A strategy for synthesis of ion‐bonded amphiphilic miktoarm star copolymers via supramolecular macro‐RAFT agent

Amphiphilic supramolecular miktoarm star copolymers linked by ionic bonds with controlled molecular weight and low polydispersity have been successfully synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using an ion‐bonded macromolecular RAFT agent (macro‐RAFT agent). Firstly, a new tetrafunctional initiator, dimethyl 4,6‐bis(bromomethyl)‐isophthalate, was synthesized and used as an initiator for atom transfer radical polymerization (ATRP) of styrene to form polystyrene (PSt) containing two ester groups at the middle of polymer chain. Then, the ester groups were converted into tertiary amino groups and the ion‐bonded supramolecular macro‐RAFT agent was obtained through the interaction between the tertiary amino group and 2‐dodecylsulfanylthiocarbonylsulfanyl‐2‐methyl propionic acid (DMP). Finally, ion‐bonded amphiphilic miktoarm star copolymer, (PSt)₂‐poly(N‐isopropyl‐acrylamide)₂, was prepared by RAFT polymerization of N‐isopropylacrylamide (NIPAM) in the presence of the supramolecular macro‐RAFT agent. The polymerization kinetics was investigated and the molecular weight and the architecture of the resulting star polymers were characterized by means of ¹H‐NMR, FTIR, and GPC techniques. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5805–5815, 2008     

A control problem for Burgers' equation with bounded input/output

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to illustrate the theoretical results.     

Separation of metals by liquid surfactant membranes containing crown ether carboxylic acids

A water-in-oil-in-water emulsion liquid membrane system is used to transport alkali metal and alkaline earth cations from an external alkaline aqueous source phase through an organic membrane containing a crown ether carboxylic acid and into the internal acidic aqueous phase of the emulsion droplet. The influence of varying the crown ether carboxylic acid structure upon the selectivity and efficiency of competitive metal ion transport is examined.     

IBMA–metal containing polymers

A new convenient route to metal containing polymers is described. This method involves emulsion co(ter) polymerization of a polar hydrocarbon soluble monomer, N-isobutoxymethylacrylamide (IBMA), with styrene or styrene/butadiene, followed by addition of metals. Metal incorporation is effected by latex or solution techniques. Preparative, atomic adsorption, spectroscopic, film observation, and dilute solution data are presented in support of metal complexation. Structures for the complexes are proposed.     

用发射光谱分析法检测地膜中金属杂质含量

本文描述农用薄膜中Ａｌ、Ｆｅ、Ｍｇ、Ｃａ、Ｓｉ、Ｃｕ、Ｔｉ杂质元素的发射光谱分析法，该方法直接压样于石墨电极中，简便，快速，取得了满意的结果。     

Infrared regularization of the massless scalar free field in two-dimensional space-time via Lorentz expansion

It is shown that Lorentz harmonics provide a natural basis for the expansion and infrared regularization of a massless scalar field in two dimensions. The negative metric operators separate out simply. Each Lorentz component of the field is partially local.     

Diffusion of ethylene glycol accompanied by reactions in poly(ethylene terephthalate) melts

Diffusion coefficients of ethylene glycol (EG) have been measured in poly(ethylene terephthlate) (PET) melts by a quartz-spring sorption apparatus. A simple mathematical model was developed to investigate the sorption behavior accompanied by chemical reactions of EG and PET at high temperatures. Diffusion coefficients are deduced from experimental data for an asymptotically thin sample in order to minimize the effects of reactions. The diffusion coefficient of EG is strongly dependent on the vapor pressure of EG and temperature but not on the molecular weight of PET in this experimental range (degree of polymerization 80–120). The diffusion coefficient of EG in PET melt at 265°C is 2.58 × 10^?7 cm²/s at the limit of zero concentration of EG. The activation energy for diffusion is 38.4 kcal/gmol, and the heat of solution for sorption is ?44.9 kcal/gmol. The concentrations of the volatile materials resulting from reactions in PET-EG system were analyzed with gas chromatography. In addition, a fit of the current model to experimental data yields frequency factors for the polymerization reaction (k₁) and the acetaldehyde formation reaction (k₂) to be 5.84 × 10⁸ cm³/mol ? min and 3.90 × 10¹¹ min^?1, respectively.     

Solutions to the Pólya–Szegö Conjecture and the Weak Eshelby Conjecture

Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, that is, that if the field inside an inclusion is uniform for all uniform loadings, then the inclusion is of elliptic or ellipsoidal shape. We call this the weak Eshelby conjecture. In this paper we prove this conjecture in three dimensions. In two dimensions, a stronger conjecture, which we call the strong Eshelby conjecture, has been proved: if the field inside an inclusion is uniform for a single uniform loading, then the inclusion is of elliptic shape. We give an alternative proof of Eshelby’s conjecture in two dimensions using a hodographic transformation. As a consequence of the weak Eshelby’s conjecture, we prove in two and three dimensions a conjecture of Pólya and Szegö on the isoperimetric inequalities for the polarization tensors (PTs). The Pólya–Szegö conjecture asserts that the inclusion whose electrical PT has the minimal trace takes the shape of a disk or a ball.