An attempt has been made to establish the relationships between the distribution F
τ (τ) of relaxation timeτand the shape and characteristic parameters of dynamic loss tangent (tanδ) -temperature (T) curve. For this purpose, the theoretical equation representing tanδ-T curve is derived for ten kinds of function formula for F
τ (τ) : seven functions of which are given by F
τ (τ) =k
n'τn' (where, k
n' : constant independent ofτ, n'=-2-3) (1), and three functions are given by triangles. WLF and Arrhenius types have been assumed for temperature dependence of τ.On the basis of the theoretical equations derived here, tanδ-T curve has numerically been calculated with the aid of an electronic computer. In the case of n'≥0 in eq. (1), the peak value of tanδ-T curve, (tanδ) max, peak tamperature Tmax, and the ratio of half value width ΔT
1/2/ΔT
1/2 (s) (the suffix s indicates the system composing of a single relaxation time) depend on the average relaxation timeτ, F
τ (τ), the total number of Maxwell elements in a system N, the ratio of elastic modulus before and after relaxation α, and the minimum relaxation time τ
l in F
τ (τ).In the case of n'≤-0.5 in eq. (1), the shoulder is significantly observed in the lower temperature region than Tmax in tanδ-T curve. The necessary conditions for appearance of this kind of shoulder is (tanδ) max≥3.5/ (n'+3)
4 and/N≥ √10.The tanδ-T curve (especially, ΔT
1/2/T
1/2 (s) , mearsured in the temper ature range of apperance of dynamic absorption arising from microbrownian movement of polymer seg ment in amorphous region of semi-crystalline polymers (α
a), is remarkably different from that calculated by using the above mentioned functions for F
τ (τ). Contrary to this, tanδ-T curve determined experimentally in the temperature range of αa absorption of amorphous polymer is in fairly agreement with that calculated by using n'=-2-0 in F
τ (τ) =kn
'τn' .In the actual experiment, no shoulder is observed in tanδ-T curve,
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