Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

SILICA PHOSPHORIC ACID/NaNO2 AS A NOVEL HETEROGENEOUS SYSTEM FOR THE COUPLING OF THIOLS TO THEIR CORRESPONDING DISULFIDES

Silica phosphoric acid was prepared via reaction of silica chloride (I) and phosphoric acid. Thiols can be readily converted to their corresponding thionitrites with a combination of silica phosphoric acid (II), wet SiO ₂ , and sodium nitrite in dichloromethane at room temperature. Disulfides result from the homolytic cleavage of the sulfur–nitrogen bond of the unstable thionitrite and subsequent coupling of the resultant thiyl radicals.     

A new liquid-phase microextraction method based on solidification of floating organic drop

In the present study, a new and versatile liquid-phase microextraction method is described. This method requires very simple and cheap apparatus and also a small amount of organic solvent. Eight microliters of 1-undecanol was delivered to the surface of solution containing analytes and solution was stirred for a desired time. Then sample vial was cooled by inserting it into an ice bath for 5 min. The solidified 1-undecanol was transferred into a suitable vial and immediately melted; then, 2 μL of it was injected into a gas chromatograph for analysis.Some polycyclic aromatic hydrocarbons (PAHs) were used as model compounds for developing and evaluating of the method performance. Analysis was carried out by gas chromatography/flame ionization detection (GC/FID).Several factors influencing the microextraction efficiency, such as the nature and volume of organic solvent, the temperature and volume of sample solution, stirring rate and extraction time were investigated and optimized. The applicability of the technique was evaluated by determination of trace amounts of PAHs in environmental samples. Under the optimized conditions, the detection limits (LOD) of the method were in the range of 0.07-1.67 μg L⁻¹ and relative standard deviations (R.S.D.) for 10 μg L⁻¹ PAHs were <7%. A good linearity (r² > 0.995) in a calibration range of 0.25-300.00 μg L⁻¹ was obtained. After 30 min extraction duration, enrichment factors were in the range of 594-1940. Finally, the proposed method was applied to the determination of trace amounts of PAHs in several real water samples, and satisfactory results were resulted. Since very simple devices were used, this new technique is affordable, efficient, and convenient for extraction and determination of low concentrations of PAHs in water samples.     

Introducing boranorcaradienes with more stability than their corresponding borepins: Reversal of tautomerization via substituents at theoretical levels

In contrast to typical borepins, which appear about 40.0 kcalmol^?1 more stable than their corresponding tautomeric boranorcaradienes, we have found 2 species, which have reversed this trend and pushed the equilibrium in favor of their corresponding boranorcaradienes. They are namely 1a,9b‐dihydro‐1H‐borireno[2,3‐h]pyridazino[4,3‐f]cinnoline and 1a,9b‐dihydro‐1H‐borireno[2,3‐h]pyrimido[5,4‐f]quinazoline which stand up among 14 isomeric systems probed, at B3LYP/AUG‐cc‐pVTZ, M06‐2X/AUG‐cc‐pVTZ, MP2/AUG‐cc‐pVTZ, and HF/AUG‐cc‐pVTZ. Energy barriers are calculated in gas‐phase, where the possibility of a rapid interconversion of the isomers is ruled out. Generally, dibenzoboranorcaradienes assume C_s symmetry with planar geometry and dihedral angle of zero degree. In contrast, their corresponding borepins show a high tendency for puckering with dihedral angle of ~66°. The preference of the latter for puckered non‐planar geometries is evidenced by natural bonding orbitals calculations and visually through their frontier molecular orbitals. Main interactions appear to be hyperconjugations of σ and π bonds across the rings. Position and number of nitrogen atoms on the fused rings seem to affect the energy gap, dipole moment, symmetry, dihedral angle, the chemical shift, NICS, bond lengths, and charge distribution.     

Synthesis of nano‐sized magnetite mesoporous carbon for removal of Reactive Yellow dye from aqueous solutions

In this study, core‐shell structures of magnetite nanoparticles coated with CMK‐8 ordered mesoporous carbon (Fe₃O₄@SiO₂‐CMK‐8 NPs) have been successfully synthesized for the first time by carbonizing sucrose inside the pores of the Kit‐6 mesoporous silica. The nano‐sized mesoporous particles were characterized by X‐ray diffraction, Fourier transform‐infrared spectroscopy, scanning electron microscope, dynamic light scattering, vibrating‐sample magnetometer, Brunauer–Emmett–Teller (BET) and transmission electron microscopy instruments. The obtained nanocomposite was used for removal of Reactive Yellow 160 (RY 160) dye from aqueous samples. The N₂ adsorption–desorption method (at 77 K) confirmed the mesoporous structure of synthesized Fe₃O₄@SiO₂‐CMK‐8 NPs. Also, the surface area was calculated by the BET method and Langmuir plot as 276.84 m²/g and 352.32 m²/g, respectively. The surface area, volume and pore diameter of synthesized nanoparticles (NPs) were calculated from the pore size distribution curves using the Barrett–Joyner–Halenda formula (BJH). To obtain the optimum experimental variables, the effect of various experimental parameters on the dye removal efficiency was studied using Taguchi orthogonal array experimental design method. According to the experimental results, about 90.0% of RY 160 was removed from aqueous solutions at the adsorbent amount of 0.06 g, pH 3 and ionic strength = 0.05 m during 10 min. The pseudo‐second order kinetic model provided a very good fit for the RY 160 dye removal (R² = 0.999). The Langmuir, Freundlich, Temkin and Dubinin–Radushkevich models were applied to describe the equilibrium isotherms, and the Langmuir isotherm showed the best fit to data with the maximum adsorption capacity of 62.893 mg/g. Furthermore, the Fe₃O₄@SiO₂‐CMK‐8 NPs could be simply recovered by external magnet, and exhibited recyclability and reusability for a subsequent six runs.     

A comparative study on the Ge6C14 heterofullerene nanocages: a density functional survey

Ten C₁₄Ge₆ heterofullerene isomers of C₂₀ have been investigated by density functional theory (DFT) methods with Becke 3‐Parameter (Exchange), Lee, Yang and Parr (B3LYP) functional at the 6‐311 + G*, 6‐311++G** and AUG‐cc‐pVTZ levels. In contrast to identical bonds in the latter, contractions of C═C double bonds are encountered at the expense of longer C―Ge bonds in the former. Vibrational frequency analysis confirms that all of the nanocages are true minima. In contrast to the common belief, for obtaining highly silicon‐doped stable heterofullerenes, that the silicon dopants must be completely isolated from each other by means of strong C═C double bonds. Here, linking the germanium substitutions together is an applicable strategy for obtaining highly doped stable isolated heterofullerenes since it avoids weak heteroatom─heteroatom bonds. Therefore, none of the computed heterofullerenes collapses to open, to deform, or to segregate fullerenic cages. As to band gaps (ΔE_HOMO‐LUMO), and nucleus‐independent chemical shifts at cage centers (NICS (0)), C₁₄Ge₆‐2 immerges with the highest value. Hence, it is predicted to be the most stable against electronic excitation. It contains 2 Ge─Ge single bonds at the cap‐equatorial positions. On the other hand, as to zero‐point vibrational energy and heat of atomization (ΔH_at), C₁₄Ge₆‐8 appears with the lowest and highest value, respectively. It contains 6 alternating germanium atoms in the equatorial and cap positions. Thus, it is predicted to be the most thermodynamically stable. So, germanium substitution leads to a high charge distribution on the surfaces of all the isomers specially C₁₄Ge₆‐9 with +1.496 charged germanum atoms. C₁₄Ge₆ isomers seem to be a good candidate for the hydrogen storage material.     

Theoretical description of electron phonon Fock space for gapless and gapped nanowires

We study the effect of electron–phonon(e–ph) interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The model is constructed using Green's function and multi-channel techniques, taking into account the local and nonlocal e–ph interactions. Then, we examine the model for the gapless(simple chain) and gapped(PA-like nanowire) systems. The results show that the tunneling conductance is improved by the e–ph interaction in both local and nonlocal regimes, while for the resonance conductance, the coherent part mainly decreases and the incoherent part increases. At the corresponding energies which depend on the phonon frequency, two dips in the elastic and two peaks in the inelastic conductance spectra appear. The reason is the absorption of the phonon by the electron in transition into inelastic channels.     

Potassium-intercalated H(2)Pc films: Alkali-induced electronic and geometrical modifications

X-ray spectroscopy studies of potassium intercalated metal-free phthalocyanine multilayers adsorbed on Al(110) have been undertaken. Photoelectron spectroscopy measurements show the presence of several charge states of the molecules upon K intercalation, due to a charge transfer from the alkali. In addition, the comparison of valence band photoemission spectra with the density functional theory calculations of the density of states of the H(2)Pc(-) anion indicates a filling of the formerly lowest unoccupied molecular orbital by charge transfer from the alkali. This is further confirmed by x-ray absorption spectroscopy (XAS) studies, which show a decreased density of unoccupied states. XAS measurements in different experimental geometries reveal that the molecules in the pristine film are standing upright on the surface or are only slightly tilted away from the surface normal but upon K intercalation, the molecular orientation is changed in that the tilt angle of the molecules increases.     

Symmetry group analysis and similarity solutions for the (2+1)‐dimensional coupled Burger's system

Symmetry group analysis and similarity reduction of nonlinear system of coupled Burger equations in the form of nonlinear partial differential equation are analyzed via symmetry method. The symmetry method has led to similarity reductions of this equation to solvable form to third‐order partial differential equation. The infinitesimal, similarity variables, dependent variables, and reduction have been tabulated. The search for solutions of these systems by using the improved tanh method has yielded certain exact solutions expressed by rational functions. Some figures are given to show the properties of the solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

Homogeneous liquid-liquid extraction of trace amounts of mononitrotoluenes from waste water samples

Homogeneous liquid-liquid extraction method was studied based on a phase separation phenomenon in a ternary solvent system. According to this procedure, mononitrotoloenes were extracted by single-phase extraction in a water/methanol/chloroform, homogeneous ternary solvent system. Methanol and chloroform were used as consolute and extraction solvents, respectively. The homogeneous solution was broken by the addition of salt and a cloudy solution was formed. After centrifugation, the fine droplets of the extraction solvent were sedimented in the bottom of the conical test tube. Analysis of the extracts was carried out by gas chromatography. The optimization procedure was performed using Box-Behnken design. The variables involved were: sample and extraction solvent volumes, consolute solvent volume and phase separator reagent concentration. Optimum results were obtained under the following conditions: sample volume of 5 mL, extraction solvent volume of 55 μL, consolute solvent volume of 1 mL and phase separator reagent concentration; 5% (w/v). Under these conditions, the enrichment factors of 354, 311 and 300, dynamic linear ranges of 0.5-500, 1-500 and 1-500 μg L⁻¹, and limit of detections (LODs) of 0.09, 0.09 and 0.1 μg L⁻¹ were obtained for o-nitrotoluene, m-nitrotoluene and p-nitrotoluene, respectively. Finally, the method was successfully applied to the extraction and determination of MNTs in the waste water samples in the range of micrograms per liter with R.S.Ds. < 13.2%.