Composition Driven Monolayer to Bilayer Transformation in a

Feb 14, 2011 - The structure and organization of dodecyl sulfate (DDS) surfactant chains intercalated in an Mg−Al layered double hydroxide (LDH), Mg...
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Composition Driven Monolayer to Bilayer Transformation in a Surfactant Intercalated Mg-Al Layered Double Hydroxide Vikrant V. Naik, Rajesh Chalasani, and S. Vasudevan* Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India

bS Supporting Information ABSTRACT: The structure and organization of dodecyl sulfate (DDS) surfactant chains intercalated in an Mg-Al layered double hydroxide (LDH), Mg(1-x)Alx(OH)2, with differing Al/Mg ratios has been investigated. The Mg-Al LDHs can be prepared over a range of compositions with x varying from 0.167 to 0.37 and therefore provides a simple system to study how the organization of the alkyl chains of the intercalated DDS anions change with packing density; the Al/Mg ratio or x providing a convenient handle to do so. Powder X-ray diffraction measurements showed that at high packing densities (x g 0.3) the alkyl chains of the intercalated dodecyl sulfate ions are anchored on opposing LDH sheets and arranged as bilayers with an interlayer spacing of ∼27 Å. At lower packing densities (x < 0.2) the surfactant chains form a monolayer with the alkyl chains oriented flat in the galleries with an interlayer spacing of ∼8 Å. For the in between compositions, 0.2 e x < 0.3, the material is biphasic. MD simulations were performed to understand how the anchoring density of the intercalated surfactant chains in the Mg-Al LDH-DDS affects the organization of the chains and the interlayer spacing. The simulations are able to reproduce the composition driven monolayer to bilayer transformation in the arrangement of the intercalated surfactant chains and in addition provide insights into the factors that decide the arrangement of the surfactant chains in the two situations. In the bilayer arrangement, it is the dispersive van der Waals interactions between chains in opposing layers of the anchored bilayer that is responsible for the cohesive energy of the solid whereas at lower packing densities, where a monolayer arrangement is favored, Coulomb interactions between the positively charged Mg-Al LDH sheets and the negatively charged headgroup of the DDS anion dominate.

’ INTRODUCTION The two-dimensional ordering in Langmuir monolayers formed by insoluble amphiphiles at the surface of water is one of the most widely studied phenomena.1 The main features of the phase transitions and phase diagrams in Langmuir monolayers are fairly well understood. The very dilute monolayer, with an area available per molecule in the range of hundreds of square angstroms, is well described as a two-dimensional gas. With decreasing area per molecule (increasing surface pressure), the monolayer proceeds into what has traditionally been called the liquid expanded phase. In this phase, as in the gas phase, there is no detectable X-ray diffraction signal; presumably as the heads of the molecules are translationally disordered and the chains conformationally disordered. Further compression of the monolayer gives rise to a transition from liquid expanded to a condensed phase, with (usually) a plateau indicating a first-order transition. A closely related system that exhibits similar phenomena are self-assembled monolayers of long chain alkyl-surfactants attached on metallic or nonmetallic surfaces via ionic bonds, thiolate bonds, ester bonds or hydrogen bonds.2 In these systems the anchoring or packing density provides the analogue of the surface pressure in the Langmuir monolayer measurements. The organization and arrangement of the grafted alkyl chains depend critically on the packing density.3 r 2011 American Chemical Society

Similar phenomena may also be observed for surfactant chains intercalated in the galleries of layered solids. The surfactant molecules in the galleries can adopt a variety of structures - monolayer, bilayer, paraffin-type monolayer or bilayer—depending on the packing density and the length of the surfactant methylene “tail”.4 When the grafting density is low the surfactant molecules usually lie flat with the molecular axis of their methylene chain parallel to the walls of the gallery. With increasing grafting density the methylene “tail” of the surfactant adopts a paraffin-type monolayer or bilayer structure depending on the size, concentration and length of the chain .4 A large number of molecular dynamics (MD) simulation studies on surfactant intercalated layered solids have been reported, primarily focusing on the structure and layering phenomena, either as a function of the alkyl chain length or grafting density.5-10 MD simulations have been used to understand changes in conformation and basal plane spacing of alkyl chains anchored to mica sheets with temperature.5,11 On the basis of these studies as well as experimental results, a relation between packing or anchoring densities and thermal transitions of the anchored bilayer was Received: November 28, 2010 Revised: January 11, 2011 Published: February 14, 2011 2308

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Langmuir established.3 The packing density, λ, of alkyl chains on the surface has been defined as the average cross-sectional area of an alkyl chain AC in relation to the available surface area AS per chain, λ = AC/AS. It has been shown that a packing density less than 0.2 leads to a nearly parallel orientation of the alkyl chains on the surface with a high degree of conformational disorder. While a packing density between 0.2 and 0.75 leads to intermediate inclination angles, semicrystalline order and reversible melting transitions on heating. A packing density above 0.75 results in nearly vertical alignment of the surfactants on the surface, a high degree of crystalline character and absence of reversible melting transitions. In this paper, the structure and organization of dodecyl sulfate (DDS) surfactant chains intercalated in Mg-Al LDH with differing Al/Mg ratios has been investigated. The Mg-Al LDHs, Mg(1-x)Alx(OH)2 can be prepared over a range of compositions with x varying from 0.167 to 0.37. The Mg-Al LDH, therefore, provides a simple system to study how the organization and dynamics of the alkyl chains of the intercalated DDS anions change with packing density; the Al/Mg ratio or x providing a convenient handle to do so. What makes the system more interesting is the fact that for small values of x (x = 0.17) the packing density λ of the intercalated surfactant alkyl chains (assuming a cross-sectional area of 18.8 Å2 for the trans alkyl chain3) has a value of 0.17 and if theoretical predictions are correct the chains should form a monolayer with orientation parallel to the LDH sheets. Whereas at the higher values of x (x = 0.37) the packing density would have a value of 0.37 and a tilted bilayer organization of the chains should be realized. The intercalated surfactant chains in the Mg-Al LDH would therefore be expected to exhibit a monolayer to bilayer transformation with increasing x. The intercalation of DDS anions in MgAl LDH (x = 0.37) has been reported earlier.12 The intercalated compound has an interlayer spacing of ∼27 Å with the surfactant chains arranged as tilted bilayers with a tilt angle of 58°. The latter was deduced from the variation of the interlayer spacing on intercalation of alkyl sulfate surfactants with differing alkyl chain length. It was also shown from spectroscopic measurements—IR, Raman and 13C contact pulse magic angle spinning NMR—that a majority of the methylene linkages of the alkyl chains of the intercalated surfactant bilayer adopt the trans conformation. Characteristic features of the gauche conformer were, however, also seen in both 13C CP-MAS NMR and Raman spectra. Chains with gauche bonds require more space as compared to all-trans chains and the presence of these conformers was used as corroborative evidence to preclude the formation of an interdigitated arrangement of the surfactant chains. In this paper the preparation and characterization of Mg(1-x)Alx(OH)2(DDS)x (0.17 e x e 0.37) is described. The structures of the surfactant intercalated LDH were deduced from X-ray diffraction measurements. The organization of the intercalated chains do indeed transform from a monolayer to a bilayer arrangement with increasing Al/Mg ratio. Molecular dynamics was used to understand the molecular origin of this transformation. In particular, the respective roles of the Coulombic interaction energy and van der Waals’ interaction in deciding the possible arrangements of the intercalated surfactant chains have been investigated. It is shown that their respective contributions toward the cohesive energy of the surfactant intercalated LDH for the monolayer and bilayer arrangement are very different.

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’ EXPERIMENTAL SECTION Materials and Methods. Mg(1-x)Alx(OH)2(NO3)x, [Mg-Al LDH-NO3] was used as the starting material for the preparation of surfactant functionalized Mg-Al LDH. Mg-Al LDH-NO3 was prepared by the coprecipitation method by dropwise addition of 100 mL of aqueous Mg(NO3)2 and Al(NO3)3 (total concentration 0.06 M) into NaOH at a constant pH of 8, under N2 atmosphere.12 By changing the relative concentrations of Mg(NO3)2 and Al(NO3)3, a series of Mg-Al LDHs was obtained. In all, six samples were prepared with differing Mg:Al ratios with x having the values 0.17, 0.2, 0.25, 0.3, 0.33, and 0.37. The resulting white precipitate was aged for 24 h prior to washing with decarbonated water. The formation of single phase Mg-Al LDH-NO3 for the differing Mg:Al ratios was confirmed by X-ray diffraction (see Supporting Information). The anionic surfactant dodecyl sulfate (DDS) was introduced within the galleries of Mg-Al LDH by ion-exchanging the NO3- ions in Mg(1-x)Alx(OH)2(NO3)x with dodecyl sulfate anions. The ion exchange reaction was carried out by stirring one equivalent of Mg-Al LDH-NO3 with 3 equiv of sodium dodecyl sulfate (SDS) (Sigma-Aldrich) for 24 h at room temperature. The ion exchanged Mg(1-x)Alx(OH)2(DDS)x [Mg-Al LDH-DDS] was filtered and washed with hot water to remove excess DDS. The formation of Mg-Al LDH-DDS was confirmed by Fourier transform infrared (FTIR) spectroscopy that showed absence of the characteristic NO3- band at 1384 cm-1 in the ion exchanged samples and the presence of new bands due to intercalated DDS ions (see Supporting Information). The formation of Mg-Al LDH-DDS was also confirmed by powder XRD which showed the complete absence of 00l reflections corresponding to Mg-Al LDH-NO3 and the presence of new 00l reflections of Mg-Al LDH-DDS. Mg-Al LDH-DDS were prepared for six different values of x = 0.37, 0.33, 0.30, 0.25, 0.20, and 0.17. These Al/Mg ratios in the LDH were determined by Inductively Coupled Plasma spectroscopy (iCAP 6500 Thermo Scientific). The intercalated DDS stoichiometries were determined by CHN analysis (Perkin-Elmer 2400 CHN/O analyzer) and the water content by TGA (Mettler Toledo thermogravimmetric analyzer and differential thermal analyzer). The final compositions are provided as part of the Supporting Information. Powder X-ray diffraction patterns were recorded on a Bruker D8 Advance X-ray diffractometer using Cu KR radiation of wavelength 1.54 Å. In the region 1-5°, a scintillation detector was used while at higher angles, a Lynxeye solid state detector was used. At each step, data was collected for 9.5 s with a step size of 0.02° and the entire scan was completed over a 9 h 15 min period. Structure refinement of the X-ray data was performed with the FullProf program,13 while the DIFFaX program14 was used to simulate the pattern with stacking faults. The peak fitting was done using Reitveld refinement procedure using the FullProf suite, and all the peaks were indexed. This was done in order to eliminate the possibility of the existence of multiphases. Molecular Dynamics Methodology. In the MD calculations two single Mg-Al LDH sheets with anchored surfactant chains were brought closer from infinite separation in incremental steps. At each value of the interlayer separation an NVT simulation was performed and the relative contributions of the electrostatic and van der Waals interaction to the total energy of the equilibrium structure at that separation evaluated. The simulations were performed at two differing anchoring densities corresponding to the compositions with Al/Mg ratios, x = 0.1875 and x = 0.375. The first step in running an MD simulation of layered solid is building the structure in the computer by assigning positions to individual atoms. The structure of the surfactant intercalated Mg-Al LDH was generated by creating the structure of the inorganic Mg-Al LDH host and the organic surfactant guest separately and then putting them together. The Mg-Al LDH host lattice was built using atomic coordinates from the previously reported crystal structure of hydrotalcite, [Mg4Al2(OH)12](CO3).3H2O (Al/Mg = 0.5), whose crystal structure had been refined in a trigonal unit cell with space group R3m 2309

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Figure 1. Arrangement of Mg and Al ions in a Mg-Al LDH layer for the two different Al/Mg ratios. (a) x = 0.375 and (b) x = 0.1875. The Mg octahedra are shown in light gray while those of Al in dark gray. and lattice parameters a = b = 3.046 Å and c = 22.81 Å.15 The Mg-Al LDH structure was generated from that of hydrotalcite that has a unit cell composition Mg2Al(OH)6(CO3) 3 0.5H2O. The interlamellar carbonate ions and the water molecules were removed. A large unit cell (LUC) was then created by a 4  4 translation of the unitcell in the a and b directions. The lattice parameters of this LUC were a = b = 12.184 Å and each cell had 3 layers. The composition of this LUC was Mg32Al16(OH)96. At this stage, all the metal ions were treated as equivalent so that in effect the composition of the LUC was Mg48(OH)96 and each layer had composition Mg16(OH)32 formed by edge-sharing Mg(OH)6 octahedra. The present study required the building of Mg-Al LDH structures with x = 0.17 and x = 0.37, the two extreme compositions described in the Experimental Section. The distribution of Mg and Al within the LDH layers was based on a Monte Carlo study of the ordering of Amþ and Bnþ (m ¼ 6 n) ions in an A(1-x)Bx alloy on a 2D triangular lattice at different compositions.16 To generate different Mg/Al ratios, the Mg atoms were substituted by Al atoms in unit increments to obtain Mg10Al6(OH)32 (x = 0.375) and Mg13Al3(OH)32 (x = 0.1875). The layer structures for x = 0.1875 and x = 0.375 are shown in Figure 1. The intercalated dodecyl sulfate (DDS) surfactant ions were constructed with the alkyl chain in an all-trans conformation such that all the C-C torsions were 180°. The surfactant ions were then placed randomly in the interlamellar region of the LDH such that they formed a tilted bilayer arrangement. The surfactant ions have a unit negative charge. The bonding interactions were modeled by using a composite force field to reflect the hybrid nature of the organic-inorganic system. The inorganic sheets require a hard potential while the intercalated alkyl chains require a softer potential to reflect their dynamic nature. The potential energy for the inorganic layers was modeled using the universal force field (UFF).17 The methylene chains of the surfactant ions were modeled using the polymer consistent force field (PCFF).18 Charges on the atoms of the inorganic lattice were obtained by a density functional theory (DFT) calculation using the DMol3 module of Materials Studio.19 A double numerical with polarization (DNP) basis set with the Perdew-Wang (PW91) functional was used to calculate the eigenstates and the eigen vectors. A Mulliken population analysis was then performed to obtain the charges on individual atoms. The charges on the surfactant chains were calculated by the charge equilibration method using the Qeq scheme.20 A total charge of -1 was assigned to the atoms of the headgroup and Rcarbon atom. The rest of the atoms of the chain carried zero charges. The total nonbonded potential interaction energy of the simulated system consisted of long-range Columbic interactions between partial atomic charges, computed using the Ewald summation technique with an accuracy of 10-6 kcal/mol. The cutoff distance for van der Waals interactions was kept at 12 Å. Two nanosecond molecular dynamics simulations were performed on the surfactant intercalated LDH at a temperature of 298 K. MD calculations were performed using the Forciteþ module of the Material Studio package.19 The velocity-Verlet integrator method was used for

Figure 2. Convergence of the total energy for the Mg-Al LDH-DDS (a) bilayer (x = 0.375) at 29.2 Å sheet separation and (b) monolayer (x = 0.1875) at 9.0 Å sheet separation. computing the positions and velocities of atoms. Simulations were initiated on a NVT ensemble with a time step of 1 fs. The temperature of the ensemble was maintained by the velocity scale thermostat with a temperature difference window of 10 K.21 Periodic boundary conditions were applied in three dimensions so that the simulation cell is effectively repeated infinitely in each direction. The LDH layers were kept rigid along all the three directions during each simulation. This was done in order to decrease the computation time and to maintain the interlayer distance during the simulation. The simulations were initiated from a geometry where the interlayer separation was at least three times greater than the experimental interlayer spacing. These values of the separation may be considered as the ’infinite’ separation limit. For the x = 0.375 composition where the experimentally determined interlayer spacing is 27 Å, the starting separation for the simulation was 77 Å while for the x = 0.1875, where the experimental spacing is 8 Å, the starting separation in the simulations was 30 Å. For both compositions, the chains were initially arranged as a tilted bilayer with random values of the tilt and the alkyl chains in an alltrans conformation (see Supporting Information). After equilibrium was attained at these separations, the layers were brought closer by a defined step size and the simulation repeated, but now with the initial configuration identical to that of the previous step except for the reduced value of the interlayer spacing. For the x = 0.375 composition, the interlayer spacing was reduced from 77.2 to 57.2 Å in steps of 10 Å, from 57.2 to 47.2 Å in steps of 5 Å, from 47.2 to 37.2 Å in steps of 2 Å and finally below 37.2 Å in intervals of 1 Å. For the x = 0.1875 composition, the interlayer spacing was reduced from 28.1 to 15.6 Å in steps of 2.5 Å, from 15.6 to 12.6 Å in steps of 1 Å, 12.6 Å to 9.6 Å in steps of 0.5 Å, 9.6 Å to 8.6 Å in steps of 0.2 Å and finally up to 7.8 Å in steps of 0.1 Å. The simulations were carried out for 2 ns at each step. Typically, convergence to equilibrium value at each step was realized within the first 50 ps. Typical plots of the convergence of the total energy for the two configurations at two different separations are shown in Figure 2.

’ RESULTS AND DISCUSSION X-ray Diffraction. The powder X-ray diffraction (XRD) patterns of the surfactant intercalated Mg-Al LDH-DDS for x = 0.37 to 0.17 are shown in Figure 3. The patterns exhibit a broad background that may be a consequence of the disorder of the intercalated surfactant chains between the layers. It may be seen that the patterns in Figure 3 fall in two categories depending on the Al/Mg ratio. For the highest values of the ratio, x = 0.37 and x = 0.33, the basal (00l) reflections may be indexed to an 2310

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Figure 3. XRD patterns for Mg-Al LDH-DDS for different values of x. The inset shows a plot of d00l against 1/l for Mg-Al LDH-DDS (x = 0.37).

unique interlayer spacing of 27.02 Å (inset Figure 3) while the Mg-Al LDH with the lowest ratio, x = 0.17, exhibits a vastly reduced interlayer spacing of 7.93 Å. For the in between compositions the X-ray reflections are either broad (x = 0.30) or show clear evidence of being biphasic (x = 0.25 and 0.20) with both the, 27.02 and 7.93 Å, interlayer spacing phases being present. The pattern for Mg-Al LDH-DDS (x = 0.17) is similar to that of Mg-Al LDH-NO3 that has an interlayer spacing of 8.9 Å. The distinctly different IR spectrum of Mg-Al LDHDDS (x = 0.17) from that of the corresponding Mg-Al LDHNO3 (see Supporting Information), however, clearly indicates complete intercalation of the DDS anions. The interlayer spacing of ∼27 Å, as mentioned in the Introduction, indicates a tilted bilayer arrangement of the intercalated DDS surfactant chains.12 The computed interlayer spacing for a bilayer considering the length of an all-trans DDS chain as 19 Å, a chain tilt angle of 58° and the thickness of the Mg-Al LDH layer as 4.8 Å is 24.9 Å as compared to the X-ray determined value of ∼27 Å. A tilted bilayer arrangement, however, cannot account for the vastly reduced interlayer spacing of 7.93 Å for the x = 0.17 Mg-Al LDH-DDS. A molecular graphics analysis shows that a monolayer arrangement with the surfactant chains oriented flat in the galleries can account for the observed interlayer spacing (Figure 4). It thus appears that there is a transformation from a bilayer arrangement of the surfactant chains at high values of x to a monolayer arrangement at x = 0.17. The bilayer arrangement persists up to an x value of 0.30. The Mg-Al LDH-DDS (x = 0.25 and 0.20) are biphasic with both the bilayer, characterized by an interlayer spacing of ∼27 Å and monolayer with the interlayer spacing of ∼8 Å, coexisting. The results of the X-ray diffraction measurements in the Mg-Al LDH-DDS with different values of x are summarized in Figure 5. A more detailed analysis of the X-ray pattern of the two extreme compositions, x = 0.37 and x = 0.17 is described in the following sections. For the x = 0.37 composition, a Reitveld refinement could be performed but for x = 0.17, the broad and asymmetric line profiles indicated the presence of stacking faults and consequently, the DIFFaX software was used to analyze the data.14 A Reitveld refinement of the X-ray diffraction patterns for Mg-Al LDH-DDS (x = 0.37) could be performed with the space group R3m, the same as that reported for the rhombohedral

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polytype of hydrotalcite.15 The experimental, calculated, and difference diffraction patterns are shown in Figure 6. The data was refined only for 2θ g 5°. It may be recalled that data below 5° was collected using a scintillation detector while for 2θ g 5°, the Lynxeye detector was used. Refinement was performed only on the coordinates of the Mg, Al, O, and H atoms. The atoms of the interlamellar surfactant chains could not be defined and hence not refined. The chains are presumably disordered and are responsible for the rather large background contribution to the experimental X-ray diffraction pattern. In the refinement procedure, a second order polynomial was used to refine this background contribution arising from the random arrangement of the surfactant chains in the crystallites. A pseudo-Voigt function was selected to fit the peak shape of the reflections. The width of the basal reflections is a consequence of the fact that the number of layers that are stacked to form the crystallites are small as opposed to sharp lines observed when a large number of layers are stacked. The line widths were fitted by refining the Gaussian size parameter. Preferred orientation coefficient was also refined to match the high intensities of the 00L reflections. The Mg and Al site occupancies were fixed and in agreement with the composition. Atomic positions for Mg and Al were kept fixed while the positions of O and H were refined but only along the c direction. Unit cell parameters a, b, and c were refined and their final values are 3.1567, 3.1567, and 81.7152 Å respectively. The interlayer d-spacing which is a third of the c parameter is 27.24 Å. The Rwp value of 0.0570 indicates a reasonably good fit. The results of the Reitveld refinement are given in Table 1 and Table 2. The observed X-ray powder pattern for Mg-Al LDH-DDS for x = 0.17 shows three reflection in the mid 2θ region that may be indexed as (01l) reflections. These reflections are broad and asymmetric and suggest the presence of stacking faults that are a result of the intergrowth of the rhombohedral and hexagonal polytypes of Mg-Al LDH.15 The Reitveld refinement procedure is not suitable for samples that have stacking faults and hence the DIFFaX program was used to simulate the powder X-ray pattern of Mg-Al LDH-DDS (x = 0.17).14 DIFFaX enables modeling of extended planar faults by a statistical recursive approach.14 The DIFFaX program constructs a crystalline solid as stacking of layers of atoms related by stacking vectors. The random intergrowth of more than one polytype is simulated by using two stacking vectors with different probabilities of occurrence. A fault probability of 1.0 indicates a pure polytype, while a value of 0.5 describes a random layer sequence. The metal hydroxide layer was defined using the atomic position coordinates of hydrotalcite available in literature.15 The coordinates of atoms of individual layers were obtained using the Diamond software.22 The DIFFaX simulation of the XRD pattern for the Mg-Al LDH-DDS (x = 0.17) was initiated from that of the pure 3R1 polytype. The positions of the reflections in the simulated pattern were matched with the positions in the experimental data but the linewidths and profiles were found to be different. In order to reproduce the observed broad (01l) reflections stacking faults were introduced. The pure 3R1 polytype was mixed with the 1H, 2H1 and 3R2 polytypes with different fault probabilities. The Bragg reflections of the different polytypes 3R1, 1H, 2H1, and 3R2 were computed by stacking the layers one above another with different stacking vectors. To generate the pattern for the pure 3R1 polytype (AC CB BA AC ...), a single layer is defined with layers related by the stacking vector (2/3, 1/3, 1/3). The stacking vector (0, 0, 1) with a defined single layer generates the pattern 2311

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Figure 4. Molecular graphics representation of DDS surfactant chains oriented flat in the galleries of Mg-Al LDH. The distance of 7.9 Å refers to the center to center distance of the layers.

Table 1. Rietveld Refinement Results for Mg-Al LDH-DDS (x = 0.37) sample space group

Mg-Al LDH-DDS (x = 0.37) R3m

lattice parameters

a = b = 3.1567 Å c = 81.7152 Å

preferred orientation coefficient

1.9596

statistical index

Rwp = 0.0570

Table 2. Atomic Positions in Mg-Al LDH-DDS (x = 0.37)

Figure 5. Plot of lattice spacing as a function of x for Mg-Al LDHDDS.

Figure 6. Experimental, calculated, and difference X-ray powder diffraction patterns for x = 0.37.

for the 1H polytype (AC AC AC ...). The pattern of the 2H1 polytype (AC CA AC CA ...) is generated by defining two layers related by the stacking vector (0, 0, 1/2) vector. For the 3R2 polytype (AC BA CB AC...), three layers are defined and stacked using the (1/3, 2/3, 1/3) stacking vector. A reasonable fit between experimental and calculated patterns in the mid 2θ region was achieved when the 3R1 polytype was mixed with the 2H1 polytype. It should be noted that the DIFFaX program is not a refinement program. Instead, it simulates the XRD patterns for layered samples where Rietveld refinement does not work. The simulated and the experimental patterns are matched visually to get the best fit. The goodness of the fit was characterized by the Rwp parameter calculated for the 2θ region (25-70°) known to be sensitive to the stacking faults. The 3R1 and 2H1 polytypes were mixed with different stacking probabilities. The best fit was

atom

x

y

Mg

0.0000

0.0000

Al

0.0000

0.0000

O

0.0000

H

0.0000

z

site

occupancy

0.0000

3a

0.62690

0.0000

3a

0.37030

0.0000

0.382 25

6c

1.00000

0.0000

0.438 17

6c

1.00000

Figure 7. Experimental and DIFFaX simulated X-ray powder diffraction patterns for Mg-Al LDH-DDS, x = 0.17. The simulated pattern is for a mixture of the 3R1 and the 2H1 polytypes in the ratio 60:40.

obtained when the probability of occurrence of 2H1 polytype was 0.4. The simulated pattern for this fault probability is shown in Figure 7 along with the experimental data. It may be seen that agreement for the low angle 00l reflection is poor. Although turbostaticity, interstratification and finite crystallite size were introduced, the agreement at low angles could not be improved. This may be a consequence of the fact that the contribution of the interlayer surfactant chains had been ignored as the atomic positions of the chains cannot be defined. The results of the DIFFaX simulation are summarized in Table 3. Molecular Dynamics. In order to understand how the anchoring density of the intercalated surfactant chains in the Mg-Al LDH-DDS affects the organization of the chains and the interlayer spacing, MD simulations were performed. The simulations 2312

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Table 3. DIFFaX Simulation Results for Mg-Al LDH-DDS (x = 0.17) sample polytype

Mg-Al LDH-DDS (x = 0.17) 3R1 = 60%

lattice parameters

a = b = 3.1208 Å c = 23.7842 Å

statistical index

Rwp = 0.0622

2H1 = 40%

Figure 9. Plot of the interaction energy between two surfactant anchored sheets of Mg-Al LDH with a Al/Mg ratio, x = 0.1875 at different interlayer separations. The structures at representative interlayer separations (as indicated) are shown in the panel below.

Figure 8. Plot of the interaction energy between two surfactant anchored sheets of Mg-Al LDH with a Al/Mg ratio, x = 0.375 at different interlayer separations. The structures at representative interlayer separations (as indicated) are shown in the panel below.

were performed for the extreme compositions that are known to form single phasic monolayer and bilayer arrangements respectively of the intercalated surfactant chains. The objectives of these calculations were first to see whether the MD simulations could reproduce the experimental results and if so provide a molecular understanding of the two different interlayer spacings. In these calculations, two single Mg-Al LDH sheets with anchored surfactant chains were brought closer from infinite separation in incremental steps. At each value of the interlayer separation an NVT simulation was performed and the relative contributions of the electrostatic and van der Waals interaction to the total energy of the equilibrium structure at that separation

evaluated. The simulations were performed at two differing anchoring densities corresponding to the compositions x = 0.1875 and x = 0.375. The calculations are similar to those reported by Heinz et al. on the cleavage of surfactant intercalated montmorillonite.9 A notable difference from the present study is that in their study, Heinz et al. considered the energetics of the stepwise separation (cleavage) of the montmorillonite sheets from the equilibrium structure to infinite separation whereas here the stepwise approach from infinite separation has been computed. The equilibrium separation is not assumed but should come out naturally if the calculations are truly representative. The results of the simulation are shown in Figures 8 and 9 where the variation in energy per unit surface area with interlayer separation have been plotted. The energy at infinite separation is defined as zero and the plots in Figures 8 and 9 are the difference in the total energy at a particular interlayer separation and the total energy at infinite separation. Figures 8 and 9 therefore represent the interaction energy per unit area as a function of interlayer spacing. The relative contributions of the electrostatic, van der Waals and internal energy to the total energy at each interlayer spacing was also evaluated and are shown in Figures 8 and 9. The internal energy includes the bond stretching, angle bending and torsional terms. The variation of the interaction energy for the two compositions are discussed separately. Figure 8 shows the variation of the interaction energy with the interlayer separation for Mg-Al LDH-DDS (x = 0.375). The inset below shows snapshots of the simulation for five representative values of the interlayer separation as indicated in the figure. It may be seen that from a separation of 77.2-39.2 Å, the total interaction energy curve is flat and shows little or no variation with separation, justifying the assumption that a 77.2 Å interlayer separation may be considered as representing the infinite limit. Below 39.2 Å, the interaction energy decreases sharply with separation with a minimum at 27.2 Å below which the interaction energy rises sharply. It is significant that the minimum occurs at 27.2 Å as compared to the experimental X-ray determined value 2313

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Figure 10. (a) Equilibrium (minimum energy) structure for the Mg-Al LDH-DDS bilayer (x = 0.375). (b) The corresponding projected density profiles for the methylene carbons of the DDS chain along the c axis. The numbering of the carbon atoms is show.

of 28.23 Å for the x = 0.37 composition. Simulations were also carried out for the reverse process, i.e., the stepwise separation of the surfactant anchored LDH sheets from an interlayer spacing of 27.2 Å corresponding to the minimum in Figure 8 to infinite separation (77.2 Å). This process corresponds to the cleavage of the layered structure. The energy values for the same interlayer spacing in the two processes are comparable. The relative contribution of the different interaction terms and their variation with interlayer spacing is also shown in Figure 8. It may be seen that both the internal energy and the electrostatic Coulomb term are essentially constant, hovering around zero. The Coulomb energy shows large fluctuations. This is a consequence of the high charge on the LDH sheets. Consequently, small changes in the position of the headgroup shows up as a large change in the electrostatic energy. It is, however, the van der Waals term that shows a significant variation with the interlayer separation and is responsible, almost in whole, for the changes in the total energy. At separations less than 39 Å, the attractive part of the dispersive interactions become increasingly significant with approach of the layers. Compression below a separation of 27 Å, however, leads to the repulsive terms dominating and a minimum obtained at 27.2 Å. The Coulombic interaction between sheets even at minima is however negligible. The structure at the minima (27.2 Å) in Figure 8 corresponds to the simulation determined equilibrium structure of Mg-Al LDH-DDS (x = 0.375). A snapshot of the simulation for the interlayer separation of 27.2 Å is shown in Figure 10a. To establish the interlayer structure of the intercalated surfactant chains, the density distribution of different methylene carbons along the c axis from the origin was constructed. This was done by projecting the methylene carbons of a chain along the c axis and averaging over all chains of the bilayer. Plots of the density profile are shown in Figure 10b. The density profiles show a pronounced layering behavior and are symmetrically displaced within the interlayer gallery. The C1 methylene unit of the alkyl chain is located close to the LDH sheet while the methylene units at the tail of the DDS chain lie midway within the gallery. The density profiles indicate that the DDS chains in opposing layers form a bilayer type arrangement. The chains of the bilayer are tilted away from the interlayer normal. The average tilt angle defined as the ensemble averaged angle between the vector joining C1 methylene carbon with the C12 methyl of the same chain and the normal to the Mg-Al LDH sheet was found to have a value of 54° as

compared to the experimentally determined value of 58°.12 The results of the simulation clearly indicate that for the x = 0.375 composition, where the interlayer spacing is 27.2 Å, the surfactant chains are arranged as a tilted bilayer and that it is the dispersive van der Waals interaction between chains belonging to the opposing layers that holds the solid together. A similar conclusion had been reported for MD simulations of the cleavage of surfactant intercalated clays.9 The variation of the interaction energy with interlayer separation for Mg-Al LDH-DDS (x = 0.1875) is shown in Figure 9. The inset below shows snapshots of the simulation for five representative values of interlayer separation as indicated in the figure. It may be seen that from a separation of 28.1 to 15.6 Å, the total interaction energy curve is flat and shows little or no variation with separation justifying the assumption that a 28.1 Å separation may be considered as a representing the infinite limit for this composition. Below 15.6 Å, the interaction energy decreases sharply with decreasing separation with a small dip at 10.6 Å. The total energy shows a minimum at 8.1 Å below which it rises sharply. The interlayer spacing at the minimum in Figure 9 is comparable to the X-ray determined interlayer spacing of 7.9 Å for the x = 0.17 composition of Mg-Al LDH-DDS. The relative contributions of the van der Waals and Coulombic interactions at various interlayer separations are shown in Figure 9. It may be seen that van der Waals interaction has a shallow minimum at 10.6 Å and is in fact responsible for the slight dip in the total energy at this separation. It is the Coulombic term, however, that shows a significant change with the interlayer separation. It shows a minimum at 7.9 Å and rises steeply below this value. It may be seen that unlike the variation for the x = 0.375 composition (Figure 8), for the x = 0.1875 composition, it is the electrostatic term that decides the minimum in the total energy versus interlayer separation. In fact, at the spacing corresponding to the minimum in the total energy, the van der Waals interaction is repulsive. Below 8.1 Å, the electrostatic and van der Waals interactions are repulsive. The structure at the minima in Figure 9 corresponds to the simulation determined equilibrium structure of Mg-Al LDHDDS (x = 0.1875). A snapshot of the simulation for this interlayer separation is shown in Figure 11a and the projected density distribution of the methylene units along c axis in Figure 11b. It may be recalled that for this composition the initial configuration had an interlayer separation of 30 Å with the DDS surfactant 2314

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Figure 11. (a) Equilibrium (minimum energy) structure for the Mg-Al LDH-DDS monolayer (x = 0.1875). (b) Corresponding projected density profiles for the methylene carbons of DDS chain along c axis. The numbering of the carbon atoms is show.

chains partitioned equally between the two surfaces and arranged as a tilted bilayer. The density profiles for the minimum energy structure show that all the methylene units lie between the two sheets and in the center of interlamellar region. The projected density profiles indicate that the DDS chains form a monolayer type arrangement with the surfactant chains oriented flat in the LDH galleries. The results of the simulation clearly indicate that for x = 0.1875 composition, where the interlayer spacing is 7.9 Å, the surfactant chains are arranged lying flat and that it is the electrostatic interaction between the surfactant head groups and the two oppositely charged layers that holds the solid together. In conclusion, the MD simulations of the variation of the energy with interlayer separation for the two compositions of Mg-Al LDH-DDS with differing Al/Mg ratios of x = 0.375 and x = 0.1875, provide insights into why the structure at these two surfactant anchoring densities are different. In both the cases, MD simulations were initiated from a configuration where the two LDH sheets were at infinite separation with the surfactant chains partitioned equally between them. The sheets were then brought closer in a stepwise fashion. The final equilibrium structures for the two compositions are, however, very different. For x = 0.375 composition, the equilibrium interlayer spacing is 27.2 Å with the DDS surfactant chains arranged as a tilted bilayer. For Mg-Al LDH-DDS (x = 0.1875), the minima occurs at an interlayer spacing of 8.1 Å with the DDS chains lying flat in the interlamellar space of the LDH. The simulations show that the factors that decide the equilibrium spacing for the two compositions are very different. For the x = 0.375 composition where the surfactant chains are arranged as a bilayer, it is the van der Waals interactions between the opposing chains of the bilayer that hold the solid together; Coulomb interaction between opposing sheets being essentially screened at this value of the separation. For the x = 0.1875 composition, it is the Coulombic interactions between the negatively charged DDS surfactant chain and the positively charged Mg-Al LDH sheets that is responsible for the stability of the solid; the van der Waals interaction at this spacing, in fact, is repulsive. It may be cautioned that the plots in Figures 8 and 9 represent the energetics of bringing surfactant anchored LDH sheets together. These should not be considered as free energy plots. As will be shown in a latter paper, there are considerable changes in the surfactant conformation and dynamics that are likely to result in a significant entropic contribution to the free energy.

’ CONCLUSION The anionic surfactant dodecyl sulfate has been intercalated in a series of Mg(1-x)Alx(OH)2 LDHs with differing Al/Mg ratios. This system has the advantage that the anionic exchange capacity can be altered by appropriate choice of x and thus offers a convenient system to study the effect of packing density on the arrangement and organization of the intercalated surfactant chains. X-ray diffraction studies showed that at higher Al/Mg ratios (x g 0.30) the interlayer spacing of the intercalated compounds is ∼27 Å, while at lower ratios (x < 0.20) the spacing is 7.9 Å. The in-between compositions are biphasic with both the phases, characterized by the interlayer spacing of 27 and 7.9 Å, present. The only variable in this system is the anchoring density of the surfactant chains which is directly related to the value of x, the Al to Mg ratio. Previous studies have indicated that at higher Al/Mg ratios the interlayer spacing of 27 Å corresponds to a tilted bilayer arrangement of the intercalated surfactant chains. The arrangement of the surfactant chains in the phase with 7.9 Å interlayer spacing is obviously different and molecular graphics analysis based on van der Waals volumes suggest that the surfactant chains are oriented flat in the galleries in the monolayer arrangement. The XRD results clearly demonstrate that the intercalated surfactant chains in Mg(1-x)Alx(OH)2(DDS)x exhibit a composition driven transformation from a monolayer arrangement of the intercalated surfactants, characterized by an interlayer spacing of 7.9 Å to a bilayer arrangement of the chains, characterized by an interlayer spacing of ∼27 Å as the value of x is increased. The XRD patterns of the x = 0.37 Mg-Al LDH-DDS could be refined using the Rietveld profile analysis in the 3R1 polytypic structure. At lower values of x (x = 0.17), where the interlayer spacing is 7.9 Å, the pattern exhibited considerable stacking faults and analysis of the pattern using the DIFFaX software indicated a 60:40 random mixture of the 3R1 and 2H1 polytypes. MD simulations were performed to understand the origin of the Al/Mg composition driven transformation in the surfactant intercalated Mg-Al LDH. In these simulations, that were performed using the NVT ensemble, two neutral Mg-Al LDH sheets with the surfactants tethered to them were brought closer from infinite separation in a stepwise fashion with the total energy as well as the relative contributions of the Coulomb, van der Waals and internal energy evaluated at each step. Simulations 2315

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Langmuir were performed for the two extreme compositions for which diffraction experiment had shown interlayer spacing values of 27 and 7.9 Å. The simulations are able to reproduce the experimental data. For the x = 0.375 the computed energy as the function of interlayer separation shows minima at 27.2 Å. The atom density profiles show that the alkyl chains of the intercalated surfactant are arranged as bilayers with an average tilt angle of 54°, comparable with the experimentally reported value of 58°. The calculations also showed that it is the van der Waals interaction between chains of the opposing layers that holds the solid together. For the lower Al/Mg ratio (x = 0.1875) the minima in the energy versus interlayer separation appears at 8.1 Å, a value comparable withe the experimental value of 7.9 Å. At the minima the surfactant chains are oriented flat in the galleries in a monolayer arrangement. For this composition it is the Coulomb interaction, rather than the dispersive interaction, that dominates. Thus, both experiment and simulation show that the DDS intercalated Mg-Al LDH show a transformation from a monolayer to a bilayer arrangement of the intercalated surfactant with composition and that the nature of the forces that hold the solid together are very different in the two situations.

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(11) Heinz, H.; Castelijns, H. J.; Suter, U. W. J. Am. Chem. Soc. 2003, 125, 9500. (12) Mohanambe, L.; Vasudevan, S. J. Phys. Chem. B 2006, 110, 14345. (13) Rodriguez-Carvajal, J. FullProf SUITE; LLB Saclay & LCSIM: Rennes, France, 2003. (14) Treacy, M. M. J.; Deem, M. W.; Newsam, J. M. DIFFaX, Version 1.807; http://www.public.asu.edu/mtreacy/DIFFaX.html, 2000. (15) Bellotto, M.; Rebours, B.; Clause, O.; Lynch, J.; Bazin, D.; Elkaïm, E. J. Phys. Chem. 1996, 100, 8527. (16) Levashov, V. A.; Thorpe, M. F. Phys. Rev. B 2003, 67, 224109. (17) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (18) Maple, J. R.; Hwang, M. J.; Stockfisch, T. P.; Dinur, U.; Waldman, M.; Ewig, C. S.; Hagler, T. J. Comput. Chem. 1994, 15, 162. (19) Materials Studio, Version 4.4.0.0, Accelrys Software, Inc.: 2008. (20) Rappe, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358. (21) Woodcock, L. V. Chem. Phys. Lett. 1971, 10, 257. (22) DIAMOND-Visual Crystal Structure Information System; CRYSTAL IMPACT: Bonn, Germany.

’ ASSOCIATED CONTENT

bS

Supporting Information. Figure S1, TGA curves for the surfactant intercalated Mg-Al LDH-DDS, Table S2, sample compositions from ICP, TGA, and CHN analysis, Figure S3, X-ray diffraction pattern of Mg-Al LDH-NO3, Figure S4, infrared spectra Mg-Al LDH-DDS and Mg-Al LDH-NO3-, and Figure S5, starting geometries of Mg-Al LDH-DDS.This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Telephone: þ91-80-2293-2661. Fax: þ91-80-2360-1552/0683.

’ ACKNOWLEDGMENT The authors would like to thank Miss S. Radha and Prof. P. Vishnu Kamath, Department of Chemistry, Central College, Bangalore University, Bangalore, India, for the help provided in running the DIFFaX simulations. ’ REFERENCES (1) Kaganer, V. M.; M€ohwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779. (2) Ulman, A. Chem. Rev. 1996, 96, 1533. (3) Heinz, H.; Vaia, R. A.; Farmer, B. L. Langmuir 2008, 24, 3727. (4) Venkataraman, N. V.; Vasudevan, S. J. Phys. Chem. B 2002, 106, 7766. (5) Heinz, H.; Suter, U. W. Angew. Chem., Int. Ed. 2004, 43, 2239. (6) Heinz, H.; Paul, W.; Suter, U. W.; Binder, K. J. Chem. Phys. 2004, 120, 3847. (7) Heinz, H.; Vaia, R. A.; Krishnamoorti, R.; Farmer, B. L. Chem. Mater. 2007, 19, 59. (8) Zeng, Q. H.; Yu, A. B.; Lu, G. Q.; Standish, R. K. Chem. Mater. 2003, 15, 4372. (9) Heinz, H.; Vaia, R. A.; Farmer, B. L. J. Chem. Phys. 2006, 124, 224713. (10) Zeng, Q. H.; Yu, A. B.; Lu, G. Q.; Standish, R. K. J. Phys. Chem. B 2004, 108, 10025. 2316

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