Analysis of Dynamic Loss Tangent (tanδ) -Temperature Curve Relating to Molecular Motion of Polymer Chain in Amorphous Region of Fiber and Fiber-Forming Polymeric Materials

Part 4 : Evaluation of Distribution of Fine Structure in Amorphous Region from Tan δ-Temperature Curve

Abstract

This paper intends to establish a method for estimating the detailed fine structur of amorphous region in polymer solid from dynamic loss tangent (tan δ) -temperature (T) curve in the temperature range corresponding to dynamic absorption (α_a absorption) due to microbrownian movement of polymer segments. The amorphous region is assumed to be composed of many very small particles (ca. 100Å; cubic), whose packing state in polymer segment is uniform. This very small particle is regarded as fundamental element. In order to express the distribution of the element, the distribution function of packing density F (n) is newly introduced. The value of tan δ for the polymer sample can be expressed by summation of the product of tan δ value and elastic modulus fraction of individual element constituting the sample. Analytical method for determining F (n) from the experimental tan δ-T curve as well as from the apparent activation energy ΔH_a is established. The validity of assumptions adopted in this method is ascertained by the following experimental facts: The possible change in fine structure of amorphous region during measurement of tan δ-T curve is practically ignorable in many cases except for nylon 6. The temperature dependence of ΔH_a, calculated from F (n), which is determined from the experimental tan δ-T curve, and WLF equation, agrees qualitatively with that directly measured. For the samples having a wide F (n), the temperature-time superposition correspondence law does not hold.