Pd immobilized on polyamide based on melamine and terephalic acid as an efficient and recyclable catalyst for Suzuki‐Miyaura coupling reaction

A simple synthetic strategy of polyamide was described from melamine and terephalic acid via one‐step polycondensation. PdCl₂ was then immobilized on the polyamide (denoted as Pd/MPA). Melamine and terephalic acid not only acted as monomers but also provided the ligand sites to help the polyamide to coordinate with Pd(II). The Pd/MPA catalyst was characterized by FT‐IR, TGA, SEM, TEM, XPS, N₂ adsorption‐desorption and atomic absorption spectroscopy. The catalyst was used in Suzuki‐Miyaura coupling reaction of various aryl halides, including less reactive chlorobenzene and benzyl chloride, to give the coupling products in moderate to excellent yields. High turnover frequencies (TOF) up to 29400 h^‐1 can be also obtained. In addition, it behaved truly as a heterogeneous catalyst with high reusability after being recycled 6 times and palladium leaching was negligible during the process. This work provides a practical polyamide support to develop heterogeneous palladium catalysts with simple synthetic procedure and low cost.     

A Galerkin spectral method based on helical‐wave decomposition for the incompressible Navier–Stokes equations

This paper presents a global Galerkin spectral method for solving the incompressible Navier–Stokes equations in three‐dimensional bounded domains. The method is based on helical‐wave decomposition (HWD), which uses the vector eigenfunctions of the curl operator as orthogonal basis functions. We shall first review the general theory of HWD in an arbitrary simply connected domain, along with some new developments. We then employ the HWD to construct a Galerkin spectral method. The current method innovates the existing HWD‐based spectral method by (a) adding a series of auxiliary fields to the HWD of the velocity field to fulfill the no‐slip boundary condition and to settle the convergence problem of the HWD of the curl fields, and (b) providing a pseudo‐spectral method that utilizes a fast spherical harmonic transform algorithm and Gaussian quadrature to calculate the nonlinear term in the Navier–Stokes equations. The auxiliary fields are uniquely determined by solving the Stokes and Stokes‐like equations under adequate boundary conditions. The implementation of the method under the spherical geometry is presented in detail. Several numerical examples are provided to validate the proposed method. The method can be easily extended to other domains once the helical‐wave bases, which depend only on the geometry of the domains, are available. Copyright © 2015 John Wiley & Sons, Ltd.     

The synthesis and structure of 1,3,4-trisubstituted 2,5-dioxopyrrolidines and their behaviour in liquid crystalline systems

To find novel compounds for liquid crystalline mixtures with improved properties, a series of optically active 1,3,4-trisubstituted 2,5-dioxopyrrolidines has been prepared. Their structure was confirmed by IR spectroscopy. The twisting ability of the compounds prepared was studied.