A complex plane representation of dielectric and mechanical relaxation processes in some polymers

In a previous paper it was shown that the complex dielectric constant data of polymers can be represented by an empirical dispersion function. In the present work it is shown that the complex polarization of the same data can be represented by a function of the same form but with different values for the constants. This means that a quantitative evaluation of Scaife's remarks can be made. The dispersion parameters for eighteen polymers were determined for the ϵ∗ (ω) or the ϱ∗ (ω) data. In general, as the ratio ϵ0≥∞ increases, the ϱ∗ (ω) data become broader and faster than the ϵ∗ (ω) data, thus 1 — α, β and τ0 decrease. The normalized loss maximum was found to be temperature dependent [ϵ∗ (ω) data] for eleven polymers where ϵ0≥∞≈2.0. However, the normalized loss maximum [ϵ∗ (ω) data] for the two acetates was found to be independent of temperature while the normalized loss maximum for the ϱ∗ (ω) behaved in a way similar to the other polymers. This observation can be traced to a fortuitous compensation of effects encountered with large dispersions. For those cases where the method of reduced variables is applicable ϵ∗ (ω) calculated from the dispersion function is in good agreement with the shifted values of ϵ∗ (ω). The two parameters α and β are shown to be uniquely related to distribution of relaxation times. The agreement between the distribution function calculated from the dispersion function is in good agreement with the approximate methods used to calculate the function from the shifted data. A complex plane plot of the complex compliance is not at all similar to the dielectric dispersions. An empirical transformation procedure is constructed by analogy with the one used to calculate the complex polarization in order to normalize the mechanical data. The locus of this complex deformation resembles the dielectric dispersion with nearly the same values of α, β and τ0. At very low frequencies, deviations from the assumed behaviour were observed. With polyisobutylene and poly(n-octyl methacrylate) the deviations were in terms of another dispersion. With poly(vinyl acetate) and poly(methyl acrylate) the deviations could be attributed to another low frequency dispersion. The similarity between the dielectric and mechanical dispersions suggests that the following mechanical model can be considered: a spherical inclusion containing the specimen of interest is perfectly bonded to an otherwise continuous homogeneous elastic continuum. Under these conditions the complex distortion of the sphere subjected to a periodic tensile field at infinity is very nearly the empirical complex deformation with Poisson's ratio of 12 for both media. It can also be shown for this model that if the distortion of the sphere is time dependent, then there will be in-phase and out-of-phase components to the distortion in a periodic field. In other words it is not necessary to postulate an internal viscosity to account for a macroscopic viscosity. The equilibrium distortion of the sphere is shown to be related to the square of the asymmetry of the orienting segments. The decay of the distortion with time of the removal of stress field is interpreted in terms of transition probabilities.