J. Phys. Chem. B 2005, 109, 471-479
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Monolayer of Aerosol-OT Surfactants Adsorbed at the Air/Water Interface: An Atomistic Computer Simulation Study Jnanojjal Chanda, Sudip Chakraborty, and Sanjoy Bandyopadhyay* Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur - 721302, India ReceiVed: April 20, 2004; In Final Form: September 1, 2004
An atomistic molecular dynamics (MD) simulation has been carried out to investigate the structural and dynamical properties of a monolayer of the anionic surfactant sodium bis(2-ethyl-1-hexyl) sulfosuccinate (aerosol-OT or AOT) adsorbed at the air/water interface. The simulation is performed at room temperature and at a surface coverage corresponding to that at its critical micelle concentration (78 Å2/molecule). The estimated thickness of the adsorbed layer is in good agreement with neutron reflection data. The study shows that the surfactants exhibit diffusive motion in the plane of the interface. It is observed that the surfactant monolayer has a strong influence in restricting both the translational and reorientational motions of the water molecules close to the interface. A drastic difference in the dipolar reorientational motion of water molecules in the aqueous layer is observed with a small variation of the distance from the surfactant headgroups. It has been observed that the water molecules in the first hydration layer (region 1) form strong hydrogen bonds with surfactant headgoups. This results in the slower structural relaxation of water-water hydrogen bonds in the first hydration layer compared to that in the pure bulk water. Most interestingly, we notice that the water molecules present in the layer immediately after the first hydration layer form weaker hydrogen bonds and thus relax faster than even pure bulk water.
1. Introduction The study of organized surfactant assemblies at interfaces and in bulk solutions is of great importance in industrial processes such as detergency, oil recovery, paints, food chemistry, purification, lubrication, and so forth.1 Much successful work has been done to understand the properties of surfactant aggregates in solutions, but at interfaces, proper systematic studies of absorbed layers are still lacking. This work has focused on the anionic surfactant sodium bis(2-ethyl-1-hexyl) sulfosuccinate ((C8H17OOC)2C2H3SO3- Na+), commonly known as aerosol-OT or AOT. AOT and its analogues represent an important class of commercial surfactants that contain small branched double tails. These compounds are salts of diesters of succinic acid that contain a sulfonate substituent group within the succinate moiety. The structure of the surfactant is shown in Figure 1. For our convenience, we identify the two ethyl hexanol chains as chain 1 and chain 2, respectively, as indicated in the Figure. The presence of a negatively charged headgroup and two alkyl chains makes these surfactants highly surface-active agents. AOT has been widely used in both technological applications and fundamental research.2 A vast number of experimental studies on AOT/water interfaces have been reported in the literature. The AOT-based surfactants are capable of forming stable reverse micelles in a large variety of solvents. Thus, a majority of the experiments involve the characterization of AOT reverse micelles. For example, Onori and co-workers3,4 have used IR spectroscopy to study the structure of water in AOT reverse micelles. They have also studied the dynamics of the micelles by varying their degree of hydration using quasi-elastic neutron scattering * To whom correspondence should be addressed. E-mail: sanjoy@ chem.iitkgp.ernet.in. Tel: 91-3222-283344. Fax: 91-3222-255303.
Figure 1. Structure of the sodium salt of the bis(2-ethyl-1-hexyl) sulfosuccinate (aerosol-OT or AOT) molecule. The two hexanol chains are identified as chain 1 and chain 2.
experiments.5 NMR spectroscopy has also been used to study the effect of hydration on AOT reverse micelles.6-8 Recently, pulsed-field gradient NMR experiments have been used to measure the diffusion coefficients of the individual components in a water-AOT-decane microemulsion at different temperatures.9 Ultrafast time-resolved fluorescence spectroscopy has been used to study the solvation response in AOT reverse micelles.10,11 Eastoe and co-workers12 have carried out smallangle neutron scattering experiments to investigate the reasons for the efficiency of AOT-based surfactants for the formation of microemulsions.
10.1021/jp0482924 CCC: $30.25 © 2005 American Chemical Society Published on Web 12/07/2004
472 J. Phys. Chem. B, Vol. 109, No. 1, 2005 Numerous experimental studies are also reported on the properties of AOT as well as other surfactant layers adsorbed at vapor/liquid, liquid/liquid, and liquid/solid interfaces. Richmond and co-workers13 have studied the structure and orientation of interfacial water molecules using vibrational sum frequency spectroscopy on both cationic and anionic surfactant monolayers at the air/water interface. They have also studied in detail the conformational order of different surfactant monolayers adsorbed at the water/carbon tetrachloride (CCl4) interface at different surface coverages.14,15 Grubb et al.16 have compared the orientation of surfactant molecules at air/water, water/decane, and water/CCl4 interfaces using second-harmonic-generation studies. Recently, a time-resolved quasi-elastic laser scattering measurement has been applied to study the dynamics and collective properties of anionic surfactant sodium dodecyl sulfate (SDS) and neutral surfactant Triton X-100 adsorbed at a water/ nitrobenzene interface.17 Fluorescence18 and resonance Raman spectra19 were also used in earlier studies on different surfactant monolayers adsorbed at liquid/liquid interfaces. Recently, Linse and co-workers20 studied the adsorption of several nonionic surfactants at liquid/vapor and solid/liquid interfaces using surface tension and ellipsometric measurements. Only recently, the relatively new technique of neutron reflection has been successfully used to study the structural characteristics of various surfactant layers, including AOT, adsorbed at air/liquid, liquid/ liquid, and liquid/solid interfaces.21-28 Neutron experiments can provide accurate information on the density profiles of the surfactant at an interface. Isotopic labeling of the molecules also allows one to obtain profiles for different fragments of the molecules comprising the monolayer.24,26 Such information can help to identify whether there are any special structural characteristics of the surfactant layers, such as the roughness of the layer, the degree of immersion of the surfactant in water, the conformation of the hydrocarbon chains, and so forth. Thomas and co-workers24 have combined neutron reflection measurements with isotopic substitution to determine the structure of self-assembled AOT monolayers adsorbed at the air/water interface. The widths of the distributions of the upper and lower halves of the molecule as well as their positions relative to the underlying water have been measured at different concentrations, varying from the critical micelle concentration or cmc (2.5 × 10-3 M) to cmc/300. They observed that in this concentration range the coverage changed from 78 ( 3 to 132 ( 8 Å2/molecule. X-ray and neutron studies26 also revealed that the structure of AOT monolayers at the air/water interface depends on the type of metal counterions. For example, at cmc (4 × 10-4 M) the structure of calcium salt Ca(AOT)2 was found to be quite different from that of NaAOT. The Ca(AOT)2 layer is relatively displaced 1 to 2 Å away from water compared to NaAOT. This resulted in a thinner chain region for the calcium surfactant. Today, with the availability of fast computers along with the development of sophisticated methodologies, computer simulations can play a crucial role in providing microscopic details of the structural and dynamical properties of surfactant assemblies. A large number of simulation studies on regular and reverse micellar solutions of surfactants have been reported in the literature.29-48 Reverse micelles formed by AOT as well as various other ionic and nonionic surfactants in different nonpolar solvents have been studied by several researchers.40-48 Ladanyi and co-workers41-43 have extensively studied the structure and dynamics of water present in the core region of AOT reverse micelles using molecular dynamics (MD) simulations. They have also shown that the properties of the
Chanda et al. core water molecules strongly depend on the counterion type.43 Recently, Cummings and co-workers44-46 used atomistic MD simulations to study the properties of reverse micellar surfactant aggregates in carbon dioxide (CO2) as the solvent. Atomistic simulations have also been employed to study ionic reverse micelles containing a calcium carbonate core.40,47 Recently, we reported MD simulations of a reverse micelle containing nonionic monododecyl diethylene glycol (C12E2) in decane.48 Prior to this work, there have been several reports on the study of the microscopic properties of surfactant assemblies at different interfaces using simulation methods. The time scales associated with the adsorption of surfactants leading to the formation of the monolayer or the exchange of monomers between the monolayer and those in the bulk solution are in the range of micro to milliseconds and therefore are beyond the scope of the current generation of atomistic molecular dynamics (MD) simulations. However, it is possible to study the microscopic properties of a monolayer formed at an interface within a reasonable amount of computer time. This approach has been employed in several simulation studies.49-62 Tarek et al.49 have carried out MD studies of cationic surfactant cetyltrimethylammonium bromide (CTAB) adsorbed at the air/water interface at two different concentrations. The simulated density profiles were found to be in good agreement with neutron reflectivity data. Wijmans and Linse50 have used the Monte Carlo method to study the self-assembly of nonionic surfactants at a hydrophilic surface. Berkowitz and co-workers51-53 have studied in detail the monolayers of ionic surfactants adsorbed at air/water and water/CCl4 interfaces. They observed a significant difference in the molecular configuration of the surfactants adsorbed at the two interfaces.51 It was also shown that the polarity of a surfactant has a strong influence on the structure and dynamics of water near the interface.52 Kuhn and Rehage54-56 have studied in detail the orientation and dynamic properties of a monododecyl pentaethylene glycol (C12E5) monolayer adsorbed at air/water and oil/water interfaces. Recently, Rossky and co-workers57,58 have reported atomistic MD simulation studies on fluorocarbon surfactant monolayers at a CO2/water interface. They noticed that water penetrated the fluorocarbon surfactants to a lesser extent than the hydrocarbon surfactants. We have recently studied a monolayer of monododecyl diethylene glycol (C12E2) at an air/water interface using atomistic MD simulations.59 It was observed that the water molecules at the interface have a strong influence on the conformation of the surfactant headgroups. Only recently, Smit and co-workers60,61 used a dissipative particle dynamics method to study the properties of surfactant monolayers at an oil/water interface. They have investigated the effect of surfactant structure on the bending moduli of the adsorbed monolayers. MD simulations of monolayers of anionic-nonionic surfactant mixtures at a liquid/liquid interface have also been reported recently.62 In this work, we have studied the microscopic properties of monolayers of the sodium salt of aerosol-OT (NaAOT) adsorbed at the air/water interface using atomistic MD simulation techniques. The aim of the work is to study the atomic-level details of the structure and dynamics of the adsorbed monolayer films as well as those of the water molecules near the interface. We have organized the article as follows. In the next section, we discuss the system setup and simulation details. This will be followed by the results obtained from our studies and their interpretation. In the last section, we will summarize the important findings from our study.
Surfactants Adsorbed at the Air/Water Interface 2. System Setup and Simulation Details To set up a surfactant monolayer system at an interface, one has to specify the boundary conditions carefully. One option is to simulate a single monolayer in contact with the aqueous solution and confine the solution by placing a hard wall below the interface,63 but this requires a relatively large bath of water molecules for a given number of surfactants to avoid artifacts arising from the long-range structuring of water by the wall.64 Another option is to simulate two separate monolayers on opposite sides of a slab of aqueous solution, whose thickness is such that the two monolayers remain effectively isolated from each other. A proper treatment of the long-range electrostatic interactions is also important for such systems. In principle, one can employ a Ewald summation method suitable for roughly two-dimensional systems with a finite extent in the third dimension, but for this, the dimension in the nonperiodic direction should be much less than that in the periodic directions.65 However, this criterion is not satisfied by the system sizes in this study. Given these considerations, we have opted to use the two monolayers on a slab arrangement and use threedimensional periodic boundary conditions and an Ewald summation with a large value for the dimension of the simulation cell in the direction normal to the interface (z). The assumption here is that the approximate mirror symmetry combined with the large z dimension results in negligible interactions between periodic replicas in the z direction. The initial configuration of our constant temperature and volume (NVT) simulation system was set up by arranging a uniform monolayer of 32 surfactants with the headgroup sulfur atoms on an appropriate 4 × 4 body-centered square lattice in the xy plane with the hydrocarbon chains extending away from the lattice plane. The lattice constants were chosen to give a surface area per molecule of 78 Å2, which corresponds to the experimentally determined value for adsorption at the air/water interface at the critical micelle concentration.24 Then two such Langmuir-type monolayers were placed, with their headgroups solvated, in the xy plane of a roughly 30 Å thick slab of water molecules. A 30 Å thick layer of water should be large enough to give a distinct bulklike region of the aqueous solution in the middle of the simulation cell. Then 64 of the water molecules were randomly replaced by sodium counterions. The resulting system contained 64 surfactant chains, 2025 water molecules, and 64 sodium counterions. The dimension of the simulation box in the x and y directions was 50 Å, and the z dimension was kept large at 150 Å. This is done to minimize the interactions between the periodic replicas in the z direction as discussed before. A short MD run of 50 ps was first performed at 500 K, keeping the surfactant headgroups, the water molecules, and the counterions fixed to randomize the surfactant chain conformations. At this point, the headgroups, the water molecules, and the counterions were unfrozen, and the temperature of the system was lowered to 10 K. The temperature of the system was then slowly increased to 298 K over the next 100 ps. The resulting configuration was then equilibrated at constant temperature (T ) 298 K) and volume (NVT) for about 2 ns. This equilibration period was followed by an NVT production run of approximately 4 ns. The trajectories were stored during the production phase of the simulation with a time resolution of 450 fs for subsequent analysis. The simulations utilized the Nose´-Hoover chain thermostat extended system method66 as implemented in the PINY-MD computational package.67 A recently developed reversible multiple time step algorithm, RESPA,66 allowed us to employ
J. Phys. Chem. B, Vol. 109, No. 1, 2005 473 a 4.5 fs MD time step. This was achieved using a three-stage force decomposition into intramolecular forces (torsion/bendbond), short-range intermolecular forces (a 7.0 Å RESPA cutoff distance), and long-range intermolecular forces. Electrostatic interactions were calculated by using the particle mesh Ewald (PME) method.68 The PME and RESPA were combined following the method suggested by Procacci et al.69,70 The minimum image convention71 was employed to calculate the Lennard-Jones interactions and the real-space part of the Ewald sum using spherical truncations of 7 and 10 Å, respectively, for the short- and the long-range parts of the RESPA decomposition. SHAKE/ROLL and RATTLE/ROLL methods66 were implemented to constrain all bonds involving hydrogen atoms to their equilibrium values. The intermolecular potential model was based on pairwise additive site-site electrostatic and Lennard-Jones contributions. The CHARMM27 all-atom force field and potential parameters for lipids72 were employed to describe the interaction between the surfactant atoms, and the TIP3P model,73 which is consistent with the chosen surfactant force field, was employed for modeling water. 3. Results and Discussion 3.1. Structure of the Monolayer. Figure 2 shows snapshots (cross-sectional view perpendicular to the plane of the interface) of the configuration of the system at the beginning (a) and at the end (b) of the simulation run. The important notable feature in the Figure is the structure of the headgroup region at the interface. It is evident that during the time scale of the simulation significant roughness (undulations) developed near the surfactant headgroup region of the interface as compared to the nearly flat interface at the beginning of the simulation. The structural properties of a monolayer can be characterized by various distribution functions. In Figure 3 we display the number density profiles (NDP) of different components along z (i.e., in the direction normal to the plane of the interface). The different components of the surfactants for which the NDPs are computed separately include the sulfonate group (SO3), the backbone ethylene (C2H3) and the carboxy groups (COO) of the succinate moiety, and the carbon atoms of the hydrocarbon chains (C). The distributions for the water molecules and the sodium counterions are also computed and displayed in the Figure. The essential features of the plot are similiar to the well-known picture of the surfactant organization at an interface.49,52,53,59,74,75 The headgroups are localized at the interface and are hydrated, whereas the hydrocarbon tails are mostly excluded from the water layer. Only a small fraction of water penetrated within the hydrocarbon tail part of the surfactants, and there is a large dry region within the hydrocarbon chains of the surfactants. The distribution of different components shows that the sulfonate headgroups (SO3) are completely hydrated whereas the degree of hydration gradually decreases along the surfactant chains. A significant fraction of the sodium counterions are found to be distributed close to the interface, near the oppositely charged sulfonate headgroups. Finally, we note that the density profiles of the two monolayers are essentially symmetric, indicating that the system is well equilibrated, with similar overall structure of the two monolayers comprising the system. The presence of a 15-20 Å thick slab of water between the two monolayers with density close to that of water in the bulk indicates that they are independent and have practically no influence on each other. It is possible to evaluate the thickness (d) of the adsorbed monolayers from MD simulations. We have measured the
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Figure 2. Snapshots of the configuration of the system (a) at the beginning and (b) at the end of the simulation. The sulfur atoms of the sulfonate headgroups and the sodium counterions are drawn as van der Waals spheres, and the other atoms are drawn according to their covalent radii. The atom coloring scheme is S, yellow; O, red; C, gray; and Na, green. Only the oxygen atoms of the water molecules are drawn as blue dots. For visual clarity, the hydrogen atoms of the surfactant chains are not displayed, and the system is replicated once on both sides of the central simulation cell.
Figure 3. Number density profiles of the sulfonate headgroup (SO3), backbone ethylene group (C2H3) of the succinate moiety, carboxy groups (COO), hydrocarbon chain atoms (C), water molecules, and sodium counterions measured with respect to the center of the simulation cell in the direction normal to the plane of the interface (i.e., along the z direction).
thickness of the monolayer from the simulated trajectory. The estimated average value of the thickness is 16.9 ((0.5) Å. The thickness reported by neutron reflectivity studies is 18 ((1) Å at the cmc.24 Thus, the simulated value of the monolayer thickness is in good agreement (∼6%) with experimental data. 3.2. Water Structure at the Interface. To understand further the properties of an adsorbed surfactant monolayer, it is important to investigate in detail the structure of water molecules
Figure 4. Radial distribution functions, g(r), of the sulfur (S) and oxygen atoms (OS) of the sulfonate group and the two oxygen atoms of the carboxy groups (ON and OE) of the surfactant with water oxygen atoms.
at the interface. With this aim, we have calculated the pairwise correlation function, commonly known as the radial distribution function, g(r), of water molecules with different atoms of the anionic surfactant chains, as presented in Figure 4. A strong peak is observed at around 2.8 Å for the oxygen atoms of the sulfonate groups (OS) as well as for the nonbonded oxygen atoms of the carboxy groups in the succinate moiety (ON). These peaks correspond to the nearest-neighbor distance between water molecules and the oxygen atoms of the surfactants. The OS atoms also exhibit a well-defined second peak. A strong peak
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Figure 6. Time evolution of the in-plane (i.e., in-xy-plane) and the out-of-plane (i.e., along z) mean square displacements of the center of mass of the surfactant chains. The diffusion coefficient values (Dxy and Dz) are estimated from a linear fit of the data using eq 1. Figure 5. Distribution of the tilt angle, θ (in degrees) of the (a) tail vectors and (b) head vectors of the two chains of the surfactant with respect to the normal to the interface, z.
is also observed at the nearest-neighbor distance (∼4 Å) for the headgroup sulfur atoms. The presence of such high-intensity peaks suggests that the sulfonate headgroups of the surfactants strongly influence the structure of water around them at the interface. This second peak is missing for the ON atoms because these are slightly away from the interface and are not as exposed to water as the OS atoms. The oxygen atoms of the carboxy groups forming the ester link (OE) do not exhibit a strong first peak, suggesting that these oxygen atoms are much less exposed to water and thus not as hydrated as the other oxygen atoms (OS and ON). We have calculated the number of water molecules that are within the first nearest-neighbor distance to the oxygen and sulfur atoms of the surfactant chains. This is done by integrating the g(r) curves up to 3.8 Å for the oxygen atoms and 5.4 Å for the sulfur atoms of the surfactants. It is found that, on average, there are approximately 4 water molecules per OS atom of the SO3 groups, 2.5 water molecules per ON atom, and 0.6 water molecules per OE atom of the carboxy groups. Eleven to twelve water molecules are found within the first coordination shell of the sulfur atom of the headgroup. These trends are quite similar to that observed in the micellar phase of sodium octanoate30 and sodium dodecyl sulfate.29 3.3. Surfactant Orientations. To characterize the overall orientation of the surfactants at the interface, we calculated separately the orientations of the two chains with respect to the normal (z) to the plane of the interface (xy plane). We define the vectors connecting the first methylene group (CH2) and the terminal methyl group (CH3) of the two hexanol chains (chain 1 and chain 2) of the surfactant (Figure 1) as the “tail” vectors and the vectors connecting the two carbon atoms of the ethylene group (C2H3) in the backbone succinate moiety and the first methylene group of the two hexanol chains as the “head” vectors. The probability distributions, F(θ), of the tilt angles (θ) between the head and tail vectors with respect to the normal to the plane of the interface, z, are displayed in Figure 5. These distributions are averaged over both monolayers. It is evident from the distributions that the head and the tail parts of both the chains are significantly tilted from the normal to the plane of the interface (z). The tail vectors of both chains are almost identically tilted (Figure 5a), with an average tilt angle of 48.5°. However, some differences are observed for the distributions of the head vectors of the two chains (Figure 5b). The distribution for chain 2 is found to be broader than that for chain 1, with a shoulder at low θ values (θ e 30°). This suggests that there is a considerable fraction of surfactant molecules with
the head vector of chain 2 oriented at small angles (θ e 30°) (i.e., perpendicular to the interfacial plane (xy)) compared to the head vector of chain 1. The average tilt angles of the head vectors as obtained from our simulation were 64.7° and 60.9° for chain 1 and chain 2, respectively. 3.4. Surfactant and Water Dynamics. To obtain a more complete microscopic understanding of the properties of an adsorbed surfactant monolayer, one should investigate the dynamics of the surfactant molecules as well as the water around them. In this section, we discuss the dynamical behavior of the surfactants and water molecules. 3.4.1. Surfactant Dynamics. The translational mobility of the surfactant chains can be studied by measuring their diffusion coefficients (D). MD simulations provide an easy method for the measurement of diffusion coefficients. This is done by directly measuring the mean square displacements (MSD) of the center of mass of the surfactant chains from the MD trajectory. Diffusion coefficients (D) can then be obtained from the slope of the mean square displacement versus time curve, using the well-known Einstein relation71
〈|ri(t) - ri(0)|〉2 〈∆r2〉 ) lim ∆tf∞ ∆tf∞ 2d∆t 2d∆t
D ) lim
(1)
where d is the dimensionality of the system, ri(t) and ri(0) are the center-of-mass coordinates of the ith surfactant chain at times t and t ) 0, respectively, and the averaging is over both time origins and the surfactant molecules. Because the monolayer system is anisotropic in the direction normal to the plane of the interface, we have separately calculated the mean square displacements of the center of mass of the surfactant chains in the plane of the interface (i.e., the xy plane) and in the direction perpendicular to it (i.e., the z direction). These are shown in Figure 6. It is clear from the Figure that the surfactant chains are more mobile in the plane of the interface. However, they exhibit a more restricted motion in the direction normal to the interfacial plane. Using appropriate Einstein relations (eq 1), we have obtained the diffusion coefficients (Dxy and Dz) of the center-of-mass motion of the surfactant chains. The calculated values of Dxy and Dz were found to be 2.7 × 10-6 and 6.8 × 10-7 cm2 s-1, respectively. These values are of the same order as those obtained from pulsed-field gradient NMR studies on AOT reverse micelles.9 3.4.2. Water Dynamics. The dynamics of water close to the interface plays an important role in determining the surfactant behavior and its practical applications. In this section, we study the translational and orientational motion of water molecules near the interface.
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Figure 7. Mean square displacement (MSD) of the water molecules in different regions of the aqueous layer. Region 1 comprises water molecules that are within 5 Å from the headgroup sulfur atoms; those that are within 5-8 Å are in region 2, and those that are beyond 8 Å are said to be in region 3. The MSD of the water molecules in pure bulk water is also shown for comparison.
TABLE 1: Diffusion Coefficients of the Water Molecules in Different Regions as Obtained from Their Mean Square Displacementsa
a
region
D (10-5 cm2 s-1)
region 1 (0-5 Å) region 2 (5-8 Å) region 3 (>8 Å) bulk water
1.32 2.09 4.19 5.34
The value for bulk water is also listed for comparison.
We have calculated the mean square displacements of water molecules at different distances from the interface. To be specific, we have defined three hydration regions. Region 1 comprises of water molecules that are within 5 Å from the headgroup sulfur atoms. This essentially corresponds to the first hydration layer with respect to the sulfur atoms of the surfactant molecules. Water molecules that are within 5-8 Å from the sulfur atoms form region 2, and those beyond 8 Å are said to be in region 3. The distances are measured with respect to both monolayers by tagging the water molecules at different time origins. These are shown in Figure 7. For comparison, we have also displayed the same for pure bulk water, which was obtained from a MD simulation of pure TIP3P water at room temperature. It is evident from the Figure that the translational motion of the water molecules is significantly restricted as one closely approaches the interface. The mobility of the water molecules increases significantly with increasing distance from the surfactant headgroups. Such restricted mobility of water near the interface of organized molecular assemblies, such as micelles,36,41 and heterogeneous macromolecules, such as proteins,76,77 was reported earlier. This might arise because of the presence of water molecules that are “bound” to the hydrophilic surfactant headgroups at the interface by strong hydrogen bonds. We will discuss this later. The diffusion coefficients of water molecules in the three regions have been calculated from a linear fit to the corresponding mean square displacements over the time interval between 2 and 10 ps. These are listed in Table 1. The data shows that water in regions 1 and 2 is much less mobile than that in region 3 and pure bulk water. A similar approach has been used recently by Faeder and Ladanyi41 to calculate the diffusion coefficients of water molecules from MD simulations of AOT reverse micelles. The diffusion coefficients obtained from our calculations are in good agreement with the simulated AOT reverse micelle data.41 At this point, we emphasize that the absolute values of the calculated diffusion coefficients may not be very authentic in this case. This is because the surfactant monolayers provide a heterogeneous
Chanda et al.
Figure 8. Reorientational time correlation function of the water dipoles, Cµ(t), for the water molecules in three regions of the aqueous layer. The definitions of the regions are the same as for Figure 7. The TCF for pure bulk water is also shown for comparison.
anisotropic environment for the water molecules that is not strictly three-dimensional.78,79 However, here we are interested in comparing the relative diffusion of water in different regions rather than reporting the absolute diffusion coefficient values. The reorientational dynamics of water molecules near the monolayer interface is also expected to be affected. The rotational motion of water can be investigated by measuring the reorientational dynamics of its electrical dipole b µ, defined as the vector connecting the oxygen atom of the water molecule to the center of the line connecting the two hydrogen atoms. The time evolution of b µ can be estimated by measuring the dipole-dipole time correlation function (TCF), defined as
Cµ(t) )
〈µˆ i(t + τ)‚µˆ i(τ)〉 〈µˆ i(τ)‚µˆ i(τ)〉
(2)
where µˆ i(t) is the unit dipole moment vector of the ith water molecule at a time t and the angular brackets denote averaging over the tagged water molecules and over initial times τ. Again, we restrict ourselves to the reorientational motion of water molecules in the three regions as discussed before. The correlation functions were calculated by averaging over these water molecules only, which are shown in Figure 8. For comparison, we have also displayed the relaxation for pure bulk water. It is clear from the Figure that the decay curves are nonexponential in nature and for water near the interface (regions 1 and 2) they do not decay to zero. This indicates that the reorientational motion of water molecules near the interface is significantly restricted compared to that of pure bulk water. It is important to obtain an estimation of the time scales associated with the reorientational motion of the water molecules from the dipolar correlation functions. We notice from the Figure that all of the curves show a slower decay at long times. Such long-time decay cannot be described by a single-exponential law. One can fit such functions either to a multiexponential form36 or to a sum of stretched exponential functions.76,77 It is a common practice to use multiexponentials because one can then directly obtain time constants associated with different motions. These time constants can be assigned to different relaxation processes of the system. Here we have used a sum of three exponentials to fit the data for each of the three TCFs. The best-fit parameters are shown in Table 2. The slow decay for water close to the interface arises because of the formation of extended hydrogen bonding with the polar headgroups of the surfactants. Because the dynamics of the surfactant chains in the monolayer assembly is much slower compared to the time scale of water dynamics, such a network of hydrogen bonding slows down the reorientational motion of these bound water molecules close to the interface. Interestingly, a significantly
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TABLE 2: Multiexponential Fitting Parameters for the Dipolar Time Correlation Functions of Water Molecules in Different Regionsa region
time constant (ps)
amplitude (%)
〈τµ〉 (ps)
region 1 (0-5 Å)
0.22 2.13 96.39
16.5 40.1 43.4
42.72
region 2 (5-8 Å)
0.22 2.28 338.56
16.2 61.5 22.3
76.94
region 3 (>8 Å)
0.21 2.27 20.59
15.1 73.6 11.3
4.03
0.41 2.54
23.2 76.8
2.04
bulk water
a 〈τµ〉 is the average time constant. Corresponding parameters for bulk water are also listed for comparison.
long time component is noticed for water molecules in region 2. The average reorientational time constant (〈τµ〉) for water in regions 1 and 2 is approximately 10 to 20 times slower than those in region 3. From our results, it is clear that the rotational motion of water near the interface is severely restricted. Such dramatic changes in the reorientational motion of water molecules with a small variation in the distance with respect to the surfactant headgroups is an interesting observation that needs to be investigated further. Such slow dipolar reorientation of water has also been observed recently in surfactant micellar systems.35,36,41 It is clear from the discussion so far that strong correlations exist between the surfactants and the water molecules near the interface. The presence of such correlations affects the normal bulk behavior of water molecules near the interface. One of the important properties of bulk water is its ability to form a distinct network of hydrogen bonds. It would be interesting to investigate how the presence of surfactant molecules disrupts the structure of the regular hydrogen bonding network of the interfacial water molecules. This is discussed in the next section. 3.5. Hydrogen Bond Analysis. The structural relaxation of hydrogen bonds can be characterized by the time correlation function
CHB(t) )
〈h(t + τ) h(τ)〉 〈h〉
(3)
where the hydrogen bond population variable h(t) is unity when a particular pair of tagged water molecules is hydrogen bonded at time t according to the definition used and zero otherwise.80-84 The angular brakets denote averaging over all water-water hydrogen bonds and over initial times τ. The correlation function CHB(t) describes the probability that a particular hydrogen bond is intact at time t + τ, given that it was intact at time τ. Thus, CHB(t) allows the reformation of a bond that is broken at some intermediate time. In other words, it allows recrossing the barrier separating the bonded and nonbonded states as well as longtime diffusive behavior. Therefore, the relaxation of CHB(t) provides information about the structural relaxation of a particular hydrogen bond. We have used an energy cutoff to define a hydrogen bond.73 A water-water hydrogen bond is said to exist if the distance between the two oxygen atoms of the tagged pair of water molecules is within 3.5 Å and if the pair energy is less than -2.5 kcal/mol.85-87 The distance of 3.5 Å is essentially the position of the first minimum in the oxygen-oxygen radial distribution function. Such an energy-based definition of a
Figure 9. Time correlation function CWW HB (t) for the hydrogen bonds formed between the water molecules in three regions of the aqueous layer. The definitions of the regions are the same as for Figure 7. The TCF for the hydrogen bonds in pure bulk water is also shown for comparison. The inset shows the relaxation of the hydrogen bonds formed between the surfactant headgroups and interfacial water molecules.
hydrogen bond has been used recently to characterize surfactant-water interfaces.35,88 With this definition, we have calculated the time correlation function CWW HB (t) for the hydrogen bonds formed between the water molecules in the three regions. These are shown in Figure 9. For comparison, we have also displayed the corresponding relaxation for pure bulk water. It is clear from the Figure that the relaxation of water-water hydrogen bonds in region 1 (i.e., within the first hydration layer with respect to the surfactant headgroups) is much slower than those corresponding to the other two regions as well as the pure bulk water. Such slow hydrogen bond dynamics has been studied recently at an air/water interface,89 near a micellar surface,88 and near protein surfaces.80,90 In this case, the slow relaxation arises because of a strong interaction between the water molecules in region 1 and the surfactant headgroups, which may lead to the replacement of a water-water hydrogen bond by a water-surfactant hydrogen bond through the headgroup oxygen atoms. The inset of Figure 9 shows the relaxation of watersurfactant hydrogen bonds (CWS HB (t)). The much slower relaxation of CWS HB (t) is clearly evident from the Figure. Thus, the water molecules in region 1 are significantly bound to the surfactant headgroups, which resulted in the slower structural relaxation of these water molecules. This agrees nicely with the slow translational and orientational relaxation of region 1 water molecules (Figures 7 and 8). The interactions between the surfactants and the water molecules diminish as the distance increases from the interface. This is evident from the faster decay for water molecules in regions 2 and 3, in agreement with the corresponding translational and orientational relaxations, as discussed before. The decay curves for the water molecules in regions 2 and 3 show an interesting behavior. They not only exhibit faster dynamics compared to that of the water in region 1 but also seem to relax faster than pure bulk water. This is particularly true for the water in region 2, whereas the relaxation for water in region 3 is very similar to that in bulk water. To obtain insight into such interesting relaxation behavior, we have calculated the hydrogen bond energies between the water molecules in the three regions. The calculated average hydrogen bond energies have been found to be -3.58 kcal/mol for region 1, -3.71 kcal/mol for region 2, and -3.77 kcal/mol for region 3 water molecules. The corresponding value for pure bulk water is -3.78 kcal/mol. In contrast, the hydrogen bond energy between the surfactant headgroup and a water molecule in region 1 has been found to be -7.39 kcal/mol. Such a difference in
478 J. Phys. Chem. B, Vol. 109, No. 1, 2005 energy can partially explain the differential dynamics of water molecules in the three regions. We note that the water-water hydrogen bonds in region 1 are weaker than in pure bulk water. However, the region 1 water molecules can form stronger hydrogen bonds with the surfactant headgroups. This more than compensates for the weaker water-water hydrogen bonds in region 1 because a significant fraction of these bonds would be disrupted in this region to form stronger hydrogen bonds with the surfactant headgroups. The presence of such bound waters eventually leads to slower dynamics of the water molecules in region 1, as compared to that in pure bulk water (Figure 9). The hydrogen bond energy of water in the middle layer (region 2) has been found to be higher than that for bulk water. This indicates that the water-water hydrogen bonds in region 2 are relatively weaker than in bulk water and hence relax faster. As the distance from the surfactant headgroups is further increased, the behavior of water molecules in region 3 approaches that of pure bulk water, which is reflected in the corresponding relaxation curve as well as the energy of the water-water hydrogen bonds. The presence of sodium counterions in the aqueous layer may also be partially responsible for such relaxation behavior of water molecules in different regions as compared to that in pure bulk water. Faster dynamics of water hydrogen bonds around sodium ions has been detected recently in an aqueous protein solution.80 Currently, we are investigating the surfactant-water and water-water hydrogen bonds in greater detail.
Chanda et al. regions of the aqueous layer. The structural relaxation of the hydrogen bonds formed between the water molecules as a function of the distance from the surfactant headgroups has been studied. It is noticed that the water molecules in the first hydration layer (region 1) form strong hydrogen bonds with the surfactant headgroups. The presence of such bound water molecules results in slow dynamics of the water-water hydrogen bonds in region 1. Most interestingly, we noticed that there is a small layer of water molecules immediately after the first hydration layer (region 2) that form weaker hydrogen bonds compared to those in pure bulk water. With further increases in distance from the surfactant headgroups, the dynamics of water molecules approachs that of bulk water. It is important to study in greater detail the formation and breaking of the various types of hydrogen bonds and their lifetimes between the water molecules and the surfactant headgroups. This will enable us to obtain a deeper microscopiclevel understanding of the correlation between the adsorbed surfactant monolayers and the interfacial water molecules. Extensive work in this direction is in progress in our laboratory. Acknowledgment. This work was supported in part by generous grants from the Council of Scientific and Industrial Research (CSIR) and the Department of Science and Technology (DST), Government of India. S.C. thanks CSIR for providing a scholarship. References and Notes
4. Conclusions In this aticle, we have presented results obtained from an atomistic MD simulation study of the structure and dynamical properties of monolayers of an anionic surfactant, sodium salt of aerosol-OT adsorbed at the air/water interface. The simulation has been performed at constant volume and at room temperature with a surface coverage of 78 Å2/molecule, which corresponds to the surface coverage of the surfactant at the cmc. The structural properties of the system, such as the density profiles of different components normal to the plane of the interface and the thickness (d) of the adsorbed monolayer, are calculated. It is observed that during the time scale of the simulation roughness developed at the interface. The estimated average thickness of the adsorbed layer has been found to be in good agreement with experimental data.24 The orientation of the surfactant chains with respect to the normal to the interface (z) has been studied. We have noticed that there is a significant fraction of surfactant molecules with chain 2 head vectors oriented at small angles to the z axis. We observed that whereas the in-plane (i.e., in-xy-plane) motion of the center of mass of the surfactant chains is diffusive in nature at long times the out-of-plane (i.e., along z) motion is more restricted. The estimated diffusion coefficient values are found to be of same order as those observed in other monolayer systems.59 The distribution of water molecules around the surfactant headgroups and their dynamics are also investigated in detail. Water around the oxygen atoms of the sulfonate groups (OS) and the nonbonded oxygen atom of the carboxy groups (ON) is found to be highly structured. Both translational and reorientational motions of the water molecules have been found to be restricted near the interface. However, an important result of this study is the observation of dramatic differences in the dipolar reorientational motion of water molecules with a small variation in the distances from the surfactant headgroups. We noticed about 10 to 20 times that there were differences in the relaxation times of water reorientational motions in different
(1) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic Press: New York, 1994. (2) Porter, M. R. Handbook of Surfactants, 2nd ed.; Blackie: London, 1994. (3) Onori, G.; Santucci, A. J. Phys. Chem. 1993, 97, 5430. (4) D’Angelo, M.; Onori, G.; Santucci, A. J. Phys. Chem. 1994, 98, 3189. (5) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. Phys. ReV. E 2003, 68, art.021406. (6) Hauser, H.; Haering, G.; Pande, A.; Luisi, P. L. J. Phys. Chem. 1989, 93, 7869. (7) Goto, A.; Yoshioka, H.; Manabe, M.; Goto, R. Langmuir 1995, 11, 4873. (8) Kene´z, P. H.; Carlstro¨m, G.; Furo´, J.; Halle, B. J. Phys. Chem. 1992, 96, 9524. (9) Schwartz, L. J.; DeCiantis, C. L.; Chapman, S.; Kelley, B. K.; Hornak, J. P. Langmuir 1999, 15, 5461. (10) Datta, A.; Mandal, D.; Pal, S. K.; Bhattacharyya, K. J. Phys. Chem. B 1997, 101, 10221. (11) Riter, R. E.; Undiks, E. P.; Levinger, N. E. J. Am. Chem. Soc. 1998, 120, 6062. (12) Nave, S.; Eastoe, J.; Heenan, R. K.; Steytler, D.; Grillo, I. Langmuir 2000, 16, 8741. (13) Gragson, D. E.; McCarty, B. M.; Richmond, G. L. J. Phys. Chem. 1996, 100, 14272. (14) Conboy, J. C.; Messmer, M. C.; Richmond, G. L. J. Phys. Chem. B 1997, 101, 6724. (15) Conboy, J. C.; Messmer, M. C.; Richmond, G. L. Langmuir 1998, 14, 6722. (16) Grubb. S. G.; Kim, M. W.; Raising, T.; Shen, Y. R. Langmuir 1988, 4, 452. (17) Zhang, Z. H.; Tsuyumoto I.; Kitamori, T.; Sawada, T. J. Phys. Chem. B 1998, 102, 10284. (18) Piasecki, D. A.; Wirth, M. J. J. Phys. Chem. 1993, 97, 7700. (19) Tian, Y.; Umemura, J.; Takenaka, T.; Kunitake, T. Langmuir 1988, 4, 1064. (20) Kjellin, U. R. M.; Claesson, P. M.; Linse, P. Langmuir 2002, 18, 6745. (21) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. J. Colloid Interface Sci. 1995, 98, 243. (22) Fragneto, G.; Li, Z. X.; Thomas, R. K.; Rennie, A. R.; Penfold, J. J. Colloid Interface Sci. 1996, 178, 531. (23) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. Faraday Discuss. 1996, 104, 127. (24) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. J. Phys. Chem. B 1997, 101, 1615. (25) Li, Z. X.; Lu, J. R.; Thomas, R. K. Langmuir 1997, 13, 3681.
Surfactants Adsorbed at the Air/Water Interface (26) Li, Z. X.; Lee, E. M.; Thomas, R. K.; Penfold, J. J. Colloid Interface Sci. 1997, 187, 492. (27) Li, Z. X.; Lu, J. R.; Fragneto, G.; Thomas, R. K.; Binks, B. P.; Fletcher, P. D. I.; Penfold, J. Colloids Surf. 1998, 135, 277. (28) Li, Z. X.; Weller, A.; Thomas, R. K.; Rennie, A. R.; Webster, J. R. P.; Penfold, J.; Heenan, R. K.; Cubitt, R. J. Phys. Chem. B 1999, 103, 10800. (29) Shelley, J. C.; Watanabe, K.; Klein, M. L. Int. J. Quantum Chem. 1990, 17, 103. (30) Watanabe, K.; Klein, M. L. J. Phys. Chem. 1991, 95, 4158. (31) Bo¨cker, J.; Brickmann, J.; Bopp, P. J. Phys. Chem. 1994, 98, 712. (32) MacKerell, A. D., Jr. J. Phys. Chem. 1995, 99, 1846. (33) Wijmans, C. M.; Linse, P. Langmuir 1995, 11, 3748. (34) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 3788. (35) Bruce, C. D.; Senapati, S.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 10902. (36) Balasubramanian, S.; Bagchi, B. J. Phys. Chem. B 2002, 106, 3668. (37) Balasubramanian, S.; Pal, S.; Bagchi, B. Phys. ReV. Lett. 2002, 89, 115505. (38) Lisal, M.; Hall, C. K.; Gubbins, K. E.; Panagiotopoulos, A. Z. J. Chem. Phys. 2002, 116, 1171. (39) Scanu, L. F.; Gubbins, K. E.; Hall, C. K. Langmuir 2004, 20, 514. (40) Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1996, 100, 6637. (41) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2000, 104, 1033. (42) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2001, 105, 11148. (43) Faeder, J.; Albert, M. V.; Ladanyi, B. M. Langmuir 2003, 19, 2514. (44) Salaniwal, S.; Cui, S. T.; Cummings, P. T.; Cochran, H. D. Langmuir 1999, 15, 5188. (45) Salaniwal, S.; Cui, S. T.; Cochran, H. D.; Cummings, P. T. Langmuir 2001, 17, 1773. (46) Salaniwal, S.; Cui, S. T.; Cochran, H. D.; Cummings, P. T. Langmuir 2001, 17, 1784. (47) Griffiths, J. A.; Heyes, D. M. Langmuir 1996, 12, 2418. (48) Allen, R.; Bandyopadhyay, S.; Klein, M. L. Langmuir 2000, 16, 10547. (49) Tarek, M.; Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1995, 99, 1393. (50) Wijmans, C. M.; Linse, P. J. Phys. Chem. 1996, 100, 12583. (51) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 3793. (52) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 10775. (53) Dominguez, H.; Berkowitz, M. L. J. Phys. Chem. B 2000, 104, 5302. (54) Kuhn, H.; Rehage, H. J. Phys. Chem. B 1999, 103, 8493. (55) Kuhn, H.; Rehage, H. Phys. Chem. Chem. Phys. 2000, 2, 1023. (56) Kuhn, H.; Rehage, H. Colloid Polym. Sci. 2000, 278, 114. (57) da Rocha, S. R. P.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. B 2002, 106, 13250. (58) Stone, M. T.; da Rocha, S. R. P.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. B 2003, 107, 10185.
J. Phys. Chem. B, Vol. 109, No. 1, 2005 479 (59) Bandyopadhyay, S.; Chanda, J. Langmuir 2003, 19, 10443. (60) Rekvig, L.; Hafskjold, B.; Smit, B. J. Chem. Phys. 2004, 120, 4897. (61) Rekvig, L.; Hafskjold, B.; Smit, B. Phys. ReV. Lett. 2004, 92, 116101. (62) Dominguez, H. J. Phys. Chem. B 2002, 106, 5915. (63) Bocker, J.; Schlenkrich, M.; Bopp, P.; Brickmann, J. J. Phys. Chem. 1992, 96, 9915. (64) Lee, C. Y.; McCammon, J. A.; Rossky, P. J. J. Chem. Phys. 1984, 80, 4448. (65) Hautman, J.; Klein, M. L. Mol. Phys. 1992, 75, 379. (66) Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117. (67) Tuckerman, M. E.; Yarne, D. A.; Samuelson, S. O.; Hughs, A. L.; Martyna, G. J. Comput. Phys. Commun. 2000, 128, 333. (68) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (69) Procacci, P.; Darden, T.; Marchi, M. J. Phys. Chem. 1996, 100, 10464. (70) Procacci, P.; Marchi, M.; Martyna, G. J. J. Chem. Phys. 1998, 108, 8799. (71) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, England, 1987. (72) Schlenkrich, M.; Brickmann, J.; MacKerell, A. D.; Karplus, M. Empirical Potential Energy Function for Phospholipids: Criteria for Parameter Optimization and Applications. Biological Membranes: A Molecular PerspectiVe from Computation and Experiment; Birkhauser: Boston, 1996. (73) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (74) Tu, K.; Tobias, D. J.; Blasie, J. K.; Klein, M. L. Biophys. J. 1996, 70, 595. (75) Forester, T. R.; Smith, W.; Clarke, J. H. R. J. Chem. Soc., Faraday Trans. 1997, 93, 613. (76) Rocchi, C.; Bizzarri, A. R.; Cannistraro, S. Phys. ReV. E 1998, 57, 3315. (77) Bizzarri, A. R.; Cannistraro, S. J. Phys. Chem. B 2002, 106, 6617. (78) Liu, P.; Harder, E.; Berne, B. J. J. Phys. Chem. B 2004, 108, 6595. (79) Christensen, M.; Pedersen, J. B. J. Chem. Phys. 2003, 119, 5171. (80) Xu, H.; Berne, B. J J. Phys. Chem. B 2001, 105, 11929. (81) Stillinger, F. H. AdV. Chem. Phys. 1975, 31, 1. (82) Luzar, A.; Chandler, D. Nature 1996, 379, 55. (83) Luzar, A.; Chandler, D. Phys. ReV. Lett. 1996, 76, 928. (84) Chandra, A. Phys. ReV. Lett. 2000, 85, 768. (85) Rahman, A.; Stillinger, F. H. J. Chem. Phys. 1971, 55, 3336. (86) Rapaport, D. C. Mol. Phys. 1983, 50, 1151. (87) Benjamin, I. J. Chem. Phys. 1999, 110, 8070. (88) Pal, S.; Balasubramanian, S.; Bagchi, B. Phys. ReV. E 2003, 67, 061502. (89) Paul, S.; Chandra, A. Chem. Phys. Lett. 2004, 386, 218. (90) Bandyopadhyay, S.; Chakraborty, S.; Balasubramanian, S.; Pal, S.; Bagchi, B. J. Phys. Chem. B 2004, 108, 12608.
