The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is

13C- and 1H-NMR and FTIR spectroscopic evidence for aggregate formation of organosilanes in toluene

 Changes in the ¹³C and ¹H NMR chemical shifts of the silane coupling agent (3-aminopropyltri-ethoxysilane, APTS) in toluene, which were detected as the concentration of APTS increased, have been interpreted in terms of the formation of micelles and the presence of a critical micelle concentration (CMC) equal to ca. 0.47 mol 1^-1. For the protons of the n-propyl segment, ¹H NMR splitting patterns have been analyzed and conformations of the propyl segment have been discussed. Plots of relative absorbance of the two NH₂ stretch IR bands at 3324 and 3384 cm^-1 against concentration provided an inflection point (corresponding to the CMC) at a value equal to 0.46 mol 1^-1. Thus, consideration of the interaction of APTS with a surface must take into account the presence of both APTS aggregates as well as APTS monomers. Received: 16 August 1996 Accepted: 26 September 1996     

Blue copper model complexes with distorted tetragonal geometry acting as effective electron-transfer mediators in dye-sensitized solar cells

The electron self-exchange rate constants of blue copper model complexes, [(-)-sparteine-N,N'](maleonitriledithiolato-S,S')copper ([Cu(SP)(mmt)])(0/)(-), bis(2,9-dimethy-1,10-phenanthroline)copper ([Cu(dmp)(2)](2+/+)), and bis(1,10-phenanthroline)copper ([Cu(phen)(2)](2+/+)) have been determined from the rate constants of electron transfer from a homologous series of ferrocene derivatives to the copper(II) complexes in light of the Marcus theory of electron transfer. The resulting electron self-exchange rate constant increases in the order: [Cu(phen)(2)](2+/+) < [Cu(SP)(mmt)](0/)(-) < [Cu(dmp)(2)](2+/+), in agreement with the order of the smaller structural change between the copper(II) and copper(I) complexes due to the distorted tetragonal geometry. The dye-sensitized solar cells (DSSC) were constructed using the copper complexes as redox couples to compare the photoelectrochemical responses with those using the conventional I(3)(-)/I(-) couple. The light energy conversion efficiency (eta) values under illumination of simulated solar light irradiation (100 mW/cm(2)) of DSSCs using [Cu(phen)(2)](2+/+), [Cu(dmp)(2)](2+/+), and [Cu(SP)(mmt)](0/)(-) were recorded as 0.1%, 1.4%, and 1.3%, respectively. The maximum eta value (2.2%) was obtained for a DSSC using the [Cu(dmp)(2)](2+/+) redox couple under the light irradiation of 20 mW/cm(2) intensity, where a higher open-circuit voltage of the cell was attained as compared to that of the conventional I(3)(-)/I(-) couple.     

Double bond isomerization of 5-vinylbicyclo[2.2.1]hept-2-ene to 5-ethylidenebicyclo[2.2.1]hept-2-ene over alkaline earth oxides

All the alkaline earth oxides exhibit activities for double, bond isomerization of 5-vinylbicyclo[2.2.1]hept-2-ene (VBH) to 5-ethylidenebicyclo[2.2.1]hept-2-ene (EBH) at a reaction temperature of 273 K. The order of the activity on the basis of unit weight of catalyst was CaO>MgO>SrO>BaO when compared under optimum pretreatment conditions. The E/Z ratio in the products is determined by the reaction temperature regardless of the type of catalyst; the ratios were 82/18 and 88/12 for the reaction temperatures of 323 and 273 K, respectively.     

Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

Note Water Vapor Sorption by the Polyelectrolyte Complex of Poly (Acrylic Acid) and Poly (4-Vinyl-N-Ethylpyridinium Bromide)

A great number of studies of polyelectrolyte complexes have been carried out by various investigators; most of them concentrated on the reaction between oppositely charged polyelectrolytes [1-3]. The structure and properties of the resultant complexes have been investigated to a lesser extent, and the understanding of this new class of polymer materials is still insufficient. Thus, we have been investigating the sorption of water vapor by the complexes and the morphological changes caused by this sorption [4,5].     

REDUCTION OF BIS(BROMO(MESITYL)-{2,4,6-TRIS[BIS(TRIMETHYLSILYL)METHYL]- PHENYL}SILYL)BUTADIYNE WITH POTASSIUM GRAPHITE: UNEXPECTED FORMATION OF 2-ALLENYL-1-BENZOSILOLE

The reductive debromination of an very crowded bis(bromodiaryl- silyl)butadiyne 2 was performed with potassium graphite to give the corresponding 2-allenyl-1-benzosilole 3 was isolated as a main product.     

Mechanism of Macroscopic Motion of Oleate Helical Assemblies: Cooperative Deprotonation of Carboxyl Groups Triggered by Photoisomerization of Azobenzene Derivatives

Macroscopic and spatially ordered motions of self‐assemblies composed of oleic acid and a small amount of an azobenzene derivative, induced by azobenzene photoisomerization, was previously reported. However, the mechanism of the generation of submillimeter‐scale motions by the nanosized structural transition of azobenzene was not clarified. Herein, an underlying mechanism of the motions is proposed in which deprotonation of carboxyl groups in cooperation with azobenzene photoisomerization causes a morphological transition of the self‐assembly, which in turn results in macroscopic forceful dynamics. The photoinduced deprotonation was investigated by potentiometric pH titration and FTIR spectroscopy. The concept of hierarchical molecular interaction generating macroscale function is expected to promote the next stage of supramolecular chemistry.     

A Novel Reactivity of Phosphanylalumane (>P−Al<): Reversible Addition of a Saturated Interelement Bond to Olefins

The reversible addition of olefins to a phosphanylalumane, P−Al single-bond species, was investigated. The P−Al bond added to ethylene and relatively small terminal alkenes (propylene and hex-1-ene) at room temperature to give the corresponding alkene adducts. Heating the terminal alkene adducts released the corresponding alkenes and regenerated the P−Al bond, but no release of ethylene was observed even under vacuum conditions. The reactivity of ethylene adduct as a new saturated C₂ vicinal P/Al-based FLP was also investigated. The ethylene adduct was found to undergo complexation with nitriles to give the corresponding nitrile adducts to the Al center, which retained the ethylene tether as in the case of the corresponding P/B-based FLP. However, the reactivity of ethylene toward CO₂ and benzaldehyde differed from that of the P/B system giving the corresponding adducts.