Amorphous polymers relaxations

The average polymer melt relaxation times between the processing temperature Tp and the solidifying temperature (the Tg in amorphous polymers and somewhere between Tg and with polycrystalline polymers). 

PTEB-Q) to the annealed ones, owing to the presence of the crystalline phase. Moreover, the temperature of the peak increases with the annealing, as well as the broadness of the relaxation. These results suggest that the liquid crystalline phase gives raise to an a relaxation similar to that of amorphous polymers despite the existence of the two-dimensional order characteristic of smectic mesophases, and it changes following the same trend than that of semicrystalline polymers. 

The WLF equation can be widely applied, and demonstrates the equivalence of time and temperature, the so-called time-temperature superposition principle, on the mechanical relaxations of an amorphous polymer. The equation holds up to about 100° above the glass transition temperature, but after that begins to break down. 

M.L. Williams, R.E. Landel, and J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming Uquids, J. Am. Chem. Soc., 77, 3701-3707, 1955. 

The temperature dependence of the compliance and the stress relaxation modulus of crystalline polymers well above Tf is greater than that of cross-linked polymers, but in the glass-to-rubber transition region the temperature dependence is less than for an amorphous polymer. A factor in this large temperature dependence at T >> TK is the decrease in the degree of Crystallinity with temperature. Other factors arc the reciystallization of strained crystallites ipto unstrained ones and the rotation of crystallites to relieve the applied stress (38). All of these effects occur more rapidly as the temperature is raised. 

The distribution of relaxation or retardation times is much broader for cystallinc than for amorphous polymers, the Boltzmann superposition... 

A method of characterising transport mechanisms in solid ionic conductors has been proposed which involves a comparison of a structural relaxation time, t, and a conductivity relaxation time, t . This differentiates between the amorphous glass electrolyte and the amorphous polymer electrolyte, the latter being a very poor conductor below the 7. A decoupling index has been defined where... 

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

M. L. Williams, R.R Landel, and J.D. Ferry The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids. ... 

For all the cases cited above, which represent those data for which a comparison can be presently made, there is a direct connection between the critical molecular weight representing the influence of entanglements on the bulk viscosity and other properties, and the NMR linewidths, or spin-spin relaxation parameters of the amorphous polymers. Thus the entanglements must modulate the segmental motions so that even in the amorphous state they are a major reason for the incomplete motional narrowing, as has been postulated by Schaefer. ( ) This effect would then be further accentuated with crystallization. 

H( P) as a function of the nondimensional relaxation time, 7 = u/x, the ratio of local to global relaxation times, and p. When Equations 3 and 5 are used simultaneously in analyzing experimental data, we have found that p= 1/2 for most amorphous polymers which will also be assumed for lightly crosslinking systems. 

FIGURE 14.10 Logarithm of the relaxation modulus as a function of temperature for three polymer samples. Sample (a) is (largely) crystalline vinyl pol5uner sample (b) is an amorphous vinyl polymer that contains light cross-linking and sample (c) is an amorphous vinyl pol5uner. The Tg for the amorphous polymer is about 100°C and the for the crystalline polymer is about 180°C. 

The time-temperature superposition principle has practical applications. Stress relaxation experiments are practical on a time scale of 10 to 10 seconds (10 to 10 hours), but stress relaxation data over much larger time periods, including fractions of a second for impacts and decades for creep, are necessary. Temperature is easily varied in stress relaxation experiments and, when used to shift experimental data over shorter time intervals, can provide a master curve over relatively large time intervals, as shown in Figure 5.65. The master curves for several crystalline and amorphous polymers are shown in Figure 5.66. 

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