ORIGINAL RESEARCH PAPER

Effect of electrode contact impedance on A.C. electrical propertiesof a wet hematite sample

Mohamed Mahmoud Gomaa • Perparim Alikaj

Received: 17 January 2010 / Accepted: 6 July 2010 / Published online: 17 July 2010

� Springer Science+Business Media B.V. 2010

Abstract Electrode polarization is a major problem in the

determination of dielectric properties of samples, particu-

larly at low frequencies. Understanding of these interfacial

phenomena is essential in order to measure correctly the

electrical properties of a sample of interest. This paper

presents a comparative study of the effect of electrode

contact impedance on A.C. electrical properties of a par-

tially and fully saturated hematitic sandstone sample. The

electrical properties of the sample were first measured using

stainless steel electrodes with high contact impedance, and

measured again with a four terminal Cu–CuSO4 electrode

of low contact impedance. Complex impedance measure-

ments at room temperature (*16�C) were performed in the

frequency range from 1 Hz to 100 kHz. Measured electrical

spectra vary strongly with the electrode type. The difference

in the electrical properties between the two electrode types

(stainless steel and Cu–CuSO4) may be attributed to the

surface contact impedance between the sample and the

electrode. Experimental data indicate that the electrical

properties vary strongly with water saturation. The dielec-

tric constant decreases with frequency and increases with

saturation up to a certain saturation limit then decreases.

Charge transport can occur either through the bulk of the

solid matrix (hematite or sand) or along the grain bound-

aries of aggregates (water). When soil minerals are exposed

to water, exchangeable ions go into solution. Most of the

ionic or covalent bonded rock forming minerals such as

quartz, mica, and feldspars are nonconductors. When the

surfaces of these minerals come into contact with liquid

water, electrolytes are formed and ionic drift associated

with the electrical field causes electrical conduction. The

anomalous dielectric properties of partially saturated rocks

can be interpreted using percolation theory. This theory

predicts that when the conductive fraction (water) increases,

clustering of conductive inclusions develops, and the

thickness of insulating gaps between conductive clusters

decreases, causing a large increment in the capacitance of

the sample. Further increases in the conductive component

causes the shunting of insulating capacitive gaps.

Keywords Electrode effect � Electrical properties �Saturation � Hematitic sandstone � Complex impedance

Introduction

The measurement of A.C. electrical properties of humid

and saturated rocks (conductivity and dielectric constant) is

important in many applications, such as environmental

geophysics where resistivity measurements can be valuable

for investigation of shallow ground-water hydrology. In

marine geophysics the effect of water in the pores (quantity

and type) plays an important role in the determination of

the electrical properties of rocks and minerals in the Earth.

One of the problems with the measurement of A.C.

electrical properties is the contribution of electrode polar-

ization impedance, which is physically in series with the

bulk impedance of the sample. The kind of electrode used

and the method cause a ‘‘departure’’ of observed imped-

ance from the true impedance. Electrodes are widely used

as impedance probes and as current injection terminals.

M. M. Gomaa (&)

National Research Centre, Geophysical Sciences Department,

El-Tahrir St., Dokki 12311, Egypt

e-mail: mmmsgomaa@yahoo.com

P. Alikaj

Head of Geophysics Section, Department of Earth Sciences

at Polytechnic University of Tirana, Tirana, Albania

e-mail: alikajp@albmail.com

123

Mar Geophys Res (2009) 30:265–276

DOI 10.1007/s11001-010-9092-y

The effect of electrode polarization impedance is not well

characterized for different types of electrodes with differ-

ent types of samples with different water content. The

problem may be eliminated when a four-electrode

arrangement or non-polarizing electrode is used for

impedance measurements. However, the disadvantage of

such methods is the complicated measurement method.

The purpose of this paper is to show the effect of

electrode electric polarization on measured hematitic

sandstone impedance at different water saturations and

frequencies using non-polarizing metal electrodes and

polarizing stainless steel electrodes. The investigated

hematitic sandstone is a sample of the Nubian Sandstone

Formation composed of conglomerates, sandstones, sandy

shales, clays and quartzitic bands (Attia 1955; Shukri and

Ayouty 1959). The iron-ore bands are often associated with

ferruginous sandstones and clays. Transitions from ferru-

ginous sandstone to oolitic iron-ore are often encountered.

This geological material is supposed to be a multicompo-

nent system of sand/hematite/water/air, with an electrical

response dependent upon the texture of the individual

components (Knight and Abad 1995).

The A.C. electrical properties of any multicomponent

system (electrical conductivity and dielectric permittivity)

depend mostly upon the volume fraction and electrical

properties of each individual component, texture, the sur-

face charge density (De and Sharma 1991, 1992), the

particle size, the particle shape (Sen 1984), the conductor

volume content in the sand and the water saturation level in

the rock (De Lima 1995). In classical mixture formulas it is

assumed that the electrical responses of the individual

components do not change when the components are

combined as a mixture, i.e., there is no interaction between

the components (Sen 1981; Gomaa 2004). In the investi-

gated saturated hematitic sandstone, three of the compo-

nents (sand, hematite and water) interact strongly, so

affecting the electrical behavior of the mixture (Olhoeft

1985; Sen 1989). The nature of the rock/water chemical

and physical interaction is not completely understood, and

depends upon the composition of the solid surface. The

surfaces of many minerals will hydroxylate (introduces a

hydroxyl groups -OH) and hydrate in the presence of

water, leading to the development of a region of distinct

chemical and physical properties (Parks 1990).

The present study shows the importance of using non-

polarizing electrodes in measuring the A.C. electrical

properties of hematitic sandstone sample at different water

contents.

Polarization properties of electrodes

Kohlrausch and Holborn (1898) were probably the first to

recognize the effects of electrode polarization on

electrolyte conductivities. In order to reduce these effects

they covered platinum electrodes with a layer of Pt-black,

thereby reducing the electrode surface impedance by

orders of magnitude. They recognized that the electrode

surface impedance has a capacitive imaginary component.

Warburg (1899, 1901) represents the electrode surface

impedance (Zel) as a series combination of electrode resis-

tance (Rel) and electrode capacitance (Cel)

Zel ¼ Rel � j=xCel ð1Þ

with x = 2pf, being the angular frequency, f is the

frequency, j ¼ffiffiffiffiffiffiffi

�1p

. Warburg developed the first theory

for the electrode polarization phenomenon, based on

diffusion considerations. He stated that the electrode

surface polarization capacitance and resistance are both

proportional to f-0.5 and that the impedance has a

frequency independent phase angle of d = 45�. Fricke

(1972) formulated his extension of the Warburg law by

generalizing the phase angle

Cel � f�m; Rel � f� 1�mð Þ and d ¼ mp=2 ð2Þ

where d is the phase angle defined by tan d ¼ RelxCel,

m = constant. Fricke’s law was not based on physical

insight, but on a description of the available data and the

realization that a power function of either component must

yield the constant phase angle rule.

Schwan (1992) studied the polarization effects on highly

conductive samples (cell suspensions and tissues). In

studying the influence of the electrode on the sample he

found that values of tand for samples increase as the fre-

quency decreases, and that the resistive component of their

impedance dominates. Thus the effects of the electrode

polarization can be approximated by

R ¼ Rs þ Rel þ RsðRxCÞ2 ð3Þ

C ¼ Cs þ 1=x2R2Cel ð4Þ

Here, Cs and Rs are parallel sample capacitance and

resistance and Cel and Rel (Fig. 1) are series polarization

impedance capacitance and resistance, C and R the mea-

sured value of capacitance and resistance. The last two

terms of Eq. 3 are usually small compared to the first.

However, the second term of Eq. 4 can be large. Thus, the

effect of the electrode is usually more pronounced on the

capacitance than on the resistance.

Influence of sample on electrodes

Electrode impedance values are influenced by the con-

centrations of conductive and/or insulating particles in the

samples especially at low frequencies. Thus, the current

passing through the sample reaches only part of the elec-

trode surface because the insulated particles shield part of

266 Mar Geophys Res (2009) 30:265–276

123

it. This shielding effect is more pronounced the higher the

particle concentration, thus causing a decrease of the

polarization parameters with increasing volume fraction of

conducting particles or with increasing frequency. Schwan

(1992) showed that there is a deviation of the polarization

capacitance and conductance as a function of insulating

particle concentration from linearity which appears to

depend strongly on the degree of preparation of the elec-

trode surface (roughness).

Methods to correct for electrode effects

Schwan (1992) showed a group of techniques to correct for

the electrode effect in order to obtain true sample values.

The first technique assumes the validity of Fricke’s power

function and extrapolates the low-frequency behavior

where polarization dominates. Subtraction of the extrapo-

lated values from the measured data yields true sample

values. As the frequency decreases comparable numbers

are subtracted from each other, limiting accuracy. The

technique extends the range of correct sample values by

about a decade, provided that the electrode polarization

impedance does not change during the frequency run.

Another technique to reduce electrode artifacts involves

reducing the conductivity of the liquid surrounding the

samples of interest. This would correspondingly increase

R in Eq. 4 and decrease its last term (Schwan 1992).

Unfortunately changes in the medium’s fluid can affect the

sample properties. Furthermore, the electrolyte’s ion con-

centration was observed to influence polarization parame-

ters. At low concentrations, the polarization capacitance

Cel appears to decrease more rapidly with decreasing

concentration. Therefore, conducting particles in a weaker

electrolyte do not reduce the electrode effect on the sample

capacitance significantly, because the gain from increasing

the R-value in Eq. 3 is compensated by the decrease of the

polarization capacitance Cel.

The most elegant technique for eliminating electrode

artifacts uses different current and potential electrodes

(Schwan 1992). If the potential sensing electrodes are

connected to a very high impedance amplifier, no current

passes through them. Hence, no A.C. electrode polarization

potential can develop, because the polarization potential is

given by the product of the electrode impedance and current

through the electrode–electrolyte interface. Thus the

potential across the sample confined by the equipotential

surfaces connecting with the sensing electrodes is correctly

recorded. The current electrode impedances do not disturb

the sample impedance because they are part of the output

impedance of the current generator. Care must be taken that

no current enters or leaves the sensing electrodes. Difficul-

ties arise when stray field components are not well con-

trolled. This can lead to apparent relaxation effects, which

are not caused by the sample. Schwan (1992) suspected that

these are caused by capacitive components across the series

resistor, which is used in modern digital equipment to

measure the sample current.

The following methods may also be used to reduce or

eliminate the electrode polarization (Levitskaya and

Sternberg 1996a, b).

(1) Varying the distance between the electrodes: This

method consists of measuring the impedance of several

samples of different thicknesses. It is assumed that the

polarization impedance does not change and may be

excluded by calculation from these measurements. This

method is limited because the value of polarization

impedance changes when the distance becomes too large.

(2) Separate the sample from the electrodes with a

dielectric: This dielectric could be the air as a spacer,

or a dielectric film as a spacer. In the case of complex

resistivity measurements, dielectric spacers are not

appropriate because of their much higher impedance

compared to the rock sample. The measured impedance

value will be determined by the impedance of the

dielectric spacer rather than that of the sample. In

the presence of water, polarization takes place near the

spacer-rock interface, thus enhancing the polarization

errors (Scott et al. 1964).

(3) Errors can be reduced by using non-polarizable

electrodes, such as platinized platinum electrodes

Fig. 1 a Sample in contact with

electrodes, b Equivalent circuit.

The polarization impedance of

the electrodes (Zel) is in series

with the sample admittance (Ys),

c Circuit of observed total

admittance Y = 1/R ? jwC(copy from Schwan 1992)

Mar Geophys Res (2009) 30:265–276 267

123

that may also be applied in two-electrode measure-

ments (Levitskaya and Sternberg 1996a).

Experimental procedures

Laboratory measurements were made on a thin, disk-

shaped, hematitic sandstone sample with the following

dimensions: thickness 6 mm and diameter 38 mm. Data

were collected in the frequency range from 1 Hz up to

100 kHz using a Hioki 3522- 50 LCR Hitester Impedance

Analyzer connected to each of the two electrodes (non-

polarizable and stainless steel electrodes) shown in Figs. 2

and 3, as discussed below. The sample is mainly ferrugi-

nous sandstone (*55–60%) with hematite (*35–40%) in

addition to other minor elements (*5%). The grain size of

the sand in the sample is in the order of *60 micrometer

and the hematite is in the form of pigment (cementing the

sand grains). A voltage of 1 V was applied (small signal).

The current density in the sample is shown in Table 1.

Electrical properties of a material can be expressed in

either the series or parallel configuration. The measured

parameters are the parallel capacitance and conductance

(Cp and Gp) and the series impedance Z at different fre-

quencies. The complex relative dielectric constant can be

written as e� ¼ e0 � ie00, where the real part of the complex

relative dielectric constant e0 ¼ Cpd=e0A and the imaginary

part e00 ¼ Gpd=xe0A, where A is the cross-sectional area of

the sample, d is its thickness, e0 is the permittivity of free

space (8.85 9 10-12 F/m), and x is the angular frequency

(Gomaa and Elsayed 2009). The conductivity and dielectric

constant were calculated from the following equations:

r ¼ dGp=A

e0 ¼ Cp=C0

Co ¼ ðA=dÞe0

In the series mode, the complex impedance Z is

measured, Z = Rs - iXs, where Rs is the series resistance

(real impedance) and Xs = 1/xCs is the reactance, Cs is the

series capacitance.

The key point in the saturation of rock samples is to

remove the air from the pore space before the fresh water is

introduced. This was achieved by first evacuating each

sample in a desiccator for 24 h, and using the vacuum in

the desiccator to suck out the humidity from the sample,

following which distilled water is driven into the sample in

the absence of air.

Measurement was done while the sample was drying

(desaturation) using the sample holder shown in Fig. 2

(stainless steel electrodes). After the sample was dried

completely the same steps were repeated and measured

using the sample holder in Fig. 3 (non-polarizable

electrodes).

First, the sample was measured in atmospheric humidity

(*65%) in an isolated chamber (desiccator). The sample

weight dry was *14.1 g. The sample was fully saturated

by initially putting it in a pressure vessel, then evacuating

vessel from air, and finally allowing water to flow into the

vessel. The saturated weight was *15.45 g. Measure-

ments, on the fully saturated sample, were made quickly

after it was removed from the pressure vessel. Subsequent

measurements with the determination of weight were made

Fig. 2 The two electrode stainless steel system (Agilant dielectric

test fixture 16451B)

Fig. 3 The four CuSO4 non-polarizable electrode system

Table 1 Compared values of current density in the sample

Frequency (Hz) Current density

(lA/cm2)

Sample

condition

10 1.1E-03 Saturation

100000 1.2E-03 Saturation

10 4.1E-06 Dry

100000 6.5E-05 Dry

268 Mar Geophys Res (2009) 30:265–276

123

while the sample was allowed to dry. The saturation levels

were calculated as

WS ¼Swet � Sdry

Sdry

� �

� 100 ð5Þ

WVol ¼Swet � Sdry

Volume

� �

ð6Þ

where WS = water content by mass, Swet = Wet sample

weight, Sdry = Dry sample weight, Wvol = water content

by volume.

The porosity / of the sample (*23%) was calculated by

/ ¼Ssat � Sdry

� �

Volume� 100 ð7Þ

Ssat = Saturated sample weight.

Sample holders

In Fig. 2, the electrodes are made from stainless steel

(Agilant dielectric test fixture 16451B). The surface of the

sample is very smooth in order to provide a good electrical

connection between the electrodes and the sample. It is

known that there will be air between the sample and the

electrode, especially in the dry case. This is a two electrode

system, with electrodes measuring 37 mm in diameter.

Figure 3 shows a schematic diagram of the non-polar-

izing electrode sample holder. A and B are the current

electrodes (thin copper discs), and M and N are the

potential electrodes (two circular copper wires). The cur-

rent and potential electrodes are immersed in the agar/

copper sulphate compartment. This gel provides a good

electrical connection between the current/potential elec-

trodes and the sample. From electrochemistry it is known

that the copper metal immersed in its salt (copper sulphate)

presents a very low electrode potential. With respect to the

sample, this is a two electrode system (AM and NB), but in

practice the current and potential electrodes are separated

and located in a low resistivity CuSO4 gel, which markedly

lowers the electrode polarization at the metal electrolyte

interface. Any kind of regular or irregular (surface) sam-

ples can be measured with this system. This sample holder

is similar to the CTU-2 System sample holder produced by

Scintrex, in which cotton-coated copper wires moistened

with CuSO4 solution and rolled around the core samples

are used. The current electrodes are 5 cm in diameter and

the sample contacts with them through the cotton pads

moistened with CuSO4 solution (Alikaj 1989). The major

modifications of this system are to provide a better resis-

tivity contact between the electrodes and the sample by

replacing the cotton pads with CuSO4 solution simply with

CuSO4/agar gel. Being a rather solidified gel it cannot

penetrate the sample pores and so CuSO4/agar–agar gel

cannot alter the electrical properties of the sample with

time. This is crucial in our study.

Experimental results

Figures 4 and 5 show the complex impedance plane rep-

resentation of the sample with non-polarizable and stain-

less steel electrodes, respectively at different saturations.

For non-polarizable electrodes low saturations show a near

semicircle in the impedance plane and with the increase of

saturation this semicircle is contracted to a part of

depressed semicircle. Stainless steel electrodes show a

depressed part of a semicircle in addition to a small tail.

Figures 6 and 7 show the logarithmic real and imaginary

impedance, respectively versus saturation percentage for

the non-polarizable and stainless steel electrodes, respec-

tively at different frequencies (10, 20 and 100 Hz, 1, 10,

and 100 kHz). There is a general decrease of the real

and imaginary impedance with the increase of saturation.

Figures 8 and 9 show the variation of the dielectric con-

stant with frequency at different levels of saturation for the

non-polarizable and stainless steel electrodes, respectively.

For non-polarizable the dielectric constant increases with

the increase of saturation level up to a certain water con-

centration (*60%), after which the dielectric constant

decreases again. Also, with the increase of frequency the

dielectric constant decreases. For stainless steel electrodes

the dielectric constant increases with the increase of satu-

ration monotonically, with different rates. Also, with

increasing frequency the dielectric constant decreases

with two different slopes. Figures 10 and 11 show the (a)

dielectric constant and (b) conductivity versus saturation at

different frequencies for stainless steel and non-polarizable

electrodes, respectively. For non-polarizable electrodes

the dielectric constant increases up to a certain saturation

(at fixed frequency) then it decreases again with the increase

of saturation. For stainless steel electrodes the dielectric

constant fluctuates at low saturations, and then increases

sharply at relatively higher saturations then tends to saturate

at high water saturations. Figures 12 and 13 show the vari-

ation of conductivity with frequency at different levels of

saturation for the non-polarizable and stainless steel elec-

trodes, respectively. The conductivity level of each curve

compared to its analogous curve is higher in the non-

polarizable electrodes than in the stainless steel electrodes.

Interpretation and discussion

Generally, the increase of humidity or saturation increases

the conductivity and the dielectric constant (Gomaa 2006,

Mar Geophys Res (2009) 30:265–276 269

123

2008). De Lima and Sharma (1991, 1992) have shown that

the effective electrical properties of shaly sands (electrical

conductivity and dielectric permittivity) depend on the

charge density on the surface of the grain, which is in turn

dependent on grain size, the conductor volume content in

the sand, the effective conductivity and dielectric constant

of the interstitial electrolyte, the water saturation level in

the rock, and the frequency of the applied electrical field

(De Lima 1995).

With the increase of saturation the water forms some

layers on the grain surfaces and these layers increase as the

saturation increase. The initiative layers of water around

the surface are supposed to be more bound to the surface of

the grains compared to later layers. The properties of

adsorbed water differ significantly from those of the bulk

liquid. This means that the properties of adsorbed molecules

are intermediate between bulk water and ice (Hoekstra and

Doyle 1971; Knight and Endres 1990). There is a critical

saturation at which the water islands begin to contact with

each other, forming continuous paths of water between the

two electrodes. As saturation increases, more continuous

paths are formed between electrodes and more conductivity

values is added (Gomaa 2007, 2009).

Figure 4 shows the complex impedance plane represen-

tation of the sample with non-polarizable electrodes at dif-

ferent saturations. Figure 5 show the complex impedance

plane representation of the sample with stainless steel

electrodes at different saturations. Generally, for

non-polarizable electrodes low saturations show a near

semicircle in the impedance plane and with the increase of

saturation this semicircle is contracted to a part of depressed

semicircle, or to an arc of a depressed semicircle at the

higher saturations. As an example, Fig. 4a (10%) may be

compared with Fig. 5 (10%); the curve measured with the

non-polarizable electrodes (Fig. 4) shows a depressed

semicircle. In contrast, the curve measured with the stainless

steel electrodes (Fig. 5) shows a depressed part of a semi-

circle in addition to a small tail that may be due to impedance

electrode polarization effect (Warburg impedance).

The level of the impedance with the stainless steel

electrode is much higher than with the non-polarizable

electrodes. We note that at low frequencies the imaginary

part of the impedance decreases for the non-polarizing

electrodes, whereas it increases or attains large values for

the stainless steel electrodes. This is characteristic of the

Warburg impedance of electrode polarization. Also, at

different saturations the phase angle with stainless steel

electrodes is nearly constant and less than 45�, as charac-

terized by Fricke’s law (Eq. 2).

Generally with the increase of saturation in the two com-

pared groups of figures the peak frequency (the frequency at

(A)

(B)

(C)

Fig. 4 The complex impedance plane representation of the sample

for saturations 100% (empty square), 92% (diamond), 87% (asterisk),

84% (cross lines), 80% (triangle), 40% (empty circle), 35% (circlewith plus), 14% (square with diagonal lines), 10% (star with plus),

respectively (non-polarizable electrodes)

270 Mar Geophys Res (2009) 30:265–276

123

the top of the depressed semicircle) moves to higher fre-

quencies with increasing saturation. The decrease of the

impedance of the semicircle increases with increasing satu-

ration, i.e. the conductivity increase (Grant 1958). Such an

increase in real impedance due to increase of water saturation

is representative to the increase in continuous conductor

(hematite or water) paths in the sample.

Figure 6 shows the logarithm of the real and imaginary

parts of the impedance, respectively versus saturation

percentage for the non-polarizable electrode at different

frequencies (10, 20 and 100 Hz, 1, 10 and 100 kHz). Fig-

ure 7 shows the corresponding results for the stainless steel

electrode. There is a general decrease (with fluctuations) of

the real and imaginary impedance with the increase of

saturation.

Comparing Figs. 6a with 7a for the real impedance, we

note that the real impedance (at low saturation) of the

non-polarizable curves ranges from 102 to 3 9 104, while

the value of the real impedance of the stainless steel curves

ranges from 103 to 108. We also note that the imaginary

impedance (at low saturation) of the non-polarizable curves

(Figs. 6b and 7b) ranges from 103 to 104, while the value

of the imaginary impedance of the stainless steel curves

ranges from 104 to 3 9 107.

Figures 8 and 9 show the variation of the dielectric con-

stant with frequency at different levels of saturation for the

non-polarizable and stainless steel electrodes, respectively.

For non-polarizable electrodes (Figs. 8 and 10a), the

dielectric constant increases with the increase of saturation

(at a definite frequency) level up to a certain water concen-

tration (*60% that may be the percolation threshold), after

which the dielectric constant decreases again. For stainless

steel electrodes (Figs. 9 and 11a) the dielectric constant

increases with the increase of saturation (at a definite fre-

quency) monotonically, with different rates, even when it

reaches the full saturation. For non-polarizable electrodes

Re Z (Ohm)

0.0E+0

4.0E+7

8.0E+7

1.2E+8

1.6E+8

- Im

Z (

Oh

m)

+7 3.0E+7 4.0E+7

Re Z (Ohm)

0.0E+0

1.0E+7

2.0E+7

3.0E+7

4.0E+7

- Im

Z (

Oh

m)

Re Z (Ohm)

0.0E+0

1.0E+6

2.0E+6

3.0E+6

4.0E+6

- Im

Z (

Oh

m)

0.0E+0 4.0E+7 8.0E+7 1.2E+8 1.6E+8 0.0E+0 1.0E+7 2.0E

0.0E+0 1.0E+6 2.0E+6 3.0E+6 4.0E+6 0.0E+0 1.0E+5 2.0E+5 3.0E+5 4.0E+5 5.0E+5

Re Z (Ohm)

0.0E+0

1.0E+5

2.0E+5

3.0E+5

4.0E+5

5.0E+5

- Im

Z (

Oh

m)

(A) (B)

(C) (D)

Fig. 5 The complex impedance plane representation of the sample

for saturations 100% (empty square), 92% (diamond), 87% (asterisk),

84% (cross lines), 80% (triangle), 40% (circle with plus), 35% (empty

circle), 14% (square with diagonal lines), 10% (star with plus),

respectively (stainless steel electrodes)

Mar Geophys Res (2009) 30:265–276 271

123

(Figs. 8 and 10a), with the variation of frequency (at a certain

saturation) the dielectric constant decrease with the increase

of frequency. For stainless steel electrodes (Figs. 9 and 11a),

with the variation of frequency (at a certain saturation) the

dielectric constant decreases with increasing frequency

generally with two different slopes. The change in slope is

not definite at a certain frequency. That region (of change in

slope with frequency) ends at nearly 100 kHz for high sat-

urations and at &20 Hz for lower saturations (Fig. 9).

Generally, comparing Fig. 8 with 9, the change of

conductivity with frequency is small using the non-polar-

izable electrodes compared to the stainless steel electrodes

case. Figures 10 and 11 show the (a) dielectric constant and

(b) conductivity versus saturation at different frequencies

(10, 20 and 100 Hz, 1, 10 and 100 kHz) for non-polariz-

able and stainless steel electrodes, respectively. In

Fig. 10a, for non-polarizable electrodes the dielectric

constant decreases with increasing frequency. The

Saturation (%)1E+1

1E+2

1E+3

1E+4

1E+5

Re

Z (

Oh

m)

0 20 40 60 80 100

0 20 40 60 80 100

Saturation (%)1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

1E+4

Im Z

(O

hm

)

(A)

(B)

Fig. 6 The logarithmic real impedance and imaginary impedance

versus saturation percentage for the non-polarizable electrode at

frequencies of (empty square) 10 Hz, (diamond) 20 Hz, (asterisk)

100 Hz, (cross lines) 1 kHz, (triangle) 10 kHz, and (empty circle)

100 kHz

Saturation (%)1E+3

1E+4

1E+5

1E+6

1E+7

1E+8

Re

Z (

Oh

m)

0 20 40 60 80 100

0 20 40 60 80 100

Saturation (%)1E+3

1E+4

1E+5

1E+6

1E+7

1E+8

Im Z

(O

hm

)

(B)

(A)

Fig. 7 The logarithmic real and imaginary impedance versus satu-

ration percentage for the stainless steel electrode at frequencies

of (empty square) 10 Hz, (diamond) 20 Hz, (asterisk) 100 Hz,

(cross lines) 1 kHz, (triangle) 10 kHz, and (empty circle) 100 kHz

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Frequency (HZ)1E+2

1E+3

1E+4

1E+5

1E+6

1E+7

Die

lect

ric C

onst

ant

Fig. 8 The variation of the real part of the dielectric constant with

frequency for saturations 100% (empty square), 92% (diamond), 87%

(asterisk), 84% (cross lines), 80% (triangle), 40% (empty circle), 35%

(circle with plus), 14% (square with diagonal lines), 10% (star withplus), respectively (non-polarizable electrodes)

272 Mar Geophys Res (2009) 30:265–276

123

dielectric constant increases up to a certain saturation

(critical saturation) at definite frequency. This may be due

to the fact (Knight and Nur 1987) that the distances

between the grains decrease due to the increase of water

layers around grains. The distances between grains

decreases until the first conductor continuous path is

formed (*60%). The first conductor continuous path

between the electrodes is called the percolation threshold.

After that the dielectric constant decreases again with the

increase of saturation because of the shunt of the air gaps

between grains (Fig. 10a).

Figure 11a shows the dielectric constant versus satura-

tion at different frequencies (10, 20 and 100 Hz, 1, 10 and

100 kHz) for stainless steel electrodes. The dielectric

constant fluctuates at low saturations, and then increases

steeply. At high frequency (100 kHz) and low (10%) sat-

uration (stainless steel electrodes, Fig. 11a) the dielectric

constant shows a value on the order of 50. The dielectric

constant increases sharply at relatively higher saturations

(Fig. 11a) and tends to saturate at high water saturations.

Figure 10b shows the conductivity versus saturation at

different frequencies (10, 20 and 100 Hz, 1, 10 and

100 kHz) for non-polarizable electrodes. The conductivity

increases generally with the increase of saturation and there

is an abrupt increase in conductivity at *20–40% satura-

tion (compared to 60% for stainless steel electrodes,

Fig. 11b), which may be the critical percolation threshold.

The ideal percolation threshold for sphere particles is

33%. Fig. 11b shows the conductivity versus saturation at

different frequencies (10, 20 and 100 Hz, 1, 10 and

100 kHz) for stainless steel electrodes. The conductivity

also generally increases with saturation; the stainless steel

electrode impedance dominates the measured conductivity.

Figures 12 and 13 show the variation of conductivity

with frequency at different levels of saturations for the non-

polarizable and stainless steel electrodes, respectively. The

conductivity level of each curve compared to its analogous

curve is higher in the non-polarizable electrodes (Fig. 12)

than in the stainless steel electrodes (Fig. 13). For non-

polarizable electrodes (Fig. 12) the conductivity for 10 and

14% saturations shows two slopes separated nearly at

1 kHz. The first low frequency slope is nearly 0.1 while the

other high frequency slope is nearly 0.5. The other satu-

rations (35, 40, 80, 84, 87, 92 and 100%, Fig. 12) show

only one slope (nearly zero) with frequency. At high sat-

urations the impedances changes slightly with frequency

for the non-polarizing electrodes because of the higher

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Frequency (Hz)1E+1

1E+2

1E+3

1E+4

1E+5

1E+6D

iele

ctric

Con

stan

t

Fig. 9 The variation of the real part of the dielectric constant with

frequency for saturations 100% (empty square), 92% (diamond), 87%

(asterisk), 84% (cross lines), 80% (triangle), 40% (circle with plus),

35% (empty circle), 14% (square with diagonal lines), 10% (star withplus), respectively (stainless steel electrodes)

Saturation (%)1E+2

1E+3

1E+4

1E+5

1E+6

Die

lect

ric C

onst

ant

0 20 40 60 80 100

0 20 40 60 80 100

Saturation (%)1E-4

1E-3

1E-2

1E-1

Con

duct

ivity

(S

/m)

(A)

(B)

Fig. 10 The dielectric constant and the conductivity versus saturation

at frequencies (empty square) 10 Hz, (diamond) 20 Hz, (asterisk)

100 Hz, (cross lines) 1 kHz, (triangle) 10 kHz, and (empty circle)

100 kHz for non-polarizable electrodes

Mar Geophys Res (2009) 30:265–276 273

123

conductivity of water, whereas impedance has larger

variations with the polarizing (stainless steel) electrodes.

At low saturations and low frequencies, few continuous

paths exist, so that we can conclude that the conductivity is

low. At lo,w saturations and higher frequencies capaci-

tances of the insulated parts to attain lower impedances,

causing the conductivity to increase (Levitskaya and

Sternberg 2000; Knight 1983).

In addition, the knees (change of slope) in the curves

(10 and 14%, Fig. 12) move to higher frequencies with

increasing saturation. The change of the curve slope moves

to higher frequencies with increasing saturation. The value

of conductivity for the fully saturated curve (Fig. 12) is

very close to the conductivity value of hematite (10-2).

The increase of frequency at certain saturations motivates

particles to overcome barriers between energy levels to

form continuous conductor paths between the grains and

accordingly the conductivity increases. At a definite fre-

quency with increasing saturation (Figs. 12 and 13) grains

are covered with water that thus increases the opportunity

for forming conductor continuous paths between the elec-

trodes and accordingly with increasing saturation the con-

ductivity increases. The stainless steel electrode impedance

dominates the measured conductivity. At higher saturations

the water around grains forms continuous paths between

the electrodes, forming a percolation threshold (Jonscher

1999).

Now it may be concluded that in the non-polarizable

electrodes there is nearly no resistance from the electrode

interface (15 Ohm) and the current flows without any

Saturation (%)1E+1

1E+2

1E+3

1E+4

1E+5

Die

lect

ric C

onst

ant

0 20 40 60 80 100

0 20 40 60 80 100

Saturation (%)1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

Con

duct

ivity

(S

/m)

(B)

(A)

Fig. 11 The dielectric constant and conductivity versus saturation at

frequencies (empty square) 10 Hz, (diamond) 20 Hz, (asterisk)

100 Hz, (cross lines) 1 kHz, (triangle) 10 kHz, and (empty circle)

100 kHz for stainless steel electrodes

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Frequency (HZ)1E-4

1E-3

1E-2

1E-1

Con

duct

ivity

(S

/m)

Fig. 12 The variation of the conductivity with frequency for

saturations 100% (empty square), 92% (diamond), 87% (asterisk),

84% (cross lines), 80% (triangle), 40% (empty circle), 35% (circlewith plus), 14% (square with diagonal lines), 10% (star with plus),

respectively (non-polarizable electrodes)

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

FREQUENCY (Hz)1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2C

ondu

ctiv

ity (

S/m

)

Fig. 13 The variation of the conductivity with frequency for

saturations 100% (empty square), 92% (diamond), 87% (asterisk),

84% (cross lines), 80% (diamond), 40% (circle with plus), 35%

(empty circle), 14% (square with diagonal lines), 10% (star withplus), respectively (stainless steel electrodes)

274 Mar Geophys Res (2009) 30:265–276

123

impediment from the electrode. In the stainless steel elec-

trodes it is clear that there is a resistance and capacitance

that is added to the sample because of the electrode itself.

This resistance was responsible for the clear difference

between the similar curves in the non-polarizable and

stainless steel electrode measurements (Figs. 12 and 13).

Generally, comparing Fig. 12 with 13, the value of con-

ductivity at similar frequencies is high using the non-

polarizable electrodes compared to the stainless steel

electrodes case. Table 2 shows the comparable values of

the dielectric constant and conductivity for the stainless

steel and non-polarizable electrodes.

The physical mechanism of the polarization of adsorbed

layers may be either the orientational polarization of dipole

molecules of water or the transfer of charges (protons)

along hydroxilic groups or chains, so-called surface charge

transfer complexes (Pride 1994), or they may be due to

surface polarization. The gradual increase in the dielectric

constant with increasing humidity may be attributed to the

decrease of the air space distance between the grains that

behave as a capacitor, especially for low saturations. The

capacitance gradually increases as the humidity increases

(Jonscher 1999). The high dielectric constant demonstrates

that the water molecules are not tightly arranged around the

particles. When the adsorbed water begins to form a con-

tinuous path additional mechanisms are involved that

contribute to an increase in the dielectric constant, namely

the gigantic low frequency polarization (Chelidze and

Gueguen 1999; Chelidze et al. 1999).

The texture of samples changes from one material to

another, so that these curves may be changed from one

sample to another, even if they have the same concentration,

because the texture is not the same (Efros and Shklovskii

1976; Parkhomenko 1967).

Conclusions

The effects of water saturation on the electrical properties

of partially and fully saturated hematitic sandstone were

investigated over the frequency range from 1 Hz to

100 kHz. Experimental data indicate that the electrical

properties vary strongly with water saturations. A transition

from nearly normal to very high values of dielectric con-

stant is observed with decreasing frequency, depending on

the saturation. The dielectric constant is found to decrease

with frequency and increase with saturation up to a certain

saturation limit.

When soil minerals are exposed to water, exchangeable

ions go into solution and electrolytes are formed. Ionic drift

associated with the electrical field then causes electrical

conduction. The changes in the electrical properties caused

by saturation variation were attributed to the charge

transport in the liquid phase. The surface effect is to the

result of surface migration and diffusion of charges under

an applied field limited by a thin grain conducting surface;

this mechanism may be either the orientational polarization

of dipole molecules of water or the transfer of charges

(protons) along chains (surface charge transfer) or may be

driven by surface polarization.

High dielectric effects are caused by the polarization of

electric double layers on the solid–liquid interface at high

saturations, whereas polarization of bound charges at grain

surfaces produces relatively weak polarization because the

charges stop at the ends of the grains. Diffusion potentials

generated by the free exchange of ions between electrode

double layers and the adjoining electrolyte produce out-of-

phase currents, and hence large values of effective

dielectric constant. This model is known as gigantic low

frequency polarization model (GLFP); it can also be

applied to heterogeneously charged surfaces.

The anomalous dielectric properties of partially satu-

rated rocks can also be interpreted using percolation theory.

This theory predicts that, when the conductive fraction

(water) increases, clustering of conductive inclusions

develops, and the thickness of insulating gaps between

conductive clusters decreases, causing a large increase in

the capacitance of the sample. Further increases in the

conductive component cause the shunting of insulating

capacitive gaps.

Table 2 Values of the

dielectric constant and

conductivity for the stainless

steel and non-polarizable

electrodes

Nonpolarizable

electrode

Stainless steel

electrode

Dielectric constant low frequency low saturation (10%) 2 9 105 2 9 103

Dielectric constant low frequency full saturation 2 9 107 2 9 106

Dielectric constant high frequency low saturation (10%) 400 30

Dielectric constant high frequency full saturation 5 9 103 150

Conductivity low frequency low saturation (10%) 2 9 10-4 3 9 10-8 (sand)

Conductivity low frequency full saturation 9 9 10-2 3 9 10-5

Conductivity high frequency low saturation (10%) 2 9 10-3 1 9 10-5

Conductivity high frequency full saturation 10-1 (water) 10-3 (*water)

Mar Geophys Res (2009) 30:265–276 275

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For non-polarizable electrodes there is nearly no resis-

tance from the electrode interface and the current flows

smoothly. In the case of using stainless steel electrodes

there is a resistance and capacitance that is added to the

sample because of the electrode itself. This resistance is

responsible for the clear difference between the similar

curves between non-polarizable and stainless steel elec-

trode measurements.

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