A Neutral Germanium/Phosphorus Frustrated Lewis Pair and Its Contrasting Reactivity Compared to Its Silicon Analogue

Chlorogermane (C₂F₅)₃GeCl with very electronegative pentafluoroethyl groups was converted with LiCH₂P(tBu)₂ to obtain the intramolecular frustrated Lewis pair (FLP) (C₂F₅)₃GeCH₂P(tBu)₂, a neutral, germanium-based FLP. Its reactivity was compared to its silicon homologue (C₂F₅)₃SiCH₂P(tBu)₂. Both FLPs cleave NO but give cyclic (Si) and open-chain oxides (Ge). In reactions with HCl both FLPs gave the same adduct type in the solid state, while the proton seems more mobile in solution in the germanium case. Reactions with PhCNO and Me₃SiCHN₂ result in ring-type adducts. The structures of (C₂F₅)₃GeCH₂P(tBu)₂ and of five adducts with substrates were elucidated by X-ray diffraction. The study clearly showed the germanium compound to have a more moderate Lewis acidity compared to the silicon analogue.     

Function composition of modified reduced graphite oxide

Reduced graphite oxide (RGO) is prospective for application as an active material for supercapacitor electrodes due to the simple synthesis, the high specific surface area and the presence of oxygen-containing functional groups. Functionalization of such materials affects hydrophilicity, surface morphology and contributes to the redox processes when potential is applied. In this article RGO was treatment by mixture of potassium hydroxide and chloroacetic acid; hydrobromic acid and oxalic acid; in various ratio of strong nitric, sulfuric and phosphoric acids. Such functionalization of RGO leads to decrease in particle size, increase the quantity of oxygen-containing groups on the surface of the materials and affects the change of carbon hybridization from sp² to sp³. Furthermore, all the samples were investigated by cyclic voltammetry (CV) to study the redox processes occurring on the electrode material surface. The peaks on the CV curves were compared with the corresponding redox reversible reactions. Furthermore, the specific capacity of all samples was calculated. Thus, at low carboxylation level of RGO specific capacity is increased due to significant contribution of redox processes while high functionalization leads to decrease in conductivity and, as well in specific capacity.     

Effect of graphene surface functionalization on the oxygen reduction reaction in alkaline media

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Upper triangular matrix walk: Cutoff for finitely many columns

We consider random walk on the space of all upper triangular matrices with entries in which forms an important example of a nilpotent group. Peres and Sly proved tight bounds on the mixing time of this walk up to constants. It is well known that the column projection of this chain is the one dimensional East process. In this article we complement the Peres‐Sly result by proving a cutoff result for the mixing of finitely many columns in the upper triangular matrix walk at the same location as the East process of the same dimension. The proof is based on a recursive argument which uses a local version of a dual process appearing in a previous study, various combinatorial consequences of mixing and concentration results for the movement of the front in the one dimensional East process.     

The structure of finite groups with trait of non-normal subgroups

In this paper, we investigate the finite groups all of whose non-normal nilpotent subgroups are cyclic. We show that such groups are solvable with cyclic centers. If G is a non-supersolvable group, then G has only one non-cyclic Sylow subgroup which is either isomorphic to Q₈ or is of type (q, q).