Prediction of 195Pt NMR chemical shifts of dissolution products of H2[Pt(OH)6] in nitric acid solutions by DFT methods: how important are the counter‐ion effects?

¹⁹⁵Pt NMR chemical shifts of octahedral Pt(IV) complexes with general formula [Pt(NO₃)_n(OH)_{6 ? n}]^2?, [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 1–6), and [Pt(NO₃)_{6 ? n ? m}(OH)_m(OH₂)_n]^{?2 + n ? m} formed by dissolution of platinic acid, H₂[Pt(OH)₆], in aqueous nitric acid solutions are calculated employing density functional theory methods. Particularly, the gauge‐including atomic orbitals (GIAO)‐PBE0/segmented all‐electron relativistically contracted–zeroth‐order regular approximation (SARC–ZORA)(Pt) ∪ 6–31G(d,p)(E)/Polarizable Continuum Model computational protocol performs the best. Excellent second‐order polynomial plots of δ_calcd(¹⁹⁵Pt) versus δ_exptl(¹⁹⁵Pt) chemical shifts and δ_calcd(¹⁹⁵Pt) versus the natural atomic charge Q_Pt are obtained. Despite of neglecting relativistic and spin orbit effects the good agreement of the calculated δ ¹⁹⁵Pt chemical shifts with experimental values is probably because of the fact that the contribution of relativistic and spin orbit effects to computed σ^{iso 195}Pt magnetic shielding of Pt(IV) coordination compounds is effectively cancelled in the computed δ ¹⁹⁵Pt chemical shifts, because the relativistic corrections are expected to be similar in the complexes and the proper reference standard used. To probe the counter‐ion effects on the ¹⁹⁵Pt NMR chemical shifts of the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? and cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 0–3) complexes we calculated the ¹⁹⁵Pt NMR chemical shifts of the neutral (PyH)₂[Pt(NO₃)_n(OH)_{6 ? n}] (n = 1–6; PyH = pyridinium cation, C₅H₅NH⁺) and [Pt(NO₃)_n(H₂O)_{6 ? n}](NO₃)_{4 ? n} (n = 0–3) complexes. Counter‐anion effects are very important for the accurate prediction of the ¹⁹⁵Pt NMR chemical shifts of the cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} complexes, while counter‐cation effects are less important for the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? complexes. The simple computational protocol is easily implemented even by synthetic chemists in platinum coordination chemistry that dispose limited software availability, or locally existing routines and knowhow. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

A 3D mesh deformation technique for irregular in‐flight ice accretion

Aircraft holding around busy airports may be requested to sustain as much as 45 min of icing before landing or being diverted to another airport. In this paper, a three‐dimensional mesh deformation scheme, based on a structural frame analogy, is proposed for the numerical simulation of ice accretion during extended exposure to adverse weather conditions. The goal is to provide an approach that is robust and efficient enough to delay or altogether avoid re‐meshing while preserving (enforcing) nearly orthogonal elements at the highly distorted ice surface. Robustness is achieved by suitably modifying the axial and torsional stiffness components of the frame elements in order to handle large and irregular grid displacements typical of in‐flight icing. Computational efficiency is obtained by applying the mesh displacement to an automatically selected small subset of the entire computational domain. The methodology is validated first in the case of deformations typical of fluid‐structure interaction problems, including wing bending, a helicopter rotor in forward flight, and the twisting of a high‐lift wing configuration. The approach is then assessed for aero‐icing on two swept wings and compared against experimental measurements where available. Copyright © 2015 John Wiley & Sons, Ltd.     

In Situ Synthesis and Characterization of Poly(aryleneethynylene)‐Grafted Reduced Graphene Oxide

Using highly soluble bromo‐functionalized reduced graphene oxide (RGBr) as a key graphene template for surface‐directing Sonogashira–Hagihara polymerization, a novel soluble poly(arylene‐ethynylene)‐grafted reduced graphene oxide, hereafter abbreviated as PAE‐g‐RGO, was prepared in situ. The entirely different electron distribution of LUMO and HOMO of PAE‐g‐RGO suggested the existence of a charge‐transfer (CT) state (PAE^.?–RGO^.+). The negative ΔG_CS value (?2.57 eV) indicates that the occurrence of the charge separation via ¹RGO* in o‐DCB is exothermic and favorable. Upon irradiation with 365 nm light, the light‐induced electron paramagnetic resonance (LEPR) spectrum of PAE‐g‐RGO showed a decrease in the spin‐state density owing to photoinduced intramolecular electron transfer events in this system. A sandwich‐type Al/PAE‐g‐RGO/ITO device showed representative bistable electrical switching behavior. The nonvolatile memory performance was attributed to the CT‐induced conductance changes, which was supported by molecular computation results and conductive atomic force microscopy (C‐AFM) images.     

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.     

Synthesis and evaluation of the anticancer activity of the water-dispersible complexes of 4-acylaminoisoxazole derivative with biocompatible nanocontainers based on Ca2+ (Mg2+) cross-linked alginate

Water-dispersible complexes of 4-methyl-N-[5-methyl-3-(3,4,5-trimethoxyphenyl)isoxazol-4-yl]benzamide possessing anticancer activity were prepared by its immobilization with biocompatible polymer nanocontainers based on sodium alginate cross-linked with Ca²⁺ and Mg²⁺ ions. It was found that this isoxazole derivative retains its structure during immobilization. Colloidal stable nanocontainers filled with this compound exhibit toxicity toward the colon carcinoma (HCT116) tumor cell line.     

Stabilization of a viscoelastic rotating Euler‐Bernoulli beam

In this paper, we consider a rotating Euler‐Bernoulli beam. The beam is made of a viscoelastic material, and it is subject to undesirable vibrations. Under a suitable control torque applied at the motor, we prove the arbitrary stabilization of the system for a large class of relaxation functions by using the multiplier method and some ideas introduced by Tatar (J. Math. Phys. 52:013502, 2011).     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters.