Carbon-13 NMR linewidths of polyethylenes and related polymers

The carbon-13 NMR linewidth (proton decoupled) of linear and branched polyethylenes crystallized so as to yield different supermolecular structures, as well as a polyethylene oxide sample, have been studied in detail. The purpose has been to assess the different molecular contributions to the linewidth in the completely amorphous polymer as well as in the amorphous regions of the semicrystalline state. These studies on a number of different structures were complemented by both proton-decoupled and dipolar-decoupled magic-angle spinning experiments on a particular sample, as well as frequency dependence studies. It is found that the abnormally broad resonance lines previously reported for the molten polymer can be significantly reduced by adopting appropriate methods of sample preparation and magnetic-field homogenization at each temperature. Relatively narrow lines result which can be interpreted in a conventional manner. In the semicrystalline state, the resonance lines are relatively broad and are shown to be morphology dependent. Specific contributions and their temperature dependence are discussed.     

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.     

Analysis of pp → K+K− π+π− around 1 GeV/c

Approximately 100 000 four-prong antiproton annihilations in hydrogen were measured. A clean, unbiased sample of 842 K⁺K^?π⁺π^? events was obtained. This reaction is dominated by $\text{K}{}^1\text{(～45\%)}$ and ?⁰(～20%) production, with smaller amounts of A₂⁰(～15%) and ?(～5%) production. 25% of the reactions involved double resonance production. No significant three-body resonance production is observed.     

Carbon-13 NMR of polyethylenes: Correlation of the crystalline component T1 with structure

The carbon-13 spin-lattice relaxation times T₁ of the crystalline portion of a set of polyethylenes have been studied. Chain structure and crystallization conditions have been varied over the widest possible extremes so that large differences are developed in the level of crystallinity, the supermolecular structure, and the crystallite thickness. Concomitantly, the observed crystalline T₁ values cover the extraordinarily wide range of about 40–4500 s. They bear a one-to-one relation with the crystallite thickness, which is found to be the key structural variable determining this property. A correlation with the temperature for the α-transition can be established, which implies a similar type of segmental motions for the two phenomena. Major changes in the interfacial structure can also have a drastic influence on the value for the crystalline T₁. Analysis of the magnetization decay curve also allows for a quantitative determination of the degree of crystallinity, which is found to be in excellent agreement with the corresponding value found from Raman spectroscopy.     

Search for f(J)(2220) in radiative J/ψ decays

We present a search for f(J)(2220) production in radiative J/ψ→γf(J)(2220) decays using 460 fb?1 of data collected with the BABAR detector at the SLAC PEP-II e(+)e? collider. The f(J)(2220) is searched for in the decays to K(+)K? and K(S)?K(S)?. No evidence of this resonance is observed, and 90% confidence level upper limits on the product of the branching fractions for J/ψ→γf(J)(2220) and f(J)(2220)→K(+)K?(K(S)?K(S)?) as a function of spin and helicity are set at the level of 10??, below the central values reported by the Mark III experiment.     

A constructive real projective plane

The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues’s Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal’s Theorem, poles and polars. The axioms used for the synthetic treatment are constructive versions of the traditional axioms. The analytic construction is used to verify the consistency of the axiom system; it is based on the usual model in three-dimensional Euclidean space, using only constructive properties of the real numbers. The methods of strict constructivism, following principles put forward by Errett Bishop, reveal the hidden constructive content of a portion of classical geometry. A number of open problems remain for future studies.     

The effect of molecular weight and crystallite structure on yielding in ethylene copolymers

Nominal stress-strain curves of a series of random ethylene-hexene copolymers having narrow composition and most probable molecular weight distributions were investigated. A series of such molecular weight copolymers with a constant concentration of branches were crystallized under a variety of conditions. In each molecular weight series the level of crystallinity was approximately constant. Particular attention was focused on the yield region and the nature of the yielding process. It was found, quite surprisingly, that the yield stress was not solely dependent on the crystallinity level. Moreover, the shape of the force-elongation curve in the yield region was very dependent on the molecular weight and the crystallization mode. These changes in yielding correlated quite well with the overall crystallite structure that was characterized by thin section transmission electron microscopy. The orthorhombic unit cell of polyethylene was maintained in all the samples despite the changes that occurred in the overall crystallite structure. © 1997 John Wiley & Sons, Inc.     

Carbon-13 NMR relaxation and transitions in polymers

High-resolution proton-decoupled carbon-13 nuclear magnetic resonance relaxation parameters have been obtained as a function of temperature for a set of completely amorphous polymers, semicrystalline polymers, and a series of ethylene–vinyl acetate copolymers. With these samples the nature of the glass temperature, other postulated amorphous transitions, and the β transition were investigated. For the completely amorphous polymers, the average correlation times depend on temperature according to the Williams–Landel–Ferry relation. Spectral collapse occurs at temperatures whose ratio to T_g is in the range 1.2–1.4 and corresponds to a correlation time of about 10^?7s. The loss of resolvable spectra is demonstrated to be a consequence of experimental methods and is not due to the occurrence of another amorphous transition. Both the methylene and methine carbons can be resolved for the ethylenevinyl acetate copolymers. Although the correlation time for the methylene carbon is continuous and resolvable through the β transition region, the methine branch-point resonance is lost. The implication of these results to the molecular nature of the β transition is discussed.