Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Atom transfer radical polymerization directly from poly(vinylidene fluoride): Surface and antifouling properties

The direct preparation of grafting polymer brushes from commercial poly (vinylidene fluoride) (PVDF) films with surface‐initiated atom transfer radical polymerization (ATRP) is demonstrated. The direct initiation of the secondary fluorinated site of PVDF facilitated grafting of the hydrophilic monomers from the PVDF surface. Homopolymer brushes of 2‐(N,N‐dimethylamino)ethyl methacrylate (DMAEMA) and poly (ethylene glycol) monomethacrylate (PEGMA) were prepared by ATRP from the PVDF surface. The chemical composition and surface topography of the graft‐functionalized PVDF surfaces were characterized by X‐ray photoelectron spectroscopy, attenuated total reflectance/Fourier transform infrared spectroscopy, and atomic force microscopy. A kinetic study revealed a linear increase in the graft concentration of poly[2‐(N,N‐dimethylamino)ethyl methacrylate] (PDMAEMA) and poly[poly(ethylene glycol) monomethacrylate] (PPEGMA) with the reaction time, indicating that the chain growth from the surface was consistent with a controlled or living process. The living chain ends were used as macroinitiators for the synthesis of diblock copolymer brushes. The water contact angles on PVDF films were reduced by the surface grafting of DMAEMA and PEGMA. Protein adsorption experiments revealed a substantial antifouling property of PPEGMA‐grafted PVDF films and PDMAEMA‐grafted PVDF films in comparison with the pristine PVDF surface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3434–3443, 2006     

Preparation and characterization of optically active polystyrene via a chiral nitroxide‐mediated polymerization

2,2,6,6‐Tetramethyl‐4‐[d‐(+)‐10‐camphorsulfonyl]‐1‐piperidinyloxy was synthesized and used as a chiral nitroxide for the bulk polymerizations of styrene initiated with benzoyl peroxide (BPO), tetraethylthiuram disulfide (TETD), and thermal initiation. The results showed that the polymerizations proceeded in a controlled/living way; that is, the kinetics presented approximately first‐order plots, and the number‐average molecular weights of the polymers with narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight) increased with the monomer conversion linearly. The molecular weight distributions in the case of thermal initiation were narrower than those in the case of BPO and TETD, whereas the polymerization rate with BPO or TETD as an initiator was obviously faster than that with thermal initiation. In addition, successful chain‐extension reactions were carried out, and the structures of the obtained polymers were characterized by gel permeation chromatography and ¹H NMR. The specific rotations of the polymers were also measured by polarimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1522–1528, 2006     

Effect of glass bead packing on the fibrillation of liquid‐crystalline polymer in polycarbonate

Polycarbonate (PC) was melt blended with small amount of liquid‐crystalline polymer (LCP) and various contents of glass beads (GB) having different diameters. The rheological measurements indicated that the GB addition increased the viscosity ratio and seemed unfavorable to the LCP fibrillation. However, the morphological observation showed that the LCP fibrillation was promoted by the GB addition and varied with the GB packing. With the increased GB packing by increasing the GB content and/or decreasing the GB diameter, LCP deformed from spheres and ellipsoids into stretched ellipsoids at lower shear rates and into long fibrils at higher shear rates. Although higher content of smaller GB jammed into the larger LCP droplets and inhibited the LCP fibrillation, very long LCP fibrils formed at higher shear rates at a high enough packing of GB. The relationship between GB packing and LCP fibrillation revealed two kinds of hydrodynamic effects of GB promoting the LCP fibrillation: at lower GB packing, the shear flow was enhanced by the high local shear between GB, in quantity; and for a high enough GB packing, the shear flow was changed, in quality, into elongational flow, which was more effective for the LCP fibrillation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1020–1030, 2006     

Effective potential for local composite operators and the problem of factorization of multi-field condensates

A new formulation of effective potential for local composite operators is given. The two-fermion condensate \(\langle \bar \Psi \Psi \rangle \) and four-fermion condensate \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) are calculated simultaneously in the Gross-Neveu model up to next-to-the-leading order in 1/N expansion. It is shown that factorization \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle = C_1 \langle \bar \Psi \Psi \rangle ^2 \) holds only in theN→∞ limit and the non-factorized part of \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) contributed by the order-1/N terms is comparable to \(C_1 \langle \bar \Psi \Psi \rangle ^2 \) when takingN=3.     

Indirect laser photoacoustic detection for trace samples on membranes

An indirect laser photoacoustic technique is described. The basic principle, the experimental set-up and the influencing factors are discussed in detail. This method was used to quantify phenylamine, arginine and methylene blue on membranes. The linear ranges of the calibration curve are up to two orders of magnitude. With 1 microliter of sample solution, the detection limits are 0.25, 1.52 and 0.14 pmol for phenylamine, arginine and methylene blue, respectively.     

Molar conductivity calculation of Li-ion battery electrolyte based on mode coupling theory

A method is proposed to calculate molar conductivity based on mode coupling theory in which the ion transference number is introduced into the theory. The molar conductivities of LiPF6, LiClO4, LiBF4, LiAsF6 in PC (propylene carbonate) are calculated based on this method. The results fit well to the literature data. This presents a potential way to calculate the conductivities of Li-ion battery electrolytes.