Relaxatory modes

Orientational polarization, as it is found in polar liquids, provides a good example for explaining the physical background of reversible retarded responses. First consider the natural state without a field. Here we have no polarization, and this arises from distributing the orientations of the polar units in the sample isotropically. If now an electric field is applied, the orientational distribution changes. Since dipole orientations in the field direction are preferred, the distribution function becomes anisotropic. As a consequence we find a non-vanishing value for the orientational polarization Por- 

For systems, where the coupling between the polar units is so weak that they can reorient largely independent from each other, Por can be calculated in simple manner. It then just emerges from the competition between the interaction energy of the dipoles with the electric field and the kinetic energy of the molecular rotation. The calculation is carried out in many textbooks of physical chemistry and the result reads, in an approximate form, 

What is the microscopic background of the retarded mechanical responses As we have learned, one can envisage a polymeric fluid as an ensemble of macromolecules which change between the various conformational states. The populations of the different states are determined by the laws of Boltzmann statistics. If a mechanical field is now applied, a change in the population numbers is induced. For example, consider a rubber to which a tensile stress is imposed. Clearly, now preferred are all conformations which are accompanied by an extension along the direction of stress. The repopulation of the conformational states and the resulting increase in the sample length require a finite time, which must correspond to the time scale of the conformational transitions. 

What is the microscopic background of the retarded mechanical responses As we have learned, one can envisage a polymeric fluid as an ensemble of ma- 

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The two groups of relaxatory modes which lead in mechanical relaxation experiments to the a-transition and the final viscous flow also emerge in the dielectric response. Figure 5.17 presents, as a first example, the frequency dependencies of the real and imaginary part of the dielectric constant, obtained for poly(vinylacetate) (PVA) at the indicated temperatures. One observes a strong relaxation process. 

Fig. 5.19. Frequency- and temperature dependence of the dielectric loss in cis-PIP (M = 1.2 10 ), indicating the activity of two groups of relaxatory modes. Spectra obtained by Boese and Kremer [58]...

Zm denotes a normal coordinate , which determines the mode amplitude. Thermal excitations of modes, oscillatory modes as well as the relaxatory modes discussed here, depend on the associated change in free energy. For our bead-and-spring model, the change in free energy per polymer chain, A/p, is given by... 

The rates of conformational transitions of a chain encompass an enormously wide range. Local rearrangements including only a few adjacent monomers are usually rapid and take place with rates similar to those in ordinary liquids. Conformational changes of more extended sequences require much longer times. In particular, relaxatory modes associated with the chain... 

The two groups of relaxatory modes that in mechanical relaxation experiments lead to the a-transition and the final viscous fiow also emerge in the dielectric... 

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