Dielectric spectroscopy as a tool for the detection of 
contamination in sandstone 

Vassilis Saltas
Department of Natural Resources and Environment
Technological Educational Institute of Crete – Branch of Chania
Romanou 3 Str, Chalepa, 73 133 – Chania, GREECE
http://www.chania.teicrete.gr

Abstract: - In the present work we study the dielectric permittivity and electrical conductivity of contaminated sandstone samples, in order to investigate a possible application to the detection and quantification of subsurface contamination. Experimental results in the frequency range of 10mHz to 1MHz on various concentrations of leachates-impregnated samples suggest that the dielectric properties are mainly controlled of those of pore fluid. Different relaxation mechanisms have been observed, due to the interaction of bound water with the pollutants and the solid surface. The low frequency range of the dielectric and conductivity spectra may serve to distinguish between different concentrations of contaminations in solid-fluid systems.

Key-Words: - dielectric permittivity, electrical conductivity, porous materials, contamination, sandstone, leachates.

1   Introduction
During the last years there has been considerable interest in the development of efficient methods for the detection of subsurface contamination and monitoring pollution in the field. For example, dense or light non-aqueous phase liquids (LNAPL and DNAPL) comprise pollution problems at landfill and buried waste areas, since they are hard to locate and remove. Traditional methods of characterizing the contaminated groundwater and soils involve sampling and laboratory chemical analyses, which are costly and time-consuming processes. In addition, the risk of samples contamination during sampling, transportation and analysis is always substantial. However, if the sampling is continuous with time, in order to monitor the diffusion and spreading of contamination, an inexpensive method must be used, enabling preliminary inspection for chemical changes in the measured samples, related with the pollutants.
Dielectric spectroscopy has been proposed by many researchers as a promising tool and experiments have been carried out to establish the sufficiency of this technique to identify subsurface contamination and its sensitivity to different kinds and concentrations of organic or inorganic pollutants [1-4].
The present work is intended to investigate whether dielectric spectroscopy can be used to detect contamination, which may appear in a natural porous material, due to the spreading of pollution. For this purpose, a local sandstone was selected as a representative silicate porous material of high porosity. Dielectric properties of porous materials, such as sandstones, have been widely investigated during the last decades, and various models have been proposed by several researchers [5-7]. AC conductivity is extremely sensitive to physical parameters like temperature and pressure, the chemical composition of the solid and liquid phases, and microstructural factors like porosity [5,6,8,9]. It is important to mention that although rocks are characterised by their low or high porosity the existing ac conductivity mechanisms depend determinately on the water content of the specimen [10-12]. 
Leachates from a landfill were used to contaminate the sandstone samples. Due to the high porosity of the samples, the pollutants may settle to the pores of the material resulting probably to detectable divergences of the dielectric dispersion in comparison to the uncontaminated samples. 

2   Experimental Setup    
2.1	Dielectric Spectroscopy technique
Dielectric spectroscopy is based on the interaction of an alternating electric field with the material under test. The relative permittivity or dielectric constant, which is a measure of the response of the sample to the applied field, is a complex and frequency dependent parameter and provides information on the characteristics of the material. Its real part () represents the polarisability of the material, while the imaginary part () represents the energy losses due to polarization and ionic conduction. There are four main types of polarization mechanisms, namely electronic, atomic, orientation and interfacial or space charge polarization [13]. Each of these mechanisms dominates a certain frequency range with a characteristic resonant frequency or relaxation frequency. 
In the present study, dielectric and conducting measurements were performed by means of a high resolution broadband spectrometer (Novocontrol Alpha-N Analyzer) connected with a BDS 1200 sample holder. The sample material was mounted in a sample cell between two parallel electrodes forming a sample capacitor. The dielectric sample placed in the capacitor can be considered electrically equivalent to a capacitance C(ω) parallel connected with a resistance R(ω). These values are the output of the dielectric analyzer and are related to the real and imaginary part of the complex dielectric constant through the relations
			(1)

and

			(2)
where d is the distance between the electrodes, R is their radius, ω = 2πf and εο is the permittivity of the vacuum.
In the case of liquids or water-saturated porous media, the existence of free ions results in a DC conductivity. This conductivity manifests itself in the imaginary part of the relative dielectric constant

			(3)

where the exponential factor N in most cases is equal to 1. The specific conductivity σ* is related to the dielectric constant by

			(4)

Good electromagnetic shielding was applied to the whole sample holder in order to avoid noise problems that are common at low frequencies. The frequency range of the applied field was between 10-2 Hz and 106 Hz.

2.2	Samples preparation
Samples of a local sandstone, with a porosity of 35%, were cut from a massive stone in a prismatic shape to fit between the electrodes of the sample Table 1. Physicochemical characteristics of the leachate liquid sample.

pH	8.40	
E.C. 	22.89 mS/cm	
Total Suspended Solids	3.3 mg/l	
Total coliforms	2.6x103 CFU/ml	
Nitrogen	3.320 mg/l	
Phosphor	24 mg/l	

cell. A leachate liquid sample was collected from a
 municipal landfill and was used to contaminate the sandstone samples. The physicochemical character-ristics of the leachates are summarized in Table 1.
The uncontaminated sandstone samples were impregnated in solutions of leachates of different concentrations (5%, 10%, 50%, 100% v/v) for 20 hours. Deionized water was used as a solvent. An uncontaminated sample remained for the same time in pure deionized water, in order to use it as a reference sample. Afterwards, the samples dried in air for 3 days and dielectric measurements were carried out in intervals of 1 day, in order to study the influence of water content to the contaminated sandstone samples. Finally, moisture was totally removed with mild heating of the samples at 40 oC for 1 day and the dielectric measurements were repeated again. 

3   Experimental results and discussion 
Although all forms of dielectric representation contain the same information, various relaxation effects should be more or less dominant, depending on the frequency range (high or low) that they appear and the type of representation. Thus, according to Eq. 3 and 4, in the dielectric loss spectra, the σDC contribution is weighted by an 1/ω factor, which masks the dielectric effects in the low frequency range. Similarly, in the conductivity spectra, the  contributions are weighted by a factor ω, and become dominant at high frequencies.
So, the, ,  formats as well as the loss tangent tan(δ)= , which is more sensitive to distinguish between different relaxation mechanisms, have been used for the evaluation of the experimental data.

3.1	Conductivity spectra
Fig. 1 shows the measured conductivity of the five samples as a function of frequency, after drying in  Fig 1: Conductivity spectra of leachates-impregnated sandstone samples at different concentrations, after drying in air for one day and after subsequent mild heating at 40 oC.

air for 24 hours and after subsequent mild heating at
40 oC. The solid line corresponds to the deionized water-impregnated sandstone sample.  The influence of water to the measured conductivity is very 
obvious in the whole frequency range, giving values between wet and dry samples that differ 4-5 orders of magnitude. Furthermore, considerable variations in conductivity are also observed in the spectra measured after 24h, for different concentrations of leachates. The results are quite different for dried samples, where at high frequencies we can hardly distinguish differences in contaminated samples. For both, pure and contaminated samples, the conductivity may be described with a power law function of frequency, as it is evident from the linear variation of  with frequency, in log-log representation. In this universal law, which has been suggested by Jonscher [6],

				(5)

the exponent n lies between 0 and 1. In the present case we found that n takes the value of 0.67 for pure sample and of 0.55±0.02 for contaminated samples. 

Fig. 2: Conductivity spectra of 100% leachates-impregnated sandstone sample, during drying. 

At low frequencies (below 10 Hz), an increase of
 concentration results in a considerable increase of conductivity. The variation in conductivity of the dry samples may be attributed to the different
amounts of contaminants, which settle to the pores of the porous sample, as well as the different type of bound water in each case, which can not desorb at such a low temperature. 
The dielectric and conductivity spectra measured after 48 h and 72 h days drying of the samples in air (not shown here), are almost identical for the same concentration, suggesting that the samples have reached an equilibrium state as far as the water content is concerned. The spectra of 50% and 100% leachates are also identical after 2 days drying in air, indicating the saturation of the pores with the water-pollutant complex. The latter is shown in Fig. 2, for a 100% leachates-impregnated sandstone sample.
In principle, fluid-bearing sandstone is a multicomponent fluid-solid system of considerable complexity. It can be considered as a polycrystalline matrix with a system of pores, which may contain free and bound water, impurities and air. Each of these components contributes to the electrical properties of the material via different physical mechanisms. In addition, surface contributions due to solid-liquid interface and clustering effects have to be taken into consideration for the determination of the electrical properties [14]. 
Previous investigations on partially filled or saturated with fluid sandstone exhibit polarization phenomena which are probably due to the electrochemical interaction of humidity with the grains surface. A dispersion, which appears in the low frequency region, has been related to the humidity that coats the solid grains and provides diffusion paths, thus, suggesting a solid-liquid interfacial phenomenon rather than an electrode effect [7, 15]. 

3.2	Dielectric spectra
The real and imaginary part of the dielectric constant of the five dried samples, are shown in Fig. 3 and 4, respectively. The limit of  at high frequencies is the same for all the measured dried samples (ε∞  ~  4),  indicative  of  sandstone samples.
However, ε∞ increases at ~ 35, for the sandstone 
samples partially filled of saturated with leachates, as they measured after one day drying (not shown here). Taking into account that the dielectric constant of pure water is about 80 in the MHz range, we may conclude that the contribution of free water is dominant at high water-contents. In the medium frequency range (1Hz to 1kHz) the evolution in  of the contaminated samples deviates from that of 

Fig. 3: Real part of dielectric permittivity of dried (at 40 oC) sandstone samples at different leachates’ concentrations, as a function of frequency.

the pure sample but it does seem to be very sensitive to different concentrations of leachates. However, at low frequencies (below 10-1Hz)  increases considerably, especially at high concentrations. This behavior is also observed in the imaginary part of dielectric constant (Figure 4) and may be attributed to the increase of conductivity due to higher concentrations of leachates, in consistency with the curves of Fig. 1. The universal power law of Jonscher may also be applied in this low frequency range with an exponential factor close to unity. The leachates samples can mainly be considered as an electrolytic solution with ions of different strengths and mobility. Apparently, at low frequencies, ions start to move resulting in an increase in the system conductivity, which contributes to ε* according to Fig 4: Dielectric loss spectra of dried sandstone samples at different leachates’ concentrations, as a function of frequency.

Eq. 3. Loss peaks are observed around 10Hz (Fig. 4) 
for low concentrations of leachates, while at higher concentrations they are screened by the
conductivity contribution to dielectric losses. However, these loss peaks are more pronounced in the tan(δ) representation of the dielectric spectra (Fig. 5), and vary with the  concentration  but  not clearly. At frequencies below 1Hz, possible relaxation mechanisms start to develop at higher leachates’ concentrations. The influence of water in water-saturated sands has been studied in the frequency range from 10-1 Hz to 106Hz by Louven et al., (2002) and by Rusiniak, (1998) but no loss peaks were observed [16, 17]. >From the above findings we may conclude that these relaxation mechanisms could be attributed to the interaction of the leachates with bound water and solid surface. The explanation for the high relaxation times is that the water

 Fig 5:  Loss tangent tan(δ) of sandstone samples at different leachates’ concentrations, as a function of frequency.
molecules are prevented from following a rapid alternating electric field, because of their different binding forces with the solid surface and
their interaction with the contaminants. These interactions may produce larger structures or clustering effects that will require a longer time to orient themselves in the direction of the applied electric field. 

4   Conclusions
In the present work dielectric and conductivity measurements were carried out in sandstone samples, partially filled or saturated with solutions of leachates, at different concentrations.
From the experimental results it can be concluded that although the role of water is dominant to the measured electrical conductivity, quantitative differences of two orders of magnitude are observed due to the different concentrations of leachates, in partially filled sandstone samples.
Low frequency measurements of dielectric permittivity in dried samples may reveal several relaxation mechanisms related to the interactions of contaminations with water and solid surface.
In the above findings, the knowledge of the characteristic signature of the relaxation mechanisms is important for the identification and quantification of contaminants’ concentration.

Acknowledgments
The author would like to thank Dr K. Maniadakis for performing the chemical analysis of the leachates and Professors D. Triantis, F. Vallianatos and P. Soupios for creative discussions on porous materials. This work is partially supported from the project Archimedes: "Support of Research Teams of Technological Educational Institute of Crete", sub-project 2.6.32 – MIS86455 entitled “Application of modern techniques in landfills” in the framework of the Operational Programme for Education and Initial Vocational Training.

References:
[1]	A. Kaya and H-Y. Fang, Identification of contaminated soils by dielectric constant and electrical conductivity, Journal of Environ-mental Engineering, Vol. 123 (2), 1997, pp. 169-177.
[2]	R. K. Rowe, J. Q. Shang and Y. Xie, Complex permittivity measurement system for detecting soil contamination, Can. Geotech. J., Vol. 38, 2001, pp. 498-506. 
[3]	J. Q. Shang, W. Ding, R. K. Rowe and L. Josic, Detecting heavy metal contamination in soil using complex permittivity and artificial neural networks, Can. Geotech. J., Vol. 41, 2004, pp. 1054-1067.
[4]	A. Kaya, Electrical spectroscopy of kaolin and bentonite slurries, Turk. J. Engin. Environ. Sci., Vol. 25, 2001, pp. 345-354.
[5]	T. L. Chelidze, Y. Gueguen and C. Ruffet, Electrical spectroscopy of porous rocks: a review-II. Experimental results and interpre-tation, Geophys. J. Int. Vol. 137, 1999, pp. 16-34.
[6]	A. K. Jonscher, Dielectric Relaxation in Solids, J. Phys. D: Appl. Phys., Vol. 32, 1999, pp. R57-R70.
[7]	A. N. Papathanassiou and J. Grammatikakis, Dielectric characterization of the water-matrix interaction in porous materials by thermal depolarization spectroscopy, Phys. Rev. B, Vol. 61, 2000, pp. 16514-16521.
[8]	D.  Triantis, C. Anastasiadis, , I. Stavrakas and  F. Vallianatos,  Dielectric characteristics of Marble rocks after the application of various stress modes before fracture, WSEAS Transactions on Systems, Vol. 3, 2004, pp. 102-107.
[9]	G. Nover, S. Heikamp and D. Freund, Electrical Impedance Spectroscopy Used as a Tool for the Detection of fractures in Rocks Samples Exposed to either Hydrostatic or Triaxial Pressure Conditions, Natural Hazards, Vol 21, 2000, pp. 317-330.
[10]	D. Triantis, I. Stavrakas, C. Anastasiadis, F. Vallianatos and S. Kershaw, Dielectric spectroscopy in crustal rocks: examples from Northeastern Sicily (Italy) and the gulf of Corinth (Greece), Proceedings 10th International Congress of the Geological Society of Greece, Vol. 4, 2004, pp. 493-497.
[11]	D. Triantis, C. Anastasiadis, I. Stavrakas and F. Vallianatos, Relaxation processes of stressed marble AC conductivity, International Confe-rence on NDT, 2003, pp. 252-257.
[12]	A. Kyritsis, M. Siakantari, A. Vassilikou-Dova, P. Pissis, P. Varotsos, Dielectric and electrical properties of polycrystalline rocks at various hydration levels, IEEE Trans. DEI, Vol. 7, 2000, pp. 493-497.
[13]	A. K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press Ltd, 1983.
[14]	T. L. Chelidze and Y. Gueguen, Electrical spectroscopy of porous rocks: a review-I. Theoretical models, Geophys. J. Int. Vol. 137, 1999, pp. 1-15.
[15]	B. Nettelblad and G.Niklasson, Effects of microgeometry on the permittivity of impregnated porous media, J. Phys.: Condens. Matter, Vol. 8, 1996, pp. 7049-7058.
[16]	I. Louven, R. Nigmatullin, A. Zavidonov, Y. Gusev, I. Manurov, S. Kaumov, R. Muslimov, Analysis of dielectric relaxation data in water-saturated sands and clays, Journal of Non-Crystalline Solids, Vol. 305, 2002, pp. 255-260.
[17]	L. Rusiniak, Dielectric constant of water in a porous rock medium, Phys. Chem. Earth, Vol. 23, 1998, pp. 1133-1139.