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Amphiphilic maleic acid-containing alternating copolymers—2. Dilute solution characterization by light scattering,intrinsic viscosity,and PGSE NMR spectroscopy

The dilute solution behavior of several alternating copolymers of maleic acid has been characterized by static and dynamic light scattering, intrinsic viscosity, and pulsed-gradient spin-echo NMR spectroscopy. The copolymer of maleic acid–sodium salt and isobutylene (IBMA-Na, M_w ∼350 kg/mol) dissolves readily in concentrated aqueous salt solutions. Changes in chain dimensions with ionic strength and pH are similar to those of the lesser salt solution-soluble poly(acrylic acid-sodium salt). The hydrophobically modified (with n-butyl, n-hexyl, n-octyl, and phenethyl amines) copolymers of maleic acid–sodium salts and isobutylene (IBMA-NHR-Na) show no sign of large intermolecular aggregation in 0.1 N sodium acetate (NaAc). However, the sizes of the copolymers are relatively small compared to that of the ionized parent copolymer (IBMA-Na, M_w ∼350 kg/mol), suggesting intramolecular aggregation of the alkyl side-chain groups along the polymer backbone. The copolymer modified with the longer chain n-decyl, on the other hand, forms stable large intermolecular aggregates containing 33 chains/aggregate. The copolymers of maleic acid–sodium salt and styrene (SMA-Na) appear to have no signs of aggregation, despite being a hydrophobic polyelectrolyte. The copolymer of maleic acid–sodium salt and di-isobutylene (DIBMA-Na) has a similar salting-out concentration as SMA-Na. The radius of gyration measurements by static light scattering suggest that at least some fraction of the DIBMA-Na chains form large intermolecular aggregates. The copolymers of maleic acid–sodium salt with n-alkenes (n-C_mMA-Na) in 0.1 N NaAc form small intermolecular aggregates (three to five chains/aggregate). In contrast to these static light scattering results, PGSE NMR diffusion measurements for the above aggregated systems indicate only one diffusion coefficient consistent with the motion of single isolated chains. A plausible explanation for this discrepancy is that the population of the aggregates is too small to be sufficiently detected in the PGSE NMR experiment. Furthermore, it is likely that the aggregate has a larger relaxation rate than the nonaggregate, and therefore has a comparatively reduced signal in the PGSE NMR experiment. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3584–3597, 2004     

Die näherungsweise Berücksichtigung der mittragenden Breite bei Spannungs-, Stabilitäts- und Schwingungsproblemen

Übersicht Um die Schubverformungen in den Deckplatten von Plattenbalken und Hohlkästen zu berücksichtigen, wird mit Hilfe eines Variationsprinzips vom Minimum der potentiellen Energie ein Näherungsverfahren entwickelt. Bei der Annahme über den Formänderungszustand wird die Bernoullische Annahme vom Ebenbleiben der Querschnitte verlassen. Die Euler-Gleichungen des Variationsproblems ergeben einfache gewöhnliche Differentialgleichungen, die eine Behandlung von Spannungs-, Stabilitäts- und Schwingungsproblemen ermöglichen. Es zeigt sich, daß die Spannungen, Knicklasten und Eigenfrequenzen ganz erheblich von den bekannten Werten der elementaren Stabtheorie abweichen können. Die Genauigkeit der Lösung wurde durch Vergleich mit der exakten Scheibentheorie überprüft, wobei sich eine gute Übereinstimmung ergab.

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Summary A method of determining the shear deformations of the cover plates of T- and box-beams is developed, employing a variational principle of minimum potential energy. In assuming a convenient shape of deformation Bernoulli's hypothesis is rendered invalid. The Euler equations yield ordinary differential equations for the solution of stress, stability, and vibration problems. It is shown that the stresses, the buckling loads and the characteristic frequencies may differ significantly from the values obtained with the elemantary theory of elasticity. The accuracy of the solution is investigated and shown to be of a high degree by comparing the results with those obtained with the exact theory of disks.