Analysis of Dynamic Loss Tangent (tan δ) -Temperature Curve Relating to Molecular Motion of Polymer Chain in Amorphous Regions in Fibers and Fiber-Forming Polymeric Materials

Part 1 : Viscoelastic Body Composed of Single Relaxation Time

Abstract

A theoretical equation has been derived to determine the tan δ-temperature (T) curve of the system constituted of a single rleaxation time. The tan δ-T curves have been calculated by the theore tically derived eqation. The experimental results have shown that :
(1) The three-element model combining the Maxwell element with a spring element is a most suitable as a viscoelastic model, which gives a peak in tan δ-T curve.
(2) Determing the peak temperature in the δ-T curve, T_max (K) and the apparent activation energy _??_H_a, the half value width inherent in a tan δ-T curve has been calculable by the equation, _??_T_1/2(3)=5.24×10^-3T_max²/_??_H_a.
(3) The log tan δ-T curve can be approximated to the equilateral triangle.
(4) The parameter B∞, defined by the equation; B∞=522vH_a/T_max, is proved to be convenient and resonable for determining the mechanism of a viscoelastic absorption.
(5) The average _??_T_{1/2 (s)} of various polymers are 13 deg and 20 deg for theabsorption (a_a) related to the microbrownian movement of segment in amorphous and the absorption (β_a) related to the local movement of the main chain respectively. Thus, the value of β_a-absorptions larger than those of a_a-absorption.
(6) The method is presented to determine the relaxation time at the glass transition temperature T_q by using _??_H_a and T_max.