Tactoid Formation in Montmorillonite - ACS Publications - American

Article pubs.acs.org/JPCC

Tactoid Formation in Montmorillonite M. Segad,*,† Bo Jönsson,† and B. Cabane‡ †

Theoretical Chemistry, Chemical Center, Lund University, POB 124, S-22100 Lund, Sweden ESPCI, 10 Rue Vauquelin, 75231 Paris Cedex 5, France

‡

ABSTRACT: Aqueous dispersions of Ca montmorillonite contain small clusters of clay platelets, often named “tactoids”. In these tactoids, the platelets are arranged parallel to each other with a constant spacing of 1 nm. We have used smallangle X-ray scattering (SAXS) to determine the average number of platelets per tactoid, ⟨N⟩. We found that this number depends on the platelet size, with larger platelets yielding larger tactoids. For a dispersion in equilibrium with a mixed electrolyte solution, the tactoid size also depends on the ratio of divalent to monovalent cations in the reservoir. Divalent counterions are strongly favored in this competition and will accumulate in the tactoids. In dispersions of pure sodium montmorillonite, that are equilibrated with a mixture of Na+ and Ca2+ cations, the Na+ cations initially cause a repulsion between the platelets, but the divalent ions rapidly replace the monovalent ones and lead to the formation of tactoids, typically within less than one hour based on the divalent to monovalent ratio. This cation exchange as well as tactoid formation can be semiquantitatively predicted from Monte Carlo simulations.

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INTRODUCTION In the early years of X-ray diffraction, a number of researchers attempted to correlate the swelling of clays with their structure.1−3 They soon found out that “swelling clays” such as montmorillonite were made of platelets separated by water layers, and that the average spacing of the platelets matched the overall swelling of the clay, at least when the clays swelled in low salinity water.3 However, when they tried to swell the same clays with water containing divalent cations, or very high concentrations of monovalent cations, they observed sharp diffraction peaks at much higher angles, indicating that the clay platelets had a regular spacing that remained locked at 1.9 nm.3 At the same time, they were surprised to find that the clays still swelled continuously, albeit at a slower rate than in the absence of calcium ions.3 The variations of the average interlayer spacing with hydration and salt were eventually explained, first by the mean field theories of the diffuse electrical double layer in the case of monovalent cations, and then by ionic correlation effects in the case of divalent cations.4 However, the fact that the clay did swell in 2:1 electrolytes was in conflict with the observation of a fixed 1.9 nm spacing between platelets. This was an important matter for agriculture on clay-rich soils, since the clay structure controls the permeability of water and nutrients in the soil. In 1961, Blackmore and Miller5 analyzed the peak widths (w) of these diffraction patterns, according to the Scherrer equation that gives the number of repeated units, N, in a given crystallographic direction. In calcium montmorillonite, prepared by ion exchange from the sodium form, they found that the diffraction peak originated from lamellar structures or “tactoids” consisting of a handful of platelets stacked parallel to each other at equidistant distances, N ≃ 5−8 platelets each, © 2012 American Chemical Society

depending on the maximum osmotic pressure that the clay had experienced (Figure 1a). In very dilute dispersions of Na/Ca montmorillonite, the formation of tactoids was found to be nearly instantaneous, whereas their breakdown occurred over times of the order of 10 min.6 In 1977, Shomer and Mingelgrin

Figure 1. Early work on tactoid formation in expandable clays. (a) Calcium montmorillonite dispersions submitted to osmotic stress, from Blackmore and Miller.5 The average number of platelets per tactoid, ⟨N⟩, varies as the logarithm of the maximum osmotic pressure experienced by the dispersion. (b) Aqueous dispersions of mixed Na and Ca montmorillonites, prepared at different Na/Ca mole ratios.7 ⟨N⟩ increases with the fraction of Ca2+ in the clay. For pure Ca montmorillonite, ⟨N⟩ = 16.1. The green squares show the average tactoid size obtained in this work for a sample obtained from preparation III with 20 mM NaCl and varying concentration of CaCl2. See the text for further discussion. Received: September 24, 2012 Revised: November 12, 2012 Published: November 14, 2012 25425

dx.doi.org/10.1021/jp3094929 | J. Phys. Chem. C 2012, 116, 25425−25433

The Journal of Physical Chemistry C

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collected through aspiration. This step resulted in a fractionation of the clay according to sedimentation rates, and therefore according to particle size. Finally, in order to remove excess electrolytes, the clay suspension was transferred to dialysis membranes (3500 MWCO) and placed in plastic containers with Millipore water. The water was changed daily until the conductivity was below 10 μS/cm. The final Na montmorillonite was used as a dispersion in preparation I (see below) or dried at 60 °C and milled to an aggregate grain size similar to that of MX-80. Purification of Ca and Mg Montmorillonites. The Ca and Mg montmorillonites were prepared through a similar process: the natural MX-80 was initially dispersed in Millipore water and allowed to stand until the large particles, >2 μm, had sedimented and various impurities were discarded. The suspension was then dispersed in 1 L of 1 M MgCl2 or CaCl2, respectively.12 The clay particles were left to settle, and a homogeneous sediment was formed. The whole sediment was recovered, and the procedure was repeated three times. Since the whole sediment was collected, there was no fractionation according to particle size. In order to remove excess electrolytes, we used the above-mentioned dialysis procedure. The final Ca/Mg montmorillonite was either used as a dry powder (as in preparation II) or as a dispersion. MX-80. A powder of MX-80 was initially dispersed in Millipore water and allowed to swell for a very long time (∼1 year). The bottom layer, containing the largest particles, >2 μm, was discarded as explained above. The rest of the suspension (from the middle layer) was used directly in preparation III. Raw MX-80, containing also the large particles, was used as it is in preparation IV. Table 1 summarizes the mean chemical composition of Wyoming bentonite (MX-80), Na, Ca, and Mg montmor-

obtained transmission electron microscopy (TEM) images of the cross sections of Na/Ca tactoids.7 According to a statistical analysis of about 100 cross sections of tactoids, the number of platelets per tactoid decreased with Na/Ca ratio, from about N = 16 for pure calcium montmorillonite to N ≃ 1 for sodium montmorillonite (Figure 1b). However, no explanation could be given for these values of N nor for their variations according to the conditions experienced by the clay. These results turned out to be very important for soil science, because the formation of dense tactoids took place together with a macroscopic swelling of the clay, implying that the distance between tactoids (Ht) was much larger than the separation of platelets, hs, within a tactoid. Indeed, Russo and Bresler demonstrated that the hydraulic conductivity of soils that contained expandable clays was related to the number of platelets per tactoid.8 Moreover, the adsorptive capacity of these clays was found to be sensitive to tactoid sizes.9 However, the origin of this intertactoid (extralamellar) swelling remained mysterious. To our knowledge, these issues are still unresolved. The literature on swelling clays does not teach us whether the numbers of platelets per tactoid are determined by the history of each clay sample or by the balance of forces in its final states, or by some combination of both. We do not know if the distances between tactoids result from packing constraints or from repulsive forces that would keep them separated and tend to increase this separation whenever osmotic swelling is possible. Maybe more important, we do not know how the platelet size and charge density influence the tactoid formation. Here we present new evidence on this problem, based on small-angle X-ray scattering (SAXS) and swelling experiments combined with Monte Carlo simulations. We observe the formation of tactoids in Ca and Mg montmorillonite, and we also investigate the evolution of tactoids in aqueous dispersions of pure Na montmorillonite when put in contact with a reservoir containing a mix of calcium and sodium ions. In addition, we have also studied MX80, which is an expandable Na dominated clay that has been selected for the confinement of nuclear waste.10,11 In contrast with previous work, we control the chemical potentials of all exchangeable species (ions and water), rather than keeping the overall composition constant. That is, the clay is in equilibrium with a reservoir of fixed concentration. This makes our results more relevant for the prediction of changes in clay composition, structure, and permeability over very long time scales.

Table 1. ICP-AES Analysis of Na, Mg, and Ca Montmorillonite and MX-80

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EXPERIMENTAL SECTION The source of natural clay used throughout this work was Wyoming bentonite (MX-80). Analytical grade sodium chloride (purity, 99.5%) was purchased from MERCK, and Millipore water was used to prepare the solutions. Calcium chloride and magnesium chloride (purity, 98%) were purchased from Aldrich. Snake skin dialysis tubing was bought from PIERCE. Purification of Na Montmorillonite. Montmorillonite with Na+ counterions was obtained from MX-80 after a careful purifying process. The procedure was as follows: 20 g of MX-80 was dispersed in 2 L of Millipore water and allowed to stand until the large particles, >2 μm, had sedimented and the rest of the suspension was recovered. In order to remove all multivalent ions, this suspension was washed by addition of 1 M NaCl solution three times: each time, the clay was mixed with the aqueous salt solution and left to settle and the supernatant was removed. Then, the clay suspension was washed three times with Millipore water. Each time, the sodium clay was left to settle for at least a week and the middle part was

composition in wt %

Na clay

Mg clay

Ca clay

MX-80

SiO2 Al2O3 Fe2O3 MgO CaO Na2O K2O TiO2

68 21 4.0 2.2 0.1 3.8 0.6 0.1

67 20 3.6 3.8 0.3 0.4 0.6 0.11

68 21 3.9 2.1 2.4 0.3 0.5 0.1

67 20 3.9 2.2 1.2 2.7 1.2 0.12

illonite samples as obtained from the inductive coupled plasmaatomic emission spectrometry technique (ICP-AES). Sample Preparation. Dialysis (Preparation I and III). A 10 g portion of Na or Ca montmorillonite or MX-80 dispersions was placed in SnakeSkin dialysis tubings. One end of the dialysis tubing was folded over twice and attached, and then, 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. The dialysis pockets of Na montmorillonite were placed in 500 mL of 5 mM CaCl2 or 50 mM CaCl2 (denoted hereafter as preparation I), whereas the pockets of MX-80 dispersion were placed in 500 mL of 20 mM NaCl with varying amounts of CaCl2 (0.5−5 mM CaCl2), denoted hereafter as preparation III, and then all samples placed on a shaking incubator hood system (from Bühler25426



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Germany) at room temperature (25 °C) for more than 3 months. Free Swelling (Preparation II and IV). In the spontaneous swelling series (swelling under no applied pressure), 0.27 g of dry Mg or Ca montmorillonite was dispersed into separate test tubes with Millipore water (labeled as preparation II). The free swelling of raw MX-80 was done in a similar way but with 20 mM NaCl and a varying amount of CaCl2 (preparation IV). These tubes were shaken until complete dispersion (the clay volume fraction, ϕc = 0.01) and left to equilibrate at 25 °C for more than 3 months. Particle Size Distributions. We carried out size distribution measurements for the different preparations using dynamic light scattering (DLS). DLS was performed using a Malvern Zetasizer NS instrument. Figure 2 shows the size distributions

clay dispersions were measured in 1 mm quartz capillaries. The background scattering of the pure water or salt was subtracted. In order to determine the tactoid size, that is, the number of clay platelets per tactoid, a model scattering peak has been fitted to the experimental data. The scattering function can be approximated with a Lorentzian line shape: w Ip(q) ∝ (q − qmax )2 + w 2 (1) where Ip(q) is the scattering function and w is a measure of the width. According to the Scherrer relation, the full width at halfmaximum of the peak, w, is related to the tactoid size through N ≈ qmax/w.19−21

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THEORETICAL SECTION Monte Carlo Simulations. The simplified montmorillonite model in Figure 3 is assumed to be in equilibrium with an

Figure 2. Particle size distributions, obtained through dynamic light scattering. The solid thick line gives the particle size distribution for natural MX-80 (preparation IV without any added salt), and the red dashed line is from MX-80 from preparation III. The thin green line shows the distribution for Na montmorillonite from preparation I.

obtained from the different preparation methods. The Na montmorillonite dispersion (preparation I) has an average size of ⟨D⟩ ≃ 350 nm,14 while the dispersion obtained from swollen MX-80 (preparation III) has a broader size distribution with an average particle size of ∼450 nm (see Figure 2). The dispersions obtained through preparation IV have very broad size distributions, with particle sizes up to 2000 nm.16 The preparation schemes are summarized in Table 2.

Figure 3. Schematic picture of two clay platelets with neutralizing counterions as well as salt ions described as charged hard spheres with a diameter of 0.4 nm and with water modeled as a dielectric continuum with a relative permittivity εr. The two infinite parallel walls have a uniform surface charge density, σ.

infinite salt reservoir of known salt concentration (bulk solution). Water is treated as a dielectric continuum with a relative dielectric permittivity of 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 of r can be formally written as

Table 2. Parameters of Preparation Routes of the Studied Claysa preparation

I

clay

Na mont.

route

dialysis pocket 350−400 5 or 50 CaCl2

⟨D⟩ (nm) salts (mM) a

II

III

IV

Ca/Mg mont. test tube

MX-80 dispersion dialysis pocket

MX-80 powder

>500 salt free

450−500 20 NaCl + xCaCl2

>500 20 NaCl + xCaCl2

test tube

u(r ) =

ZiZje 2 4πε0εrr

u(r ) = ∞

x = 0.5−5 mM.

r > dhc r ≤ dhc

(2) (3)

where Zi is the ion valency, e the elementary charge, ε0 the permittivity of vacuum, and dhc = 0.4 nm 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.22−24 The osmotic pressure of the confined solution, pconf osm , may be calculated according to4,24

Small Angle X-ray Scattering (SAXS). The small-angle Xray scattering (SAXS) experiments were performed at the synchrotron radiation facility at the MAX II storage ring at beamline I911-4 in Lund, Sweden.17 A monochromatic beam of 0.91 Å wavelength was used together with point collimation and a two-dimensional position-sensitive CCD detector (165 mm in diameter active area, from Marresearch, Gmbh). The sample to detector distance was 1.24 m (q = 0.2−3.8 nm−1). The SAXS data were analyzed with the program FIT2D.18 The

conf posm = kBT ∑ ci(mp) + pcorr + p hc i

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(4)



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copy.14 The constant peak position (see Figure 5) indicates that the forces between the platelets are indeed very steep. The

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. The finite ion size, dhc, gives rise to the term phc. Equation 4 gives the osmotic pressure in the confined region and the net osmotic pressure is conf bulk posm = posm − posm

(5)

The bulk pressure is calculated for a bulk with the same chemical potential(s) as the double layer. Bulk simulations are performed in the canonical ensemble, where the osmotic pressure is calculated from the virial25,26 and the chemical potential is obtained via Widom’s perturbation technique.27

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Figure 5. SAXS spectra from Na montmorillonite dispersions equilibrated during 30 min with CaCl2 solutions in dialysis pockets. In 5 mM CaCl2 solution (red circles), the fitting procedure gives qmax = 3.29, w = 0.56, and ⟨N⟩ ≃ 6, and in 50 mM CaCl2 (green squares), qmax = 3.29, w = 0.28, and ⟨N⟩ ≃ 12. The solid lines are fits to eq 1. Samples from preparation I.

RESULTS Formation of Tactoids through Cation Exchange. In this section, we describe how tactoids are formed in aqueous dispersions of Na montmorillonite when they are equilibrated with a solution containing Ca2+ cations. The starting point for each sample was an aqueous dispersion of Na montmorillonite (Ca/Na composition given in Table 1). Since the clay platelets had initially Na+ cations, the clay platelets repelled each other and since the dispersion was dilute, the clay platelets were initially far apart from each other and no peak was observed in SAXS. This dispersion was placed in a dialysis pocket and immersed in a solution of CaCl2 (5 mM) and allowed to equilibrate through exchange of ions. After seven days, the Ca2+/Na+ ratio in the pocket determined through the ICP-AES analysis was already ∼15, indicating a fast cation exchange and an almost complete calcium dominance. SAXS spectra were recorded at regular time intervals (Figure 4). Initially, when

change in peak width shows that the average number of platelets per tactoid, ⟨N⟩, increases with equilibration time (Figure 6).

Figure 6. SAXS spectra from Na montmorillonite dispersions equilibrated in a dialysis pocket with 5 mM CaCl2. After 1 day (red circles), the fitting procedure gives qmax = 3.29, w = 0.32, and ⟨N⟩ ≃ 10, and after 75 days (green squares), qmax = 3.29, w = 0.271, and ⟨N⟩ ≃ 12. The latter curve has been shifted vertically to facilitate the reading. The solid lines are fits to eq 1. Samples from preparation I.

Figure 7 presents the variation of ⟨N⟩ as a function of time. This plot shows the growth from the first peak observation at t = 30 min with ⟨N⟩ = 5.8 to ⟨N⟩ = 8.2 after the first hour, and then a much slower growth between 1 h and 75 days. Figure 7a shows that the initial regime has the same rate as a kinetic aggregation process with a rate constant that is 2 × 10−5 times the universal Smoluchowski rate constant.15 In other words, if the tactoids form through recombination during Brownian collisions, then the efficiency of these collisions is 2 × 10−5 in comparison with recombinations that would be successful at each collision. Figure 7b shows that the second growth regime is a drift to an asymptotic value Nmax = 12.15. The decay of Nmax − ⟨N⟩ is exponential with a time constant of t0 = 300 h.

Figure 4. SAXS spectra from Na montmorillonite dispersions equilibrated with a 5 mM CaCl2 solution for increasing time intervals indicated in the graphs. Note that a peak appears after 30 min of cation exchange. The samples were obtained from preparation I.

very few Ca2+ ions had crossed into the dialysis pocket (after 10 and 20 min), the spectra were still characteristic of isolated platelets, the intensity decayed with the magnitude of the scattering vector q as a power law I(q) ∝ q−1.9. At longer equilibration times (t > 30 min), a broad peak grew at a q value that corresponds to a repeat distance of 1.9 nm. The width of the peak diminished and its height increased with equilibration time, but its position on the q scale did not change throughout the process. Finally, at long times, the position and width of the peak no longer changed. These peaks correspond to tactoids formed under the effect of the Ca2+/Na+ exchange. The peak position matches the separation of platelets in tactoids that have been observed through SAXS13 and cryo-TEM micros-

Nmax − ⟨N ⟩ = Nmax exp[−t /t0]

(6)

These kinetic experiments reveal two successive processes: a first growth through recombination events that starts with individual platelets and leads to an aggregation number that is within 33% of the final aggregation number and then a very 25428



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water for 4 months, deswelled through osmotic stress, and then allowed to swell again. The dialysis pocket was weighed at regular intervals and the measured weights are plotted in Figure 9. For comparison, a dashed line indicating the amount of water

Figure 7. Growth of tactoids through Ca2+/Na+ exchange in aqueous dispersions of Na montmorillonite from preparation I. Horizontal scale: duration of Ca2+/Na+ exchange. (a) Evolution of the average number of platelets per tactoid, ⟨N⟩, at short times of Ca2+/Na+ exchange. The dashed black line is the rate expected from Brownian collisions with a sticking efficiency of 2 × 10−5 at each collision, while the solid red line shows the measured growth of the tactoids which continues beyond 20 000 s. (b) Late evolution of the average number of platelets per tactoid. The solid black line corresponds to an exponential approach to an asymptotic value of ⟨N⟩, calculated from the width of the SAXS peaks (see the text).

Figure 9. Swelling of a Ca montmorillonite in water. First swelling (open circles): a dry powder was placed in a dialysis pocket and immersed in Millipore water. After 128 days, the pocket was immersed for 1 day in a 16 wt % solution of poly(ethylene glycol); this osmotic stress caused the measured weight to drop to 1.2 g. Second swelling (closed circles): the pocket was immersed again in Millipore water and allowed to swell for 400 days. The dashed line indicates the repeat distance to 1.9 nm.

slow structural relaxation toward this final aggregation number, which is nearly reached after 75 days. Formation of Tactoids through Swelling from a Dry State. In this section, we describe our observations of tactoid formation through a swelling process from a dry powder of Ca or Mg montmorillonite. In the first experiment, this powder was mixed with Millipore water in a test tube and shaken until complete dispersion. Figure 8a shows the spectra from samples

that is contained within a tactoid between the platelets is shown. This comparison shows that the swelling of the intratactoid layers is fast, taking place in less than a day. The swelling of the intertactoid space is much slower, extending over more than 100 days. Moreover, osmotic stress at a pressure of 1 atm almost completely reduces the intertactoid volume; hence, the intertactoid swelling pressure must be small, especially at large swelling ratios. The slow swelling rate is most likely a consequence of the low osmotic pressures of the intertactoid space. It is instructive to compare the corresponding volume fractions. The initial weight of clay was 1 g, and the weight of water absorbed at long times was 4.8 g, of which ∼0.4 g was intratactoid and ∼4.4 g was intertactoid. The volume fraction of clay within a tactoid was 0.5, and the overall volume fraction of clay in the sample was 0.07. The distance between two platelets (hs) in a tactoid is 2 nm, whereas the distance between two tactoids (Ht) must be of the order of ∼200 nm. Effect of the Ca2+/Na+ Ratio on the Final State. In order to further study the effects of ion exchange on the final state of the samples, we placed a series of natural Na dominated clays (MX-80) in equilibrium with a large volume of mixed salt solutions: the Na+ concentration was kept constant at 20 mM, while the Ca2+ concentration was varied between 0.5 and 5 mM. First, a sample of MX-80 obtained from preparation III (average platelet size, ⟨D⟩ ≈ 450 nm) was placed in a dialysis pocket and observed after 3 months. We know that, at such long times, the tactoid size does not change any longer (see Figure 7). Figure 10a shows the spectra obtained at the different calcium concentrations in the bulk solution; the corresponding number of platelets per tactoid varied from ⟨N⟩ = 12.4 at [Ca2+] = 0.5 mM to ⟨N⟩ = 14.1 at [Ca2+] = 5 mM. A similar experiment was performed but with a sample of dry MX-80 (preparation IV) that has a broader size distribution, ⟨D⟩ > 500 nm. It was placed in a test tube and swelled immediately with the mixed Ca/Na solution. The final state, observed after 3 months, consisted of larger tactoids, with ⟨N⟩ = 15.6 for [Ca2+] = 0.5 mM and ⟨N⟩ = 20.2 for [Ca2+] = 5 mM.

Figure 8. SAXS spectra of Ca (red circles) and Mg montmorillonite (green squares) equilibrated with Millipore water. (a) Dry Ca and Mg montmorillonite were allowed to swell in tubes (preparation II) during 3 months. The average number of platelets per tactoid, calculated from the peak widths, are ⟨N⟩ = 19.3 (Ca) and ⟨N⟩ = 18.2 (Mg). (b) Dispersions of Ca and Mg montmorillonite have been equilibrated in a dialysis pocket for 3 months. The average numbers of platelets per tactoid, calculated from the peak widths, are ⟨N⟩ = 19 (Ca) and ⟨N⟩ = 18.1 (Mg). The solid lines are fits to eq 1.

prepared in this way, equilibrated at 25 °C for more than 3 months and then examined through SAXS. We observe peaks at a q value corresponding to a repeat distance of 1.9 nm. This is also the case if the starting point is a dilute aqueous dispersion of Ca and Mg montmorillonites equilibrated in a dialysis pocket (see Figure 8b). The width of these peaks is in excellent agreement, but they are narrower than those observed in Figure 6 even though the ionic compositions are the same. We attribute this difference to a difference in platelet size for the clay samples, as explained below in the discussion. A similar experiment was performed with a dry Ca montmorillonite that was placed in a dialysis pocket, allowed to swell in Millipore 25429



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swelled with Millipore water (preparation II) or with a Ca2+ solution (preparation IV) gave ⟨N⟩ ≈ 20. Tactoids in Fractionated Clays. The main part of our experimental results indicates a larger effect of the platelet size on ⟨N⟩. To investigate whether this is the case, we performed further SAXS measurements on fractionated dispersions of Na montmorillonite. Interestingly, we found that there was a clear effect of different average platelet sizes on the average number of platelets per tactoid. Figure 12a shows the effect of ⟨D⟩ on the Figure 10. SAXS spectra of MX-80 equilibrated with a mixed electrolyte solution. The NaCl concentration is kept fixed at 20 mM, while the CaCl2 concentration is varied as indicated in the graph. (a) Dispersions of MX-80 have been equilibrated in a dialysis pocket for 3 months (preparation III). The tactoid size is from top to bottom 14.1, 13.4, 13.0, and 12.4. (b) Dry MX-80 samples have been mixed and equilibrated in a tube for 3 months (preparation IV). The tactoid size is from top to bottom 20.2, 18.3, 17.3, and 15.6.

For the samples with the higher Ca2+ bulk concentrations (2 and 5 mM), elemental analysis was done at the same equilibration time as the SAXS experiments. The results (Table 3) show that the Ca2+ concentration within the clay

Figure 12. Effect of different average platelet sizes on ⟨N⟩. (a) SAXS spectra of dispersions of Na montmorillonite from preparation I equilibrated in dialysis pockets for 60 min with 50 mM CaCl2 solutions. Green squares, diameters ≈ 350 nm and ⟨N⟩ ≃ 12; red circles, diameters ≈ 200 nm and ⟨N⟩ ≃ 7; open circles, diameters ≈ 60 nm, which does not form any tactoid. The solid lines are fits to eq 1. (b) The corresponding platelet size distributions of clay fractions, obtained through dynamic light scattering. Green squares: Na montmorillonite from preparation I. Filled red circles: supernatant obtained by centrifugation of Na montmorillonite at 12000g during 60 min. Open blue circles: supernatant of the same dispersion obtained after recentrifugation at 35000g.

Table 3. ICP-AES Analysis of Clay Samples Shown in Figure 10 samples preparation IV (tube): 20 mM NaCl + 2 mM CaCl2 preparation IV (tube): 20 mM NaCl + 5 mM CaCl2 preparation III (dialysis): 20 mM NaCl + 2 mM CaCl2 preparation III (dialysis): 20 mM NaCl + 5 mM CaCl2

Na+ (mM)

Ca2+ (mM)

45.5 44.2 32.5

13.4 16.1 13.1

24.9

13.2

SAXS spectra for dispersions of Na montmorillonite from preparation I. The width of these peaks depends and varies with the sizes of the platelets (see Figure 12b). These findings demonstrate that the platelet attraction (i.e., the tactoid size) increases with platelet size, which explains the difference in ⟨N⟩ between different preparation routes. Conversely, we found no tactoid formation in dispersions that were fractionated through centrifugation and contained small platelets only (⟨D⟩ < 60 nm).

was nearly constant at 13−16 mM; hence, the clay was saturated with Ca2+ ions even though the bulk solution contained much more Na+. The variation of ⟨N⟩ with Ca2+ concentration in the bulk solution shows that Ca2+ ions cause tactoid formation already at rather low Ca/Na ratios (Figure 11). The values of ⟨N⟩ are in agreement with the data shown in Figures 7 and 8; that is, samples from preparation I and preparation III (initially with Na+ cations only, then exchanged with a Ca2+ solution), with average platelet size 450 nm, gave ⟨N⟩ ≈ 14, whereas dry samples with larger platelets and directly

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DISCUSSION The results presented above can be summarized as follows: • Aqueous dispersions of montmorillonite with Ca2+ counterions form tactoids, i.e., small clusters of a few platelets that are parallel to each other and separated by a constant spacing equal to 1 nm. • When montmorillonite is equilibrated with a bulk solution containing both monovalent (Na+) and divalent (Ca2+ or Mg2+) counterions, it still forms tactoids and the divalent cations accumulate in the slit between platelets of the tactoids. The spacing between platelets is independent of the bulk ionic composition, but the number of platelets per tactoid does depends on this composition. • The average number of platelets in a tactoid is rather low (range 6−20). It is strongly dependent on the sizes of the platelets, and no tactoids are found when the average platelet size is below 60 nm.

Figure 11. Effect of Ca2+/Na+ exchange and the size of the particles or the preparation routes on the average number of platelets per tactoid, ⟨N⟩, for MX-80. The difference between the two preparations (III and IV) is due to the difference in platelet size. 25430



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• The dispersions with Ca2+ counterions swell spontaneously to volumes that are much larger than the volume of the tactoids; hence, the space between tactoids becomes quite large, on the order of 200 nm. In this discussion, we present Monte Carlo simulation results based on a model for the interactions of two parallel platelets in equilibrium with a bulk solution containing monovalent and divalent ions. We show that this model takes care of the two first points above. The explanation of the two others remains an open problem at this stage, although some arguments can be proposed. Two Infinite Parallel Platelets in Equilibrium with a Mixed Bulk. It is by now well established that ion−ion correlations can give rise to attractive forces that eventually can dominate over the entropic double layer force.4 This happens when the electrostatic coupling is strong, typically with di- or multivalent counterions. The formation of tactoids in montmorillonite as described above can be understood as a consequence of ion−ion correlations when divalent calcium or magnesium ions are available in the dispersion. Figure 13a

Figure 14. Simulated concentrations of mono- and divalent counterions in the slit between the two charged surfaces. The slit is in equilibrium with a bulk solution. The bulk concentration of NaCl is kept fixed at 20 mM, while the bulk concentration of CaCl2 is varied. Lines without symbols represent MC simulation, and lines with symbols represent Poisson−Boltzmann results.

in agreement with experiments. However, the bulk calcium concentration still has an effect on the kinetics of tactoid formation, as demonstrated in Figure 5, where identical dispersions of Na montmorillonite were equilibrated for 30 min in CaCl2 solutions of different ionic strengths. Figure 14 shows how the slit concentration of calcium ions varies with its bulk concentration; the concentration can be 1000 times higher in the slit. One can note that, with 1 mM divalent counterions in the bulk, the slit concentration of divalent ions is still much higher than the concentration of monovalent ions. It is evident that the calcium concentration in the dialysis samples in Table 3 remains the same despite the fact that the bulk concentration of CaCl2 increases from 2 to 5 mM. This is in agreement with the simulated concentrations shown in Figure 14 where the slit concentration of calcium is virtually constant when the bulk calcium concentration varies from 0.5 to 5 mM. The absolute numbers cannot be compared, since the experimental concentration refers to both intra- and intertactoid volumes. It is interesting to see that the mean-field Poisson−Boltzmann (PB) calculations for the ionic concentrations are in good agreement with simulation results, despite the fact that the PB equation predicts repulsive pressures in contradicting with Figure 13. This should not come as a surprise, since particle distributions can often be insensitive to the thermodynamics of the system. Since the attraction is a generic phenomenon of electrostatic origin depending only on valency and not ion specificity, one should expect, for example, Ca and Mg montmorillonite to form tactoids of similar size. Indeed, this is also found in the SAXS experiments (Figure 8) and lends further support to the theoretical model. The early work of Shomer and Mingelgrin presented a variation of tactoid size as a function of calcium content in the clay (see Figure 1b). We have tried to add the data from Figure 11 by estimating the calcium concentration in the slit from our simulations (Figure 14). As can be seen in Figure 1b, our mixed experimental as well as theoretical estimate is in excellent agreement with the old experimental results. Note that in our case the clay has been in equilibrium with a salt reservoir, while in the early measurements7 Na and Ca montmorillonite were mixed to obtain the desired ratio of counterions. Finite Platelets with Orientational Degree of Freedom. Even if it is too costly to simulate two large discs in a salt solution in equilibrium with a bulk, we can, however, still

Figure 13. Monte Carlo simulation results for the net osmotic pressure between two negatively charged infinite planar walls. The slit is in equilibrium with a salt reservoir containing a mix of model CaCl2 and NaCl salt solution. The CaCl2 concentration is indicated in the graph. The uniformly smeared out surface charge density, σ, is taken from a cation exchange capacity measurement28,29 and σ = 0.737 e/ nm2. (a) The NaCl concentration is 20 mM; (b) no NaCl, only CaCl2.

shows the net osmotic pressure between two infinite charged planes, which are in equilibrium with a salt reservoir with a mix of mono- and divalent counterions (the co-ion is monovalent). An interesting observation is the strong influence of divalent ions even at very low concentrations. That is, with 20 mM NaCl in the bulk, a CaCl2 concentration of 1 mM is more than enough to turn the pressure from repulsion to attraction. This can be understood from the strong competition between mono- and divalent counterions for the charged surfaces. If we, however, reduce the calcium concentration in the bulk to 0.2 mM, then the slit concentrations of mono- and divalent species become approximately equal (see Figure 14). This also has an effect on the pressure, which then turns from attractive to repulsive (see Figure 13a), and the clay starts to swell depending on the size of the platelets. The sodium content in MX-80 is higher than the calcium content (see Table 1), and as a consequence, MX-80 will swell when put in contact with pure water. If the reservoir only contains divalent counterions, then the attractive pressure will be virtually independent of the bulk concentration (cf. Figure 13b). The sample equilibrated in 5 mM CaCl2 eventually reached the same widths that had already been reached by the sample in 50 mM CaCl2 but at times that were longer by ∼3 weeks. Thus, the theoretical predictions are 25431



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theoretical point of view, but at the present stage, we are inclined to attribute it to the presence of very small clay platelets in the dispersions.

approximate the free energy of interaction between two freely rotating charged discs by combining an electrostatic term calculated for two infinite charged plates with the rotational entropy of two uncharged discs. The van der Waals interaction should also be added in order to complete the picture. This allows us to calculate the total free energy of interaction for two discs of arbitrary size in equilibrium with an appropriate salt reservoir. It is of course an approximation, but we argue that it contains all important physical ingredients and gives a qualitatively correct behavior of the system. By integrating the pressures shown in Figure 13 and adding the appropriate correction term, we can obtain an approximate free energy for the system. Figure 15 shows the free energy of interaction when

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Phone: 46462224501. Fax: 46462228648. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Swedish Research Council through a Linnaeus grant (Center Organizing Molecular Matter).

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REFERENCES

(1) Olphen, H. V. Clays Clay Miner. 1953, 2, 418−438. (2) Olphen, H. V. J. Colloid Interface Sci. 1964, 19, 313−322. (3) Norrish, K.; Quirk, J. P. Nature 1954, 173, 255−265. (4) Guldbrand, L.; Jönsson, B.; Wennerström, H.; Linse, P. J. Chem. Phys. 1984, 80, 2221−2228. (5) Blackmore, A. V.; Miller, R. D. Soil Sci. Soc. Am. Proc. 1961, 25, 169−173. (6) Shainberg, I.; Kaiserman, A. Soil Sci. Soc. Am. J. 1969, 33, 547− 551. (7) Shomer, I.; Mingelgrin, U. Clays Clay Miner. 1978, 2, 135−138. (8) Russo, D.; Bresler, E. Soil Sci. Soc. Am. J. 1977, 41, 706−710. (9) Albert, J. T.; Harter, R. D. Soil Sci. 1973, 115, 130−136. (10) Buzzi, O.; Boulon, M.; Deleruyelle, F.; Besnus, F. Rock Mech. Rock Eng. 2008, 41, 343−371. (11) Komine, H.; Ogata, N. Soils Found. 1999, 39, 83−97. (12) Jönsson, B.; Åkesson, T.; Jönsson, B.; Segad, M.; Janiak, J.; Wallenberg, R. SKB Tech. Rep. 2009, TR-09-06, 1−34. (13) Segad, M.; Jönsson, B.; Åkesson, T.; Cabane, B. Langmuir 2010, 26, 5782−5790. (14) Segad, M.; Hanski, S.; Olsson, U.; Ruokolainen, J.; Åkesson, T.; Jönsson, B. J. Phys. Chem. C 2012, 116, 7596−7601. (15) Evans, D. F.; Wennerström, H. The Colloidal Domain Where Physics Chemistry, Biology, and Technology Meet, 2nd ed.; Wiley-VCH: New York, 1999. (16) Karnland, O. SKB Tech. Rep. 2010, TR-10-60, 1−29. (17) Knaapila, M.; Svensson, C.; Barauskas, J.; Zackrisson, M.; Nielsen, S. S.; Toft, K. N.; Vestergaard, B. J.; Arleth, L.; Olsson, U.; Pedersen, J. S.; Cerenius, Y. J. Synchrotron Radiat. 2009, 16, 498−504. (18) Hammersley, A. P.; Svensson, S. O.; Thompson, A.; Graafsma, H.; Kvick, E.; Moy, J. P. Rev. Sci. Instrum. 1995, 66, 2729−2733. (19) Klug, H. P.; Alexander, L. E. X-ray diffraction procedures for polycrystalline and amorphous materials; Wiley-Blackwell: Chichester, U.K., 1974. (20) Segad, M. 2012, submitted for publication. (21) Glatter, O.; Kratky, O. Small Angle X-ray Scattering; Academic Press: London, 1982. (22) Jönsson, B.; Wennerström, H.; Halle, B. J. Phys. Chem. 1980, 84, 2179−2185. (23) Greberg, H.; Kjellander, R.; Åkesson, T. Mol. Phys. 1996, 87, 407−422. (24) Valleau, J. P.; Ivkov, R.; Torrie, G. M. J. Chem. Phys. 1991, 95, 520−532. (25) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1989. (26) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: San Diego, CA, 1996. (27) Widom, B. J. Chem. Phys. 1963, 39, 2808−2812. (28) Michot, L. J.; Bihannic, I.; Porsch, K.; Maddi, S.; Baravian, C.; Mougel, J.; Levitz, P. Langmuir 2004, 20, 10829−10837.

Figure 15. The total free energy of interaction between two charged and infinitely thin discs as a function of their radius (see text for details of calculation). The system is in equilibrium with a salt reservoir containing a mix of mono- and divalent counterions plus monovalent co-ions; e.g., a mix of NaCl and CaCl2 and their concentration in mM are shown in the figure legend. The center-to-center distance is fixed at 1 nm.

two platelets are at a center-to-center separation of 1 nm, approximately the water layer thickness found in the SAXS measurements. It is shown as a function of platelet radius. For the lower calcium concentrations (0.2 and 1 mM, see legend in Figure 15), there is a continuous increase in free energy with platelet size. Hence, no tactoid will form. With an increased calcium concentration, the free energy eventually becomes negative and there is a formation of tactoids for sufficiently large R. Figure 15 also tells us that the presence of small platelets can give rise to a swelling pressure (i.e., extra-lamellar swelling), which is under investigation experimentally in an ongoing study. The important message is that tactoids can form provided that the platelets are sufficiently large and that the concentration of divalent ions in the reservoir is high enough. The present simulation model with infinite surfaces is of course an unnecessary simplification and is used for technical and pedagogical reasons. Small platelets of finite size have recently been studied by Delhorme and co-workers.30 The results are in agreement with the present simulations with respect to salt competition and the importance of ion−ion correlations in the presence of divalent counterions.

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CONCLUSIONS The formation of tactoids in clay dispersion is a consequence of ion−ion correlations, which lead to a very weak repulsive or even attractive double layer interaction. The tactoid size varies with platelet size as well as ionic composition in the dispersion. Below a certain platelet size, no tactoids form. These results are generic electrostatic effects and can be predicted from Monte Carlo simulations of a continuum model of the clay dispersion. The observed intertactoid swelling is more troublesome from a 25432



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(29) Michot, L. J.; Bihannic, I.; Maddi, S.; Funari, S. S.; Baravian, C.; Levitz, P.; Davidson, P. Proc. Natl Acad. Sci. U.S.A. 2006, 103, 16101− 16104. (30) Delhorme, M. Thermodynamics and Structure of Plate-Like Particle Dispersions. Ph.D. Thesis, University of Lund, Lund, Sweden, 2012.

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Tactoid Formation in Montmorillonite - ACS Publications - American

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