Activation Energy Of Relaxation Process Research Articles

結晶性高分子における弾性率の温度分散曲線の解析

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.

Dependence of mechanical relaxation spectra of linear amorphous polymers on the distribution of molecular weights

AbstractAn expression is obtained in the form of an integral equation of the Fredholm type which correlates the mechanical relaxation distribution of a linear amorphous polymer with its molecular weight distribution. A method of approximate solution of this integral equation is given on the basis of the assumptions that: (1) the relaxation spectrum of a monodisperse sample in the rubbery region is approximated by a box‐shaped function; (2) the steady‐flow viscosity of a monodisperse sample increases with the 3.4 power of molecular weight above a certain critical molecular weight M̄c; and (3) the relaxation modulus (or the real part of the complex dynamic elasticity), Ē, in the initial zone of the rubbery region is independent of molecular weight and may be calculated in terms of Alfrey's approximation. The method permits predicting the molecular weight distribution from experimental relaxation data obtained over the entire region of rubbery timescale, provided the values of Mc, Ē, and M̄z (z‐average molecular weight) of the given sample are known. Stress‐relaxation data on unfractionated samples of polystyrene and polyvinyl acetate are analyzed in terms of this method, and it is found that the predicted molecular weight distributions agree quite satisfactorily with the observed data for both polymers, except in regions of low molecular weight where the theory gives rise to a fictitious maximum and minimum, neither of which is observed in the experimental data. This anomaly is attributed to the effect of the transition region on the initial zone of the rubbery region which is neglected in the present theory. The experimental data on polyvinyl acetate used for the tests are taken from our previous study, and those on polystyrene are newly obtained for this work. Since no complete stressrelaxation data covering the entire region from glassy state to rubbery flow are yet available on polystyrene, those obtained in this work are presented in rather great detail. The relaxation spectrum in the transition region is compared with that of Grandine and Ferry and of Becker from dynamic mechanical measurements in an audiofrequency range, with a fair agreement with the former of the two. The shift factor aT determined over the temperature range from about 80 to 150°C. follows a similar curve to that found previously for polyvinyl acetate when reduced to an appropriate reference temperature, and yields a maximum activation energy for relaxation processes of 210 kcal. mole−1 at a temperature of 92 ± 1°C. This temperature is in the middle of the reported second order transition temperatures on polystyrene of high molecular weight.