Relaxation activation energy, polymers

Figure 8.36. The B-relaxation hardly shifts as a function of the measuring frequency due to the presence of a large crystalline phase. The y-relaxation is deary much stronger frequency dependent. An activation energy value of 63 kJ/mole was calculated for the y-relaxation from the slope of this curve. Some typical y-relaxation activation energy values for linear polymers are 63, 54 and 54 kJ/mole for respectively PVC [14], PC and PET [15]. The mechanisms of these y-relaxations are often described as local mode relaxation effects [15]. The same mechanism might also be responsible for the y-relaxation effect in polyketone polymers.

The temperature dependence of the relaxation activation energy of hydroxy-terminated polybutadiene-methyl methacrylate AB cross-linked polymer in the glass transition region is shown in Figure 4.8. The parameters C, = 8.77 °C, C2 = 85.07 °C and = 340 K were measured by means of the dynamic mechanical spectra 381 K was chosen as the reference temperature Tq. 

Relaxation Activation Energy of Polymers in the Glass Transition Region... 

Figure 4.8 Relaxation activation energy of hydroxy-terminated polybutadicne-methyl methacrylate AB cross-linked polymer in the gla.ss transition region as a function of temperature (Tj. = 340 K, T = 380 K) [141...

The only previous report of activation energies for poly (methyl o chloroacrylates) is for the "conventional" free radical polymer which can be assumed to be reasonably syndiotactic (16). The values quoted are 130 kcal/mole for the a relaxation and 26 kcal/mole for the 3 relaxation. The present results (Table II) are in qualitative agreement with these values. In general the activation energies for the relaxations decrease with increasing ester side chain length or bulkiness and the isotactic isomers have a relaxation activation energies about 35-50 kcal/mole lower than the comparable syndiotactic isomers. This effect, as already discussed, is a consequence of the Tg difference between the i somers. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

For PIB the apparent activation energy found for the structural relaxation time in the NSE window is almost twice that determined by NMR [136] (see Fig. 4.9 [125]). For aPP, the temperature dependence of NMR results [138] seems, however, to be quite compatible with that of the NSE data nevertheless, 2D exchange NMR studies on this polymer [139] reveal a steeper dependence. This can be seen in Fig. 4.11 [ 126]. 

Work in groups of three. The shift factor, or, in the WLF Equation [Eq. (5.76)], is actually a ratio of stress relaxation times, f , in the polymer at an elevated temperature, T, relative to some reference temperature. To, and can be related via an Arrhenius-type expression to the activation energy for relaxation, Erei as... 

You have developed a new semicrystalline polymer, which has a typical activation energy for relaxation of Erei = 120 kJ/mol. You wish to know the creep compliance for 10 years at 27°C. You know that, in principle, you can obtain the same information in a much shorter period of time by conducting your compliance tests at a temperature above 27°C. 

Table 1. Apparent activation energies for relaxation processes in crossEnked polymers calculated from broad line NMR...

Table 2. Apparent Activation energies for relaxation processes in crosstinked polymers calculated from T, relaxation...

The activation energy of isothermal contraction in polymer blends calculated in 9 is considerably lower than for pure components, this pointing to the appearance of the free-volume as well, which facilitates the relaxation processes and diminishes the activation energy. 

The study of the relaxation of dipole polarization, as well as of the dipole moments of cholesterol-containing polymers and copolymers128 "134,191 193) presents a sensitive confirmation for the existence of intramolecular structuration of mesogenic groups. This is indicated for instance, by the high values of relaxation times (Tjj p) and activation energy (EJ p) of dipole polarization, as well as by the large values of correlation parameter g, which is a relative measure of the internal rotational retardation in macromolecules (Table 18). 

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