Toughness mechanism in polypropylene composites: Polypropylene toughened with elastomer and calcium carbonate

Polypropylene (PP) was modified with elastomer or CaCO₃ particles of two different sizes (1 μm and 50 nm) in various volume fractions. The dispersion morphology and mechanical properties of the two systems were investigated as functions of the particle size and volume fraction of the modifier. The brittle‐to‐tough transition occurred when the matrix ligament thickness was less than the critical ligament thickness, which was about 0.1 μm for the PP used here, being independent of the type of modifier. At the same matrix ligament thickness, the improvement of the toughness was obviously higher with the elastomer rather than with CaCO₃, but adding CaCO₃ increased the modulus of PP. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1656–1662, 2004     

Microwave-assisted extraction of quercetin and acid degradation of its glycosides in Psidium guajava leaves.

Microwave-assisted extraction (MAE) and microwave-assisted hydrolysis (MAAH) were developed for the sample preparation of guava leaves prior to GC determination of quercetin and its glycosides. Ethanol was selected as the solvent. The optimum MAE temperature, particle size, solvent volume and MAE time are 120 degrees C, 40 - 60 mesh, 20 mL and 5 min, respectively; the optimum MAAH temperature and time, HCl concentration, solvent are 100 degrees C, 5 min, 1.2 mol L(-1) HCl and ethanol, respectively.     

Concentrations of hazardous heavy metals in environmental samples collected in Xiamen, China, as determined by vapor generation non-dispersive atomic fluorescence spectrometry.

Non-dispersive atomic fluorescence spectrometry (NDAFS) coupled with vapor generation (VG) sample introduction was applied to the determination of the concentrations of hazardous heavy metals, such as arsenic, cadmium, lead and mercury, in seawater, soils and total airborne particulate matter (PM) collected around the Xiamen area in China. Almost 100% sample introduction efficiency was achieved by using thiourea and ascorbic acid for the pre-reduction of As(V) to As(III), K3Fe(CN)6 and tartaric acid for pre-oxidation of Pb(II) to Pb(IV), and masking the interferences arising from the co-existing transition metals to As, Cd, Hg and Pb during their vapor generation process. Moreover, a novel sample pretreatment device was developed to avoid the loss of mercury, lead, cadmium and arsenic during sample pretreatment. With such methods, the detection limit (DL) of arsenic, cadmium, lead and mercury was down to 0.08, 0.03, 0.05, 0.01 ng mL(-1) (3sigma), respectively. The relative standard deviations (RSD, n = 11) for arsenic, cadmium, lead and mercury at 10 ng mL(-1) were 0.9%, 1.6%, 1.3% and 2.0%, respectively. The concentrations of hazardous heavy metals in the environmental samples collected in Xiamen, China are in the range from 0.02 +/- 0.001 ng mL(-1) in seawater to 15.3 +/- 0.2 microg g(-1) in soils. Besides flame/GF-AAS and ICP-AES/MS, VG-NDAFS should be another choice for the determination of hazardous heavy metals in environmental samples.     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

Dispersion and distribution of organically modified montmorillonite in nylon‐66 matrix

Nylon‐66 nanocomposites were prepared by melt‐compounding nylon‐66 with an alkyl ammonium surfactant pretreated montmorillonite (MMT). The thermal stability of the organic MMT powders was measured by thermogravimetric analysis. The decomposition of the surfactant on the MMT occurred from 200 to 500 °C. The low onset decomposition temperature of the organic MMT is one shortcoming when it is used to prepare polymer nanocomposites at high melt‐compounding temperatures. To provide greater property enhancement and better thermal stability of the polymer/MMT nanocomposites, it is necessary to develop MMT modified with more thermally stable surfactants. The dispersion and spatial distribution of the organic MMT layers in the nylon‐66 matrix were characterized by X‐ray diffraction. The organic MMT layers were exfoliated but not randomly dispersed in the nylon‐66 matrix. A model was proposed to describe the spatial distribution of the organic MMT layers in an injection‐molded rectangular bar of nylon‐66/organic MMT nanocomposites. Most organic MMT layers were oriented in the injection‐molding direction. Layers near the four surfaces of the bar were parallel to their corresponding surfaces; whereas those in the bulk differed from the near‐surface layers and rotated themselves about the injection‐molding direction. The influence of the spatial distribution of the organic MMT on crystallization of nylon‐66 was also investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1234–1243, 2003     

Erds方程的全等解

本文运用初等方法给出了Erds方程的所有全等解.     

On the decomposition of Kn into complete m-partite graphs

Graham and Pollak [3] proved that n ?1 is the minimum number of edge-disjoint complete bipartite subgraphs into which the edges of K_n can be decomposed. Using a linear algebraic technique, Tverberg [2] gives a different proof of that result. We apply his technique to show that for “almost all n,” ? (n + m ?3)/(m ?1) ? is the minimum number of edge-disjoint complete m-partite subgraphs in a decomposition of K_n.     

Dependence of slow crack growth in polyethylene on butyl branch density: Morphology and theory

A theoretical equation has been developed to described the rate of slow crack growth in an ethylene-hexene copolymer in terms of the basic morphological parameters. These parameters are spacing of the butyl branches, number of tie molecules, and the thickness of the lamellar crystal. Experimentally, the thickness of the lamellae and the long period were determined as functions of the branch density. The calculation of the number of tie molecules is based on the values of the molecular weight and the long period. The model of slow crack growth is based on the rate of disentanglement of the tie molecules. The rate of disentanglement varies inversely with the number of tie molecules and directly with the number of tie molecules that are not pinned by the branches.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007