Shear and normal stress relaxation in polymer blends: stress predictions from interface velocity and Laplace pressure terms

We derived for the first time the relationships among shear stress and normal stress differences for ellipsoidal interfaces under large step shear strains considering interface velocity term and Laplace pressure term in the expression of the stress tensor for mixtures of two Newtonian fluids. In the derivation, orientation angle of the interface is assumed to be given by the affine deformation assumption and is independent of time based on experimental results for blends with 0.048 ≤ K ≤ 0.54 where K is the ratio of droplet viscosity to matrix viscosity. For ellipsoidal droplets, the shear stress is only proportional to the first normal stress difference. On the other hand, for spheroidal droplets, proportionality among the shear stress, the first and the second normal stress differences was derived, and the ratio of the second normal stress difference to the first normal stress difference was given as a function of step strain. The shear stress and the first normal stress difference obtained experimentally satisfy the derived relationship, indicating applicability of the stress expression for polymer blends.     

Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation

The Boltzmann equation without Grad’s angular cutoff assumption is believed to have a regularizing effect on the solutions because of the non-integrable angular singularity of the cross-section. However, even though this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo-differential operators, we prove the regularizing effect in all (time, space and velocity) variables on the solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and a Maxwellian type decay in the velocity variable, there exists a unique local solution with the same regularity, so that this solution acquires the C ^∞ regularity for any positive time.     

Initial testing of a high-repetition-rate electron-beam-pumped KrF laser amplifier

The initial test results of the high-repetition-rate (rep-rate) electron-beam (e-beam) pumped KrF laser amplifier under development in our laboratory are reported. This amplifier is aimed at producing a laser energy of 20 J per pulse at a rep rate of 1 Hz. Thus far, 700 consecutive e-beampulses (250 kV, 270 J/pulse) were generated at a rep rate of 1 Hz. The laser gas was repetitively pumped by the e-beams injected through the water-cooled diaphragm foils. Received: 5 February 2001 / Published online: 21 March 2001     

Growth of single-wall carbon nanotubes dependent on laser power density and ambient gas pressure during room-temperature CO2 laser vaporization

Single-wall carbon nanotubes (SWNTs) were synthesized by the irradiation of 20-ms CO₂ laser pulses onto a graphite–Co/Ni target at room temperature. We investigated the effect of laser power density (10–150 kW/cm²) and ambient Ar gas pressure (150–760 Torr) on the abundance of SWNTs with lengths of up to about 200 nm in soot-like carbonaceous deposits. For a constant power density (30 kW/cm²), depending on the Ar gas pressure, SWNTs with diameters of 1.2–1.4 nm were synthesized. Expansion behavior and temperature-fall rates of clusters and/or particles in laser plumes were also analyzed by high-speed video imaging and temporally and spatially resolved emission spectroscopy. The temperature-fall rates were estimated to be 171–427 K/ms. The SWNT growth on the time scale of a few milliseconds appeared to be related to some features of condensing clusters and/or particles, including resident densities, collision frequencies and temperatures. Received: 16 July 2001 / Accepted: 23 July 2001 / Published online: 30 August 2001     

Estimation of the latent track size of CR-39 using atomic force microscope

As a frame work of the study for the latent track size measurement using atomic force microscope, we have measured the minute etch pits and the extremely small amount of bulk etch of CR-39 at the beginning of chemical etching, and obtained its growth curves in nanometer dimensions. The pieces of CR-39 were exposed to 6 MeV/nC and Fe ions with normal incidence angle and were etched in 70°C 7 N NaOH solution for 0.5,1,2,3,5 min. The diameters of latent track were estimated to be 17 nm for Fe ions and 8 nm for C ions, respectively. These values are comparable to the experimental data on the average ‘track core diameters’ that have been obtained by various experimental techniques.     

Simultaneous separation of common mono- and divalent cations on a zirconium-modified silica gel column by ion chromatography with non-suppressed conductimetric detection and tartaric acid–15-crown-5 as eluent

The application of laboratory-made zirconium-modified silica gels (Zr-silicas) as cation-exchange stationary phases to ion chromatography with conductimetric detection (IC–CD) for common mono- and divalent cations (Li⁺, Na⁺, NH₄⁺, K⁺, Mg²⁺ and Ca²⁺) was carried out. Zr-silicas were prepared by the reaction of the silanol group on the surface of silica gel with zirconium tetrabutoxide (Zr(OCH₂CH₂CH₂CH₃)₄) in ethanol. Zr-silica adsorbed on 10 mg zirconium g⁻¹ silica gel was a suitable cation-exchange stationary phase in IC–CD for the separation of these mono- and divalent cations. Excellent simultaneous separation and highly sensitive detection for these cations were achieved in 10 min by IC–CD using a Zr-silica column (150×4.6 mm I.D.) and 10 mM tartaric acid containing 10 mM 15-crown-5 (1,4,7,10,13-pentaoxacyclopentadecane) as the eluent. The proposed IC–CD method was successfully applied to the determination of major mono- and divalent cations in natural water samples.     

Preparation and reactions of pyridinyl tellurides

Tellurium‐metal exchange reaction of n‐butyl 2‐pyridinyl telluride derivatives with n‐butyllithium or dilithium dimethylcyanocuprate proceeded smoothly to give the corresponding 2‐pyridinylmetal derivatives, which are important intermediates for functionalization of pyridines.     

Theoretical prediction of vertical transition energies of diaminosilylenes and aminosubstituted disilenes

Vertical electronic transition energies of diaminosilylenes and their dimers (disilenes and nitrogen‐bridged) were investigated by ab initio and density functional calculations. A good linear correlation was found between the observed UV transition energies of various silylenes and disilenes and those of model compounds calculated using the CIS and TD–DFT methods. On the basis of these computations the experimental UV absorption maximum observed for the dimer of (i‐Pr₂N)₂Si: (λ_max 439 nm at 77 K), could be assigned to an Si? Si bonded dimer with an unusually long Si? Si distance of 2.472 Å, and the isomeric amino‐bridged cyclic dimer could be discarded. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1536–1541, 2001     

Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

Multiple ligand transfer reaction between [CpRu(L)(AN)2][PF6] (L=AN, CO, P(OMe)3; AN=acetonitrile) and CpFe(CO)L′X (L′=CO, PMe3, PMe2Ph, PMePh2, PPh3, P(OPh)3; X=Cl, Br, I)

Treatment of ruthenium complexes [CpRu(AN)₃][PF₆] (1a) (AN=acetonitrile) with iron complexes CpFe(CO)₂X (2a–2c) (X=Cl, Br, I) and CpFe(CO)L′X (6a–6g) (L′=PMe₃, PMe₂Ph, PMePh₂, PPh₃, P(OPh)₃; X=Cl, Br, I) in refluxing CH₂Cl₂ for 3 h results in a triple ligand transfer reaction from iron to ruthenium to give stable ruthenium complexes CpRu(CO)₂X (3a–3c) (X=Cl, Br, I) and CpRu(CO)L′X (7a–7g) (L′=PMe₃, PMe₂Ph, PMePh₂, PPh₃, P(OPh)₃; X=Br, I), respectively. Similar reaction of [CpRu(L)(AN)₂][PF₆] (1b: L=CO, 1c: P(OMe)₃) causes double ligand transfer to yield complexes 3a–3c and 7a–7h. Halide on iron, CO on iron or ruthenium, and two acetonitrile ligands on ruthenium are essential for the present ligand transfer reaction. The dinuclear ruthenium complex 11a [CpRu(CO)(μ-I)]₂ was isolated from the reaction of 1a with 6a at 0°C. Complex 11a slowly decomposes in CH₂Cl₂ at room temperature to give 3a, and transforms into 7a by the reaction with PMe₃.