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Molecular Dynamics Study of the Effect of Calcium Ions on the Monolayer of SDC and SDSn Surfactants at the Vapor/Liquid Interface Hui Yan, Xin-Li Guo, Shi-Ling Yuan,* and Cheng-Bu Liu Key Lab of Colloid and Interface Chemistry, Shandong University, Jinan 250100, China
bS Supporting Information ABSTRACT: The effect of Ca2þ ions on the hydration shell of sodium dodecyl carboxylate (SDC) and sodium dodecyl sulfonate (SDSn) monolayer at vapor/liquid interfaces was studied using molecular dynamics simulations. For each surfactant, two different surface concentrations were used to perform the simulations, and the aggregation morphologies and structural details have been reported. The results showed that the aggregation structures relate to both the surface coverage and the calcium ions. The divalent ions can screen the interaction between the polar head and Naþ ions. Thus, Ca2þ ions locate near the vapor/liquid interface to bind to the headgroup, making the aggregations much more compact via the salt bridge. The potential of mean force (PMF) between Ca2þ and the headgroups shows that the interaction is decided by a stabilizing solvent-separated minimum in the PMF. To bind to the headgroup, Ca2þ should overcome the energy barrier. Among contributions to the PMF, the major repulsive interaction was due to the rearrangement of the hydration shell after the calcium ions entered into the hydration shell of the headgroup. The PMFs between the headgroup and Ca2þ in the SDSn systems showed higher energy barriers than those in the SDC systems. This result indicated that SDSn binds the divalent ions with more difficulty compared with SDC, so the ions have a strong effect on the hydration shell of SDC. That is why sulfonate surfactants have better efficiency in salt solutions with Ca2þ ions for enhanced oil recovery.
1. INTRODUCTION The study of organized surfactant assemblies at interfaces is of great importance in industrial applications such as oil recovery, detergency, purification, and solid dispersion.1 These applications motivate efforts toward describing surfactant aggregates and surfactant monolayer at various interfaces.2,3 Surfactant adsorption depends on their unique amphiphilic properties, which is known as the balance between hydrophobic and hydrophilic forces of the tail and headgroups.4 When a surfactant adsorbs at the interface, the hydrophilic portion (i.e., headgroup) points into the water and the hydrophobic end (i.e., the tail) is directed out of the water. In order to obtain information about the microscopic nature of the aggregates or the monolayer of amphiphilic molecules at the interface, many modern experimental methods including smallangle neutron scattering, X-ray reflection, and sum-frequency vibrational spectroscopy have been widely used.57 Special attention has been paid to the structure and dynamic properties of the surfactants including extension of the chains, different hydrophilic heads, and thickness of the monolayer. For instance, Thomas and co-workers employed neutron reflection to assess the structure of adsorbed anionic surfactant sodium dodecyl sulfate (SDS) at the air/water interface.8 They report that the tail groups of SDS are oriented less perpendicularly to the interface than dodecanol tail groups, and thus the thickness of the interfacial dodecanol layer is larger than that of SDS. Lavoie et al. used the X-ray reflection technique to investigate the monolayer of r 2011 American Chemical Society
membrane protein rhodopsin at the air/water interface and discussed its secondary structure and the thickness of the monolayer film.9 Richmond and co-workers used vibrational sum frequency spectroscopy to study the structure and orientation of interfacial water molecules on both anionic and cationic surfactant monolayers dodecylammonium (DDA) and SDS at the air/water interface.10 They observe that with a cationic surfactant present at the interface the water oxygen atoms point toward the air, whereas for an anionic surfactant the water molecules in the double-layer region align with their oxygen atoms pointed into the solution. These investigations in different systems are helpful to understand the structures and properties of the monolayer at the interface. In recent years, due to the substantial increase in computational power, computer simulations such as Monte Carlo (MC) and molecular dynamics (MD) have played a crucial role in providing microscopic details of the structural and dynamics properties of surfactant assemblies.1114 There have been many reports on the study of the microscopic properties of surfactant assemblies at different interfaces using simulation methods. Tarek et al.14 carried out MD simulations of a monolayer formed by tetradecyltrimethylammonium bromide (C14TAB) at the vapor/water interface at two different surface areas of surfactant. Received: December 16, 2010 Revised: April 5, 2011 Published: April 15, 2011 5762
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Langmuir The simulated densities were found to be in good agreement with those obtained by fitting to the neutron reflectivity data. Recently, Striolo and co-workers4 compared the behavior of hexaethylene glycol monododecyl ether (C12E6) and SDS at vacuumwater interfaces using MD simulations to investigate the effect of the surface density on the surfactant orientation structure. They found that the longer surfactant tails are more tilted toward the aqueous phase than the shorter ones. These kinds of studies give more information about the dynamic and structural properties from a microscopic level, which is not easy to get from experiments. In this work, atomistic MD simulations were employed to study two different anionic surfactant sodium dodecyl carboxylate (C11H23COONa, SDC) and sodium dodecyl sulfonate (C12H25SO3Na, SDSn) adsorbed at the aqueous solution/vapor interface for two interface coverages (surface area per molecule). They have the similar tail length but different headgroups. The two surfactants show many different physicochemical properties; for example, the critical micelle concentrations (cmc) of SDC and SDSn are 2.6 102 and 9.7 103 mol L1, respectively.15,16 Until now, both carboxylate and sulfonate surfactants have been widely adopted as flooding agents in enhanced oil recovery (EOR) in some regions under different geological conditions.17 However, at some special conditions under which there are amount of inorganic ions such as Ca2þ, Mg2þ, and Naþ ions existing, the sulfonate surfactant has better efficiency than the carboxylate surfactant. That is to say, in the case of high salt concentration, the inorganic cations have less effect on the physical character of sulfonate surfactants than that of carboxylate surfactants. Thus, the sulfonate surfactant will maintain surface activity in high salt solution. In other words, the salt tolerance of sulfonate surfactants is superior to carboxylate surfactants. Inorganic ions can strongly influence the properties of ionic surfactants via the cations interacting with an anionic surfactant. As there are amount of Ca2þ in geological conditions, it is meaningful to investigate the interaction between an anionic surfactant and Ca2þ ions at an atomistic level in order to provide more microscopic information in EOR and other industrial processes. During the past few decades, there have been theoretical studies on the surfactants with counterions or excess inorganic salt. For example, Berkowitz et al.13 performed MD simulation to investigate SDS micelle in water and the behavior of counterion Naþ was investigated. The sodium ions were found to form contact-ion pairs with the micelle headgroups rather than to be completely dissociated. Jedlovszky and Gilanyi performed a series of MD simulations of the adsorption layer of decyl sulfate with five alkali cations (Liþ, Naþ, Kþ, Rbþ, and Csþ) at the vapor/aqueous solution interface.18 Their findings revealed an increasing outer Helmholtz plate thickness with increasing cation size. Recently, Sammalkorpi et al.19 studied the properties of SDS aggregates in saline solutions of excess NaCl or CaCl2. They found that the ionic strength of the solution affected both the aggregate size and the structure of the micelles. Moreover, the presence of CaCl2 induced more compact and densely packed micelles with a significant reduction in gauche defects in the SDS hydrocarbon chains in comparison with NaCl. In earlier work, we investigated the effect of Ca2þ and Mg2þ on the hydration shell of two surfactants, SDS and SDSn, in their solution.20 By calculating the potential of mean force (PMF), we found that the energy barriers of ion pairs between the headgroup and Ca2þ and Mg2þ in the SDSn systems are higher than those in the SDS system, which means the salt tolerance of SDSn is superior to
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SDS. Although many of these prior simulations concentrated on the properties of the monolayer at the interface or the aggregated structures in solution, fewer have noticed the sulfonate and carboxyl surfactants. Also, the effect of inorganic salts on an adsorbed monolayer is far from being systematically explored. In this paper, an all-atom MD simulation study of SDC and SDSn at a vapor/aqueous interface is reported. Particular attention has been paid to the effect of Ca2þ on the aggregation of carboxylate or sulfonate surfactants at the saline solution interface and their interactions with ions. Another focus of this paper is to characterize the structural and dynamical information on the hydration shell of the surfactant headgroups. The simulation and models are first discussed, and then the main results obtained from the simulations and the interpretations are given in detail.
2. SIMULATION DETAILS Molecular dynamics simulations of the adsorption layers of two kinds of surfactants SDC and SDSn at different aqueous solution/vapor interfaces were performed, using the all-atom optimized performance for liquid systems (OPLS-AA) force field.21 The force field parameters for COO and SO3 groups were not available in OPLS-AA. In ref 22, their study combined new developed parameters with OPLS-AA and obtained reasonable structures. Therefore, we carried out MD following their parameters for the two groups in the present study. The atomic charges used in the Coulombic potential were assigned on the basis of the atomic charges specified in the OPLS-AA force field with some modification. The ions including Naþ, Ca2þ, and Cl were described by the OPLS Aaqvist potential.23 More detailed information about the force field parameters applied in this work is provided in Supporting Information Table S1. The simple extended point-charge (SPC/E) model was used to describe water molecules, which provided a good representation of the dielectric properties as well as the thermodynamic properties.24 Although OPLS-AA was parametrized for use with the TIP3P water model, it has generally been found to work well with the SPC/E model as well.2527 The total potential energy is given as a combination of valence terms, including bond stretching, angle bending, torsion, and nonbonded interactions. The nonelectrostatic parts of the interaction between the atoms were described by the Lennard-Jones potential, and the standard geometric mean combination rules were used for the van der Waals interactions between different atom species. In this work, we concentrated on the effects of Ca2þ on the hydration structure of the two surfactants at the vapor/liquid interface. To construct the surfactant monolayer system at an interface, a method which has been successfully used in recent studies was taken.12,28 That is, setting up the simulation system by placing two monolayers on opposite sides of a slab of aqueous solution which is thick enough for the two monolayers to remain effectively isolated from each other. In the simulation, a rectangular basic box of 30 30 130 Å3 was used, with the z-axis being perpendicular to the interface. The z dimension was kept as large as 130 Å to minimize interactions between the periodic replicas in the z direction. A water slab containing 900 water molecules corresponding to the density of bulk water was placed in the center of the basic box. In order to compare the different adsorption characters at the same condition, the surface concentration for the two surfactants were set the same. For each kind of surfactant, we simulated at two different surface concentrations, and the effect of the salt CaCl2 5763
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Table 1. Simulation Systems: Numbers of Each Component in Different Systems system
SDC
A
18
B C0
18 36
C
36
D
SDSn
Cl
Ca2þ
36
18
36
18
36
18
36
18
18
E
18
F0
36
F
36
was studied. Thus, both salt-free and saline solution interface were simulated. The use of the two concentrations of surfactants allowed for investigating the effect of ions on different adsorption monolayers. In preparing the initial configuration of the simulations, 900 water molecules were placed in a rectangular box with a size of 30.0 30.0 29.9 Å3, corresponding to the water slab. Then, the surfactant monolayer consisting of 9 or 18 monomers was prepared and placed on both side of water slab to form the two concentrations water/vapor interfaces, following the method of Jang and Goddard.12 The two concentrations were calculated to be ∼1.7 and ∼3.4 μmol/m2. The number of Naþ is equal to that of the DC or DSn, and no excess NaCl is added. Thus, a number of 18 or 36 Naþ ions have been inserted into the corresponding systems randomly. To present the saline solution systems, a number of 18 CaCl2 ion pairs were inserted into the salt-free systems to obtain the saline systems, which yielded ∼1 mol/L solutions of Ca2þ. For each surfactant, four simulation systems were obtained and summarized in Table 1. For brief, some useful information for system C0 and F0 is provided separately in the Supporting Information to argue the views in the following section. Snapshots of the initial configurations for the other six systems are provided in the Supporting Information, Figure S1. These systems were first minimized for 5000 steps using a steepest descent algorithm to remove the possible overlapping in the initial configurations. The simulations were performed using the GROMACS free software package (version 4.0.5).29 The temperature of the systems was kept constant at 298 K by the Berendsen thermostat algorithm with a coupling constant of 0.1 ps.30 Bond lengths were constrained using LINCS algorithm31 for the surfactant and water molecules. Periodic boundary conditions were applied in all directions. The nonbonded potential truncation was performed with a cutoff distance at 12 Å for Lennard-Jones potential. The long-range part of the electrostatic interactions was treated by the particle mesh Ewald method.32 All the MD simulations were carried out under canonical ensemble (NVT) with a time step of 1 fs according to previous studies.18 First a 2 ns MD run was performed to equilibrate the system. Then another long time of MD simulation was continued extending to 10 ns. The trajectories were collected in an interval of 1 ps, and the last 5 ns were used for further analysis.
3. RESULTS AND DISCUSSION Structural Properties of Surfactants Monolayer. The equilibration of the simulation systems was determined by monitoring the distance between the headgroups that belong to the two
Figure 1. Snapshots of the configurations of the eight systems at the end of the simulation. For clarity, the surfactants and the cations (Ca2þ and Naþ) are drawn as van der Waals spheres, Cl is shown as small green sphere, and water molecules are drawn in line style. The atom coloring scheme is O, red; C, blue; S, yellow; Ca2þ, green; Naþ, violet; and H, white.
opposite adsorption surfactant layers.28 The time evolution of the distances of the six systems over the whole simulation time is shown in Figure S2 of the Supporting Information. From the plots the distances can be found to achieve a stable equilibrium after a short period of simulation. During the long production run, i.e., the last 5 ns, these quantities fluctuated but did not show any drift, indicating that the systems was well equilibrated. Next, the detailed structural properties of the adsorbed monolayer and the effect of the inorganic salts on the monolayer will be investigated further. The microscopic behavior of the surfactants at different interfaces was obtained by developing the molecular picture of the structure of the surfactants used by the simulation. Figure 1 shows the snapshots of the configurations of the eight simulation systems at the end of the simulation run (only the cross-sectional views which are perpendicular to the interface are provided; the top views are supported in Supporting Information, Figure S3, and the configurations for system C0 and F0 are shown in Figure S4). The arrangement of the surfactants is found to be in good agreement with the well-known picture of the surfactant organization at the water/vapor interface;28 i.e., the hydrophilic headgroups (COO and SO3) tend to penetrate the interface while the hydrophobic tails are mostly excluded from the water layer. Different aggregation structures of the surfactants among these systems can be seen from both top and side views. We derived the average size of the micelles by calculating the average distance between S atom and the COM (center of mass) of the aggregates or monolayer of the SDSn systems which was taken as an example, shown in Figure S5 of the Supporting Information. We find that, throughout the last production MD run (the last 5 ns), the quantities of the distances in the saline systems (systems E and F) drift weaker than those in the salt-free system (systems D and F0 ). For example, the distance in system F0 can fluctuate to an extent of ∼1.5 nm. This indicates two points. One is that it is much possible for the surfactants to aggregate in the saline systems. In the salt-free systems, it is possible that not all the surfactants aggregate to a micelle (from the final configuration of MD run, only several surfactants aggregates). The other one is that even if the micelle forms, the surface micelle is fluctuating as the average drifts during the MD run. These findings can also be 5764
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Figure 3. Radial distribution functions between surfactant headgroups and water oxygen for each simulation system: (a) SDC systems and (b) SDSn systems.
Figure 2. Number density profiles of components with respect to the center of the simulation cell in the direction normal to the plane of the interface for SDC simulation systems (lower coverage: systems A and B; larger coverage: systems C0 and C). The Gibbs dividing surface is the point at which the water density is half of its value in the bulk phase.
confirmed by the 2D density number density maps of the headgroups over the xy plane (shown in Figure S6 of the Supporting Information). The locations of different components in the simulation systems can be characterized by the average number density distribution functions. The different components including headgroups, the hydrocarbon chains, Naþ, Ca2þ, and Cl were separately computed. The hydrogen atoms were omitted when calculating the number density of each component; i.e., the number density profiles of water molecules were represented by the position of oxygen atoms, while the hydrocarbon chains were represented by their carbon atoms. All the profiles were calculated with the density symmetrized over the two interfaces along the z axis with respect to the center. Since the profiles are symmetrical, only one interface has been presented for clarity. Figure 2 shows the density profile of each component along the z direction (i.e., in the direction normal to the plane of the interface) in the four SDC systems. To make a comparison between the systems with and without CaCl2 in the same surface coverage systems, we find that in saltfree systems most of the Naþ ions distribute close to the oppositely charged headgroups, which means Naþ ions are bound to the headgroup at the interface. In contrast, in saline systems we find Ca2þ ions are bound to the headgroups and most Naþ ions are located in the bulk aqueous phase. The feature is also visible in Figure 1. This means Ca2þ can screen the interaction between Naþ ions and headgroups. For the distribution of the surfactants, there is a slight shift out of the interface if CaCl2 is present in the system at both lower and larger coverage systems. We think it is due to the salting-out effect of the Ca2þ ions which are adsorbed at the interface. Another interesting feature with the CaCl2 presence is the synergic effects between various types of ions. The distribution of Cl ions is also through the aqueous phase similar to that of Naþ, which means Cl and Naþ coexist in the aqueous. Another significant feature is the extent of the chain distribution. In the case of high coverage systems, it is extended to around 20 Å. The average length of the surfactant is calculated to be 10 Å based on the two peaks of
the headgroup and chain distribution. While the chain length of the optimized structure of a single surfactant is ∼14 Å. It indicates at least two aspects. One is the tails of the surfactants is bended or the micelle forms. Another is the dynamics of the surfactants, since the results are statistic through the MD trajectories. The density profiles for SDSn systems are provided in the Supporting Information, Figure S7, and similar results can be obtained. To characterize the orientation of the surfactants at the interface, the orientation of the hydrocarbon tail vectors with respect to the normal (i.e., z axis) to the plane of the interface (xy plane) was calculated. The vector connecting the R-CH2 and the terminal methyl group (CH3) is defined as the tail vector. Figure S8 (shown in Supporting Information) displays the probability distribution F(θ) of the tilt angle θ between the tail vector with respect to the normal to the surface in the simulation systems. The tail vectors of both SDC and SDSn are tilted with an average tilt angle of 52.55 and 48.70, respectively, at the lower coverage without Ca2þ (i.e., systems A and D). In the presence of Ca2þ at the lower coverage, the populations of the tilt angle tend to smaller angles for both the two surfactants, as there are drifts of cos(θ) to a higher value (close to 1). At the higher coverage, the orientations of both surfactants tail vectors are almost perpendicular to the interface, i.e., ∼15. These findings indicate that the divalent ions indeed affect the packing of surfactants at the interface. With the existence of Ca2þ, the monolayer becomes more compact due to strong interactions between the negatively charged surfactant headgroups and the positive ions. Because of counterion condensation, the charged heads strongly associate with each other. This aggregation forces the surfactant tails to become more perpendicular to the interface due to the spatial restriction of the molecules. However, the difference of the tilt angle between SDC and SDSn is very small. This finding indicates that divalent ions can make both kinds of surfactants into a more compact self-assembled aggregate. More detail about the interaction between the headgroups and cations will be discussed next. Interaction between Surfactant and Water. To quantitatively characterize the headgroupwater interactions, the radial distribution functions (RDFs) between relevant atoms have been calculated. The dotted lines in Figure 3 show the RDF g(rOheadgroupOwater) for SDC and SDSn at salt-free water/vapor interface (systems A and D), respectively. As the headgroup oxygen atoms can form H-bonds with the water oxygen atoms, information pertaining to the formation of primary, secondary, or more interaction shells can be extracted from the RDF.33 From each RDF, there is a preferential hydration shell at the first peak distance and a well-defined second solvation shell. The presence of such high-intensity peaks suggests that the headgroups of both 5765
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Figure 4. H-bonds structure around the headgroup, drawn by randomly selecting one surfactant molecule and some water molecules which are around the headgroup from the MD configurations: (a, c) H-bond structure around headgroup in salt-free system; (b, d) H-bond structure around headgroup in saline system.
SDC and SDSn strongly influence the structure of the surrounding water at the interface. There is also a weakly formed third hydration shell at ∼6.7 Å in the two RDFs. It is possible that the water molecules in the first hydration shell are H-bonded to the headgroup oxygen atoms. In the external shells, although the water is not directly bound to the headgroup by H-bonds, it surrounds the headgroup in well-defined solvation shells. The curves of both RDFs levels out beyond a radial distance of 8 Å, indicating the presence of bulk liquid at this distance. The interactions of oxygen atoms with water indicate that H-bonds provide an important contribution to the properties of the surfactants at the interface. To investigate how the hydration structure changes with the existence of CaCl2, the corresponding RDFs were also checked which exhibit some interesting discrepancies, as shown in Figure 3. It is evident that the intensity of the first peaks of RDF becomes weak for both the two surfactants when CaCl2 is introduced to the systems. Moreover, the first minimum of the first peak is extended. We observe that the first minima with the existence of Ca2þ (systems B and C) shift to ∼3.7 Å from ∼3.2 Å of system A, and for systems E and F they shift to ∼3.4 Å from ∼3.2 Å of system D. We conclude that as Ca2þ ions enter into the first hydration shell of the headgroup, the first hydration shell of SDC changes more evidently than SDSn. However, an evident effect is on the second peak which corresponds to the second hydration shell of the SDSn headgroup, which changes drastically with the addition of inorganic salts. As shown in Figure 3b, an intermediate peak appears between the first and second peaks. We believe that the middle peak observed in the RDF of headgroup OOw is also related to the invasive Ca2þ ions, which interferes with the hydration shell of the headgroups. It is
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possible that water will bind to the Ca2þ counterions, and these waters in turn bind to the headgroup oxygen atoms.27 The RDFs g(rOheadgroupCa2þ) for the two surfactants show the distribution of the Ca2þ around the headgroup and confirm the above supposition (Supporting Information, Figure S9). From the locations of the peaks in the corresponding RDFs, we conclude that Ca2þ may enter into the first and second water shells. Ca2þ can screen the interaction between the headgroup and Naþ, which can be confirmed by the weak intensity of g(ONaþ). Ca2þ ions which enter into the hydration shell of the headgroups can disturb the original water orientation around the polar head, changing the hydrogen-bond structure around the headgroup. Based on the analysis above, the H-bond structures around the headgroups which were randomly selected from the MD configurations were used to show how the hydration shell is affected by Ca2þ. Figure 4a shows the case in the absence of CaCl2 (system A). Water molecules assemble around the SDC headgroup via a compact H-bond network, forming the headgroup hydration shells. It is also clear that the water molecules locate in the first hydration shell (i.e., the water molecules that directly form H-bonds to the surfactant headgroup) with water hydrogen atom pointing toward the headgroup. This was shown in the earlier work.11 Since the headgroup oxygen atom is the acceptor atom forming H-bonds between the headgroup oxygen and water, the oxygen in the first shell should be the donor atom of the H-bonds. Correspondingly, most of the water molecules in the second shell can still be the H-bond donors to oxygen atoms in the first shell. As a result, the hydration shells consist of a compact H-bond network. When Ca2þ is present, the headgroup can pull it into the hydration shell due to strong electrostatic force between the polar head and the ion. As shown in Figure 4b, one Ca2þ enters into the hydration shell to bind with the surfactant. We found that the original water orientation around the headgroup changes; i.e., the water molecules nearby the Ca2þ bind to the ion with their O atoms pointing to the ion. Thus, the H-bonds network is disturbed, and some H-bonds formed between the first and second shell break off. We conclude that some water molecules may come close to the first shell from the bulk water either by H-bonding interaction or Coulomb attraction of the divalent ion. These water molecules that were attracted into the hydration shell by the Ca2þ will extend the first hydration shell or cause middle assembled peak around the headgroup as shown in the RDF. For SDSn, very similar results are obtained. It is not very important whether the ion enters into the first or the second shell of the polar head because when an ion enters, the orientation of water molecules around the ion changes, leading to pronounced structural changes within the H-bond network. Spatial Distribution Functions of Water Molecules and Ions around the Headgroup. To obtain visual information on the nature of the interactions between the various molecules in the solution, many groups have defined the spatial distribution function (SDF).34,35 SDF is a useful tool to reveal detailed information about the neighboring molecules of a specific type of atom around a central atom of interest and can give a detailed description of the immediate environment. In Figure 5, the SDFs around the carboxyl groups and sulfonate groups in each simulation system are displayed. The neighboring water molecules around the headgroup are drawn at a value of 3.5 Å, which corresponds to the first hydration shell. For the SDC headgroup, two circular rings are observed around the headgroup oxygen atoms while for the SDSn, there 5766
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Figure 5. SDFs of water oxygen (blue) and Ca2þ (yellow) around the headgroup of SDC (left) and SDSn (right) of systems AF. The contour levels for water atoms were set at 20 times the bulk atomic density of water in the solution. Data averaging of neighboring bins in the Cartesian grid was performed to reduce the statistical noise in the SDFs. The headgroups of the two surfactants along with the CR are selected as the central atoms. Oxygen, sulfur, and carbon are shown in red, yellow, and green, respectively.
are three rings around atoms O13. These circular rings represent the probability distribution of water molecules around these headgroup oxygen atoms. It indicates that water molecules will preferentially interact with the surfactant around the O sites of the headgroups. For the two groups, the SDFs show holes in the contour along the CO or SO axes, which is similar to the previous works.20,27 The headgroup oxygen atoms of the two kinds of surfactants can only accept hydrogen bonds and the angle of OwHwOheadgroup (Ow and Hw represent O atom and H atom in a water molecule) is defined to be ∼135. In consequence, more water molecules in the first hydration shell locate around the direction of CO or SO bond in a toroidal area. This demonstrates that water is bonded at a preferred angle. It is interesting to find changes of the water molecules distributed around the headgroup with Ca2þ present. The water distributions around the two surfactants are quite different from those in salt-free systems. Especially the changes of the SDC systems are more drastic than SDSn systems. We find that the original two circular clouds disappear in the low coverage system (system B). Instead, a new circular-shaped cloud forms in the vicinity of the carboxyl group as marked I in Figure 5c, and there is a ribbon present to the area besides the circle which is marked II. Also, there are still two ribbons surrounding the two headgroup oxygen atoms as marked III. The position of these ribbons is identical to the circled segments known from the salt-free system. In the high coverage system (system C), the hydration shell is found to zoom out. It is mainly due to the aggregation of the surfactants with Ca2þ present. As a consequence, more Ca2þ ions are adsorbed to stabilize the increased electrostatic repulsion between the charged headgroups. Thus, the water molecules are expelled because of the higher coverage of the surfactants for SDC system. For the SDSn systems, the first hydration shell of
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the headgroups changes relatively slightly. In the presence of CaCl2, there are still circular clouds around the headgroup oxygen atoms. Outside the circles, three distinguishable lobes appear as indicated by black arrows. In the high coverage system of SDSn (Figure 5F), there is almost no difference from the lowcoverage system. This indicates that when binding with more Ca2þ, the first hydration shell of the SDSn headgroup is less affected than that of the SDC headgroup. As discussed on the RDF above, the divalent ions can enter into the hydration shell of the headgroup, and they cause the H-bond network to change. In Figure 5 the distribution of Ca2þ ions in the first hydration shell of the surfactant headgroup is also illustrated. (For the distribution of Naþ, please see Figure S10 of the Supporting Information.) For both two surfactants, Ca2þ ions prefer to locate at the region along the CO or SO axis, and they also distribute between the two headgroup O atoms of SDC. But the ions can hardly be found between two O atoms of the SDSn headgroup. There is a common point between the two surfactant systems; i.e., only when the ions occupy the center of the circular ring formed by the distributions of water molecules around the headgroup, the ions can attract more water molecules to form a headionwater structure. This shows that water molecules bind to the headgroup oxygen atoms either directly or bridged by the Ca2þ ions. Since the steric configuration of the COO group is a planar structure while that of the SO3 group is a tetrahedral structure, it is possible that Ca2þ ions can distribute around the SDC head by sharing two O atoms. If Ca2þ locates along the CO axis, the original circular distributions of water will be destroyed with residual water molecules around one O atom. To explore the binding behavior between the surfactant and the ion, the probability of salt bridges between nearest-neighbor headgroups has been assessed. It is assumed that one cation bridges two anionic headgroups in an aqueous system, if one ion resides within a distance of 7.2 Å from two nearest-neighbor headgroup pairs. From the saline systems (both the low and high surfactant coverage systems), several binding distributions between ions and surfactants can be observed. According to the number of surfactant headgroups which are bridged by one cation, several types of salt bridges are defined. For example, a calcium ion bound to two SDC or to three SDSn has been obtained from the MD results, and the snapshots of salt bridge configurations are shown in Figure 6. There is something special when one calcium atom is binding to two or more SDC surfactants as shown in Figure 6a. One Ca2þ bridges two surfactants but it is shared by four headgroup O atoms. That reflects that Ca2þ can distribute in the middle region of the two headgroup O atoms. However, this phenomenon is hardly found for the SDSn system. These findings also correspond to the spatial distribution functions of Ca2þ around the two surfactant headgroups as shown in Figure 5. For Naþ at the low surfactant coverage systems (systems B and E), there is still part of the Naþ in the interfacial area. But it is still hard to find a Naþ binding to two or more surfactants. To study the character of the salt bridges further, the percentage of Ca2þ or Naþ forming salt bridges was calculated. A salt bridge exists when two headgroups are bridged by one cation, and the cation resides within a distance of 7.2 Å from the two nearest-neighbor headgroup pairs.34 In the systems without CaCl2 (systems A and D), of the sodium ions that are in the first shell of the headgroup, more than 90% interact with only one headgroup for both the two surfactants. In the saline systems, we 5767
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Figure 6. Snapshots for typical configurations of Ca2þ bridging as observed within the SDC (inset a) and SDSn (inset b) adsorption interfaces. The color code is the same as that of Figure 1. Water molecules are omitted, and the headgroups are highlighted for clarity. (c) Schematic representation of counterion bridging is indicated by the blue circle or ellipses in (a) and (b).
were only concerned with the Ca2þ bridging the surfactants. Taking SDC systems (systems B and C), for example, we found that in system B there are 57% of calcium ions in the first shell binding only one SDC surfactant. The remaining ions are bridging two headgroups. In contrast, for an increased surfactant density (system C) we found that the percentage of calcium ions that interact with one surfactant decrease to less than 30%, whereas about 43% are bridging two headgroups. Also, there are still nearly 30% bridging three headgroups (Figure 6b). For SDSn, very similar results were found. These results indicate that contact ion pairs exist and that interactions between a single ion and two or more headgroups have occurred. Also, we consider that the case that one calcium ions bind to only one surfactant decrease, which indicates that the existing salt bridges that connect two or more surfactants can make the adsorbed monolayer more compact. Interactions between the Headgroup and Ions. From the discussion above, we conclude that Ca2þ can enter into the hydration shell of the headgroup and thus change the orientation of water molecules surrounding the headgroup. Ca2þ can screen the interaction between the polar head and Naþ in systems containing Ca2þ. In contrast, the effect of Naþ is still not clear. In systems without CaCl2, Naþ ions are attracted to the interfacial region (see Figure 1A,D). However, from Figure 3 we found that the RDFs of OheadOw are very different from those in the present of Ca2þ. Thus, we concluded that Naþ has different effects on the H-bonds network of the headgroup comparing to Ca2þ. Because of the electrostatic interaction, both the cations Ca2þ and Naþ can bind to the headgroups of SDC and SDSn. The binding energy should be related to the ability of the ions to interact with the headgroups. In this study, a two-ion bond is defined as one ion pair which was brought from infinite separation and gradually reduced to a distance r. The energy profile between the ion and the surfactant headgroup was determined by the potential of mean of force (PMF). In this simulation, the ionpair PMF was calculated by the pair distribution function g(rOheadions) through the equation E(r) = kBT ln g(r),36,37
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Figure 7. Pair potential of mean force between headgroups and ions: (a) and (b) are for the SDC systems while (c) and (d) are for the SDSn systems. CM: contact minimum; SSM: solvent-separated minimum; BARR: barrier.
where kB is Boltzmann’s constant and T is the simulation temperature. Figure 7 shows the headgroup and ion PMFs in the six simulation systems from the correlation g(r). The headgroupCa2þ and headgroupNaþ PMFs are shown separately for both SDSn and SDC surfactants. Taking the headgroupCa2þ ion pair in the SDC systems for instance (Figure 7b), the following observations can be made: (i) The contact minimum (CM) in free energy is at about 2.27 Å, corresponding to the direct contact between the headgroup and a Ca2þ ion, which means the headgroupCa2þ separation is about 2.27 Å. (ii) The second minimum is at a distance of ∼4.50 Å, which corresponds to the solvent-separated minimum (SSM). The relative stabilization of the SSM is with respect to the CM. Both CM and SSM determine the binding affinity of ions to the headgroup. (iii) The CM and SSM are separated by a desolvation barrier (BARR) that must be overcome for transitions between the two minima to occur. The calculated PMFs tend to be zero with the increasing distance between the headgroup and cation. The binding energy barrier for the headgroup and ion pair is related to SSM and BARR, i.e., ΔEþ = EBARR ESSM, while the dissociation energy barrier for the ion pair is related to CM and BARR, i.e., ΔE= EBARR ECM. The calculated energies of ionsurfactant in each system are listed in Table 2. The SDC systems are used to illustrate several observations from the data in Table 2. The CM and BARR of headNaþ are fairly low in the salt-free system (system A). The binding and dissociation energy are 4.08 and 9.15 kJ/mol, respectively (the data were obtained by ΔEþ = EBARR ESSM = 0.40 (4.48) = 4.08 kJ/mol while ΔE= EBARR ECM= 0.40 (9.55) = 9.15 kJ/mol). Comparing with the data obtained from saline systems, the two energies in salt-free systems are the lowest. This means it is easy for Naþ to enter into the first water shell of the headgroup to form the ion pair in the absence of Ca2þ. On the other hand, Naþ ion also can easily escape from the headgroup as the dissociation energy is fairly low. Even in saline systems (system B and C), the energies of Naþheadgroup pair are lower than those of Ca2þheadgroup pair. Similar observations can also be found in the SDSn systems. The observations show that it is fairly 5768
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Table 2. Values of Free Energies Corresponding to the SSM (ΔEþ) and CM (ΔE) with Respect to the Energy Barriers in Each Systema Naþ ΔE
system
a
Ca2þ ΔEþ
ΔE
ΔEþ
A
9.15 ( 0.2
4.08 ( 0.2
B
9.60 ( 0.5
6.53 ( 0.5
17.60 ( 0.5
8.66 ( 0.5
C
9.76 ( 0.5
5.19 ( 0.5
16.55 ( 0.5
9.52 ( 0.5
23.52 ( 0.5 25.24 ( 0.5
19.12 ( 0.5 20.84 ( 0.5
D
8.69 ( 0.2
6.65 ( 0.2
E F
9.82 ( 0.5 8.75 ( 0.5
7.78 ( 0.5 6.34 ( 0.5
The data are calculated based on Figure 7, and the unit is in kJ/mol. þ
hard for Na to persist in the hydration shell of the headgroup. Therefore, Naþ ions have little effects on the H-bonds structure of the headgroup. There is a significant increase of the barrier and the two minima between headgroups and Naþ in the case of the systems containing Ca2þ (Figure 7a,c). The corresponding energies also increase compared to the systems without Ca2þ as shown in Table 2. We think that this is mainly due to the contribution from the direct interaction between surfactant and calcium ions. As discussed above, with the addition of Ca2þ the interaction between the headgroups and sodium ions can be reduced, and this may be reflected by the PMF. For the binding ability between Ca2þ and the surfactants, ΔEþ in SDSn systems (systems E and F: 19.12 and 20.84 kJ/mol, respectively) is rather higher than in SDC systems (systems B and C: 8.66 and 9.52 kJ/mol, respectively), which means that it is more difficult for SDSn to bind to Ca2þ than SDC. In other words, the salt tolerance of SDSn is greater than that of SDC. With the increase of surfactant coverage, the binding energies between the headgroup and Ca2þ are slightly heightened. In larger coverage systems most calcium ions locate in the interfacial region, and the aggregation structure of the surfactants is more compact, with several surfactant monomers bridged by Ca2þ. The competitive adsorption between different ions and headgroups induces an increase of binding energy. The PMFs calculated in this work are composed of the contribution from the direct surfactantcation interaction and the solvent-induced contribution. These data can successfully report the trends that reflect the binding ability of ions with headgroups using the potential model. It is also possible to consider the energy barrier as qualitative analysis of the efficiency for a variety of surfactants in saline solution conditions, such as in EOR experiments. Within the statistical uncertainty, the PMFs shown in Figure 7 approach the correct long-range limit of zero beyond the ion-pair separations of about 7 Å. The stronger hydrophilic interactions between the headgroup and water molecules cause ordering of water layers around the headgroup through H-bonds and electrostatic interactions, leading to nonzero PMF only at smaller separations. The PMF can be used to interpret the salt tolerance of the headgroup in the solution. Hydrogen Bond Analysis. The structural relaxation of hydrogen bonds formed between water molecules and headgroups of surfactants can be characterized by the time correlation function: CHB ðtÞ ¼
Æhðt þ τÞhðτÞæ Æhæ
ð1Þ
Figure 8. Time correlation function CHB(t) for the hydrogen bonds formed between the water molecules and the headgroup in different systems: (a) SDC systems and (b) SDSn systems.
where the hydrogen bond population variable h(t) is unity when a particular water molecule is hydrogen bonded with the headgroups in time t and 0 otherwise.38 To determine if an H-bond exists, a geometrical criterion is used: the distance between the selected donoracceptor pair is within 3.5 Å, which is the position within the first hydrated shell of the headgroups,39 and their OH 3 3 3 H angles should be less than 120. With this definition the time correlation function for the hydrogen bonds formed between water molecules and headgroups has been calculated for the two kinds of surfactants systems. The correlations are shown in Figure 8. It is clear that the relaxation curves for systems containing CaCl2 (systems B, C, E, and F) decay much slower to zero than those corresponding to salt-free systems. The similar slow hydrogen bond dynamics have been recently studied at an air/water interface or near a micellar surface.40 As Ca2þ enters into the first hydration shell of the headgroup, Ca2þ ions should interact with water molecules surrounding them. Thus, the interaction between headgroups and those water molecules in the first shell will be influenced. The headgroupwater H-bond was replaced by the ionwater interaction; this is consistent with the findings from Figure 4. This indicates that the presence of Ca2þ can make the water molecules significantly restricted and form more stable H-bond structure with the headgroups. It is possible to calculate a residence time by fitting the correlation functions to a single exponential. The values are listed in Table S2 (provided in Supporting Information), which may be taken as qualitative estimates. The residence probability of water in the first shell is enhanced in the presence of Ca2þ. The residence times also depend on the concentration as shown in the table. The present observations support that the residence time depends on the environment surrounding the group. The residence time of H-bonds should be related to the hydrogen bond energies between the headgroups and water molecules. Taking SDC systems, for instance, the calculated average hydrogen bond dissociated energies have been found to be increased when Ca2þ are added in the system. These changes are consistent with that of the residence time, and they can partially explain the different dynamics of H-bonds formed between headgroups and water molecules. It shows that when the energy is higher, the dissociation of headgroupwater is more difficult, and therefore the residence time is larger. Beside this, the dissociation energies of H-bond between SDSn and water are higher than those in the SDC system in both the absence and presence of Ca2þ, but the cases of binding energies are just the opposite. Therefore, the H-bond between the SDSn headgroup and water forms more easily, and it is difficult to break them. 5769
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Langmuir The organization of the H-bond around the headgroup can be analyzed by examining the H-bonds numbers. The H-bond number clearly decreased if Ca2þ is present. It reflects that the ions can compete with the surfactants hydrating waters, in spite of the number of water molecules increasing in the first shell due to the interaction between ions and water. So the ions can exclude the hydration water of surfactants, which can result in the surfactants losing their interfacial activity. The numbers of H-bonds in SDC systems are less than that in SDSn systems since there are only two O atoms which can be H-bond donors in SDC. Moreover, from the total H-bond energy (EBARRþ EBARR, see Table S2 in the Supporting Information), we find ΔEBARR < 0 for SDC. Thus, it is difficulty for SDC to form H-bond than for SDSn. The weaker interaction between SDC and water molecules makes the H-bonds less stable, and SDC will be more easily affected by the divalent ions.
4. CONCLUSIONS Molecular dynamic simulations were employed to study the effects of divalent ions Ca2þ on the headgroup hydration shell of two surfactants SDC and SDSn at the vapor/liquid interface. The simulations indicate that the adsorption structure of both surfactants depends not only on the surfactant surface coverage but also on the Ca2þ ions circumstances. In the absence of Ca2þ, the aggregates of the surfactants are looser, while in the presence of Ca2þ, the surfactants will form more compact aggregations via a salt bridge. At high surfactant surface coverage, the tails of the two surfactants are oriented almost vertically to the interface. By checking the adsorption location of each component, we found that the influence of Ca2þ on the SDC monolayer is stronger than on the SDSn monolayer. The hydration shells of the surfactants can be affected by Ca2þ ions due to the binding between headgroup and Ca2þ. The binding is decided by a deep stabilizing minimum in the potential of mean force between the interaction pair. The PMFs show that the energy barrier of ion pairs between the SDSn headgroup and Ca2þ is higher than that in SDC systems, which means sulfonate surfactants are more efficient in saline circumstance in EOR experiments. When Ca2þ ions enter into the hydration shell of the headgroup, they can break the H-bond structure around the headgroup, leading to a decrease of H-bond number and an increase of H-bond residence time. Water molecules in the first hydration shell can bind to the headgroup either by direct H-bond or bridged by ions. We found that the hydration shell of the carboxyl group changes more drastically than that of the sulfonate group. ’ ASSOCIATED CONTENT
bS Supporting Information. Force field parameters; H-bond information; snapshots of the initial configurations; average distance between two monolayers; top views of final configurations; average distance of sulfur atoms from the monolayer COM; 2D number density maps of SDSn headgroups over the xy plane; number density profiles of SDC systems; distribution of the tilt angle of the tail vectors; RDF between headgroups and ions. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ ACKNOWLEDGMENT This work was financially supported by the PetroChina Innovation Foundation, the National Science Foundation (21043008 and 20873074), and the National Basic Research program (2009CB930104) of China. Thanks to Dr. Edward C. Mignot, Shandong University, for linguistic advice. We are thankful to the referees for their constructive comments, which are help to improve the quality of our manuscript. ’ REFERENCES (1) Paria, S.; Khilar, K. C. Adv. Colloid Interface Sci. 2004, 110, 75. (2) Lu, T.; Huang, J.; Liang, D. Langmuir 2008, 24, 1740. (3) Gutig, C.; Grady, B. P.; Striolo, A. Langmuir 2008, 24, 13814. (4) Shi, L.; Tummala, N. R.; Striolo, A. Langmuir 2010, 26, 5462. (5) Berret, J.-F.; Herve, P.; Aguerre-Chariol, O.; Oberdisse, J. J. Phys. Chem. B 2003, 107, 8111. (6) Larson, K.; Vaknin, D.; Villavicencio, O.; McGrath, D.; Tsukruk, V. V. J. Phys. Chem. B 2002, 106, 7246. (7) Reynolds, P. A.; McGillivray, D. J.; Gilbert, E. P.; Holt, S. A.; Henderson, M. J.; White, J. W. Langmuir 2003, 19, 752. (8) Purcell, I. P.; Thomas, R. K.; Penfold, J.; Howe, A. M. Colloids Surf., A 1995, 94, 125. (9) Lavoie, H.; Desbat, B.; Vaknin, D.; Salesse, C. Biochemistry 2002, 41, 13424. (10) Gragson, D. E.; McCarty, B. M.; Richmond, G. L. J. Phys. Chem. 1996, 100, 14272. (11) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 3793. (12) Jang, S. S.; Goddard, W. A., III J. Phys. Chem. B 2006, 110, 7992. (13) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 3788. (14) Tarek, M.; Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1995, 99, 1393. (15) Klevens, H. B. J. Am. Oil Chem. Soc. 1953, 30, 74. (16) Bujake, J. E.; Goddard, E. D. Trans. Faraday Soc. 1965, 61, 190. (17) Yang, J.; Qiao, W.; Li, Z.; Cheng, L. Fuel 2005, 84, 1607. (18) Hantal, G.; Partay, L. B.; Varga, I.; Jedlovszky, P.; Gilanyi, T. J. Phys. Chem. B 2007, 111, 1769. (19) Sammalkorpi, M.; Karttunen, M.; Haataja, M. J. Phys. Chem. B 2009, 113, 5863. (20) Yan, H.; Yuan, S. L.; Xu, G. Y.; Liu, C. B. Langmuir 2010, 26, 10448. (21) Jorgensen, W. L.; Maxwell, D. S.; Tirada-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (22) Tsuzuki, S. T.; Shinoda, W.; Saito, H.; Mikami, M.; Tokuda, H.; Watanabe, M. J. Phys. Chem. B 2009, 113, 10641. (23) Aaqvist, J. J. Phys. Chem. 1990, 94, 8021. (24) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (25) Stephenson, B. C.; Goldsipe, A.; Beers, K. J.; Blankschtein, D. J. Phys. Chem. B 2007, 111, 1025. (26) Yang, W. H.; Wu, R. L.; Kong, Bin.; Zhang, X. F.; Yang, X. Z. J. Phys. Chem. B 2009, 113, 8332. (27) Daub, C. D.; Leung, K.; Luzar, A. J. Phys. Chem. B 2009, 113, 7687. (28) Bandyopadhyay, S.; Tarek, M.; Lynch, M. L.; Klein, M. L. Langmuir 2000, 16, 942. (29) Spoel, D. V.; van Buuren, A. R.; Apol, E.; Meulenhoff, P. J.; Tieleman, D. P.; Sijbers, A.; Feenstra, K. Gromacs User Manual, version 4.0; Gromacs: Groningen, The Netherlands, 2009; www.Gromacs.org. (30) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 2190. (31) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. J. Comput. Chem. 1997, 18, 1463. (32) Essman, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577. 5770
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