Dielectric characterization of the water-matrix interaction in porous materials
by thermal depolarization spectroscopy
Anthony N. Papathanassiou and John Grammatikakis
University of Athens, Department of Physics, Section of Solid State Physics, Papepistimiopolis, GR15784 Zografos, Athens, Greece
Received 7 September 1999
We investigate the dielectric behavior of sandstone, which consists of a porous matrix with a small amount
of inherent humidity, by the thermal-stimulated depolarization current technique. Nine different relaxation
mechanisms are detected by the thermal sampling scheme, and are characterized. The activation energy dis-
tribution and the pre-exponential factor are obtained by analyzing the signals under the constraint of a normal
distribution in the activation energy. The drying of the specimen at elevated temperature under dynamic
vacuum affects some of the relaxation mechanisms. The model of freely rotating dipoles may not account for
all the drying-sensitive mechanisms. It is probable that water molecules are organized in a way that provide
either conductive layers over the surface of the grains or for conductive inclusions inside the bulk. Long-
distance charge-transport mechanisms are also affected by the removal of the humidity.
I. INTRODUCTION
During the last decade, there has been considerable inter-
est in the dielectric properties of multiphase porous materi-
als, which are either partially filled or saturated with
fluids.
1–7
Sandstone has been employed widely as the porous
matrix host material in such investigations.
1,3,5–7
It was ob-
served that the dielectric behavior of the multicomponent
rock-water system exhibits a polarization phenomenon
which is probably due to the electrochemical interaction of
the humidity with the grains’ surface. A dispersion, which
appears in the low-frequency region of the dielectric spec-
trum, is related to the humidity that coats the solid grains and
provides diffusion paths.
4,6,8
The current assertion is that this
low-frequency response is a ‘‘bulk’’ solid-liquid interfacial
phenomenon, rather than an electrode effect.
1
To the best of our knowledge, the vast majority of dielec-
tric experiments has been performed in the frequency do-
main. In this sense, the formulation of the complex dielectric
constant is employed: * = ' -i , where * , ' , and
denote the complex dielectric constant, and its real and
imaginary parts, respectively. Most researchers work with
' , so as to investigate the solid-liquid interaction
phenomena.
1,3,4,6,7
On the other hand, the imaginary part
of the dielectric constant, when plotted as a function of fre-
quency, may reveal relaxation mechanisms. Unfortunately,
despite the broad working frequency, the standard imped-
ance spectroscopy is a low-resolution technique, and is un-
able to resolve the spectrum to its constituting individual
relaxation mechanisms. Therefore it is hard to characterize
the particular dispersions i.e., to distinguish between dipole
rotation, interfacial polarization, or long-distance charge
transport and evaluate the relaxation parameters of each re-
sponse accurately.
In the present work, we employ the thermal-stimulated
depolarization current TSDC scheme, which operates in the
time domain and is equivalent to the low-frequency spectros-
copy. TSDC spectroscopy is capable of detecting very weak
responses and resolving different overlapping relaxations. It
also has the unique advantage of selectivity: the choice of
appropriate experimental conditions, in combination with the
elimination of the undesirable contributions, may yield the
detection of a particular single mechanism. Analyses of the
TSDC signals lead directly to an evaluation of the relaxation
parameters, which are the activation energy distribution and
the pre-exponential factor.
In the present work, the elementary responses, which are
responsible for the dielectric behavior of as-received sand-
stone, are identified. Characterization is attained by different
TSDC modes. The removal of the inherent humidity from
the pores’ network affects the dielectric spectrum, and there-
fore, the relationship between the specific types of relaxation
and different hydrophilic sites inside the porous material is
revealed. The distribution in the values of the relaxation pa-
rameters is obtained experimentally through different experi-
mental schemes and subsequent computer analyses. The ac-
tivation energy is related to the height of the potential barrier
that has to be overcome by the migrating free or bound
charges, the broadening parameter represents the perturba-
tion caused in the potential barriers, and the pre-exponential
factor
0
yields the migration entropy.
II. THEORY
The dielectric relaxation of an insulator originates from
the rotation of inherent permanent dipoles, the impedance of
free-charge carriers from obstacles existing in the matrix
i.e., dislocations, grain boundaries, interfaces separating the
conductive inclusions from the matrix and the non-Ohmic
sample-electrode interface, which leads to the space-charge
formation.
9
The dielectric relaxation is characterized by the
relaxation time . The temperature dependence of the relax-
ation time is usually described by an exponential Arrhenius
law
T =
0
exp
E
kT
1
where E denotes the activation energy,
0
is the pre-
exponential factor, and k is Boltzmann’s constant.
PHYSICAL REVIEW B 15 JUNE 2000-II VOLUME 61, NUMBER 24
PRB 61 0163-1829/2000/6124/165148/$15.00 16 514 ©2000 The American Physical Society