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Pattern Formation in a Self-Assembled Soap Monolayer on the Surface of Water: A Computer Simulation Study M. Y. Shelley,*,† M. Sprik,‡ and J. C. Shelley§ Department of Chemistry and Biochemistry, Miami University, Oxford, Ohio 45056, Department of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, U.K., and Department of Chemistry, University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada Received June 3, 1999. In Final Form: July 27, 1999 A classical molecular dynamics simulation of a monolayer of sodium laurate (dodecanoate) at the airwater interface has been carried out. We found highly curved, dynamic structural features within the soap monolayer during the simulation. Introduction of salt in the water appears to suppress the formation of these structural patterns, indicating that electrostatic repulsion among anionic headgroups is a key component in creating these structures.
Introduction On the surface of water, surfactant molecules can spontaneously form a monolayer that is generally considered to have a planar structure with the hydrophilic headgroups of molecules immersed in water and the hydrophobic tail pointing away from the water. For the surfactants with a very low solubility in water, it has been shown that the self-assembled monolayer can be considered a separate phase and that several distinct states, some with well-ordered crystalline structures within the monolayer, can exist.1 This class of monolayers of nearly insoluble surfactants is called the Langmuir monolayers. Soluble, ionic surfactants, such as alkyl carboxylates, also form a monolayer by adsorption on the surface of water. Understanding of the formation and the structural integrity of these self-assembled structures is important in a wide variety of industrial processes. While the reduction in surface tension is a clear indication that soap ions accumulate at the surface of water, the microscopic structure of a soap monolayer has yet to emerge. It is not obvious that the well-established planar structure for the Langmuir monolayers is an adequate description of the microscopic structure of soap monolayers, because electrostatic repulsion among ionic headgroups and the bulky hydration shell surrounding the headgroups may significantly perturb the organized packing of alkyl chains. The neutron reflectivity data Lee et al. obtained for decyltrimethylammonium bromide (C10TAB) at the airwater interface indicate an increase in the thickness of headgroup region when the surface density of surfactants is increased from a sub-monolayer level to the monolayer (saturation) level.2 This result cannot easily be explained in terms of a simple model of monolayer adsorption. Lee et al. proposed that, at saturation surface density, ionic surfactants are immersed in water at staggered depths so as to reduce electrostatic repulsion, resulting in an enhanced thickness of the headgroup region. * To whom correspondence may be addressed. † Miami University. ‡ Cambridge University. § University of British Columbia. (1) (a) Knobler, C. M. Science 1990, 249, 870. (b) Andelman, D.; Brochard, F.; Knobler, C. M. In Micelles, membranes, microemulsions, and monolayers; Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; SpringerVerlag: New York, 1994; pp 559-602. (2) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381.
Another structural arrangement that can achieve reduction in electrostatic repulsion is the formation of a curved structure resembling spherical or cylindrical micelles that form within bulk aqueous solutions of surfactants. Recently, it has been shown that the formation of such curved surfactant structures is not limited to bulk aqueous solutions. For example, using atomic force microscopy, Manne and co-workers have made an intriguing discovery of curved assemblies of ionic surfactants at water-solid interfaces involving various solid supports.3 The structures they observed include hemicylinders, full cylinders, and spheres. They have been able to rationalize the observed structures in terms of the hydrophilicity of the solid surface. At the interface between water and a hydrophobic surface, for instance, they found that some surfactants can form hemicylinders. A recent computer simulation supports this result.4 If the driving forces for the formation of such novel structures are hydrophobic and hydrophilic interactions, would such surfactant structures also form on the surface of liquid water, i.e., at the liquid-vapor interface of water? If these structures indeed form, how does the dynamic nature of the underlying liquid phase affect the shape and the stability of assembled structures? Is it possible to control or utilize the formation of such structures? In this paper, we report the results of molecular dynamics simulations of a monolayer of sodium laurate (dodecanoate) on water, in which curved, dynamic, structural patterns of surfactant assemblies were observed. In addition to a laurate soap monolayer on pure water, we also simulated the same soap monolayer on salty water to investigate the effect of electrostatic screening on the interfacial structures of the soap monolayer. Our results indicate that dissolved salt suppresses the formation of these structural patterns. Methods A classical molecular dynamics simulation method using the Verlet algorithm5 was used in the present study. Nose´(3) (a) Manne, S.; Gaub, H. E. Science 1995, 270, 1480. (b) Manne, S. Prog. Colloid. Polym. Sci. 1997, 103, 226. (4) Bandyopadhyay, S.; Shelley, J. C.; Tarek, M.; Moore, P. B.; Klein, M. L. J. Phys. Chem. B 1998, 102, 6318. (5) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Clarendon: Oxford, 1987.
10.1021/la990704q CCC: $19.00 © 2000 American Chemical Society Published on Web 10/12/1999
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Hoover thermostats6 were used to maintain a constant temperature of 298 K. Interactions among the components of the system were modeled using effective empirical potentials. Water molecules are represented by the SPC/E water model,7 and Na+-water and Cl--water interaction parameters are adapted from Chandrasekhar et al.8 with minor modifications to make them suitable for use with the SPC/E water model. For laurate ions (CH3(CH2)10COO-), we used a polarizable model that has been developed and tested for sodium octanoate micellar systems in aqueous solution.9 The 42 sites that were used to model one laurate ion can be divided into two types: 14 normal sites and 28 polarization sites. The normal sites are atomic or pseudoatomic sites. A site is used for each of the carbon and oxygen atoms in the headgroup. Each of the CH2 groups along the alkyl chain as well as the terminal CH3 group are represented by single pseudoatomic sites. All bond lengths are fixed using the SHAKE algorithm,10 while bond angles and torsional angles may vary under potentials taken from the literature.11 In addition to the normal sites, a pair of polarization sites are located at equal distances from, but on opposite sides of, each of the 14 normal sites in the laurate ion. Each pair is an electric dipole; that is, they carry charges of the same magnitude and opposite sign. The intercharge distance of a dipole is fixed at 0.3 Å. The magnitude of the charges and the orientation of a dipole change in response to the local electric field during the simulation. A more detailed description of the polarizable model can be found in ref 12. The simulation box in this study has a rectangular shape, measuring 40 Å × 40 Å × 49 Å. The longer side (z axis) is in the direction perpendicular to the plane of water surface. System A consists of 1340 water (H2O) molecules, 32 laurate ions (CH3(CH2)10COO-), and 32 Na+ counterions. System B consists of 1324 water, 32 laurate, 40 Na+, and 8 Cl- ions. In both systems, surface area per laurate ion is 50 Å2, which was chosen to roughly match the experimentally determined monolayer coverage.13,14 The salt concentration in system B would be 0.3 M, if Na+ and Cl- ions were uniformly distributed in water. We are not aware of any evidence that the composition of a solution very near an interface should be the same as the bulk composition, and it is possible that system B more appropriately models a salt solution with a NaCl concentration significantly lower than 0.3 M. To imitate the bulk system, we employed three-dimensional periodic boundary conditions; that is, the simulation box was replicated an infinite number of times in all three dimensions. Ewald sums were used to treat the long-range electrostatic interactions. Short-range interactions (the van der Waals interactions and the real space part of the Ewald sums) were cut off at 15 Å. We used a time step of 2.5 fs. (6) Hoover, W. G. Phys. Rev. 1985, A31, 1695. (7) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6259. (8) Chandrasekhar, J.; Spellmeyer D. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1984, 106, 903. (9) (a) Shelley, J. C.; Sprik, M.; Klein, M. L. Prog. Colloid Polym. Sci. 1997, 103, 146. (b) Shelley, J. C.; Sprik, M.; Klein, M. L. Langmuir 1993, 9, 916. (10) Rychaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327. (11) van der Ploeg, P.; Berendsen, H. J. C. J. Chem. Phys. 1982, 76, 3271. (12) Sprik, M. Metals in Solution. J. Phys. IV 1991; 1, 99-102. (13) Trevino, L.; Postel, M.; Riess, J. G. J. Colloid Interface Sci. 1994, 166, 414. (14) von Voorst Vader, F. Trans. Faraday Soc. 1960, 56, 1067.
Figure 1. Snapshots of a configuration of system A (soap monolayer on pure water) after 408 ps of simulation: (a) side view; (b) top view; (c) top view with highlighted headgroup oxygen atoms. Oxygen and hydrogen atoms of water are black and white; Na+ ions, gray; oxygen atoms in the laurate headgroup, dark gray; carbon and hydrocarbon in the laurate, gray.
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Figure 2. Snapshots of another configuration of system A (soap monolayer on pure water) after 468 ps of simulation: (a) side view showing curved laurate assemblies; (b) top view with highlighted terminal CH3 groups. The color scheme is the same as used in Figure 1.
Initially, a smaller system with a simulation box of size 20 Å × 20 Å × 49 Å was prepared by arranging 335 water molecules and 8 Na+ ions on arbitrarily chosen lattice points and placing 8 laurate ions on top of one of the 20 Å × 20 Å water surfaces. This system was simulated for 900 ps to ensure that it was well equilibrated. This configuration S was used to prepare the initial configuration of the two main systems, A and B. We quadruplicated the volume of the simulation box by duplicating in each of the x and y directions to yield system A. This system was then simulated for 614 ps. The initial configuration for system B, involving salty water, was prepared by replacing 4 water molecules of the configuration S by 2 pairs of Na+ and Clions. This system was simulated for 1.1 ns, before it was replicated in the same way as described above, giving the
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Figure 3. Snapshots of a configuration of system B (soap monolayer on salty water) after 1 ns of simulation: (a) side view; (b) top view with highlighted terminal CH3 groups. The color scheme is the same as used in Figure 1.
initial configuration for system B, which was then simulated for 1 ns. Results and Discussion We found that the surface of the water coated with sodium laurate is quite rough. The carboxylate headgroups are solvated by at least one shell of water molecules. The majority of sodium ions are closely associated with the oxygen atoms in the headgroups, forming solventseparated ion pairs. The rest of the sodium ions are distributed throughout the solution. No contact ion pairs between Na+ and carboxylate headgroups have been found, in agreement with previous simulation9 and experimental15 studies involving sodium octanoate micelles. Snapshots showing the side and top views of system A are shown in Figure 1. At first sight, the top view in Figure
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Figure 4. Snapshots including an isodensity surface to define the local shape of the water surface: (a) configuration of system A, (b) configuration of system B. Water molecules are colored blue; oxygen atoms in the laurate headgroup, red; carbon and hydrocarbon in the laurate, gray.
1b may suggest that the surface coverage of laurate ions used in this simulation may be less than a monolayer. To examine this possibility, we plotted the top view of the same configuration showing only the water molecules and the headgroup oxygen atoms in Figure 1c. This clearly shows that the headgroup distribution is uniform over the surface and supports the idea that the coverage we adapted from previous experimental studies13,14 is adequate for a monolayer. The contrast between the spatial distribution of heads and tails shown in parts b and c of Figure 1 in fact provides a key to understanding the structural patterns that we report in this paper. While the optimum packing of linear alkanes is achieved at a cross-sectional area of roughly 25 Å2 per molecule, carboxylate headgroups require at least twice as much area in aqueous solutions, due to electrostatic repulsions and solvation. While the surface density at saturation is largely dictated by the requirement for the headgroups to be sufficiently far apart, the tails optimize their dispersion interactions by aggregating together. This leads to the curved structure in which hydrocarbon tails are more densely packed than the headgroups. In some configurations, the grouping of tails leads to obvious patterns, as shown in Figure 2. The side view of such a configuration shown in Figure 2a suggests that laurate ions are forming either hemispherical or hemicylindrical structures. As shown in the top view, Figure 2b, of the same configuration, the aggregate structure appears to be somewhat closer to a hemicylindrical structure rather than a hemispherical structure. The highlighted terminal CH3 groups clearly illustrate the grouping of hydrocarbon chains. The structure is not (15) (a) Wennerstro¨m, H.; Lindman, B. Phys. Rep. 1979, 52, 1. (b) Lindman, B.; Wennerstro¨m, H. Topics in Current Chemistry; Springer: New York, 1980; Vol. 87.
stationary but disappears and reappears in different regions in a very dynamic manner characteristic of the liquid state. It has been proposed that the geometry and the curvature of surfactant assemblies may be understood in terms of surfactant packing parameter, V/a0lc, where V is the volume of the hydrocarbon chain, a0 is the optimal surface area, and lc the critical chain length.16 For a laurate ion that has 12 carbon atoms, lc is 16.7 Å and V is 350.2 Å3 according to Tanford’s equations.17 Setting a0 to 50 Å2 (area per laurate ion in a monolayer) results in the packing parameter of 0.42, which indicates a preference for cylindrical micelles (packing parameter of 1/3 to 1/2). This reasoning suggests that a monolayer structure with this surface density could have as much curvature as present in cylindrical micelles. If the electrostatic repulsion among ionic headgroups is key to the formation of curved self-assembled structures, added salt should have significant impact on the structure by screening electrostatic interactions. Figure 3 shows a typical configuration from the simulation of system B, a laurate monolayer on salty water. During our simulation (1 ns), we have not found any configuration with a clear grouping of the laurate hydrocarbon tails. To compare the roughness of the water-surfactant interface, we analyzed the shape of local water surface using a reference surface that followed the local density of the water.18 Snapshots of systems A and B with such an isodensity surface of water in Figure 4 show that the roughness of the surface of water is somewhat reduced in system B. (16) Israelachvili, J. N. Intermolecular and Surface forces, 2nd ed.; Academic Press: San Diego, CA, 1992. (17) Tanford, C. The hydrophobic effect; John Wiley & Sons: New York, 1973. (18) Shelley, J. C. Ph.D. Thesis, University of Pennsylvania, 1992.
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reached, the soap monolayer becomes curved due to geometric packing, resulting in the increased thickness of the headgroup region. The structural pattern we found is somewhat reminiscent of the wavelike structure reported in an earlier simulation of C16TACl (hexadecyltrimethylammonium chloride) monolayer at the air-water interface.19 However, a more recent simulation on a closely related system, C14TAB (tetradecyltrimethylammonium bromide) monolayer,20 did not find the wavelike structure. The differences in these simulation results may be due to one or a combination of subtle effects such as a higher fraction of bromides21 in the immediate vicinity of the headgroups, the chain length of the surfactants, or the size of the simulation box (see below). The characteristic time scale for variation in these patterns is on the order of 100 ps, making it difficult to consistently observe them in simulations.
Figure 5. Surface profiles at the air-water interface (a) and at the water surface covered by a soap monolayer (b). The z axis is perpendicular to the monolayer, starting from the bottom of Figure 4. Calculated surface profiles for system A (soap monolayer on pure water) are plotted with filled squares and those for system B (soap monolayer on salty water) with open triangles. The two peaks in the surface profile of system B are fitted to Gaussian line shapes with σ ) 1.4 Å (for the air-water interface, in (a)) and σ ) 2.15 Å (for the water surface covered by a soap monolayer, in (b)). The predicted surface profile for a perfect hemicylindrical surface is plotted with solid line in (b).
In an attempt to quantify the surface roughness, we determined the surface profile (shown in Figure 5) which is a plot as a function of z of the distribution of points that lie on the isodensity surface such as shown in Figure 4. In both systems, A and B, the water surface covered by a soap monolayer is rougher than the air-water interface. The surface profile has a Gaussian-shaped peak with σ of 1.4 Å at the air-water interface (Figure 5a) in both systems. The surface profile at the surface covered by a soap monolayer (Figure 5b) is different in the two systems: In system B (soap monolayer on salty water), this peak is roughly 50% broader than the peak at the air-water interface but is still close to a Gaussian shape. In system A (soap monolayer on pure water), this peak is somewhat broader than the corresponding peak in system B. More significantly, it is skewed toward the water region, consistent with hemicylindrical pattern formation. An idealized surface profile, predicted from a perfectly hemicylindrical surface without thermal fluctuations, is also plotted in Figure 5b for comparison. Our results do not contradict the findings of neutron reflectivity measurements2 that indicate that the thickness of the headgroup region of the ionic surfactant monolayer increases with increasing surface density of surfactants near the saturation density. The structural patterns we found present an alternative explanation for such increased thickness. As the saturation density is
Conclusion The dynamic surfactant structures we observed are held together by weak intermolecular forces such as dispersion interactions and other electrostatic interactions. They are structurally similar to the surfactant aggregates which form within the aqueous solutions. We can only study structures on length scales shorter than the simulation box, 40 Å. The artificial periodicity imposed by the boundary conditions used in a simulation may have impact on the relative stability of competing structures. In extreme cases, artificial structures entirely due to the boundary conditions or the suppression of a real structure due to the mismatch with the box size might occur. A more complete picture of these structures would likely emerge from the simulation of a bigger system, which we plan to do in the future. To the best of our knowledge, no experimental observations have been reported for structures such as those we describe in this paper. Could these structures be observed in future experiments? We note that there are a few obstacles that need to be overcome. First, the surfactant structures that we found are very dynamic, appearing and disappearing on sub-nanosecond time scales. As a result, these structures would escape detection by any of the imaging techniques that require structural stability in time or that yield structural information averaged over more than 100 ps. Second, it would be essential to have a gentle, nondestructive experimental technique, as these structures are induced by weak intermolecular interactions. Our results point out the danger of assuming that interfaces are uniform and flat. The structures of surfactant assemblies are closely correlated with the rough structure of underlying water surface at the molecular level. The curved structure we found in this simulation bears resemblance to the cylindrical structure predicted by the model developed for surfactant structures in bulk aqueous solution. The reason this model can be useful for our system may lie in the common underlying physics of the collective interactions of ionic surfactants and water. Acknowledgment. We thank Dr. Roger Sayle for making RasMol freely available. We used RasMol to produce Figures 1, 2, and 3 in this article. LA990704Q (19) Bo¨cker, J.; Schlenkrich, M.; Bopp, P.; Brickmann, J. J. Phys. Chem. 1992, 96, 9915. (20) Tarek, M.; Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1995, 99, 1393. (21) Bongiovanni, R.; Ottewill, R. H.; Rennie, A. R.; Laughlin, R. G. Langmuir 1996, 12, 4681.
