An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.     

A molecular orbital rationalization of ligand effects in N2 activation

Molecular orbital theory has been used to study a series of [(micro-N2){ML3}2] complexes as models for dinitrogen activation, with M=Mo, Ta, W, Re and L=NH2, PH2, AsH2, SbH2 and N(BH2)2. The main aims of this study have been to provide a thorough electronic analysis of the complexes and to extend previous work involving molecular orbital analyses. Molecular orbital diagrams have been used to rationalize why for L=NH2 ligand rotation is important for the singlet state but not the triplet, to confirm the effect of ligand pi donation, and to rationalize the importance of the metal d-electron configuration. The outcomes of this study will assist with a more in-depth understanding of the electronic basis for N2 activation and allow clearer predictions to be made about the structure and multiplicity of systems involved in transition-metal catalysis.     

MgO Nanoparticles as a Recyclable Heterogeneous Catalyst for the Synthesis of Polyhydroquinoline Derivatives under Solvent Free Conditions

Magnesium oxide nanopartticels in average size between 35–120 nm were prepared by sonochemistry method. Synthesis of polyhydroquinoline derivatives using MgO nanoparticles from the reaction of dimedone, benzaldehyde, ethyl acetoacetate and ammonium acetate under solvent‐free conditions is reported. Easy handling, reusability, thermal stability and non‐toxicity of the catalyst make the present protocol as an eco‐friendly and economically acceptable method for synthesis of these heterocycles.     

Ion transport in polymerized lyotropic liquid crystals containing ionic liquid

In this work, we investigate the effect of morphology and segmental dynamics on ion transport in polymerized lyotropic liquid crystals (polyLLCs) containing 1-butyl-3-methylimidazolium tetrafluoroborate as ionic liquid (IL). We demonstrate that two important factors, which affect ion conduction in polyLLCs, are grain size and chain density at the interface. The polyLLC with large grain size (70 nm) shows significant reduction in ion conductivity (one order of magnitude) compared to its homopolymer/IL mixture. However, the polyLLC with small grain size (20 nm) has little difference in ion conductivity compared to its homopolymer/IL mixture. It is observed that decreasing the chain density enhances the interaction of IL with polymer chains and consequently slows the relaxation of polymer chains. In addition, comparing the dynamics of polymer chains in mixtures of homopolymer/IL and templated LLC mesophases shows that the confinement in LLC structure prolongs the relaxation of polymer chains.     

Scission of Carbon Monoxide Using TaR3, R=(N(tBu)Ph) or OSi(tBu)3: A DFT Investigation

The experimentally known reduction of carbon monoxide using a 3‐coordinate [Ta(silox)₃] (silox=OSi(tBu)₃) complex initially forms a ketenylidene [(silox)₃Ta? CCO], followed by a dicarbide [(silox)₃Ta? CC? Ta(silox)₃] structure. The mechanism for this intricate reaction has finally been revealed by using density functional theory, and importantly a likely structure for the previously unknown intermediate [(silox)₃Ta? CO]₂ has been identified. The analysis of the reaction pathway and the numerous intermediates has also uncovered an interesting pattern that results in CO cleavage, that being scission from a structure of the general form [(silox)₃Ta? C_nO] in which n is even. When n is odd, cleavage cannot occur. The mechanism has been extended to consider the effect of altering both the metal species and the ligand environment. Specifically, we predict that introducing electron‐rich metals to the right of Ta in the periodic table to create mixed‐metal dinuclear intermediates shows great promise, as does the ligand environment of the Cummins‐style 3‐coordinate amide structure. This latter environment has the added complexity of improved electron donation from amide rotation that can significantly increase the reaction exothermicity.     

Solvent-free one-pot synthesis of 4-aryl-3,5-dimethyl-1,4,7,8-tetrahydrodipyrazolo[3,4-b:4′,3′-e]pyridines using Fe3O4@SiO2@(BuSO3H)3 catalytic Fe3+ system as selective colorimetric

Research on Chemical Intermediates - The synthesis of 4-Aryl-(3,5-dimethyl-1,4,7,8-tetrahydro-dipyrazolo[3,4b:4′,3′e]pyridine derivatives was accomplished using Fe3O4@SiO2@(BuSO3H)3...     

Superior performance of the machine-learning GAP force field for fullerene structures

Structural Chemistry - Carbon force fields are widely used for obtaining structural properties of carbon nanomaterials. We evaluate the performance of a wide range of carbon force fields for...     

Improve the heat exchanger efficiency via examine the Graphene Oxide nanoparticles: a comprehensive study of the preparation and stability,predict the thermal conductivity and rheological properties,convection heat transfer and pressure drop

Journal of Thermal Analysis and Calorimetry - In this research, the effect of using GO/ water nanofluid as a coolant fluid in an isothermal heat transfer system was studied. At first, to evaluate...