Comments on “Low Frequency Impedance Behavior of Montmorillonite Suspensions

Dudley et al. (2003) performed two-electrode impedance measurements on Naand Ca-saturated montmorillonite specimens (water content 10 000 g kg ) at frequencies between 100 Hz and 14 MHz. As noted by the authors, the main problem with this type of measurement system is electrode polarization. Klein and Santamarina (1997) developed a relationship for the frequency at which electrode polarization overwhelms the true material behavior using a simple circuit consisting of a capacitor (representing electrode polarization) in series with a capacitor and resistor in parallel (representing the specimen). This limiting frequency increases as the specimen conductivity increases. In the latter study, serious difficulties were encountered in attempting to accurately model and remove the effects of electrode polarization from low frequency, twoelectrode measurements. Dudley et al. (2003) presented impedance data for the montmorillonite specimens in several forms, and attempted to identify relaxations and associate these relaxations with doublelayer, Maxwell–Wagner, and electrode polarization. Figures 1 to 4 show data for deionized water performed with a twoelectrode system, in conjunction with a Hewlett-Packard 4192A impedance analyzer (Agilent Technologies, Palo Alto, CA) at frequencies between 5 Hz and 1 MHz. There are Fig. 1. Spectral response of deionized water: (top) real relative permany similarities between the montmorillonite plots and the mittivity and (bottom) effective conductivity eff. deionized water plots, even though deionized water does not experience double-layer or Maxwell–Wagner polarization. Electrode polarization in the deionized water specimen manifests as a large increase in real relative permittivity and decrease in effective conductivity ( eff dc ′′εo ) with decreasing frequency, as shown in Fig. 1. Similarly, the increase in Z and Z′′ with decreasing frequency at frequencies less than approximately 3 kHz suggests electrode polarization (Fig. 2). Electrode polarization is also evident in the impedance plane plot of Z vs. Z′′ at frequencies less than about 3 kHz (Fig. 3). Dudley et al. (2003) interpreted the low frequency part of their impedance plane plot (Fig. 2 from Dudley et al., 2003) as a straight line with a slope approximately equal to ; however, they present very few data points between 2 and 0.1 kHz. The deionized water data include frequencies as low as 5 Hz, and the figure shows that the low frequency part of the Fig. 2. Impedance spectra for deionized water. curve is not a straight line. The impedance plane plots of Z vs. Z′′ and M vs. M′′ for the deionized water specimen show a depressed semicircle, similar to the data for the montmorillonite specimens (Fig. 3 and 4). The impedance spectra for the montmorillonite specimens (Fig. 5 from Dudley et al., 2003) suggest a relaxation at frequencies greater than megahertz. A similar relaxation is evident for the deionized water impedance spectra, but it occurs at approximately 200 kHz (Fig. 2). Free water does not experience any polarization mechanisms at frequencies less than gigahertz (Hasted, 1973). The authors interpret the relaxations at 1 and 7 MHz for the Caand Na-saturated montmorillonite specimens as either Maxwell–Wagner polarization or double-layer polarization, depending on which model is used. Using time domain reflecFig. 3. Plot of the real Z vs. imaginary Z′′ components of the complex tometry (TDR) to perform dielectric permittivity measureimpedance for deionized water. ments on a Na–montmorillonite specimen (water content ≈ 7240 g kg ), Ishida et al. (2000) found a relaxation at f ≈ 10 MHz, which was attributed to bound or adsorbed water polarization. They also found another relaxation at f ≈ 1 MHz, 1 The complex modulus M* is the inverse of the complex relative permittivity * ε*/εo and is dimensionless. which was interpreted as being because of low frequency po-