Broadband Complex Permittivity Spectra: Cole–Cole vs Circuit Models

Hydraulic properties such as porosity, water, and clay content can be inferred from electrical parameters like permittivity, conductivity, and resistivity. Spectral data enhance this analysis by revealing features such as pore size and clay type in wet particulate media. In liquid samples, electrode polarization is clearly observed, as orientational polarization occurs only at higher frequencies (MHz to sub-GHz). In contrast, particulate media exhibit electrode polarization artifacts that obscure spatial polarization peaks within the Hz-MHz range, especially in highly conductive materials like wet clayey soils, making the Cole-Cole model insufficient for distinguishing these effects. Therefore, a general circuit model using a parallel form of a resistor and a constant phase element configuration more effectively separates inherent material polarization from electrode polarization. The electrode polarization limiting frequency (<i>f</i> _EP) correlates with both material conductivity and electrode properties, even with low-polarization electrodes like Ag/AgCl. A novel method is introduced to estimate the effective constant phase element exponent ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>η</mml:mi> <mml:mo>~</mml:mo></mml:mover> </mml:math> ) using the slope of log permittivity vs log frequency. Finally, the chargeability of kaolinite (<i>m</i> = 0.83-0.86), derived from the ratio of critical frequencies between the Cole-Cole and Pelton models, aligns with its fundamental definition: <i>m</i> = (σ_∞ - σ₀)/σ_∞, where σ₀ is the DC conductivity and σ_∞ is the high-frequency conductivity.