Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Combined effects of clay modifications and compatibilizers on the formation and physical properties of melt‐mixed polypropylene/clay nanocomposites

The melt mixing technique was used to prepare various polypropylene (PP)‐based (nano)composites. Two commercial organoclays (denoted 20A and 30B) served as the fillers for the PP matrix, and two different maleated (so‐called) compatibilizers (denoted PP‐MA and SMA) were employed as the third component. The results from X‐ray diffraction (XRD) and transmission electron microscope (TEM) experiments revealed that 190 °C was an adequate temperature for preparing the nanocomposites. Nanocomposites were achieved only if specific pairs of organoclay and compatibilizer were simultaneously incorporated in the PP matrix. For example, PP/20A(5 wt %)/PP‐MA(10 wt %) and PP/30B(5 wt %)/SMA(5 wt %) composites exhibited nanoscaled dispersion of 20A or 30B in the PP matrix. Differential scanning calorimetry (DSC) results indicated that the organoclays served as nucleation agents for the PP matrix. Generally, their nucleation effectiveness increased with the addition of compatibilizers. The thermal stability enhancement of PP after adding 20A was confirmed with thermogravimetric analysis (TGA). The enhancement became more evident as a suitable compatibilizer was further added. However, for the 30B‐included composites, thermal stability enhancement was not evident. The dynamic mechanical properties (i.e., storage modulus and loss modulus) of PP increased as the nanocomposites were formed; the properties increment corresponded to the organoclay dispersion status in the matrix. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4139–4150, 2004     

The reaction pattern of norbornene with excited state carbonyl compounds: Photochemical preparations of norbornene derivatives

We established that acetylacetone and acetone photolytically sensitize norbornene to undergo an efficient radical addition of solvent (ranging from hexane, cyclic ethers, haloalkanes, acetone, alcohols and acetonitrile) across the double bond. In view of its synthetic applicability, sensitized photoreactions of norbornene were reviewed and their mechanisms were compared. Photolysis of acetylacetone in the presence of norbornene in hexane induced i) acetylacetone to cycloadd to norbornene giving the expected 1,5-diketone, and ii) sensitization by triplet excited acetylacetone to generate reactive norbornene, which underwent dimerization as well as the addition of a solvent molecule by radical chain processes. In other solvents, the radical chain addition of solvent dominated the photoreaction, and superseded the cycloaddition, to give excellent to good yields of adducts to norbornene. While the excited species of acetylacetone for the sensitization was deduced to be its spectroscopic triplet excited state, that for the cycloaddition should involve a different one which may be a twisted triplet acetylacetone; sensitization experiments showed that the cycloaddition did not occur from the spectroscopic triplet state. Triplet excited acetone sensitized norbornene to undergo the same solvent addition more efficiently and cleanly than acetylacetone did. In view of various conflicts existing in the proposed energy transfer mechanism, the sensitized norbornene reactions were rationalized with electron transfer and a cation radical chain mechanism.     

Controlled/living polymerization of 2‐(diethylamino)ethyl methacrylate and its block copolymer with tert‐butyl methacrylate by atom transfer radical polymerization

Polymerization of 2‐(diethylamino)ethyl methacrylate (DEAEMA) via homogeneous atom transfer radical polymerization under various reaction conditions is described. The effects of the initiators and solvents were examined. With 1,1,4,7,10,10‐hexamethyl triethylenetetramine/copper(I) chloride/p‐toluenesulfonyl chloride as the ligand/catalyst/initiator system in methanol, poly(DEAEMA) with a polydispersity index as low as 1.07 was synthesized. Kinetic studies demonstrated the polymerization was very well controlled and exhibited the living characteristic of the process. Well‐defined block copolymers of DEAEMA and tert‐butyl methacrylate (tBMA) were successfully synthesized. The copolymers could be synthesized with equally good results by starting with either p(DEAEMA) or p(tBMA) as the macroinitiators. However, only the macroinitiators terminated with chlorine should be used. The corresponding macroinitiators with bromine as a transferable group did not yield well‐defined copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2688–2695, 2003     

One Alkenylphenol and Steroids from the Aquatic Plant Monochoria Vaginalis

Two new compounds have been isolated from the whole plant of Monochoria vaginalis and characterized as: (10Z)‐1‐(2,6‐dihydroxyphenyl)octadec‐10‐en‐1‐one ( 1 ) (20R, 24R)‐campest‐5‐ene‐3β, 4β‐diol ( 2 ) together with nine known ones. The structures of these compounds were elucidated on the basis of spectral data and chemical evidence.     

Finite element error estimates for non-linear elliptic equations of monotone type

Summary In this paper we shall consider the application of the finite element method to a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient, and the derivation of error estimates for the finite element approximations. Such problems arise in many practical situations — for example, in shock-free airfoil design, seepage through coarse grained porous media, and in some glaciological problems. By making use of certain properties of the nonlinear coefficients, we shall demonstrate that the variational formulations associated with these boundary value problems are well-posed. We shall also prove that the abstract operators accompanying such problems satisfy certain continuity and monotonicity inequalities. With the aid of these inequalities and some standard results from approximation theory, we show how one may derive error estimates for the finite element approximations in the energy norm.     

Preparation,thermal properties,and flame retardance of epoxy–silica hybrid resins

A novel epoxy system was developed through the in situ curing of bisphenol A type epoxy and 4,4′‐diaminodiphenylmethane with the sol–gel reaction of a phosphorus‐containing trimethoxysilane (DOPO–GPTMS), which was prepared from the reaction of 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO) with 3‐glycidoxypropyltrimethoxysilane (GPTMS). The preparation of DOPO–GPTMS was confirmed with Fourier transform infrared, ¹H and ³¹P NMR, and elemental analysis. The resulting organic–inorganic hybrid epoxy resins exhibited a high glass‐transition temperature (167 °C), good thermal stability over 320 °C, and a high limited oxygen index of 28.5. The synergism of phosphorus and silicon on flame retardance was observed. Moreover, the kinetics of the thermal oxidative degradation of the hybrid epoxy resins were studied. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2354–2367, 2003