Article pubs.acs.org/est
Seeming Steady-State Uphill Diffusion of Montmorillonite
22
Na+ in Compacted
Martin A. Glaus,*,† Martin Birgersson,‡ Ola Karnland,‡ and Luc R. Van Loon† †
Laboratory for Waste Management, Paul Scherrer Institut, CH-5232 Villigen, Switzerland Clay Technology AB, IDEON Science Park, S-223 70 Lund, Sweden
‡
S Supporting Information *
ABSTRACT: Whereas the transport of solutes in nonreactive porous media can mostly be described by diffusion driven by the concentration gradients in the external bulk water phase, the situation for dense clays and clay rocks has been less clear for a long time. The presence of fixed negative surface charges complicates the application of Fick’s laws in the case of ionic species. Here we report the seeming uphill diffusion of a 22Na+ tracer in compacted sodium montmorillonite, that is, transport directed from a low to a high tracer concentration reservoir. In contrast to the classical through-diffusion technique the present experiments were carried out under the conditions of a gradient in the background electrolyte and using equal initial 22Na+ tracer concentrations on both sides of the clay sample. We conclude that the dominant driving force for diffusion is the concentration gradient of exchangeable cations in the nanopores. Commonly used diffusion models, based on concentration gradients in the external bulk water phase, may thus predict incorrect fluxes both in terms of magnitude and direction.
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INTRODUCTION Ion diffusion in smectite-rich soils and rocks has been studied quite extensively during the past half-century for geological, biological, and engineering applications. Special focus has been on transport capacity of clay-based barriers in planned repositories for radioactive wastes. The transport of solutes in dense clays and clay rocks is mainly governed by molecular diffusion.1−3 This is particularly true for bentonite, whose main constituent is montmorillonitea member of the smectite mineral group. The diffusive behavior in these systems is complicated4,5 by the fact that they function as cation exchangers due to the presence of fixed negative surface charges, which are compensated by exchangeable countercations. As early as the mid-1930s it was hypothesized that these exchangeable ions provide an independent passage for diffusion of cations in bentonite.6 In the following, this mode of transport is referred to as surface diffusion. Models for diffusion in smectite-rich systems are commonly founded on the assumption of the existence of a pore structure containing bulk-like water, that is, water uninfluenced by the surface charges (“free water”). Many researchers have found it necessary to extend such models with a surface diffusion component in order to reproduce experimental data.7−10 Current transport models commonly involve a multiporosity structure assuming that the diffusion of cationic species in compacted smectites can be explained by the presence of two parallel fluxes (see, e.g., refs 11 and 12), one being the surface diffusion and the other one the aqueous phase diffusion component. Since it has not been possible yet to discriminate experimentally between the magnitudes of the individual components, the assignment of the individual fluxes remains © 2013 American Chemical Society
arbitrary. On the one hand the importance of surface diffusion has been questioned (see, e.g., refs 13 and 14), and on the other hand, tracer through-diffusion tests made on highly compacted sodium montmorillonite indicated that surface diffusion not only contributes significantly to the mass transfer in dense systems, but that it completely dominates in the case of exchangeable tracer cations.15 Furthermore, at the conceptual level, it has been proposed that the latter data, as well as the diffusive behavior of anions, can be explained by assuming that the entire pore volume is made up only of the nanopores formed between adjacent smectite mineral layers.16 Hence, it is rather the role of a possible bulk-like water phase as a relevant transport porosity that could be questioned. The ambiguity regarding possible transport mechanisms has consequently led to an unsatisfactory situation, where different concepts and parameter values have been used in the literature to “explain” experimental results for the past 50 years. The experimental approach applied in the present work basically makes it possible to discriminate qualitatively between the magnitudes of surface and aqueous phase diffusion. The classical setup for tracer through-diffusion experiments17 has two sides of a clay sample contactedvia porous filterswith identical electrolyte solution reservoirs (further denoted to as iso-saline conditions). After addition to one of the reservoirs of a tracer species (typically a radioactive isotope) at negligible concentration level, diffusion through the sample is tracked Received: Revised: Accepted: Published: 11522
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Figure 1. Temporal evolution of the concentration of 22Na+ in the contacting reservoir solutions in the experiment with a ∼5 mm thick clay plug and reservoir volumes of ∼250 mL (a) and a 10 mm thick clay plug and reservoir volumes of ∼100 mL (b). The model curves show the expected evolution of concentration for aqueous phase diffusion being the only transport mode.
energy windows (0−15 keV, 15−600 keV) were used. Ion chromatographic measurements were carried out according to previously reported procedures.18,19 The present work includes diffusion experiments both under salt gradient and iso-saline conditions. The experiments under salt gradient conditions were carried out at a temperature of 25 ± 1 °C on cylinder shaped samples of homoionic Namontmorillonite from Milos (for methods of preparation and characterization, the reader is referred to ref 20). The samples were compacted in axial direction as slightly wetted powder (∼3% water) to a bulk dry density of ∼1900 kg m−3 and had a diameter of 25.6 mm and a thickness of either ∼5 or 10 mm. They were saturated with 0.1 M NaClO4 for 10 days from one side, while the other side was left open in order to enable escape of displaced air. Subsequently the samples were contacted with a second solution of 0.5 M NaClO4 on one side for ∼2 months in order to establish salt gradient conditions. The Na+ concentrations of the saturating solutions, which were regularly monitored by ion chromatography, showed no significant changes during the preparation phase. It was also verified by ion-chromatographic measurements that an almost linear decrease of ClO4− concentrations in the clay plug established after the preparation phase. After preparation the NaClO4 solutions were replaced by corresponding solutions spiked with ∼50 Bq cm−3 of 22Na+. An “aliquot cycling” sampling regime was applied during which the volume of the freshly taken sample for γ-counting was replaced by the previously measured one. The reservoir volume was thereby kept constant, while sufficient activity could be taken for obtaining very low errors in the counting statistics. The concentrations of the tracer in the actual reservoir solution and in the previously taken sample were not perfectly identical. Owing to the moderate changes in concentration with time, the error introduced by the aliquot cycling procedure was quite acceptable. After a diffusion time of 126 days for 22Na+, HTO was added to the 0.5 M NaClO4 reservoir at an activity concentration of ∼12 kBq cm−3. The combined diffusion of HTO and 22Na+ was monitored for an additional duration of 36 days, but with an increased analytical uncertainty for 22Na+ owing to the change in the sampling regime from aliquot cycling to a periodical daily
from one to the other reservoir. The boundary condition of the typical through-diffusion test is thus a nonzero tracer concentration difference between the external reservoirs, under iso-saline conditions. Under these conditions the steady-state ion flux is always directed toward the low tracer concentration side, and a diffusion coefficient is usually evaluated by relating the steady-state flux to the tracer concentration difference between the reservoirs. The initial condition of one type of the present experiments is converse. Compacted sodium montmorillonite was conditioned with NaClO4 solutions of different concentrations on the two sides of the diffusion cell (further denoted to as salt gradient conditions). Subsequently, radioactive 22Na+ tracer is added to both reservoir solutions at the same concentration. Under these conditions the total 22Na+ concentration in the clay will be higher at the low salinity side of the clay in comparison to the high salinity side. The magnitude and direction of the resulting tracer flux gives direct evidence of whether diffusion in a bulk water phase or surface diffusion is the dominating transport mechanism under such conditions. A possible surface diffusion flux component is thereby expected to be directed from the low toward the high salinity side. The other type of experiments is carried out under iso-saline conditions. The comparison between the two types of experiments will allow for an assessment of the dominating driving force for diffusion to be made in these systems.
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MATERIALS AND METHODS Reagents of highest purity were obtained from Fluka (Buchs, Switzerland) or Merck (Dietikon, Switzerland). Deionised water (Milli-Q water) was used throughout for the preparation of solutions. Radioisotopically pure 22Na+ and HTO were obtained from Eckert & Ziegler (Berlin, Germany). Radiochemical assays of 22Na+ were carried out with a γ-counter (Minaxi-γ, Autogamma 5000 series, Canberra-Packard) using an energy window of 433−1417 keV. Radiochemical assays of mixtures of HTO and 22Na+ were done by liquid scintillation counting (Tricarb 2250 CA, Canberra-Packard) using Ultima Gold XR (Canberra-Packard) as the scintillation cocktail at a ratio of 15 cm3 of cocktail to 5 cm3 of sample. For a discrimination of HTO and 22Na+ activities, two separate 11523
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withdrawal of smaller solution aliquots. This change in sampling regime was necessary in order to monitor the concentration of HTO in the source reservoir and its flux to the target reservoir. Subsequently, the clay plugs were cut into segments along the axis according to procedures previously published,18 and the activities of 22Na+ were directly measured by γ-counting in suspensions of the dried segments equilibrated with 5 cm3 of 0.1 M HCl. During the various phases of the diffusion experiments, the concentrations of stable Na+ were periodically monitored by ion chromatography. Again, no significant change in the electrolyte concentration could be ascertained by these measurements. The diffusion experiments under iso-saline conditions were performed with 0.5 and 1.0 M salinity (NaClO4) using published procedures.15,20 In addition, iso-saline experiments with 0.1 M salinity (NaClO4) were carried out using diffusion cells with advectively flushed filters. The background electrolyte solution containing the tracer species circulated through the filters at a flow rate of 0.1 cm3 min−1 maintaining thereby an almost homogeneous concentration distribution in the filters. The resulting diffusive resistance of the filters is almost negligible which significantly increases result reliability. Simulation of the diffusion experiments was accomplished by numerical procedures provided by the software package Comsol Multiphysics (Comsol AB, Switzerland) and the geochemical transport and speciation code Phreeqc.21
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RESULTS Figure 1 shows the measured concentrations of 22Na+ as a function of time for two experiments differing in their amounts of tracer ions present in solution and amount of exchangeable ions in the clays, respectively. An increasing tracer concentration difference between the reservoirs spontaneously developed over time, that is, 22Na+ was transported “uphill” from the reservoir of lower (and decreasing) to the reservoir of higher (and increasing) tracer concentration. Initially the tracer concentration dropped in both reservoirs as the clay sample accumulated tracer cations, but a quasi-steady state was achieved in a later phase of the experiment where the rate of concentration increase in the high salinity reservoir basically equaled the rate of concentration decrease in the low salinity reservoir (i.e., equal in- and outflow). As can be expected for a smaller clay sample in combination with a larger reservoir volume, the relative concentration changes in the experiment with the 5 mm clay plug (Figure 1a) are smaller than in the experiment with the 10 mm clay plug (Figure 1b). The effect is explained as follows. The experiment starts with equal concentrations of 22Na+ on both sides of the clay which is a nonequilibrium situation (cf. the upper scheme in Figure 2). When local equilibrium prevails at the clay/reservoir interfaces the concentration ratio between reservoir and clay is identical for the radioactive and the stable Na isotope. This can be understood from the definition of the exchange reaction of the two isotopes on the cation exchange sites (X), 22
Na + + NaX ⇄
22
NaX + Na +
Figure 2. Through-diffusion experiment under salt gradient conditions. The clay sample (1) is in contact with a low salinity reservoir (2) and high salinity reservoir (3) by liquid lines. Blue colors represent the concentration of the background electrolyte; the red bars indicate that the experiment started with equal initial concentrations of the 22Na+ tracer in the two reservoirs. The solution concentrations of the stable and the tracer species in a later steady-state flux situation with a maintained constant concentration difference of the background salt are shown in the lower scheme. As the fraction of trace ions should be equal at the interfaces when exchange equilibrium is obtained, an internal nonzero gradient of the tracer cations is induced in the clay. Note that this gradient is directed oppositely to the concentration difference of the tracer and background ions in the reservoir solutions.
Square brackets indicate activity (equivalent or mole fraction of the exchange capacity on the clay). Since [NaX] is ∼1 and [Na+] is constant, it follows that the tracer concentration is enhanced in the clay by a factor inversely proportional to the concentration of the stable isotope in the reservoir. The tracer concentration enhancement in the present test is consequently considerably larger at the interface to the low salinity reservoir. As a result, a tracer concentration profile is induced in the clay with a slope directed opposite to that suggested by the concentration difference between the external reservoirs. (cf. the lower scheme in Figure 2). Model curves representing the expectations for diffusion driven by the concentration gradients in the external bulk water phase only, are also shown in Figure 1. These curves exhibit much slower dynamics and result in a decrease of concentration only instead of the observed increase in the reservoir with 0.5 M NaClO4. A diffusion model based on such a concept is therefore in qualitative and quantitative disagreement with the experimental data. It is shown in the Supporting Information (Figures S1 and S2) that a satisfactory agreement can be obtained using an appropriate modeling approach involving concentration gradients of exchangeable
(1)
involving an equilibrium constant (KNa/22Na): KNa/22Na =
[Na +]· [22 NaX] [NaX]·[22 Na +]
(2) 11524
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Figure 3. Tracer profile of 22Na+ measured at the end of through-diffusion in the experiment with a ∼5 mm thick clay plug and reservoir volumes of ∼250 mL (a) and a 10 mm thick clay plug and reservoir volumes of ∼100 mL (b). The arrows indicate the concentrations of the background electrolyte (NaClO4) at the two boundaries of the clay plugs.
carried out similar measurements for bulk dry densities of 1300 and 1600 kg m−3 (Table 1). The steady-state tracer fluxes of all
cations present in the nanopores as the driving force. The proposed explanation is further supported by the measured profile of total amount of tracer cations across the clay measured after through-diffusion (Figure 3.). Note that the linear character of the profiles is characteristic of a (quasi) steady-state flux situation of diffusion in a homogeneous medium. The internal total tracer gradient is thus in qualitative and quantitative agreement with the observed tracer flux. The following complicating circumstances, all related to the present salt gradient conditions, should be considered: (i) Water is expected to be transported from the low to the high salinity side due to osmosis. This transport, however, is negligible because of the very low hydraulic conductivity in montmorillonite at these large densities (∼10−15 m s−1, ref 22). This conclusion was confirmed in the subsequent combined tracer experiments with 22Na+ and tritiated water (HTO) (Supporting Information Figure S3). (ii) The background electrolyte (NaClO4) diffuses from the high to the low salinity reservoir. It is however demonstrated by ion-chromatographic measurements that the concentrations of the background electrolyte basically remain unchanged during the time of observation (data not shown). This is explained by the very low anion diffusion rates in compacted montmorillonite19 which is limiting the diffusion of the background electrolyte.16 (iii) From an electrochemical perspective, there is an electrical potential difference between the two reservoirs under salt gradient conditions.23 It is however obvious that this potential difference is not a driving force for the “uphill” mass transfer as the setup does not constitute a closed circuit and thus does not maintain an electrical current. This is also confirmed by the observation that the background concentration of the reservoirs does not vary with time (while the tracer concentrations change by up to 20%). By comparing the present results with tracer tests made on similar systems under iso-saline conditions it is possible to further quantify the influence of surface diffusion in compacted montmorillonite. Measurements under iso-saline conditions have been previously published for the diffusion of 22Na+ tracer in a sodium montmorillonite compacted to a bulk dry density of 1900 kg m−3 and NaClO4 concentrations ranging from 0.1 to 1.0 M.15 In the course of the present investigations we also
Table 1. Results of through-Diffusion Experiments Carried out under Iso-Saline Conditions ρdba [kg m−3]
[A]b [mol dm−3]
1297 1300 1290 1597 1559 1564
0.1 0.5 1.0 0.1 0.5 1.0
De (HTO)c [m2 s−1] (1.3 ± 0.4) × (8.6 ± 1.3) × (7.8 ± 1.3) × not measured (4.1 ± 0.7) × (3.8 ± 0.7) ×
10−10 10−11 10−11 10−11 10−11
De (22Na+)c [m2 s−1] (7.0 (1.4 (6.2 (3.3 (9.5 (4.4
± ± ± ± ± ±
0.9) 0.4) 1.2) 0.4) 2.0) 0.6)
× × × × × ×
10−10 10−10 10−11 10−10 10−11 10−11
a
Bulk-dry density of the clay plug. bSalinity (NaClO4) in the external solution, viz. the solution in equilibrium with the clay. cEffective diffusion coefficients calculated using the tracer concentrations in the external solution as the driving force (‘traditional’ evaluation, cf. ref 20).
experiments are plotted as a function of the gradients in the mean tracer concentration (cn̅ p) in the nanopore space of the clay (Figure 4). The latter concentrations were calculated either from the tracer profiles or from the corresponding tracer fluxes taking into account filter effects,18 and the tracer fluxes where normalized for the various clay densities. The data processing is in accordance with procedures proposed by Gimmi et al.24 Details are given in the Supporting Information. The normalized fluxes measured in the iso-saline and salt-gradient tests show a consistent diffusional behavior. From this observation we conclude that surface diffusion generally is the dominating mass transfer mechanism for exchangeable ions in compacted montmorillonite, thus supporting the previously given explanation of observed mass fluxes under iso-saline conditions.15,16,20 The excellent agreement of flux data under iso-saline and salt gradient conditions at a bulk dry density of 1900 kg m−3 (Figure 4) also confirms that the mentioned minor effects related to the salt gradient conditions in the presented “uphill” diffusion tests are insignificant. It should be emphasized that diffusion in the present work actually does not occur against a local concentration gradient, in contrast to “real” uphill diffusion phenomena which rely on 11525
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ACKNOWLEDGMENTS We thank the Swiss National Cooperative for the Disposal of Radioactive Waste (Nagra) for partially financing this work. The technical assistance by Sabrina Frick is greatly acknowledged. The work by Martin Birgersson and Ola Karnland was part of the Task Force on Engineered Barrier Systems, financed by the Swedish Nuclear Fuel and Waste Management Co. (SKB).
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Figure 4. Comparison between steady-state tracer fluxes and gradients of mean tracer concentration in the clay. The plot shows the correlation of normalized steady-state tracer fluxes of 22Na+ (Js,n) in sodium montmorillonite with gradients in cn̅ p for diffusion experiments carried out under iso-saline (empty symbols, 0.1−1.0 M NaClO4) and salt gradient conditions (full symbols, 0.1/0.5 M NaClO4).
couplings between several diffusing components.25 The present effect is not critically dependent on such couplings, and is rather related to mass transfer mechanisms observed in synthetic charged membranes.26 To our knowledge, it has not before been observed in natural clay material. The current results have important implications for transport quantification of charged species in smectite-rich systems which should be considered when assessing the geosphere transport of radioactive and chemical-toxic species. Disregarding concentration gradients caused by species accumulation in the clay may result in nonphysical effective diffusion coefficients of cations, disproportionally high compared to uncharged tracers.27 The present study undeniably shows that data evaluated in this way must be treated with caution in order to avoid erroneous predictions of magnitudes and possibly also, directions of ion fluxes. In systems as those treated here, it is instead more appropriate to relate the flux to exchangeable ion concentration gradients and, consequently, to associate the resulting diffusion coefficients to the molecular mobility of these ions. It can be anticipated that the latter parameter depends on the specific interaction between the diffusing specie and the charged mineral surfaces.
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ASSOCIATED CONTENT
S Supporting Information *
Model calculations for the time evolution of tracer and electrolyte concentrations in the reservoirs. Combined 22Na+ and HTO tracer experiments. Details on procedures to calculate the data in Figure 4. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*(M.G.) Phone: +41 56 310 22 93; fax: +41 56 310 35 65; email:
[email protected]. Notes
The authors declare no competing financial interest. 11526
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(19) Glaus, M. A.; Frick, S.; Rossé, R.; Van Loon, L. R. Consistent interpretation of the results of through-, out-diffusion and tracer profile analysis for trace anion diffusion in compacted montmorillonite. J. Contam. Hydrol. 2011, 123 (1−2), 1−10. (20) Glaus, M. A.; Frick, S.; Rossé, R.; Van Loon, L. R. Comparative study of tracer diffusion of HTO, 22Na+ and 36Cl− in compacted kaolinite, illite and montmorillonite. Geochim. Cosmochim. Acta 2010, 74 (7), 1999−2010. (21) Parkhurst, D. L.; Appelo, C. A. J. User’s guide to PHREEQC (version 2); U.S. Geological Survey: Washington, DC, 1999. (22) Karnland, O.; Olsson, S.; Nilsson, U. Mineralogy and sealing properties of various bentonites and smectite-rich clay materials. In SKB Technical Report TR-06-30, SKB; Stockholm: Sweden, 2006. (23) Yaroshchuk, A.; Glaus, M. A.; Van Loon, L. R. Studies of electrochemical properties of compacted clays by concentration potential method. J. Colloid Interface Sci. 2007, 309, 262−271. (24) Gimmi, T.; Kosakowski, G. How mobile are sorbed cations in clays and clay rocks? Environ. Sci. Technol. 2011, 45 (4), 1443−1449. (25) Onsager, L. Theories and problems of liquid diffusion. Ann. N.Y. Acad. Sci. 1945, 46 (5), 241−265. (26) Higa, M.; Tanioka, A.; Miyasaka, K. A study of ion permeation across a charged membrane in multicomponent ion systems as a function of membrane charge density. J. Membr. Sci. 1990, 49 (2), 145−169. (27) Melkior, T.; Yahiaoui, S.; Thoby, D.; Motellier, S.; Bartès, V. Diffusion coefficients of alkaline cations in Bure mudrock. Phys. Chem. Earth 2007, 32, 453−462.
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