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Monte Carlo Study of Surfactant Adsorption on Heterogeneous Solid Surfaces U. Reimer, M. Wahab, P. Schiller, and H.-J. Mo¨gel* Department of Physical Chemistry, Freiberg University of Mining and Technology, Leipziger Strasse 29, 09596 Freiberg, Germany Received August 25, 2004. In Final Form: November 8, 2004 The equilibrium between free surfactant molecules in aqueous solution and adsorbed layers on structured solid surfaces is investigated by lattice Monte Carlo simulation. The solid surfaces are composed of hydrophilic and hydrophobic surface regions. The structures of the surfactant adsorbate above isolated surface domains and domains arranged in a checkerboard-like pattern are characterized. At the domain boundary, the adsorption layers display a different behavior for hydrophilic and hydrophobic surface domains. For the checkerboard-like surfaces, additional adsorption takes place at the boundaries between surface domains.
Introduction Surfactant adsorption on solid surfaces is widely used in many technical applications, i.e., in wetting, adhesion, detergency, dispersion stability, ore flotation, nanofabrication, and synthesis of ceramic materials and composites.1-6 The technical importance of adsorbed surfactant layers results from peculiar properties of their phase structure. Solid surfaces structured on the nanometer scale are presently assumed to play a key role in the development of new electronic devices, sensor materials, or surfaces with special wetting properties.7-16 Nanometer structures can either be based on chemical heterogeneity and/ or surface roughness. Apart from artificial structured surfaces, many technically important surfaces are heterogeneous.1,17-19 The heterogeneities are mainly caused by chemical impurity inclusions, surface functional groups, lattice defects, or peculiar binding sites. The adsorption behavior of surfactants is strongly influenced if the dimension of the surface pattern (or defects respectively) reaches the size of the surfactant molecules. In an experimental work, it was shown20 that self-assembled monolayers on modified silicon surfaces change from (1) Hankins, N. P.; O’Haver, J. H.; Harwell, J. H. Ind. Eng. Chem. Res. 1996, 35, 2844. (2) Xu, S.; Miller, S.; Laibinis, P. E.; Liu, G. Langmuir 1999, 15, 7244. (3) Messer, B.; Song, J. H.; Huang, M.; Wu, Y.; Kim, F.; Yang, P. Adv. Mater. 2000, 12, 1526. (4) Jung, M.; German, A. L.; Fisher, H. R. Colloid Polym. Sci. 2000, 278, 1114. (5) Jo¨nsson, B.; Lindmann, B.; Holmberg, K.; Kronberg, B. Surfactants and Polymers in Aqueous Solution, 1st ed.; Wiley: Chichester, 1998. (6) Kielbassa, S.; Kinne, M.; Behm, R. J. Langmuir 2004, 20, 6644. (7) Piner, R.; Zhu, J.; Xu, F.; Hong, S.; Mirkin, C. Science 1999, 283, 661. (8) Liu, G.-Y.; Xu, S.; Oian, Y. Acc. Chem. Res. 2000, 33, 457. (9) Kato, T.; Kameyama, M.; Ehara, M.; Limura, K. Langmuir 1998, 14, 1786. (10) Fang, J.; Knobler, C. M. Langmuir 1996, 12, 1368. (11) Thurn-Albrecht, T.; Steiner, R.; DeRouchev, J.; Stafford, C. M.; Huang, E.; Bal, M.; Tuominen, M.; Hawker, C. J.; Russell, T. P. Adv. Mater. 2000, 12, 2000. (12) Fadeev, A. Y.; McCarthy, T. Langmuir 1999, 15, 7238. (13) Mauthauer, K.; Frank, C. W. Langmuir 1993, 12, 3446. (14) Offord, D.; Griffin, J. H. Langmuir 1993, 9, 3015. (15) Cho, G.; Jang, J.; Jung, S.; Moon, I.-S.; Lee, J.-S.; Cho, Y.-S.; Fung, B. M.; Yuan, W.-L.; O’Rear, E. A. Langmuir 2002, 18, 3430. (16) Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. Langmuir 2004, 20, 3824. (17) Modaressi, H.; Garnier, G. Langmuir 2001, 18, 642. (18) Sevastinov, V.; Kulik, E.; Kalinin, I. J. Colloid Interface Sci. 1991, 145, 191. (19) Rudzinski, W.; Haber, J. Appl. Surf. Sci. 2002, 196, 1.
continuous layer to island structures when the surface becomes partly hydrophobized. A recent Monte Carlo (MC) simulation of wetting on nanopatterned surfaces21 revealed evidence for dramatic change in wetting behavior if the lateral dimension of the surface pattern is comparable to the size of the molecules. To describe the selfassembly of surfactants in combination with adsorption, one has to understand the relationship between molecular surfactant properties, surface characteristics, and adsorption thermodynamics. The analogy between hydrophobic association behavior in the bulk solution and on solid surfaces is generally accepted.22,23 Over the past two decades, some general thermodynamic features of surfactant adsorption such as a principal form of adsorption isotherms were found.24-27 To describe adsorption isotherms from thermodynamic theory, the knowledge of the shape of all possible aggregates is required.28,29 Most thermodynamic and statistical theories allow for surface heterogeneity by patchwise summation of homogeneous domains and averaging the surface properties, neglecting domain boundary and superposition effects.1,30 In addition to analytic approaches, computer simulation methods are capable of contributing to better understanding of adsorption effects on heterogeneous surfaces. As a consequence of limited computation time, models with serious simplifications are used. Systems with realistic interaction potentials are restricted to relatively small numbers of molecules, since most of the effort is spent to calculate the behavior of the solvent. For small subsystems, it is possible to calculate the bulk structure of water by ab initio methods.31 Gas adsorption on heterogeneous surfaces has been studied with density functional theory (DFT) tech(20) Foisner, J.; Glaser, A.; Leitner, T.; Hoffmann, H.; Friedbacher, G. Langmuir 2004, 20, 2701. (21) Schneemilch, M.; Quirke, N.; Henderson, J. R. J. Chem. Phys. 2004, 120, 2901. (22) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain, 1st ed.; VCH: New York, 1992. (23) Israelachvili, J. N. Intermolecular and Surface Forces, 1st ed.; Academic Press: London, 1991. (24) Chandar, P.; Somasundaran, P.; Turro, N. J. J. Colloid Interface Sci. 1987, 117, 31. (25) Fan, A.; Somasundaran, P.; Turro, N. J. Langmuir 1997, 13, 506. (26) Bo¨hmer, M. R.; Koopal, L. K. Langmuir 1992, 8, 2649. (27) Bo¨hmer, M. R.; Koopal, L. K. Langmuir 1992, 8, 2660. (28) Nagarajan, R.; Johnson, R. A. Colloids Surf., A 2000, 167, 21. (29) Nagarajan, R.; Johnson, R. A. Colloids Surf., A 2000, 167, 31. (30) Cases, J. M.; Villieras, F. Langmuir 1992, 8, 1251. (31) Kuo, I.-F. W.; Mundy, C. J. Science 2004, 303, 658.
10.1021/la0478797 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/08/2005
Surfactant Adsorption on Heterogeneous Surfaces Table 1. Interaction Parameters segment i
segment j
interaction parameter i,j
head tail head tail head head tail water head tail water
head tail tail water water hydrophilic surface hydrophilic surface hydrophilic surface hydrophobic surface hydrophobic surface hydrophobic surface
0 0 1 1 0 -1 1 0 1 0 1
niques32 or molecular dynamics (MD) simulation.33 Systems with explicit solvent contain either very small nonsolvent molecules34 or are restricted in the case of MD simulations to a very short time scale.35-37 Coarse-grained latttice models have been shown to yield a satisfactory description of the adsorption and self-assembly of amphiphilic molecules from a surfactant solution.38-43 A recent MC simulation of the adsorption of chain molecules on heterogeneous surfaces yielded some interesting results but was restricted to two dimensions.44 The aim of this article is to present results about the self-assembly of surfactants on structured surfaces, where an aqueous solution is in equilibrium with the adsorbate. Model and Simulation Details The model is analogous to one used in previous papers on adsorption of surfactants from aqueous solution on solid hydrophilic43,45 and hydrophobic45 surfaces. We use a coarse-grained lattice model with a box size of Lx ) Ly ) Lz ) 48 lattice units. This box size was chosen to achieve a good compromise between the minimization of finite size effects and computing time. An amphiphilic molecule consists of a hydrophilic head connected to a flexible hydrophobic tail with two segments. Each segment occupies one lattice site of the simple cubic lattice. Empty lattice sites represent water as the solvent. Along the xand y-axis, the periodic boundary condition is applied. The layer at z ) 0 represents the flat structured solid surface. For z ) 47 a layer of impenetrable water sites is defined. Apart from the excluded volume condition, only nearest neighbor interactions are taken into account, which resemble screened electrostatic interactions with Debye lengths smaller than 3 nm. These effective interactions are repulsive between hydrophobic and hydrophilic segments and attractive between polar heads and hydrophilic surface sites (see Table 1). Basically a repulsion (32) Lischka, M. Adsorption of simple molecules on structured surfaces. Thesis, Technical University Munich, Munich, Germany, 2003. (33) Gelb, L. D.; Gubbins, K. E. Langmuir 1998, 14, 2097. (34) Neves, R. S.; Motheo, A. J.; Silva Fernandes, F. M. S.; Fartaria, R. P. S. J. Braz. Chem. Soc. 2004, 15 (2), 224. (35) Janezˇicˇ, D.; Praprotnik, M. J. Chem. Inf. Comput. Sci. 2003, 43, 1922. (36) Ferrara, P.; Apostolakis, J.; Caflisch, A. Proteins 2002, 46, 24. (37) Salaniwal, S.; Cui, S. T.; Cummings, P. T.; Cochran, H. D. Langmuir 1999, 15, 5188. (38) Flory, P. J. Principles of Polymer Chemistry, 1st ed.; Cornell University Press: New York, 1953. (39) Harris, J.; Rice, S. A. J. Chem. Phys. 1988, 88 (2), 1298. (40) Larson, R. G. J. Chem. Phys. 1992, 96, 7904. (41) Wijmans, C. M.; Linse, P. Langmuir 1995, 11, 3748. (42) Drefahl, A.; Wahab, M.; Schiller, P.; Mo¨gel, H.-J. Thin Solid Films 1998, 327-29, 846. (43) Reimer, U.; Wahab, M.; Schiller, P.; Mo¨gel, H.-J. Langmuir 2001, 17, 8444. (44) Cabral, V. F.; Abreu, C. R. A.; Castier, M.; Tavares, F. W. Langmuir 2003, 19, 1429. (45) Reimer, U. Monte-Carlo-Simulation der Adsorption amphiphiler Moleku¨le an Feststoffoberfla¨chen. Thesis, TU Bergakademie Freiberg, Freiberg, Germany, 2002.
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between polar and nonpolar segments is defined and hydrophobic surface sites are considered to be energetically equivalent to hydrophobic molecule segments. In simulations the Hamiltonian
H )
i,j∆i,j ∑ i 3, the value of Rphob decreases monotonically with increasing D. At T* ) 1.3 the hydrophilic environment is covered by admicelles and single surfactant molecules. The surface concentration above the hydrophobic domain is always larger than Rphil at this temperature regime. At D ) 3 the value of Rphob exhibits a maximum in Figure 2c and declines for larger domains. Obviously, molecules in the boundary region are more densely packed than in the undisturbed monolayer. This can also be seen in the plot of the local surface concentration R(x, y) in Figure 3. Additional surfactants are adsorbed at the boundary of the monolayer.
A similar effect of an increased surfactant adsorption on a heterogeneous surface was found in a DFT study.47 The effect was interpreted as an increase in configurational space for the surfactants at the boundary. At D ) 3 the hydrophobic domain consists mainly of domain boundary sites; therefore Rphob reaches a maximum value. For larger domains, the contribution of the boundary effect diminishes, but the surface concentration remains higher compared to a homogeneous surface. The boundary effects for the bilayer and the monolayer regime are summarized in Figure 4. This sketch explains intuitively why a bilayer patch below a critical size is not stable. For small domains, the available area would be insufficient to contain the plateau region depicted in Figure 4a. As suggested by Figure 1a,b, a hole is formed in the case of small hydrophilic domains. Surfactants adsorb randomly but do not aggregate. Small hydrophilic heterogeneities in a hydrophobic surface will therefore lead to a rupture of the surfactant layer and expose the hydrophilic surface to the solvent. Large hydrophilic heterogeneities will increase surfactant adsorption shielding the surface from an aqueous solvent. In contrast, the boundary regime of a monolayer consists of a region of increased surface concentration (Figure 4b). In the case of hydrophobic heterogeneities in a hydrophilic surface, the adsorption layer always remains intact with increased surface concentration at the border to the bilayer. The surface is always shielded from the solvent. Checkerboard Arrangement. Let the solid surface consist of hydrophilic and hydrophobic domains which are arranged in a checkerboard-like manner. The size of the domains varies between D ) 1 and D ) 24, while the fraction of hydrophilic (x1) and hydrophobic (x2) surface sites remains constant (x1 ) x2 ) 0.5). (47) Seidel, O. Berechnung und Modellierung von Schichten amphiphiler Moleku¨le auf ebenen Oberfla¨chen. Thesis, TU Bergakademie Freiberg, Freiberg, Germany, 2000.
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Figure 5. Total surface concentration above checkerboard surfaces. R is given in segments per surface lattice sites. The dashed lines represent the surface concentration of a hypothetical unstructured surface evaluated by eq 5.
First we can compare the overall adsorption on the checkerboard surface Rtotal with that of a hypothetical unstructured surface. The unstructured surface consists of one-half hydrophilic and one-half hydrophobic surface sites. The resulting surface concentration R°(T*) is calculated with data from Table 2 as
R°(T*) ) 0.5Rphob,°(T*) + 0.5Rphil,°(T*)
(5)
The average surface concentration as a function of the domain size is shown in Figure 5. In the case of small domains D < 6, there is a maximum of the surface concentration for all temperatures. For domains D > 6, two different scenarios can be distinguished. In the bilayer regime (T* ) 0.9 and T* ) 1.2), the surface concentration increases again with increasing domain size D. For large domains, a constant value of the surface concentration that is higher than the value expected for an unstructured surface is obtained. In the admicelle regime (T* ) 1.3), Rtotal diminishes below the value of an unstructured surface for D > 6. To separate the contribution of the hydrophilic and hydrophobic domains, the surface concentrations Rphil and Rphob are separately evaluated for hydrophilic and hydrophobic surface sites. The resulting plots are shown in Figure 6. At T* ) 0.9 the solid surface with the smallest domain size (D ) 1) is covered by a homogeneous bilayer. The hydrophobic surface sites cause some disturbance of the internal structure of the adsorption layer, but it is of statistical nature. The surface concentration above hydrophobic sites is on average a little lower than above hydrophilic sites. For domains 2 e D < 6, a heterogeneous bilayer structure is observed. At the boundary of the domains, surfactants adsorb flatly onto the surface with the head attached to hydrophilic and the tail attached to hydrophobic sites. Above hydrophobic domains, the second half of the bilayer consists of surfactants standing with their tail on the underlying surfactants. These molecules are packed very densely. The molecules above hydrophilic domains are less ordered and a few hydrophilic surface sites remain occupied by water; therefore the value of Rphil is lower than Rphob. Nevertheless, the surface remains completely shielded from the bulk solution. For large domains with D > 6, monolayers form on hydrophobic domains and bilayers on hydrophilic ones. The larger the domains, the less significant the effect of domain boundaries on the value of the surface concentration. At T* ) 1.2 a similar dependency of R on D can be observed in Figure 6b. For the smallest pattern with D ) 1, a homogeneous bilayer forms. The region of increased surface concentration above hydrophobic domains extends up to D ) 6. Here the critical size for a stable bilayer patch above hydrophilic domains is not reached. Therefore
Figure 6. Surface concentration R above a checkerboard surface with domain size D. The terms phil and phob denote the concentration above the hydrophilic and hydrophobic surface sites.
adsorption of surfactants takes place at the boundary of the hydrophilic domains, leaving most of the hydrophilic surface sites exposed to the bulk solution. In case of large domains D > 8, homogeneous bilayer patches form on hydrophilic domains. The structure is similar to the bilayer on a homogeneous hydrophilic surface. The hydrophobic domains are covered by monolayer patches. At T* ) 1.3 the coexistence of admicelles and gaslike adsorption of surfactants is observed for the smallest domain size D ) 1. For larger domains, monolayer patches form on hydrophobic sites, which exhibit the characteristic boundary effect drawn in Figure 4b. The surface concentration above hydrophilic lattice sites profits from increased concentration at the boundary, since surfactants adsorb with head on hydrophilic and with tail on hydrophobic sites. For larger domains D > 3, this effect declines and only gaslike adsorption is observed on hydrophilic domains. The different behavior of R(D) in the bilayer (T* ) 0.9 and T* ) 1.2) and the admicelle (T* ) 1.3) regime reflects a different overall structure of the adsorption layer. A plot of the local surface concentration in these two regimes is shown in Figure 7. All plots have a hydophobic domain in the upper left corner. For D ) 1 a homogeneous adsorption layer exists. At D ) 3 the local surface concentration is higher above hydrophobic lattice sites. Therefore the hydrophobic domains are recognized as dark squares. For large domains, the behavior of Rphil is different at T* ) 1.2 and T* ) 1.3. At D ) 8 the structure of the adsorption layer changes qualitatively as indicated by
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Figure 7. Local surface concentration R(x, y) above checkerboard surfaces. The solid surface is situated in the middle row. Black lattice sites are hydrophilic, and gray lattice sites are hydrophobic.
Figure 6b, where Rphil equals Rphob for T* ) 1.2. Above hydrophilic domains, small bilayer patches exist. They are “thicker” at the center as described by the sketch of the boundaries in Figure 4. Above hydrophobic domains, monolayer patches with an increased concentration at their boundary exist. At D ) 12 and T* ) 1.2, the surface concentration above hydrophilic domains is higher than above hydrophobic ones. In the admicelle regime at T* ) 1.3, the reverse picture results. The arrangement of surface domains in a checkerboard pattern changes the adsorption behavior of surfactants, because an interaction of the adsorbed molecules along sides and corners of the domains becomes evident. To quantify this additional adsorption effect, the difference of Rphil and Rphob for isolated domains and checkerboard domains is calculated as
∆Rphil(D) ) Rchecker (D) - Risol phil phil(D) isol ∆Rphob(D) ) Rchecker phob (D) - Rphob(D)
(6)
The resulting plots are shown in Figure 8. In the case of small domains D e 6, additional adsorption at the boundaries contributes significantly to the surface concentration for all temperatures. As mentioned before, the length of 6 lattice sites corresponds to twice the size of the surfactant molecules. At T* ) 0.9 there is an enormous increase of ∆Rphil and a decrease of ∆Rphob for small domains. The increase of ∆Rphil arises from the fact that small bilayer patches are not stable in the case of isolated domains. However, in the checkerboard arrangement
Figure 8. Difference of the surface concentration above isolated domains and checkerboard-like arrangement. ∆R(D) is evaluated by using eq 6.
small bilayer fragments are stabilized. This leads to a special structure where the surface concentration above hydrophobic domains is higher than above hydrophilic domains. The opposite can be observed for the surface concentration above hydrophobic domains. The negative value of ∆Rphob in Figure 8 results from the fact that a small isolated hydrophobic domain acts as a disturbance in the surrounding bilayer. Compared to the checkerboard surfaces, the surface concentration above isolated hydrophobic domains is higher. For large domains D > 6, there is no difference between the surface concentration above isolated and checkerboard domains. A similar dependence of ∆R(D) is found at T* ) 1.2. In the admicelle regime (T* ) 1.3), the increase of ∆Rphil is low for small domains. This arises from a preferred adsorption of surfactant heads on hydrophilic and tails on hydrophobic domains. A bilayer structure is not stable at this temperature. Conclusions The adsorption of surfactants from aqueous solutions on inhomogeneous solid surfaces has been studied. Surfactant molecules considered in this paper have a single flexible chain with the same cross section as the hydrophilic head. Three different surface patterns are taken into account, namely, a hydrophilic domain in a hydrophobic environment, a hydrophobic domain in a hydrophilic environment, and a checkerboard-like arrangement of surface domains. For large domain sizes, specific boundary regimes were observed. In the case of adsorbed
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bilayers, the surface concentration declines toward the boundary. In case of monolayers, the surface concentration increases at the domain boundary even in the absence of a surrounding bilayer. The boundary regimes have a range of 6 lattice sites, i.e., twice the length of one molecule. In the checkerboard-like arrangement, nonadditive adsorption effects are observed. For small domain sizes, a heterogeneous adsorption layer is formed at low temperatures, where dense monolayer patches stabilize small bilayer patches. For large domains, the values of the surface concentrations change from Rphil < Rphob to Rphil > Rphob and the reverse picture results in the plot of the local surface concentration. Another interesting point is that a few isolated hydrophilic sites in a hydrophobic surface lead to holes in the adsorption layer. If the hydrophilic sites are close enough
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or if their number is increased, the overall adsorption is enhanced and the surface is covered completely. Small hydrophobic domains in a hydrophilic surface just act as local disturbances in the structure of the adsorption layer and would not be detectable in experiments. The results refer to surface patterns with characteristic length scales of a few nanometers. Although the surfactant adsorption on such fine structured surfaces has not been experimentally studied yet, data might become available soon. Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft (SFB 285 and SCHI 368/3-1) is gratefully acknowledged. LA0478797
