Miscibility of linear low density polyethylene (LLDPE)-graft-poly(methyl methacrylate) with poly(vinylidene fluoride) (PVF2) and its application as compatibilizer LLDPE/PVF2 blends

Differential scanning calorimetry (DSC), Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS) were used to study the miscibility of blends of a graft copolymer of poly(methyl methacrylate) on linear low density polyethylene (LLDPE-g-PMMA, G-3) with poly(vinylidene fluoride)(b) (PVF2) and the compatibilization of blends of LLDPE/PVF2. The specific interaction between PMMA side chains and PVF2 in G-3/PVF2 binary blends is weaker than that between the homopolymers PMMA and PVF2. There are two states of PVF2 in the melt of a G-3/PVF2 (60/40, w/w) blend, one as pure PVF2 and the other interacting with PMMA side chains. The miscibility between PMMA side chains and PVF2 affects the crystallization of PVF2. LLDPE-g-PMMA was demonstrated to be a good compatibilizer in LLDPE/PVF2 blends, improving the interfacial adhesion and dispersion in the latter. Diffusion of PMMA side chains into PVF2 in the interfacial region reduces the crystallization rate and lowers the melting point (T-m) and the crystallization temperature (T-c) of PVF2 in the blends.

SYNTHESIS OF A POLYETHYLENE-GRAFT-POLYSTYRENE COPOLYMER AND ITS COMPATIBILIZATION FOR LINEAR LOW-DENSITY POLYETHYLENE/POLY(PHENYLENE OXIDE) BLENDS

Based on unsteady diffusion kinetics, polyethylene(PE)-graft-polystyrene (PS) copolymers were designed and synthesized with a heterogeneous high yield titanium-based catalyst by copolymerization of ethylene with a PS-macromonomer using 1-hexene as a short chain agent to promote the incorporation of the PS-macromonomer. The presence of 1-hexene facilitated the diffusion of the PS-macromonomer, giving rise to the significantly increased incorporation of the PS-macromonomer. Compatibilization of blends of linear low density polyethylene (LLDPE)/poly(phenylene oxide) (PPO) with the PE-g-PS copolymer were investigated using scanning electron microscopy (SEM) and dynamic mechanical analysis (DMA).

Effective response of a non-linear composite in external AC electric field

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets <(. . .)> denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.