of Self-Decomposability on the Half-Line

Two novel characterizations of self-decomposable Bernstein functions are provided. The first one is purely analytic, stating that a function \(\varPsi \) is the Bernstein function of a self-decomposable probability law \(\pi \) on the positive half-axis if and only if alternating sums of \(\varPsi \) satisfy certain monotonicity conditions. The second characterization is of probabilistic nature, showing that \(\varPsi \) is a self-decomposable Bernstein function if and only if a related d-variate function \(C_{\psi ,d}\), \(\psi :=\exp (-\varPsi )\), is a d-variate copula for each \(d \ge 2\). A canonical stochastic construction is presented, in which \(\pi \) (respectively \(\varPsi \)) determines the probability law of an exchangeable sequence of random variables \(\{U_k\}_{k\in {\mathbb {N}}}\) such that \((U_1,\ldots ,U_d) \sim C_{\psi ,d}\) for each \(d \ge 2\). The random variables \(\{U_k\}_{k\in {\mathbb {N}}},\) are i.i.d. conditioned on an increasing Sato process whose law is characterized by \(\varPsi \). The probability law of \(\{U_k\}_{k \in {\mathbb {N}}}\) is studied in quite some detail.     

A spectral method for nonlinear elliptic equations

Let Ω be an open, simply connected, and bounded region in \(\mathbb {R}^{d}\), d ≥ 2, and assume its boundary ?Ω is smooth and homeomorphic to \(\mathbb {S}^{d-1}\). Consider solving an elliptic partial differential equation L u = f(?, u) over Ω with zero Dirichlet boundary value. The function f is a nonlinear function of the solution u. The problem is converted to an equivalent elliptic problem over the open unit ball \(\mathbb {B}^{d}\) in \(\mathbb {R}^{d}\), say \(\widetilde {L}\widetilde {u} =\widetilde {f}(\cdot ,\widetilde {u})\). Then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials \(\widetilde {u} _{n}\) of degree ≤ n that is convergent to \(\widetilde {u}\). The transformation from Ω to \(\mathbb {B}^{d}\) requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For \(u\in C^{\infty } \left (\overline {\Omega }\right ) \) and assuming ?Ω is a C ^∞ boundary, the convergence of \(\left \Vert \widetilde {u} -\widetilde {u}_{n}\right \Vert _{H^{1}}\) to zero is faster than any power of 1/n. The error analysis uses a reformulation of the boundary value problem as an integral equation, and then it uses tools from nonlinear integral equations to analyze the numerical method. Numerical examples illustrate experimentally an exponential rate of convergence. A generalization to ?Δu + γ u = f(u) with a zero Neumann boundary condition is also presented.