A Family of Fifth-Order Runge-Kutta Pairs

The construction of a Runge-Kutta pair of order with the minimal number of stages requires the solution of a nonlinear system of order conditions in unknowns. We define a new family of pairs which includes pairs using function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of Kutta's simplifying assumption on the original system of the order conditions, i.e., that all the internal nodes of a method contributing to the estimation of the endpoint solution provide, at these nodes, cost-free second-order approximations to the true solution of any differential equation. In both cases the solution of the resulting system of nonlinear equations is completely classified and described in terms of five free parameters. Optimal Runge-Kutta pairs with respect to minimized truncation error coefficients, maximal phase-lag order and various stability characteristics are presented. These pairs were selected under the assumption that they are used in Local Extrapolation Mode (the propagated solution of a problem is the one provided by the fifth-order formula of the pair). Numerical results obtained by testing the new pairs over a standard set of test problems suggest a significant improvement in efficiency when using a specific pair of the new family with minimized truncation error coefficients, instead of some other existing pairs.

     

On the stereochemistry of the Horner—Emmons reaction between 3-functionally substituted 2-methyl-2-propenylphosphonates and aliphatic aldehydes

The reaction of diethyl 3-ethoxycarbonyl-2-methyl-2-propenylphosphonate (1) with 3-methylbutanal (2) in the system solid MOH (M=K, Na, Li)-benzene without phase transfer catalysts affords ethyl 3,7-dimethyl-2,4-octadienoate with the ratios of 2E,4E stereoisomer (3a) to 2Z,4E-stereoisomer (3b) of 4456, 4654, and 6040 for KOH, NaOH, and LiOH, respectively. The similar tendency is observed when DMSO is substituted for benzene, although the proportion of3a in this case is 65% with any MOH used. The reaction of1 with2 in the presence of a stoichiometric amount of a quaternary ammonium hydroxide QOH (Q=NMe₄, BnNMe₃, (n-Bu)₄N) in benzene gives higher3a3b ratios than those obtained with LiOH in the former reaction system. The increase in the content of 2E,4E-isomer3a is possibly due to the growth of the population of solvent-separated ion pairs or, generally, to the increase in the distance between the charge centers in the ionic intermediates on passing from KOH to LiOH and from [Me₄N]OH to [(n-Bu)₄N]OH. The position of the equilibrium betweenE- and Z-isomers of phosphonate1 under the reaction conditions (E-1Z-13565) is almost unaffected by the nature of the cation of the base.Part 5, see ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1089–1094, June, 1993.     

An Investigation on the Effect of Arsenic Poisoning on Humans,Agriculture, and Fisheries

The purpose of this investigation is to try and understand the degree of arsenic poisoning in the waste water from agricultural chemical factories which release effluents into the waterways in their vicinity. The method of determination is to use the water samples, soil, fish, clams, shell-fish, etc. found in the areas along the canals and aqueducts and those which lie upstream, midstream, and downstream and also the hair samples of people living in the contiguous areas, to check for the levels of arsenic in them by emission spectroscopy. From the analysis during a one year investigation, we find that the level of As in the water creatures of Chungkang Stream and Lu-Er-Men Stream is much higher than in the other water areas of Taiwan such as along beaches and the other rivers; the levels in the hair of the people who live nearby these water courses have a certain degree of correspondence with their eating habits and the quantity of food eaten; however, even those people who eat relatively little have almost 3% As, beyond the 2 mg/kg limit allowed for human beings. We are fully aware of the high level of food contamination on Taiwan, and this fact has been taken into consideration. The effect of As contamination in the soil on agricultural produce does not seem to have any apparent relationship. By the way, the influence of the monthly average rainfall on As contamination in the soil is not obvious.     

Cis-trans-isomerization of cationic-anionic polymethine dyes

The effect of solvent polarity and ion pair formation oncis-trans-isomerization of cationic-anionic polymethine dyes and of related simple cationic and anionic dyes is studied by flash photolysis. The change in the rate constant for reversecis-trans- isomerization of photoisomers due to the interaction of a cation with an anion in an ion pair is observed in nonpolar solvents. A drop in the yield of the photoisomers to zero is observed for a number of cationic-anionic dyes in weakly polar and nonpolar solvents which is possibly due to steric hindrances in the photoisomerization process in ion pairs.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 719–724, April, 1993.     

Electron traps on oxide surfaces: (H+)(e-) pairs stabilized on the surface of 17O enriched CaO.

(H+)(e-) pairs generated at the surface of polycrystalline CaO are analyzed for the first time in terms of the interaction of the unpaired electron spin with the nuclear spin of the 17O anions of the surface. CaO crystals enriched in the 17O isotope are prepared and the corresponding hyperfine coupling constants are measured in electron paramagentic resonance (EPR) spectra. The results are analyzed on the basis of cluster model density functional theory calculations. The computed hyperfine coupling constants for (H+)(e-) pairs formed on the edge, corner, and reverse corner sites of the CaO surface allow a tentative assignment of two observed spectral features to specific morphological surface sites.     

Photochromic crown ethers

An amphiphilic crown-containing styryl dye (1) was synthesized, and the effects of irradiation, temperature, and alkali and alkali-earth metal ions on the conductivity and optical spectra of its solutions in dioctyl phthalate were studied. Compound1 in thetrans-form almost completely exists as ion pairs (IP). Irradiation at a long-wavelength absorption maximum (λ_max) results in a reversible increase in the conductivity and, hence, a degree of dissociation of IP (α); these parameters decrease when complexes with metal ions are formed. The relaxation times for the photoinduced conductivity coincide with a decrease in the extinction within experimental error in the 20–60°C temperature range. The photoinduced increase in α is caused bytrans—cis-isomerization and an increase in steric hindrances for the interaction of the ClO₄ ⁻ anion with the N⁺ atom of benzothiazolium in thecis-form of1. The activation energies for the darkcis—trans-relaxation, absolute α values, and thermodynamic parameters of dissociation of IP in thetrans-form, as well as the α values in a photostationary mixture ofcis—trans-isomers, were estimated. The decrease in α after binding with metal ions is likely caused by the redistribution of the positive charge to benzothiazolium through the conjugated system of1. Correlations between the decrease in conductivity (decrease in α) and the hypsochromic shift Δλ_max after the formation of complexes between1 and metal ions were observed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1296–1301, July, 1997.     

Ion pairing, H-bonding, and π–π interactions in copper(II) complex-organo-networks derived from a proton-transfer compound of the 1,10-phenanthroline-2,9-dicarboxylic acid

The one-pot reaction between the novel proton transfer compound (pydaH₂)²⁺(phendc)²⁻, LH₂, and Cu(II) afforded the compounds (pydaH)₂[Cu(phendc)₂]·10H₂O, 1, and (pydaH)₂[Cu(phendc)(phendcH)]₂·5H₂O, 2, where pyda=2,6-diaminopyridine, and phendcH₂=1,10-phenanthroline-2,9-dicarboxylic acid. The single crystal X-ray diffraction analysis of 1 and 2 revealed that these are two novel self-assembled 3D Cu(II) complex-organo-networks, in which (pydaH)⁺ ions and [Cu(phendc)₂]²⁻ or complex units are held together by ion pairing, H-bonding, and π–π interactions. Magnetic measurements over the temperature range 1.8–310 K revealed no significant magnetic coupling between Cu(II) centers in 1 or 2.     

The mixed valent tellurate SrTe3O8: Electronic lone pair effect of Te

A novel mixed valent tellurium oxide, SrTe₃O₈, has been synthesized and its crystal structure was determined ab initio from powder X-ray diffraction data. This oxide, which crystallizes in a tetragonal unit-cell, P4₂/m space group, with very close a and c cell parameters (6.8257(1) and 6.7603(1) Å, respectively), exhibits a very original structure built up of corner-sharing TeO₆ (Te⁶⁺) octahedra and Te₂O₈ (Te⁴⁺) twin-pyramidal units. The latter ones form [Te₃O₈]_∞ chains running along the [001] and the [110] directions. Besides the four sided tunnels where the Sr²⁺ cations are located, there are very large four sided tunnels running along the c-axis which are obstructed by the electronic lone pairs of the Te⁴⁺ cations.     

Optochemical Sensor for Ammonia Based on a Lipophilized pH Indicator in a Hydrophobic Matrix

Abstract

An optical sensor for the determination of ammonia in water based on ion pairing has been investigated. A pH-sensitive dye is immobilized as an ion pair in a silicone matrix. The colour of the dye changes from yellow to blue depending on the concentration of ammonia in the sample solution. This change is reversible. The concentration of ammonia can be determined by measuring the transmittance at a given wavelength.

All measurements were performed with a dual-beam optical meter. The measurement range was from 5.9 × 10^?7 to 1 × 10^?3 M (0.01 to 17 mg/l) in 0.1 M phosphate buffer of pH 8. The detection limit was 10 μg/l. The response times at a flow rate of 2.5 ml/min were 4 min for t₉₀ and 10 min for t₁₀₀ at a change from 41.9 to 82.5 μM ammonia and 12 min for t₉₀ and 48 min for t₁₀₀ at a change from 160 to 0 μM ammonia. The operational lifetime of the ammonia sensor was limited to a period of a few days only. A continuous decrease in baseline signal and relative signal change was observed over the whole measurement. The storage stability was more than 10 months (dry). With respect to possible application of the ammonia sensor to environmental analysis, the influence of pH, typical interferences, such as amines and various detergents on the sensor response was investigated. No interference due to pH was observed in the range from pH 5 to pH 9. With methyl- and ethylamine the response was not completely reversible. The sensor was affected by cationic detergents, but not by anionic or neutral detergents.