Applied Clay Science 33 (2006) 278 – 286 www.elsevier.com/locate/clay
Estimating the fully developed diffuse double layer thickness from the bulk electrical conductivity in clay M.A. Mojid a,⁎, H. Cho b,1 a
Department of Irrigation and Water Management, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh b Department of Agricultural Sciences, Saga University, Saga 840-8502, Japan Received 8 December 2005; received in revised form 8 June 2006; accepted 14 June 2006 Available online 17 July 2006
Abstract The possibility of estimating the thickness (t) of the fully developed diffuse double layer (DDL) and the specific surface area (S) of clay from its bulk electrical conductivity (the composite electrical conductivity of the clay–water–air mixture), hereafter called the electrical conductivity and denoted by EC, was investigated. The assumption is that when a clay is wetted with distilled water, the fully developed DDLs around the clay particles create the maximum number of electrically conductive pathways that provide the highest electrical conductivity of the clay. This assumption was tested by measuring the electrical conductivity of 17 samples of different clays over a wide range of water content by time-domain reflectometry (TDR), and by using 2 relevant sets of data from the literature. Good agreement between the thicknesses of the DDLs estimated from the water content at fully developed DDLs, hereafter called the critical water content and denoted by w, and that calculated by the method of Schofield [Schofield, R.K., 1947. Calculation of surface areas from measurements of negative adsorption. Nature (London) 160, 408−410] for different samples proves the validity of our assumption. The critical water content being a direct function of the specific surface area of the clay and the thickness of the fully developed DDLs, provides a way of estimating any one of these two parameters when the other parameter is known. When the clay is wetted with salt solutions, the bulk electrical conductivity is governed by the electrical conductivity of both the DDLs as well as the salt solution outside the DDLs, and the above assumption does not hold true under such condition. © 2006 Elsevier B.V. All rights reserved. Keywords: Water content; Electrical conductivity; DDL thickness; Specific surface area
1. Introduction Clay particles being, usually, negatively charged are surface-active materials and many of their properties depend on the activity of boundary phenomena between the particles and water molecules. When suspended in ⁎ Corresponding author. Fax: +88 091 55810. E-mail addresses:
[email protected] (M.A. Mojid),
[email protected] (H. Cho). 1 Fax: +81 952 28 8709. 0169-1317/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.clay.2006.06.002
water, clay particles are surrounded by a hydrosphere of adsorbed water, which contains soluble cations of difcferent charges. These cations, called the exchangeable cations, balance the negative charges on the clay particles by forming diffuse double layer, DDL, and increase the electrical conductivity of the DDLs (Waxman and Smith, 1968; Mogi et al., 1986). The thickness of the DDLs is an important controlling factor for the structural development, hydraulic conductivity, and other physico-chemical and mechanical properties of soils (Fukue et al., 1999, 2001). The mechanical
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properties of cohesive soils depend on their water content, which is also a major function of clay content of the soils. The consistency of such soils defined by Atterberg Limits (Atterberg, 1911), such as the plastic limit and liquid limit, is a function of clay content of the soils (Sridharan et al., 1986, 2000). Clay also determines the adsorption capacity of soils and, thus, controls the retention of nutrients for plants as well as pollutants. Heavy clays, such as bentonites and sand–bentonite mixtures, are often used as buffer and backfill materials for repositories of high-level nuclear wastes (Komine, 2004). The buffer materials create a very low permeable zone around the radioactive wastes and keep them separate from the surrounding environment. The density of the buffer materials is kept such that they, on swelling, make an impermeable barrier. The appropriate degree of swelling of these materials is quantified by the thickness of the DDLs. However, it is the surface area of clay that determines the extent of most of its role in various properties of the soils. So, it is equally important to know the thickness of the DDLs and surface area of various soils for agricultural, engineering and environmental purposes. The surface area of a soil is usually expressed by the specific surface area, S, defined by the surface area per unit mass of the soil. Although significant advances have been realized in the field of soil characterization, thickness of the DDLs remains, in many respects, a theoretical concept. The specific surface area, on the other hand, remains as an operational concept, dependent upon both the measurement technique and sample preparation (Pennell, 2002). In addition to a large number of particles of different shapes and sizes arranged in various orientations in a soil, chemical pre-treatments and drying of the samples alter their composition and exerts considerable effects on the measured surface area. Two general experimental approaches, direct and indirect, are employed to estimate S. The direct approach, based on physical measurement, typically involves the use of electron microscopy or Xray diffraction techniques to determine the shapes and dimensions of individual soil particle from which S is calculated. This technique, although useful for pure clay samples and sands, is not applicable for natural soils due to the presence of metal oxides, organic matter and also for the specific surface area of natural soils not being a strict additive property due to their complex structural organization (Pennell, 2002). The indirect approach, such as gas-phase adsorption, liquid-phase adsorption, and retention of polar liquids, is based on measurements of the adsorption or retention of probe molecules on the soil mineral surface at monolayer coverage. Such experimental methods are strongly dependent on the nature
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and extent of interactions between the selected probe molecule and the soil mineral surface. Due to pretreatments of the samples and use of different probe molecules, different measurement techniques yield widely divergent values of specific surface area for the same soil (Greenland and Mott, 1978; Ong and Lion, 1991; Rhue et al., 1988; Call, 1957). Schofield (1947) developed a different method to determine the thickness of DDLs and the specific surface area, S, from cation: anion valence ratio, salt concentration of the wetting liquid, surface charge density, and cation exchange capacity (CEC) of soils. Although reliable, this method is, however, laborious, time consuming and expensive when intended to apply for a large number of soils. Banin and Amiel (1969) reported an empirical equation to estimate S from the clay content of the soils. The mineralogy of the clay, which has an enormous effect on S, was not considered in this method and hence it gives only a mere approximation. The thickness of DDLs around clay particles is governed by the concentration of salt and type of cation(s) in the soil water (Schofield, 1947; van Olphen, 1963). It also depends on the degree of expansion of the DDLs, which is controlled by soil–water content; the DDLs expand fully only in the abundance of water. In dry soils, the thickness of the DDLs is very small since the DDLs cannot expand fully, and most clay particles remain isolated resulting in discontinuous pathways for the flow of electrical current (Nye, 1979). The cloud of adsorbed ions in DDLs also becomes isolated by demineralized water (Shainberg and Levy, 1975). Increase in continuous pathways for the flow of electrical current, which occurs with increasing contact of clay particles with increasing water content, is related to the developmental stage of the DDLs. Since water is strongly attracted to the mineral surfaces of the clay, it may be assumed, as a first approximation, that when demineralized water is gradually added to clay, the entire quantity of water remains within the DDLs until they are expanded fully. This leads to the hypothesis that the total quantity of adsorbed water in clay, at the state of fully developed DDLs, is a function of the specific surface area of the clay particles. This study explores the possibility of determining the thickness of the DDLs in clay from the water content at the state of fully developed DDLs when the specific surface area is known, or to determine the specific surface area when the thickness of the DDLs is known. 2. Theoretical consideration The shape of clay particles in a soil varies (e.g., platy or flaky) depending on their mineral type. Assuming that all clay particles can be represented by a plate of
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length x, width y and thickness z, the volume and mass of a particle is given by xyz and ρρwxyz, respectively, where ρ is the specific gravity of the particle and ρw is the specific gravity of water. The specific surface area of the particle, S, is expressed from its geometry by
and the thickness of the fully developed DDL is expressed (from Eq. (4)) by
2ðxy þ yz þ zxÞ S¼ xyzqqw
It is noted that when the clay content of a soil is only a fraction of its mass, S represents the surface area of the fractional mass of the clay instead of the specific surface area of the soil. However, in soils with high clay content, S closely approximates their specific surface area since silt and sand particles have negligible surface area in comparison to that of the clay. Eqs. (1)–(5) are valid only when demineralized water is used as the wetting liquid for a clay. For water containing appreciable quantities of salt, the EC of the clay is governed by the electrical conductivity of water both within and outside the DDLs. Under this condition, the highest EC of the soil is not related to the thickness of the fully developed DDLs. Following Schofield (1947), the general equation for the thickness of the DDL, t, is given by
ð1Þ
On addition of a small quantity of demineralized water, an initially dry clay particle strongly attracts the water molecules and forms a DDL with the antecedent cations, that is, the cations that already existed in the clay. The DDL continues to expand with increasing water content and comes in contact with that of the adjacent clay particles resulting in the maximum number of continuous pathways for the flow of electrical current at full expansion of the DDLs. Because of the higher electrical conductivity of water in the DDLs (the surface conductivity) than their surrounding water (Waxman and Smith, 1968), the bulk electrical conductivity of the soil, EC, increases as more and more DDLs come in contact. Eventually, the highest EC is reached when the DDLs develop fully to their maximum thickness at certain water content, called the critical water content, w. Further increase in demineralized water in the clay starts isolating the DDLs from each other with a resultant decrease in electrical conductivity. The critical water content, w, is a function of the thickness of the fully developed DDLs and the surface area of the clay. As suggested by Dolinar (2002), the interaction forces between surfaces of different clay particles and adsorbed water may be assumed the same due to structural similarity of the particles. So, the thickness of adsorbed water is expected to be the same and the total quantity of this water is a direct function of the specific surface area, S, of the clay particles in a soil. Denoting the thickness of a fully developed DDL by t, the mass of water in the DDL is expressed by ½2ðx þ 2tÞðy þ 2tÞt þ 2ðx þ 2tÞzt þ 2yztqw
ð2Þ
The critical water content, w (mass of water per unit mass of clay and expressed as a percentage), is given by w¼
½2ðx þ 2tÞðy þ 2tÞt þ 2ðx þ 2tÞzt þ 2yztqw 100% xyzqqw ð3Þ
Simplifying Eq. (3) and neglecting the higher-order terms of t, which represent the thickness of the DDL at the corner edges of the particle, the critical water content is given by w ¼ Stqw
ð4Þ
t¼
w Sqw
q 4 t ¼ pffiffiffiffiffiffiffi − mbc mbu
ð5Þ
ð6Þ
where q is a factor that depends on the cation: anion valence ratio of the bulk solution (2 for NaCl, 1.46 for CaCl2), v is the valence of the cation, β is the DDL constant (1.08 × 1016 m molc− 1 at 20 °C), c is the concentration of salt in soil water, and φ is the density of surface charge on the clay (molc/m2). The second term on the r. h. s. of Eq. (6) is usually much smaller than the first term, especially at low concentration of salt in soil water, and so it can be ignored for a first approximation of t. It is now justified to assume that t in Eq. (5) is identical to t in Eq. (6) when the DDLs are fully developed in demineralized water. The specific surface area of the clay, S, is then expressed by S¼
pffiffiffiffiffiffiffi w mbc qw q
ð7Þ
3. Materials and methods This study was conducted by measuring the bulk electrical conductivity of bentonite clays, sand–bentonite clay mixtures, and marine clays over a wide range of water content. The bentonite clays were: Kunipia-F Na-bentonite and Kunigel VI Na-bentonite, both from the Kunimine Industries Co. Tokyo, Japan. The sand was from the Tottori Bay and the marine clays were from 2 different locations of the Ariake Bay, both in Japan. The sand–bentonite mixtures were prepared by using the sand and Kunipia-F Na-bentonite. The composition of the
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different samples, their clay content, and wetting liquid are listed in Table 1. For further details of the properties of the bentonites and clays, the readers are referred to Ito et al. (1993), Sridharan et al. (2000), and Komine (2004). In addition to our experimental data, 2 relevant sets of data of Fukue et al. (2001), extracted from their graphs, were also used.
Table 1 The composition of different samples, their clay content, and wetting liquid used for the samples
3.1. EC measurement in sand-Kunipia F Na-bentonite mixtures
2
The sand was washed 5 times with distilled water to remove its antecedent salts and clay that naturally existed in the sand. Both the sand and Kunipia-F Na-bentonite were dried in oven at 105 °C for 24 h before preparing the samples for the experiment. Five samples of sand–bentonite mixtures, each of mass 250 g, having 10, 30, 50, 70 and 100% (by weight) bentonite were prepared from the dry sand and bentonite, and each sample was mixed thoroughly to make homogeneous mixtures. Depending on the sand:clay ratio in the samples, different quantities of distilled water (electrical conductivity= 1.36 μS/m) was added with them and mixed with an electric stirrer to make homogeneous mixtures in glass beakers of 1–3 L size. The quantity of water for each sample was chosen so that their water content exceeds well the level of saturation. The samples were kept undisturbed for 48 h to reach equilibrium with the top of the beakers closed to prevent evaporation. The equilibrium samples were transferred to separate aluminum trays (size: 30 cm × 20 cm × 5 cm) with known mass. Inserting a 7-cm long 3-rod TDR probe horizontally into each sample their electrical conductivity was measured by using a Tektronix 1502C cable tester. The preparation of the samples and their EC measurements were carried out at a constant temperature of 25 ± 1 °C. The samples were then spread in the trays and kept in laboratory at the constant room temperature for 24 h with intermittent manual mixing of 4–5 times to reduce their water content by evaporation. Recording the mass of the samples after mixing thoroughly with a wide spatula their electrical conductivity was measured as before. Repeating this procedure of drying the samples and measuring their EC was continued until the samples were so dried that TDR could no longer measure their EC correctly. It is noted that, in the dry state, the samples were mixed carefully to achieve maximum possible homogeneity by manual means and packed in acrylic cylinders, 5-cm diameter and 10-cm height with the bottom closed, to measure their electrical conductivity.
3
3.2. EC measurement in Kunigel VI Na-bentonite Along with the Kunigel VI Na-bentonite, Ca-homoionized Kunigel VI bentonite was also used in this experiment. The Ca-bentonite was prepared by saturating the Kunigel VI Nabentonite with 1 M CaCl2 solution and washing the mixture repeatedly with distilled water under pressure in a pressure plate apparatus. Calcium saturation of this bentonite mass was achieved by mixing it with 1 M CaCl2 solution 2 more times and subsequent washing with distilled water. The wet bentonite was dried in air and grinded into fine particles. Both Naand Ca-bentonites were dried in oven at 105 °C for 24 h before preparing the samples for experiment. One sample from Na-
Sample no. Composition of the samples
Clay content Wetting liquid (kg/kg)
1
0.10
Distilled water
0.30
Distilled water
0.50
Distilled water
0.70
Distilled water
1.00
Distilled water
0.65 0.65 0.65 0.65
Distilled water 0.001 M NaCl 0.01 M NaCl Distilled water
0.65
0.001 M NaCl
0.65
0.01 M NaCl
0.77
Distilled water
0.77
Distilled water
0.77
Distilled water
0.77
Distilled water
0.77
Distilled water
0.77
Distilled water
⁎
Distilled water
⁎
0.134 M KCl
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Kunipia-F Na-bentonite: sand = 10:90 Kunipia-F Na-bentonite: sand = 30:70 Kunipia-F Na-bentonite: sand = 50:50 Kunipia-F Na-bentonite: sand = 70:30 Kunipia-F Na-bentonite: sand = 100:00 Kunigel VI Na-bentonite Kunigel VI Na-bentonite Kunigel VI Na-bentonite Kunigel VI Na-bentonite Ca-homoionized Kunigel VI Na-bentonite Ca-homoionized Kunigel VI Na-bentonite Ca-homoionized Ariake marine clay 1: washed Ariake marine clay 1: Na-homoionized Ariake marine clay 1: Ca-homoionized Ariake marine clay 2: washed Ariake marine clay 2: Na-homoionized Ariake marine clay 2: Ca-homoionized Na-bentonite of Fukue et al. (2001) Na-bentonite of Fukue et al. (2001)
⁎Data not available.
bentonite and one from Ca-bentonite, each of mass 250 g, was prepared and saturated with distilled water as described above. Following exactly the similar procedure of the experiment with the sand-Kunipia F Na-bentonite mixtures, the electrical conductivity of these samples was measured by TDR over a wide range of water content. In order to know the effects of salt concentration in the wetting liquid on the EC of the samples and thickness of the DDLs, the EC of 2 samples of the Kunigel VI Na-bentonite was also measured by wetting them with 0.001 and 0.01 M NaCl solutions. To avoid salt accumulation during the drying process, the measurement of EC of these samples were performed by gradually increasing the water content of the samples. Spreading the samples in separate aluminum trays, approximately 10 ml previously prepared salt solution was sprayed on each sample in the first step and mixed manually as uniformly as possible. The wet samples were packed in
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separate acrylic cylinders of known mass, and of diameter and height 5 cm and 10 cm, respectively, with the bottom closed. Closing the top of the cylinders to prevent evaporation, the samples were kept at 25 ± 1 °C for one week to reach equilibrium distribution of water in the samples. Recording the mass of the samples their electrical conductivity was measured by inserting TDR probes into them. The samples were then transferred into the trays and approximately 7 ml of the same salt solution (as added in the first step) was sprayed on them in the second step. Mixing the solutions with the samples, they were packed in the acrylic cylinders as before. After achieving equilibrium distribution of water in the samples, their mass was recorded before measuring the EC. Following this procedure, the water content of the samples was increased in incremental steps until their dilute state. With increasing water content of the samples, the quantity of solution added in a step was also increased successively and the mixing of the solution with the samples was accomplished with an electric stirrer when water content increased substantially. Also at high water content, the time to reach equilibrium distribution of solution in the samples was reduced gradually to 24 h in successive steps. The room temperature was maintained at 25 ± 1 °C during the whole course of the experiment.
intersection of the nonlinear and linear sections of the curves. The specific surface area of the samples was measured by ethylene glycol monoethyl ether (EGME) retention method as described by Pennell (2002). It is, however, also possible to estimate S from the density of surface charge, φ, and cation exchange capacity, η, of the clays following Bolt and Bruggenwert (1978, p.55) as S ¼ g=u
ð8Þ
Although the surface charge density varies with detailed clay mineralogy and composition of the soil water, but typically are 1, 2 and 3 (× 10− 6) molc/m2 (Bolt and Bruggenwert, 1978, p.55) for montmorillonite, kaolinite and illite clays, respectively. The surface area of the fractional mass of clay per unit mass of a sample was calculated by multiplying S by the fraction of clay in the samples. In addition to the estimation of t from Eq. (5), the thickness of the fully developed DDLs of all samples was also calculated independently by using Eq. (6). The two sets of t were compared to check the validity of Eq. (7). The specific surface area of the samples, S, was then calculated from their critical water content, w, by using Eq. (7) and the parameters there in.
3.3. EC measurement in Ariake clays
4. Results and discussion
The 2 Ariake marine clays were naturally saline, and so they were washed repeatedly with distilled water to remove their antecedent salts. The washed clays were dried in air and grinded into fine particles. Some quantity of the both washed clays was homoionized with Na+ and some with Ca+. The homoionization of the clays was done by saturating the washed dry clay with 1 M NaCl solution (for Na-homoionization) and 1 M CaCl2 solution (for Ca-homoionization) and washing them with distilled water as described for the preparation of the Kunigel VI Ca-homoionized bentonite. The electrical conductivity of the 2 Ariake clays was measured over a wide range of water content both for the washed, Na-homoionized and Cahomoionized samples by wetting them with distilled water. The preparation of the samples and recording the data were similar to that as described for the Kunigel VI bentonite wetted with distilled water.
4.1. Developmental stages of DDLs The variation of the bulk electrical conductivity of the 19 samples of different materials (Table 1) with the changing water content is displayed in Figs. 1–4. Although the rate of variation of the EC with water content differs in different clays, also reported by Cremers and Laudelout (1966), the general trend of this variation is
3.4. Calculation of DDL thickness and specific surface area The thickness of the fully developed DDLs was calculated from the critical water content, w, and specific surface area, S, for the different samples described in Table 1 by using Eq. (5). The critical water content of the samples was determined from their EC versus water content data. The electrical conductivity of all samples increased nonlinearly over low water content that is specific to each sample and linearly over high water content. The nonlinear section of the EC versus water content curve is governed by semi-logarithmic function. The point of intersection between the nonlinear and linear sections of the EC versus water content curve is the state of fully developed DDLs. The critical water content, w, was determined at the
Fig. 1. Variation of the electrical conductivity of sand-Kunipia F Nabentonite mixtures with their water content.
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Fig. 2. Variation of the electrical conductivity with the water content of different samples for: (a) Kunigel VI Na-bentonite, and (b) Kunigel VI Na-bentonite homoionized with calcium (Ca++).
very similar. The EC of the samples, wetted with distilled water, is low at their dry state and increases gradually to a maximum value at certain high water content that depends on the type and quantity of the clay in the samples. The highest EC remains relatively constant over a small range of water content after which it decreases linearly with the increasing water content. The EC of the samples with salt solution as the wetting liquid (Kunigel VI Naand Ca-bentonites in Fig. 2, one data set of Fukue et al., 2001 in Fig. 4) differs from the general trend observed in the samples wetted with distilled water. After an initial increase, the EC of these samples decreases with increasing water content at slower but different rates than the decrease of the EC in the samples wetted with distilled water. At much higher salt concentration of the wetting liquid, the EC of the samples would continuously increase with increasing water content without giving a peak value of EC. The observed variation of the electrical conductivity of different samples with their water content can be explained by the developmental stages of the DDLs around clay particles in the samples. On addition of a small quantity of distilled water to a dry sample, the cations (Na+ or Ca+) already residing on the surface of the clay come in contact with the water. Both the cations and water remain adsorbed on the surfaces of the clay to form DDLs. The adsorbed water molecules and cations cover up the clay particles and increase their electrical conductivity (the surface conductivity) by creating continuous electrically conductive pathways. At low water content,
