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While recently many attentions have been paid to the temperature characteristics of elastic modulus in crystalline high polymers, especially from the point of view that they reflect the variations of the fine structure such as chemical constitution, crystallinity or orientation, only the limited qualitative knowledges about them are obtained. In this paper, quantitative analysis of the temperature dispersion curves was tried with regard to the primary dispersion (α-dispersion), and more profound meaning of it was pursued.If it is assumed that the relaxation spectrum (logH vs. logτ) concerning to the primary dispersion takes the shape of wedge with negative slope of β(<1/2), and its intensity, H0, at τ=1sec., the temperature dependence of dynamic modulus, E', is expressed by the following equation, logEW=log(E'-EB)=logH0+βlogaT+βlogω-logβ, where aT is the shifting factor, taking unity at the second-order transition temperature Tg, EB is the contribution to the modulus E' from the relaxation spectrum corresponding to the intermolecular relaxation mechanism (box-type distribution corresponds to this for amorphous polymers), which exists in the far longer time region than the observation time for crystalline polymers, and EW is the contribution to E' from wedge-type distribution. According to the above equation, logEW vs. T curves corresponding to the various values of ω can be reduced to a single curve by shifting them along logEW-axis by βlogω. The shape of logEW(T) curves is described by βlogaT. When the observation time exists on the shorter time region than the lower limit τl of wedge-type spectrum, the modulus levels off to the ω-independent constant value towards the lower temperature. The typical example for this can be found in the case of polyethylene terephthalate reported by Thompson and Woods.When the time, t, always exists in the region of wedge-type spectrum irrespective of temperature, the inflexion point of logEW(T)-curve corresponds to the maximum apparent activation energy for relaxation process and is considered to agree with Tg. This fact is supported by the experimental results on several fibers. Moreover it should be noted that the position of Tg remains on the same point on the T-axis irrespective of ω. If the observation time exists on the shorter time region than τl, the temperature dispersion of modulus occurrs at the higher temperature than Tg and depends remarkably on ω.According to the analyzing method described above, it was concluded that the values of C1' and C2' in the WLF-equation must increase in crystalline high polymers due to the existence of crystalline region.

Analysis of Temperature Dispersion Curves of Elastic Modulus in Crystalline High Polymers