Amorphous polymers relaxation times

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). 

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. 

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.

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. 

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. 

The sensitivity of the three relaxation times to the molecular dynamics and structure will be discussed in a subsequent section. The general temperature dependence of Tj, T1 and T2 for a typical linear amorphous polymer with one side group attached to a backbone is shown in Fig. 4. 

The temperature dependence of the relaxation times introduced into mechanical equations by means of Eq. (2.93) was used to calculate the residual stresses in cooling amorphous polymers. 

Spin-lattice relaxation measurements (7j) are also common,78 83 though these of course monitor more rapid motions. Spin lattice relaxation times have nevertheless proved a simple but effective means of distinguishing different structural regions within polymer samples, i.e. crystalline and amorphous regions and interfacial regions between crystalline and amorphous parts. 

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