DiMarzio-Bishop model

Figure 3. Dipole centered in a sphere (represented by the arrow) surrounded by an environment with properties that depend on the model. In the case of the Debye model, the environment has a viscosity tj independent of time. In the DiMarzio-Bishop model the viscosity is a complex time-dependent viscosity = lit). In the Havriliak-Havriliak model the cavity is not spherical and the environment is taken to be represented by a complex tensile compliance D(

Figure 4. Plot of the elastic energy with time for various ellipse ratios. Included here is the electrostatic energy whose sign has been reversed. Complex plane plots calculated from the DIMarzio-Bishop model for various values of K (multiplied by lo ) listed in the legend.

The evidence presented in Section VI shows the importance of incorporating this strain energy term in the perturbation term of the Hamiltonian. In this work only the results of Eq. (46) were discussed for cases where the reaction field can represent long-range interactions. Although this equation was derived for the equilibrium case, the time dependence of the tensile (or shear) converts this into a time-dependent case. The agreement between the DiMarzio-Bishop model is also a verification of the basic assumption. Consequences of a fortuitous cancellation of terms in the denominator, that is, (eq -t- 2), due to the acceptance of the reaction field, was studied. 

The second work to be reviewed is that of DiMarzio and Bishop (D-B) who introduced a time-dependent viscosity into the hydrodynamic equations of Debye s model and then solved the hydrodynamic equations... 

In the case of DiMarzio and Bishop, they solved the hydrodynamic equations for the Debye model and the non-Newtonian case exactly. The important result of their analysis is that the dielectric response is no longer a Debye type but depends explicitly on how the local viscosity depends on time. In other words the nature of the viscoelastic properties surrounding the sphere determines the shape of the dielectric relaxation process. This result is in marked contrast to the results of the model... 

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