Fundamentals of Impedance Spectral Analysis Applied to Determine Permittivity of Dielectric Particles

Abstract

It is demonstrated that the permittivity (dielectric constant) of powders suspended in suitable liquids can be determined by impedance spectroscopy techniques. A prior knowledge on the solids loading of particles in the slurry, the permittivity, and the electrical conductivity of the liquid is not required to determine the permittivity of particles by this technique. Some theoretical considerations of this method supported with experimental studies are described toward understanding of the physical phenomena involved with the characterization of slurries, which implemented to determine the permittivity of particulate materials.

Impedance Analysis of Dielectric Nanoparticles Enabled via a Self‐Assembled Monolayer

“…The complex impedance spectra ( Z ″ versus Z ′, where Z ′ and Z ″ are real and imaginary parts of the complex impedance) of pure, organic BOE solvent (ε ~ 10) contains only one semicircle associated with a Maxwell relaxation process in a “lossy” dielectric liquid (Fig. ) . The leakiness of the 99+% pure but not anhydrous BOE fluid, which had a measured resistivity, ρ ~ 83.4 kΩ·m, can be varied by the concentration of impurities such as water and/or soluble, dissociating salts .…”

“…Resistivity scaling or ρ‐scaling of the data, where Z ′ 1 = Z ′ × r , Z ″ 1 = Z ″ × r and frequency, f 1 = f / r where r = ρ 1 /ρ is the ratio of the resistivities, normalizes the impedance spectra by their solvent relaxations [Fig. (b)] and allows visualization of the effect of the SAM on the impedance spectrum of the particles without influence of the solvent phase . Table values calculated from the impedance spectrum showed that minimal changes resulted in the fitted and calculated equivalent circuit resistivity, capacitance, and calculated permittivity values, respectively, as a result of the scaling process.…”

“…The accuracy and the limitations of the above described methodology have been discussed in our previous investigations . A selected list from those investigations are: particle size in itself does not influence the spectra, although particle properties are size dependent; it is desirable to have the solids loading as high as possible for greater particle signal but which is limited by percolation threshold that influences dispersion quality, including the presence of air voids and particle gravimetric settling; and, DC conductivity of the host liquid should be adjusted to have both semicircles, i.e., of the low‐ and high‐frequency relaxations for particle and host liquid components, respectively, to be within the range of equipment used, in our case from 1 Hz–1 MHz.…”

“…We have applied impedance spectroscopy techniques to measure the relative permittivity (ε r ) of ceramic particles using a slurry approach where particles to be characterized are suspended in a Maxwell liquid. The particles dielectric properties are then extracted from low‐frequency spectra using equivalent circuit models …”

The Importance of the Solids Loading on Confirming the Dielectric Nanosize Dependence of BaTiO3Powders by Slurry Method

“…So it is very difficult to obtain the exact critical size of BaTiO 3 by means of using traditional solid-state pellet technique. Recently, the dielectric evaluation of ceramic slurries as an in situ method has been of primary interest [6, 7]. However, the slurry method presented that the permittivity of BaTiO 3 powders keeps basically constant when the particle size is above 200 nm [8].…”