Dielectric relaxation kinetic mechanisms

Electroreduction and electrooxidation of salene (7V,N -bis(salicylidene)-ethyledi-amine) complexes of cobalt and copper studied by Kapturkiewicz and Behr [147] in eight aprotic solvents obey these conditions. These authors were the first to demonstrate experimentally the significant influence of the dielectric relaxation time of solvents on the electrode kinetics. They found earlier [171] that the mechanism of electrode reactions of salene complexes is independent of the solvents applied. No correlation with the prediction of the Marcus theory was found, but the kinetic data correlated well with the viscosity of the solvents and their dielectric relaxation time. However, because the ohmic drop was not well compensated, their rate constants are likely to be too low, as was shown in DMSO by Lasia and coworkers [172]. 

It has to be mentioned that such equivalent circuits as circuits (Cl) or (C2) above, which can represent the kinetic behavior of electrode reactions in terms of the electrical response to a modulation or discontinuity of potential or current, do not necessarily uniquely represent this behavior that is other equivalent circuits with different arrangements and different values of the components can also represent the frequency-response behavior, especially for the cases of more complex multistep reactions, for example, as represented above in circuit (C2). In such cases, it is preferable to make a mathematical or numerical analysis of the frequency response, based on a supposed mechanism of the reaction and its kinetic equations. This was the basis of the important paper of Armstrong and Henderson (108) and later developments by Bai and Conway (113), and by McDonald (114) and MacDonald (115). In these cases, the real (Z ) and imaginary (Z") components of the overall impedance vector (Z) can be evaluated as a function of frequency and are often plotted against one another in a so-called complex-plane or Argand diagram (110). The procedures follow closely those developed earlier for the representation of dielectric relaxation and dielectric loss in dielectric materials and solutions [e.g., the Cole and Cole plots (116) ]. 

These considerations indicate that structural (X-ray analysis, and optical and electron microscopy), relaxation (mechanical and dielectric relaxation, NMR, and RTL), and thermodynamic (phase diagrams, thermodynamic cycles, RGC) methods of investigation are currently used to determine the limits of the mutual solubihfy of polymers. At the same time it must be noted that evaluation of polymer compatibility is complicated by kinetic factors and because thermodynamically unstable systems are formed in the course of mixing of polymer. The effects of the nature of the polymers and of foreign impurities on compatibility do not yield to a complete explanation and this problem is far from being solved, despite its importance in the fact that the problem of modifying the properties of polymeric material is related to evaluation of the compatibility of polymers. 

McCnun et al. (1967) have listed the various secondary relaxations observed in PMMA. The one that has been most widely studied is the p-relaxation of the COOCH3 ester side group. It has been studied extensively both by dielectric relaxation and by mechanical relaxation. We consider here only the latter mechanical relaxations, which are summarized in Fig. 5.10, where the relaxation information is plotted as either the temperature of the loss peak in dynamic experiments at constant frequency or as the frequency of the loss peak in experiments conducted at constant temperature. All results are plotted along the slanted P-line. The figure also shows on the left side a steep line that represents the a-relaxation. This should not have appeared on this kinetic plot, and its slope is too steep to show its characteristic curvature representing the WLF form of relaxation. It is included only to show the relative positions of the specific secondary relaxations against the a-relaxation. 

Kinetic information on the molecular conformational change can be extracted from dynamic mechanical studies, as described in Chapter 10, from the closely related acoustic relaxation experiments described in Chapter 11, and from dielectric relaxation covered in Chapter 12. In all of these, the observation of a transition in the frequency dependence of the property under study yields a relaxation time for the molecular process. This in turn transforms into the kinetics of the movement. Again, the activation energy associated with the conformational change is obtained from the effect of temperature on the relaxation time, using either the Arrhenius equation or a related analysis. 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

The models (26) and (27), used to explain the kinetics of chemical reaction rates, were also found to be very useful for other applications. Taking into account the relationship x 1 ik, these equations can describe the temperature dependence of the relaxation time x for dielectric or mechanical relaxations provided by the transition between the initial and final states separated by an energy barrier. 

In summary, a substantial number of possible motions exist for water molecules associated with proteinaceous materials at low temperatures. A very wide range of frequencies exists from a few Hz to a few GHz. A combination of studies, involving NMR measurements of the frequency dependence of relaxation rates and the dielectric and mechanical techniques described above, will be required to characterize and assign all these motions. Our present interpretation is that the water motions appear to reflect the total spectrum of kinetic events in the system. 

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