High preconcentration of ultra-trace metal ions by liquid–liquid extraction using water/oil/water emulsions as liquid surfactant membranes

A high preconcentration method by liquid–liquid extraction using liquid surfactant membranes was developed. The water-in-oil (w/o) emulsion containing dilute hydrochloric acid, 2-ethylhexyl hydrogen 2-ethylhexylphosphonate (PC-88A), liquid paraffin, and kerosene was used for the extraction. In a resulting volume of 1000 cm³ of an aqueous sample solution (pH 5.0) containing less than 1 mg of each metal ion, 2 cm³ of w/o emulsion droplets coated with sorbitan monooleate were dispersed. The analyte metal ions in the outer bulk aqueous phase were extracted into the organic phase to form a complex with PC-88A and successively back-extracted into the inner aqueous phase. The analytes in the resulting inner aqueous phase were determined subsequently by graphite furnace atomic absorption spectrometry applied as a detector. By this procedure, concentration factors of 570, 820, 750, 970, 860, and 880 were achieved for chromium(III), manganese(II), cobalt(II), nickel(II), copper(II), and cadmium(II), respectively, and also the respective detection limits (3σ) of 0.4, 20, 1.2, 18, 18, and 0.7 pg cm⁻³ were obtained.     

Periodic and Homoclinic Motions in Forced,Coupled Oscillators

We study periodic and homoclinic motions in periodically forced, weakly coupled oscillators with a form of perturbations of two independent planar Hamiltonian systems. First, we extend the subharmonic Melnikov method, and give existence, stability and bifurcation theorems for periodic orbits. Second, we directly apply or modify a version of the homoclinic Melnikov method for orbits homoclinic to two types of periodic orbits. The first type of periodic orbit results from persistence of the unperturbed hyperbolic periodic orbit, and the second type is born out of resonances in the unperturbed invariant manifolds. So we see that some different types of homoclinic motions occur. The relationship between the subharmonic and homoclinic Melnikov theories is also discussed. We apply these theories to the weakly coupled Duffing oscillators.     

Homoclinic Tangles, Phase Locking, and Chaos in a Two-Frequency Perturbation of Duffing's Equation

Summary. We study a two-frequency perturbation of Duffing's equation. When the perturbation is small, this system has a normally hyperbolic invariant torus which may be subjected to phase locking. Applying a version of Melnikov's method for multifrequency systems, we detect the occurrence of transverse intersection between the stable and unstable manifolds of the invariant torus. We show that if the invariant torus is not subjected to phase locking, then such a transverse intersection yields chaotic dynamics. When the invariant torus is subjected to phase locking, the situation is different. In this case, there exist two periodic orbits which are created in a saddle-node bifurcation. Using another version of Melnikov's method for slowly varying oscillators, we also give conditions under which the stable and unstable manifolds of the periodic orbits intersect transversely and hence chaotic dynamics may occur. Our results reveal that when the invariant torus is subjected to phase locking, chaotic dynamics resulting from transverse intersection between its stable and unstable manifolds may be interrupted. Received November 18, 1993; final revision received September 9, 1997; accepted October 27,1997     

Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes

The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t₀=t is naturally understood where t₀ is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation is semi-simple, i.e., diagonalizable; when A is not semi-simple and has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink–anti-kink and soliton–soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears.     

Free‐volume change in volume phase transition of polyacrylamide gel as studied by positron annihilation: Salt dependence

Variation of free‐volume parameters—average radius size, number concentration, and size distribution—of a polyacrylamide (PAAm) gel containing 4 mol % carboxylate anions is studied during a volume phase transition (VPT) caused by a change of sodium chloride (NaCl) concentration. A positron annihilation lifetime technique is used for the determination of the free‐volume characteristics. The measurement is performed in an acetone–water 3 : 2 (v/v) [0.27 : 0.73 (mol/mol)] mixed solvent at 20°C, and the free‐volume parameters deduced from the analysis of a positron annihilation curve are utilized. An average free‐volume size of the swollen PAAm gel, ∼ 0.32 nm in radius, almost agrees with that of the mixed solvent for a corresponding salt concentration, while the size of the collapsed gel, which is ∼ 0.28 nm in radius, is smaller than that of the mixed solvent. The results for the collapsed gel indicate that the hydrogen bond plays a significant role in the nanoscopic environment. The radius of the free‐volume of the swollen PAAm gel seems to be influenced by the composition between acetone and water. An inhomogeneity of the nanoscopic structure inside the PAAm gels is discussed in terms of a dispersion of a size distribution of the free‐volume. It is concluded that a change of the nanoscopic environment of the PAAm gel during the VPT can be monitored through the free‐volume parameters obtained by the positron annihilation lifetime technique. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2634–2641, 1999     

Photoconductivity of a polyimide with an alicyclic diamine: Charge carrier photogeneration in the mixed layer packing arrangement

Photoconduction mechanism of a polyimide with an alicyclic diamine, PI(PMDA/DCHM), prepared from pyromellitic dianhydride (PMDA) and 4,4′-diaminodicyclohexylmethane (DCHM) was investigated. Its UV absorption spectra, fluorescence spectra, photoconductivity, and annealing effects on the photocurrent generation were measured and compared to those of CPD, N,N′-dicyclohexylpyromellitic diimide, and PI(PMDA/DMDHM) prepared from PMDA and 3,3′-dimethyl-4,4′-diaminodicyclohexylmethane (DMDHM). Photoconductivity of PI(PMDA/DCHM) depends upon the degree of molecular packing between polymer backbones. PI(PMDA/DMDHM) has no photoconductivity, probably due to a barrier to their intermolecular packing by the existence of two methyl substituents. Photoconductivity of PI(PMDA/DCHM) would be the result of the weak intermolecular interaction formed by mixed layer packing arrangement between pyromellitic moiety of one polymer backbone and N-cyclohexyl ring of another one in the ground state. Radiation absorption of this weak intermolecular interaction immediately forms a charge–transfer complex in the excited state and produces radical cation and anion charge carriers, which lead to the photoconductivity in the bulk polyimide film of PI(PMDA/DCHM). © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1433–1442, 1998     

Synthesis of ordered polymer by direct polycondensation. VIII. Ordered polymer from two nonsymmetric monomers

The ordered (-aacdbbdc-) polymer was prepared by the direct polycondensation of a pair of symmetric monomers (XabX), 4,4′-(oxydi-p-phenylene)dibutanoic acid (XaaX) and 2-methoxyisophthalic acid (XbbX), with a nonsymmetric monomer (YcdY), 4-aminobenzhydrazide, using the condensing agent diphenyl (2,3-dihydro-2-thioxo-3-benzoxazolyl)phosphonate ( 1 ). The polymerization was carried out by a one-pot procedure, that is, mixing the dicarboxylic acids, condensing agent 1 and triethylamine in NMP for 2 h at room temperature, followed by the addition of 4-aminobenzhydrazide. This polymerization proceeded smoothly, yielding the ordered polymer with an inherent viscosity of 0.34 dL g⁻¹. The microstructure of the ordered polymer was confirmed by comparing the authentic ordered polymer in their ¹³C-NMR spectrum. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. A Polym. Chem. 36: 2309–2314, 1998     

Radical polyaddition of bis(α-trifluoromethyl-β-difluorovinyl) terephthalate with 1,4-dioxane

To develop a radical polyaddition reaction of 2-benzoyloxypentafluoropropene [CF₂C(CF₃)-OCOC₆H₅] (BPFP) with tetrahydrofuran (THF), the reactions of bis(α-trifluoromethyl-β-difluorovinyl) terephthalate [CF₂C(CF₃)OCOC₆H₄COOC(CF₃)CF₂] (BFP) with THF and of BPFP with 1,4-dioxane were investigated as model reactions to form 1 : 1 and 1:2 addition products of BFP with THF. This evidenced that THF is monofunctional, and dioxane is bifunctional since the 1:1 and 2:1 addition products of BPFP with dioxane were formed. The polyaddition reaction of BFP with dioxane turned out to produce a white powdery substance which was found to possess a mole ratio of BFP units to dioxane units in the polymers of 1:1. The highest molecular weight obtained was M _n = 9.9 × 10³.     

Photochemical hole burning in macromolecular complexes

Photochemical hole burning (PHB) of free-base porphyrins in host polymers as a site-selective spectroscopy reveals the existence of vibronic structure in a porphyrin Q-band peak and low-energy excitation modes of host polymers. A new mechanism of photon-gated PHB by two-color sensitization of photoreactive polymers with a zinc porphyrin is also presented.