The Internal Timescale of High Polymers

Abstract

The dynamic viscosity η and the imaginary part of the complex dynamic compliance J' of many high polymers measured in frequency ranges, which are remote from the region of the anomalous dispersion of the complex dynamic modulus, conform to the following equations, respectively: 1/τ[2/2]・1/ω²(η-η₂-η₃)+(η-η₃)=0, and 1/τ[2/2]・1/ω²・η₂/η₂+η₃(1/J''ω-η₂η₃/η₂+η₃)=0, where, η₂, η₃ and τ₂ are constants, and ω is angular frequency. The first equation is the one used by Lyons, which is a modified form of the one used by Tobolsky and Eyring. Both the internal timescales, τ₂ in these equations, depend solely upon the experimental timescale and are independent of the nature of materials to be tested and of the environmental conditions. The values of τ₂ obtained from the data in the frequency range of the order of 10-10² cps are not of the order of second, as was erroneously reported by the previous authors, but of 10⁻³ second. The internal timescale of the order of seconds can only be obtained in much lower frequency range of 10⁻²-10⁻¹ cps. Thus, it seems very difficult to correlate the parameters of mechanical models simply with molecular mechanisms. Some characteristics of dynamic properties of high-polymeric materials are also discussed. Furthermore, in the appendix, the analysis of viscoelastic hysteresis loop obtainable from the Wakeham-type of apparatus is described.