New synthesis strategies for effective functionalization of kaolinite and saponite with silylating agents

Functionalization of Brazilian São Simão kaolinite and Spanish Yunclillos saponite with the alkoxysilanes 3-aminopropyltriethoxysilane and 3-mercaptopropyltrimethoxysilane is reported. The resulting hybrids were characterized by X-ray diffraction, thermal analysis, infrared absorption spectroscopy, and scanning electron microscopy, which demonstrated the effectiveness of the interlamellar grafting process. The X-ray diffractograms revealed incorporation of the alkoxide molecules into the interlayer space of the clays. The displacement of the stretching bands of interlayer hydroxyls in the infrared spectra of the modified kaolinites and the increased intensity of the Mg–OH vibrations in the spectra of the modified saponites confirmed the functionalization of the clays. The thermal behavior of the organoclays confirmed the stability of the hybrids, which was dependent on the clay used for preparation of the materials.     

Cu−NHC Complex for Chan-Evans-Lam Cross-Coupling Reactions of N-Heterocyclic Compounds and Arylboronic Acids

An efficient copper(II) N-heterocyclic carbene (NHC) complex with an NCN coordination mode was optimized to catalyze the Chan–Evans-Lam (CEL) cross-coupling reaction of imidazole and other N-heterocyclic nucleophiles with arylboronic acid. This air-stable copper catalyst shows robust catalytic performance and tolerates a diverse array of functional groups on both the N-nucleophile and arylboronic acid coupling partners in C−N bond forming reactions with up to 95 % yield. Formation of the Cu−NHC complex in situ generated similar catalytic performance for CEL coupling. Alternative metal ions (Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Zn²⁺, Ru²⁺, and Pd²⁺) were also screened in the presence of the NHC precursor as CEL catalysts.     

Coating of polyamide 12 by sol–gel methodology

The combination of sol–gel methodology with rapid prototyping (RP) produces functionalized 3D structures with potential applications in various fields. However, this combination has been little explored. In this paper, we used the sol–gel method to deposit vanadium isopropoxide onto polyamide (PA12) constructed by RP and pretreated with acetic acid, to obtain a functionalized substrate with new thermal, physical, and chemical properties. Vanadium isopropoxide (one, five, or ten layers) was deposited onto the PA12 piece by dip-coating. We characterized the coated PA12 by thermal analyses, X-ray diffraction, and infrared spectroscopy, which revealed that V=O and Si–O–Si groups exist on the PA12 surface. PA12 coating with vanadium isopropoxide enhanced the decomposition temperature. Differential scanning calorimetry revealed increased fusion and decomposition enthalpy as a function of the PA12 coating. Therefore, deposition of vanadium isopropoxide onto PA12 pretreated with acetic acid improves the thermal stability of PA12 prepared by RP.     

Kramers’ problem and the Knudsen minimum: a theoretical analysis using a linearized 26-moment approach

A set of linearized 26 moment equations, along with their wall boundary conditions, are derived and used to study low-speed gas flows dominated by Knudsen layers. Analytical solutions are obtained for Kramers’ defect velocity and the velocity-slip coefficient. These results are compared to the numerical solution of the BGK kinetic equation. From the analysis, a new effective viscosity model for the Navier–Stokes equations is proposed. In addition, an analytical expression for the velocity field in planar pressure-driven Poiseuille flow is derived. The mass flow rate obtained from integrating the velocity profile shows good agreement with the results from the numerical solution of the linearized Boltzmann equation. These results are good for Knudsen numbers up to 3 and for a wide range of accommodation coefficients. The Knudsen minimum phenomenon is also well captured by the present linearized 26-moment equations.     

Supersolvable Frobenius groups with nilpotent centralizers

Let FH be a supersolvable Frobenius group with kernel F and complement H. Suppose that a finite group G admits FH as a group of automorphisms in such a manner that $C_G(F)=1$ and $C_G(H)$ is nilpotent of class c. We show that G is nilpotent of $(c,\left|FH\right|)$-bounded class.     

Properties of positive harmonic functions on the half-space with a nonlinear boundary condition

In this paper we study existence and properties of solutions of the problem Δw=0 on the half-space with nonlinear boundary condition ∂w/∂η+w=|w|^p−2w where 2<p<2(N−1)/(N−2) and N?3. We obtain a ground state solution w=w(x₁,…,xN−1,t) which is radial and has exponential decay in the first N−1 variables. Moreover, w has sharp polynomial decay in the variable t.     

Crystal structure of tetrachlorobisd[μ-imidocarbonylchloridato]diboron

Boron trichloride and mercuric cyanide react slowly to form the title compound, B₂N₂C₂Cl₈, which contains a four-membered B₂N₂ ring with alternating BCl₂ and N—CCl₂. Crystals are triclinic, space group P , a = 6.1198(1), b = 7.4457(3), c = 7.9186(3) Å, = 117.064(2), = 106.923, = 93.712(2)°, Z = 1, and V = 299.07(2) ų. The compound has a crystallographic center of symmetry but the metric symmetry is close to the expected mmm.     

Fitting Height of a Finite Group with a Metabelian Group of Automorphisms

Let M = FH be a finite group that is a product of a normal abelian subgroup F and an abelian subgroup H. Assume that all elements in M?F have prime order p, and F has at most one subgroup of order p. Examples of such groups are dihedral groups for p = 2 and the semidirect product of a cyclic group F by a group H of prime order p such that C _F (H) = 1 or |C _F (H)| =p and C _{F/C F (H)}(H) = 1. Suppose that M acts on a finite group G in such a manner that C _G (F) = 1. We prove that the Fitting height h(G) of G is at most h(C _G (H))+ 1. Moreover, the Fitting series of C _G (H) coincides with the intersection of C _G (H) with the Fitting series of G.     

Scalable and robust randomized benchmarking of quantum processes

In this Letter we propose a fully scalable randomized benchmarking protocol for quantum information processors. We prove that the protocol provides an efficient and reliable estimate of the average error-rate for a set operations (gates) under a very general noise model that allows for both time and gate-dependent errors. In particular we obtain a sequence of fitting models for the observable fidelity decay as a function of a (convergent) perturbative expansion of the gate errors about the mean error. We illustrate the protocol through numerical examples.     

Modular Construction of Fluoroarenes from a New Difluorinated Building Block by Cross‐Coupling/Electrocyclisation/Dehydrofluorination Reactions

Palladium‐catalysed coupling reactions based on a novel and easy‐to‐synthesise difluorinated organotrifluoroborate were used to assemble precursors to 6π‐electrocyclisations of three different types. Electrocyclisations took place at temperatures between 90 and 240 °C, depending on the central component of the π‐system; nonaromatic trienes were most reactive, but even systems that required the temporary dearomatisation of two arenyl subunits underwent electrocyclisation, albeit at elevated temperatures. Photochemical conditions were effective for these more demanding reactions. The package of methods delivered a structurally diverse set of fluorinated arenes, spanning a 20 kcal mol^?1 range of reactivity, by a flexible route.