Shape Optimization and Electron Bubbles

We present an analytical treatment of the shape optimization problem that arises in the study of electron bubbles. The problem is to minimize a weighted sum of a Laplace eigenvalue, volume, and surface area with respect to the shape of the domain. The analysis employs the calculus of moving surfaces and yields surprising conclusions regarding the stability of equilibrium spherical configurations. Namely, all but the lowest eigenvalue result in unstable configurations and certain combinations of parameters, near-spherical equilibrium stable configurations exist. Two-dimensional and three-dimensional problems are considered and numerical results are presented for the two-dimensional case.     

Embedding of dendriform algebras into Rota-Baxter algebras

Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var^!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var.     

A Jahn–Teller analysis of K3 and Rb3 in the electronic states 1E′ and 1E″

The potential energy surfaces (PES) of the Jahn–Teller distorted doublet 1²E′ (1B₂/1A₁) ground state and 1²E″ (2B₁/1A₂) excited state of alkali metal trimers (K₃, Rb₃) are studied with three high-level computational chemistry methods whose results are compared: single-reference coupled cluster, equation-of-motion coupled cluster and multi-reference second-order Rayleigh–Schrödinger perturbation theory. The doubly degenerate E electronic state interacts with the twofold degenerate vibrational e mode. We use the E ⊗ e Jahn–Teller effect theory to analyze in detail one- and two-dimensional cuts of the PES as a function of the symmetry-adapted internal coordinates Q_s, Q_x and Q_y and we extract the associated Jahn–Teller parameters. Spin-orbit coupling is accounted for by means of the Effective-Core-Potential-LS technique and spin-orbit splitting constants are extracted. We also provide the geometries, the binding energies and tentative vibronic spectra for the 1²E″ ← 1²E′ transitions.     

Synthesis of silica-coated ZnO nanocomposite: the resonance structure of polyvinyl pyrrolidone (PVP) as a coupling agent

The preparation of silica-coated ZnO nanocomposite using polyvinyl pyrrolidone (PVP) as a coupling agent was investigated. Transmission electron microscopy analysis revealed that silica has been deposited on the surface of PVP-capped ZnO nanoparticles as a continuous thin layer. Two-dimensional correlation analysis based on the time-dependent UV–vis spectra was introduced to study the interaction governing the deposition of silica on to PVP-capped ZnO. Strong hydrogen bonds formed between the amphiphilic PVP molecules and silica in the silica-coated PVP-capped ZnO composites. The reduced photocatalytic activity of silica-coated ZnO nanoparticles will enhance their performance as durable, safe, and non-reactive UV blockers in plastics, paints, and coating for outdoor textile and timber products.     

Anodic reactions of sulphate in molten salts

Electrochemical behaviour of sulphate under anodic polarization in molten sodium chloride, cryolite and sodium fluoride was investigated by cyclic voltammetry and chronopotentiometry at the temperatures of 820°C, 1010°C, and 1000°C, respectively. Using a platinum working electrode, two waves were observed on the chronopotentiograms in the systems: NaCl-Na₂SO₄ and Na₃AlF₆-Na₂SO₄. The first wave was attributed to the formation of oxygen. The second wave probably originated from the reaction of oxygen with platinum, or from oxidation of SO₃ decomposition products. Three waves were observed for the anodic process of sulphate ions dissolved in molten sodium fluoride. The first wave was attributed to the formation of oxygen. The second and the third wave were attributed to the formation of PtO and PtO₂. This conclusion was supported by cyclic voltammetry experiments of the in-situ formed sulphide in molten NaCl at 820°C and by chronopotentiometry on a gold working electrode in the system NaCl-Na₂SO₄, where no anodic wave was observed.     

The remarkable chemistry of trannulenes: green fluorinated fullerenes with unconventional aromaticity

We report the first reaction of trannulenes involving their thermal isomerization to a new class of compounds termed "triumphenes". The thermodynamically controlled conversion of trannulenes into triumphenes is accompanied by an unprecedented migration of three organic addends from one hemisphere of the fullerene cage to another. The reaction products, bearing aliphatic substituents, might find applications in materials science as strong electron acceptors due to the presence of fifteen electron-withdrawing fluorine atoms in their molecular framework. It was revealed that the isomerization of trannulenes can be affected by the presence of unsaturated compounds in the reaction mixture. Heating of trannulenes C(60)F(15)R(3) with C(60), C(70), anthracene, or pentacene at reflux in 1,2-dichlorobenzene yields fluorinated derivatives C(60)F(14)R(2)A, which possess a fused cyclic addend A. The products of this reaction have "triumphene-type" addition patterns and seem to be formed through an unprecedented sequence of elimination, addition, and isomerization steps. The molecular structure of a representative triumphene was proven unambiguously by X-ray single-crystal diffraction analysis and by NMR spectroscopy. The reactions revealed here open up numerous opportunities for chemical derivatization of fluorinated fullerenes. This method promises to provide a new path towards valuable photoactive materials and a new generation of fullerene-based compounds that are suitable for biomedical applications.     

Theoretical Studies on the Intermolecular Interactions of Potentially Primordial Base‐Pair Analogues

Recent experimental studies on the Watson–Crick type base pairing of triazine and aminopyrimidine derivatives suggest that acid/base properties of the constituent bases might be related to the duplex stabilities measured in solution. Herein we use high‐level quantum chemical calculations and molecular dynamics simulations to evaluate the base pairing and stacking interactions of seven selected base pairs, which are common in that they are stabilized by two N? H???O hydrogen bonds separated by one N? H???N hydrogen bond. We show that neither the base pairing nor the base stacking interaction energies correlate with the reported pK_a data of the bases and the melting points of the duplexes. This suggests that the experimentally observed correlation between the melting point data of the duplexes and the pK_a values of the constituent bases is not rooted in the intrinsic base pairing and stacking properties. The physical chemistry origin of the observed experimental correlation thus remains unexplained and requires further investigations. In addition, since our calculations are carried out with extrapolation to the complete basis set of atomic orbitals and with inclusion of higher electron correlation effects, they provide reference data for stacking and base pairing energies of non‐natural bases.