Sonocrystallization of polycarbonate melts

In this paper, we showed the simplified continuous process to crystallize the polycarbonate (PC) melts using sonocrystallization which is based on ultrasonic cavitation and ‘hot spot’ theory. High power ultrasonic wave was introduced to crystallize the PC prepolymers which is generally used for solid‐state polymerization (SSP) to obtain the ultra‐high molecular weight PCs. The structure and properties of PC treated with ultrasonic wave such as torque changes and crystallinities were studied. The experimental results showed that ultrasonic wave could improve the crystallinities of PCs and sonication time was proportional to their crystallinity. This is attributed to the decrease of the specific volume and the resulting shrinkage is compensated by a flux of a polymer melt toward the crystallization front. Torque data were collected directly from the Haake internal mixer and crystallinities were evaluated from differential scanning calorimeter (DSC). This process is an environmentally benign process so that no additional solvents or treatments are needed and will be very useful in the conventional solid‐state process which is used industrially. Copyright © 2007 John Wiley & Sons, Ltd.     

A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s ₁ψ₁ summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33D15 B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency. A. J. Yee: Research partially supported by a grant from The Number Theory Foundation.     

Analysis ofK→3Π decays in chiral perturbation theory

Using the recently proposed higher-order chiral Lagrangians determined from the integration of nontopological chiral anomalies, we calculate corrections to the current-algebra analysis ofK→3Π decay amplitudes expanded in powers of the Dalitz variables. Effects of quartic-derivative weak chiral Lagrangians are determined through the use of short-distance effective weak Hamiltonian and the factorization method. We find that (1) the constant and linear terms in the amplitude for ΔI=1/2K→3Π are in excellent agreement with experiment; the previous discrepancy of (20–35)% between current algebra and data is thus accounted for by the higher-order effective Lagrangians, (2) the penguin interaction does not play an essential role in the ΔI=1/2 rule, for otherwise it will lead to a large disagreement for the constant and linear terms, (3) one of the two quadratic terms in the ΔI=1/2 process, which arise from the quartic chiral Lagrangians, is in accord with data within experimental errors, while the other is off by four standard deviations, (4) the linear term in the ΔI=3/2 transitions is in good agreement with experiment and contributions from quadratic terms are sizable.     

Effect of cyclic stress on structural changes in polycarbonate as probed by positron annihilation lifetime spectroscopy

Positron annihilation lifetime spectroscopy (PALS) is used to probe structural changes in glassy polycarbonate in terms of changes in the hole volume and the number density of holes during fatigue (cyclic stress) aging. The ortho-positronium (o-Ps) pickoff annihilation lifetime τ₃, as well as the intensity I₃, were measured as a function of cyclic stresses and various previous thermophysical aging histories. It is found that τ₃, the longest of the three lifetime components resolved in the PALS of glassy polycarbonate, increases when a cyclic stress is applied. These results indicate that there is a structural change during fatigue aging. The “holes” where o-Ps can localize become larger upon fatigue aging. These results also suggest that a significant distinction exists between structural changes induced by thermophysical aging and fatigue aging. The o-Ps annihilation intensity, which is a relative measure of the hole density in a material, showed a continuous decrease upon fatigue aging, indicating the possibility of hole coalescence, which could be a precursor of crazing. The interaction between thermophysical aging and fatigue aging corresponds very well with the enthalpy relaxation behavior as reported previously, viz., a well-aged sample is much more sensitive to cyclic stress. More importantly, it is hypothesized that fatigue failure initiation is probably closely related to hole size and density fluctuation.     

Optical gain of interdiffused GaInNAs/GaAs quantum wells

A self-consistent model for the band structure and optical gain spectra in interdiffused Ga_xIn_1-xN_0.04As_0.96/GaAs single quantum wells are studied theoretically using Fick’s Law and the Fermi Golden Rule. Due to quantum-well interdiffusion, the peak gain and its peak vary with the annealing time. Our results show that the interdiffusion technique can be used to tune the operation wavelength for multi-wavelength applications without degradation of device performance. Received: 18 April 2001 / Accepted: 19 September 2001 / Published online: 20 December 2001     

THE ANALYTICAL SOLUTION FOR SEDIMENT REACTION AND DIFFUSION EQUATION WITH GENERALIZED INITIAL-BOUNDARY CONDITIONS

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香港花岗岩风化分级化学指标体系与风化壳分带

火成岩的化学风化过程实质上就是碱、碱土金属组分水解淋失与脱硅富铁铝化的地球化学过程。不同风化程度的岩石处于整个化学风化过程的不同阶段,因而具有不同的化学成分和风化度指标。笔者在对香港九龙两个地方5个钻孔共计150件不同深度、不同风化程度的样品化学全分析结果与岩土风化程度宏观判别结果的相互对比、选择和确认的基础上,建立了香港地区花岗岩风化岩土风化程度工程分级的化学指标体系。这一研究成果的提出不仅有利于提高花岗岩风化岩土工程分类的科。学性、可靠性和实用性,而且可以为风化岩土工程特性与风化作用关系研究提供理论依据。     

Graphene Liquid Marbles as Photothermal Miniature Reactors for Reaction Kinetics Modulation

We demonstrate the fabrication of graphene liquid marbles as photothermal miniature reactors with precise temperature control for reaction kinetics modulation. Graphene liquid marbles show rapid and highly reproducible photothermal behavior while maintaining their excellent mechanical robustness. By tuning the applied laser power, swift regulation of graphene liquid marble’s surface temperature between 21–135 °C and its encapsulated water temperature between 21–74 °C are demonstrated. The temperature regulation modulates the reaction kinetics in our graphene liquid marble, achieving a 12‐fold superior reaction rate constant for methylene blue degradation than at room temperature.     

Enantioselective Synthesis of Spiroindenes by Enol‐Directed Rhodium(III)‐Catalyzed C?H Functionalization and Spiroannulation

Chiral cyclopentadienyl rhodium complexes promote highly enantioselective enol‐directed C(sp²)‐H functionalization and oxidative annulation with alkynes to give spiroindenes containing all‐carbon quaternary stereocenters. High selectivity between two possible directing groups, as well as control of the direction of rotation in the isomerization of an O‐bound rhodium enolate into the C‐bound isomer, appear to be critical for high enantiomeric excesses.