Monte Carlo Study of the Adsorption and Aggregation of

Aug 15, 2012 - All systems were equilibrated in the NVT ensemble at a temperature of 298 K employing the in-house-developed mclay code.(22) This code ...
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Monte Carlo Study of the Adsorption and Aggregation of Alkyltrimethylammonium Chloride on the Montmorillonite−Water Interface Birthe Klebow* and Artur Meleshyn† Institute of Radioecology and Radiation Protection, Leibniz Universität Hannover, Herrenhäuser Strasse 2, D-30419 Hannover, Germany ABSTRACT: Organically modified clays exhibit adsorption capacities for cations, anions, and nonpolar organic compounds, which make them valuable for various environmental technical applications. To improve the understanding of the adsorption processes, the molecular-scale characterization of the structures of organic aggregates assembled on the external basal surfaces of clay particles is essential. The focus of this Monte Carlo simulation study was on the effects of the surface coverage and the alkyl chain length n on the structures of alkyltrimethylammonium chloride ((CnTMA)Cl) aggregates assembled on the montmorillonite−water interface. We found that the amount of adsorbed CnTMA+ ions is independent of the alkyl chain length and increases with the CnTMA+ surface coverage. The CnTMA+ ions predominantly adsorb as inner-sphere complexes; the fraction of outer-sphere adsorbed ions equals only about 10%. The conformational order of the CnTMA+ alkyl chains substantially decreases with decreasing alkyl chain length. In agreement with previous experiments, the amount of CnTMA+ ions that are aggregated at the mineral surface increases with increasing chain length. The maximum value of 0.66 CnTMA+ adsorption complex per unit cell area of the clay surface considerably exceeds the amount of cations required to compensate the negative charge of the montmorillonite surface. Furthermore, in most of the studied systems, fractions of Na+ surface cations remain adsorbed on montmorillonite. The resulting interfacial positive charge excess is counterbalanced by coadsorbed chloride ions forming ion pairs with both CnTMA+ and Na+.

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INTRODUCTION Organically modified clays exhibit adsorption capacities for cations, anions, and nonpolar organic compounds. These adsorption properties make them valuable for their use in various environmental technical applications. For example, they serve as adsorbents to remove ionic and organic pollutantsas, e.g., herbicides, fats, or solventsfrom soil, groundwater, or wastewater.1−3 Due to their anion adsorption property, they are furthermore discussed as possible additives to geotechnical barriers of radioactive waste disposals.4−6 The largest dimension of clay particles is on the scale of 1 μm.7 A montmorillonite particle consists of up to a few dozen negatively charged silicate layers, which are held together by charge-balancing inorganic cations. Each of these silicate layers is composed of a sheet of octahedrally coordinated trivalent cations, mainly Al3+, which is sandwiched by two sheets of tetrahedrally coordinated tetravalent cations, mainly Si4+. Naturally occurring montmorillonites exhibit excess negative charges in both the octahedral and the tetrahedral sheets. These charges result from the exchange of structural Al3+ and Si4+ with ions of lower valence. During the production of organoclays, the inorganic cations in the interlayer spaces and on the external surfaces of clay particles are exchanged by certain organic cations, for example, quaternary alkylammonium ions. The organic cations form aggregates on the external surfaces of the clay particles and © 2012 American Chemical Society

intercalate in the interlayer spaces. Adsorption of organic cations on clays by cation exchange can be followed by their adsorption through hydrophobic bonding, in which case an accompanying uptake of their inorganic counterions occurs. The ability of organoclays to retain anionic pollutants is supposed to result from the exchange with these previously coadsorbed counterions.8−10 Due to the adsorption of organic cations on the external surfaces of clay particles, the hydrophobicity of the organoclays is increased, which makes them capable to adsorb nonpolar organic substances.1−3 Even though to a moderately decreased extent, a certain cation exchange capacity is retained by organoclays due to an incomplete exchange of the inorganic clay cations during the production of organoclays.10,11 To improve the understanding of the pollutant adsorption processes, the molecular-scale characterization of the structures of the aggregates formed by organic cations on the external basal surfaces of clay particles is essential. In contrast to experimental methods, which face fundamental difficulties caused by, e.g., the intrinsically small size of clay particles, their low crystallinity, and their swelling in the presence of water, classical molecular Monte Carlo and molecular dynamics Received: July 3, 2012 Revised: August 14, 2012 Published: August 15, 2012 13274

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facing the water−vacuum interface. The CnTMA+ ions were uniformly distributed in the lateral direction, and the vertical distances z between the nitrogen atoms of the headgroups and the mineral surfaces were set to 4.95 Å for the inner layers and to 32.5, 27.5, and 22.45 Å for the outer layers of C16TMA+, C12TMA+, and C8TMA+ ions, respectively. The monolayer and bilayer aggregates were studied at coverages ranging from 0.125 to 1 CnTMA+ ion/Auc and from 0.5 to 1.5 CnTMA+ ions/Auc, respectively. To maintain charge balance, corresponding amounts of chloride were positioned at z = 15 Å. A total of 33 systems containing organic cations were modeled. In addition to this, a reference system containing the unmodified montmorillonite surface and water only was studied. The water molecules were described by the TIP4P36 water model and accordingly considered rigid. In each simulation cell, 463 water molecules (∼58 TIP4P water molecules/Auc) were distributed randomly above the mineral surface in a slab, the thickness of which was obtained for each simulated CnTMA+ coverage from extensive preliminary test runs. For the unmodified montmorillonite surface, the used amount of water resulted in a water film thickness of approximately 38 Å, which is less than twice the end-to-end distance of approximately 23.5 Å of a fully extended C16TMA+ ion. Because an addition of CnTMA+ ions leads to the displacement of water molecules and thus to an increase of the water film thickness, it was ensured that the examined monolayer and bilayer aggregates were fully immersed in water. The energies of the interactions between the mineral surface, organic cations, inorganic ions, and water molecules were calculated using the OPLS-AA37 force field, which incorporates the TIP4P water model. Accordingly, the total potential energy of each model system is composed of pairwise nonbonded inter- and intramolecular interaction energies (Coulomb and Lennard-Jones potentials) and bonded intramolecular interaction energies (bond bending and torsional angle potentials) between all atoms in the systems. The OPLS-AA force field has been widely used for the simulation of 2:1 minerals, and the simulation results of previous studies have shown good agreement with experimental data.12,14,25,38−41 All OPLS-AA interaction parameters were taken from the literature,22,36,37,42−46 except for the energetically optimized bond angles of the CnTMA+ ions and their partial charges, which were calculated as described elsewhere.47 According to our calculations, the bulk (84%) of the partial charge of CnTMA+ resides on the headgroup and the α-methylene group, and the remaining positive charge (16%) is delocalized over the alkyl chain. For the short-range Lennard-Jones interactions, a cutoff radius of 9 Å and the all-image convention were applied. The long-range Coulomb interactions were treated by Ewald summation as modified for systems with a slab geometry.48 To keep the computational effort within reasonable boundaries, all bond lengths within the CnTMA+ ions were fixed, and only bond bending and torsional angles were given the freedom to change during the Monte Carlo simulations. For the same reason, bond angles within CH2 and CH3 groups were kept constant, assuming that changes of intramolecular energy within these groups have a negligible impact on the equilibrium structures of the simulated aggregates. Even with these constraints, up to several months of CPU time was needed to complete a simulation run for one system on an Intel Xeon CPU X5670, 2.93 GHz processor. All systems were equilibrated in the NVT ensemble at a temperature of 298 K employing the in-house-developed mclay code.22 This code implements the Metropolis Monte Carlo algorithm49 for translation of movable particles and rotation of water molecules as well as the configurational-bias Monte Carlo algorithm50,51 to allow for conformational changes of the CnTMA+ ions. To ensure that the ions and the mineral surface were hydrated prior to the start of the equilibration, only water molecules were allowed to move in the first 2000 Monte Carlo cycles, each comprising m trials of either translation or rotation of a water molecule, with m being the number of movable particles in the studied system. After this pre-equilibration phase, trial moves were allowed for all particles. The structural changes were monitored for each system on the basis of short test samplings carried out every 100 000 Monte Carlo cycles

simulations have proven to be powerful tools for the exploration of mineral structures on a molecular scale. Since the molecular simulation of mineral−water (−organics) systems is computationally very expensive, the size of model systems is generally limited to extensions of several nanometers, which is significantly smaller than the lateral extension of a clay particle. Therefore, simulation studies are generally limited to the investigation of the properties of either interlayer spaces12−22 or basal20,23−27 or lateral28−30 surfaces of clay particles. Currently, the simulation of systems with dimensions on the micrometer scale can only be carried out with the aid of supercomputers executing massively parallel codes under the acceptance of extremely long computation times of several tens of thousands of CPU hours.31 The aim of this work was a molecular-scale characterization of the structures of alkyltrimethylammonium (CnTMA+ = ((CH3)3N)+(CH2)n−1CH3; n ∈ {8, 12, 16}) surfactant aggregates formed on the external basal surface of montmorillonite in aqueous solution. The focus of our research was set on the impacts of the CnTMA+ surface coverage and the alkyl chain length n on the structures of the interfacial surfactant aggregates.

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METHODS OF SIMULATION32

The formula unit of the studied Wyoming-type montmorillonite is Na0.375(Si3.875Al0.125)(Al1.625Fe0.1253+Mg0.25)O10(OH)2. Each simulation cell contained one montmorillonite layer and had a lateral extension of eight unit cells (Auc = 46.36 Å2; Auc represents the area of the montmorillonite surface that corresponds to the area of one unit cell in the crystallographic a−b plane), corresponding to a montmorillonite surface area of 20.65 Å × 17.96 Å. Employing three-dimensional periodic boundary conditions, simulation cells with such lateral dimensions have been proven to be sufficiently large to reproduce macroscopic properties of clay−water systems without being influenced by the artificial long-range system periodicity.33 The charge substitutions were uniformly distributed within the tetrahedral sheets. Within the octahedral sheet, the charge substitutions were uniformly distributed over the cis-octahedral positions. The charges resulting from the substitutions were delocalized between the oxygen atoms surrounding the tetrahedral and the octahedral charge substitutions by means of the method developed by Skipper et al. for rigid clay minerals.33 The coordinates of the atoms within the mineral layer were determined following the algorithm developed by Smoliar-Zviagina.34 In each simulation cell, the montmorillonite layer of a thickness of 6.6 Å was fixed at the bottom of the simulation cell and considered rigid during the Monte Carlo simulations. To model external montmorillonite surfaces, starting from the dehydrated montmorillonite with a layer spacing of 9.6 Å, each simulation cell was expanded in the z direction by a vacuum slab pulling the mineral layer 100 Å away from its neighboring periodic image. As a result of the cleaving, the mineral surfaces exposed to the vacuum interface exhibit cation coverages of 0.375 Na+ ion/Auc, corresponding to half of the montmorillonite interlayer coverage. For the initial configurations, the inorganic sodium cations were uniformly distributed in the lateral direction and positioned 7.5 Å above the mineral surfaces (z = 7.5 Å). Previous simulation studies on the hydration behavior of Wyomingtype montmorillonite35 have shown that the number of clay sheets considered in a certain model can significantly influence the calculated distributions of water molecules and ions in the interlayer spaces. Thus, the influence of the number of modeled clay layers is an important aspect which should be carefully investigated in future simulation studies of montmorillonite−water−organics systems. Both monolayer and bilayer aggregate structures of CnTMA+ were studied. For the monolayer arrangements and the inner layers of the bilayer arrangements, the CnTMA+ ions were oriented with their headgroups facing the montmorillonite surface. For the outer layers of the bilayer arrangements, they were oriented with their headgroups 13275

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over 100 Monte Carlo cycles. In several of the simulated systems, even though the average total potential energy seemed to have converged, drifts of ions toward or away from the mineral surface still occurred in excess of the random displacements around their equilibrium positions expected otherwise. The analysis of the various vertical atomic density profiles sampled for each system indicated that the chosen equilibration phase of four million Monte Carlo cycles was sufficient for system equilibration. The final sampling of the potential energies and structural properties of the montmorillonite−water−organics systems was carried out for one million Monte Carlo cycles, collecting data once each 50th Monte Carlo cycle.

density at z = 2.7 Å, is particularly pronounced. The majority of the water molecules constituting this layer are oriented in such a way that one of their two hydrogen atoms points toward the montmorillonite surface and donates a hydrogen bond to one of the basal oxygen atoms (see Figure 2a). Correspondingly,

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RESULTS AND DISCUSSION Structure of the Interfacial Water Films. The negatively charged montmorillonite surface induces a layering of the interfacial water film, which is extended over several molecular layers (see Figure 1). This layered water structure is consistent with the results of previous simulation studies.23−25,29 Of the hydrating layers, the first one, which has its maximum oxygen

Figure 2. (a) Side view of C16TMA+ ions adsorbed as inner-sphere (left ion) and outer-sphere (right ion) complexes on the montmorillonite surface for the bilayer arrangement at a coverage of 0.75 C16TMA+ ion/Auc. (b) Top view of a C16TMA+ ion adsorbed as an inner-sphere complex on the montmorillonite surface for the monolayer arrangement at a coverage of 0.375 C16TMA+ ion/Auc. (a) and (b) show snapshots of the simulated equilibrium configurations. Ball and stick color key: beige (Si), gray-blue (Al), red (O), white (H), blue (N), brown (C), yellow (Na+), red (Cl−).

the hydrogen density profile exhibits two maxima at 1.8 and 3.05 Å (see Figure 1c). The first peak of the oxygen density profile and the second peak of the hydrogen density profile are notably broadened toward higher z values. This broadening is a consequence of the location of some of the water molecules of the first water layer slightly farther away from the montmorillonite surface. These molecules are not hydrogenbonded to the mineral surface, but donate at least one hydrogen bond to those water molecules that are singly hydrogen-bonded to the montmorillonite surface. The presence of (CnTMA)Cl at the montmorillonite−water interface changes the structure of the adsorbed water film. For example, for the monolayer arrangement at a coverage of 0.375 C16TMA+ ion/Auc, the average water density in the interfacial region that is limited to z ∈ [8 Å, 23 Å] decreases by 21%. At a coverage of 1 C16TMA+ ion/Auc, the average water density in the same region decreases by 54% for the monolayer arrangement and by 50% for the bilayer arrangement (see Figure 1a). For systems containing C12TMA+ and C8TMA+ ions, similar percentage decreases were observed. However, due to the shorter alkyl chains, the decreases of the water densities are limited to smaller vertical regions. At all simulated surfactant coverages, water molecules remain between the hydrophilic headgroups and in the regions of the hydrophobic alkyl chains. The relative decreases of the water densities in the aggregate regions are comparable to those observed for water films adsorbed on CnTMA+-modified muscovite in our preceding simulation study.47 Adsorption Positions of the CnTMA+ Ions. The simulation results indicate that CnTMA+ ions form both inner-sphere and outer-sphere surface complexes on montmorillonite. The most frequently occurring distances between inner-sphere adsorbed CnTMA+ ions and the basal oxygen atoms of the montmorillonite surface are represented by the first maxima of the radial distribution functions g(r) of basal oxygen around the surfactant headgroups and are in the ranges of 2.7−3.2 Å for headgroup hydrogen, 3.5−3.8 Å for headgroup

Figure 1. Vertical atomic density profiles for (a, b) water oxygen and (c) water hydrogen atoms as functions of the distance z from the montmorillonite surface for CnTMA+ monolayer and bilayer arrangements at coverages of 0, 0.375, and 1 C16TMA+ ion/Auc. 13276

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In the lateral direction, the vast majority of the CnTMA+ ions adsorb with their headgroups positioned above the centers of ditrigonal cavities of the montmorillonite surface (see Figure 2). No adsorption of CnTMA + ions above aluminum substitutions of the basal tetrahedral sheet could be observed. In contrast to their adsorption on muscovite,47 single CnTMA+ ions were found to be adsorbed above structural Si atoms of the montmorillonite surface as well. For instance, for the monolayer arrangement at a coverage of 0.5 C12TMA+ ion/ Auc, surfactant ions form inner-sphere surface complexes above both centers of ditrigonal cavities at (x, y) ≈ (2.5 Å, 17.5 Å) and structural Si atoms of the montmorillonite surface at (x, y) ≈ (5 Å, 10.5 Å) (see Figure 5). CnTMA+ ions that form outer-sphere surface complexes on the montmorillonite surface retain their complete first hydration shells (see Figures 2a and 5 at (x, y) ≈ (18 Å, 10 Å)). In comparison to inner-sphere adsorbed ions, they show a higher mobility in both the vertical and the lateral directions. Their vertical nitrogen density distributions exhibit maxima in the ranges of z ∈ [6.4 Å, 8 Å]. In the lateral direction, outersphere adsorbed CnTMA+ ions do not exhibit specific adsorption positions. Amounts of CnTMA+ Adsorbed on the External Surface of Montmorillonite. The amounts of CnTMA+ adsorbed on the montmorillonite surface were estimated from the cumulative density profiles for their nitrogen atoms (see Figure 6). In all simulated systems, at least 0.125 CnTMA+ ion/Auc, corresponding to the lowest simulated CnTMA+ coverage, is adsorbed as inner-sphere surface complexes on the montmorillonite surface. In several systems with coverages of at least 0.75 CnTMA+ ion/Auc, CnTMA+ inner-sphere complexes were observed in excess of the amount required to compensate the charge of the montmorillonite surface of −0.375 e/Auc (see, e.g., the cumulative nitrogen density profile for the bilayer arrangement at a coverage of 1 C16TMA+ ion/ Auc in Figure 6). Contrary to the formation of inner-sphere surface complexes, the formation of outer-sphere complexes was found to occur only in one-fifth of the simulated systems. In general, significantly more inner-sphere than outer-sphere complexes are formed on the montmorillonite surface: On average, only 10% of all adsorption complexes in the simulated systems are outer-sphere ones. This is in contrast to the simulation results for the adsorption of CnTMA+ ions on the cleaved muscovite surface, in which case more than 50% of all adsorption complexes were found to be outer-sphere ones.47 This significantly higher fraction of outer-sphere complexes formed on muscovite can be attributed to the stronger binding of water molecules to the muscovite surface, which has an about 2.7 times higher layer charge than the studied montmorillonite. On muscovite, adsorbing CnTMA+ ions have to overcome comparatively high energy barriers to desorb the doubly hydrogen-bonded water molecules from the mineral surface, whereas on montmorillonite, the first hydrating water layer is only singly hydrogen-bonded to the clay surface. An overview of the total amounts of CnTMA+ adsorbed on the montmorillonite surface with respect to the CnTMA+ coverage is given in Figure 7. In general, the number of CnTMA+ surface complexes increases with increasing surface coverage. At the lowest simulated coverages corresponding to 0.125 CnTMA+ ion/Auc for the monolayer arrangements and to 0.25 CnTMA+ ion/Auc for the bilayer arrangements, all available CnTMA+ ions are adsorbed on the montmorillonite surface.

carbon, and 4.1−4.8 Å for headgroup nitrogen atoms. These values agree well with the distances between headgroup atoms of CnTMA+ ions and oxygen atoms of hydrating water molecules, which equal 2.9 Å for hydrogen, 3.5 Å for carbon, and 4.6 Å for nitrogen.47 Accordingly, the inner-sphere adsorption of CnTMA+ is accompanied by the desorption of water molecules hydrating the clay surface, and some of the water molecules of the first hydration shells of inner-sphere adsorbed CnTMA+ ions are replaced by basal oxygen atoms of the montmorillonite surface (cf. Figure 2). The atomic density profiles for CnTMA+ headgroup carbon atoms, as shown for C16TMA+ in Figure 3, indicate that

Figure 3. Vertical atomic density profiles for carbon atoms of C16TMA+ headgroups and alkyl chains as functions of the distance z from the montmorillonite surface. Coverages ranging from 0.125 to 1 C16TMA+ ion/Auc and from 0.5 to 1.5 C16TMA+ ions /Auc are shown for monolayer and bilayer arrangements, respectively. For each simulated system, the extension of the water film between the montmorillonite−water interface (z = 0 Å) and the water−vacuum interface is indicated by a black bar.

CnTMA+ ions approach the montmorillonite surface to vertical distances of approximately 2 Å. The first maxima of the respective atomic density profiles correspond to the most frequently occurring vertical distances between the atoms of inner-sphere adsorbed CnTMA+ ions and the montmorillonite surface. The calculated values are in the ranges of z ∈ [1.5 Å, 2.95 Å] for hydrogen, z ∈ [2.35 Å, 3.45 Å] for carbon, and z ∈ [3.65 Å, 4.25 Å] for nitrogen atoms of CnTMA+ headgroups. The comparison of the atomic density profiles for the hydrogen atoms of CnTMA+ ions and water molecules hydrating the montmorillonite surface further indicates that their vertical distributions start at very similar z values (cf. Figure 4). 13277

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Figure 4. Vertical atomic density profiles for water, C16TMA+, sodium, and chloride as functions of the distance z from the montmorillonite surface for the bilayer arrangement at a coverage of 0.75 C16TMA+ ion/Auc. The density profiles for Na+ and Cl− are scaled by a factor of 4.

Figure 5. Lateral atomic density profiles for (a) water hydrogen and (b) C12TMA+ headgroup carbon, nitrogen, and potassium atoms at the montmorillonite−water interface for the monolayer arrangement at a coverage of 0.5 C12TMA+ ion/Auc. The hydrogen density was sampled within the first peak of the corresponding atomic density profile (z < 2.3 Å). The headgroup carbon, nitrogen, and sodium densities were sampled within 8.5, 8.5, and 5.5 Å from the montmorillonite surface to ensure that all inner-sphere and outer-sphere adsorbed cations were taken into account. The circles, crossed circles, and triangles represent silicon, aluminum, and basal oxygen atoms of the basal tetrahedral sheet of the montmorillonite surface, respectively.

With increasing CnTMA+ coverage, the surfactant ions are only partially adsorbed. Figure 7 further indicates that, at a given CnTMA+ coverage, the fraction of the CnTMA+ ions that form surface complexes is independent of the alkyl chain length. The highest value of 0.66 C16TMA+ adsorption complex per Auc, corresponding to approximately 1.8 times the negative charge of the montmorillonite surface, was observed for the monolayer arrangement at a coverage of 1 C16TMA+ ion/Auc. For the bilayer arrangements, the highest value of 0.5 CnTMA+ adsorption complex per Auc was observed at the coverages of 1 and 1.5 C8TMA+ ions/Auc. The simulation results indicate that montmorillonite can adsorb significantly more CnTMA+ cations on its external surfaces than required to compensate its negative surface charge. Albeit previous experiments did not distinguish between the amounts of organic cations adsorbed in the interlayer spaces and on the external surfaces of clay particles, their results showed corresponding trends.52−54 Lee and Kim52 and Zhu et al.53 observed that an increased concentration of CnTMA+ ions in solution leads to an increased amount of CnTMA+ adsorbed by montmorillonite. The maximum uptake of CnTMA+ ions by montmorillonite was determined to equal

Figure 6. Cumulative contents of nitrogen atoms as functions of the distance z from the montmorillonite surface for monolayer and bilayer arrangements at different C16TMA+ coverages. The vertical gray lines highlight the maximum z values compatible with the formation of inner-sphere and outer-sphere adsorption complexes. The gray shaded area marks those amounts of CnTMA+ that do not compensate the charge of the clay surface of −0.375 e/Auc.

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Figure 8. Number of molecules in the first water layer adsorbed on the montmorillonite surface with zoxygen ≤ 4.7 Å as a function of the number of CnTMA+ inner-sphere surface complexes. The data point for the monolayer arrangement at a coverage of 0.75 C8TMA+ ion/Auc (marked in red) was not taken into account for the regression as discussed in the text.

arrangement at a coverage of 0.75 C8TMA+ ion/Auc. This is because of an adsorption of 0.125 C8TMA+ ion/Auc with their alkyl chains arranged parallel to the montmorillonite surface, resulting in an exceptionally strong decrease of the density of the first water layer. The regression line indicates that, with each adsorbed CnTMA+ inner-sphere complex per Auc, the density of the first water layer is decreased by approximately 4.2 water molecules per Auc, corresponding to approximately 70% of the density of the water film adsorbed on the unmodified montmorillonite. The values estimated by the regression line exhibit a standard deviation of 0.18 molecule/Auc from the plotted data points. Structures of the Adsorbed CnTMA+ Aggregates. The analysis of the simulated aggregate structures shows that up to coverages of 0.375 CnTMA+ ion/Auc, the surfactant ions are adsorbed on the montmorillonite surface as single ions or in pairs. At higher coverages, the CnTMA+ ions form aggregates, which partially cover the montmorillonite surface and are laterally separated from water. This aggregation behavior is in close analogy to the previously studied aggregation of CnTMA+ ions on muscovite.47 For the bilayer arrangements, the alkyl chains of the two opposed CnTMA+ layers composing the aggregates are interdigitated. This interdigitation is less pronounced for the aggregates formed by the short-chained C8TMA+ ions. With decreasing alkyl chain length, increasing amounts of CnTMA+ are desorbed from the aggregates (cf. Figure 9). These desorbed surfactant ions reside as monomers in the solution or are located at the water−vacuum interface (cf., e.g., Figure 3 for the monolayer arrangement at a coverage of 0.25 C16TMA+ ion/Auc). Thus, even though the total number of adsorbed CnTMA+ ions is independent of the alkyl chain length, the amount of CnTMA+ aggregated at the montmorillonite surface increases with increasing surfactant alkyl chain length. This observation can be attributed to an increased hydrophobic interaction between the longer surfactant alkyl chains. The increase of the amount of aggregated CnTMA+ ions with the alkyl chain length is in good agreement with reflectometry measurements by Atkin et al., which indicate that the surface excess of CnTMA+ ions on silica at a given concentration increases with the surfactant alkyl chain length.55 The degree of conformational order within the surfactant aggregates is reflected by the gauche conformation fractions of the alkyl chains. With decreasing alkyl chain length, a trend of

Figure 7. Amounts of CnTMA+ adsorbed on the montmorillonite surface for (a) C16TMA+, (b) C12TMA+, and (c) C8TMA+ monolayer and bilayer arrangements as functions of the CnTMA+ coverage of the surfactant layers facing the montmorillonite surface. The dotted gray lines mark those amounts of CnTMA+ that correspond to the adsorption of all available surfactant ions at a given CnTMA+ coverage. The gray shaded areas mark those amounts of adsorbed CnTMA+ that do not compensate the charge of the clay surface of −0.375 e/Auc.

approximately 2.5 times its cation exchange capacity. Schampera and Dultz54 observed that the organic cations BE+, TPP+, and HDPy+ are completely adsorbed by Wyoming montmorillonite up to offered amounts corresponding to approximately 80% of the cation exchange capacity of the clay. In agreement with our simulation results, at higher applied concentrations, the organic cations are only partially adsorbed.54 The adsorption of CnTMA+ ions on the external surface of montmorillonite leads to a significant decrease of the density of the first water layers (see Figure 1b). We plotted the number of CnTMA+ inner-sphere surface complexes against the number of water molecules in the first water layer with zoxygen ≤ 4.7 Å, as shown in Figure 8, and applied a linear least-squares fit to the approximately linear relationship between the two parameters. The intercept of the axis, which describes the number of water molecules per Auc in the first layer adsorbed on the unmodified montmorillonite, was not fixed. An outlier, which was not taken into account for the regression, was observed for the monolayer 13279

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increasing surface coverage, the apparent aggregate thicknesses increase to up to 35 and 32 Å at coverages of 0.75 and 1 C16TMA+ ion/Auc, respectively. This increase of aggregate thickness is due to C16TMA+ ions that are located with their headgroup atoms at z values of approximately 15 Å. These ions are not adsorbed on the montmorillonite surface but nevertheless take part in the aggregation through hydrophobic interactions of their alkyl chains (see Figure 9a). These detached but yet aggregated CnTMA+ ions exhibit higher z values of the carbon atoms of their alkyl chains than those ions that are adsorbed on montmorillonite as inner-sphere or outersphere surface complexes. For the monolayer aggregates formed by the shorter chained C12TMA+ and C8TMA+ ions, a similar dependence of the surfactant surface coverage was observed. The determined aggregate thicknesses are in the ranges of 18−25 and 13−17 Å, respectively. In single systems, carbon atoms of the alkyl chains are located at z values of up to 32 Å for C12TMA+ and up to 27 Å for C8TMA+. These ions are detached from the surfactant aggregates and are located at the aggregate−solution interface (cf. Figure 9b). Similarly, the thicknesses of the CnTMA+ bilayer aggregates slightly increase with the surfactant surface coverage. The calculated thicknesses are in the ranges of 30−39 Å for C16TMA+ and 23−36 Å for C12TMA+. The simulated C8TMA+ bilayer aggregates exhibit thicknesses of 23 and 20 Å at coverages of 0.75 and 1 C8TMA+ ion/Auc, respectively. At the other simulated coverages, significant fractions of the C8TMA+ ions are characterized by large separations from the surface and are desorbed from the aggregates. For these systems, the aggregate thicknesses could not be determined unambiguously. The determined aggregate thicknesses are consistent with the thicknesses of CnTMA+ aggregates assembled on muscovite.47 In general, slightly smaller extensions in the z direction were observed for the aggregates formed on the external surface of montmorillonite. This effect can be attributed to the significantly greater fraction of inner-sphere surface complexes formed on montmorillonite, resulting in a closer approach of the surfactant ions to the mineral surface. Arrangement of Inorganic Ions within the Aggregate Regions. At surfactant coverages smaller than 0.75 CnTMA+ ion/Auc, in all simulated systems, 0.125 Na+ ion/Auc is adsorbed as inner-sphere complexes above the tetrahedral charge substitutions of the basal surface of montmorillonite (cf. Figure 5). The maxima of the corresponding vertical density distributions for sodium are in the range of z ∈ [1.6 Å, 1.65 Å]. This amount of adsorbed Na+ equals the amount of tetrahedral charge substitutions of the basal surface. In single systems with higher CnTMA+ coverages, the desorption of sodium ions from their positions above the tetrahedral substitutions was observed. Sodium ions residing at distances of z ∈ [4.1 Å, 4.7 Å] away from the montmorillonite surface are adsorbed as outer-sphere complexes. Their vertical positions coincide with the first minimum of the water oxygen density distribution (cf. Figure 4). A maximum of 0.71 cation surface complex per Auc, comprising all inner-sphere and outer-sphere surface complexes of sodium and CnTMA+ ions, was observed for the bilayer arrangement at a coverage of 1.5 C16TMA+ ions/Auc. This amount corresponds to approximately twice the charge density required to compensate the negative charge of the clay surface. The excess positive charge is counterbalanced by chloride anions residing close to the montmorillonite surface. A comparison of the vertical atomic density profiles for

Figure 9. Snapshots of the simulated equilibrium configurations for (a) C16TMA+ and (b) C8TMA+ monolayer arrangements at coverages of 1 CnTMA+ ion/Auc, viewed parallel to the montmorillonite−water interface. Ball and stick color key: yellow (Na+), red (Cl−), brown (C), blue (N), white (H), light gray (O), beige (Si), light blue (Al), green (Mg).

decreasing conformational order was observed. The calculated gauche conformation fractions of the alkyl chains vary in the ranges of 10−33% for C16TMA+, 8−26% for C12TMA+, and 25−38% for C8TMA+ monolayer aggregates. For bilayer aggregates, the calculated gauche conformation fractions are in the ranges of 6−15% for C16TMA+, 9−16% for C12TMA+, and 23−34% for C8TMA+. With increasing surface coverage, a slight increase of the conformational order was observed to occur within the monolayer aggregates of the long-chained C16TMA+ ions. This trend could not be observed for the aggregates formed by the shorter chained C12TMA+ and C8TMA+ ions. The calculated gauche conformation fractions exhibit comparatively high standard deviations of up to 19%. This manifests the coexistence of nearly fully extended chains and chains with high numbers of gauche conformations in the same systems. The apparent aggregate thicknesses were estimated on the basis of the vertical atomic density profiles for the carbon atoms of CnTMA+ alkyl chains (monolayer aggregates) and headgroups (bilayer aggregates) (cf. Figure 3). The C16TMA+ monolayer aggregates exhibit thicknesses of approximately 23 Å at coverages of 0.125 and 0.25 C16TMA+ ion/Auc. With 13280

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external surfaces of organoclay particles can thus be attributed to their exchange with inorganic counterions (in the case of this study, Cl−), which were coadsorbed on the clay surfaces during the production of the organoclays. Up to simulated coverages of 0.375 CnTMA+ ion/Auc, the surfactant ions are adsorbed on the montmorillonite surface as single ions or in pairs. At higher coverages, the CnTMA+ ions form aggregates that are laterally separated from water and partially cover the montmorillonite surface. The amount of water in the alkyl chain regions decreases by approximately 50% upon the addition of 1 CnTMA+ ion/Auc. The alkyl chain length n of the CnTMA+ ions considerably influences the structure of the assembled surfactant aggregates. As expected, the extension of the aggregates in the vertical direction increases with the alkyl chain length. The simulated monolayer aggregates exhibit thicknesses of 23−35 Å for C16TMA+, 18−25 Å for C12TMA+, and 13−17 Å for C8TMA+. The bilayer aggregates show a strong interdigitation and exhibit thicknesses of 30−39 Å for C16TMA+, 23−36 Å for C12TMA+, and 20−23 Å for C8TMA+. With decreasing chain length, increasing amounts of CnTMA+ are desorbed from the aggregates. These desorbed surfactant ions reside as monomers in the solution or are located at the water−vacuum interface. Thus, in agreement with reflectometry measurements,55 even though the number of adsorption complexes is independent of the alkyl chain length, the number of CnTMA+ ions that are aggregated at the clay surface increases with increasing chain length. The weaker hydrophobic interactions between shorter chained CnTMA+ ions are likewise reflected by the calculated gauche conformation fractions of the alkyl chains: the conformational order of the alkyl chains of the CnTMA+ ions considerably decreases with decreasing alkyl chain length.

headgroup carbon atoms and chloride indicates that the vast majority of the chloride ions assemble in the vicinity of CnTMA+ headgroups at the montmorillonite−aggregate interface and, for bilayer aggregates, likewise at the aggregate−water interface. The analysis of the radial distribution functions of chloride around sodium ions and CnTMA+ headgroups confirms that both contact and solvent-separated ion pairs of chloride are formed with sodium and CnTMA+ ions adsorbed on or desorbed from the montmorillonite surface. The adsorption of anionic pollutants on the external surfaces of organoclay particles can thus be attributed to their exchange with inorganic counterions (in the case of this study, Cl−), which were coadsorbed on the clay surfaces during the production of the organoclays. This observation strongly supports previous adsorption theories derived from experiments.8−10 The observation that, in most of the simulated systems, fractions of sodium remain adsorbed on the montmorillonite surface explains the outcomes of batch experiments that even those organoclays possess adsorption capacities for cations, which exhibit uptakes of organic cations exceeding their cation exchange capacities.10,11

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CONCLUSIONS The simulation results indicate that approximately 90% of the adsorbed CnTMA+ ions form inner-sphere complexes on the montmorillonite surface. In the lateral direction, they are mainly adsorbed above the ditrigonal cavities of the clay surface. The distances between their nitrogen atoms and the clay surface are in the range of 3.65−4.25 Å. Inner-sphere adsorbed CnTMA+ ions penetrate the first water layer that is adsorbed on montmorillonite and displace water molecules from their adsorption positions. On average, with each adsorbed CnTMA+ inner-sphere surface complex per Auc, the density of the first water layer is decreased by approximately 70%. Those 10% of the CnTMA+ ions which form outer-sphere complexes on the montmorillonite surface are characterized by z values of their nitrogen atoms varying between 6.4 and 8 Å. In contrast to inner-sphere adsorbed CnTMA+ ions, they do not show specific lateral adsorption positions. In agreement with previous experiments,52−54 the amount of adsorbed CnTMA+ ions increases with the CnTMA+ surface coverage. At the lowest simulated coverages, for both the monolayer and the bilayer arrangements, all available CnTMA+ ions are adsorbed on the montmorillonite surface. At higher coverages, only parts of the aggregated surfactant ions form adsorption complexes. The highest observed value of 0.66 CnTMA+ adsorption complex per Auc considerably exceeds the amount of surface complexes required to compensate the negative charge of the montmorillonite surface. Even at these high amounts of adsorbed CnTMA+ ions, in most of the simulated systems, a fraction of surface Na+ remains adsorbed above the tetrahedral substitutions of the montmorillonite surface. This presence of inorganic surface cations at the montmorillonite surface explains the results of batch experiments that even those organoclays possess adsorption capacities for cations, which exhibit uptakes of organic cations exceeding their cation exchange capacities.10,11 The excess positive charge at the montmorillonite surface is counterbalanced by chloride anions, which are mostly located in the regions around the hydrophilic CnTMA+ headgroups and form ion pairs with both CnTMA+ and sodium ions. In accordance with previous adsorption theories derived from experiments,8−10 the adsorption of anionic pollutants on the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH, Theodor-Heuss-Strasse 4, D-38122 Braunschweig, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The vast majority of the calculations presented in this work were performed on the Central Services Information Technology (RRZN) compute cluster. The support of the compute cluster team is gratefully acknowledged.

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REFERENCES

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