Technical Physics, Vol. 46, No. 11, 2001, pp. 1473–1474. Translated from Zhurnal Tekhnichesko

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Fiziki, Vol. 71, No. 11, 2001, pp. 127–129.Original Russian Text Copyright © 2001 by Lunev, Nigmatullin, Zavidonov, Gusev, Manyurov.

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The Effect of Clay Morphology on Water RelaxationI. V. Lunev, R. R. Nigmatullin, A. Yu. Zavidonov, Yu. A. Gusev, and I. R. Manyurov

Kazan State University, ul. Lenina 18, Kazan, 420008 Tatarstan, Russiae-mail: Ivan.Lounev@ksu.ru

Received October 27, 2000

Abstract—The frequency dependence of the permittivity of water in calcium kaolinite (clay) is measured. It isshown that two mechanisms contribute to dipole relaxation of water. One refers to water in the free volume ofpores in the clay. The other is associated with bound water covering the porous surface. Experimental data aretreated in terms of a fractal model of the medium. The frequency dependence of the permittivity in a wide rangeof water content in the clay is accounted for theoretically. © 2001 MAIK “Nauka/Interperiodica”.

The physical effects observed when water interactswith clay materials play a decisive role in constructionengineering, geodesy, oil-extracting industry, and otherbranches of the industry. Information on the interactionbetween near-surface water molecules and the molecu-lar structure of alumina is of crucial importance. Water-saturated clays containing a great amount of boundH2O are widely used in construction engineering. Theeffect of clay saturation by large amounts of water isalso exploited in many domains of technology. Yet,clay–water interaction at the molecular and mesoscopiclevels has been poorly understood.

Dielectric spectroscopy [1] provides importantinformation on water–alumina interaction at the meso-scopic level. We obtained the low-frequency spectra inthe clay–water system for different H2O concentrations(12, 33, 52, 75, and 92%) at 22°C. Clay (calciumkaolinite) was made in the Laboratory of Disperse Sys-tems (Kiev, Ukraine) headed by academicianOvcharenko [2]. For measurements, a 0.2-mm-thickpellet made by pressing was placed in a vacuum cham-ber preevacuated for 48 h. Saturation by water was car-ried out in a desiccator arranged over saturated saltsolutions for 48 h. The measurements were performedwith the Shlumberger low-frequency dielectric spec-trometer in the frequency range of 10–4–105 Hz using adouble-electrode titanium measuring cell with an innerdiameter of 30 mm. The temperature of the cell wasthermostatically controlled with an accuracy of±0.1°C.

Figure 1 shows the frequency dependence of theimaginary part of the permittivity. These data will beinterpreted within a model of fractal medium [3]. In thismodel, a conducting medium (water) filling pores inclay is described in terms of recap (resistance + capac-itance) elements. A recap is a self-similar RC network(Fig. 2) comprising Foster circuits [3]. To produce arecap with an impedance in the form Z(jω) = Cν(jω)–ν

1063-7842/01/4611- $21.00 © 21473

(0 ≤ ν ≤ 1), the components of a self-similar RC net-work must obey the relationships

where a and b are frequency-independent constants.Below, we will show that clay contains bound water

and water filling the free volume. Hence, the equivalentcircuit of the medium can be represented as two paral-lel-connected recaps (Fig. 3). The conductivity of theresulting recap is given by [3]

(1)

where C1, C2, n, and m are constants.These constants depend on the ratio lna/lnb and

define the self-similarity (fractality) of the medium. To

Rn

Rn 1+----------- a,

Cn

Cn 1+------------ b,= =

G ω( ) C1 jω( )n C2 jω( )m,+=

–12

–14–2

logε''

log f

–10

–8

–6

0 2 4

Fig. 1. Imaginary part of the permittivity vs. frequency fora water content of (s) 92, (d) 75, (h) 53, (j) 33, and(e) 12%. Continuous curves are obtained analytically.

001 MAIK “Nauka/Interperiodica”

1474

LUNEV

et al

.

calculate these parameters, a detailed fractal model isneeded (in this work, it is omitted). Therefore, we willcalculate them by approximating the experimental datawith theoretical formulas using the least squaresmethod (the first approximation). Following the fre-quency dependence of the imaginary part of the permit-tivity ε'' (Fig. 1), we relate the conductivity G(ω) andε''(ω) as

(2)ε'' ω( ) RejG ω( )G0ω

---------------- ,–=

R1

Rn

Rn+1 Cn+1

Cn

C1

Fig. 2. Recap element formed by self-similar Foster cir-cuits.

I

II

Fig. 3. Equivalent circuit of the clay–water system. I, boundwater; II, water in the free volume.

0.2

0 20

1 – n, 1 – m

H2O, %40 60 80 100

0.4

0.6

0.8

1.0

Fig. 4. Exponents (s) 1 – n and (d) 1 – m vs. water contentin the sample.

where C0 is the capacitance of a spectrometer cell.

In view of formulas (1) and (2), the expression forε''(ω) can be written as

(3)

where

Here, f is the linear frequency in hertz (ω = 2πf). Usingthe least squares method, we found the parameters A, B,1 – n, and 1 – m, approximating the experimental databy formula (3). As follows from Fig. 1, our theory ade-quately approximates the experimental data. Figure 4shows the exponents 1 – n and 1 – m vs. humidity. If thehumidity exceeds 33%, the exponents 1 – n and 1 – mare almost humidity-independent within the experi-mental error and the accuracy of the least squaresmethod. Since in this range, 1 – n ≈ 1, the term A/f1 – n

in (3) corresponds to Debye relaxation. Consequently,this contribution should be assigned to water filling thefree volume. On the other hand, the exponent 1 – mnoticeably differs from 1 (1 – m ≈ 0.4). This implies thatthe contribution B/f1 – m in (3) is due to bound water, i.e.,to water covering the porous surface of the clay. Thefundamental difference between bound water and waterin the free volume has been noted in [2]. This differencestems from interaction between water and the poroussurface and from the fractal properties of the pores[3, 4]. At a humidity of 12%, the exponent 1 – n sharplydrops, while 1 – m changes insignificantly (Fig. 4). Wetherefore can assume that water is almost entirely in thebound state at this value of the humidity.

Thus, from our experimental data, it follows that thefrequency dependence of the permittivity of a saturat-ing fluid is significantly affected by the fractal geome-try of the pores.

REFERENCES

1. M. Shahidi, J. B. Hasted, and A. K. Jonsher, Nature 258,595 (1975).

2. F. D. Ovcharenko, Hydrophily of Clays and Clay Miner-als (Akad. Nauk USSR, Kiev, 1961).

3. A. Mehaute, R. R. Nigmatullin, and L. Nivanen, Flechesdu temps et geometrie fractale (Hermes, Paris, 1998).

4. Yu. D. Feldman, R. R. Nigmatullin, and E. Polygalov,Phys. Rev. E 58, 7561 (1998).

Translated by V. Isaakyan

ε'' f( ) A

f 1 n–-----------

B

f 1 m–------------,+=

AC1

C0------ πn/2( )exp

2π( )1 n–--------------------------, B

C2

C0------ πn/2( )cos

2π( )1 m–-------------------------.= =

TECHNICAL PHYSICS Vol. 46 No. 11 2001