Article pubs.acs.org/JPCB

Structure and Rheology of Mixed Suspensions of Montmorillonite and Silica Nanoparticles Jan Hilhorst,*,† Vera Meester,† Esther Groeneveld,† Jan K. G. Dhont,‡,§ and Henk N. W. Lekkerkerker† †

Van’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH, Utrecht, The Netherlands ‡ Institute of Complex Systems, ICS-3, Research Centre Jülich, D-52425 Jülich, Germany § Department of Physics, Heinrich-Heine-Universität Düsseldorf, D-40255 Düsseldorf, Germany ABSTRACT: We present a study of the structure and rheology of mixed suspensions of montmorillonite clay platelets and Ludox TMA silica spheres at pH 5, 7, and 9. Using cryogenic transmission electron microscopy (cryo-TEM), we probe the changes in the structure of the montmorillonite suspensions induced by changing the pH and by adding silica particles. Using oscillatory and transient rheological measurements, we examine the changes in storage modulus and yield stress of the montmorillonite suspensions upon changing the pH and adding silica particles. Cryo-TEM images reveal that changes in pH have a significant effect on the structure of the suspensions, which can be related to the change in charge of the edges from positive at pH 5 to negative at higher pH. Furthermore, at pH 7, the cryo-TEM images show indications of a microphase separation between clay and silica particles. The addition of silica leads to lowering of the storage modulus and yield stress, which we connect to the structural changes of the suspension.

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INTRODUCTION One of the most striking properties of swelling clay minerals dispersed in water is their ability to form yield stress materials at very low concentrations (1 vol % and sometimes even lower).1 This feature is extensively used in various industrial applications: drilling fluids, antisettling agents, cosmetics, etc.1−6 Both naturally occurring and synthetic polymers have been used extensively to enhance the rheological properties of clay suspensions.2 The use of colloidal particles to enhance the rheological properties of clay suspensions is of more recent date. Twenty-five years ago, Burba and Barnes7 published a patent describing the use of platelike hydrotalcite (Mg−Al mixed metal hydroxide) colloids as thickeners of montmorillonite suspensions. The rheology of this extended clay system is remarkable: it displays an elevated yield stress and a low plastic viscosity at high shear rates, and it rapidly gels. These remarkable rheological properties, thought to be caused by the complexation of the positively charged hydrotalcite particles with the negatively charged montmorillonite particles,8 have led to its widespread use as a drilling fluid in oil well and construction drilling (Drilplex MI-Swaco). Van der Kooij et al.9 and Ten Brinke et al.10 discovered that similar rheological behavior could be brought about by the addition of platelike gibbsite and rodlike boehmite colloids to clay suspensions. Not only anisometric colloids but also the addition of spherical colloids can lead to significant effects on the rheology of clay suspensions. Tombacz et al.11,12 studied the effect of adding magnetite and hematite to montmorillonite suspensions at pH about 4 where oxide (+) and clay mineral (−) particles are oppositely charged. Because of the formation © XXXX American Chemical Society

of a heterocoagulated particle network, this leads to a significant enhancement of the gel strength. Baird and Walz13,14 investigated the effect of added silica nanospheres on the structure and rheology of an aqueous suspension of disk-shaped kaolinite particles. Adding nanoparticles and salt (NaCl or KCl) to a kaolinite suspension caused the entire suspension to turn from a fluid to a stiff gel that was strong enough to actually be sliced. Cousin et al.15 investigated aqueous mixtures of laponite nanodisks and silicacoated maghemite nanoparticles. The addition of the smaller maghemite spheres shifted the rheological fluid−solid transition to much lower laponite concentrations. Ten Brinke et al.10 and Bailey et al.16 studied the effect of both anionic and cationic silica nanoparticles on hectorite and montmorillonite suspensions. While cationic silica particles in all cases led to rheology enhancement, the behavior of mixed suspensions of clay and anionic silica appears more subtle. Above the hydrodynamic overlap concentration of the clay, addition of small quantities (10% of the clay concentration) of anionic silica significantly enhances the rheology of the clay suspensions.10,16 On the other hand, Bailey et al.16 and Kleshchanok et al.17 observed that, at low clay concentrations (i.e., below the hydrodynamic overlap concentration), the addition of anionic silica colloids led to gel collapse and even complete liquefaction. Here we study the effect of the addition of anionic spherical silica colloids on the structure and rheology of dispersions of a Received: April 30, 2014 Revised: September 9, 2014

A

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well-characterized Wyoming montmorillonite clay (SWy-2, Source Clays Minerals Repository). We pay special attention to the effect of pH on the suspension behavior. It has been observed experimentally,18 confirmed by theory18 and simulation,19 that the point of zero charge for AlOH edge groups in montmorillonite lies between pH 5 and 6, i.e., lower than in pure aluminas.20 In order to elucidate the role of the edge charge in the behavior of mixed clay−silica suspensions, we prepared a range of systems with pH = 5, 7, and 9 and different silica concentrations by the osmotic stress method.21,22 Rheological measurements revealed that the gel strength increased at both high and low pH and that the addition of anionic Ludox TMA silica nanoparticles leads to a weakening of the gels at all pH values considered. Cryo-TEM was used to study the changes in the microstructure caused by the pH variation and the addition of silica nanoparticles.

Figure 1. Left-hand graph shows the spherical silica particles with an average diameter of 23.8 ± 2.5 nm.17 The right-hand graph clearly shows the irregular polygonal nature of individual montmorillonite platelets of roughly 400 nm diameter.23

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matching that of the surrounding PEG solution. Typically, 25 mL of dispersion was transferred to a dialysis tube (Visking, 12−14 kDa molecular weight cutoff) and put into 1 L of PEG (Aldrich, average Mn 20 000 g/mol) solutions with concentrations ranging from 0.5 to 2.0 wt % at an ionic strength of 10−4 M (pH 7) and 10−3 M (pH 5 and pH 9). Based on a calibration curve for the osmotic pressure of PEG-20 solutions described in ref 26, these concentrations result in osmotic pressures ranging from 0.9 × 103 to 5.6 × 103 Pa. For samples at pH 7, the ionic strength was fixed at 10−4 M by NaCl. For the samples with pH 5 and 9, the pH and ionic strength were adjusted using acetic acid and ammonia buffers, respectively. In order to achieve a stable pH, the buffer strength was kept at 10−3 M in these cases. Over a period of 4 weeks, the samples were equilibrated with the PEG solutions,25 while shaking at 150 rpm at an Ika KS 260 Basic shaker. After 2 weeks, the PEG solutions were refreshed to keep the osmotic pressure and salt concentrations constant. Final concentrations were determined by weighing approximately 1 g of sample, drying it, and weighing again. Knowing the silica to clay ratio and the salt concentration, the clay concentrations could be accurately determined. Cryo-TEM. Cryo-TEM experiments were carried out on an FEI Tecnai12 and an FEI Tecnai20, operating at 120 and 200 kV, respectively, by using a Gatan 626 cryo-transfer holder. Samples were made by preparing a frozen film of a clay sample on a copper grid containing a holey carbon film. Before sample preparation the grid was made hydrophilic by electrically charging using glow discharge. The film was prepared by placing a droplet of 3−5 μL clay suspension on the grid and using a VITROBOT to automatically blot the grid. The grid is blotted on both sides by filter paper during a preset number of seconds (typically 3−5 s). Subsequently, the film is instantly frozen by plunging the grid into liquid ethane, which is maintained at approximately −180 °C by a liquid nitrogen reservoir. After vitrification the grid is transferred to the cryotransfer holder via a cryo-transfer unit. Rheological Measurements. Rheological measurements were performed on gelled samples with clay concentrations in the range of 2.6−3.4 wt % on an Anton Paar Physica MCR300 rheometer set up in cone−plate geometry. A microroughened plate was used in conjunction with a microroughened cone of angle 1° and diameter 25 mm. The cone was truncated at a distance of 49 μm. To prevent unwanted evaporation of the solvent, a solvent trap with complete liquid seal was used. After sample loading, the samples underwent a 300 s preshear treatment at a shear strain of 1000% and a frequency

MATERIALS AND METHODS Sample Preparation. Natural montmorillonite SWy-2 was purchased from the Source Clays Minerals Repository of the Clay Mineral Society (Purdue University). Montmorillonite is a dioctahedral swelling clay mineral, whose average structural formula, as determined by Vantelon et al., is23,24 (Si 7.74Al 0.26)(Al3.06Fe3 +0.42Fe 2 +0.03Mg 0.48)O20 (OH)4 Na 0.77

Before use, raw samples were purified following a procedure adapted from Michot et al.25 Typically, 50 g of as-received clay powder was hydrated for 3 days in 1 L of Millipore water (18 MΩ·cm) on an Ika KS 260 Basic shaker at 150 rpm. After that, the resulting suspension was transferred to a high 1 L graduated cylinder and left to sediment for 2 days to remove the largest particles. Subsequently, 58.4 g of NaCl (Merck, for analysis) was added and dissolved, and the dispersion was centrifuged at 829g for 1 h, after which the supernatant was removed and replaced with a fresh 1 M NaCl solution. This was repeated three times to exchange all ions for Na+ or Cl−. The resulting dispersion was repeatedly centrifuged to sediment the clay particles and redispersed in Millipore water until the conductivity of the dispersion reached 5 μS cm−1. Because of the increasing degree of exfoliation and lower ionic strength in the dispersions, centrifugation was done at increasing speed and duration at each step in order to sediment all particles. After preparation, dispersions were diluted to ∼1 wt % and mixed with as-received Ludox TMA (Sigma-Aldrich) dispersions at known silica concentration. Ludox TMA is bought as a deionized silica dispersion, and its addition therefore has little effect on the overall salt concentration of the final samples. Also, the dispersions are at neutral pH when acquired. The buffer capacity of the small amounts of silica used is negligible compared to that of the utilized buffers at pH 5 and pH 9. Electron micrographs of pure silica and montmorillonite samples are shown in Figure 1. The TEM measurements were performed on a FEI Tecnai12 microscope operated at 120 kV. Samples for TEM imaging were prepared by drop-casting diluted dispersions on a carbon-coated polymer film copper grid (300 mesh). Samples with 0.05, 0.1, 0.2, and 0.5 weight to weight ratios of silica to montmorillonite were prepared and concentrated via the osmotic stress method.25 In this method, poly(ethylene glycol) (PEG) solutions, separated from the clay dispersions by a semipermeable membrane, are used to extract water from the clay dispersions and concentrate them to an osmotic pressure B

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of 1 Hz. The preshear treatment was followed by a 300 s waiting time. The linear viscoelastic regime was probed by stress and frequency sweep measurements. Stress sweeps were performed at 1 Hz, and for all samples, a stress of 1 Pa was found to be suitable to perform frequency sweeps ranging from 10−2 to 10 Hz. An important rheological parameter for a gel is the yield stress. However, determination of the yield stress and even its very existence have given rise to much debate.27,28 Here, we use a method which is known as the viscosity bifurcation29−32 or sustainable flow test.33 In this method, a series of constant stresses are imposed on the sample and the shear rate is monitored over time. The shear rate of the samples was recorded as a function of time from 10−2 to 1000 s. When the applied stress is above the yield stress of the fluid, the shear rate will eventually reach a steady value. When, on the contrary, the applied stress is below the yield stress, the fluid may initially flow, but over time the shear rate will keep on decreasing. When plotting a series of curves following the shear rate over time, for different stresses, a bifurcation becomes evident. The stress at which this bifurcation occurs is the yield stress of the fluid, below which sustainable flow will not occur. A simple model to analyze these measurements was put forward by Coussot and Bonn and co-workers.28−32 This model, from here on labeled the CB model, describes a yield stress fluid as a system characterized by a structure parameter λ, which describes the local degree of interconnection of the microstructure. The rate of change of λ is due to the competition between recovery at rest, characterized by the relaxation time θ, and breakdown due to flow that is proportional to the shear rate, γ̇. These effects are expressed in the equation dλ 1 = − αγλ̇ dt θ

y=

t̃ =

γ̇

(6)

t θ

(7)

then eq 5 can be written in the form dy σ σ 1 = −y 2 + ̅ y 2 − ̅ y3 dt ̃ σy σy β

(8)

where we have introduced

σy =

η0β (9)

αθ

which, as will become clear, has the meaning of a yield stress. For σ̅/σy < 1, the right-hand side of eq 8 is negative for any (positive) value of y, and hence no stationary solution for y exists and no sustainable flow is possible. In this case, y is decreasing toward zero for large times. The cubic term in eq 8 can therefore be neglected for sufficiently large times, which then takes the form ⎛ dy σ⎞ = −⎜⎜1 − ̅ ⎟⎟y 2 dt ̃ σy ⎠ ⎝

(10)

which has the solution y=

1 t −̃ 1 1 − σ ̅ /σy

(11)

or in terms of the original variables

γ̇ =

(1)

σ ̅ /σy

1 −1 t 1 − σ ̅ /σy α

(12)

The shear rate is thus predicted to decrease as ∼1/t for sufficiently large times for applied stresses smaller than the yield stress. For σ̅/σy > 1, eq 8 has a stationary solution that is reminiscent of the Bingham model34 σy ⎞ ⎛ ystat = ⎜1 − ⎟β ⎝ (13) σ̅ ⎠

(2)

with β > 0. In the following analysis we will take n = 1. This choice allows for a full analytical treatment, and it correctly describes what is seen experimentally. In particular, the temporal decrease of the shear rate after a reduction of the stress to a value below the yield stress is correctly predicted for n = 1. For this choice for n, the relation between an imposed stress σ̅ and the value of λ is given by 1 σ̅ − λ= η0γβ̇ β (3)

or in terms of the original variables γ̇ =

σ ̅ − σy η0

(14)

Hence, we see that sustainable flow is only possible for σ̅/σy > 1, which leads us to identify σy as the yield stress. Using eq 14, the yield stress could be determined from creep measurements of the steady state shear rate as a function of the imposed stress. In addition to this, an estimate of the yield stress was made from the bifurcation in the creep measurements. The limitation of this approach is that samples may still undergo structural changes even after an hour of continuous shear which makes it difficult to determine the precise location of the bifurcation value. This may cause the visual method to underestimate the yield stress. On the other hand, the fits obtained using eq 14 overestimate the yield stress, as the samples are typically shear thinning above the yield stress, and a linear fit of constant shear rates versus shear stress does not accurately capture the behavior at the onset of flow. The real value of the yield stress

from which it follows that dλ σ dγ ̇ =− ̅2 dt ηβγ ̇ dt

σ̅

and dimensionless time t ̃

with α > 0. The relation between the stress σ and the structure parameter λ is given by the empirical relation σ = η0γ(1 ̇ + βλ n)

η0β

(4)

substituting eqs 3 and 4 into eq 1, we find η βγ 2̇ ηα dγ ̇ =− 0 + αγ 2̇ − 0 γ 3̇ (5) dt σθ σ̅ ̅ For the analysis of this equation it is convenient to introduce a dimensionless shear rate y C

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Figure 2. Results of the osmotic stress method, displaying the final clay concentrations as a function of osmotic pressure. Panels a−c contain data for pH 7, 5, and 9 from left to right.

Figure 3. Panels a−c show rheological results of fixed stress frequency sweeps at ∼3 wt % clay with different silica concentrations for pH 7, 5, and 9 from left to right.

pressure of 2.1 × 103 Pa (Figure 2c), similar to the behavior at pH 7. However, at pH 9 the clay concentrations at higher osmotic pressure level off, as was observed in the case of pH 5. Moreover, at high osmotic pressure, a trend that clearly indicates a dependence on silica concentration can be seen, with the largest silica concentrations leading to the smallest clay concentration. Rheology. pH 7, 10−4 M Ionic Strength. Results of frequency sweeps on pH 7 samples compressed at 2.1 × 103 Pa and 10−4 M ionic strength are presented in Figure 3a. Stress sweeps (not shown) revealed a linear viscoelastic regime that ranges at least from 0.2 to 20 Pa at 1 Hz, except for the 0.5 silica sample. Frequency sweeps were performed at 1 Pa. For all frequencies, the storage modulus is larger than the loss modulus (not shown) and is approximately constant with frequency, indicating a gelled nature of the samples compressed at 2.1 × 103 Pa. The only exception is the 0.5 silica to clay ratio, which was found to be liquid. The results of fixed stress creep measurements on the pure clay sample and the sample containing an 0.1 silica to clay w/w ratio are displayed in Figure 4a,b. For the highest applied stresses, the shear rate reaches a steady value, while for low stresses there is a continuous decrease in shear rate which follows a t−1 trend, as predicted in eq 12. As discussed in the Materials and Methods section, the bifurcation value can be identified as the yield stress. Using this method, a yield stress could even be determined for the seemingly liquid sample with an 0.5 silica to clay ratio. The results for both shear moduli and yield stress values are summarized in Table 1.

will therefore lie in between the values obtained by both methods.

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RESULTS Osmotic Stress. pH 7, 10−4 M Ionic Strength. The concentration of montmorillonite in samples formed at pH 7 and 10−4 M salt as a function of osmotic pressure is shown in Figure 2a. For osmotic pressures ranging from 0.9 × 103 to 5.6 × 103 Pa, the clay concentrations varied from 1 wt % to almost 6 wt % with a continuous increase of concentration. Samples at the lowest two osmotic pressures, 0.9 × 103 and 1.4 × 103 Pa, and the sample with an 0.5 silica to clay ratio at 2.1 × 103 Pa were liquid, while all other samples were gels. No systematic effect of silica on the resulting clay concentration at a given osmotic pressure could be discerned. pH 5, 10−3 M Ionic Strength. Comparing Figure 2a (pH 7) and Figure 2b (pH 5), the effect of pH on the osmotic pressure is clearly visible. At pH 5 the clay concentration obtained at 0.9 × 103 Pa is higher than at pH 7 and shows a moderate increase with osmotic pressure up to 2.1 × 103 Pa. At even higher osmotic pressures, the clay concentration hardly increases anymore. As a result, the clay concentration for pH 5 at 5.6 × 103 Pa is approximately 1 wt % lower than at pH 7. At pH 5, even the samples at the lowest osmotic pressure were gelled, while the samples at pH 7 required at least 2.1 × 103 Pa of osmotic pressure to form a gel. The effect of the addition of silica on the osmotic compression is again limited. pH 9, 10−3 M Ionic Strength. At pH 9, the clay concentration steeply increases with osmotic pressure up to a D

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Figure 4. Fixed stress creep measurements for several stresses beneath and above the sample yield stress. These curves were used to determine the yield stress. Panels a and b are for two samples at pH 7, while panels c and d are for pH 5 and panels e and f for pH 9. The left column, i.e., panels a, c and e, was obtained on samples without silica. The right column contains data on samples with a 0.1 silica to clay ratio.

pH 5, 10−3 M Ionic Strength. The samples investigated at pH 5 were taken from the batch prepared at 8.9 × 102 Pa at 10−3 M ionic strength, as these had similar clay concentrations to the samples for pH 7 obtained at 2.1 × 103 Pa. The samples at pH 5 formed much stronger gels than those at pH 7 at all silica concentrations. Frequency sweep results are shown in Figure 3b. Again, stress sweeps showed linear behavior over the whole applied range of stresses (not shown), allowing for frequency sweeps at 1 Pa. The frequency sweeps confirm the gelled state of all samples, with storage moduli given in Table 1. The storage moduli at pH 5, while much larger than at pH 7, show a distinct decrease with increasing silica concentration. The same holds for the yield stresses, as determined from steady-state shear rates obtained from fixed stress creep curves such as the one in

Figure 4c,d. The results are given in Table 1 and show a decrease with silica concentration similar to the decrease in storage moduli. In Figure 4c, the predicted t−1 decay of the shear rate below the yield stress is also observed again. pH 9, 10−3 M Ionic Strength. Frequency sweeps on pH 9 samples that were made at 1.4 × 103 Pa for best comparison to pH 5 and 7 are shown in Figure 3c. Rheological results are similar to pH 5 and 7: Linear viscoelasticity over a stress range of 0.2−20 Pa (not shown) and frequency-independent storage moduli indicating gelled systems. The sample without silica clearly forms the strongest gel, and a decrease in gel strength is observed with increasing silica concentration, as summarized in Table 1. The yield stresses, as determined from creep measurements such as the ones in Figure 4e,f, follow the same trend as the storage moduli. Storage moduli and yield E

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it in mixtures of niobate and aluminosilicate nanosheets. In other cases, suspensions of platelike particles with spheres36 as well as plate−plate mixtures37 have been observed to phase separate macroscopically. Nakato et al.37 suggest that the explanation for microphase separation versus full macroscopic phase separation is related to subtle details of the interaction between the colloidal particles. The result in this case is that the silica is homogeneously dispersed in the continuous phase, while, due to the microphase separation, the clay interconnectedness is lost. This provides experimental underpinning of the tentative microstructural model proposed by Bailey et al.16 to explain the observed liquefaction upon addition of anionic silica. pH 5, 10−3 M Ionic Strength. The cryo-TEM images without added silica are rather similar to those at pH 7 (Figure 6a,b),

Table 1. Sample Details and Rheological Parameters of All Samples Investigated by Rheology and Cryo-TEM

pH 7

5

9

silica/clay w/w ratio

montmorillonite concn (wt %)

storage modulus (Pa) at 1 Pa, 1 Hz

0 0.1 0.5 0 0.1 0.5 0 0.1 0.5

2.9 3.4 2.8 2.7 3.2 3.0 3.2 2.9 2.6

505 436 34 1355 1011 473 978 572 500

yield stress (Pa) Coussot− Bonn model

yield stress (Pa) bifurcation value

55 53 51 169 136 74 133 101 85

20−30 20−30 10−20 140−150 100−110 40−50 100−120 80−90 80−90

stresses are of similar magnitude, though a bit smaller than at pH 5, except at the highest silica concentration. Once again, the t−1 trend is clearly visible in Figure 4e,f. Figure 4e contains the only data set that contained enough points below the yield stress to do a reliable fit using eq 12. This resulted in a yield stress of 128 Pa, which fits perfectly to the tabulated values for the sample without silica in Table 1. Cryo-TEM. pH 7, 10−4 M Ionic Strength. All cryo-TEM images at pH 7 show samples produced at an osmotic pressure of 2.1 × 103 Pa. The samples without silica show a combination of stacked platelets and randomly oriented single clay particles (Figure 5a,b). The dark spots in these images are not silica

Figure 6. Cryo-TEM images of samples at pH 5 without silica (a, b) and with 0.5 silica to clay ratio (c, d).

without conclusive evidence for a significantly higher amount of edge-face contacts. However, with added silica, the positive edge charge at pH 5 attracts the negative silica spheres around the clay platelets (as indicated by the arrows in Figure 6c,d), although a lot of free silica particles are present as well. pH 9, 10−3 M Ionic Strength. The structures, like the rheological samples all imaged at 1.4 × 103 Pa, appear to be dominated by strong repulsive interactions, leading to a cellular structure of the clay platelets, where the platelets surround water pockets (Figure 7a,b). Similar structures have been observed in montmorillonite gels before by Bihannic et al.38 and Zbik et al.39 The latter propose that electrostatic repulsion pushing individual smectite sheets outward results in an expanded structure. Added silica particles seem to accumulate in the holes created by the surrounding clay platelets (Figure 7c,d).

Figure 5. Cryo-TEM images of samples at pH 7 without silica (a, b) and with 0.5 silica to clay ratio (c, d).

particles, but small ice crystals formed as a result of beam damage. At 0.5 silica/clay weight ratio (Figure 5c,d), microphase separation between silica spheres and stacks of clay platelets can be seen. Microphase separation in mixtures of colloids with different shapes has been reported before. For example, Cousin et al.15 observed it in a binary colloidal mixture of disklike nanoparticles of laponite and spherical nanoparticles of maghemite. Miyamoto and Nakato35 observed

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DISCUSSION Osmotic Stress. The osmotic stress method has been applied in earlier studies to determine the swelling pressure of lamellar phases of phospholipids40 and surfactants21 and

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would yield h = 100 nm, whereas SAXS at a salt concentration of 10−4 M yields h = 70 nm.23 Using the latter h value, eq 15 yields an osmotic pressure of about 1500 Pa, in reasonable agreement with the measurements at pH 7. This may to some extent be fortuitous, as the osmotic pressure depends significantly on the pH of the clay. This is understandable in view of the pH dependence of the charge of the different crystal faces.18,46 At pH 7 and 9, both the edges and the faces of the clay particles are negatively charged. At pH 9, stronger deprotonation leads to a stronger repulsion between the particles. At pH 5, protonation of the edges leads to a positive charge there and the potential to form attractive structures, like a house-of-cards structure, although we did not observe this directly in cryo-TEM. This influence of pH can be seen in the curves of concentration as a function of osmotic stress (Figure 2a−c), where both fully repulsive systems (pH 7 and 9) have a linearly increasing concentration going through the origin at low osmotic pressures. The samples at pH 5 form structures with much higher concentrations at low osmotic pressure, resulting from attractive interactions. The more surprising result of the osmotic compression is the fact that the clay concentration for a given imposed osmotic stress hardly depends on the amount of added silica particles. Unfortunately, no expressions for the osmotic pressure of a mixed colloidal suspension of plates and spheres are available.47 To get some feeling for the osmotic effect of the added silica particles, we consider the osmotic pressure of pure silica dispersions. The total osmotic pressure of the silica dispersions can be written as the sum of the contributions of the colloidal particles and the ions. Assuming Van’t Hoffs law to be valid the contribution of the colloidal particles, Πp, is simply

Figure 7. Cryo-TEM images of samples at pH 9 without silica (a, b) and with 0.5 silica to clay ratio (c, d).

smectite clay suspensions.23,25,41−43 The classical theory of the diffuse electrical double layer based on the Poisson−Boltzmann equation44 has been used successfully to explain the swelling pressures in those experiments.21,23,41−43 To explain the osmotic compression of our mixed clay−silica systems, we used a similar treatment. For distances h between the plates much larger than the Debye length, which is the case here, the weak overlap approximation of the double layers of the interacting platelets can be applied,44 and one obtains for the swelling pressure Π = 64n0kBT e−κh

Π p = n pkBT where np is the number density of the silica colloids. The contribution of the ions can be derived using the concept of the Wigner−Seitz (WS) cell.48,49 In this model the influence of the other colloids is accounted for by confining the colloid into a cell, with global electroneutrality. The size of the cell, RWS, is computed from the number density of the colloids, np

(15)

where n0 is the salt concentration in the osmotic reservoir, kB is Boltzmann’s constant, and

κ=

8πn0lB

⎛ 4πn p ⎞−1/3 R WS = ⎜ ⎟ ⎝ 3 ⎠

is the Debye screening constant with

lB =

e2 4πεkBT

In the cell model the ionic contribution to the osmotic pressure is given by50−53

the Bjerrum length (ε being the dielectric constant of the solvent): lB = 0.7 nm for water at room temperature. At the salt concentrations used in our experiments, the Debye screening length, 1/κ, is large enough, roughly 10 nm at 10−3 M ionic strength, to neglect contributions of van der Waals interactions to the osmotic pressure.1 In order to relate osmotic pressures to particle concentrations, we have to be able to translate particle concentrations into interparticle distances. From small-angle X-ray scattering studies on different smectite clay suspensions it is known that h is somewhat smaller than the value one would obtain assuming ideal swelling, i.e., assuming a perfect smectic structure of parallel clay plates.23,43,45 For example, at a montmorillonite concentration of 2.7 wt % (corresponding to 1 vol %, as the density montmorillonite is 2.7 g cm−3) and assuming a thickness of 1 nm for the montmorillonite plates ideal swelling

Π ion = kBT[n+(R WS) + n−(R WS) − 2n0]

(16)

where n+(RWS) and n−(RWS) are the ionic densities at the WS cell boundary and n0 is the salt concentration in the reservoir. No closed-form analytical expressions are known for these quantities, but they can be approximated by the mean densities n+ and n−.54 By applying elementary Donnan equilibrium theory, we then obtain55 ⎧ ⎡ ⎤⎫ ⎛ Zn p ⎞2 ⎪ ⎢ ⎥⎪ Π = kBT ⎨n p + 2n0⎢ 1 + ⎜ ⎟ − 1⎥⎬ ⎝ 2n0 ⎠ ⎪ ⎪ ⎣ ⎦⎭ ⎩ ⎧ ⎫ (Zn p)2 ⎪ ⎨n p + ⎬ ≈ kBT ⎪ 4n0 ⎪ ⎩ ⎭ ⎪

G

(17)

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between the positive edges of the clay particles and the negative silica particles. At pH 7, we observe a microphase separation between stacks of parallel clay platelets and a continuous phase of silica particles. This may be caused by depletion interaction between clay and silica57−59 and indicates a tendency for the clay particles to form large stacks under compression. The weak repulsion between the platelets is apparently not enough to prevent stacking when the silica concentration is sufficiently high. The resulting concentrated stacks of montmorillonite lead to a sufficiently disconnected system of clay platelets to explain the liquefaction of the sample with 0.5 silica to clay ratio at 2.1 × 103 Pa.16 At pH 9, it appears as if the silica particles are homogeneously distributed over the water pockets present in the system, with little apparent effect on the clay structure. Rheology. For the pure clay gels, at comparable concentrations, the gel strength at pH 5 comes out highest, while the gel at pH 7 is weakest (see Table 1). This was also observed by Brandenburg and Lagaly.60 The explanation lies in the dependency of particle charge on the pH. At pH 5 the edge-face attraction leads to a gel or attractive glass,61 with a high modulus and yield stress. At pH 7 and 9, the edges and faces have the same charge, but at pH 7 the repulsive interactions are weaker due to the lower surface charge. This is reflected in a lower modulus and yield strength than at pH 9. For all pH, addition of silica leads to a weakening of the rheology. However, the underlying cause is different in each case. At pH 5, the shielding of the positive edge charges by adsorption of silica particles, as identified by cryo-TEM, leads to a weakening of the attraction and, hence, to a weakening of the rheology. At pH 7, the microphase separation between clay and silica leads to a loss of connectivity in the clay structure and therefore to a complete liquefaction of the system at 2.1 × 103 Pa. Finally, in the case of pH 9, the systematic lowering of the clay concentration with increasing silica concentration leads to a weakening of the rheology. Here, the underlying mechanism is not entirely clear, but the formation of a foam structure, as seen in cryo-TEM images, may lead to a trapping of silica particles in foam pockets. This particular structure may give silica a more important contribution to the osmotic pressure than would be expected on the basis of its osmotic pressure in a pure system.

The latter approximation is justified in the strong screening limit where Zn p ≪ n0

For high surface charges the bare charge Z of the colloidal particles must be replaced by the renormalized one, Zeff, for which Trizac et al.49 derived the expression Zeff =

4κa(1 + κa) lB

Madeline et al.42 obtained good agreement between eq 17 and experimental data for silica dispersions.42,56 For silica dispersions of 1 vol % one obtains an osmotic pressure of about 50 Pa, i.e., much lower than for montmorillonite dispersions with the same volume fraction. This may explain the limited effect of the added silica on the osmotic pressure. Of course, there is an interaction between the silica and the clay. Therefore, the total osmotic pressure is not simply additive, but in the weak overlap regime the added effect of silica will still be marginal. Only at the highest clay concentrations at pH 9, where the clay particles are strongly charged, do we see an influence of the silica concentration. Also at pH 5, where silica particles might be expected to reduce any edge-face attraction, no consistent influence of silica concentration could be observed. Cryo-TEM. Performing cryo-TEM on gelled samples requires delicate preparation procedures. The blotting procedure as described in the experimental section often resulted in too thick samples or broken membranes. For samples that were thin enough, beam damage often resulted in formation of ice crystals, recognizable as dark spots in images, or destruction of a sample. This implies that the interpretation of cryo-TEM images is delicate and requires many images to obtain a consistent picture. In total, we made hundreds of pictures at different pH and silica concentrations, where consistently different features were observed that are highly interesting and shed light on the rheological properties. At first sight, the samples of pure clay gels at pH 5 and 7 show similar structures (Figures 6 and 5, respectively), with stacks of parallel clay platelets and no clear indication of a house-of-cards structure. As mentioned in the previous section, the tendency to form parallel stacks may be the reason for the high clay concentrations obtained at pH 7 at high osmotic pressures. The structures of the pH 9 gels are clearly different from those at pH 5 and 7. We observe wrinkled structures, as can be seen in Figure 7. On close inspection, the wrinkled structures look like foams of clay platelets around water pockets, reminiscent of the structures proposed by Morvan et al.41 At pH 9, almost all surface charge groups on the clay particles will be deprotonated, resulting in strongly negatively charged platelets, and the foam structure may be a way for the system to minimize the total repulsion between platelets. The formation of such a structure also explains the leveling off of the clay concentration with increased osmotic pressure, resisting further compression as osmotic pressure increases. The clay structures at different pH respond differently to the addition of silica. At pH 5, in addition to free silica particles, we clearly see strings of silica particles around the edges of the clay particles (arrows in Figure 6c,d), indicating a weak attraction

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CONCLUDING REMARKS The present study shows that the montmorillonite−silica mixed system comprises a varied set of interactions that give rise to complex behavior of samples as a function of clay and silica concentration as well as of pH. The reduction of the storage modulus and yield stress of the montmorillonite suspensions in the concentration range studied by addition of anionic silica appears to be a robust feature. However, the underlying mechanism is different at each pH, ranging from modification of the interaction by silica adsorption to microphase separation through depletion interaction. The identification of these underlying mechanisms of gel formation and liquefaction was possible through a combined application of osmotic stress, rheology, and cryo-TEM measurements.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.H.). H

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Present Addresses

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J.H.: ESRF - The European Synchrotron, CS 40220, F-38043, Grenoble Cedex 9, France. V.M.: Soft Matter Physics, Huygens-Kamerlingh Onnes Lab, Universiteit Leiden, Postbus 9504, 2300 RA Leiden, The Netherlands. E.G.: Basf Nederland BV, Strijkviertel 61, P.O. Box 19, 3454 ZG, De Meern, The Netherlands. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Louise Bailey, Geoff Maitland, Rik Wensink, and Emmanuel Trizac for valuable discussions. We are grateful to Laurent Michot for taking the time to explain and demonstrate the osmotic stress method. This work was financially supported by the Academy Professorship of the Royal Netherlands Academy of Arts and Sciences of HNWL.

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