pubs.acs.org/Langmuir © 2010 American Chemical Society
Ca/Na Montmorillonite: Structure, Forces and Swelling Properties M. Segad,† Bo J€onsson,*,† T. A˚kesson,† and B. Cabane‡ †
Theoretical Chemistry, Chemical Center, POB 124, S-221 00 Lund, Sweden, and ‡Laboratoire PMMH, ESPCI,10 Rue Vauquelin, 75231 Paris Cedex 5, France Received September 25, 2009. Revised Manuscript Received February 9, 2010
Ca/Na montmorillonite and natural Wyoming bentonite (MX-80) have been studied experimentally and theoretically. For a clay system in equilibrium with pure water, Monte Carlo simulations predict a large swelling when the clay counterions are monovalent, while in presence of divalent counterions a limited swelling is obtained with an aqueous layer between the clay platelets of about 10 A˚. This latter result is in excellent agreement with X-ray scattering data, while dialysis experiments give a significantly larger swelling for Ca montmorillonite in pure water. Obviously, there is one “intra-lamellar” and a second “extra-lamellar” swelling. Montmorillonite in contact with a salt reservoir containing both Naþ and Ca2þ counterions will only show a modest swelling unless the Naþ concentration in the bulk is several orders of magnitude larger than the Ca2þ concentration. The limited swelling of clay in presence of divalent counterions is a consequence of ion-ion correlations, which reduce the entropic repulsion as well as give rise to an attractive component in the total osmotic pressure. Ion-ion correlations also favor divalent counterions in a situation with a competition with monovalent ones. A more fundamental result of ion-ion correlations is that the osmotic pressure as a function of clay sheet separation becomes nonmonotonic, which indicates the possibility of a phase separation into a concentrated and a dilute clay phase, which would correspond to the “extra-lamellar” swelling found in dialysis experiments. This idea also finds support in the X-ray scattering spectra, where sometimes two peaks corresponding to different lamellar spacings appear.
Introduction During the past few decades the structure of clay-water systems and interfacial water structure in clay minerals such as the smectite group (montmorillonite) have been extensively studied.1-5 Many authors have focused on this topic because of its importance in agricultural as well as technological applications.6 Different European countries, Japan, the US, and Canada plan to deposit high level nuclear waste in deep geological repositories in rocks, salt, or clay sediments.7,8 When storing nuclear waste, it is essential that no radioactivity leaks into the environment, and considerable efforts have been invested in an attempt to evaluate the sealing properties of bentonite clay (MX-80).9-12 One alternative is to put the nuclear waste into copper containers placed underground embedded in bentonite. The success for such a containment depends of course on the clay structure and its stability under varying conditions. In this context, stable means that the clay should be able to sustain considerable changes in the surrounding groundwater including salinities of glacial meltwater as well as seawater, while still being an effective hydraulic barrier.
Dry bentonite, or more correctly its main component montmorillonite, is built up by two tetrahedral and one octahedral unit forming a platelet approximately 10 A˚ thick. The octahedral part consists of Al(III), coordinated with oxygen, and is surrounded by the two tetrahedral sheets consisting of oxygen coordinating Si(IV). In bentonite (montmorillonite) one aluminum atom shares oxygen atoms with the two silica sheets, which gives the unit cell formula, [Al2(OH)2(Si2O5)2].13 The bentonite platelets are negatively charged due to exchange of Al(III) with for example Mg(II) and/or Fe(II). To obtain electroneutrality bentonite clay holds, most commonly, Naþ or Ca2þ as counterions. The platelets form a lamellar structure making bentonite clay a seemingly perfect model system for an electrical double layer where the swelling and stability in saline solution depend strongly on counterion valency and surface charge density.12,14-18 The situation is, however, from a structural point slightly less ideal. Clay is normally not a homogeneous lamellar material. It might be better described as a disordered structure of stacks of platelets, sometimes called tactoids-a tactoid typically consists of 5-20 platelets.19-21 The term tactoid was already used by Langmuir22
*Corresponding author. (1) Swartzen-Allen, S. L.; Matijevic, E. Chem. Rev. 1974, 74, 385. (2) Lubetkin, S. D.; Middleton, S. R.; Ottewill, R. H.; Barnes, P.; Nadeau, P.; Fripiat, J. Phil. Trans. R. Soc. 1984, 311, 353. (3) Luckham, P. F.; Rossi, S. Adv. Coll. Interf. Sci. 1999, 82, 43. (4) Le Baron, P. C.; Wang, Z.; Pinnavaia, T. J. Appl. Clay Sci. 1999, 15, 11. (5) Tchoubar, D.; Cohaut, N. In Handbook of Clay Science; Bergaya, F., Theng, B. K. G., Lagaly, G., Eds.; Elsevier: New York, 2006. (6) Faisandier, K.; Pons, C. H.; Tchoubar, D.; Thomas, F. Clays Clay Miner. 1998, 46, 636. (7) Komine, H.; Ogata, N. Soils Foundations 1999, 39-2, 83. (8) Buzzi, O.; Boulon, M.; Deleruyelle, F.; Besnus, F. Rock Mech. Rock Eng. 2008, 41, 343. (9) Pusch, R. Clay Miner. 1992, 27, 353. (10) Pusch, R. SKB Tech. Rep. 2001, TR-01-08, 1. (11) Komine, H.; Ogata, N. Can. Geotech. J. 2003, 40, 460. (12) Karnland, O.; Olsson, S.; Nilsson, U.; Sellin, P. SKB Tech. Rep. 2006, TR06-30, 1.
5782 DOI: 10.1021/la9036293
(13) van Olphen, H. An Introduction to Clay Colloid Chemistry, 2nd ed.; John Wiley and Sons Inc.: New York, 1977. (14) Blackmore, A. V.; Warkentin, B. P. Nature 1960, 186, 823. (15) van Olphen, H. J. Colloid Sci. 1962, 17, 660. (16) Pellenq, R. J.-M.; Caillol, J. M.; Delville, A. J. Phys. Chem. B 1997, 101, 8584. (17) Delville, A.; Gasmi, N.; Pellenq, R. J.-M.; Caillol, J. M.; van Damme, H. Langmuir 1998, 14, 5077. (18) J€onsson, B.; Wennerstr€om, H. When ion-ion corelations are important in charged colloidal systems. In. Electrostatic Effects in Soft Matter and Biophysics; Holm, C., Kekicheff, P., Podgornik, R., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001. (19) Banin, A. Science 1967, 155, 71. (20) Meunier, A., Clays; Springer: New York, 2005. (21) Shalkevich, A.; Stradner, A.; Bhat, S. K.; Muller, F.; Schurtenberger, P. Langmuir 2007, 23, 3570. (22) Langmuir, I. J. Chem. Phys. 1938, 6, 873.
Published on Web 03/17/2010
Langmuir 2010, 26(8), 5782–5790
Segad et al.
Article
Theoretical Section
Figure 1. Schematic picture of two clay platelets with neutralizing counterions as well as salt ions. The ions are described as charged hard spheres with a radius of 2 A˚, and water is modeled as a dielectric continuum with a relative permittivity εr. The two infinite parallel walls have a uniform surface charge density, σ.
and Bernal and Fankuchen23 in order to describe the aggregation and gel formation in various colloidal solutions. The existence of larger aggregates complicates the theoretical analysis, which always has been limited to the swelling of the tactoids themselves (intralamellar swelling). A further modeling complication is the presence of pH-dependent positive charges on the edge of the platelets.15 Various hypotheses have been put forward for the arrangement of tactoids6,15,24 (the extra-lamellar swelling), but none are really convincing and few are based on possibly existing forces between the tactoids. In this work we choose a combined experimental and theoretical approach, where dialysis and scattering data are confronted with corresponding Monte Carlo (MC) results. The first part of the paper deals with the simulations of a clay model system, see Figure 1. The importance of ion-ion correlations in the presence of divalent counterions is well-known for these systems16,25,26 and the resulting attractive double layer forces lead to a limited intralamellar swelling provided that the ratio between calcium and sodium ions in the surrounding bulk solution is sufficiently high. The attraction can be understood as a competition between repulsive entropic forces on one hand and attractive energetic terms on the other. The change from, for example, Naþ to Ca2þ as counterions means that the entropic term is strongly reduced and the attractive forces due to ion-ion correlations are allowed to dominate. The simulations also predict a phase transition with a water rich (swollen) phase in equilibrium with a water poor phase. These results are based on the assumption that the clay platelets build lamellar structures of the sort depicted in Figure 1. In the second part of the paper we report experimental studies on swelling properties of natural MX-80 bentonite as well as purified Ca/Na montmorillonite under various conditions. Clay samples are studied through small-angle X-ray scattering (SAXS) using a Kratky camera and also more sophisticated beamlines at different installations. Finally, we try to reconcile the theoretical and experimental results and draw some conclusions regarding the structure of the swollen clays. (23) Bernal, J. D.; Fankuchen, I. J. Gen. Phys. 1941, 25, 111. (24) Morvan, M.; Espinat, D.; Lambard, J.; Zemb, Th. Colloids Surf. 1994, 82, 193. (25) Guldbrand, L.; J€onsson, B.; Wennerstr€om, H.; Linse, P. J. Chem. Phys. 1984, 80, 2221. (26) Kjellander, R.; Marcelja, S.; Quirk, J. P. J. Colloid Interface Sci. 1988, 126, 194.
Langmuir 2010, 26(8), 5782–5790
Model System and Interactions. A simplified model of montmorillonite is to treat it as two planar negatively charged surfaces neutralized by sodium and/or calcium counterions-see Figure 1. The lamellar structure is assumed to be in equilibrium with an infinite salt reservoir of known salt concentration (bulk solution). This has for a long time been the generally accepted model system,15,27-29 and the statistical mechanical problem has been solved using the Poisson-Boltzmann (PB) equation.30,31 The latter is an acceptable approximation in the presence of monovalent counterions, but it fails when divalent counterions dominate.25,32-37 In order to obtain reliable results, one has to go beyond the mean-field approximation inherent in the PB equation and use, e.g., Monte Carlo simulation techniques38 or more advanced liquid state theories.39,40 In the model system, the clay platelets have a uniform surface charge density, σ, and the separation between two platelets is denoted h. The water molecules are treated as a dielectric continuum with a relative dielectric permittivity, εr = 78. In this primitive model, all charged species are treated as hard spheres and the interaction, between two particles i and j separated a distance r, can be formally written as uðrÞ ¼
Zi Zj e 2 r > dhc 4πε0 εr r
uðrÞ ¼ ¥ r e dhc
ð1Þ ð2Þ
where Zi is the ion valency, e the elementary charge, and ε0 the permittivity of vacuum and dhc = 4 A˚ is the ion diameter. The ions also interact with the charged walls and an external potential is included in order to take care of the interactions ranging outside the rectangular simulation box.34,41,42 Image charges are not included in the model i.e. there is no dielectric discontinuity at the surfaces. Periodic boundary conditions were used in the directions parallel to the surfaces, and conventional minimum image technique was applied. The number of ions varied between 100 and 1000, depending on salt conditions and separation, and the simulation box contained 200 surface charges. To check the convergence with system size, systems with twice as many particles have been tested. No significant differences have been observed. For small interlamellar distances (less than about 15 A˚) the use of a continuum description of the solvent and clay surfaces might be questionable because of the structuring of the solvent.42 At these separations a full atomistic description of the system would be more appropriate, and a number of molecular simulation studies treating the intra-lamellar swelling on an atomistic level (27) Norrish, K.; Quirke, J. P. Nature 1954, 18, 120. (28) Spitzer, J. J. Langmuir 1989, 5, 199. (29) Karnland, O. SKB Tech. Rep. 1997, TR-97-31, 1. (30) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier Publishing Company Inc.: Amsterdam, 1948. (31) Derjaguin, B. V.; Landau, L. Acta Phys. Chim. URSS 1941, 14, 633. (32) Wennerstr€om, H.; J€onsson, B.; Linse, P. J. Chem. Phys. 1982, 76, 4665. (33) Kjellander, R.; Marcelja, S. Chem. Phys. Lett. 1984, 112, 49. (34) Valleau, J. P.; Ivkov, R.; Torrie, G. M. J. Chem. Phys. 1991, 95, 520. (35) Kjellander, R.; A˚kesson, T.; J€onsson, B.; Marcelja, S. J. Chem. Phys. 1992, 97, 1424. (36) Delville, A. J. Phys. Chem. B 2002, 106, 7860. (37) Kjellander, R. J. Chem. Soc. Faraday Trans. 2 1984, 80, 1323. (38) Metropolis, N. A.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A.; Teller, E. J. Chem. Phys. 1953, 21, 1087. (39) Kjellander, R.; Marcelja, S.; Pashley, R. M.; Quirk, J. P. J. Chem. Phys. 1990, 92, 4399. (40) Forsman, J. J. Phys. Chem. B 2004, 108, 9236. (41) J€onsson, B.; Wennerstr€om, H.; Halle, B. J. Phys. Chem. 1980, 84, 2179. (42) Greberg, H.; Kjellander, R.; A˚kesson, T. Mol. Phys. 1996, 87, 407.
DOI: 10.1021/la9036293
5783
Article
Segad et al.
have been published during the last decade.43-49 Atomistic simulations, however, are time consuming and restricted to rather limited swelling conditions, while in the present study we are interested in much larger separations. Simulations at constant chemical potential of both water and salt are non-trivial, and the force between the surfaces could be strongly model dependent.50 In addition, there are ample examples where the continuum model seems to be applicable down to surprisingly short separations.51,52 Thus, there is still room for a more coarse grained approach like the one pursued in this study-cf. also refs 26 and 53. Osmotic Pressure. The osmotic pressure of the confined solution, pconf osm , may be calculated according to refs 25 and 34: pconf osm ¼ kB T
X
ci ðmpÞ þ pcorr þ phc
ð3Þ
i
where kB is the Boltzmann factor, T the temperature equal to 298 K, ci is the concentration of species i and mp stands for midplane. The term pcorr comes from the fact that ions on either side of the midplane correlate and give an attractive contribution to the pressure. In the mean-field description this term disappears, since correlations across the midplane are neglected. The finite ion size, dhc, gives rise to the term phc. The hard core radius has a clear physical origin, that is, ions can not overlap due to the quantum mechanical exchange repulsion. In simulations, or other theories of electrolyte solutions, it tends to become a fitting parameter incorporating a whole range of physical effects not included in the primitive model. It could, for example, be used to describe the difference in hydration or polarizability of different ions. Thus, there is in our opinion no clear-cut choice for the numerical value of dhc. Fortunately for the present study, there is a relatively broad range for dhc where it has only a weak effect on the net osmotic pressure. With the present choice of dhc, the phc term only gives a significant contribution to the pressure well inside the minimum in the pressure curve. Equation 3 gives the osmotic pressure in the confined region, but the experimentally interesting quantity is the net osmotic pressure bulk posm ¼ pconf osm - posm
ð4Þ
where the bulk pressure is calculated for a bulk with the same chemical potential(s) as the double layer. The bulk simulations are performed in the canonical (NVT) ensemble. The osmotic pressure is in this case calculated from the virial equation54,55 and the chemical potential is obtained via Widom’s perturbation technique.56 (43) Williams, G. D.; Soper, A. K.; Skipper, N. T.; Smalley, M. V. J. Phys. Chem. B 1998, 102, 8945. (44) Delville, A. J. Phys. Chem. 1993, 97, 9703. (45) Karaborni, S.; Smit, B.; Heidug, W.; van Oort, E. Science 1996, 271, 1102. (46) Chavez-Paez, M.; dePablo, L.; dePablo, J. J. J. Chem. Phys. 2001, 114, 10948. (47) Tambach, T. J.; Bolhuis, P. G.; Hensen, E. J. M.; Smit, B. Langmuir 2001, 22, 1223. (48) Young, D. A.; Smith, D. E. J. Phys. Chem. B 2000, 104, 9163. (49) Smith, D. E.; Yu Wang; Whitley, H. D. J. Phys. Chem. B 2006, 110, 20046. (50) Pegado, L.; J€onsson, B.; Wennerstr€om, H. J. Chem. Phys. 2008, 129, 184503. (51) Shubin, V. E.; Kekicheff, P. J. Colloid Interface Sci. 1993, 155, 108. (52) Sonneville, O.; Bergeronand, V.; Gulik-Krzywicki, T.; Bo J€onsson, H.; Wennerstr€om, P.; Lindner; Cabane, B. Langmuir 2000, 16, 1566. (53) Kjellander, R.; Marcelja, S.; Pashley, R. M.; Quirk, J. P. J. Phys. Chem. 1988, 92, 6489. (54) Allen, M. P.; Tildesley, D. J., Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1989. (55) Frenkel, D.; Smit, B., Understanding Molecular Simulation; Academic Press: San Diego, CA, 1996. (56) Widom, B. J. Chem. Phys. 1963, 39, 2808.
5784 DOI: 10.1021/la9036293
In addition to the electrostatic pressure there is also a contribution from the so-called van der Waals interaction30,31,57 ptot osm ¼ posm -
A 3 6πh^
ð5Þ
where h^ = h þ dhc. A is the Hamaker constant, for which we have used the value of 2 10-20 J.58,59 Below we only report the net electrostatic osmotic pressure unless otherwise stated. Ion Composition. With both mono- and divalent ions neutralizing the surface charges, the osmotic pressure becomes strongly dependent on the counterion composition in the double layer. In this work we compare pressure curves as a function of surface separation for two cases: the ratio of counterions is fixed (i.e., we use the NVT ensemble), or the lamellar system is in equilibrium with a bulk electrolyte (μVT ensemble). In the latter case, the concentration of a species in the double layer and in the bulk can differ, and it is only the chemical potentials that are equal. The chemical potential can be written as a sum of a standard chemical potential, an ideal and an excess part60 μ ¼ kB T ln Λ3 þ kB T ln c þ μex
ð6Þ
where Λ is the thermal de Broglie length (for simplicity chosen to 1 A˚), c is the average concentration in A˚-3, and μex is the excess chemical potential. Note that it is only the total chemical potential that is the same in the bulk and in the double layer for a given species. Because of electrostatic interactions μB,ex and μDL,ex can be quite different, where B and DL stand for bulk and double layer, respectively. At surface charge densities studied in this work, μDL,ex is rather sensitive to the counterion valency and, as a consequence, there exists a strong competition for different valency counterions in the double layer. That is, a relatively small concentration of divalent counterions in the bulk is enough to have a double layer that is completely dominated by the divalent ions. For example, the concentration ratio cCa/cNa in the double layer and in the bulk can easily differ by a factor of 100. Formally, this can be seen from moving one Ca2þ from the bulk solution to the double layer and at the same time transferring two Naþ ions in the opposite direction. At equilibrium we have B B DL μDL Ca - μCa þ 2ðμNa - μNa Þ ¼ 0
ð7Þ
Combining eqs 6 and 7 gives the following: kB T ln
B 2 cDL Ca ðcNa Þ 2 B ðcDL Na Þ cCa
, ex - 2μDL, ex Þ -ðμB, ex - 2μB, ex Þ ¼ 0 þ ðμDL Na Na Ca Ca ð8Þ
The last parentheses on the lhs, describing the excess difference in the bulk, is small and can be neglected, while - 2μDL,ex is a large negative number in comparison Δμex = μDL,ex Ca Na to kBT. Since the concentration of sodium ions in the double layer is larger than in the bulk, we obtain finally cDL cB cB Ca > BCa expð -Δμex =kB TÞ . BCa DL cNa cNa cNa
ð9Þ
(57) Lyklema, J. Fundamentals of Interface and Colloid Science; Elsevier: Amsterdam, 2005; Vol. IV. (58) Israelachvili, J., Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. (59) Novich, B. E.; Ring, T. A. Clays Clay Miner. 1984, 32, 400. (60) Hill, T. L., Statistical Mechanics; McGraw-Hill: New York, 1956.
Langmuir 2010, 26(8), 5782–5790
Segad et al.
Article
Experimental Section Materials and Chemicals. Three types of smectite clays were investigated in the this study: natural Wyoming bentonite (MX-80) and pure Na or Ca montmorillonite. We have performed chemical analysis for clay samples and also determined the composition by the inductive coupled plasma-atomic emission spectrometry technique (ICP-AES). The mean chemical composition of MX-80 was found to be (in weight percent): SiO2 (67), Al2O3 (20), CaO (1.2), MgO (2.18), K2O (1.2), TiO (0.12), Na2O (2.7), and Fe2O3 (3.9). The Ca montmorillonite was obtained after purifying MX-80 at the laboratory of Clay Technology AB. The procedure was as follows: 10 g of MX-80 was dispersed in 1 L of 1 M analytical grade calcium chloride solution and left to settle. The supernatant was removed and the procedure repeated three times. The material was washed three times with deionized water and the supernatant was removed after centrifugation. The suspension was separated from the accessory minerals by decanting. In order to remove excess electrolytes, the clay suspension was transferred to dialysis membranes (Spectrapore 3, 3500 MWCO) and placed in plastic containers with deionized water. The water was changed daily until the conductivity was below 10 μS/cm. The material was redispersed in 1 L of 1 M analytical grade CaCl2, and the process was repeated. The final montmorillonite was dried at 60 oC and milled to an aggregate grain size similar to that of MX-80. The Na montmorillonite was prepared using the same procedure except that the MX-80 was initially dispersed in 1 L of 1 M NaCl. The structural formula of the Na-exchanged montmorillonite was determined by ICP-AES elementary analysis:12 ðNa0:64 K0:01 ÞðAl3:11 Ti0:01 Fe0:36 Mg0:47 Þ½ðSi7:93 Al0:07 ÞO20 ðOHÞ4 3 nH2 O and that of the Ca-exchanged form as ðCa0:25 Na0:01 K0:01 ÞðAl3:14 Ti0:01 Fe0:37 Mg0:47 Þ½ðSi7:93 Al0:04 ÞO20 ðOHÞ4 3 nH2 O Sodium chloride (NaCl, Mw = 58.44 g/mol) was purchased from MERCK and Milli-Q water was used to prepare the solutions. Calcium chloride (CaCl2 = 110.99 g/mol) was purchased from Aldrich. Snake skin dialysis tubing (3.5 K MWCO, 1 mils) for the dialysis experiments was bought from Pierce, US. Instruments and Methods. Osmotic Swelling. The series of experiment used SnakeSkin dialysis tubings, which were cut to appropriate length (8 cm) and put into Milli-Q water for 24 h. One end of the tubing was folded over twice and attached. Then 1 g of clay was added and the SnakeSkin tubing was rolled up in the open end and pressed slightly to remove the air inside the pocket, and then folded over twice and attached to make a clay pocket. The tubings were placed in 500 mL of Milli-Q water and stirred/ placed on shaking incubator hood system from (B€ uhler, Germany) at room temperature (25 C)-see Figure 2 for a picture of the setup. Small Angle X-ray Scattering. Small angle X-ray scattering (SAXS)61-63 was used to study the structure in the clay suspensions. Initial studies were performed with a Kratky compact camera with a linear position sensitive detector (MBraun, Graz), and a Seifert ID 3000 (3.5 kW) generator. This instrument is equipped with two separate detectors and it may record the scattered intensity at both low and wide angles. In addition to this we have also used the synchrotron radiation beamline (I711) at the MAX-lab II storage ring in Lund and the beamline ID02 at the European Synchrotron Radiation Facility (ESRF) in Grenoble. A (61) Norrish, K.; Rausell-Colom, J. A. Clays Clay Miner. 1963, 10, 123. (62) Pons, C. H.; Rousseaux, F.; Tchoubar, D. Clay Miner. 1981, 16, 23. (63) Glatter, O.; Kratky, O., Small Angle X-ray Scattering; Academic Press: London, 1982.
Langmuir 2010, 26(8), 5782–5790
Figure 2. Dialysis pocket with clay in a beaker placed on shaking incubator hood system. fourth installation used was a Nanostar instrument at IBBMC in Orsay. Two types of holders were used: one made from aluminum sheets where a paste sample was placed between two mica sheets and the other was quartz capillary for the liquid samples. MX-80 as well as Na/Ca montmorillonite have been studied at varying water and salt content. The samples were either taken from dialysis experiments, that had been running for more than a month to reach equilibrium, or prepared as follows: 0.5 g of clay was dispersed in a known amount of Milli-Q water (limited swelling) or added to 500 mL NaCl-solution of varying concentrations (free swelling), thereafter shaken and placed to equilibrate at 25 oC for a month.
Results Monte Carlo Simulations. The simulations were carried out with the Metropolis algorithm38 in the canonical or the grand canonical ensemble.54,55 The canonical ensemble was used when the clay slit, i.e., the intralamellar space, was in equilibrium with pure water, while the grand canonical ensemble was used for systems in equilibrium with a salt reservoir of finite concentration. In the former case the requirement of electroneutrality prevents any ion exchange with the bulk solution. We want to emphasize that a system with a fixed ratio of Naþ and Ca2þ ions in the slit and no exchange with a bulk behaves differently from a system with the same ratio of the two species in the bulk, with which it is in equilibrium. Initially we studied a salt free system with surface charge densities between -0.05 and -0.13 C/m2. Monovalent counterions always lead to a monotonic repulsion between the clay particles (results not shown here), while with divalent counterions and a high surface charge density an attraction appears due to ion-ion correlations-see Figure 3. An interesting feature is that an increase in surface charge density leads to an enhanced attraction with divalent counterions, while with monovalent counterions it gives a larger repulsion. The former observation is in agreement with the difference in so-called crystalline swelling of montmorillonite and vermiculite, where the latter clay has a higher absolute surface charge density and also shows the smallest swelling in the presence of divalent counterions.64 Figure 3 covers (64) Norrish, K. Discuss. Faraday Soc. 1954, 18, 120.
DOI: 10.1021/la9036293
5785
Article
Segad et al.
Figure 3. Electrostatic component of the osmotic pressure as a function of separation for a system with divalent counterions. The bulk solution consists of pure water; i.e., pbulk osm = 0 and the surface charge density is indicated in the figure.
Figure 5. Salt effect on the net osmotic pressure with σ = -0.14
C/m2. (a) The slit is in equilibrium with a bulk solution containing a 1:1 salt (e.g., NaCl), and (b) the bulk contains a 2:1 salt (e.g., CaCl2).
Figure 4. Total osmotic pressure as a function of separation for a
surface charge density of -0.16 C/m2. The total pressure, including both electrostatic and van der Waals interaction, is drawn as lines without symbols, while the electrostatic component only is drawn as lines with filled circles. Solid lines are for a system with monovalent counterions and dashed lines for divalent. Finally, the dashed line with squares is the electrostatic pressure as obtained from the PB equation with divalent counterions.
a range in surface charge density and shows that electrostatic interactions alone is enough to give an attractive pressure if |σ| > 0.08 C/m2 in the presence of divalent counterions. Replacing, for example, divalent calcium ions with trivalent aluminum ions further enhances this effect in agreement with flocculation experiments.65 Note that the nonmonotonic curves in Figure 3 have weak maxima showing the possibility of two phases in coexistence. NMR studies on Ca hectorite66 indicate that this actually happen. We will return to this matter in the Discussion. The pressure curves in Figure 3 lack the attractive van der Waals component included in eq 5. Addition of this term introduces a small decrease of the pressures as can be seen in Figure 4-with monovalent counterions, the pressure is still repulsive. The corresponding pressure calculated with the PB equation is also added for comparison. Obviously, the latter gives a qualitatively incorrect result with divalent counterions!25 Figure 5a shows the result of adding a 1:1 salt to a system with monovalent counterions. The salt leads to a screening of the repulsion as predicted by the PB equation. The actual values are in fair agreement with experiments67 considering that there is no adjustable parameter in the theoretical curves. Figure 5b shows that a system with divalent counterions in the reservoir is less (65) Kahn, A. J. Colloid Interface Sci. 1958, 13, 51. (66) Weiss, C. A.; Gerasimowicz, W. V. Geochim. Cosmochim. Acta 1996, 60, 265. (67) Callaghan, I. C.; Ottewill, R. H. Faraday Discuss. Chem. Soc. 1974, 57, 110. (68) Kekicheff, P.; Marcelja, S.; Senden, T. J.; Shubin, V. E. J. Chem. Phys. 1993, 99, 6098.
5786 DOI: 10.1021/la9036293
sensitive to salt addition, a fact which has also been seen experimentally.68 The van der Waals interaction becomes important with monovalent counterions when the double layer repulsion has been screened out by a high salt content-approximately 1 M NaCl is needed.69 Under these conditions, the van der Waals attraction dominates and even a clay with exclusively monovalent counterions shows a limited swelling-the water layer reaches a maximum of about 10 A˚ similar to systems with divalent counterions and in good agreement with the SAXS measurements-see the section on SAXS Results. We have also simulated a clay system in equilibrium with a salt solution containing a mixture of Naþ and Ca2þ ions. The valency of the co-ion is of less importance and we have for simplicity taken it to be monovalent. With both Naþ and Ca2þ ions in the bulk there will be a competition for the charged surfaces. Ca2þ ions will dominate in the double layer in general, but the detailed outcome will depend mainly on two factors, the surface charge density and the concentration ratio between mono- and divalent counterions in the bulk. Figure 6a shows that a system with σ = -0.14 C/m2 and 100 mM NaCl can sustain a ratio of almost 100 and still maintain a net attraction between the clay particles. If the surface charge density is increased then an even higher ratio is possible. In the opposite situation, with a lower surface charge density, ion-ion correlations become less important and calcium ions will not dominate the double layer interaction. The curve in Figure 6b with an attractive minimum corresponds approximately to the salt conditions in ocean water (500 mM monovalent cations and 10 mM divalent cations). In a situation where the clay is in equilibrium with a mixture of mono- and divalent salts, the amount of monovalent counterions neutralizing the surface charges is typically very low (about a few percent). On the other hand, if we prepare the system such that the amount of Naþ ions in the slit is fixed, then it suffices to increase (69) J€onsson, B.; A˚kesson, T.; J€onsson, B.; Meehdi, M. S.; Janiak, J.; Wallenberg, R. SKB Technical Report; 2009; TR-09-06.
Langmuir 2010, 26(8), 5782–5790
Segad et al.
Article
Figure 8. Dialysis result for MX-80 (squares) and Ca montmorillonite (spheres). One gram of clay was placed in the dialysis pocket, which was placed in Milli-Q water. The weight increase of the pocket is plotted as a function of square root of time. The dashed line indicates a swelling of the water layer to approximately 10 A˚ as predicted by simulations.
Figure 6. Net osmotic pressure as a function of separation. The bulk contains a mixture of NaCl and CaCl2 and σ = -0.14 C/m2. The NaCl concentration is kept constant at (a) 100 and (b) 500 mM, while the CaCl2 concentration is varied as indicated in the graphs.
Figure 7. Net osmotic pressure as a function of separation. The system is in equilibrium with pure water and the amount of monovalent/divalent counterions has been varied. The fraction of surface charge neutralized by monovalent counterions is indicated in the figure. The surface charge density is -0.11 C/m2.
the relative amount of Naþ ions to approximately 10% in order to obtain a repulsive double layer interaction. This is shown in Figure 7, where the fraction of sodium ions has been varied in three different simulations. Note that these are canonical simulations; i.e., the double layer is in equilibrium with pure water. A possible consequence of this phenomenon is that even a small nonelectrostatic effect, e.g., a weak specific adsorption to the clay surface, that favors the monovalent counterions can change the interaction from attraction to repulsion. Dialysis Experiments. We have analyzed the swelling of MX80 as well as Ca montmorillonite in a dialysis pocket immersed in pure (Milli-Q) water. One g of clay was placed in a pocket made from a semipermeable membrane and was allowed to equilibrate in Milli-Q water. During a period of 5 weeks, both samples swelled continuously. MX-80 contains a mix of Naþ and Ca2þ (plus a small amount of Mg2þ) counterions. The ratio of monoand divalent counterions is approximately three and the swelling Langmuir 2010, 26(8), 5782–5790
behavior is dominated by the monovalent species. As expected, the swelling of MX-80 was significantly larger than for Ca montmorillonite-see Figure 8-and if we assume a purely lamellar swelling, it corresponds to a thickness of the water layer of approximately 3-400 A˚. Ca montmorillonite swells much less, corresponding to a water layer of about 100 A˚, but still much more than the 10 A˚ predicted by simulations-the dashed line in Figure 8 indicates a 10 A˚ swelling. The discrepancy will, however, be resolved by the SAXS experiments reported below. The swelling dynamics are qualitatively different for MX-80 and Ca montmorillonite. The former varies linearly with the square root of time during the first few weeks indicating a diffusion controlled process.70 At longer times, more than a month, the swelling rate is reduced due to the limited size of the dialysis bag. Ca montmorillonite, on the other hand, has an initial fast swelling,√but already after 1 day its swelling varies more slowly than t. In this case, the dialysis pocket is large enough, and we can only speculate that the reduced swelling rate at long times is due to attractive forces between the tactoids or to a slow phase transition. The difference between the MX-80 and Ca montmorillonite could be due to the fact that the latter only have a limited intralamellar swelling and that the major part is due to extra-lamellar tactoid swelling. If we assume that the initial swelling of MX-80 is limited by the rate of permeation, then we can use Darcy’s law71 to calculate the permeability, ∂V kp AΠ ¼ sη ∂t
ð10Þ
where V is the water volume that permeates across the sample during swelling, t the time, kp the permeability, A the cross section area, s the height of the sediment and η the water viscosity. In a free swelling experiment, the clay exchanges water with a surrounding bulk under the effect of an osmotic pressure difference Π. Therefore, the swelling as well as the flux is nonuniform. In a first approximation, we ignore this complication and assume that the water flux is uniform across the dialysis pocket. We also assume that we can consider the dialysis volume V to be an approximate parallelepiped with area A and thickness s. Thus, we can rewrite eq 10 in terms of the increased mass m = FV and solve (70) Martin, C.; Pignon, F.; Magnin, A.; Meireles, M.; Lelievre, V.; Lindner, P.; Cabane, B. Langmuir 2006, 22, 4065. (71) Darcy, H. Les Fountaines Publiques de la Ville de Dijon; Dalmont: Paris, 1856.
DOI: 10.1021/la9036293
5787
Article
Segad et al.
Figure 9. X-ray scattering intensity as a function of wave vector for Na montmorillonite in contact with a NaCl solution: (a) 1 M and (b) 100 mM (free swelling). The peak in a) corresponds to a repeat distance of 20 A˚. The scattering curve in part a is recorded with the Nanostar instrument, while the curve in part b is obtained with the Kratky camera.
the differential equation to obtain m2 ¼
F2 A2 kp Π t þ m20 η
ð11Þ
where m0 is the initial mass. In solving the differential equation, we have made use of the assumption that kpΠ is constant, since according to the Carman-Kozeny relations kp φ-2 and from the Poisson-Boltzmann equation we can derive that Π φ2, where φ is the volume fraction of clay. From Figure 8 we can derive the slope and the osmotic pressure was determined from the MC simulations to be of the order 0.5 105 Pa at a volume fraction of 0.13. This gives an estimate of the permeability of kp ≈ 3 10-18 m2, which is in fair agreement with other measurements on bentonite.72 This value can also be compared to a measured permeability, kp = 0.6 10-18 m2, for a laponite dispersion at the same volume fraction.70 SAXS Results. The results of the simulations and free swelling experiments do not seem to agree. Simulations predict a limited swelling for Ca montmorillonite even if the system is in equilibrium with a bulk solution that is dominated by sodium ions. In order to obtain some insight into this question we have performed a set of SAXS studies. Details of the experimental procedure can be found elsewhere,63,73 and here we concentrate on the analysis of the spectra. With a conventional X-ray source the instrumental limitations are such that repeat distances above a few hundred angstroms are difficult to detect. It would of course be desirable to go beyond this limitation, something that can be achieved with ultrasmall-angle X-ray scattering either on a (72) Pusch, R. SKB Tech. Rep. 1980, TR-80-16, 1. (73) Lindner, P.; Zemb, Th. Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter; North-Holland: Amsterdam, 2002. (74) Lemaire, B. J.; Panine, P.; Gabriel, J. C. P.; Davidson, P. Europhys. Lett. 2002, 59, 55.
5788 DOI: 10.1021/la9036293
Figure 10. X-ray scattering intensity as a function of wave vector for (a) MX-80 and (b) Ca montmorillonite in pure water (limited swelling). The weight % of water is given in the graph. The curves were recorded at beamline I711 at Max-II.
standard setup24 or, in particular, on a more advanced instrument with high-brilliance.74 For our discussion, however, it suffices with the present accuracy. Figure 9a shows that Na montmorillonite in contact with a salt solution containing 1 M NaCl only swells to a water layer thickness of about 10 A˚, in agreement with simulations69 and with earlier scattering studies on Na montmorillonite6,24 as well as natural bentonite (MX-80).75 The limited swelling in this case indicates that the double layer repulsion has been screened and van der Waals forces dominate. If the NaCl concentration is reduced to 100 mM, Figure 9b, the clay starts to swell and the peak moves to smaller q values, unfortunately not reached by the instrument. However, the swelling by successive addition of water can be followed as is done in Figure 10a. In the regime 50-80% water one can observe two peaks in the scattering curves. This can be taken as an indication of the existence of two lamellar phases-one with a limited amount of water and a conserved repeat distance of 10 A˚ and a second phase that incorporates the major part of the added water. In order to verify if this observation is a true equilibrium state or not requires further studies. This type of equilibrium between two lamellar phases has been observed in surfactant solutions with mixed counterions.76 Ca montmorillonite shows a completely different swelling behavior-see Figure 10b. Successive addition of Milli-Q water to the Na dominated MX-80 leads to increasing separation between the clay platelets, but in Ca montmorillonite the maximal thickness of the water layer stays constant at approximately 10 A˚ corresponding to a repeat distance of 20 A˚. Ca montmorillonite in equilibrium with pure water, Figure 11a, shows the same behavior with a Bragg peak at a q value corresponding to a repeat distance in real space of 20 A˚. This (75) Saiyouri, N.; Tessier, D.; Hicher, P. Y. Clay Miner. 2004, 39, 469. (76) Khan, A.; J€onsson, B.; Wennerstr€om, H. J. Phys. Chem. 1985, 89, 5180.
Langmuir 2010, 26(8), 5782–5790
Segad et al.
Article
Figure 12. Simulated osmotic pressure as a function of separation with divalent counterions and σ = -0.08 C/m2. The two stable separations are shown as black spheres and connected with a dot-dashed line.
Figure 11. X-ray scattering intensity as a function of wave vector for (a) Ca montmorillonite in excess water and (b) MX-80 in equilibrium with different salt solutions. The NaCl concentration is kept fixed at 200 mM, while the CaCl2 concentration is varied as indicated in the graph. The data in part a are obtained at beamline I711 at MAX-II, while the curves in part b are recorded at beamline ID02 at ESRF. The samples are taken from dialysis experiment.
result is in agreement with the simulated force curve in Figure 3 with a surface charge density of -0.13 C/m2. Figure 11b shows the same scattering pattern, but now for a clay in equilibrium with a bulk of mixed NaCl and CaCl2 salt. A single peak at approximately 20 A˚ is observed revealing that despite the high NaCl concentration in the surrounding bulk solution, the clay is still dominated by Ca2þ counterions. The same results have been obtained from competition experiments with Na bentonite in an oedometer test cell.77 We have repeated the swelling and scattering experiments with Mg2þ instead of Ca2þ in order to check for ion specificity and found virtually identical results, which is in agreement with earlier findings of Norrish.64 That is, both the intensities and the positions of the peak at 20 A˚ in the scattering curve are the same supporting the conclusion that ion-ion correlations are responsible for the attractive interaction.
Discussion In the dialysis experiments, we found that Ca montmorillonite was incorporating much more water than expected from simulations and scattering data, which both predict a water layer of approximately 10 A˚, while the dialysis data correspond to an average swelling of about 100 A˚. Similar results have been found in a number of other experimental studies.14,24,78 This means that the simple picture of clay consisting of well organized platelets in a perfect lamellar structure is incomplete. One possible explanation is the formation of tactoids containing a small number of platelets. From the peak width in the scattering curves, we can (77) Guyonnet, D.; Gaucher, E.; Gaboriau, H.; Pons, C.-H.; Clinard, C.; Norotte, V.; Didier, G. J. Geotech. Geoenv. Eng. 2005, 131, 740. (78) Dvinskikh, S., Personal commun. (2008). (79) Klug, H. P.; Alexander, L. E. X-ray diffraction procedures for polycrystalline and amorphous materials; Wiley-Blackwell: Chichester, U.K., 1974.
Langmuir 2010, 26(8), 5782–5790
estimate the number of platelets per tactoid to 10-20 in Ca montmorillonite.79 From this estimate and the observed swelling, we obtain an approximate average separation between the tactoids of about 500-1000 A˚ (in this estimate we have assumed that the platelet diameter is 500 A˚).80 Thus, the main part of the swelling in Ca montmorillonite takes place between the tactoids and not between the single platelets. The extra-lamellar swelling may be the cause of higher permeability observed for water and ions in calcium dominated montmorillonites.12 A similar increased permeability has been found for laponite clay in the presence of MgCl2.81 In the case of nuclear waste storage this could lead to a lack of confinement of the actinide ions. The structural arrangement of the tactoids is unknown but an X-ray scattering instrument with a wider q range could be helpful in order to obtain further structural information. We might summarize the swelling in terms of a “traditional” intralamellar swelling, well described by simulations and SAXS, combined with an extra-lamellar swelling, of which we need further experimental structural information. We may speculate of the origin for the unexpected swelling of calcium montmorillonite. An enlargement of the simulated osmotic pressures in Figure 3 shows that the pressure curves are nonmonotonic-Figure 12. For such a situation, there exists in principle two stable separations as indicated in the figure (cf. van der Waals loop). Thus, the swelling seen in the dialysis experiments with Ca montmorillonite could be a result of this effect. In principle, one should be able to observe a macroscopic phase separation,76,82 but its absence could be due to kinetic barriers. The importance of ion-ion correlations depends on the valency of the counterions, the surface charge density and on the solvent used, which for clay in a natural setting will exclusively be water. In a system with mixed counterions, e.g., Naþ and Ca2þ, there will be a competition, and if Naþ dominates in the slit, then the clay will swell, while in the opposite situation we will have a nonswelling system incorporating a water layer of approximately 10 A˚. This competition will depend on the surface charge density and a higher surface charge density favors calcium counterions and a nonswelling behavior. In a clay with only calcium counterions, the transition between swelling and nonswelling happens at a surface charge density around -0.08 C/m2 (not taking the van der Waals interaction into account). (80) Michot, L. J.; Bihannic, I.; Porsch, K.; Maddi, S.; Baravian, C.; Mougel, J.; Levitz, P. Langmuir 2004, 20, 10829. (81) V. Lelievre. Rheologie et filtration de dispersions aqueuses de nanoparticles d’hectorite en relation avec la structuration des depots. Ph.D. Thesis, Institut National Polytechnique de Grenoble: Grenoble, France, 2005. (82) Turesson, M.; Forsman, J.; A˚kesson, T.; J€onsson, B. Langmuir 2004, 20, 5123.
DOI: 10.1021/la9036293
5789
Article
The surface charge density of bentonite is often quoted to be on the order of -0.10 to -0.16 C/m2. A consequence is that in a mixed salt environment, with both mono- and divalent cations, bentonite clay will only swell in a limited salt region. At low sodium concentrations, ion-ion correlations will ensure a net attractive pressure and at high sodium levels (83) Karnland, O. Personal communication, 2008.
5790 DOI: 10.1021/la9036293
Segad et al.
van der Waals forces will do the same. A similar conclusion was reached by Karnland et al.83 based on sedimentation experiments. Acknowledgment. This study was supported by the Swedish Nuclear Fuel and Waste Management Company (SKB), the Foundation for Strategic Research (SSF) and the Swedish Research Council through a Linnaeus grant (OMM).
Langmuir 2010, 26(8), 5782–5790
