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.     

Synthesis and Crystal Structure of Blue Luminescent Cadmium(II) Coordination Networks with 4,4′-Bis(imidazol-1-ylmethyl)biphenyl from Different Solvent Systems

Two supramolecular complexes, [Cd(bimb)²Cl²] (1) and [Cd(bimb)(DMF)Cl²]·DMF (2) [bimb=4,4′-bis(imidazol-1-ylmethyl)biphenyl], were synthesized by reactions of CdCl²·2.5H²O with bimb ligand in ethanol and N,N′-dimethylformamide (DMF), respectively, and their structures were determined by X-ray crystallography. Complex 1 is an infinite 2D grid network bridged by bimb ligands, and the 2D sheets were further linked by C–H ?Cl hydrogen bonds to form a polycatenated 3D framework. Complex 2 has dicadmium(II) di-μ-chloride units which are connected by bimb bridging ligands to form an infinite non-interpenetrating 2D network. The results provide a nice example of the solvent system exerting a great effect on the construction of supramolecular frameworks.     

Simultaneous Determination of Pyridine-Triphenylborane Anti-Fouling Agent and Its Degradation Products in Artificial Seawater by CZE

We developed a CZE method for simultaneous determination of pyridine-triphenylborane (PTPB) anti-fouling agent and its degradation products such as diphenylborinic acid (DPB), phenylboronic acid (MPB), and phenol in artificial seawater (ASW) with no extraction procedure. The ASW samples, in which 20 % (v/v) acetonitrile was added, were injected directly into the capillary using vacuum injection. As the background electrolyte, 60 mM sodium tetraborate adjusted to pH 9.8 was used. The LODs (S/N = 3) for PTPB, DPB, MPB, and phenol were, respectively, 55, 78, 126, and 30 μg L^?1. The RSDs (n = 4) for analytes listed above were in the respective ranges of 2.7–5.7, 0.68–6.1, and 0.69–1.1 % for the peak area, peak height, and migration time. Simple degradation experiments were conducted to verify the usefulness of the proposed method. The PTPB samples dissolved in ASW were put in the open air, and rooms with and without light. The sample solutions were analyzed over time. We inferred that PTPB in ASW was more degraded by photolysis than by hydrolysis. The proposed CZE method has been demonstrated as a useful tool to elucidate the PTPB degradation process and its degradation products in ASW.     

Synthesis of (+)-boronolide and (+)-deacetylboronolide using Pd-catalyzed carbonylation and lactonization

(+)-Boronolide and (+)-deacetylboronolide were synthesized using Pd-catalyzed CO insertion and lactonization as the key step. As to the ¹³C NMR data of (+)-deacetylboronolide, the assignment at C-6 position should be revised.     

Cyclization from Higher Excited States of Diarylethenes Having a Substituted Azulene Ring

The cyclization reaction of diarylethenes having an azulene ring occurs only via higher excited states. Novel diarylethenes having an azulene ring with a strong donor or acceptor were synthesized and examined in these reactions. A derivative having an electron-donating 1,3-benzodithiol-2-ylidenemethyl group at the 1-position of the azulene ring showed photochromism, whereas neither a derivative having a π-conjugated electron-donating group at the 3-position of the azulene ring nor derivatives having a π-conjugated electron-withdrawing group at the 1- or 3-position of the azulene ring showed any photochromism. The photoreactivities of these compounds were explained by calculating forces and bond orders on the excited states using density functional theory (DFT) and time-dependent (TD)-DFT.