Environ. Sci. Technol. 2009, 43, 3487–3493
Linking the Diffusion of Water in Compacted Clays at Two Different Time Scales: Tracer Through-Diffusion and Quasielastic Neutron Scattering ´ TIMA GONZA ´ LEZ SA ´ N C H E Z , * ,† FA ´ NYI,§ T H O M A S G I M M I , †,‡ F A N N I J U R A LUC VAN LOON,† AND LARRYN W. DIAMOND‡ Laboratories for Waste Management and for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen PSI, and Institute of Geological Sciences, University of Bern, CH-3012 Bern, Switzerland
Received December 19, 2008. Revised manuscript received February 20, 2009. Accepted March 3, 2009.
Diffusion of water and solutes through compacted clays or claystones is important when assessing the barrier function of engineered or geological barriers in waste disposal. The shape and the connectivity of the pore network as well as electrostatic interactions between the diffusant and the charged clay surfaces or cations compensating negative surface charges affect the resistance of the porous medium to diffusion. Comparing diffusion measurements performed at different spatial or time scales allows identification and extraction of the different factors. We quantified the electrostatic constraint q for five different, highly compacted clays (Fb ) 1.85 ( 0.05 g/cm3) using quasielastic neutron scattering (QENS) data. We then compared the QENS data with macroscopic diffusion data for the same clays and could derive the true geometric tortuosities G of the samples. Knowing the geometric and electrostatic factors for the different clays is essential when trying to predict diffusion coefficients for other conditions. We furthermore compared the activation energies Ea for diffusion at the two measurement scales. Because Ea is mostly influenced by the local, pore scale surroundings of the water, we expected the results to be similar at both scales. This was indeed the case for the nonswelling clays kaolinite and illite, which had Ea values lower than that of bulk water, but not for montmorillonite, which had values lower than that in bulk water at the microscopic scale, but larger at the macroscopic scale. The differences could be connected to the strongly temperature dependent mobility of the cations in the clays, which may act as local barriers in the narrow pores at low temperatures.
1. Introduction Clays such as bentonite are minerals with large specific surface areas and very small pores. Such clays or clay rocks * Corresponding author phone: +41765054129; e-mail: fatima_oti@ yahoo.com; Fax: +41563103565. † Laboratory for Waste Management, Paul Scherrer Institute. ‡ Institute of Geological Science, University of Bern. § Laboratory for Neutron Scattering, Paul Scherrer Institute. 10.1021/es8035362 CCC: $40.75
Published on Web 04/08/2009
2009 American Chemical Society
are considered as buffer material for engineered barriers or potential host rocks for the disposal of radioactive waste. Their well-suited properties such as large retention capacity and low hydraulic conductivity offer a perfect environment that retains radionuclides and slows their migration. To reliably predict the spreading of radionuclides through such barriers for the long time scales envisaged, a good understanding of the mechanisms governing the interactions among the clay solids, the water, and the radionuclides or other solutes is necessary. Of specific concern in this context are the diffusion properties of solutes in clays, which can be investigated with sorbing (1) or water tracers (2, 3). Diffusion is considered as the dominant transport mechanism in clays under natural hydraulic gradients. A wide variety of experimental techniques were applied in the past few years to determine diffusion coefficients of solutes or water tracers in clays or clay rocks. Each of the experimental methods is characterized by a particular time and space scale. Quasielastic neutron scattering (QENS) measures the average local diffusion coefficient of a sample at a time scale of picoseconds to nanoseconds and over a spatial scale of several angstroms (4). At a mesoscopic scale nuclear magnetic resonance (NMR) techniques (5, 6) allow correlation times on the order of a few microseconds to be obtained for diffusion taking place over a few hundred angstroms. On a macroscopic scale, tracer through-diffusion experiments (2, 3, 7) are performed on samples with a thickness of millimeters to centimeters over hours to days, and field investigations consider even larger scales of meters to several decameters (8, 9). Different observation time scales can lead to different diffusivities for porous media (10, 11), resulting from the different lengths of the diffusion paths compared to the basic pore scale, or compared to the size of relevant structural heterogeneities in general. By comparing results obtained at different scales, valuable insight into various factors affecting diffusion can be gained. Some studies comparing results at similar scales can be found in the literature. Malikova et al. (12), for instance, investigated the dynamics of water in Naand Cs-montmorillonite at a microscopic scale by comparing results from QENS using neutron spin-echo (NSE) and timeof-flight (TOF) experiments, as well as from molecular modeling. They found a good correspondence between the TOF and simulated results for bihydrated samples, but a factor of 2 faster dynamics compared to the NSE. For monohydrated clays, however, the diffusion coefficients obtained from TOF data tended to overestimate the dynamics because of the limited range of observation times up to about 100 ps, where the other two techniques were in agreement. The aim of this study was mostly to check the appropriateness or consistency of the used methods. Studies that link diffusion data obtained at different experimental scales are much scarcer. Rollet et al. (13) compared the dynamics of N(CH3)4+ ions in nafion membranes at micro-, meso-, and macroscopic scales using QENS, NMR, and radiotracer measurements. They interpreted the diffusion coefficients at the different time scales according to the known geometric and chemical restrictions of the nafion and the concentration of the diffusant. However, they did not link the diffusion results at the three different experimental time scales. Marry and Turq (14) found a good agreement between their simulated diffusion coefficients of water in montmorillonite and the values obtained by others (15, 16) by neutron scattering. They found also that introducing the microscopic simulated data in macroscopic models, using literature data for the additionally required macroscopic parameters such as tortuosity VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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or constrictivity, resulted in a good agreement with tracer experiments. To our knowledge, however, so far there is no study that compares and links experimentally two extreme scales in clay minerals, such as microscopic QENS measurements and macroscopic tracer through-diffusion. Here, we combine two data sets obtained for highly compacted pellets of Na- and Ca-montmorillonite, Na- and Ca-illite, and kaolinite at the microscopic scale by QENS (17) and at the macroscopic scale by HTO through-diffusion (18) and derive from this combined set the factors that connect the diffusivity of water in clays at the two different scales. These factors are related to the geometrical pore network (tortuosity) and the interactions between the water molecules and the clay surfaces and cations (electrostatic constraint). We furthermore compared the activation energies for diffusion at the two different scales. Our hypothesis was that activation energies are not or are weakly influenced by the geometry factor, but strongly by the local microscopic interactions, and thus should be comparable at the two different scales.
2. Diffusion Coefficients in Porous Media Diffusion coefficients in porous media are, unfortunately, not consistently defined among different disciplines. Here, the pore diffusion coefficient Dp (m2/s) refers to the porous cross section only; it equals the effective diffusion coefficient, which is defined for the whole porous medium, divided by the porosity ε (dimensionless). For tracers with no electrostatic interactions with the pore surface, Dp can be given as (19) Dp )
Dw G
(1)
where G is the overall geometric factor or tortuosity and Dw (m2/s) the tracer diffusion coefficient in bulk water. Some attempts were made in the past to further split G into a specific tortuosity and a geometrical constrictivity, but for natural porous materials these factors can hardly be determined independently, which makes such a distinction futile. If water diffuses in narrow pores, and especially when the surfaces are charged and electrostatic interactions occur as in clays, the local motion of water is impeded as compared to that of bulk water (20). Accordingly, an additional parameter has to be added to eq 1 to account for the possibly reduced water viscosity and the electrostatic interaction between the water and the clay surfaces (e.g., refs 21 and 22): Dp )
qDw G
(2)
where q (dimensionless) is the electrostatic constraint factor. Note that often the distinction between q and G is not made properly because of experimental difficulties, and a factor G′ is calculated for clays as Dw/Dp. Clearly, G′ ) G/q, and G′ and G are only equal if q ) 1. Diffusion coefficients obtained from macroscopic experiments are influenced by both factors, G and q, according to eq 2. In contrast, at a microscopic scale, that is, if water molecules move only over a distance of a few molecular diameters, the geometric factor is negligible (G ≈ 1). Consequently, the microscopic diffusion coefficient obtained by QENS experiments can be given as Dclay,QENS ) Dp,QENS ) Dwq
(3)
In the case of smectites at low degrees of hydration with most water in the interlayers, the assumption G ≈ 1 requires that a 2D model for the movement along the surfaces for the analysis of the QENS data is used (23, 24) or that the time 3488
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scale of the QENS measurement is too short for the 2D restrictions to become relevant. Bourg et al. (25) recently proposed a model for the dependence of water diffusion coefficients on the clay density, which is based on estimates of G, q, and the fraction of interlayer water in smectites. There have been many attempts to relate the parameter G or G′ to the porosity or other relatively easily derived properties of the porous medium (e.g., ref 21). It is clear, however, that no unique relation exists for different types of porous materials, such that G or G′ must be considered as a largely empirical factor. While the geometric factors have been extensively studied for swelling clays at different bulk dry densities, less is known about the electrostatic interaction q due to the clay-water interface. For nonswelling clays such as illite and kaolinite the lack of information is even larger. Kemper et al. (22) were probably among the first to determine q experimentally for HDO in films of oriented Na-montmorillonite crystals. In the past few years, molecular modeling was also used to determine local diffusion coefficients of water molecules or cations between layers of smectites (26, 27).
3. Materials Clays are layered aluminosilicates, where a single clay layer is formed by tetrahedra of Si4+ oxides and octahedra of Al3+ or Mg2+ oxide sheets, and where one octahedral sheet is bound either to one tetrahedral sheet (a 1:1 clay) or to one on each side (a 2:1 clay). Isomorphic substitutions in the basic layers lead to a deficit of charge which is balanced by cations near the surfaces. The clays selected for this study behave rather differently in contact with water. In the case of montmorillonite, a 2:1 clay, water is located between particles and in the interlayer space, which gives rise to the swelling character of this clay. Illite and kaolinite are nonswelling clays. In illite (a 2:1 clay), water is found only between particles, because the interlayer surfaces are tightly linked by potassium cations. The layers of kaolinite (a 1:1 clay) are uncharged. Consequently, no interlayer space can be defined, and water is located only between particles (see Figure 1). The specific clays studied were montmorillonite from Milos (28) and illite du Puy (29), both conditioned to the homoionic Na- and Ca-forms, and kaolinite from Georgia [KGa-2 (30)]. The characteristics of these clays are reported in detail in previous studies (17, 18). The hydrated clay powders were compacted into a pellet to reach a bulk dry density of Fb ) 1.85 ( 0.05 g/cm3. In the macroscopic HTO through-diffusion experiments, the fully hydrated pellets had a cylindrical shape 2.55 ( 0.01 cm in diameter and a thickness of 1.00 ( 0.05 cm. In the QENS measurements rectangular fully hydrated pellets of 5 × 1.5 × 0.1 cm3 were used, enclosed in vapor-tight aluminum containers. With QENS we measured also, at a single temperature of 27 °C, half-hydrated samples. Table S1 in the Supporting Information contains the most relevant structural data for the current study, i.e., particle size, porosity, gravimetric water content w (gwater/gsolid), and the average number of water layers between two clay surfaces. The last column gives the average number of water molecules per cation (for the charged clays).
4. Methods The macroscopic results (18) were obtained from onedimensional through-diffusion experiments parallel to the direction of compaction, using HTO as tracer and different salt concentrations in the reservoir solutions. The diffusion coefficients were evaluated correcting for the influence of the filter plates. The filter effect becomes relevant in clays with effective diffusion coefficients of the same order of magnitude as those of the filter (kaolinite and illite for our
FIGURE 1. Schematic representation of the structure of the clays studied. The minus symbols represent the deficit of charge present in the corresponding clay layer (T or O). experimental setup of 1 cm sample thickness). However, for montmorillonite with effective diffusion coefficients 1 order of magnitude or more lower than those of the filters, this effect is not significant. The activation energy Ea for diffusion was calculated from the temperature dependence of diffusion in the range from 0 to 60 or 70 °C using the Arrhenius equation: D ) Ae-Ea/RT
(4)
where D is the diffusion coefficient, A the so-called preexponential factor, T the temperature, and R ) 8.314 J/(K · mol) the molar gas constant. The diffusion coefficients discussed in the present paper were measured at salt concentrations of 0.01 M NaCl (for Na-montmorillonite and Na-illite) and 0.005 M CaCl2 (for Ca-montmorillonite and Ca-illite) in the reservoirs that are in contact with the sample. The values of kaolinite shown here were obtained in samples in contact with pure water (Milli-Q). These data are compared with the microscopic values of diffusion where the clays were saturated with small amounts of Milli-Q water. The different compositions of the saturating solutions do not affect the results, as shown in the Supporting Information. The Arrhenius plot of the diffusion coefficients is shown in Figure S1, Supporting Information. The microscopic experiments (17) were carried out with two different neutron scattering spectrometers, FOCUS (SINQ, Paul Scherrer Institut) and TOF-TOF (FRM II, Garching). The data presented here were obtained at temperatures between 27 and 95 °C. At the molecular scale the translational diffusion can be described by distinct jumps. Because the jump length distribution is unknown for our samples, the data were evaluated by two different models (17): the Singwi-Sjo¨lander model (assumes an exponential jump length distribution) and the Hall-Ross model (Gaussian distribution). The diffusion coefficients used here represent averages of the values for the two models, as shown in an Arrhenius plot in Figure S2, Supporting Information. For all
materials, a model for a 3D motion was applied. In the case of the montmorillonite samples, a 2D model was also tested, but it was found that the restriction in the third dimension did not affect our data (17). We linked the macro- and microscopic experiments through eqs 1-3. The electrostatic constraint factor q was obtained as the ratio Dp,QENS/Dw,QENS between the diffusion coefficients of water in clay and of bulk water both obtained by QENS (Dw,QENS(20 °C) ) (2.04 ( 0.26) × 10-9 m2/s). The ratio Dp,QENS/Dp,macro of the water diffusion coefficients for the clays measured by QENS and in the through-diffusion experiments gave us the values of G. Additionally, we calculated G′ (for comparison purposes) as the ratio Dw,QENS/Dp,macro. Because the diffusion data at the macro- and microscopic experiments were obtained at slightly different temperatures, we had to interpolate or (for the results at 20 °C) extrapolate the microscopic results to the specified temperatures. We did this according to the Arrhenius equation (eq 4) and the estimated activation energies. The uncertainties of the diffusion coefficients were obtained from the propagation of the uncertainties of the slope and intercept of the linear regression function, taking into account the covariance of these two parameters.
5. Results and Discussion 5.1. Electrostatic Constraint q, Geometric Factor G, and Combined G′ Factor. Table 1 contains the electrostatic constraint q, the geometric factor G, and the combined factor G′. The values of the electrostatic constraint q factor are generally expected to fall between 0 and 1, with 1 meaning no electrostatic effect and 0 meaning complete inhibition of the mobility. The q values determined here from the QENS measurements represent average values over all mobile water fractions in the samples. The interaction was found to be stronger (q smaller) in the case of swelling clays than in the case of nonswelling clays. Na-illite and kaolinite have values close to 1. The value for kaolinite is even slightly larger than VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Values for All Studied Clays of the Electrostatic Constraint q = Dclay,QENS/Dw,QENS, the Geometrical Factor G = Dclay,QENS/Dp, and the Combination of Both, G′ = Dw,QENS/Dp T(°C)
q
20 30 40 50 60 27a 27b
0.5 ( 0.2 0.4 ( 0.1 0.4 ( 0.1 0.4 ( 0.1 0.4 ( 0.1 0.21 ( 0.03 0.20 ( 0.03
20 30 40 50 60 27a
0.9 ( 0.1 0.8 ( 0.1 0.8 ( 0.1 0.8 ( 0.1 0.8 ( 0.1 0.7 ( 0.1
20 30 40 50 60 27a
1.2 ( 0.2 1.1 ( 0.1 1.1 ( 0.1 1.1 ( 0.1 1.1 ( 0.1 1.0 ( 0.1
a
Half-hydrated sample.
b
G
G′
q
Na-montmorillonite 21.1 ( 2.0 18.6 ( 1.4 16.5 ( 1.0 14.8 ( 0.8 13.4 ( 0.8
45.0 ( 5.8 42.7 ( 4.4 40.6 ( 3.4 38.8 ( 2.8 37.1 ( 2.6
0.5 ( 0.1 0.4 ( 0.1 0.4 ( 0.1 0.4 ( 0.1 0.4 ( 0.1 0.18 ( 0.02
Na-illite 3.9 ( 0.4 3.9 ( 0.4 3.9 ( 0.4 3.9 ( 0.4 3.9 ( 0.4
4.4 ( 0.7 4.6 ( 0.7 4.8 ( 0.6 5.0 ( 0.6 5.3 ( 0.6
0.6 ( 0.1 0.6 ( 0.1 0.6 ( 0.1 0.6 ( 0.1 0.6 ( 0.1 0.47 ( 0.06
kaolinite 4.6 ( 0.5 4.6 ( 0.4 4.6 ( 0.3 4.5 ( 0.2 4.5 ( 0.2
4.0 ( 0.6 4.1 ( 0.5 4.2 ( 0.4 4.3 ( 0.4 4.4 ( 0.4
9
G′
Ca-montmorillonite 8.0 ( 0.8 7.2 ( 0.6 6.5 ( 0.5 6.0 ( 0.4 5.4 ( 0.4
17.1 ( 2.8 16.5 ( 2.2 16.0 ( 1.7 15.6 ( 1.5 15.2 ( 1.4
Ca-Iillite 4.2 ( 0.4 4.1 ( 0.3 4.1 ( 0.3 4.1 ( 0.3 4.0 ( 0.3
6.5 ( 1.0 6.6 ( 0.8 6.6 ( 0.7 6.7 ( 0.6 6.8 ( 0.6
Quarter-hydrated sample.
1, which can be attributed to its hydrophobic behavior (31), which results especially at low temperatures in higher diffusion coefficients than those of bulk water (32, 33). The lowest values correspond to Na- and Ca-montmorillonite with q ) (0.5-0.4) ( 0.1. Both forms of this clay showed similar interaction with water, despite the different hydration properties of Na and Ca cations (34). The interlayer spaces were hydrated on average with only two water layers in both cases (Table S1, Supporting Information). This may have masked the specific effects of the cations. A difference of the cation form was present when the cations were only located on the external clay surfaces, as in the case of Na- and Caillite. Ca-illite had a q value of 0.6, intermediate between those of the montmorillonites and that of Na-illite (q ) 0.9). The q results obtained for Na-montmorillonite are in agreement with those of Kemper et al. (22). From the estimation of the geometric factor of ∼1.1-1.25 in the diffusion of HDO parallel to oriented films of Na-montmorillonite, these authors obtained values of q ) 0.3 for twolayer-hydrated samples (our case) and q ≈ 0.7-0.8 for samples hydrated with thirty-two layers. For Ca-montmorillonite, they obtained values between 0.05 (two-layer hydrate) and about 0.4 (six-layer hydrate). They attributed the low value of 0.05 for the two-layer hydrate to association of some water molecules with immobile Ca ions. In our QENS measurements, such associated water may be observed through the intensity of the elastic line, but would not contribute to the broadening of the quasielastic line and thus Dp,QENS, if it were indeed immobile during the characteristic time of the measurement. This could in principle explain the larger q value obtained in our measurements for Ca-montmorillonite. However, we did not observe a significant difference in the intensity of the elastic line between Na- and Ca-montmorillonite, making this interpretation unlikely. On the other hand, the analysis of Kemper et al. (22) relies on an estimated value of the tortuosity of about 1.2. A larger value for their Ca samples would increase their estimate of q accordingly. Our q values for Na- and Ca-montmorillonite are in fair agreement with results calculated by molecular modeling. For instance, Chang et al. (35) reported values of 0.1 and 0.6 in mono- and bihydrated montmorillonite, respectively. Kosakowski et al. (27) calculated values between about 0.2 3490
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and 0.6 for mono- and bilayer hydrated Na-Cs-montmorillonite, respectively. The electrostatic constraints q obtained from our measurements represent averages over all water fractions present in each clay (interlayer, external, or bulk pore water). Kemper et al. (22) showed that q values increase quickly beyond the first two surface water layers. If we divide the pore water into just two fractions, one that is not affected and another that is affected by the surfaces, similarly to what Bourg et al. (25) did, we have q ) wSLqSL + (1 - wSL)qPW
(5)
with wSL the fraction of water on clay surfaces, qSL the electrostatic constraint for this surface layer (SL) water, and qPW the electrostatic constraint factor of the free pore water, which is assumed to be 1 (no constraint). This allows estimation of the qSL values for our clays based on estimates of wSL from the average number of water layers (Table S1, Supporting Information). When assuming that two water layers are affected by the surfaces on each side, we obtained qSL ) 0.55 for Na-illite and 0.1 for Ca-illite. For a thickness of only one water layer, which is the configuration within our montmorillonites, one would even obtain negative values. Bourg et al. (25) could describe montmorillonite systems up to densities of Fb ) 1.5 g/cm3 with their model. Our results show that assuming just two water fractions and setting qPW ) 1 is probably an oversimplification for higher densities. Notably, the cation content in the free pore water may also reduce qPW and thus also contribute to the lowering of the overall q. As expected and consistent with the observations of ref 22 or molecular modeling results (26, 27), the half-hydrated samples showed in general a reduction in the q factor, except for kaolinite. Kaolinite at the reduced water content may still have mostly free pore water (Table S1, Supporting Information), such that the average properties remain similar to those of bulk water. Both montmorillonites still kept the similarity of their q values and were the most affected by dehydration (reduction by more than a factor of 2). A further reduction in the water content of Na-montmorillonite (quarterhydrated) had no additional effect on q. Most probably, the
further reduction of the water content resulted in a more heterogeneous hydration state, with some interlayers having one water layer and others being totally dry. Accordingly, the average water properties were about identical in the halfand quarter-hydrated samples. In the case of illite, the Ca-form was slightly more affected than the Na-form. We think that this small difference between the Na- and Ca-forms would disappear with a further reduction in the average number of water layers, as in the case of the montmorillonites. The geometric factor G reflects the tortuosity of the diffusion paths of the water, whereas G′ also includes the differences in the electrostatic interactions at the clay-water interface. For q values on the order of 1, G and G′ are about equal, whereas the differences are considerable for Na- and Ca-montmorillonite (difference of about 50%) and Ca-illite (35%). Thus, we conclude that, for the swelling clays (Naand Ca-montmorillonite) and Ca-illite, Dw/Dp ratios ()G′ values) calculated from macroscopic diffusion experiments lead to values that overestimate the truly geometric constraints up to a factor of 2-3 at our bulk density. The correct tortuosity G can only be determined when the electrostatic constraint factor q is known. As can be seen in Table 1 the G values of Na- and Camontmorillonite differed by about 60% whereas the q factors were identical. These results indicate that the differences found in the macroscopic effective diffusion coefficients for these two clays were mostly based on the different diffusion paths, and not on the local interaction with the saturating cations. Na-montmorillonite has a more tortuous path than the Ca-form, because of its smaller particle sizes (Table S1, Supporting Information), smaller pore sizes, and larger surface area, which originate from the smaller number of layers per stack (about 3-5) as compared with that of Camontmorillonite (about 10-15 (36)). For Na- and Ca-illite, the geometric factors G are nearly equal, which confirms that they have a very similar structure, resulting from their similarities in the particle sizes (Table S1) and in their way of producing stacks of 20-30 layers (37). In contrast, the q values differ clearly, with values of 0.6 for Ca-illite and of 0.8-0.9 for Na-illite. These results show that the difference in macroscopic diffusion of water between these two clays is due to the different hydration of the Na as compared with the Ca cation. Kaolinite has particle sizes larger than those of illite (Table S1), and it forms larger stacks (60 layers (38)). Nevertheless, it has a G value similar to that of the illites. This result could be related to a broader particle size distribution for kaolinite as compared with illite clays. In fact, the kaolinite used is KGa-2 type, which is a low crystallized kaolinite. That typically results in a large variability of the number of layers per stack (12-54 (38)) and a broad distribution of particle sizes and thus a more tortuous path for the diffusion of water. Our tortuosities were derived for diffusion parallel to the direction of compaction of the samples. At high densities (above about 1.5 g/cm3), diffusion through clays is anisotropic with lower tortuosities perpendicular to the direction of compaction. Bourg et al. (25) estimated a mean principal value of G ) 4.0 ( 1.6 for clays with 50-100% Namontmorillonite for bulk dry densities between 0.2 and 1.5 g/cm3 or higher. To compare our tortuosities with his value, we calculated the mean principal value of the pore diffusion coefficient in our Na-montmorillonite sample (Fb ) 1.85 ( 0.05 g/cm3) assuming a component perpendicular to compaction 2-4 times larger than that parallel. The factor of 2 is based on the experimental data of Suzuki et al. (2) for Na-montmorillonite at a density of 1.35 g/cm3, the factor of 4 arises from the data of Van Loon et al. (3) for Opalinus clay (Fb ) 2.5 g/cm3). With a mean principal value at room temperature of Dp ) (8.69 ( 0.9) × 10-11 m2/s (anisotropy
FIGURE 2. Comparison of the Ea values for the clays studied and water at the two different time scales. The abbreviations correspond to Na-montmorillonite (Na-m), Ca-montmorillonite (Ca-m), Na-illite (Na-i), Ca-illite (Ca-i), kaolinite (Kao), tracer through-diffusion results (macro), and QENS results (micro). factor of 2) or Dp ) (1.56 ( 0.2) × 10-11 m2/s (anisotropy factor of 4) and the value for Na-montmorillonite Dclay,QENS ) (1.11 ( 0.09) × 10-9 m2/s, we obtained mean principal values for G of 12.8 ( 1.8 (anisotropy factor of 2) and 7.1 ( 1.1 (anisotropy factor of 4). These values are clearly larger than the value used in ref 25. This suggests that at high bulk densities the tortuosity G does not remain constant, but increases with the bulk dry density. The q and G values that were determined in this paper help to unravel the relation between structural and diffusion properties of the investigated clay minerals. They may be used as input parameters for models that relate diffusion coefficients with the bulk dry densities and the hydration state or the fractions of surface-near or interlayer water in clays. They can serve as a basis of detailed, microscopic or even pore-scale modeling of complex clay rocks that represent a mixture of clay and other minerals. 5.2. Temperature Dependence: Activation Energies. An illustrative plot regarding the differences between the activation energies Ea at the two different scales is shown in Figure 2. The two scales of observation led to comparable values of the activation energy in the case of nonswelling clays (Naand Ca-illite and kaolinite), as expected. These clays have activation energies lower than that of bulk water (17 ( 1 kJ/mol). It seems that the interaction with the illite and kaolinite surfaces tends to reduce the Ea. The limited space for the water to diffuse, and the competing influence of the cations and the clay surfaces, could distort the H-bonds between two water molecules and result in a lower Ea, as discussed in refs 17 and 18. The two types of montmorillonite had similar Ea values at each scale, confirming that at the degree of compaction studied the water is more influenced by the interlayer confinement than by the differences in the hydration of the cations (17). However, the macroscopic Ea values were twice as large as the microscopic activation energies. We see in Table 1 that only for montmorillonite G decreases clearly with increasing temperature, whereas q remains about constant (with a slight tendency to decrease). This means that the larger Ea obtained from macroscopic experiments is related to a decrease in the tortuosity with increasing temperature and not to a decrease in the electrostatic interaction and corresponding increase of q. The reduced tortuosity at higher temperatures in the case of montmorillonite could be related to a slight expansion of the samples at these temperatures. However, a reduction of the tortuosity by a factor of about 2/3 as a result of a slight expansion seems to be rather large. Alternatively, the reduced G could be related to an increased mobility of cations, which act VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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partly as barriers at low temperatures in macroscopic through-diffusion experiments, but not at the scale of the microscopic experiments. At low temperatures, the cations in the clay structure are relatively immobile and thus may “block” some pores, as discussed by Greathouse et al. (39). In QENS, the time (and space) scale of observation is so short that the barrier function of the cations, being part of the geometric factor, does not yet come into play (40). At higher temperatures the barrier function at the macroscopic scale may decrease because these cations become more mobile within the clay structure. This interpretation is consistent with the relatively large activation energies observed for cation diffusion at the macroscopic scale (7), which means that the cation diffusion increases overproportionally (as compared with HTO) at higher temperatures. The increased mobility of the cations at higher temperatures may partly be related to a temperature dependence of cation sorption, as postulated in ref 7. One could put the question, of course, of whether the supposed blocking effect of the cations should really be considered as part of the geometrical factor (and the cations as part of the solid surface, accordingly), or whether one should consider it as a specific local interaction. We think that there might be no clear answer to this question, even on a molecular scale, but further experiments may shed more light on these issues.
Acknowledgments We are thankful to B. Baeyens, U. Berner, and M. Glaus for many helpful discussions. M. Bradbury is acknowledged for his comments on this manuscript. Additional thanks go to W. Mu ¨ ller for support in the laboratory as well as T. Unruh, responsible for the QENS measurements at FRM II, Garching, Germany. We also thank the two anonymous reviewers for their very useful comments.
Supporting Information Available Structural characteristics of the samples, composition of solutions used to saturate the samples, and diffusion coefficients obtained at the two time scales. This material is available free of charge via the Internet at http://pubs.acs.org.
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