A 13C NMR study of mesomorphic solutions of poly(p-phenylene terephthalamide)

Solutions of poly(p-phenylene terephthalamide) in fuming sulfuric acid were characterized by ¹³C NMR spectroscopy and solution viscosity measurements over the 2–28% w/w concentration range. The spectra showed the presence of two distinct amide carbonyl resonances at low concentration, tentatively assigned to cis and trans conformations. As the concentration increased, additional carbonyl lines were observed along with significant broadening. Peak area measurements showed that only the polymer molecules in the isotropic environments contributed to the ¹³C NMR spectra and a considerable amount of the polymer remained in the isotropic phase at concentrations previously considered to consist of polymer in highly anisotropic regions. Spin-lattice relaxation times were measured at six concentrations using the inversion recovery method. The aromatic carbons relaxed at a much faster rate (ca. 0.10 s) than the carbonyls (ca. 0.45 s), but the relaxation rates for both carbons were essentially constant over the concentration range, indicating that the observed isotropic phase is not affected by changes in the macroscopic solution behavior so as to alter spin-lattice relaxation mechanisms.     

Holographic displacement analysis using wave front modulation techniques

The wave fronts from two holographic displacement patterns are modulated by equal but opposite plate rotations and are superimposed to form a moiré pattern. Displacement information contained in the Fraunhofer diffraction pattern of the two superimposed gratings is analysed, and spatial filtering techniques are used to isolate full-field projections of displacement along and normal to the line of sight. Experimental results taken from a pipe subjected to pure torsion show that the method is not only accurate but that the technique is applicable to curved surfaces.     

Intramolecular photocycloaddition reactions of 4-phenoxybut-1-enes

4-Phenoxybut-1-ene undergoes both ortho and meta intramolecular photocycloaddition on 254 nm irradiation: in the latter process the addition is directed by the alkoxy tether to the arene 2,6-positions. Methyl substitution on the ethene and arene units does not affect the regiochemistry of the reaction but the presence of a 2′-methoxy group inhibits the meta process and only the ortho addition occurs.     

Interior radiances in optically deep absorbing media—I Exact solutions for one-dimensional model

The exact solutions are obtained for a one-dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth-order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values. Except for extremely large values of the optical thickness of a layer, the reflection and transmission operators calculated from accurate starting values obtained by the Runge-Kutta method are orders of magnitude (a factor of 10¹¹ better in a typical case at unit optical depth) more accurate than those obtained by the use of the single scattering approximation for an optically thin layer. The relative error in the reflection and transmission operators is less than 10^-12 and 10^-8 respectively up to an optical thickness of 32,768 when calculated by this procedure, while the relative error in the interior radiance is less than 10^-8 at all points within a layer of optical thickness 32,768. It is shown that flux conservation is a poor test of the accuracy of a numerical method, since flux is conserved to all orders for a conservative medium when the doubling method is used, no matter how inaccurate the starting values may be.     

Solid-state cpmas 13C-NMR studies of the reaction of an epoxy resin with masked isocyanates

It has been shown that incorporation of masked isocyanates in the MY720/DDS epoxy significantly reduces the equilibrium moisture absorption by blocking of residual functional groups ( oxirane group) by the isocyanates released in the deblocking reaction of the masked isocyanates. We have now used high resolution ¹³C-CP/MAS NMR to follow the reactions in the solid state and to identify intermediates and by-products. The deblocking reaction of the masked isocyanates also releases the corresponding alcohol, part of which may evaporate during the curing reaction. The resolution in the solid-state spectra is good enough to identify all the reactants and the intermediates involved in the curing reaction. Difference spectra are used to emphasize changes between systems that differ in treatment or composition.     

Explicit solutions to the reverse order law (AB)+ = B-mrA-lr

Shinozaki and Sibuya have shown that the Moore-Penrose inverse (AB)⁺ can always be expressed as B^-A^- for generalized inverses A^- and B^- of matrices A and B, respectively. In this paper, explicit solutions B^-_mr and A^-_lr to (AB)⁺ = B^-_mrA^-_lr are given. A class of solutions is obtained which is related to an equation of Greville, and expressions for the general solutions are presented.     

Hypergeometrics and the cost structure of quadtrees

Several characteristic parameters of randomly grown quadtrees of any dimension are analyzed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation.