Equation, Arrhenius macromolecules

The variation of tan 8a (referred to the polarizability a) as function of temperature is shown in Fig. 2.79. The activation energy value for this relaxation, calculated according to an Arrhenius equation for the five maxima, is 16kcal mol 1. This is a small value for a glass transition temperature, but not too much considering that in this case a small part of the macromolecule is activated from the dielectric point of view at higher temperatures than that of the p relaxation. 

The model assumes that when a segment of a macromolecule has to move to an adjacent site it must pass over an energy barrier represented as AE (see Fig. 14.13a). In the absence of stress, the segments of the polymer jump over the barrier infrequently, and they do so in random directions. The frequency with which the segments jump the barrier is represented by the Arrhenius equation,... 

In this paper, general principles of physical kinetics are used for the descnption of creep, relaxation of stress and Young s modulus, and fracture of a special group of polymers The rates of change of the mechanical properties as a function of temperature and time, for stressed or strained highly oriented polymers, is described by Arrhenius type equations The kinetics of the above-mentioned processes is found to be determined hy the probability of formation of excited chemical bonds in macromolecules. The statistics of certain modes of the fundamental vibrations of macromolecules influence the kinetics of their formation decisively If the quantum statistics of fundamental vibrations is taken into account, an Arrhenius type equation adequately describes the changes in the kinetics of deformation and fracture over a wide temperature range. Relaxation transitions m the polymers studied are explained by the substitution of classical statistics by quantum statistics of the fundamental vibrations. 

We outline briefly the physical basis of the Arrhenius equation as applied to atomic or molecular movements in a solid. All viscoelastic effects, including large strain effects (see Gtapter S), are due to thermally activated movements of segments of macromolecules under imposed mechanical stress. There is no question of the stress generating molecular movements which, in the absence of the stress, would not take place. What in fact occurs is that molecular movements or jumps occur spontaneous, and it is the function of the stress to bias them so that th no longer occur in random directions. This results in a molecular flux which leads to time-dependent mechanical strain. 

The relationship revealed between Q,g c< /3 and Q, is illustrated by Fig. 19 which confirms the assignment of a low-temperature -relaxation to the small-angle torsional vibrations of some molecular unit close in size to a repeat unit of macromolecule. Table 2 gives both experimental and calculated values ci the 5-transition temperature Tg using the Arrhenius equation 10 exp — Q/RI at V = 1 Hzandp,ar = /3. niese values are of the order of20-70 IQLe. in the temperature range typical for excess (super-E>ebye) specific heat and 5 loss peak observed in dynamic medianical measurements. 

Figure 11 (Left) Temperature dependence of the relaxation times for the different processes in PEMA (/I4=2.0 x lO g moE ). At higher tEmperatures, the process due to the ion motion (squares) and the (ap)-relaxation (circles) are shown, while at lower temperatures, the a- (up triangles) and p- (down triangles) processes are shown. The lines are fits to the VFT equation forthe slow, (ap)-, and a-processes, and to the Arrhenius equation forthe p-process. (Right) Apparent activation volume, Al/, as a function of temperature forthe a- (filled squares), the (ap)- (open up triangles), the p-(filled circles), and the ion mobility (filled down triangles) processes of PEMA. The horizontal line gives the repeat unit volume (14,=102 cm moE ). Erom Mpoukouvalas, K. Floudas, G. Williams, G. Macromolecules 2009, 42, 4690. ...

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