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Monte Carlo Simulation of the Adsorption Equilibrium of a Model Surfactant Solution on Hydrophilic Solid Surfaces U. Reimer,* M. Wahab, P. Schiller, and H.-J. Mo¨gel* Department of Physical Chemistry, Technical University Freiberg, Leipziger Strasse 29, 09596 Freiberg, Germany Received June 6, 2001. In Final Form: October 10, 2001 We performed Monte Carlo simulations to study the adsorption behavior of a small flexible model surfactant on hydrophilic surfaces. A coarse-grained lattice model was used to account for excluded-volume effects and nearest-neighbor interactions. The model predicts adsorption isotherms that agree qualitatively with experimental results. The results of the simulation complete and support experimental structure investigations made with AFM, ellipsometry, and neutron reflectometry. Adsorbed bilayer structures depend on the adsorption energy. The efficiency of hydrophobization and the shielding against small polar molecules increase strongly with increasing surfactant concentration.
1. Introduction Surfactant solutions exposed to a hydrophilic surface are capable of forming adsorption layers at the liquid/ solid interface. Such solid-supported layers attract considerable interest because of the increasing number of their technological applications such as colloid stability, froth flotation, enhanced oil recovery, detergency,1-3 filtration,4 lubrication,5 electrochemistry,6 sensors,7-10 nanofabrication,11,12 and synthesis of ceramic materials13 and composites.14 Furthermore, adsorption of lipids is widely used to form model biological membranes.15-18 Mesoscopic structures of these membranes can be investigated by several experimental techniques.19-24 The (1) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1997. (2) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain; VCH: New York, 1994. (3) Jo¨nsson, B.; Lindman, B.; Holmberg, K.; Kronberg, B. Surfactants and Polymers in Aqueous Solution; John Wiley & Sons: New York, 1998. (4) Bakx, A.; Timmerman, A.; Frens, G. Colloid Polym. Sci. 2000, 278, 418. (5) Lio, A.; Charych, D. H.; Salmeron, M. J. Phys. Chem. B 1997, 101, 3800. (6) Jaschke, M.; Butt, H.-J.; Gaub, H. E.; Manne, S. Langmuir 1997, 13, 1381. (7) Nikolelis, D. P.; Pantoulias, S. Biosens. Bioelectron. 2000, 15, 439. (8) Nikolelis, D. P.; Hianik, T.; Krull, U. J. Electroanalysis 1999, 11, 7. (9) Fisher, M. I.; Tja¨rnhage, T. Biosens. Bioelectron. 2000, 15, 463. (10) Salafsky, J.; Groves, J. T.; Boxer, S. G. Biochemistry 1996, 35, 14773. (11) Xu, S.; Miller, S.; Laibinis, P. E.; Liu, G. Langmuir 1999, 15, 7244. (12) Messer, B.; Song, J. H.; Huang, M.; Wu, Y.; Kim, F.; Yang, P. Adv. Mater. 2000, 12, 1526. (13) Liu, J.; Kim, A. Y.; Wang, L. Q.; Palmer, B. J.; Chen, Y. L.; Bruinsma, P.; Bunker, B. C.; Exarhos, G. J.; Graff, G. L.; Rieke, P. C.; Fryxell, G. E.; Virden, J. W.; Tarasevich, B. J.; Chick, L. A. Adv. Colloid Interface Sci. 1996, 69, 131. (14) Jung, M.; German, A. L.; Fisher H. R. Colloid Polym. Sci. 2000, 278, 1114. (15) Sackmann, E. Science 1996, 271, 43. (16) Plant, A. L. Langmuir 1999, 15, 5128. (17) Ulman, A. An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-Assembly; Academic Press: New York, 1991. (18) Rapuano, R.; Carmona-Ribeiro, A. M. J. Colloid Interface Sci. 1997, 193, 104. (19) Manne, S.; Cleveland, J. P.; Gaub, H. E.; Stucky, G. D.; Hansma, P. K. Langmuir 1994, 10, 4409. (20) Hui, S. W.; Viswanathan, R.; Zasadzinski, J. A.; Israelachvili, J. N. Biophys. J. 1995, 68, 171.
thermodynamic equilibrium between the surfactant solution and the phase of adsorbed amphiphilic molecules is balanced by a complex interplay of hydrophobic interactions in the solution volume, the competition between adsorption of water and surfactants, and the self-assembly of amphiphilic molecules near the solid surface. Adsorption layers at the interface between aqueous solutions and hydrophilic solid surfaces display various phase structures that give rise to different interface properties. In recent years, different analytical methods have been used to detect layer structures and properties on a mesoscopic scale in the lateral direction and on a molecular scale in the normal direction. In particular, application of the AFM method has contributed to the knowledge about the structure and properties of self-assembled adsorbed layers of surfactants.6,25,26 Thermodynamic and statistical theories have been developed to describe these systems. To interpret experimental data, one has to understand how molecular and surface parameters correlate with layer properties. As this problem is quite complex, the application of analytical theories requires essential approximations. In particular, the evaluation of statistical integrals is impossible if a specific molecular shape is taken into account. Therefore, computer simulations are useful for completing theoretical considerations on the phase structure and properties of complex systems. During the past 10 years, it has been demonstrated that Monte Carlo simulations of coarse-grained lattice models can map many qualitative and semiquantitative features of self-assembled structures formed by amphiphilic molecules in aqueous solutions.27-39 Recently, molecular dynamics40 (21) Leonenko, Z. V.; Carnini, A.; Cramb, D. T. Biochim. Biophys. Acta 2000, 1509, 131. (22) Tiberg, F. J. Chem. Soc., Faraday Trans. 1996, 92, 531. (23) Pashley, R. M.; Israelachvili, J. N. J. Colloid Interface Sci. 1984, 101, 511. (24) McGuiggan, P. M.; Pashley, R. M. J. Colloid Interface Sci. 1988, 124, 560. (25) Dong, J.; Mao, G. Langmuir 2000, 16, 6641. (26) Sakai, H.; Nakamura, H.; Kozawa, K.; Abe, M. Langmuir 2001, 17, 1817. (27) Harris, J.; Rice, S. R. J. Chem. Phys. 1988, 88, 1298. (28) Larson, R. G. J. Chem. Phys. 1988, 89, 1642. (29) Larson, R. G. J. Chem. Phys. 1992, 96, 7904. (30) Brindle, D.; Care, C. M. J. Chem. Soc., Faraday Trans. 1992, 88, 2163. (31) Wijmans, C. M.; Linse, P. Langmuir 1995, 11, 3748. (32) Gelbart, W. M.; Ben-Shaul, A. J. J. Phys. Chem. 1996, 100, 13169.
10.1021/la010846w CCC: $20.00 © 2001 American Chemical Society Published on Web 12/01/2001
Monte Carlo Simulation of Adsorption Equilibrium
and Monte Carlo41 simulations for coarse-grained offlattice models have confirmed that the self-assembly of surfactants is not induced by the underlying lattice but arises as a result of the effective hydrophobic interactions. The hydrophobic effect resulting from many different subtle interaction energies and entropic contributions to the free energy can be represented in terms of only a few effective nearest-neighbor interactions, which give rise to self-assembly into monolayers, bilayers, micelles, tubular phases, sponge phases, and vesicles. To obtain these structures, it is sufficient to apply the excluded-volume condition and an effective repulsion interaction between hydrophobic segments and water or hydrophilic molecular segments. Using a coarse-grained lattice model,29,31 we present results of Monte Carlo simulations of the self-assembly of amphiphilic molecules under the conditions of thermodynamic equilibrium between a three-dimensional surfactant solution and the quasi-two-dimensional phase adsorbed on a hydrophilic solid surface. We address the question of the connection between adsorption isotherms at different temperatures and the properties of interface layers resulting from the self-assembly of flexible amphiphilic molecules. The density profile, thickness, and molecular orientational order of the layer have been determined. The influence of the adsorption strength on the layer symmetry and other properties has been studied. Properties that are important for technical applications, such as hydrophobicity, roughness, and protection capability against small hydrophilic molecules, have been obtained as functions of surfactant concentration and temperature. 2. Model and Simulation Details An amphiphilic molecule consists of one hydrophilic head connected to two hydrophobic tail segments. In the framework of the lattice model, this is the smallest flexible molecule. Each segment occupies one lattice site in a simple cubic lattice of size Lx × Ly × Lz ) 48 × 48 × 48. Empty sites represent water as the solvent. Periodic boundary conditions are applied for the x and y directions. The bottom of the simulation box at z ) 0 represents a smooth hydrophilic surface, while the upper surface of the box (z ) 47) is a wall of impenetrable water sites. In addition to the excluded-volume condition, only nearest-neighbor interactions are taken into account. This resembles screened electrostatic interactions with small Debye lengths of i N(N - 1)
(6)
where the angles θi,j are measured between the end-end vectors of different molecules. The end-end vector is defined as the vector from the head segment to the last tail segment of the molecule. The molecules in layer A exhibit a much higher orientational order, whereas molecules at the solvent interface are generally less ordered. The lower the temperature, the larger the difference between the two sublayers. Hence, the particularly thick bilayer at T ) 0.9 is connected to a highly ordered layer A, where most of the molecules stand upright at the solid surface. The molecules in layer B are generally less ordered in both thin and thick bilayers. At T ) 1.3, a significant orientational order can only be detected in layer A above the percolation threshold. The hydrophobic cores of all bilayers, bilayer patches, and admicelles consist of interdigitated hydrophobic chains. As an example, cross sections of snapshots of a bilayer and an admicelle are shown in Figure 9. An interdigitated structure of adsorbed bilayers was verified by neutron reflection studies.25 For
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Figure 12. Orientational order S at different adsorption energies and T ) (a) 0.9, (b) 1.1, and (c) 1.3.
temperatures above T ) 1.0, the interfacial bilayer is quite rough and often connected to elongated micelles extending into the bulk solution. This can be regarded as a confirmation of the structures proposed for the explanation of the unusually long-range repulsive forces between coated mica surfaces.57 Surfactant layers are commonly used to protect solid surfaces against oxidation and hydrolysis. This is especially important for highly disperse powders. Therefore, a complete shielding of the surface against small hydrophilic molecules is desired. In our simulations, the surface is never completely covered with molecules in the sense that every lattice site at the surface is occupied by an amphiphile. Even after the transition of the film thickness from 4 to 5 lattice units at T ) 0.9, at least 15% of the surface is covered by water. To characterize the surface protection, we calculated the number of surface sites connected with the bulk solution via pores in the adsorption layer. A pore consists of adjacent lattice sites occupied by water and can have any shape. The results in Figure 10 show that very effective shielding of the surface occurs only for thick adsorption layers. For all other temperatures, complete protection of the surface is impossible even at higher concentrations. Surfactant adsorption is widely used to make solid surfaces more hydrophobic, e.g., for application to froth flotation or colloid stabilization. In the framework of our model, the surface hydrophobicity was calculated by counting the fraction of hydrophobic sites of the adsorbed aggregates in contact with bulk solution in the normal direction. Independent of temperature, the maximum achievable hydrophobicity is 55%, as shown in Figure 11. At low temperatures, the fraction of hydrophobic surface reaches a maximum, and at the thickness transition, it decreases to about 40%. At intermediate temperatures, the hydrophobicity jumps from a low value to a plateau value just below the cmc. At higher temperatures, the hydrophobicity increases continuously with increasing surface coverage. With varying surfactant concentration in froth-flotation experiments, a pronounced maximum of the flotation rate was measured.58-60 This corresponds to the concentration dependence of the hydrophobicity at low temperatures in our simulations. Until now, the adsorption energy (headsurface interaction) was chosen to be equal to the other interaction parameters for the sake of simplicity. Experimental work is often carried out on different surfaces. Especially in the case of ionic amphiphiles adsorbed on oppositely charged surfaces, the adsorption strength can reach high values. To describe the influence of the substrate on the surface aggregates, we varied the adsorption energies for the three temperatures T ) 0.9, 1.1, and 1.3. In these simulations, the number of molecules was held constant at N ) 3686 (β ) 0.1) for the first two temperatures and at N ) 7066 (β ) 0.2) for T ) 1.3. With (57) Giasson, S.; Kuhl, T. L.; Israelachvili, J. N. Langmuir 1998, 14, 891.
Figure 13. Fraction of shielded surface AS (i.e., surface that is not accessible via pores) versus adsorption energy (arrows indicate transition from thin to thick bilayers).
increasing temperature, the minimum attractive energy required to form adsorption layers increases. A common feature of adsorption layers at all temperatures is that, with increasing adsorption energy, their asymmetry increases. At T ) 0.9, the adsorbed bilayer is generally 5 lattice units thick, and with increasing adsorption strength, the orientational order in layer B decreases, whereas it increases in layer A. At higher temperatures, the orientational order in layer A increases, whereas layer B remains unchanged. Above a certain surface concentration threshold, the layer thickness increases from 4 to 5 lattice units (Figure 12). Again, only a thick bilayer is able to shield the surface effectively, as shown in Figure 13. 4. Conclusions We performed Monte Carlo simulation studies of the adsorption equilibrium of aqueous surfactant solutions on a solid/liquid interface using a coarse-grained lattice model with excluded-volume and nearest-neighbor interactions. The amphiphilic model molecule used consists of three segments and represents the smallest-possible flexible molecule. The simulation results provide adsorption isotherms similar to those found in experiments. Various thermodynamic and structural properties of the interface layers were calculated and visualized. On the solid hydrophilic surface, phases that are topologically similar to those in the three-dimensional volume phase without an adsorbing surface are obtained. The phase diagram for the quasi-two-dimensional interface region is shifted to lower temperatures compared to the corresponding diagram for three-dimensional surfactant solutions. The surface adsorption energy plays the role of an external field that changes quantitative structural phase (58) Schwarz, R.; Heckmann, K.; Strnad, J. J. Colloid Interface Sci. 1988, 124, 50. (59) Pitsch, M.; Heckmann, K.; Kohler, H.-H.; Strnad, J. Prog. Colloid Polym. Sci. 1988, 77, 152. (60) Strnad, J.; Kohler, H.-H.; Heckmann, K.; Pitsch, M. J. Colloid Interface Sci. 1989, 132, 283.
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properties including the variation of the layer thickness. Layer structures are asymmetric in the direction normal to the solid surface with respect to density and orientational order. This asymmetry increases with increasing adsorption energy. The simulation results explain the nonmonotonic dependence of the flotation rate on the surfactant concentration found experimentally at various temperatures. The protective effect of surfactant layers against hydrolysis and oxidation on small powder particles is evaluated for different temperatures and volume surfactant concentrations. Saturation at relatively low concentration thresholds is observed. Complete shielding against the penetration of small polar molecules through the layer can be obtained because fluctuations in the layer
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density of the inner hydrophobic part are small. In the immediate vicinity of the solid surface, water molecules are fixed, and channels through the hydrophobic layer region are not formed at low temperatures. At higher temperatures, there is a different adsorption regime that prevents an effective shielding of the surface against polar molecules by the surfactant layer. Acknowledgment. The authors thank K. Heckmann (Regensburg) for useful discussions. Financial support of the Deutsche Forschungsgemeinschaft (SFB 285) is gratefully acknowledged. LA010846W
