Relaxation activation energies

Activation energy Relaxation temperature (K) (kJ/mol) Molecular motion... 

Meagher J F, Chao K J, Barker J R and Rabinovitch B S 1974 Intramolecular vibrational energy relaxation. Decomposition of a series of chemically activated fluoroalkyl cyclopropanes J. Phys. Chem. 78 2535 3... 

The dynamic mechanical properties of PTFE have been measured at frequencies from 0.033 to 90 Uz. Abmpt changes in the distribution of relaxation times are associated with the crystalline transitions at 19 and 30°C (75). The activation energies are 102.5 kj/mol (24.5 kcal/mol) below 19°C, 510.4 kJ/mol (122 kcal/mol) between the transitions, and 31.4 kJ/mol (7.5 kcal/mol) above 30°C. 

The y relaxation takes place at the lowest temperature, overlaps with the )3 relaxation (Fig. 15), and coincides in location and activation energy with the typical y relaxation of polyethylene [35,36], and also of polyethers [37], and polyesters [38] with three or more consecutive methylene units. It appears, for 3 Hz and tan6 basis, at - 120°C (P7MB) and - 126°C (P8MB), and its location and activation energy (35-45 kJ mol ) agree with the values of a similar relaxation associated with kink motions of polymethylenic sequences. 

On the contrary, the phase structure and the thermal history do not have important effects on the location and intensity of the /3 relaxation. This relaxation is very broad in all the samples and overlaps the y relaxation. The activation energy of the /3 peak is about 85 kJ mol for the three samples, of the same order of magnitude as that of other polyesters [38,40]. Finally, the y relaxation is found in the three samples of PTEB with no remarkable influence of the thermal history. 

The y relaxation appears around - 120°C (Fig. 19). PTEB and the copolyesters show the y maximum at a temperature that is practically constant, slightly lower than the one for P8MB. The low activation energy values (Table 3) are the usual ones for this relaxation. 

Table 3 Temperature Location (tan5 basis, 3 Hz) and Activation Energies of the /3 and y Relaxations for Different Samples with Varying Content in Oxyethylene Units (frEo)...

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 Equation 1, t is a thermal vibration frequency, U and P are, respectively activation energy and volume whereas c is a local stress. The physical significance and values for these parameters are discussed in Reference 1. Processes (a)-(c) are performed with the help of a Monte-Carlo procedure which, at regular short time intervals, also relaxes the entanglement network to its minimum energy configuration (for more details, see Reference 1). 

Fig. 17. High-spin low-spin relaxation of [Fe(ptz)j](BF4)2 a normalized relaxation curves at temperatures between 57.5 and 66.5 K b activation energy AE as a function of n. The solid line represents a simultaneous fit of the five experimental curves displayed under a. The broken line is the result of a linear regression determined by AE° = — 164 cm" = — 0.47 kcal mol" as slope and AE = 797 cm" = 2.28 kcal mol" as intercept. Notation in the figure uses yi, A instead of Hl,...

Figure 1. Effect of activation energy on width of relaxation process (AH > AH 2). 

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