4456
Langmuir 2008, 24, 4456-4460
Molecular Dynamics Investigation of the Effects of a Water Surface on the Aggregation of Bent-Core Molecules Nathan Duff,†,§ Elizabeth K. Mann,‡ and Daniel J. Lacks*,† Department of Chemical Engineering, Case Western ReserVe UniVersity, CleVeland, Ohio 44106, and Department of Physics, Kent State UniVersity, Kent, Ohio 44242 ReceiVed January 30, 2008. In Final Form: March 7, 2008 Molecular dynamics simulations are used to determine how the presence of a water surface affects the way that bent-core surfactant molecules interact with one another. The simulations are carried out for isolated pairs of bent-core molecules, and for pairs of bent-core molecules on a water surface. The results show that the water surface fundamentally alters the nature of the interaction between the bent-core molecules: a stable complex is formed when the two molecules are on the water surface, but not for an isolated pair of molecules. This difference occurs because the water surface constrains the internal structure and orientation of the molecules, which makes the packing of the molecules into a stable complex more thermodynamically favorable.
Introduction Soft matter is very sensitive to the external environment. This sensitivity is exploited both in nature, such as in the relation between protein configuration and function, and in technology, such as liquid crystals in electro-optical and other applications. In this way, the presence of a surface can alter how molecules aggregate and ultimately self-assemble. We investigate here how the presence of a water surface affects the intermolecular structures for a class of surfactant molecules characterized by a rigid bent core. These bent-core molecules are important because they form anti-ferroelectric liquid crystalline phases1,2 with possible applications for light shutters,3 artificial muscles,4 and nonlinear optics.2,5 Furthermore, the behavior of these molecules at a water surface is of interest, because the self-assembly that occurs on a surface serves to seed the alignment of bulk phases. We have previously shown that a water surface fundamentally changes the equilibrium intramolecular structure of these molecules;6 the present investigation addresses further consequences of the water surface, in regard to how pairs of these molecules interact with one another. Molecular dynamics (MD) simulations are carried out for a pair of bent-core molecules, in two cases: with the molecules isolated, and with them at a water surface. The MD approach incorporates details of the interaction of bent-core molecules not found with coarse grained approaches,7-14 and allows for simulations at water surfaces that are too computationally * Corresponding author. † Case Western Reserve University. ‡ Kent State University. § Present address: Department of Chemical Engineering, University of California, Santa Barbara, CA. (1) Link, D. R.; Natale, G.; Shao, R.; Maclennan, J. E.; Clark, N. A.; Korblova, E.; Walba, D. M. Science 1997, 278, 1924. (2) Pelzl, G.; Diele, S.; Weissflog, W. AdV. Mater. 1999, 11, 707. (3) Ja´kli, A.; Chien, L. C.; Kru¨erke, D.; Sawade, H.; Heppke, G. Liq. Cryst. 2002, 29, 377. (4) Ja´kli, A.; Kru¨erke, D.; Nair, G. G. Phys. ReV. E. 2003, 67, 051702. (5) Reddy, R. A.; Tschierske, C. J. Mater. Chem. 2006, 16, 907. (6) Duff, N.; Wang, J.; Mann, E. K.; Lacks, D. J. Langmuir 2006, 22, 9082. (7) Schiller, P.; Schlacken, H. Liq. Cryst. 1998, 24, 619. (8) Xu, J. L; Selinger, R. L. B.; Selinger, J. V.; Shashidhar, R. J. Chem. Phys. 2001, 115, 4333. (9) Johnston, S. J.; Low, R. J.; Neal, M. P. Phys. ReV. E. 2002, 65, 051706. (10) Johnston, S. J.; Low, R. J.; Neal, M. P. Phys. ReV. E. 2002, 66, 061702. (11) Lansac, Y.; Maiti, P. K.; Clark, N. A.; Glaser, M. A. Phys. ReV. E. 2003, 67, 011703. (12) Dewar, A.; Camp, P. J. Phys. ReV. E. 2004, 70, 011704.
intensive for quantum mechanical approaches.15-18 The simulations are carried out for the particular bent-core molecule shown in Figure 1: this molecule has a rigid bent core composed of five phenyl rings, and floppy hydrocarbon tails at either end of the core. In the simulations, the bent-core molecules are modeled using the general AMBER force field19 with partial charges assigned by the BCC charge fitting method.20 The water molecules are modeled with the TIP3P water potential.21 The MD simulations are carried out using the AMBER 8 software package.22 The simulations are run at a temperature of 300 K, with the temperature controlled by a Langevin dynamics thermostat.23 The Coulomb interactions are summed using the particle mesh Ewald method,24 and the non-Coulomb interactions are cut off at a distance of 10 Å. The SHAKE algorithm25 is used to constrain the C-H and O-H bonds, and thus allow a larger time step (2 fs) to be used. For the isolated molecules, two simulations are carried out, from different initial conditions (i.e., starting configurations from which the simulation is run). In the first initial condition, the two molecules are oriented parallel to each other (side-by-side) and ∼20 Å apart, with their internal structure being the annealed structure for a single isolated molecule obtained in our previous work.6 The second initial condition is the final configuration from one of the simulations of the molecules on the water surface (13) Orlandi, S.; Berardi, R.; Steltzer, J.; Zannoni, C. J. Chem. Phys. 2006, 124, 124907. (14) Dewar, A.; Camp, P. J. J. Chem. Phys. 2005, 123, 174907. (15) Imase, T.; Kawauchi, S.; Watanabe, J. J. Mol. Struct. 2001, 560, 275. (16) Dong, R. Y.; Fodor-Csorba, K.; Xu, J.; Domenici, V.; Prampolini, G.; Veracini, C. A. J. Phys. Chem. B 2004, 108, 7694. (17) Cacelli, I.; Prampolini, G. Chem. Phys. 2005, 314, 283. (18) Krichnan, S. A. R.; Weissflog, W.; Pelzl, G.; Diele, S.; Kresse, H.; Vakhovskaya, Z.; Friedemann, R. Phys. Chem. Chem. Phys. 2006, 8, 1170. (19) Wang, J. M.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. J. Comput. Chem. 2004, 25, 1157. (20) Jakalian, A.; Jack, D. B.; Bayly, C. I. J. Comput. Chem. 2002, 23, 1623. (21) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (22) Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Wang, B.; Pearlman, D. A.; Crowley, M.; Brozell, S.; Tsui, V.; Gohlke, H.; Mongan, J.; Hornak, V.; Cui, G.; Beroza, P.; Schafmeister, C.; Caldwell, J. W.; Ross, W. S.; Kollman, P. A. AMBER 8; University of California, San Francisco, 2004. (23) Pastor, R. W.; Brooks, B. R.; Szabo, A. Mol. Phys. 1988, 65, 1409. (24) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577. (25) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327.
10.1021/la8003307 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/27/2008
Letters
Langmuir, Vol. 24, No. 9, 2008 4457
Figure 1. (a) The bent-core molecule examined in the present study, with X ) Cl. (b) Sites used to characterize structure, corresponding to the central phenyl ring (black), the inner phenyl rings (red), the outer phenyl rings (blue), and the end-carbon atom of the hydrocarbon tail (green). Each site corresponding to a phenyl ring is characterized by the position of the center of mass of the ring, and an orientation defined by the vector normal to the plane of the ring (gray arrow). The core composed of the five phenyl rings is relatively rigid, and the spatial orientation of this core is described by the orientation of the vector between the centers of mass of the central phenyl ring and an inner phenyl ring (black arrow). The picture in Figure 1b was created with the VMD software package.26
(but with the water molecules removed). These simulations are carried out for 30 ns. The simulations with the water surface are carried out for a periodic slab geometry. A simulation cell with dimensions 67.1 × 66.9 × 100 Å is used, with periodic boundary conditions in all three dimensions; the large z dimension minimizes the effects of periodicity along the z axis, and the dimensions along the x and y axes are large enough so that the periodic images of the bent core molecules are separated by more than 20 Å. The simulations include 2883 water molecules, which creates a slab of water ∼20 Å thick. Simulations are run from two distinct initial conditions, to determine whether the results are independent of this choice. For the first initial condition, the two bent-core molecules are oriented parallel (side-by-side) and ∼20 Å apart, and ∼4 Å above the water surface. For the second initial condition the two bent-core molecules are oriented perpendicularly (crossed), and ∼14 Å above the water surface. In both cases, the initial configuration of each bent-core molecule is the annealed structure for a single isolated molecule obtained in our previous work.6 The simulations are carried out for 60 and 45 ns, for the first and second set of initial conditions, respectively. Results for the distance between the central rings of the two molecules, as a function of time, are shown in Figure 2. These results indicate a significant difference between the behaviors of the isolated molecules and the molecules on the water surface. For the isolated pair of molecules, the relative positions of the molecules undergo large variations throughout the course of the simulation. In contrast, when on a water surface, the bent-core molecules become locked together at a fixed separation (after an equilibration period); the magnitude of the fixed separation is the same in the simulations from the two different initial conditions. Snapshots from the simulations, shown in Figure 3, clarify the contrasting behaviors of the isolated molecules and the molecules on the water surface. For the isolated pair of molecules, the two molecules are somewhat intertwined and loosely aligned, but the relative positions of the two molecules appear to be somewhat arbitrary. In contrast, when on the water surface, the relative (26) Humphrey, W.; Dalke, A.; Schulten, K. J. Molec. Graphics 1996, 14, 33.
Figure 2. Distance between the centers of mass of the central rings for pairs of bent-core molecules: (a) on a water surface, from the first initial condition; (b) on a water surface, from the second initial condition; (c) isolated pair of molecules.
positions of the two molecules appear to be ordered: the two bent-core molecules are oriented in the same way, and each segment of the bent core on one molecule is locked in place with the analogous segment of the other molecule. Furthermore, the
4458 Langmuir, Vol. 24, No. 9, 2008
Letters
Figure 4. Probability distributions of the distances separating analogous sites of the two bent-core molecules (see Figure 1b). Results for the distances between the central phenyl rings, inner phenyl rings, outer phenyl rings and terminal carbon atoms are shown as black, red, blue, and green, respectively. (a) Results for the bentcore molecules on a water surface. (b) Results for an isolated pair of bent-core molecules.
Figure 3. Snapshots from the simulations showing typical structures. (a-c) Bent-core molecules on a water surface, viewed from different perspectives; for clarity, the hydrocarbon chains are not shown in panel b, and only the central ring is shown in panel c. Note that these pictures do not show the full simulation cell. (d,e) Isolated pairs of bent-core molecules. In panels a, b, d, and e, one chain is colored green and the other is colored blue (for the simulations with the water surface, the molecule closer to the surface is green). In panel c, the atoms are colored by atom type: blue ) carbon; red ) oxygen; green ) chlorine; white ) hydrogen. These pictures were created with the VMD software package.26
cores of the molecules are stacked one upon the other. Note that it is just the cores that appear to be well ordered, and that the hydrocarbon tails appear to flop independently. In the following, we quantify these ideas apparent in the snapshots by describing the bent-core molecule in terms of the seven sites shown in Figure 1b. For both sets of simulations (i.e., with and without the water surface), the results obtained from the two initial conditions are very similar. For this reason, only the results obtained from the first initial condition are shown in the following. Furthermore, the fact that the results do not depend on the initial conditions suggests that the structures obtained represent the thermodynamic equilibrium state. Figure 4 shows the distribution of separations between analogous sites on the two molecules, where the sites are defined in Figure 1b. When on the water surface, the distributions are narrow for sites that are part of the core, but are broad for the
Figure 5. Probability distribution for the angle describing the relative alignment of the two bent-core molecules. This angle is defined by the dot product of the orientation vector on the first molecule with the orientation vector on the second molecule, where the orientation vectors are defined by the black arrow in Figure 1b. The black line represents molecules on water surface, and the gray line represents the isolated pair of molecules. The probability distributions are normalized such that (180/π)∫90 0 P(β) sin β dβ ) 1.
sites representing the hydrocarbon tails. These results indicate that the core of one molecule is locked in place with the core of the other molecule, while the hydrocarbon tails flop independently. Note that the inner rings, rather than the central rings, are the most tightly locked in place; this is a result of one bent core sitting within the bend of the other, and being “pinched” at the position of the inner rings. In contrast, for the isolated molecules, the distributions for the core sites are much broader, indicating a looser ordering; however, these distributions for the core sites are still significantly narrower than those for the hydrocarbon tails, indicating that some loose ordering nevertheless exists. The bimodal nature of some of the distributions for the
Letters
Figure 6. Probability distributions for the angles describing the alignment of analogous phenyl rings on the two bent-core molecules. This angle is defined by the dot product of the normal vector of a phenyl ring on the first molecule with the normal vector of the analogous phenyl ring on the second molecule, where the normal vectors are defined by the gray arrow in Figure 1b. Black line: center rings; gray line: inner rings; dotted line: outer rings. (a) Molecules on water surface; (b) isolated pair of molecules. Note the difference in y-axis scales for parts a and b. The probability distributions are normalized such that (180/π)∫90 0 P(γ) sin γ dγ ) 1.
isolated pair of molecules implies that the intermolecular structure moves between distinct states (also apparent in Figure 2). The orientation of each molecule can be defined by the vector between the central ring and an inner ring, as shown in Figure
Langmuir, Vol. 24, No. 9, 2008 4459
1b. The relative orientation of the two molecules is then characterized by the angle between these vectors on the two molecules (obtained from the dot product of the vectors). Figure 5 shows the distribution of these relative orientation angles, both for the isolated molecules and for the molecules on the water surface; the molecules are much more highly aligned on the water surface than when isolated. Not only does the water surface cause the two molecules to be aligned spatially, but the water surface also causes the orientations of the phenyl rings to be correlated as well. The phenyl ring orientations are defined by vectors normal to the plane of the phenyl ring (see Figure 1b). Figure 6 shows the distributions of the angles between these vectors for analogous phenyl rings on the two molecules; the rings on the different molecules are aligned in the same direction when the molecules are on the water surface, but not when the molecules are isolated (again, the inner rings, rather than the central rings, are most aligned). Thus the water surface causes a pair of bent-core molecules to pack together in a stable configuration, when they would not do so in the absence of the water surface. We believe this occurs because the water surface restricts the degrees of freedom of the bent-core molecules. The overall hydrophobic nature of the bentcore prevents the molecules from mixing with the water, while the amphiphilicity tethers at least one such molecule to the surface; thus the water surface limits the positions accessible to the bentcore molecules. Additionally, the interactions of the water surface with the phenyl rings and associated groups locks the torsional state of the molecule and, to some extent, the molecule’s orientation: (1) Figure 7 shows the results for the Φ1L and Φ1R torsion angles (defined in Figure 1a). For the isolated molecules, the molecules move between several torsional states, but are most likely to be in the state that furthest separates the polar groups on the two arms of the molecule, as also found in quantum studies of single isolated molecules.15,17 But the water surface causes the molecules to be restricted to a single torsional state, in which the carbonyl side groups are closer to the water surface; this effect also occurs for a single bent-core molecule on a water surface.6
Figure 7. Probability distribution as a function of torsion angles for the bent-core molecules, where the torsion angles are defined in Figure 1a. Each panel shows the probability that a particular molecule has values of the φ1L and φ1R torsion angles (both torsion angles are on the same molecule, as shown in Figure 1a). Each line represents an increase in probability of 0.00005. The crosses mark the point of highest probability for a single isolated molecule. (a,b) Results for pair of bent-core molecules on a water surface. (c,d) Results for isolated pair of bent-core molecules. For the molecules on the water surface, one molecule is stacked upon the other (see Figure 3c); results for the lower molecule are in panel a, and results for the upper molecule are in panel b.
4460 Langmuir, Vol. 24, No. 9, 2008
Figure 8. Probability distributions for the angles describing the orientation of the phenyl rings of the bent-core molecules with respect to the water surface. This angle is defined by the dot product of the normal vector of the phenyl ring (see Figure 1b) with the vector normal to the water surface. (a) Central ring; (b) inner rings; (c) outer ring. As shown in Figure 3c, the molecules are stacked one on top of the other: results for the lower molecule are solid lines, and results for the upper molecule are dashed lines. The probability distributions are normalized such that (180/π)∫90 0 P(θ) sin θ dθ ) 1.
(2) Figure 8 shows results for the orientation of the molecules relative to the plane of the water surface, as quantified by the angles between vectors normal to the planes of the phenyl rings,
Letters
and the vector normal to the plane of the water surface. This figure shows that the water surface restricts the orientation of the bent-core molecules; again, this effect also occurs for a single bent-core molecule on a water surface.6 We interpret the role of the water surface in stabilizing the complex of two bent-core molecules as follows: A stable complex forms when the decrease in energy associated with unbound molecules forming the complex overcomes the entropy loss. Since the water surface restricts the torsional state, position, and orientation of the individual molecules, as shown above, the entropy of the unbound molecules is reduced when they are on the water surface (in comparison to isolated unbound molecules). Thus, the entropy loss upon forming a stable complex is smaller when the water surface is present, and with this smaller entropy loss, it is thermodynamically more favorable for the molecules to form the stable complex. We know that the water surface acts to thermodynamically stabilize that particular configuration of the complex, rather than just direct the system to this configuration, because, when we begin a simulation of the isolated molecules from the final structure of the water surface simulation, the stable complex falls apart very quickly (within 100 ps). Experiments show that these bent-core molecules form incompletely ordered crystals in bulk at room temperatures.2 Our results are consistent with these experiments, in that the isolated two molecules remain attached to each other, and loosely ordered (see Figure 4 and associated text). Furthermore, our results suggest that more fully ordered crystals could be obtained by using a water surface to seed the crystal growth. While this paper shows how the presence of the water surface affects the structure of the bent-core molecules, the converse also occurs, i.e., the presence of the bent-core molecules affects the structure of the water surface. We plan to address such effects in the future. Acknowledgment. This material is based upon work supported by the National Science Foundation under grant number DMR-0402867, and a grant of computing time from the Ohio Supercomputer Center. LA8003307
