Quantitative NMR measurements in copolymers of vinylidene chloride and acrylonitrile: The effect of saturation and varying nuclear Overhauser enhancements

Spin-lattice relaxation times and nuclear Overhauser enhancements (NOE) for ¹³C nuclei in copolymers of acrylonitrile and vinylidene chloride were measured at 20.1 and 67.9 MHz. In the ? CCl₂? region of the spectrum T₁ and NOE values of the various resonances are equal within experimental error and are invariant to changes in composition. The T₁ and NOE values of the ? CCl₂? region, however, are not equal to those of the ? CH? or ? CN region. As a result compositions cannot be calculated by direct comparison of the areas in the ? CCl₂? region and either the ? CH? or the ? CN region. Discrepancies can be corrected for the ? CH? resonances by multiplication of the area by an empirical constant. A similar constant for the ? CN region is composition-dependent at 20.1 and 67.9 MHz. A chemical shift anisotropy mechanism is postulated as important for relaxation of the ? CN resonances. The overall influence of variable T₁ and NOE values on quantitative determination of polymer composition is considered.     

On a more precise statement of Hamilton's principle

It has been recognized in the literature of the calculus of variations that the classical statement of the principle of least action (Hamilton's principle for conservative systems) is not strictly correct. Recently, mathematical proofs have been offered for what is claimed to be a more precise statement of Hamilton's principle for conservative systems. According to a widely publicized version of this more precise statement, the action integral for conservative systems is a minimum for discrete systems for small time intervals only and is never minimum for continuous systems. In this paper, two contradictions to this more precise statement are demonstrated, one for a discrete system and one for a continuous system.     

The synthesis and crystal structure of a new diprotonated Schiff base cryptand

Abstract

The synthesis and crystal structure of the diprotonated cryptand derived from the reaction of tren and 2,6-diacetyl pyridine is reported. The imino nitrogens of the Schiff base linkages are directed so that the dicarbimine functions are in trans, trans geometry relative to the pyridine C-N bond. This configuration has not previously been reported in related pyridine-derived Schiff base macrocycles.     

A Simple One-Step Synthesis of Alkyl Benzazol-2-carboxylates

A simple one-step synthesis of alkyl benzazol-2-carboxylates employing alkyl trialkoxyacetate is described.     

Preparation and reactions of 3-oxa- and 4-oxa-5-hexenyllithiums

Low-temperature lithium–iodine exchange between tert-butyllithium and the appropriate iodide has been used to generate 3-oxa-5-hexenyllithium and a variety of 4-oxa-5-hexenyllithiums. The 3-oxa system is inherently unstable and fragments via facile β-elimination to give the anion of allyl alcohol and ethylene. The 4-oxa-5-hexenyllithiums, in contrast, are stable at low temperatures but undergo novel isomerization upon warming to deliver the lithium salt of a 4-alken-1-ol in the formal equivalent of an unprecedented [1,4]-Wittig rearrangement. The rearrangement is most likely mediated by 5-exo-trig ring closure of the 4-oxa-5-hexenyllithium to a (2-tetrahydrofuranyl)methyllithium followed by rapid opening to the alkoxide.     

Direct analytical solutions to non-uniform beam problems

The direct analytical solution to the vibration of non-uniform beams with and without discontinuities and with various boundary conditions is presented. Results are compared to results from the exact solution for certain cases where the exact solution has been obtained. It is shown that the direct solution converges to the exact solution, in fact, with “indefinite accuracy” just as Hamilton stated that it would.