Arrhenius-type relaxation activation energy

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... 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

An Arrhenius-type analysis of temperature dependence can be used to calculate the enthalpy and entropy of activation for the relaxation process. For liquid water, the enthalpy of activation is 19 kjmol-1, which corresponds approximately to the energy required to break one hydrogen bond. For ice, the equivalent enthalpy is 54 kj mol-1,... 

From an Arrhenius type plot like that of Fig. 2.82 the activation energies for these processes are obtained an the values are 14.6 and 57.0 kcal mol-1. these results give some idea about the differences in sizes of groups involved in the relaxation. 

The pre-exponential factor Df (or rf) is the diffusion constant (or correlation time) of a freely rotating methyl group and is given by an equation analogous to Eq. 21. A rigorous approach to this problem is to calculate activation energies from variable-temperature relaxation measurements, using an Arrhenius-type plot of D, (or tc i ) versus 1/T(K).67... 

The secondary f)-relaxation is also observed in a-chitin from 80 °C to the onset of thermal degradation ( 210°C). It exhibits a normal Arrhenius-type temperature dependence with activation energy of 113 3 kJ/mol. 

High Temperature Relaxation The high temperature relaxation arises at 80 °C until the onset of degradation 210 °C (Figs. 2.13a and b). It can be well described by the Arrhenius model and is present in both neutralized and nonneutralized CS. The slope of these curve represent the activation energy of each process. The temperature dependence of dc conductivity and relaxation time are Arrhenius type. For this relaxation, nonneutralized CS films seem to be more sensitive to water, since in the dry state... 

The well-known secondary a-relaxation often associated with proton mobility is also observed in CS (neutralized and nonneutralized) from 80 °C to the onset of degradation. On minimum moisture content conditions, this relaxation process could be noticed in the whole temperature range before the onset of thermal degradation. It is strongly affected by moisture content for dry samples by water effects, the activation energy shifts to lower values when compared to dry annealed samples. The nonneutralized CS showed an easier mobility in this ion motion process. This relaxation process exhibits a normal Arrhenius-type temperature dependence with activation energy of 80-90 kJ/mol. 

Figure 6 shows the master curves for the PS films with M of 4.9k and 140k drawn by horizontal and vertical shifts of each curve shown in Fig. 5 at the reference temperatures of 267 and 333 K, respectively [26]. The master curves obtained from the dependence of lateral force on the scanning rate were very similar to the lateral force-temperature curves, as shown in Fig. 3. Hence, it seems plausible as a general concept that the scanning rate dependence of the lateral force exhibits a peak in a glass-rubber transition. Also, it is clear that the time-temperature superposition principle, which is characteristic of bulk viscoelastic materials [35], can be applied to the surface relaxation process as well. Assuming that Uj has a functional form of Arrhenius type [36, 37], the apparent activation energy for the aa-relaxati(Mi process, A//, is given by ...

Pulsed NQR measurements of the spin-lattice relaxation time, T, also give detailed information on the mechanisms and dynamics of molecular motion in solids. For example, quadrupole relaxation times for solid triethylenediamine show a Ti minimum at a temperature close to 260 K. when 7j equals 0.048 On either side of the minimum, 7j depends exponentially on temperature, according to an Arrhenius-type equation with an activation energy of 34 kJ moP . The mechanism of the relaxation is shown to be hindered rotation of the triethylenediamine molecule about its threefold symmetry axis, which modulates the dipolar coupling between N and the adjacent CH2 protons. 

Thermal Activation Energies. The relaxation that occurs as the polymer passes from the glassy state to the elastomeric state can be described using an Arrhenius type equation. 

In this Section, the process of deformation, relaxation, and fracture are examined only within a restricted temperature range between the main 0 and a) relaxational transitions, Tp < T < T. The kinetics of creep, relaxation of stress and Young s modulus, and fracture are investigated experimentally as a function of the external stress applied to a sample and/or the increase in temperature. It is shown that the kinetics of the processes considered are described by Arrhenius-type equations. Then, the activation parameters (the energy and the volume) of the kinetic equations are calculated and compared with each other. This procedure demonstrates the identical physical nature of these processes. 

Partial master curves of 10 g.dL"l solutions of a,o)-alkaline earth dicarboxylato PBD in xylene at 297 K are reported in Figure 10, and result from a good frequency-temperature superposition of the experimental data.l7 Only the G" master curve of the solution of Be-based HTP is ill-defined due to the poor accuracy in the determination of the very small values of G". The shift factors support an apparent Arrhenius-type of dependence (Figure 11), from which the activation energy of the observed secondary ionic relaxation process was calculated and found to decrease as the radius of the alkaline earth cations increases (Figure 12). One also observes that the relaxation spectrum calculated by the first order approximation of Ninomiya and Ferry S is displaced along the time scale in relation with the cation size (Figure 13). The dynamic behavior of the 10 g.dL solution is obviously... 

Fig. 37 Activation energy Q vs characteristic glass transition temperature (Tg, Tg, T ) dependencies for the PDMS blocks in different types of block copolymers [25,26,128,129]. The hatched zone corresponds to the non-cooperative, Arrhenius relaxations at frequencies of ca. 10 Hz. The numbers 1-5 in the circles indicate the Q levels for cooperative, low-cooperative and non-cooperative segmental motion in PDMS blocks with different conformations and locations between rigid domains blocks), shown schematically below...

Thus the Arrhenius type of temperature dependence applies, but here the prediction that AHa is the same for all systems irrespective of molecular constitution is certainly incorrect. Among liquids far above their freezing (or vitrification) points, where the proportion of free volume is far higher (perhaps 0.3 instead of 0.03) the apparent activation energies vary widely and can be correlated with chemical structure. We must expect, then, the WLF equation to become inapplicable at high temperatures and the temperature dependence of relaxation processes to be governed by more specific features. 

---