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Published in Soil Sci. Soc. Am. J. 68:1023-1024 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

COMMENTS & LETTERS TO THE EDITOR

Comments on "Low Frequency Impedance Behavior of Montmorillonite Suspensions

Polarization Mechanisms in the Low Frequency Domain"

Katherine Klein

Dep. of Civil Engineering, Univ. of Toronto Toronto, Canada M5S 1A4

klein{at}civ.utoronto.ca

Dudley et al. (2003) performed two-electrode impedance measurements on Na- and Ca-saturated montmorillonite specimens (water content = 10000 g kg–1) 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, two-electrode 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 double-layer, Maxwell–Wagner, and electrode polarization. Figures 1 to 4 show data for deionized water performed with a two-electrode 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 many similarities between the montmorillonite plots and the deionized water plots, even though deionized water does not experience double-layer or Maxwell–Wagner polarization.



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  		Fig. 1. Spectral response of deionized water: (top) real relative permittivity {kappa}' and (bottom) effective conductivity {sigma}eff.

 


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  		Fig. 4. Plot of the real M' vs. imaginary M'' components of the complex modulus for deionized water.

 


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  		Fig. 2. Impedance spectra for deionized water.

 


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  		Fig. 3. Plot of the real Z' vs. imaginary Z'' components of the complex impedance for deionized water.

 
Electrode polarization in the deionized water specimen manifests as a large increase in real relative permittivity {kappa}' and decrease in effective conductivity ({sigma}eff = {sigma}dc + {kappa}''{epsilon}o{omega}) 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 {omega}–1/2; 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 curve is not a straight line.

The impedance plane plots of Z' vs. Z'' and M' vs. M''1 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 Ca- and Na-saturated montmorillonite specimens as either Maxwell–Wagner polarization or double-layer polarization, depending on which model is used. Using time domain reflectometry (TDR) to perform dielectric permittivity measurements on a Na–montmorillonite specimen (water content {approx} 7240 g kg–1), Ishida et al. (2000) found a relaxation at f {approx} 10 MHz, which was attributed to bound or adsorbed water polarization. They also found another relaxation at f {approx} 1 MHz, which was interpreted as being because of low frequency polarization mechanisms such Maxwell–Wagner and double-layer polarization.

Two-electrode measurements are difficult to perform because of electrode polarization effects, which mask the true material behavior. The similarities between the various plots for the montmorillonite specimens and deionized water highlight the difficulties with data interpretation when this measurement technique is used.

NOTES

1 The complex modulus M* is the inverse of the complex relative permittivity {kappa}* = {epsilon}*/{epsilon}o and is dimensionless. Back

REFERENCES





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