Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A

Apr 27, 2009 - Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India. J. Phys. Chem. C , 2009, 113 (20)...
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Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A Molecular Dynamics Study Vikrant V. Naik and S. Vasudevan* Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India ReceiVed: December 4, 2008; ReVised Manuscript ReceiVed: April 1, 2009

Molecular dynamics (MD) simulations are reported for an anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) and CH3(CH2)15N+(CH3) ions in a layered solid, CdPS3. The intercalated CTA ions are organized with the cationic headgroups tethered to the inorganic sheet and the hydrocarbon tails arranged as bilayers. Simulations were performed at three temperatures, 65, 180, and 298 K, using an isothermal-isobaric ensemble that was subsequently switched once macroscopic parameters had converged to a canonical isothermal-isochoric ensemble. The simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and layer-to-layer separation distance. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained a planar all-trans conformation, and that gauche bonds occurred as part of a “kink” (gauche+-trans-gauche-) sequence and not as isolated gauche bonds. Trans-gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. A two-dimensional periodic Voronoi tessellation analysis was performed to obtain the single-molecular area of an alkyl chain in the bilayer. The single-molecular area relaxation times are an order of magnitude longer than the trans-gauche isomerization times. The results indicate that the trans-gauche isomerization is associated with the creation and annihilation of a kink defect sequence. The results of the present MD simulation explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C nuclear magnetic resonance measurements.6 Introduction Intercalation of long chain ionic surfactants in layered inorganic solids has been a subject of considerable interest. These organic-inorganic hybrids find utility as adsorbents of organic pollutants in soil and water remediation1-4 as well as in rheological control in paints and grease.5 In these systems, the charged headgroup of the surfactant is tethered to the internal surface of the galleries of the layered solid via a Columbic interaction with the hydrocarbon “tail” organized in a bilayer arrangement (Figure 1). The tethered or anchored bilayer bears a striking structural resemblance to lipid bilayers that are an integral feature of cell membranes. A notable difference is that unlike in lipid bilayers, where individual molecules can undergo lateral diffusion and also flip-flop between layers, the anchored bilayer is characterized by the total absence of translational mobility. The degrees of freedom of the alkyl chains of the anchored bilayer are restricted to changes in conformation. In lipid bilayers, it is well-established that the conformation and dynamics play a central role in defining the temperature dependence and critical temperatures associated with the different phases of the bilayer. The intercalated bilayers usually do not exhibit any changes in phase because the density of the anchored alkyl chains is below the critical density. They, however, have the advantage of being essentially a solid state system, where detailed and quantitative information of the conformation of the alkyl chains of the bilayer may be obtained by conventional spectroscopic methods. * Author to whom correspondence may be addressed. E-mail: svipc@ ipc.iisc.ernet.in. Telephone: +91-80-2293-2661. Fax: +91-80-2360-1552 or +91-80-2360-0683.

The conformation of alkyl chains of an intercalated bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) ions in the layered solid CdPS3 has been recently reported.6 This intercalated compound provides an ideal system to investigate the evolution of a conformational disorder with temperature in an anchored bilayer because the density of the anchored CTA surfactant chains is less than the critical density required for a phase transition. 13C nuclear magnetic resonance (NMR) and infrared vibrational spectroscopic measurements as a function of temperature were used to characterize the thermal evolution of a gauche conformational disorder. The two techniques return widely differing estimates of the extent of a gauche disorder with the NMR, indicating a much greater extent of disorder. The 13C NMR experiment can differentiate between gauche and trans conformers by virtue of the so-called γ-gauche effect that leads to an upfield-shifted resonance for methylene carbons two bonds removed from the gauche bond.7,8 The NMR measurements gave a rather surprising result that at 310 K all methylene carbons of the anchored bilayer experienced the γ-gauche effect implying that 50% of all bonds were gauche. It may be noted that for a methylene chain with no constraints the expected population of gauche bonds at 310 K, assuming a gauche-trans energy difference of 500 cal/mol,9 is ∼30%. In addition, because the chains are anchored, space available per chain is limited, and the structure cannot sustain high concentrations of gauche bonds without breaking. The infrared measurements, on the other hand, indicated that at low temperatures (75 K) all methylene chains of the bilayer adopt an all-trans conformation, i.e., do not have a single gauche bond and, even at 300 K, 20% of all chains retain a planar all-trans conformation.6,10 The infrared spectra also indicated that gauche bonds were present either as

10.1021/jp810674c CCC: $40.75  2009 American Chemical Society Published on Web 04/27/2009

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Figure 1. Anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) ions in layered CdPS3, showing a snapshot of the simulation of the intercalated Cd0.75PS3(CTA)0.5. Color code: C is gray, H is white, N is blue, S is yellow, P2S6 polyhedra is magenta, and CdS6 polyhedra is light orange.

part of a gauche-trans-gauche′ (g-t-g′) “kink” defect sequence or as an end-gauche defect, which is a penultimate bond oriented such that the terminal methyl group is in a gauche conformation relative to the methylene group three carbon atoms away. To reconcile the apparent difference in the estimates of the gauche disorder, we suggested that the kink defects once formed are mobile along the length of the chain, resulting in all methylene carbon atoms of the chain atoms experiencing the γ-gauche effect on NMR time scales.6 Here we report a molecular dynamics (MD) study of an anchored bilayer to understand the structure, conformation, and dynamic properties at the atomistic level. MD simulations of lipid bilayers have been widely reported.12-17 These studies have provided a detailed molecular-level understanding of these complex systems and the nature of single molecules as well as the collective motion in the bilayer. The structure of alkyl chains in organoclays has also been investigated by classical MD simulations.18-22 The anchored bilayer system that we have studied is the same as that for which detailed spectroscopic studies have been reported, i.e., CTA ions intercalated in layered CdPS3.6,11 In this system, CTA ions are introduced in the galleries of CdPS3 by ion exchange intercalation to form Cd0.83PS3 (CTA)0.34 with a basal spacing of 33 Å; charge neutrality is preserved by loss of the Cd2+ ions from the CdPS3 layers. The intercalated surfactant chains form a tilted bilayer with the cationic headgroup anchored at the negatively charged, cadmium deficient Cd0.83PS3 layer, with a mean head-to-head distance of ∼9 Å. Our simulations are able to reproduce the

experimental details of the system and in addition provide detailed insights into the nature of the conformational dynamics and mobilities in the anchored bilayer. The simulations are also able to provide an explanation as to why the NMR and infrared vibrational spectroscopic measurements return such widely differing estimates of the gauche disorder. Methodology Molecular dynamics simulations were performed using the Materials Studio23 suite running on an IBM M PRO Intellistation workstation. The first step in the simulation was the preparation of the negatively charged Cd1-xPS3 layers. As mentioned in the Introduction, the introduction of cationic CTA ions in the interlamellar space occurs by an ion exchange intercalation reaction with charge neutrality maintained by an equivalent loss of Cd2+ ions from the layers to give Cd0.75PS3(CTA)0.5. The CdPS3 lattice was constructed using atomic coordinates from the reported crystal structure data.24 CdPS3 crystallizes in the C2/m space group with lattice parameters of a ) 6.218 Å, b ) 10.763 Å, c ) 6.867 Å, R ) β ) 90°, and γ ) 107.58°. A super cell was then constructed containing 48 crystallographic unit cells. The super cell parameters were a ) 37.308, b ) 43.052, c ) 66.4 Å; R ) β ) 90°, and γ ) 107.58° (equivalent to 6 × 4 CdPS3 unit cells in the ab plane and a two layer repeat with an initial interlayer spacing of 30 Å). Forty-eight Cd2+ ions were then removed to give a supercell with a composition of [Cd144P192S576]96-. The Cd0.75PS3 layers were obtained from

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the CdPS3 sheets by removing 1/4 of the Cd2+ ions taking care that no two vacancies were adjacent to each other. Although there is no X-ray crystallographic evidence for long-range ordering of the Cd2+ion vacancies in intercalation compounds of CdPS3, we were forced to assume complete ordering because of the periodic boundary condition imposed on the simulation super cell and the fact that partial occupancy was disallowed. Except for the periodic boundary condition, no symmetry constraints were imposed. The structure was treated as triclinic (P1), and all lattice parameters were treated as independent variables in the simulation. Charges on the atoms of the supercell were obtained by a DFT calculation using the DMol3 module of Material Studio.23 A double numerical with polarization (DNP) basis set with the Perdew-Wang (PW91) functional was used. Charges on atoms were obtained from a Mulliken population analysis, using the eigenstates and eigenvectors from the above calculation. The charge on the Cd atom was 0.59-0.65, depending on the position; P was 0.78-0.80, while the S atoms carried a charge between -0.52 and -0.60. The calculated charges indicate that the excess negative charge of the sheet due to Cd2+ ion vacancies is effectively canceled so that the layer may, to a first approximation, be considered as a uniformly charged insulating sheet. The intercalated surfactant CTA ions were constructed using atomic coordinates from the reported crystal structure of cetyltrimethyl ammonium bromide.25 The ion has a unit positive charge. Charges on individual atoms of the CTA chain were obtained by a Mulliken population analysis of the molecular orbitals calculated by the Hartree-Fock method using a 6-31G** basis set (Gaussian 98).26 An integral number of CTA cations with their methylene chains in an all-trans conformation were then introduced between the CdPS3 layers such that overall charge neutrality was maintained. The CTA surfactant chains were grafted randomly to the negatively charged Cd0.75PS3 sheets. Care was taken to ensure that in the initial configuration no two chains were closer than twice the van der Waals diameter of an all-trans alkyl chain (4.5 Å). We have tried different initial surfactant arrangements, keeping this constraint in consideration, and found a convergence to similar trans/gauche ratios. The final composition of the superstructure so obtained was Cd144P192S576(CTA)96. The average area available per CTA chain was 57.5 Å2. The CTA ions were placed in the galleries with the axis of the all-trans methylene chains parallel to each other and the trimethyl ammonium headgroups anchored to opposing CdPS3 layers, thus, forming a bilayer arrangement. The total nonbonded potential interaction energy of the simulated system consisted of long-range Columbic interactions between partial atomic charges and van der Waals interactions, computed using the Ewald summation technique. The cutoff distance for both interactions was kept at 18.5 Å. The bonding interactions were modeled by a composite force field to reflect the hybrid nature of this organic-inorganic system. The inorganic part is not dynamic and requires a hard potential, while the organic component requires a softer potential that can reflect its dynamic nature. The potential energy was computed using the Universal force field (UFF)27 for the CdPS3 layers, while that of the methylene chains of the CTA ion used the polymer consistent force field (PCFF).28 PCFF parameters are optimized for predicting the structure and conformation of alkyl chains. Two nanosecond molecular dynamics simulations were performed on the anchored bilayer at three different temperatures: 65, 180, and 298 K. The wide temperature range was chosen to ensure that differences in structure, conformation, and dynamics are easily discernible. MD calculations were per-

Naik and Vasudevan

Figure 2. Convergence of the total energy of the anchored bilayer at 298 K. The point at which the simulations were switched from a NPT to NVT ensemble is indicated.

formed with the Material Studio package using the Forcite+ module, which uses the velocity-Verlet integrator method for computing the positions and velocities of atoms.23 The MD simulations were carried out in two steps. Simulations were initiated on a constant composition isothermal-isobaric (NPT) ensemble. Once lattice parameters and the energy of the system were judged to have converged to equilibrium values, subsequent longtime (2 ns) simulations were then performed on a NVT ensemble with a time step of 1 fs. Equilibrium values of the lattice parameters were judged to have been reached when these quantities fluctuate around their average values that remain constant over time. Equilibrium values of the lattice parameters and thermodynamic quantities were also checked by repeating the simulations with a different interlayer spacing. Convergence to similar conformations and properties from different initial values is a good indicator that equilibrium has occurred. Typically, equilibrium values were reached within the first 350-400 ps. Subsequently, simulations were then performed in the canonical (NVT) ensemble. In this protocol, dynamic quantities are extracted, starting from the NPT ensemble to the NVT ensemble. Structural data such as the lattice parameters are, however, derived from the NVT ensemble after equilibrating for a constant volume. During simulation, we maintained the temperature of the ensemble by the velocity scale thermostat.29 The temperature difference window was kept at 10 K, implying that the temperature would hover between (5° of the simulation temperature. For the NPT simulations, an Anderson barostat with a cell time constant of 1 ps was used. The equivalent hydrostatic pressure was set to 0.1 MPa. Periodic boundary conditions were applied in three dimensions so that the simulation cell is effectively repeated infinitely in each direction. Results and Discussion Convergence. As described in Methodology, the simulations were initiated using an NPT ensemble, wherein the basal spacing as well as the in plane lattice parameters were free to vary. Most bulk properties such as the volume, lattice parameters, and total energy converged within the first 400 ps, after which they fluctuated about a mean value. The convergence of the total energy for an MD run at 298 K is shown in Figure 2. The system showed similar convergence of bulk properties at 180 and 65 K. The rather longtime for convergence is because the configuration at the start of the simulation was highly constrained as the randomly placed surfactant chains were in an all-trans

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Figure 3. Distribution function of the methylene carbon atom positions projected on a vector parallel to the tilt axis of the surfactant chains. (a) Distribution profiles of the C1-C9 methylene carbons. (b) Distribution profiles of the C10-C16 methylene units. Numbering of the methylene carbons is indicated. The C16 and C12 methylene units as well as the C13 and C15 methylenes of the opposing layer overlap.

conformation. At convergence, the basal spacing was found to have a value of 32.5 Å, which is close to the experimentally determined spacing of 33 Å. The values of the basal spacing at 298, 180, and 65 K are similar. The in plane CdPS3 structure shows a small deformation from the reported crystal structure, probably due to the small size of the supercell compared to the macroscopic dimensions of a true crystal. The deformation is, however, small and is ignored in the rest of the discussion (Supporting Information). Thus, an equilibrium state of the system is successfully attained from an arbitrary initial structure using the NPT ensemble. Once bulk properties of the system were judged to have converged to their equilibrium value, subsequent simulations were performed using an NVT ensemble. The point at which the ensemble is switched from a NPT to NVT ensemble during the MD run is indicated in Figure 2. The static properties of the anchored bilayer discussed in the subsequent sections were obtained by averaging over the final 1500 ps. Structure and Conformation of the Intercalated CTA Surfactant Chains A snapshot of the ensemble at the end of the simulation shows that the intercalated surfactant chains are arranged as a tilted bilayer (Figure 1). The chains tilt relative to the surface normal at an almost constant angle, thus optimizing interchain van der Waals interactions. The average tilt angle, defined as the ensemble averaged angle between the vector joining the C1 methylene carbon with the C16 methyl of the same chain and the normal to the inorganic CdPS3 sheet, was found to have a value of 53°. The experimentally determined value for CTA ions intercalated in CdPS3 is 55°.11 To establish the interlayer structure of the anchored bilayer, the density distribution of different methylene carbons along the tilt axis from the center of the bilayer was constructed. This was done by projecting the methylene carbons of a chain along its molecular tilt axis and averaging over all of the chains of the bilayer. Plots of the density profiles are shown in Figure 3. The density profiles show a pronounced layering behavior and are symmetrically displaced from the center of the interlayer gallery. The C1 methylene unit of the alkyl chain is located close to the inorganic CdPS3 sheet, while the methylene units at the tail of the CTA chain lie midway within the gallery. The density profiles indicate that the methyl units at the tail of the

CTA chains in opposing layers are interdigitated (Figure 3b). The C14 methylene units of the alkyl chains of opposing layers are both located in the middle of the bilayer. The CTA surfactant chains are arranged randomly within the layers and do not have any site specific location. The superposition of all of the trajectories of the N atoms of the ammonium headgroup over 2 ns indicates that there is neither significant lateral diffusion of the headgroup nor any positional exchange of the surfactant chains (Supporting Information). The intercalated CTA surfactant chains thus truly qualify to be described as an anchored bilayer. The conformation of the chains was analyzed by determining the dihedral angles for all simulation trajectories longer than 500 ps. The distribution of dihedral angles at the three simulation temperatures is shown in Figure 4a. A conformation is assigned trans (t) with a dihedral angle of 180 ( 60°, gauche+ (g+) with an angle of 60 ( 60°, and gauche- (g-) with an angle of -60 ( 60°. As expected the average gauche population increases with temperature. At 65 K, it is 5.0%, and at 298 K, it is 8.5% of all C-C bonds (Figure 4b). It was observed that for all of the trajectories a fraction of the hydrocarbon chains remained in an all-trans conformation, i.e., did not possess a single gauche bond. At room temperature, the fraction of alltrans chains was 44%, while at 65 K, it is ∼64% (Figure 4b). These results are in agreement with the infrared spectroscopic measurements for this system that showed a fraction of the intercalated surfactant methylene chains retain an all-trans planar conformation even at room temperature.6 The percentage values of the population of all-trans chains indicate that chains that are not all-trans have an average of 2 gauche defects per chain at 298 K, with the value dropping to 1.8 gauche defects per chain at 65 K. These values suggest that a majority of the gauche defects are present as part of a g+-t-g- kink defect sequence and not as isolated gauche bonds. This was confirmed by a more detailed analysis of the occurrence of gauche bonds along the hydrocarbon chain. Figure 5a shows the probability of occurrence of a gauche bond at different locations along the chain, and Figure 5b shows the probability that the gauche bond is present as part of a kink sequence. The dihedral torsions are defined such that C2-C3 is torsion 1, C3-C4 is torsion 2, etc. Figure 5a shows that the probability of occurrence of a gauche bond increases as one proceeds from head to tail, and that a majority of the gauche conformers are part of a kink sequence.

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Figure 4. (a) Probability distribution of the dihedral angle at three temperatures. The region between -120° and + 120° has been magnified by a factor of 10. (b) The percentage fraction of all chains in the anchored bilayer that are all-trans and the percentage fraction of the gauche bonds in the ensemble at different temperatures.

Figure 5. (a) Probability of a gauche bond at different torsion numbers at three temperatures. (b) The probability that a gauche bond is part of a kink (gauche+-trans-gauche-) sequence for different torsion numbers.

trans-gauche isomerization rate, while the latter by the fluctuations in the area per surfactant chain projected in the plane of the bilayer. Trans-Gauche Isomerization. The distribution of dihedral angles of the hydrocarbon chains shown in Figure 4a indicates that trans and gauche isomers may clearly be defined for the C-C bonds. The correlation times characterizing the state-tostate transition dynamics may be obtained from the autocorrelation function defined below. It is convenient to describe the trans and gauche states by using a state function S (t, A), where A stands for all the C-C torsions.17 Figure 6. Calculated correlation times for the trans-gauche isomerization at different torsion numbers at three temperatures.

S(t, A) ) + 1, for |A| g 2π ⁄ 3 : (trans) ) -1, for |A| < 2π ⁄ 3 : (gauche) The autocorrelation function

The probability of the occurrence of a kink shows little variation with torsion number, except toward the tail. Isolated gauche bonds usually appear only at the end of the hydrocarbon chain. The odd-even oscillation in the gauche population as a function of the carbon atom number is similar to that reported from simulation studies on lipid bilayers.12 The oscillation is due to the preferred alignment of the chain segments with respect to the bilayer normal so as to optimize dispersive interactions between chains. Dynamics of the Anchored Bilayer The conformational mobility of the hydrocarbon surfactant chains in the anchored bilayer was characterized on short and long length scales. The former is characterized by the

C(t) )

- < S>2 1 - < S>2

(1)

was calculated for all torsions of the surfactant chain; the average is evaluated over all anchored surfactant chains and simulation times, t. Because gauche+ to gauche- transitions do not occur, the autocorrelation function, eq 1, would represent the trans-gauche isomerization. The relaxation time τt-g was obtained by fitting the correlation function to a single exponential (Supporting Information). The relaxation times show a significant decrease with temperature and also a decrease with increasing torsion number, indicating increased conformational mobility about the C-C bond as one proceeds from the head to tail of the anchored surfactant (Figure

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Figure 7. (a) Periodic two-dimensional Voronoi tessellation for the projection of the center of mass of the surfactant chains of the anchored bilayer onto the plane of the bilayer. (b) Distribution of the single-molecular area of a surfactant chain of the bilayer at three temperatures. Black 9 are the distribution at the start of the simulation.

6). The absence of variation of τt-g for low torsion numbers at 65 K is probably due to poor statistics; the number of gauche bonds is too few at this temperature (Figure 4a). At 298 K, the correlation times vary from 350 ps for the C-C torsions close to the anchored surfactant head to 150 ps for the methylene carbons of the tail of the surfactant that lie midway in the interlamellar region. In contrast, typical trans-gauche isomerization times in lipid bilayers are 150 - 200 ps.17 These results show the same trend as those obtained from the 13C variable contact time NMR measurements that showed a gradient of increasing mobility as one proceeded from the head to the tail of the anchored surfactant.30 Molecular Area Fluctuations. The area of a surfactant molecule in the plane of the anchored bilayer may be directly related to the conformation of the methylene chain of the surfactant. An all-trans chain, i.e., a chain with no gauche defects, would occupy the least area, while the molecular area of a chain with one or more isolated gauche bonds would be larger and also change significantly with the position of the gauche bond along the chain. The presence of a kink would increase the area of the surfactant molecule as compared to an all-trans conformation, but its value would be independent of the position along the chain where the kink occurs (Supporting Information). To estimate the area occupied by individual surfactant molecules, we performed a periodic, two-dimensional Voronoi tessellation. The center of mass of each surfactant chain was projected onto the xy plane of the bilayer, and a two-dimensional Voronoi tessellation analysis performed.15,31,32 Voronoi polygons were constructed using Mathematica33 with the upper and lower layers of Figure 1 analyzed separately. The need for periodic tessellation was necessitated to include surfactant chains at the edges of the periodic cell, which would otherwise form incomplete polygons. Figure 7a shows a snapshot of the Voronoi tessellation for the center of mass of the surfactant chains projected along the normal to the plane of the anchored bilayer. A single-molecular area Ai is defined by the area of the completed Voronoi polygon, i. The analysis provides not only a single-molecular area, but also the shape of the molecular occupation with the number of sides of the Voronoi polygon equal to the number of the nearest neighbors. The analysis provides the area occupied by each surfactant molecule throughout the simulation trajectory. The distribution of molecular areas for the three

Figure 8. Time autocorrelation of the single-molecular area of an alkyl chain in the anchored bilayer as defined by the Voronoi tessellation. Relaxation times at the three temperatures are indicated.

temperatures for which simulations were performed is shown in Figure 7b. The distribution exhibits an asymmetric broadening with increasing temperature. This is expected because the number of gauche conformers per chain increases with temperature (Figure 4b), and these chains have a larger molecular area. The peak value of the distribution, however, shows no change with temperature. This is because, as mentioned in the Introduction, the surfactant chains of the anchored bilayer are not close packed; the average area available per chain (57.5 Å2) is larger than the area of an-all trans chain (20 Å2).34 The average area per anchored surfactant chain, i.e., the area of the Voronoi polygons, Ai, is time dependent (Supporting Information). The time autocorrelation function, CA(t) for the fluctuation of the singlemolecular area is given by

CA(t) )

〈δAi(t)δAi(0) 〉

〈δAi(0)2〉

)

〈Ai(t)Ai(0) 〉 - 〈Ai〉2

〈Ai2 〉 -〈Ai〉2

(2)

where Ai is the single-molecular area defined by the area of the Voronoi polygon and δAi(t) ) Ai(t) - 〈Ai 〉. The results are plotted in Figure 8, and the relaxation times estimated. The time constants associated with the fluctuations of the Voronoi polygons are typically in nanoseconds and are therefore 1-2 orders of magnitude longer than the trans-gauche isomerization time constants, τt-g, at the same temperature. This indicates that a large number of trans-gauche conversions occur with no significant change in the area occupied by a surfactant

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chain. This rules out the possibility of the occurrence of isolated gauche bonds because the area occupied by the chains would show considerable change, depending on where the gauche-totrans and trans-to-gauche conversions occurs. The creation and annihilation of kinks irrespective of where it occurs, on the other hand, would not lead to any change in the projected area of a chain (Supporting Information); the only consideration is that their concentration at a particular temperature should be conserved for all trajectories. The trans-gauche isomerization rates are therefore characteristic of the creation and annihilation of kink defect sequences, and these events occur at different locations along the chain (except toward the tail) with almost constant probability. Conclusions Molecular dynamics simulations were performed on an anchored bilayer formed by the intercalation of the cationic CTA surfactant ions in layered CdPS3 using an isothermal-isobaric ensemble that was subsequently switched to a canonical isothermal-isochoric ensemble. The simulations were carried out at three widely separated temperatures: 65, 180, and 298 K. MD simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and the layer-to-layer separation distance. The bilayer is formed with the cationic headgroup of the CTA surfactant chains anchored to the negatively charged inorganic sheets and is tilted at an angle of 53° away from the normal, which is in agreement with the experiment. The distribution of dihedral angles of the anchored chains showed that trans and gauche conformers could be clearly defined. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained planar all-trans conformation, which is in agreement with infrared spectroscopic measurements reported for this system. The remaining chains have on average two gauche bonds per chain and most were found to occur as part of a kink (gauche+-trans-gauche-) sequence and not as isolated gauche bonds. The probability of finding a kink was almost constant across the length of the chain, except toward the tail. The methylene units at the tail of the surfactant located midway in the bilayer gap have a higher concentration of gauche defects and a greater probability of isolated or “end-gauche” defects than those of methylene units at other locations. Trans-gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. The single-molecular area of an alkyl chain in the bilayer correlates with the number and nature of the gauche bonds present in the chain. The single-molecular area may be defined by the area of the polygon obtained by a periodic Voronoi tessellation of the center of mass of the chains projected on the plane of the bilayer. The fluctuations of the single-molecular area were characterized by time autocorrelation. The associated relaxation times are an order of magnitude longer than the trans-gauche isomerization times. These results indicate that the trans-gauche isomerization is associated with the creation and annihilation of a kink defect sequence because the projected area of the chain would then be independent of the position along the chain where the gauche bond appears. The results of the present MD simulation are able to explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C NMR measurements. It may be recalled that the 13C NMR had estimated that at least half of all C-C bonds in the intercalated bilayer had gauche conformation. This value is unphysical, not only because it

Naik and Vasudevan would imply unreasonable values of the energy difference between trans and gauche conformers, but also because volume constraints imposed by the anchoring of the bilayer would not be able sustain such high levels of disorder. The MD results show that most gauche defects in the anchored bilayer occur as part of a kink sequence, and there is at most one kink per chain. Unlike isolated gauche defects, the location of the kink along the chain would not alter the area occupied by the chain. The dynamic quantities derived from the simulation indicate that the creation and annihilation of kinks occur on the ps time scale and that the probability of their occurrence is almost constant across the length of the chain. In the NMR experiment, the trans and gauche conformers are identified by the values of their chemical shift that differ typically by -4 ppm (301.9 Hz at a Larmor frequency of 75.47 MHz).6 The creation and annihilation of the kinks on the ps time scale would therefore lead to dynamic averaging of these features of the NMR spectrum and the consequent unphysical inference that most bonds are gauche. The time scales associated with the infrared spectroscopic measurements, on the other hand, being much shorter than the trans-gauche isomerization times does not suffer from dynamic averaging and provides a more realistic estimate of the disorder in the anchored bilayer. Acknowledgment. The authors thank Mrs. J. Lakshmi and the Supercomputer Education and Research Centre, Indian Institute of Science, for help and the use of the computational facilities. Supporting Information Available: Figure S1: Normalized atomic probability density distribution of Cd, P, and S atoms projected on the normal to the CdPS3 layer in the CTA intercalated CdPS3. The probability density distribution for the N atom of the CTA headgroup is also shown. Distances are measured from the Cd atom of the CdPS3 sheet. Figure S2: Trajectory of the N atoms of the CTA headgroups in the xy plane of the interlamellar space over the entire 2 ns simulation period. Figure S3: Typical time autocorrelation function for the trans-gauche isomerization. The plot is for the C7-C8 torsion at 298 K. Figure S4: Cylindrical molecular volumes of an alltrans C16 chain and a C16 chain with kinks at different locations. Figure S5: Variation of the single-molecular area as a function of the positions of kinks as obtained from the Voronoi tessellation analysis. Figure S6: Fluctuation of the average area Ai of the Voronoi polygons at 298 K. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Holsen, T. M.; Taylor, E. R.; Seo, Y. C.; Anderson, P. R. EnViron. Sci. Technol. 1991, 25, 1585. (2) Wolfe, T. A.; Demirel, T.; Baumann, R. Clays Clay Miner. 1985, 33, 301. (3) Mortland, M. M.; Shaobai, S.; Boyd, S. A. Clays Clay Miner. 1986, 34, 581. (4) Brown, M. J.; Burris, D. R. Groundwater 1996, 34, 734. (5) Krishnamoorti, R.; Vaia, R. A.; Giannelis, E. P. Chem. Mater. 1996, 8, 1728. (6) Suresh, R.; Venkataraman, N.; Vasudevan, S.; Ramanathan, K. V. J. Phys. Chem. C 2007, 111, 495. (7) Bovey, F. A.; Mirau, P. A. NMR of Polymers; Academic Press: San Diego, CA, 1996. (8) Tonelli, A.; Schilling, F. C. Acc. Chem. Res. 1981, 14, 233. (9) Flory, P. J. Statistical Mechanics of Chain Molecules; WileyInterscience: New York, 1969. (10) Venkataraman, N. V.; Vasudevan, S. J. Phys. Chem. B 2003, 107, 10119. (11) Venkataraman, N. V.; Vasudevan, S. J. Phys. Chem. B 2001, 105, 7639.

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