Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω, and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2ω. The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω. A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2ω. It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials

Equilibria in polyamide systems from e-caprolactam and water

Nylon 6 type polyamide equilibrium products prepared from e-caprolactam and water in closed systems at temperatures of 222 and 254° C have been investigated. Unconverted caprolactam, higher membered cyclic compounds, chain fractions and end-groups (-NH2 and -COOH) were determined quantitatively. Percentages of caprolactam and higher rings increase with increasing temperature and/or increasing water content (corresponding to decreasing DP) of equilibrium products. Number-average DP of chain fractions varied from ~ 100 ¿ 10 in the range investigated. The results have been evaluated in terms of equilibrium constants on the basis of plausible theoretical considerations including the Flory-Schulz distribution of chain lengths. The equilibrium constant of the polycondensation reaction has been found to decrease with decreasing DP of products. This behaviour is in accordance with similar results obtained for different polyamide equilibrium products. Possible explanations are discussed. A comparison with some data available from the literature is included