Dielectric relaxation activation volume

In Figure 11.17 we show Arrhenius plots of the isobaric [t (7)]/> (F = 0.1 MPa) and isochoric [t (7)] v/ (vy = 20 to 30 mm /g) dielectric relaxation times of PMPhS, where the free volume Vf was obtained from the S-S equation of state. The slopes at the intersection of the isochoric and isobaric curves yield the respective activation enthalpies for ambient pressure. 

Fig. 2.16. Temperature dependences of the dielectric relaxation times for PVAc at atmospheric pressure ( ) and at a constant volume equal to 0.847 mlg (A), 0.849 ml ( ), and 0.852 ml g (V). The slopes at the intersection of the iso-baric and isochoric lines yield values for the respective activation energies at constant pressure and constant volume a = 238 and 448kJmol (r = 2.5 s) and = 166 and 293 kJ mol (r = 0.003 s). The ratio of the isochoric and isobaric activation energies is a measure of the relative contribution of thermal energy and volume that is, this ratio would be unity if the molecular motion were thermally activated, and zero if it were strictly dominated by density. For PVAc, the ratio is 0.6, indicating that both contributions are significant. From Roland and Casalini by permission [132].

The greater degree of freedom enjoyed by the 1-naphthyl label in P/VN is most likely ascribable to motion independent of the polymer chain about the bond of attachment. Since the vectors for absorption and emission are located within different planes within the molecular framework for triplet emission, such motions constitute a mechanism of enhanced depolarization for the P/VN system. In the case of PMMA it has been shown (H) that independent motion of a 1-VN label occurs in the vincinity of the relaxation of the polymer but is characterized by an apparent activation energy inferior to that sensed by an ester label or as afforded by dielectric and dynamic relaxation data for the g-process. Consequently whilst the onset of motion might be consistent with an increased degree of free volume released by the g-mechanism, the activation energy for naphthyl group reorientation within the lifetime of the excited states should not be equated with that of the g-process itself in PBA. 

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