Effect of molecular weight on the radial growth rates of polymer spherulites

Data existing in the literature for the spherulitic growth rate of molecular weight fractions of linear polyethylene, poly-(tetramethyl-p-silphenylene)siloxane, and trans-1,4-polyisoprene have been analyzed according to nucleation theory on taking into account the influence of chain length on the free energy of fusion. All three polymers display very similar behavior in that the interfacial free energy reaches an asymptotic value at high molecular weights, decreases as the molecular weight is lowered, and appears to also reach an asymptotic value at low molecular weights. Although the changes in the interfacial energy with molecular weight are quite distinct, the relative change is much less than has been previously reported when a molecular crystal analysis is used. The same general behavior observed points out the dominating influence of the chain-like character of the molecules in governing the growth rate.     

Multiple melting transitions in fractions of partially isotactic poly(propylene oxide)

Three transitions are detected dilatometrically when partially isotactic poly(propylene oxide) melts. One transition, the temperature of which is independent of the crystallization temperature over a wide range below 60°C, is ascribed to the melting of lamellar crystallites which are limited in thickness by the average isotactic sequence length alone. The other two transitions, the temperatures of which vary with the crystallization temperature, are ascribed to the melting of lamellar crystallites with thickness determined predominantly by three- and two-dimensional primary nucleation acts. The theory of Flory is adapted and applied quantitatively to the melting points of three crystalline fractions of poly(propylene oxide), obtained from a polymer produced via the zinc diethyl and water catalyst system. This method leads to a thermodynamic melting point of isotactic poly(propylene oxide) near 82°C.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

粉粒体两相流的电容层析成象测量

粉粒体系统中的固相浓度分布的在线测量是十分困难的问题．电容层析成象技术是一种近年来发展起来的非侵入式快速浓度场测量技术．它不干扰流场，不受流动中颗粒浓度、加速度、不透明等因素的制约．本文讨论其测量原理、应用、近期进展、存在的主要问题及其解决的对策．     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.     

Silica-modified electrode for the selective detection of mercury

Pure silica particles were dispersed within carbon paste and the resulting modified electrode was applied to the selective voltammetric detection of mercury(II) species after their accumulation at open circuit. The remarkable selectivity observed between pH 4 and 7 was attributed to the intrinsic adsorption mechanism which involves a condensation reaction between mercury(II) hydroxide and hydroxyl groups on the silica surface, leading to the formation of an inner-sphere-type surface complex. After optimization with respect to the electrode composition, the detection medium, and the voltammetric scan mode, a linear response was obtained in the concentration range between 2 × 10⁻⁷ M to 1 × 10⁻⁵ M, by applying anodic stripping square wave voltammetry. Various silica samples were used and their sorption behavior was discussed in relation to their specific surface area and porosity. The effect of chloride and pH on the accumulation of mercury(II) on silica was also investigated. Received: 4 September 1999 / Accepted: 5 January 2000