Proof of the Fukui conjecture via resolution of singularities and related methods. II $$^{\star}$$

The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism. Dedicated to the memory of Prof. Kenichi Fukui (1918–1998).     

Characterization of molecular transport in poly(dimethylsiloxane) microchannels for electrophoresis fabricated with synchrotron radiation-lithography and UV-photolithography

In the present paper, a study was undertaken of molecular transport in ploy(dimethylsiloxane) microchannels that were fabricated by ultraviolet (UV)-photolithography and synchrotron radiation (SR)-lithography characterized and compared for microchip capillary electrophoresis by evaluating in-channel molecular dispersion. A fluorescent tag, sulforhodamine B was used as the probing molecule. It was found that microchannels made by SR-lithography fabrication were superior to those made by UV-photolithography fabrication in terms of molecular transport performance. A deep insight into surface conditions characterized by scanning electron microscopy suggested it was related to the difference in surface roughness. Chromatographic retention in electropherograms further supported such a conclusion, which depended on the phase ratio of the channel surface. The results revealed for PDMS microchannels in this work were in good agreement with the phenomenon found for glass microchannels in the literature.     

Side chain-directed assembly of triangular molecular panels into a tetrahedron vs. open cone

Despite their structural similarity, triangular tetradentate ligands 2b and 2c experience different assembly pathways on complexation with (en)Pd(NO3)2 to give M8L4 tetrahedral (3) and open cone (4) structures, respectively, due to steric restriction by side chains at the corner or on the edge of the ligands.     

New Proof of the Fukui Conjecture by the Functional Asymptotic Linearity Theorem

The present article provides a new proof of the Fukui conjecture concerning the additivity problem of the zero-point vibrational energies of hydrocarbons. This conjecture played a prominent role in the initial development of the repeat space theory (RST), and continues to be of vital significance in the recent development of the theory of the generalized repeat space X _r (q,d). The new proof of the Fukui conjecture has been given here by establishing the functional version of the Asymptotic Linearity Theorem (ALT), the Functional ALT. This enhanced version of the ALT directly implies the validity of the Fukui conjecture; it easily unifies, in a broad perspective, a variety of additivity phenomena in physico-chemical network systems having many identical moieties, and efficiently solves some interpretational problems of the empirical additivity formulae from experimental chemistry. The proof of the functional version of the ALT is based on a new method transferable to the extended theoretical framework of the generalized repeat space X _r (q,d).     

Infrared spectroscopic study on the reaction mechanism of CO hydrogenation over Pd/CeO2

In situ infrared spectroscopy was applied to elucidate the reaction mechanism of CO hydrogenation over Pd/CeO₂. Instead of direct dissociation of CO, a new reaction pathway is proposed for methane formation, involving geminal dicarbonyl intermediates and (HCO)₂(a) intermediates, which may be located on the surface of Pd covered with thin layers of reduced ceria (SMSI effect). Transformation of methane formation sites into methanol formation ones by the oxidation with water vapor formed during the CO?H₂ reaction is proposed, which may be located on the Pd (111) planes adjacent to ceria support.     

Synthesis of Optically Active P‐Chiral and Optically Inactive Oligophosphines

A series of optically active P‐chiral oligophosphines (S,R,R,S)‐ 2 , (S,R,S,S,R,S)‐ 3 , (S,R,S,R,R,S,R,S)‐ 4 , and (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 with four, six, eight, and 12 chiral phosphorus atoms, respectively, were successfully synthesized by a step‐by‐step oxidative‐coupling reaction from (S,S)‐ 1 . The corresponding optically inactive oligophosphines 1′ – 5′ were also prepared. Their properties were characterized by DSC, XRD, and optical‐rotation analyses. While optically active bisphosphine (S,S)‐ 1 and tetraphosphine (S,R,R,S)‐ 2 behaved as small molecules, octaphosphine (S,R,S,R,R,S,R,S)‐ 4 and dodecaphosphine (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 exhibited the features of a polymer. Furthermore, DSC and XRD analyses showed that hexaphosphine (S,R,S,S,R,S)‐ 3 is an intermediate between a small molecule and a polymer. Comparison of optically active oligophosphines 1 – 5 with the corresponding optically inactive oligophosphines 1′ – 5′ revealed that the optically active phosphines have higher crystallinity than the optically inactive counterparts. It is considered that the properties of oligophosphines depend on the enantiomeric purity as well as the oligomer chain length.     

Polyhydrazides. III. N-methylated polyhydrazides by ring-opening of poly-p-phenylene-1,3,4-oxadiazole

A new ring-opening reaction of 1,3,4-oxadiazole by methylating reagents was developed in fuming sulfuric acid or polyphosphoric acid and then, by applying this reaction to poly-p-phenylene-1,3,4-oxadiazole, a high molecular weight poly-N-methylterephthalylhydrazide was obtained. Various methylating reagents were investigated as ring-opening reagents. The degrees of ring-opening in polymers were estimated and related to the properties of the polymers.     

Interaction between peroxide ion and phenol group which are coordinated to the same iron(III) ion

We have prepared several new iron(III) complexes with ligands which contain a phenol group; these are tetradentate [(X-phpy)H, X and H(phpy) represent the substituents on the phenol ring and N,N-bis(2-pyridylmethyl)-N-(2-hydroxybenzyl)amine, respectively] and pentadentate ligands [(R-enph-X)H; R=ethyl(Et) or methyl(Me) derivative and H(Me-enph) denotes N,N-bis(2-pyridylmethyl)-N″-methyl-N″-(2″-hydroxyl-benzylamine)ethylenediamine] and have determined the crystal structures of Fe(phpy)Cl₂, Fe(5-NO₂-phpy)Cl₂, and Fe(Me-enph)ClPF₆, which are of a mononuclear six-coordinate iron(III) complex with coordination of one or two chloride ion(s). These compounds are highly colored (dark violet) due to the coordination of phenol group to an iron(III) atom. When hydrogen peroxide was added to the solution of the iron(III) complex, a color change occurs with bleaching of the violet color, indicating that oxidative degradation of the phenol moiety occurred in the ligand system. The bleaching of the violet color was also observed by the addition of t-butylhydroperoxide. The rate of the disappearance of the violet color is highly dependent on the substituent on the phenol ring; introduction of an electron-withdrawing group in the phenol ring decreases the rate of bleaching, suggesting that disappearance of the violet band should be due to a chemical reaction between the phenol group and a peroxide adduct of the iron(III) species with an η¹-coordination mode and that in this reaction the peroxide adduct acts as an electrophile towards phenol ring. The intramolecular interaction between the phenol moiety and an iron(III)-peroxide adduct may induce activation of the peroxide ion, and this was supported by several facts that the solution containing an iron(III) complex and hydrogen peroxide exhibits high activities for degradation of nucleosides and albumin.     

Quartz crystal microbalance immunosensor for highly sensitive 2,3,7,8-tetrachlorodibenzo-p-dioxin detection in fly ash from municipal solid waste incinerators

A quartz crystal microbalance (QCM) immunosensor was developed for the detection of 2,3,7,8-tetrachlorodibenzo-p-dioxins (TCDD) in environmental pollutants. An anti-TCDD antibody was immobilized on the gold surface of the QCM via chemical coupling, and its immunologic activity was then maintained by treatment with an artificial stabilizing reagent such as poly(2-methacryloyloxyethyl phosphorylcholine-co-n-butyl methacrylate). A competitive immunoreaction with TCDD conjugated ovalbumin (TCDD-ovalbumin) was used to detect TCDD. A calibration curve was obtained through the competitive immunoreaction, and linearity was shown from 100 ng mL(-1) to 0.1 ng mL(-1). Also, the cross-reactivities of the anti-TCDD monoclonal antibody were thoroughly evaluated with several TCDD derivatives. The relationships between GC-MS, ELISA, and QCM were compared using fly ash samples from a municipal solid waste, which were prepared using an accelerated solvent extractor. For 23 samples, the experimental relationship between the TCDD concentration by QCM vs. the TCDD concentration by ELISA was y= 1.07x + 2.70, r= 0.99, and the TCDD concentration by QCM vs. the toxic equivalent quantity (TEQ) value by GC-MS was y= 2.46x - 14.98, r= 0.89.     

Sensitive and high-throughput analyses of purine metabolites by dynamic pH junction multiplexed capillary electrophoresis: a new tool for metabolomic studies.

On-line sample preconcentration by a dynamic pH junction in conjunction with multiplexed capillary electrophoresis (CE) and UV detection represents a sensitive and high-throughput format for future metabolomic research, such as purine analysis. The optimization of purine focusing can be rapidly assessed by systematically altering the sample matrix properties, such as the buffer co-ion, pH and ionic strength using a 96-capillary array format. This method permits focusing of large sample injection volumes, resulting in over a 50-fold improvement in the concentration sensitivity. The limit of detection (S/N = 3) for purine metabolites was less than 8.0 x 10(-8) M under optimum conditions when using UV absorbance. Dynamic pH junction multiplexed CE demonstrated excellent linearity over a hundred-fold concentration range, as well as low inter-capillary precision in terms of normalized migration times and peak areas. The potential for clinically relevant high-throughput analyses of micromolar amounts of purine metabolites in urine was also demonstrated.