Broadband Complex Permittivity and Electric Modulus Spectra for Dielectric Materials Research

Measurement of the complex permittivity of a substance in a wide frequency range, for example, from 10 mHz to 100 kHz, provides useful information on the dielectric properties of the substance. In this regard, some of such dielectric properties can be analyzed more clearly if we pay attention to the frequency spectra of electric modulus, which is a reciprocal of complex relative permittivity. Especially, the imaginary part of the electric modulus can be a powerful tool for dielectric materials research. In this paper, this fact is demonstrated clearly by showing abundant examples acquired by the author's laboratory. First, the equations of electric modulus that hold for various dielectric relaxation processes, including their derivation, are shown in an easy-to-understand manner. After that, for several insulating polymers, actual measurement examples of broadband complex permittivity spectra are shown, up to frequencies of about 100 kHz and a much broader range up to several THz. In the first example of showing permittivity spectra, polyamide exhibits an incredibly high relative permittivity value of 10⁶ at high temperatures such as 200 °C at a frequency as low as 10 mHz. This is a result of the phenomenon often called electrode polarization. In other words, if electric charge carriers accumulate in an insulator facing a nearby electrode and have the polarity opposite to that of the electrode, the permittivity of the insulator goes up. In such a case, the dielectric loss factor usually shows a very high value in the low-frequency range and decreases in inverse proportion to the frequency. This reflects the fact that the charge carriers are transported, and the conductivity can be derived from this frequency dependence much more easily with apparently higher reliability than measuring the dc leakage current. Furthermore, it is shown that the coefficient of thermal expansion can be estimated from the permittivity spectra relatively accurately for several polymers that satisfy the necessary condition. Next, taking examples in electric modulus spectra measured in important insulating polymers such as engineering ones, it is demonstrated that the processes of dielectric polarization and relaxation, which are difficult to see in permittivity spectra, can be recognized obviously. Moreover, the effects of the addition of nanosized or microsized fillers to epoxy resin on its thermal property and filler-induced inhomogeneity are analyzed using the electric modulus spectra measured in these samples. The effects of thermal aging treatment and simultaneous aging treatment with heat and radiation on the degradation of cross-linked polyethylene are also analyzed by paying attention to the frequency spectra of its imaginary electric modulus.