Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]manganese(III) acetate as a novel carrier for a selective iodide PVC membrane electrode.

[5,10,15,20-Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]Mn(III) acetate (MnTDPAc) was applied as an ionophore for an iodide-selective PVC membrane electrode. The influences of the membrane composition, pH of the test solution and foreign ions on the electrode performance were investigated. The sensor exhibited not only excellent selectivity to iodide ion compared to Cl- and lipophilic anions such as ClO4- and salicylate, but also a Nernstian response with a slope of -59.4 +/- 1.2 mV per decade for iodide ions over a wide concentration range from 1.0 x 10(-2) to 7.5 x 10(-6) M at 25 degrees C. The potentiometric response was independent of the pH of the solution in the pH range of 2 - 8. The electrode could be used for at least 2 months without any considerable divergence in the potential. Good selectivity for iodide ion, a very short response time, simple preparation and relatively long-term stability were the silent characteristics of this electrode. It was successfully used as an indicator electrode in the potentiometric titration of iodide ions, and also in the determination of iodide from seawater samples and drug formulations.     

Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.     

Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) method is an efficient mesh free technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. In a meshless method, a set of scattered nodes are used instead of meshing the domain of the problem. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes.     

Kinetic study of the oxidation of ethanol by 3,4-lutidine chromium(VI) peroxide in dichloromethane solution

The oxidation kinetics of ethanol with 3,4-lutindine chromium(VI) peroxide (LCP) were investigated by monitoring the absorbance change at 565 nm in dichloromethane solution. The reaction had a first-order dependence on oxidant and a fractional (one half) dependence on reactant. The stoichiometric ratio between LCP and ethanol was 1 : 2. The activation parameters were determined from temperature dependence of the reaction rate. It was found that the cleavage of the peroxide groups of LCP is primarily responsible for the oxidant of ethanol to acetaldehyde. Based on the kinetic results obtained (including deuterium isotope effect) a plausible mechanism is proposed. © 1994 John Wiley & Sons, Inc.     

“Living” radical graft polymerization of styrene to styrene butadiene rubber (SBR) with 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO)

Well‐defined graft copolymers with styrene butadiene rubber (SBR) backbones and polystyrene branches were synthesized by living free radical polymerization (LFRP) techniques. Thus 1‐ benzoyl‐2‐phenyl‐2‐(2′,2′,6′,6′‐tetramethyl‐piperidinyl‐1′‐oxy)ethane (BZ‐TEMPO) was synthesized and hydrolyzed to the corresponding 1‐hydroxyl derivative. This functional nitroxyl compound was coupled with brominated SBR (SBR‐Br). The resulting macroinitiator (SBR‐TEMPO) for “living” free radical polymerization was then heated in the presence of styrene for the formation of the controlled graft copolymer. ¹H‐NMR and IR spectroscopy were used to investigate the structure of the polymers. Copyright © 2004 John Wiley & Sons, Ltd.     

Nitroxide mediated living radical polymerization of styrene onto poly (vinyl chloride)

Nitroxide‐mediated ‘living’ free radical polymerisation (LREP) was employed for the first time to prepare graft copolymer by having arylated poly (vinyl chloride) (PVC‐Ph) as a backbone and polystyrene (PS) as branches. The graft copolymerization of styrene was initiated by arylated PVC carrying 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) groups as a macroinitiator. Thus, the arylated PVC was prepared in the mild conditions and these reaction conditions could overcome the problem of gelation and crosslinking in polymers. Then, 1‐hydroxy TEMPO was synthesized by the reduction of TEMPO with sodium ascorbate. This functional nitroxyl compound was coupled with brominated arylated PVC (PVC‐Ph‐Br). The resulting macro‐initiator (PVC‐Ph‐TEMPO) for ‘living’ free radical polymerization was then heated in the presence of styrene to form graft copolymer. DSC, GPC, ¹HNMR, and FT‐IR spectroscopy were employed to investigate the structure of the polymers. Copyright © 2007 John Wiley & Sons, Ltd.     

The Importance of Polarity/Polarizability Interaction on the Acidity Behavior of 9,10-Anthraquinone and 9-Anthrone Derivatives in Methanol-Water Mixed Solvents Using Target Factor Analysis and QSPR Approaches

The influence of solvent properties on acidity constants of some newly synthesized 9,10-anthraquinone and 9-anthrone derivatives was studied in methanol-water mixtures in a composition range of 0.57 to 1.0 methanol mole fraction. The model was established by using both multiple linear regression and target factor analysis. Both methods revealed that the solvent polarity/polarizability parameter ^* is a major factor in controlling the acidity behavior of the anthraquinones and anthrones studied in binary methanol-water mixed solvents. A QSPR study was conducted to drive the relationships between the ^* coefficient s and the polarity/polarizability of molecules. Both dipole moment and polarizability were found to have a linear relationship with s. The results confirm that, in the dipolar protic solvents used, the dipole-dipole interaction (for neutral molecules) and the ion-dipole interaction (for ionized molecules) are the major factors controlling the acidity behavior of these compounds.     

Specific Uphill Transport of Zinc as Zn(SCN)42− Ion using Na+-Dicyclohexyl-18-Crown-6 as Carrier

Sodium-dicyclohexyl- 18-crown-6 complex cation was used as carrier for the uphill transport of zinc as Zn(SCN)₄^2? complex anion. By using L-cysteine as a metal ion acceptor in the receiving phase at the optimized pH of 7.6, the amount of zinc transport through the liquid membrane after 90 min was 97.2 ± 1.0%. The selectivity and efficiency of zinc transport from aqueous solutions containing equimolar mixtures of Ag⁺, Cd²⁺ Co²⁺, Cu²⁺, Fe²⁺, Ni²⁺, Pb²⁺, Pd²⁺, Sr²⁺, Bi³⁺, Cr³⁺ and Fe³⁺ ions was investigated. In the presence of NH₂OH.HCl as a suitable masking agent in the source phase, the interfering effect of Cu²⁺ and Pb²⁺ ions was diminished drastically.