Finite Linear Spaces II

Batten and Beutelspacher have characterized Finite Linear Spaces with lines of size n,n + 1 and n + 2, and with v (n + 1)²for n 22, and some of the cases for smaller n. In this article, using the structuredapproach we presented in our earlier article [8], we complete this characterization for smalln.     

A cyclic hexacopper(II) fluoro complex that encapsulates two fluoride anions

The complex [[Cu3(HpztBu)4(mu-pztBu)2(mu-F)2(mu 3-F)]2]F2 (HpztBu = 3[5]-tert-butylpyrazole) has a cyclic, C2v-symmetric hexacopper core. The two non-coordinated F- anions are encapsulated within cavities formed by three HpztBu ligands.     

Small-angle X-ray scattering study of liquid crystalline polycarbonates based on α-methyl stilbene mesogen and methylene-containing flexible spacer

Crystallization and melting behavior are studied by small-angle X-ray scattering (SAXS) for a series of recently synthesized monotropic liquid crystalline polycarbonates based on α-methyl stilbene mesogen and methylene flexible spacer. The one-dimensional electron density correlation function is used to obtain long period, crystal thickness, and linear crystallinity from the Lorentz-corrected SAXS intensity. Changes in these parameters during nonisothermal crystallization and melting are explained by a model of dual crystal populations. The primary crystals form first using the liquid crystalline phase as crystal nuclei, while smaller and less perfect crystals form later from the isotropic phase at low temperature. The results of the real-time SAXS study of isothermal crystallization also support the view that the nematic phase serves as crystal nuclei for fast crystallization. An odd-even effect in crystal thickness and linear crystallinity is observed in all the SAXS experiments mentioned above. The results of this study and our complementary wide-angle X-ray scattering (WAXS) investigation show clearly that the difference in the position of the neighboring carbonate dipoles on a chain affects structural organization both at the unit cell level and at the level of the crystal in these monotropic LCPs. © 1995 John Wiley & Sons, Inc.     

A critical appraisal of the use of branched capillaries in analytical flame spectroscopy

The operating pressure of a pneumatic nebulizer has been measured. The rsult has been used to explain the problems associated with the variation in flame spectroscopy signal with sample position when a capillary T piece is used for continuous addition of releasing agent. The way to minimize this variation is outlined.     

Thermodynamics of polyether solutions

Measurements are reported of the vapor pressures and the heats and volumes of mixing of solutions of poly(ethylene glycol dimethyl ether) in chloroform and in carbon tetrachloride. The measurements have been used to calculate the thermodynamic mixing functions for mixing with zero volume change. These values have been compared with the predictions of the lattice theory of mixtures at three different levels of approximation, viz., the generalized “first approximation” theory of Barker, the “zeroth approximation” theory, and the Flory theory. In the hydrogen-bonding chloroform solutions the Barker theory is more successful than the other forms of the lattice theory. The results have also been used, in conjunction with those for solutions of poly(propylene glycol dimethyl ether) in the same two solvents, to test the ability of the Barker theory to correlate the properties of related systems. Good correlation is found between the two carbon tetrachloride solutions but not between the chloroform solutions. It is probable that the side-chain methyl groups in the propylene oxide repeating unit cause the hydrogen-bonding interaction to be weaker in this polymer than it is in the polymer with the ethylene oxide repeating unit.     

Radiation chemistry of linear low-density polyethylene. II. Kinetics of alkyl and allyl free-radical decay reactions

Quenched and annealed samples of linear low-density polyethylene (LLDPE) were γ irradiated in vacuo at 77 K; the kinetics of the alkyl free-radical decay reactions were studied at room temperature, and of the allyl free-radical reactions at 60, 70, and 80°C. The ESR signals saturate at a slightly higher microwave power in the LLDPE than in high-density polyethylene (HDPE), and the alkyl radicals start decaying at a lower temperature in the LLDPE than in the HDPE. As in the HDPE the decay of the alkyl free radicals at room temperature in the LLDPE follows the kinetic equation for two simultaneous first-order reactions with the fraction of the faster-decaying component being slightly greater in the quenched than in the annealed samples. In the case of the allyl free radicals the decay at 60°C follows the equation based on one fraction of the radicals decaying according to second-order kinetics in the presence of other nondecaying radicals. At higher temperatures the data are best understood in terms of a second-order rate equation with a continuously variable time-dependent rate constant as suggested by Hamill and Funabashi.     

The motion of a charged particle as viewed from heaven

A new approach to the problem of the motion of a self-interacting massive charged particle in general relativity is presented. A charged Robinson-Trautman (RT) solution is used as a general relativity model for such a particle. Such a solution is shown to generate a unique world-line in its ownH-space. This is argued to be the asymptotically observed world-line of the particle. Using the RT dynamical relations, the equation of motion is derived, and, in the limiting case of zero curvature, it is shown to be the same as the classical Lorentz-Dirac equation of motion.This essay received an honorable mention (1977) from the Gravity Research Foundation-Ed.     

Radiation chemistry of linear low-density polyethylene. I. Gel formation and unsaturation effects

Quenched and annealed samples of linear low-density polyethylene (LLDPE) were irradiated with ⁶⁰Co γ rays in vacuo at room temperature. The data follow rather accurately Charlesby's equation s = k/r, where s is the soluble fraction, r the dose, and k a constant from which G(X), the G-value for crosslinks, was calculated. Crosslinking in the LLDPE is about twice as extensive at equal doses as in LHDPE. Production of vinylene unsaturation was approximately the same in the two types of polyethylene.