Aggregation of Alkyltrimethylammonium Ions at the Cleaved Muscovite

Sep 12, 2011 - pubs.acs.org/Langmuir. Aggregation of Alkyltrimethylammonium Ions at the Cleaved. Muscovite MicaАWater Interface: A Monte Carlo Study...
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Aggregation of Alkyltrimethylammonium Ions at the Cleaved Muscovite Mica Water Interface: A Monte Carlo Study Birthe Klebow* and Artur Meleshyn† Institute of Radioecology and Radiation Protection, Leibniz Universit€at Hannover, Herrenh€auser Strasse 2, D-30419 Hannover, Germany

bS Supporting Information ABSTRACT: The precise molecular structure of organically modified mineral surfaces is still not well understood. To establish a relation between experimental observations and underlying molecular structure, we performed Monte Carlo simulations of the aggregation behavior of alkyltrimethylammonium surfactants (CnTMA+) at the interface between CnTMACl solution and cleaved K+muscovite. The structures were examined with regard to the influence of varying alkyl chain length n (n = 8, 12, 16) and surface coverage of CnTMA+ ions. The simulation results indicate that the water film structure at the muscovite surface is considerably influenced by the adsorption of CnTMA+. A fraction of the CnTMA+ ions forms inner-sphere and outer-sphere adsorption complexes with nitrogen surface distances of 3.3 3.8 and 5.5 8.4 Å, respectively. The simulated monolayer aggregates exhibit thicknesses of 31 35, 22 27, and ∼18 Å for C16TMA+, C12TMA+, and C8TMA+, respectively. C16TMA+ and C12TMA+ ions form bilayer aggregates, which show a strong interdigitation of the two opposing layers composing them. The aggregate thicknesses equal 35 39 and 30 35 Å, respectively, and are in agreement with available experimental data. In contrast, the short-chained C8TMA+ ions do not form bilayer aggregates. In agreement with previous experimental studies, the alkyl chains of the aggregated ions show high conformational order markedly decreasing with decreasing chain length. We suggest that the simulated structures represent CnTMA+ aggregates, which are formed on muscovite during the experimentally observed initial equilibration phase characterized by the presence of inorganic ions within the aggregates.

1. INTRODUCTION Organically modified surfaces are of interest in various industrial and environmental engineering processes. In past decades, many experimental studies (e.g., atomic force microscopy (AFM),1 9 surface force apparatus (SFA),10 13 X-ray photoelectron spectroscopy (XPS),13 Fourier transform infrared spectroscopy (FTIR),14 nuclear magnetic resonance spectroscopy (NMR),14 near edge X-ray absorption fine structure spectroscopy (NEXAFS),15,16 and neutron reflectometry (NR)8,17,18) have been performed to elucidate the structure of surfactant aggregates assembled on mineral surfaces. Muscovite mica is a widely used substrate, which can easily be cleaved along the plane of its interlayer cations. It does not swell in aqueous solutions, and its interlayer cations are not exchangeable under ambient conditions. Alkyltrimethylammonium surfactants (CnTMA+, with n being the number of methyl(ene) groups in the surfactants’ alkyl chains) adsorb with their positively charged hydrophilic headgroups facing the surface and aggregate at the muscovite surface.10,11,13 At solution concentrations far below the critical micelle concentration (CMC), island-like aggregate structures are formed.2,9 With increasing concentration, monolayer aggregates covering the surface are observed.11,13,15 The hydrophobic alkyl chains of the aggregated surfactant ions face the solution, so that the organically modified muscovite surface becomes hydrophobic. r 2011 American Chemical Society

At concentrations around the CMC, a second layer with headgroups facing solution builds up, and the surface is rendered hydrophilic again. AFM images of CnTMABr (n = 12, 14, 16) aggregates self-assembled on mica at concentrations of about twice the critical micelle concentration show striped aggregate structures, which are commonly interpreted as cylindrical micelles.1,3 6,8 In IR and NEXAFS experiments, the conformational order within the aggregates was observed to increase with increasing alkyl chain length14,16 and surface coverage.2,9 SFA and NR studies indicate that a certain amount of water remains within the aggregate regions.12,13,17 However, because of lacking information on the lateral structure within the aggregates, it could not yet be inferred, whether chain and water regions are laterally segregated from each other or whether the water molecules are distributed homogenously within the aggregates. Depending on the conditions of the studied systems, the final equilibration of the aggregate structures can proceed very slowly. For C16TMA+, the striped aggregates evolve into flat bilayer structures within about a day,3 5 whereas the striped structures of the aggregates formed by shorter-chained CnTMA+ ions Received: July 1, 2011 Revised: September 8, 2011 Published: September 12, 2011 12968

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Langmuir remain stable. In some cases, structural changes are observed to occur for time spans of days or even months.2,9,13 Prevalently, a rapidly occurring initial surfactant adsorption phase is followed by a very slowly occurring equilibration phase, which is characterized by low surfactant adsorption rates, exchange competition between surfactants and inorganic muscovite cations, rearrangement of surfactant aggregates, and gradual release of inorganic surface cations paired with initially coadsorbed surfactant counterions out of the aggregate regions. Classical molecular simulation methods, which use force fields to describe intra- and intermolecular interactions, successfully contribute to the interpretation of experimental observations made for inorganic19 24 and organically modified25 35 minerals. The expansion of clays due to intercalation of organic cations as well as the arrangement, tilt angles, and conformational order of intercalated chain molecules have successfully been modeled in agreement with experimental measurements.26,28 33 Regarding the external surfaces of muscovite and montmorillonite, the vertical and lateral structures of adsorbed water films have been successfully modeled in agreement with experimental measurements.21,22,24,36,37 Lateral and vertical adsorption positions for both both inorganic22,37 40 and organic cations25,27,29,34,35 in dehydrated and hydrated states have been identified, and transformation energies between different adsorption states have been calculated. Tilt angles and thermal phase transitions of C18TMA+ and dioctadecyldimethylammonium aggregates adsorbed on dehydrated mica have successfully been modeled in agreement with experimental measurements.27,29 A model connecting the packing density of alkyl chains on mineral surfaces with average tilt angles, conformational order, and thermal behavior has been introduced.41 In this study, classical Monte Carlo simulations were performed to elucidate the structure of CnTMA+ monolayer and bilayer aggregates formed in aqueous solution at the cleaved muscovite water interface with regard to the influences of varying alkyl chain length (n = 8, 12, 16) and surface coverage of CnTMA+ ions.

2. METHODS OF SIMULATION The formula unit of muscovite mica is KAl2(OH)2(AlSi3O10) with, on average, every fourth silicon atom in the tetrahedral sheets being replaced by aluminum and the octahedral sheets of the muscovite layers being occupied by aluminum only. The resulting negative layer charge is compensated by K+ cations with a coverage of two cations per unit cell area in the interlayers (Auc = 46.72 Å2; Auc represents that area of the muscovite surface that corresponds to the area of one unit cell in the crystallographic a b plane). The simulation cell (Figure 1) contained two layers of muscovite mica with a total thickness of ∼20 Å and an area of ∼374 Å2 corresponding to eight unit cells in lateral direction. The atomic coordinates were adopted from an experimental study by Schlegel et al.42 The Al substitutions in the tetrahedral layers were arranged according to Loewenstein’s rule (Al O Al avoidance),43 and the charges resulting from the tetrahedral substitutions were delocalized between the basal oxygens of the mineral surface according to the method of Skipper et al.20 (Supporting Information). The muscovite layer was treated as a rigid molecule. Three-dimensional periodic boundary conditions were applied, and the simulation cell was expanded in z-direction by a vacuum slab pulling the muscovite layer 100 Å apart from its next periodic image. This results in a model of a cleaved muscovite surface infinitely extended in two dimensions. As a result of cleaving, the exposed muscovite surface exhibits a K+ coverage of 1 K+/ Auc. For the start configuration, the K+ ions at the cleaved surface were

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Figure 1. Snapshot of a simulated equilibrium configuration viewed parallel to the muscovite water interface for bilayer arrangement at a coverage of 1.25 C12TMA+/Auc. Note a pronounced interdigitation within the bilayer aggregate. Ball and stick colors: yellow (K+), light blue (Al), light green (Si), light gray (O), white (H), turquoise (N), blue (C), red (Cl ). uniformly distributed in the lateral direction and positioned 7.5 Å above the surface (z = 7.5 Å). To model CnTMA+, geometry optimizations were conducted with the GAMESS-US44,45 quantum chemistry software package employing the B3LYP46 48 density functional as implemented in GAMESS-US, incorporating the correlation functional VWN I49 and the SVP basis set.50 The geometry optimizations were conducted without symmetry constraints. The initial geometry for C16TMA+ was taken from an X-ray diffractometry study of C16TMABr in crystalline state.51 The partial charges within C16TMA+ were calculated by means of Mulliken population analysis. To calculate the charge distributions of C12TMA+ and C8TMA+, the optimized C16TMA+ geometry with a correspondingly shortened alkyl chain was used as input. The resulting partial charges (Supporting Information), bond lengths, and angles are virtually independent of the alkyl chain length. The bulk of the positive charge of CnTMA+ (84%) resides on the headgroup and the α-methylene group, and the remaining positive charge (16%) is delocalized over the alkyl chain. During the Monte Carlo simulations, all bond lengths within the CnTMA+ ions were fixed, and only bond and torsional angles were 12969

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Langmuir allowed to change to save CPU time and facilitate the simulations, which even with these constraints needed CPU times of up to several months. For the same reason, bond angles within CH2 and CH3 groups were kept constant, assuming that changes of intramolecular energy within these groups have negligible influence on the equilibrium structure of the simulated aggregates. Monolayer and bilayer aggregates were studied at coverages of 0.25 1.25 and 0.5 1.5 CnTMA+/Auc, respectively. The CnTMA+ ions were oriented with their headgroups facing either the muscovite surface (monolayer arrangement and inner layer for bilayer arrangement) or the water vacuum interface (outer layer for bilayer arrangement). The distances z between headgroup nitrogens and the surface were set to 4.95 Å for the inner layer and to 32.5, 27.5, and 22.45 Å for the outer layer for C16TMA+, C12TMA+, and C8TMA+, respectively. To maintain charge balance, a corresponding amount of Cl was positioned at z = 15 Å. A total of 26 systems containing organic cations and a reference system consisting of muscovite and water only were modeled. Water molecules were described by the TIP4P water model52 and accordingly considered rigid. 463 water molecules per simulation cell (∼58 TIP4P/Auc) were distributed randomly above the muscovite surface in a slab, the thickness of which was estimated for each simulated CnTMA+ coverage based on a preliminary test run. For unmodified muscovite, this amount of water results in a water film thickness of ∼38 Å, which is less than twice the end-to-end distance of a C16TMA+ ion in all-trans conformation (∼23.5 Å). Because, however, an addition of CnTMA+ ions leads to the displacement of water molecules and therefore to an increase of water film thickness, it is ensured that the examined monolayer and bilayer aggregates are fully immersed in water. The interactions between muscovite, organic cations, inorganic ions, and water molecules were described using the OPLS-AA53 force field, which includes the TIP4P water model. The choice of both the force field and the procedures to determine partial charges are approaches that are necessary to conduct the Monte Carlo simulations, but inherently involve significant approximations. However, these methods have been widely used for the simulation of 2:1 minerals and have shown good agreement with experimental data.19,23,34 36,39,54 For short-range interactions (Lennard-Jones, bond bending, and bond torsion terms), a cutoff radius of 9 Å and the minimum-image convention were applied. Long-range Coulomb interactions were treated by Ewald summation as modified for systems with slab geometry.55 All interaction parameters were taken from the literature,31,52,53,56 60 except for the equilibrium angles of CnTMA+, which were taken from the above-described quantum chemical calculations. All systems were equilibrated in canonical ensemble (NVT) at a temperature of 298 K using the in-house developed mclay-code.31 This code implements the Metropolis Monte Carlo algorithm61 for translation of movable particles and rotation of water molecules as well as the configurational-bias Monte Carlo algorithm62 for conformational changes of CnTMA+ as described elsewhere.63,64 To ensure that ions and the mineral surface were hydrated before the start of the equilibration, only water molecules were moved in the first 2000 Monte Carlo cycles, each comprising m trials of either translation or rotation with m being the number of movable particles in the studied system. After this preequilibration phase, all trial moves were allowed. A system was judged to be equilibrated upon the convergence of its average total potential energy to a constant value, which was as a rule achieved after several 100 000 Monte Carlo cycles. However, in some of the simulated systems, even though the average total potential energy seemed to have converged, drifts of ions toward or away from the muscovite surface still occurred in excess of the random displacements around their equilibrium positions expected otherwise. These movements eventually led to energy decreases after several additional 100 000 cycles. Besides, the bilayer systems showed slower equilibration than the monolayer ones. Therefore, the simulations were carried out for at least

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Figure 2. Density profiles for carbon atoms of C16TMA+ headgroups and alkyl chains as functions of the distance from the muscovite surface. Coverages of 0.25 1.25 and 0.5 1.5 C16TMA+/Auc are shown for monolayer and bilayer arrangements, respectively. For each simulated system, the extension of the water film between the muscovite water interface (z = 0) and the water vacuum interface is indicated by a black bar. two million cycles for monolayer and three million cycles for bilayer arrangements, before the final sampling was started. Final sampling of potential energies and structural properties was carried out over 20 000 MC cycles (sampling each MC cycle) for all systems containing CnTMA+ ions and over 1 000 000 MC cycles (sampling every 50th MC cycle) for the inorganic reference system. Because the applied Monte Carlo algorithms can hardly be parallelized, up to several months of CPU time was needed to complete a simulation run of one system on an Intel Xeon E5472, 3.0 GHz processor.

3. RESULTS AND DISCUSSION 3.1. Adsorption Positions of CnTMA+ Ions. Figure 2 gives an overview of the vertical density profiles for the C16TMA+ ions at the muscovite water interface. They indicate that headgroup carbons of C16TMA+ can approach as close as ∼2 Å to the muscovite surface (the same applies for C12TMA+ and C8TMA+, data not shown) with no other ions or molecules interposed between. These organic cations are thus adsorbed as inner-sphere complexes on muscovite. The radius of their hydration shell can be used as a rough measure for the maximum separation of innersphere adsorbed CnTMA+ ions from the muscovite surface. Representative radial distribution functions around C16TMA+ headgroup atoms are shown in Figure 3. The calculated hydration shell radii are very similar for all three studied chain lengths (rH O = 3.6 Å; rC O = 4.4 Å; rN O = 6.2 Å) and agree well with those obtained by a molecular dynamics study of C16TMACl micelles in water utilizing the GROMOS96 force field.65 Headgroup methyls of inner-sphere adsorbed CnTMA+ ions penetrate the first adsorbed water layer as indicated by z-values 12970

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Figure 3. Radial distribution functions for water oxygens around C16TMA+ headgroups for bilayer arrangement at a coverage of 0.5 C16TMA+/Auc. According to the definition by Allen and Tildesley,63 the radial distribution function represents the probability of finding a pair of atoms a distance r apart in the considered system relative to the probability expected for a completely random distribution at the same density.

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Figure 5. (a) Top view and (b) side view of an inner-sphere (left ion) and an outer-sphere (right ion) adsorption complex of C16TMA+ at the muscovite surface (snapshot of a simulated equilibrium configuration for monolayer arrangement at a coverage of 1 C16TMA+/Auc). Ball and stick colors: dark yellow (Si), gray-blue (Al), dark rose (basal O), dark blue (C), turquoise (N), white (H), red (water O).

Figure 6. Cumulative contents of nitrogen atoms as functions of the distance from the muscovite surface. Data for monolayer and bilayer arrangements at different C16TMA+ coverages are shown. The vertical gray lines highlight the maximum z-values indicating the formation of inner-sphere and outer-sphere adsorption complexes, respectively. Figure 4. Atomic density profiles for water, C16TMA+, K+, and Cl as functions of the distance from the muscovite surface for monolayer arrangement at a coverage of 1 C16TMA+/Auc.

of ∼1.2 Å for the first maxima of the hydrogen density distributions for water and CnTMA+ (Figure 4). The z-values for the first maxima of the atomic density profiles for inner-sphere adsorbed CnTMA+ ions show no dependence on chain length and vary in the ranges of 1.2 1.7 Å for hydrogen, 2.1 2.6 Å for carbon, and 3.3 3.8 Å for nitrogen. The surfactants adsorb above ditrigonal cavities with the methyl group closest to the surface positioned directly above the cavity center (Figure 5), the adsorption site occupied by water molecules in the case of unmodified muscovite.21,36 This lateral adsorption position agrees with that of C18TMA+ on dehydrated muscovite as calculated in a molecular dynamics study by Heinz et al.27 However, the therein stated preference of cavities with more than one Al-defect could not be observed in this simulation study. At 20 °C, Heinz et al. report an adsorption height of 3.8 ( 0.1 Å above the plane of tetrahedral Si and Al atoms, corresponding to a height of 3.15 ( 0.1 Å above the basal plane of muscovite, which is significantly lower than the values we calculated. We attribute this height difference to the absence of water in the cited simulation study. Additionally performed simulations of systems devoid of water molecules with coverages ranging from 0.25 to 1.25 C16TMA+/Auc confirmed this assumption. With C16TMA+ adsorbed at heights of 3.05 3.3 Å above the basal plane, our results for dehydrated muscovite are in very good agreement with those calculated by Heinz et al.

CnTMA+ ions characterized by z-values for the first maxima for nitrogen varying between 5.5 and 8.4 Å are adsorbed as outersphere complexes on muscovite. Their first coordination shells contain water molecules of the first water layer hydrogen-bonded to the muscovite surface, but no basal oxygens of the muscovite surface. In contrast to inner-sphere adsorbed CnTMA+ ions, they do not show specific lateral adsorption positions. CnTMA+ ions with larger z-values are separated from the muscovite surface by at least two interposed water molecules and are not adsorbed as outer-sphere complexes any more. Single C16TMA+ ions reside as far as ∼16 Å away from the surface (Figure 4). The observed maximum headgroup surface separation increases further for C12TMA+ (∼19 Å) and C8TMA+ ions (∼21 Å). Following these observations, the amount of adsorbed CnTMA+ ions can readily be estimated from cumulative density profiles for nitrogen (Figure 6). For monolayer arrangement of CnTMA+ ions, the amount of adsorption complexes increases with increasing surface coverage. For instance, a total of 0.125, 0.55, and 0.75 adsorption complexes, about one-half of them being innersphere ones, are observed at coverages of 0.25, 0.75, and 1 C16TMA+/Auc (Figure 6). For bilayer arrangement, the number of adsorption complexes is significantly smaller, and no distinct dependence on surface coverage was observed. For instance, for C16TMA+, about 0.25 adsorption complexes per Auc are observed at all simulated coverages (0.5 1.5 C16TMA+/ Auc). Maximum numbers of 0.75 and 0.5 CnTMA+ adsorption complexes per Auc were observed for monolayer and bilayer 12971

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Figure 8. Density profiles for water oxygen as functions of the distance from the muscovite surface at coverages of 0 C16TMA+/Auc and 1 C16TMA+/Auc for monolayer and bilayer arrangement. Regard that the first two maxima of the water oxygen density profiles are due to sublayers of water molecules doubly and singly hydrogen bonded to the muscovite surface.

Figure 7. Density profiles for (a) potassium and (b) chloride ions as functions of the distance from the muscovite surface. Coverages of 0.25 1.25 and 0.5 1.5 C16TMA+/Auc are shown for monolayer (lower panels) and bilayer (upper panels) arrangements, respectively. For each simulated system, the extension of the water film between the muscovite water interface (z = 0) and the water vacuum interface is indicated by a black bar.

arrangements, respectively. This is less than the amount of cations necessary to compensate the negative surface charge of muscovite. In all simulated systems, a fraction of CnTMA+ ions remained detached from the muscovite surface, which agrees with the simulation results obtained for the adsorption of CP+ on muscovite mica.34 3.2. Structure of the Water Film and Positions of Inorganic Ions. Even at simulated surfactant coverages exceeding 1 CnTMA+/ Auc, which corresponds to the amount of cations necessary to compensate the negative surface charge of muscovite, a fraction of K+ ions remains adsorbed at the muscovite surface, as shown in Figure 7 for C16TMA+ systems. For monolayer arrangement at a coverage of 1 CnTMA+/Auc, only one-half of the K+ ions are desorbed from muscovite. For bilayer arrangement, the amount of desorbed K+ ions is even smaller with a maximum desorption of 0.125, 0.25, and 0.375 K+/Auc for C16TMA+, C12TMA+, and C8TMA+ systems, respectively. Those K+ ions remaining at the surface form inner-sphere adsorption complexes either above Alsubstitutions, the preferred adsorption positions in the case of unmodified muscovite,39 or above ditrigonal cavity centers. The bulk of Cl ions resides in the vicinity of CnTMA+ headgroups (cf., the z-values for headgroup carbon atoms and Cl in Figures 2 and 7). For bilayer arrangement, about one-half of the Cl ions are located around the headgroups of the outer layer of the aggregate. They form contact and solvent separated ion pairs with CnTMA+ headgroups as well as with K+ ions adsorbed on or desorbed from muscovite. For bilayer arrangement, the regions occupied by hydrophobic alkyl chains contain only a small fraction of inorganic ions.

The presence of CnTMACl influences the structure of the water film at the muscovite surface. At a coverage of 1 C16TMA+/ Auc, the water density decreases by up to ∼45% for bilayer and ∼60% for monolayer arrangement in the interfacial regions limited to z ≈ 7 35 Å and z ≈ 7 30 Å, respectively (Figure 8). The larger percentaged decrease of water density for monolayer arrangement is consistent with the smaller extension of the depleted region. For C12TMA+ and C8TMA+ ions, similar decreases are observed, which, however, are limited to smaller interfacial regions due to their shorter alkyl chains. Furthermore, the amount of water hydrogen-bonded to the muscovite surface with z e 3.3 Å is negligibly influenced by increased CnTMA+ contents (inset in Figure 8), which is in accordance with previous observations for CP+.34 Although the ratio between the number of water molecules adsorbed in the two hydrogen-bonded water sublayers varies, the average amount of water in the first water layer is maintained (∼3.4 TIP4P/Auc for z e 3.3 Å). At all simulated coverages, a fraction of water molecules remains between the hydrophilic headgroups as well as in the hydrophobic regions of alkyl chains, which is consistent with the findings of SFA studies of the self-assembly of C16TMA+ on mica.12,13 The displacement of water molecules from the regions occupied by CnTMA+ ions leads to an increase of water film thickness with increasing CnTMA+ coverage. For instance, the thickness of the water film increases from ∼38 Å for unmodified muscovite to ∼51 and ∼57 Å for modified muscovite at coverages of 1 and 1.5 C16TMA+/Auc, respectively (Figures 8 and 9). We found that the increase of thickness does not depend on aggregate type (monolayer or bilayer) and is directly proportional to the amount of added CnTMA+ ions (Figure 8). This observation allows a calculation of the solvent volumes displaced by CnTMACl (n = 8, 12, 16) at the muscovite water interface (Table 1). Futhermore, the volume displaced by CnTMACl depends linearly on the volumes VC3H9NCl of 172 ( 13 Å and VCH2 of 25.9 ( 1.0 Å displaced by its headgroup and its methyl(ene) groups, respectively. The calculated values VC3H9NCl and VCH2 allow the extrapolation of volumes displaced by CnTMA+ ions with chain lengths n differing from those of 8, 12, and 16 considered in this study. 3.3. Structure of the Adsorbed CnTMA+ Aggregates. Further analysis of molecular structures reveals that up to simulated 12972

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Figure 9. Water film thickness (Å) as a function of the CnTMA+ coverage for n = 8, 12, 16.

Table 1. Volume (Å3) Displaced per CnTMACl, Methyl(ene), or Head Group C16TMACl C12TMACl

589.2 ( 7.3 478.3 ( 7.7

C8TMACl

381.8 ( 6.1

CH2/CH3

25.9 ( 1.0

C3H9NCl

172 ( 13

coverages of 0.5 CnTMA+/Auc, the surfactant molecules reside as monomers or dimers on the muscovite surface. At higher coverages, patches of surfactant aggregates form, which cover only parts of the muscovite surface and are laterally segregated from water at all simulated C16TMA+ coverages. Albeit on a different scale (the island-like structures observed in the experiments exhibited diameters of less than 500 nm, which cannot be represented by our simulation cell having a lateral extension of only ∼2 nm), these patchy aggregate structures compare well to experimental AFM observations of island-like C18TMA+ aggregate growth on mica below the critical micelle concentration.2,9 Our results indicate that the area occupied per headgroup of aggregated CnTMA+ ions is smaller than the area of a unit cell. At a monolayer coverage of 1 CnTMA+/Auc, about one-half of the inorganic muscovite cations (0.5, 0.625, and 0.5 K+/Auc for C16TMA+, C12TMA+, and C8TMA+, respectively) remain adsorbed at the muscovite surface in those regions devoid of organic aggregates. This calculation is in agreement with the results of an AFM study estimating the occupied area of CnTMA+ to equal about one-half of the area of a unit cell (23 24 Å2).7 For bilayer aggregates of C16TMA+ and C12TMA+ ions, which remain as well incomplete at all simulated coverages, a pronounced interdigitation of the two layers composing them is observed (Figure 1). In contrast, for the short-chained C8TMA+ at all simulated coverages, about one-half of the surfactant ions are characterized by large separations from the surface and do not participate in aggregation. This is an indication of the comparably weak interactions between the short hydrophobic alkyl chains of C8TMA+ ions. As a result, incomplete C8TMA+ monolayer aggregates with single headgroups facing the aggregate solution interface are formed instead of bilayer aggregates. The apparent aggregate thickness, which describes the extension of the CnTMA+ aggregates in the z-direction, was estimated on the basis of atomic density profiles for the carbons of alkyl chains (monolayer aggregates) or headgroups (bilayer aggregates) (Figure 2). The estimated thicknesses equal 30 35 Å for

C12TMA+ and 35 39 Å for C16TMA+ bilayer aggregates. The values for C8TMA+, C12TMA+, and C16TMA+ monolayer aggregates are ∼18, 22 27, and 31 35 Å, respectively. Noteworthy, the latter value is significantly larger than those of 15 18 Å determined experimentally by SFA,10,11 being even smaller than the length of a fully extended C16TMA+ ion (∼23.5 Å). This difference can be understood considering that in the SFA, two distant mica surfaces with C16TMA+ monolayer aggregates adsorbed on each one are brought into contact. Afterward, the thickness of the adsorbed aggregates is derived by halving the measured separation (30 36 Å) of the two surfaces. However, this approach does not take into account that the hydrophobic alkyl chains of the surfactant ions adsorbed on the opposing surfaces interact during the measurement. After a complete exchange of interfacial K+ ions by CnTMA+ ions, the available surface area per CnTMA+ headgroup is ∼47 Å2, which is more than twice the cross-sectional area of hydrocarbon chains of ∼20 Å2.66 Thus, upon approach of the two opposing mica surfaces, a close packing of the interacting hydrophobic alkyl chains can be assumed to occur and lead to the formation of interdigitated bilayer aggregates confined between the two mica surfaces. Indeed, the measured separation of 30 36 Å is comparable to the simulated thickness of 35 39 Å of C16TMA+ bilayer aggregates formed on the cleaved muscovite surface. For similar reasons, the thicknesses of CnTMA+ aggregates intercalated between delaminated mica sheets67 or into the interlayers of vermiculites exhibiting surface charges comparable to that of muscovite mica68,69 are significantly smaller than those of the unconstrained aggregates formed on the external muscovite surface. In contrast, measuring aggregate thickness by AFM in softcontact mode is a method that corresponds to the consideration of a cleaved muscovite surface in our study. Indeed, with this method, thickness ranges from 30 to 45 Å, which agree well with the simulated ones, were measured for C16TMA+ bilayer aggregates.3 5 Unfortunately, no similar comparison can be made for monolayer aggregates, as aggregate headgroups facing solution are required to exert a repulsive force on the AFM tip. The degree of conformational order in the surfactant aggregates was analyzed with the help of the calculated gauche conformation fractions (Figure 10). With a maximum of ∼0.45, the C8TMA+ aggregates show by far the highest values, as compared to ∼0.19 and ∼0.12 for C12TMA+ and C16TMA+ aggregates, respectively. This increasing degree of conformational order with increasing alkyl chain length can be inferred to be induced by increased hydrophobic interaction between the longer surfactant alkyl chains and agrees with experimental observations of the self-assembly of dialkylammonium surfactants on mica studied by FTIR, NMR, and NEXAFS.14,16 Furthermore, in agreement with IR measurements performed during the growth of C18TMA+ aggregates,2,9 we observed a slight decrease of gauche conformation fraction with increasing surface coverage for all studied chain lengths, which might reflect a closer packing of the alkyl chains due to spatial limitations. No significant distinction between the conformational order of monolayer and bilayer aggregates was observed. The calculated gauche conformation fractions have comparably high standard deviations of up to ∼0.18, which manifest the coexistence of nearly fully extended chains and those with high numbers of gauche conformations in the same systems. The averaged end-toend distances decrease by 5 13% for C16TMA+, 4 21% for C12TMA+, and 14 23% for C8TMA+, as compared to the 12973

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Figure 10. Fraction of gauche conformations of the alkyl chains as a function of the CnTMA+ (n = 8, 12, 16) coverage for monolayer and bilayer arrangements. Torsion angles of 60° ( 60° and 300° ( 60° were counted as gauche conformations. Lines were added as guides to the eye.

respective distances of the surfactant ions with completely extended alkyl chains. Therefore, our simulation results suggest a model of C16TMA+ and C12TMA+ bilayer aggregates that consists of two opposed monolayers with highly interdigitated alkyl chains exhibiting a low percentage of gauche conformations. This model agrees well with those developed from XPS and NR studies13,17 and explains the small differences of only a few angstroms between the thicknesses of monolayer and bilayer aggregates. A thorough consideration should be given to the significantly lower amount of adsorption complexes formed by CnTMA+ ions for bilayer arrangements as compared to monolayer ones. Simultaneously, K+ ions remain largely adsorbed at the muscovite surface for bilayer arrangements (g0.875 K+/Auc), and up to one-half of the Cl ions reside near surfactant head groups facing the muscovite surface. A similar accumulation of inorganic ions at the mineral aggregate interface was observed in experiments by Chen et al.13 The authors concluded that during the assembly of C16TMA+ aggregates, a rapidly occurring phase of adsorption of C16TMA+ ions accompanied by their counterions is followed by an equilibration phase, which proceeds unexpectedly slowly at surfactant concentrations leading to the formation of bilayer aggregates. During this second phase, organic cations can only displace K+ ions trapped between the bilayer aggregates and the mica surface in a slowly occurring two-step process: (i) formation of inorganic ion pairs with counterions (as a rule, Cl or Br ) introduced into the system with the C16TMA+ ions, and (ii) diffusion of the ion pairs through the hydrophobic part of the bilayer aggregates. This release of interfacial cations from the surface region eventually results in an increasingly stronger binding of the C16TMA+ ions to the muscovite surface. Up to several weeks were reported necessary to accomplish this slowly proceeding second step of the adsorption process for experimental setups corresponding to the formation of C16TMA+ bilayer aggregates, as compared to only 1 h needed for those setups corresponding to the formation of monolayer aggregates.13 In terms of the simulated systems, to leave the muscovite surface, K+ ions have to (i) overcome the Coulomb repulsion barrier of CnTMA+ headgroups facing the muscovite surface, (ii) diffuse through the hydrophobic parts of the bilayer aggregates becoming thicker with increasing alkyl chain length, and (iii) overcome a second Coulomb repulsion barrier of CnTMA+ headgroups facing the aggregate solution interface. Accordingly, the maximum amount of desorbed K+ ions in the simulated

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bilayer systems decreases with increasing chain length (0.375, 0.25, and 0.125 K+/Auc for C8TMA+, C12TMA+, and C16TMA+, respectively). The energy barriers, which, particularly at high simulated C16TMA+ surface coverages, appear too high to be overcome in reasonable computation times with the applied simulation method, impede the desorption of K+ ions from muscovite and thus the achievement of the final equilibrium state observed in experiments after times of hours up to weeks.3,4,13 Therefore, the simulated structures rather correspond to the aggregate structures observed in experiments after the first step of the above-discussed process when inorganic ions (Cl and K+) are still present at the mineral aggregate interface. An increased equilibration speed for the simulated systems can possibly be obtained by further optimization of the applied simulation algorithms, for example, by the implementation of cluster moves or the allowance of tunneling of inorganic ion pairs and water through hydrophobic bilayer aggregate regions. An increased diffusion of K Cl ion pairs out of the bilayer aggregate will presumably lead to an increased number of CnTMA+ innersphere adsorption complexes and consequently to a slight decrease of apparent aggregate thickness with time.

4. CONCLUSIONS The simulations reveal that the adsorption of CnTMA+ ions on muscovite does not markedly influence the average amount of ∼3.4 water molecules per Auc, which are hydrogen bonded to the mineral surface for z e 3.3 Å. Beyond that distance, the water density decreases considerably with increasing surfactant surface coverage. A fraction of water molecules remains between the headgroups and in the hydrophobic regions of alkyl chains for both monolayer and bilayer arrangements of CnTMA+ ions at all simulated coverages, which is consistent with the findings of SFA studies of the self-assembly of C16TMA+ on mica.12,13 The volume of water displaced by a C16TMA+ Cl , C12TMA+ Cl , or C8TMA+ Cl ion pair is estimated to be ∼590, ∼480, or ∼380 Å3, respectively. CnTMA+ ions form inner-sphere and outer-sphere adsorption complexes at the muscovite surface. However, in all simulated systems, a fraction of CnTMA+ ions remains detached from the muscovite surface, and a maximum of 0.75 adsorption complexes per Auc is observed. Inner-sphere adsorbed CnTMA+ ions are arranged directly above ditrigonal cavities of the muscovite surface, the adsorption site being occupied by water molecules on unmodified muscovite. The distance between their nitrogen atoms and the muscovite surface equals 3.3 3.8 Å, about 0.4 Å more than in the case of dehydrated CnTMA+ muscovite . The vertical and lateral adsorption positions of outer-sphere adsorbed CnTMA+ ions are less specified with nitrogen muscovite distances of 5.5 8.4 Å. CnTMA+ ions with larger z-values are separated from the muscovite surface by at least two water layers and not adsorbed as outer-sphere complexes any more. The simulated aggregates remain incomplete at all simulated CnTMA+ coverages. The simulated monolayer aggregates exhibit thicknesses of 31 35, 22 27, and ∼18 Å, for C16TMA+, C12TMA+, and C8TMA+, respectively. C16TMA+ and C12TMA+ bilayer aggregates with thicknesses of 35 39 and 30 35 Å, respectively, show a strong interdigitation of the two opposing layers composing the aggregates. Accordingly, the thicknesses of monolayer and bilayer aggregates deviate only by a few angstroms from each other. The simulated thicknesses of C16TMA+ bilayer aggregates agree well with those of 30 45 Å measured 12974

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Langmuir by AFM in soft-contact mode at twice the critical micelle concentration.3 5 In contrast, a significant fraction of the short-chained C8TMA+ ions ions did not aggregate, and we did not observe bilayer aggregates in either of the simulated C8TMA+ systems. The fraction of gauche conformations of the alkyl chains decreases considerably with increasing chain length (up to 44% for C8TMA+, as compared to 19% for C12TMA+ and 13% for C16TMA+). A similar dependence on chain length was observed in FTIR, NMR,14 and NEXAFS16 studies of the self-assembly of dialkylammonium surfactants on mica. In the case of bilayer arrangement, the majority of K+ ions did not desorb from the muscovite surface (more than 87%, 75%, and 62% for C16TMA+, C12TMA+, and C8TMA+ aggregates, respectively), and up to one-half of the Cl ions were observed in the regions occupied by hydrophilic head groups facing the muscovite surface. Furthermore, significantly smaller amounts of CnTMA+ adsorption complexes were found in bilayer systems as compared to monolayer ones. Therefore, we suggest that these simulated structures correspond to experimental observations of aggregate structures formed after an initial equilibration phase of the self-assembly of CnTMA+ ions at the muscovite water interface, which is characterized by the presence of inorganic ions within the aggregates.3,4,13 To reach the final equilibrium state characterized by aggregates devoid of inorganic ions, the experimental structures require days or even months.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional tables and calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

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

Gesellschaft f€ur Anlagen- und Reaktorsicherheit (GRS) mbH, Theodor-Heuss-Strasse 4, D-38122 Braunschweig, Germany.

’ ACKNOWLEDGMENT The main part of the calculations for this work was conducted on the computing clusters of the Regional Computing Centre for Lower Saxony (RRZN). We thank Henryk Wicke for his assistance in calculating the refined geometries and the charge distributions of the CnTMA+ ions, and we are grateful for the helpful comments from three anonymous reviewers. ’ REFERENCES (1) Manne, S.; Gaub, H. E. Science 1995, 270, 1480–1482. (2) Hayes, W. A.; Schwartz, D. K. Langmuir 1998, 14, 5913–5917. (3) Lamont, R. E.; Ducker, W. A. J. Am. Chem. Soc. 1998, 120, 7602–7607. (4) Ducker, W. A.; Wanless, E. J. Langmuir 1999, 15, 160–168. (5) Liu, J. F.; Ducker, W. A. J. Phys. Chem. B 1999, 103, 8558–8567. (6) Warr, G. G. Curr. Opin. Colloid Interface Sci. 2000, 5, 88–94. (7) Fujii, M.; Li, B.; Fukada, K.; Kato, T.; Seimiya, T. Langmuir 2001, 17, 1138–1142. (8) Atkin, R. Adv. Colloid Interface Sci. 2003, 103, 219–304. (9) Mellott, J. M.; Hayes, W. A.; Schwartz, D. K. Langmuir 2004, 20, 2341–2348.

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