Specific Counterion Effects on the Atomistic Structure and Capillary

Article pubs.acs.org/JPCC

Specific Counterion Effects on the Atomistic Structure and CapillaryWaves Fluctuation of the Water/Vapor Interface Covered by Sodium Dodecyl Sulfate Meng Chen,† Xiancai Lu,*,† Xiandong Liu,† Qingfeng Hou,‡ Youyi Zhu,‡ and Huiqun Zhou† †

State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering, Nanjing University, Nanjing Jiangsu 210093, China ‡ State Key Laboratory of Enhanced Oil Recovery, Research Institute of Petroleum Exploration and Development, CNPC, Beijing 100083, China S Supporting Information *

ABSTRACT: The structure of the water/vapor interface covered by a sodium dodecyl sulfate (SDS) monolayer can be remarkably affected by salts in aqueous phase. Molecular dynamics simulations have been performed to reveal the microstructure of the interface with different salts, including NaCl, CaCl2, and MgCl2. The bending modulus κ of the interface exhibits the order: with MgCl2 < with CaCl2 < with NaCl ≈ without salt, while the surface tension γ almost remains unchanged. The smaller κ characterizes larger interfacial fluctuation. In the systems with CaCl2 or MgCl2, the intrinsic density of Na+ adsorbed beside the monolayer is much lower than that without salt or with NaCl due to the adsorption of Ca2+ or Mg2+. However, less Ca2+ or Mg2+ ions enter the hydration shells of sulfate groups while Na+ ions normally coordinate the sulfate groups together with water. So in the systems with CaCl2 or MgCl2, sulfate groups are less bridged by ions and more solvated by water. Thus, the alkyl tails become more disordered. The above microstructure change with the addition of divalent ions leads to more fluctuated interface. This finding helps in understanding the mechanism of the influence of salts on the stability of foam films. dimyristoylphosphatidate (DMPA−), while Ca2+ ions keep stably hydrated which are independent of their position. In the presence of Ca2+ ions, the lipids are more disordered.9 However, the MD studies on sodium hexadecane benzene sulfonate, sodium dodecyl carboxylate (SDC) and sodium dodecyl sulfonate (SDSn) monolayers reveal that stable salt bridges between Ca2+ ions and hydrophilic groups lead to more compact structure of monolayers.10,11 So the influence of Ca2+ ions on the monolayer structure is hard to be determined. This difference is probably due to the different molecular structures. In systems of foam films covered by sodium dodecyl sulfate (SDS) monolayers, stable black films hardly exist with Mg2+ ions rather than Na+ ions, which is attributed to the rupturing of the films caused by thermally excited fluctuation capillary waves due to the existence of Mg2+ ions.12 The relationship between the SDS monolayer and salt ions is important to the foam film stability, but to our knowledge, it has not been studied in detail by MD simulations. In order to evaluate the influences of ions on structure of a surfactant monolayer at the water/vapor interface, it is necessary to disclose the capillary-waves fluctuation of the

1. INTRODUCTION Ionic surfactants are widely used in lots of fields, such as pharmacy, chemical industry, mineral engineering, environmental remediation, and petroleum recovery.1 Alkali (Na+, K+) and alkaline-earth (Ca2+, Mg2+) metal ions are common in environments for application of ionic surfactants. Due to the electrostatic interaction between the ionic surfactants at the water/vapor interface and solvated counterions, an electrical double layer (EDL) is present in the vicinity of the interface. The classical Gouy−Chapman (GC) model has been used to describe the structure of the EDL since a century ago. However, because the GC model simplifies ions as point charges and the charged interface as a planar homogeneously charged surface, remarkable deviation caused by such oversimplifications of the model has been conformed as comparing with experimental results.2,3 Due to differences in charge, specific ion sizes and hydrated properties of counterions, effects of different counterions on the structures of the EDL and monolayer2−11 and the stability of foam12−14 have been studied through experiments and molecular dynamics (MD) simulations. It is experimentally found that univalent counterions (Cs+) with small hydrated radii15 are more preferred in the EDL than divalent ones (Mg2+) if the surface charge density is high enough.2 An MD study also shows that Na+ ions are dehydrated and almost “naked” in the deepest zones of the anionic lipid monolayer of © 2014 American Chemical Society

Received: June 10, 2014 Revised: August 1, 2014 Published: August 4, 2014 19205

dx.doi.org/10.1021/jp505738s | J. Phys. Chem. C 2014, 118, 19205−19213

The Journal of Physical Chemistry C

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monolayer with different counterions. For an interface with cross-sectional area A0, the fluctuation ⟨|ξq̂ |2⟩ for certain wave vector q is controlled by elastic constants including surface tension γ and bending modulus κ, according to the equation:16−20 kT 1 ⟨|ξq̂ |2 ⟩ = B 2 A 0 γq + κq 4

(1)

where kB and T are Boltzmann constant and temperature, respectively. In the late 1980s, Winterhalter and Helfrich21 and Lekkerkerker22 studied the influences of EDL on the bending modulus κ theoretically based on Debye−Hückel and Poisson− Boltzmann equations. They predicted that the charged monolayer becomes more flexible as the ionic strength increases. But this prediction was in contradiction to later experimental results, which showed that κ hardly depends on salt concentrations.23−25 The discrepancy between theories and experiments can be attributed to the above-mentioned oversimplification in the EDL model. Later, the self-consistent field lattice model was adopted to study the monolayer bending elasticity, and revealed that the bending modulus increases significantly with the size of counterions.26 However, this model also oversimplified the specific counterion−water, water−monolayer, and counterion−monolayer interactions. More realistic models should be employed for approaching reliable results. MD simulations have been proved as reliable methods to study undulations and bending elasticity of membranes27−29 and monolayers.18−20,30,31 The influences of surfactant interfacial coverage and surfactant chain structures on monolayer elasticity have been investigated,18,19,30 but the influence of EDL has not been considered. As the foam film stability is related to counterion types, it is meaningful to study the differences in interfacial fluctuation with the existence of different counterions. This study aims to reveal the relationship between elastic properties (surface tension γ and bending modulus κ) and counterion types. Based on the analytic methods used by Chacón et al.,20,32 the intrinsic surface structure and elastic properties of SDS monolayers at the water/vapor interface with/without salt NaCl, CaCl2, or MgCl2 were investigated by using MD simulations. The interfacial structure influences on the capillary-waves fluctuation of the interface are further discussed.

Figure 1. Initial configuration of the simulated model of the system without salt. The cyan bonds stand for alkyl chains, yellow balls for S atoms, red balls for O atoms, blue balls for Na+ ions, and red points for water molecules.

406 Cl− ions were inserted, corresponding to about 0.5 mol/L CaCl2 or MgCl2. For the system with NaCl, 406 Na+ and 406 Cl− ions were inserted, corresponding to about 1.0 mol/L NaCl. The initial configuration was constructed by using Packmol.34 Periodic boundary conditions were applied in all three directions. Force Fields. GROMACS 4.0 package35−38 was used to perform MD simulations. Force field is the same as that in our previous study.39 The SPC/E model40 was used to describe water molecules. The OPLS-AA force field41 was used for SDS molecules and ions (Supporting Information). The LennardJones potential was calculated with the equation ULJ = 4πεij[(σij/rij)12 − (σij/rij)6] (σij and εij represent the effective diameter and interaction strength between atoms i and j, and rij represents the distance between two atoms). The geometric averages were used in constructing parameters of the potential between different atoms as σij = (σiiσjj)1/2 and εij = (εiiεjj)1/2.41 For bonded potential of sulfate, we used the force field developed by Berkowitz et al.42,43 The cutoff distance for Lennard-Jones potential was as long as 1.6 nm, to reduce errors in calculating surface tension.44 The particle-mesh Ewald (PME) method45,46 was used to describe long-range electrostatic interactions. MD Simulation Details. In each MD simulation, an energy minimization was carried out to relax the system at first. Then, the LINCS algorithm47 was applied to constrain bonds with H atoms. We performed simulations in NVT canonical ensemble at 298 K using velocity rescaling thermostat48 to control the temperature. The equations of motion are integrated with a time step of 1.0 fs. Systems were set to 348 K then annealed to 298 K in 0.5 ns as to overcome possible local energy minima.49 Then 17 ns equilibration runs were performed for all the systems. Ten nanosecond production runs were subsequently executed, evaluating properties every 1 ps. Statistics and Calculation. As to describe the interfacial fluctuation, the position of the intrinsic surface should be

2. SIMULATION DETAILS AND ANALYTIC METHODS Models. Four systems (without salt, with NaCl, with CaCl2, and with MgCl2) of water/vapor interfaces with SDS as surfactants were studied. The simulation model is an orthogonal box with Lx = Ly = 10.613 nm, and Lz = 16.000 nm. The water phase is a slab with a thickness of 6 nm parallel with the x−y plane. It was positioned in the middle of the box, sandwiched by two vapor phases, which were initially set to vacuum for simplicity (Figure 1). Two SDS monolayers with 256 molecules each were placed at the water/vapor interfaces. The distance between two monolayers (approximately 6 nm) is large enough to ignore their interaction. The area per SDS molecule is approximately 0.44 nm2, corresponding to a neutron reflection-based measurement of SDS solution with critical micelle concentration (CMC) at 298 K.33 Na+ ions of SDS and salt ions were inserted into the water phase randomly. For the system with CaCl2 or MgCl2, 203 Ca2+ or Mg2+ and 19206



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3. RESULTS AND DISCUSSION 3.1. Elastic Properties and Interfacial Fluctuation. The surface tensions and errors are shown in Table 1. Taking the

defined. The equation of the intrinsic surface is described through its Fourier components as32,50 ξ(R) =

∑

ξq̂ eiq·R

|q|≤ qu

(2)

Table 1. Surface Tensions (γ) and Bending Moduli (κ) of the Systems

where R = (x, y) is the location of the intrinsic surface, q = 2π(nx,ny)/L is the wave vector, L is the length in the x or y direction of the cross section, and nx,ny = 0, ± 1, ± 2···. The upper limit qu = 2π/λc, where λc is the cutoff wavelength.20,32 The intrinsic sampling method (ISM) proposed by Chacón and Tarazona50 was used to construct the intrinsic surface. The S atoms of SDS were used as pivots characterizing positions of the surface.20,51,52 The surface with minimal surface area passing through all the pivots is constructed with the ISM method.32,53 The cutoff wavelength λc was set to 0.5 nm, approximately corresponding to the peak position of the radial distribution function (RDF) between S atoms (Figure 2).

However, it should be noted that the surface passing through S atoms pivots are in fact several layers beneath the water/vapor interface, as disclosed by Abranko-Rideg et al.54 Selecting different atoms as pivots can lead to different characterizations of the intrinsic surface. However, since our study is focused on the solvation and ionic coordination structure around sulfate groups, and the interaction between sulfate groups largely determines the mechanical properties of the interface, selecting atoms from sulfate groups as pivots is meaningful. Bresme et al. pointed out that as compared to other atoms, S atoms provide a better definition of the intrinsic profile, which features stronger oscillations.20 After constructing the intrinsic surface, the intrinsic density profile ρ̃(z,qu) is calculated with the equation50 1 A0

A A ≈ A0 + 0 2

N

(3)

Instead of fitting two parameters (γ and κ) in eq 1 at the same time, we calculated surface tension γ by using the pressure tensor method (eq 4),55,56 which is thought as a more accurate method.20 Then, the value of κ was alone fit with eq 1. γ=

⟨Px⟩ + ⟨Py⟩ ⎤ Lz ⎡ ⎢⟨Pz⟩ − ⎥ 2⎣ 2 ⎦

± ± ± ±

0.6 0.5 0.4 0.8

κ (kBT) 0.87 0.93 0.56 0.38

± ± ± ±

0.04 0.11 0.05 0.04

qu

∑ 0 0), there is always a peak of O atoms of water (Ow) in every profile, characterizing a dense adsorbed water layer beside the SDS monolayer. A shoulder in the intrinsic density profile of Ow is found at around z = 0, probably corresponding to the solvation shells around sulfate groups. An adsorption layer of counterions Na+ very close to the intrinsic surface is observed in every profile. Two plateaus can be seen at the right side of the Na+ adsorption peak, exactly corresponding to the peak and well on the Ow intrinsic density profile. The first plateau of Na+ corresponding to the peak of water represents the fully hydrated Na+ ions, and the second Na+ plateau corresponding to the well water characterizes the bridge Na+ ions connecting water in the adsorption layer and in the bulk. When NaCl is added, the adsorption peak of Na+ only becomes wider, and clearly more Na+ ions appear in bulk water (Figure 6b). As CaCl2 or MgCl2 is added, the peak of Na+ obviously drops

Figure 4. Function lines of 1/(γq2) and 1/(κq4).

3.2. Intrinsic Density Profiles. The intrinsic density profiles (Figure 6) were calculated with eq 3, in which the intrinsic surface passing through all S atoms pivots is described

Figure 5. (a) Probability distributions of intrinsic surface area A. (b) Evolutions of intrinsic surface area A with simulation time t. Each data point of surface area A is averaged every 100 ps. The averages of surface area A in the production time are also shown with straight lines. Legend in panel b is the same as that in panel a. 19208



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Figure 6. Intrinsic density profiles of ions and O atoms of water (Ow) in systems without salt (a), with NaCl (b), with CaCl2 (c), and with MgCl2 (d). Densities of Ow are scaled by 0.125. The black dotted lines at z = 0 characterize positions of intrinsic surfaces, which are also the positions of S atoms.

Figure 7. (a) Intrinsic density profiles of O atoms of water (Ow); (b) Intrinsic density profiles of several C atoms numbered according to their distances to the sulfate group. The nearest C atom to the sulfate group is numbered as 1, and the furthest C atom to the sulfate group is numbered as 12. Legend in panel b is the same as in panel a. Inset exhibits the SCD order parameter as a function of the carbon position.

down and lots of Na+ ions move into bulk water (Figure 6c,d). However, most Ca2+ or Mg2+ ions are adsorbed, and hardly any exists in bulk water, because of the strong electrostatic interaction between divalent ions and the anion monolayer. Whereas the adsorption peak of Ca2+ or Mg2+ is farther to the interface than that of Na+, which can be attributed to the larger hydrated radii of Ca2+ and Mg2+ ions.15 Meanwhile, we find that with the addition of Ca2+ or Mg2+ ions, the intrinsic density of Ow at z = 0 rises from about 17 nm−3 to 20 nm−3 (Figure 7a). However, adding NaCl almost makes no difference. Such changes may be caused by that the Ca2+ or Mg2+ ions are much farther from the sulfate groups than Na+ (Figure 6c,d), so the sulfate groups are more solvated by water. Different counterions also influence the structure of surfactant chains. Broader intrinsic density distributions of alkyl carbon atoms imply looser structure. It is found that adding NaCl almost makes no difference to intrinsic density distributions of C atoms, while adding divalent ions especially

Mg2+ leads to obviously broader distributions (Figure 7b). The ordering of the chains is studied by the deuterium order parameter SCD, which is calculated with the following formulas: SCD =

Sij =

2 1 Sxx + Syy 3 3

1 ⟨3 cos θi cos θj − δij⟩ 2

(6)

(7)

where i,j = x, y, z representing the molecular axis, and θi is the angle between the ith molecular axis and the normal to the interface.59 The result shows that ⟨|SCD|⟩ is lower in the presence of divalent ions especially Mg2+, while NaCl makes no obvious difference in ⟨|SCD|⟩ (inset in Figure 7b). This finding is consistent with a previous study on a DMPA− lipid monolayer that more ordered structure of amphiphilic molecules appears in the system with Na+ ions rather than that with Ca2+ ions.9 However, it seems to be opposite to the 19209



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Figure 8. RDFs of S atoms from sulfate groups and elements in aqueous phase (Na+, Mg2+, Ca2+ and O atoms of water) in systems without salt (a), with NaCl (b), with CaCl2 (c), and with MgCl2 (d). Data of RDF (S−Ow) are scaled by 8. Inset in panel a exhibits the schematic of the coordination structure.

With the addition of CaCl2, a narrow first peak and a broad second peak of RDF (S−Ca) (referred to as narrow and broad peaks later) appear at the positions of the second and third peaks of RDF (S−Na) (Figure 8c), showing that the role of Ca2+ ions is similar to Na+ ions, i.e., connecting water molecules. But no RDF (S−Ca) peak appears before the peak of RDF (S−Ow), showing that Ca2+ ions cannot be dehydrated and enter the hydration shells of sulfate groups as Na+ ions. In the system with MgCl2, three peaks of RDF (S−Mg) appear. The first peak, which appears on the left of that of RDF (S−Ow), is very tiny (the height ≈ 2). It suggests that few Mg2+ ions can enter the hydration shell of sulfate groups. The second and third peaks, though similar in shapes and positions with the narrow and broad peaks of RDF (S−Ca), are closer to S atoms (Figure 8d). It reveals that Mg2+ ions are more close to hydrophilic groups than Ca2+ ions, which was also found in the study of alkyl benzene sulfonate monolayers.10 The spatial distribution of aqueous species around sulfate groups of some SDS molecules gives an intuitive graphic view of the coordination structure (Figure 9). No matter which system, three separate Na+ ions zones close to the charged O atoms of sulfate groups are found corresponding to the first and second peaks of RDF (S−Na) (Figure 8). It is clear that Na+ ions can cross the hydration shell of sulfate groups and form a strong relationship with charged O atoms. Dense zones of Ca2+ and Mg2+ ions appear outside the hydration shell, corresponding to the broad peaks in RDF (S−Ca) and RDF (S−Mg) (Figure 8c,d). They also correspond to second plateaus in the coordination number (CN) curve of Ca2+ or Mg2+, which appear at about 0.60 nm (Figure 10b). Only a very small Ca2+ zone appears at a similar position as a Na+ zone (Figure 9c), and no Mg2+ zone is found inside the hydration shell (Figure 9d). It implies that some divalent ions can cross the hydration

study on a SDC or SDSn monolayer in which the presence of Ca2+ ions leads to more compact structure of monolayers.11 Since they also used the OPLS-AA force field to describe the interaction between SDC or SDSn monolayers and ions,11 we deduce that this difference appears due to the specificity of hydrophilic groups. MD simulation studies on SDS micelles reveal that stable salt bridges can be formed between Ca2+ ions and sulfate groups, leading to more compact micelles.60,61 However, the situation of micelles is different from that of surfactant monolayers, since alkyl tails are closely packed in micelles, but there are cavities within monolayers.62 An experimental study has revealed that Ca2+ ions can induce ordered or disordered monolayers depending on the surface coverage.5 So it is reasonable that in the presence of Ca2+ ions SDS micelles become more compact but alkyl tails of SDS monolayers become more disordered. 3.3. Relationship between Sulfate Groups and Aqueous Species. In the four studied systems, the peak and well positions of RDF (S−Ow) and RDF (S−Na) are similar (Figure 8). The peaks at about 0.4 nm of RDF (S−Ow) exactly correspond to the peak positions of Ow intrinsic densities (Figure 6), which implies the adsorbed water layer of sulfate groups. The first and second peaks of RDF (S−Na) are overlapping. The first peak, appearing on the left of that of RDF (S−Ow), represents the Na+ ions inside the hydration shells around sulfate groups. The second one denotes Na+ ions solvated by water, corresponding to positions of the peak of RDF (S−Ow) and the first Na+ intrinsic density plateau (Figure 6). The third one at the positions of the well of RDF (S−Ow) and the second Na+ intrinsic density plateau (Figure 6) exhibits the role Na+ ions play in connecting adjacent shells of water. The schematic of the coordination structure is shown in the inset of Figure 8a. 19210



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CaCl2 and with MgCl2. So in the system with divalent counterions, the sulfate groups are less coordinated by counterions and more solvated by water. However, adding NaCl makes no significant change to the coordination structure. Na+ ions cross the hydration shells and bridge sulfate groups directly, while most Ca2+ or Mg2+ ions bridge sulfate groups with full hydration shells. So the average distance between sulfate groups is larger in systems with divalent ions. The peak in RDF (S−S) is weaken in systems with CaCl2 or MgCl2 (Figure 2), suggesting a less compact structure, which is responsible for a less ordered structure of alkyl tails (Figure 7b). As adding NaCl does not affect the coordination structure of sulfate groups obviously, the RDF (S−S) and atomistic structure of alkyl tails almost remain unchanged. According to the above structure analyses, adding CaCl2 or MgCl2 weakens the interaction between sulfate groups, and leads to more disordered alkyl tails, which are responsible for the lower value of κ. However, the influence of Ca2+ or Mg2+ ions on the elastic properties of monolayers should not be unique due to the specificity of amphiphilic molecules structure as stated above. More MD simulation studies should be performed to reveal the influence of salt on the elastic properties of different kinds of surfactant and lipid monolayers.

Figure 9. Spatial distributions of species around sulfate groups in systems without salt (a), with NaCl (b), with CaCl2 (c), and with MgCl2 (d). The blue wireframes stand for Na+ ions. The green isosurfaces stand for Ca2+ ions, the orange ones for Mg2+ ions, and the silver ones for water O atoms. The O and S atoms of the sulfate groups are characterized by red and yellow balls, respectively. The width of bins is set to 0.05 nm in calculating the spatial distribution. The grid size in the figure is 0.1 nm. The distribution is averaged for species around certain sulfate group in 10 ns.

4. CONCLUSIONS MD simulations have been performed to study the intrinsic surface structure and interfacial fluctuation of the water/vapor interface covered by SDS. With the addition of different kinds of salt, the interfacial tension γ of the systems does not change significantly. But the bending modulus κ obviously decreases with divalent ions, especially with Mg2+. As smaller κ characterizes larger interfacial fluctuation, the foam film stability will be influenced by adding divalent ions. The influence of the interfacial structure on the capillarywaves fluctuation of the interface is disclosed. This study first reveals the intrinsic density distributions of water and ions are inherently correlated to the relationship between sulfate groups and them. Na+ ions can cross the hydration shells of sulfate groups, but Ca2+ or Mg2+ ions do less and most of them coordinate outside the shells. However, Ca2+ or Mg2+ can decrease the adsorption of counterions Na+ to the interface, and thus sulfate groups are less bridged by Na+ ions and more solvated by water. The change in coordination structure further leads to the more disordered structure of alkyl tails. All the changes in atomistic structure of interfaces due to the addition of Ca2+ or Mg2+ result in lower κ. The influence of MgCl2 is much stronger than that of CaCl2 because the coordination

+

shell and interact with sulfate groups as Na ions, which corresponds to the narrow peak in RDF (S−Ca). However, the probability for such interaction is very low, so that those divalent ions are seldom found in the spatial distribution. This phenomenon is distinct from the study on the SDSn monolayers, in which Ca2+ ions can cross the hydration shell and form three dense zones11 as Na+ ions in this study. It reveals that the molecular structure difference can lead to the different relationship between hydrophilic groups and ions, further leading to the different order of alkyl tails as analyzed above. Similar to the analysis of spatial distributions, CN of Ca2+ or Mg2+ ions is much lower than that of Na+ ions at the position of the hydration shell (Figure 10b). CN at about 0.44 nm (corresponding to the first plateaus positions) is a little higher for Ca2+ (ca. 0.4) than for Mg2+ (ca. 0.2), which should lead to the slightly higher intrinsic density of Ca2+ adsorbed at the surface (Figure 6c,d). Also, CN of Na+ ions is much lower in the system with of CaCl2 or MgCl2. However, CN of Ow around S atoms in systems with CaCl2 or MgCl2 is slightly higher (Figure 10a). At about 0.48 nm, where dCN/dr is approximately smallest, the coordination numbers of Ow are ca. 7.7, 7.5, 8.8, and 8.8 for systems without salt, with NaCl, with

Figure 10. (a) Coordination numbers of Ow atoms around S atoms. (b) Coordination numbers of Na+, Ca2+, and Mg2+ ions around S atoms. 19211



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number of Mg2+ is lower than that of Ca2+ and alkyl tails are more disordered. Additionally, the influence of adding NaCl is scarcely found as the interactions between aqueous species and sulfate groups, alkyl tails structure, and interfacial fluctuation are hardly changed. Due to the molecular specificity, further study of the counterion effect on the elastic properties of other kinds of monolayers is needed.

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(10) Zhao, T.; Xu, G.; Yuan, S.; Chen, Y.; Yan, H. Molecular Dynamics Study of Alkyl Benzene Sulfonate at Air/Water Interface: Effect of Inorganic Salts. J. Phys. Chem. B 2010, 114, 5025−5033. (11) Yan, H.; Guo, X.-L.; Yuan, S.-L.; Liu, C.-B. Molecular Dynamics Study of the Effect of Calcium Ions on the Monolayer of SDC and SDSn Surfactants at the Vapor/Liquid Interface. Langmuir 2011, 27, 5762−5771. (12) Angarska, J.; Tachev, K.; Kralchevsky, P.; Mehreteab, A.; Broze, G. Effects of Counterions and Co-ions on the Drainage and Stability of Liquid Films and Foams. J. Colloid Interface Sci. 1998, 200, 31−45. (13) Pandey, S.; Bagwe, R. P.; Shah, D. O. Effect of Counterions on Surface and Foaming Properties of Dodecyl Sulfate. J. Colloid Interface Sci. 2003, 267, 160−166. (14) Schelero, N.; Hedicke, G.; Linse, P.; Klitzing, R. v. Effects of Counterions and Co-ions on Foam Films Stabilized by Anionic Dodecyl Sulfate. J. Phys. Chem. B 2010, 114, 15523−15529. (15) Nightingale, E., Jr Phenomenological Theory of Ion Solvation. Effective Radii of Hydrated Ions. J. Phys. Chem. 1959, 63, 1381−1387. (16) Helfrich, W. Elastic Properties of Lipid Bilayers: Theory and Possible Experiments. Z. Naturforsch. 1973, 28, 693. (17) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley Reading: MA, 1994. (18) Laradji, M.; Mouritsen, O. G. Elastic Properties of Surfactant Monolayers at Liquid−Liquid Interfaces: A Molecular Dynamics Study. J. Chem. Phys. 2000, 112, 8621. (19) Rekvig, L.; Hafskjold, B.; Smit, B. Chain Length Dependencies of the Bending Modulus of Surfactant Monolayers. Phys. Rev. Lett. 2004, 92, 116101. (20) Martínez, H.; Chacón, E.; Tarazona, P.; Bresme, F. The Intrinsic Interfacial Structure of Ionic Surfactant Monolayers at Water−Oil and Water−Vapour Interfaces. Proc. R. Soc. A 2011, 467, 1939−1958. (21) Winterhalter, M.; Helfrich, W. Effect of Surface Charge on the Curvature Elasticity of Membranes. J. Phys. Chem. 1988, 92, 6865− 6867. (22) Lekkerkerker, H. Contribution of the Electric Double Layer to the Curvature Elasticity of Charged Amphiphilic Monolayers. Physica A 1989, 159, 319−328. (23) Binks, B.; Kellay, H.; Meunier, J. Effects of Alkane Chain Length on the Bending Elasticity Constant k of AOT Monolayers at the Planar Oil−Water Interface. Europhys. Lett. 1991, 16, 53. (24) Kellay, H.; Meunier, J. Elastic Properties of Monolayers of Soluble Surfactants at Oil−Brine Interfaces. J. Phys.: Condens. Matter 1996, 8, A49. (25) Farago, B.; Gradzielski, M. The Effect of the Charge Density of Microemulsion Droplets on the Bending Elasticity of Their Amphiphilic Film. J. Chem. Phys. 2001, 114, 10105−10122. (26) Barneveld, P.; Hesselink, D.; Leermakers, F.; Lyklema, J.; Scheutjens, J. Bending Moduli and Spontaneous Curvature. 2. Bilayers and Monolayers of Pure and Mixed Ionic Surfactants. Langmuir 1994, 10, 1084−1092. (27) Goetz, R.; Gompper, G.; Lipowsky, R. Mobility and Elasticity of Self-Assembled Membranes. Phys. Rev. Lett. 1999, 82, 221. (28) Lindahl, E.; Edholm, O. Mesoscopic Undulations and Thickness Fluctuations in Lipid Bilayers from Molecular Dynamics Simulations. Biophys. J. 2000, 79, 426−433. (29) Tarazona, P.; Chacón, E.; Bresme, F. Thermal Fluctuations and Bending Rigidity of Bilayer Membranes. J. Chem. Phys. 2013, 139, 094902. (30) Rekvig, L.; Hafskjold, B.; Smit, B. Simulating the Effect of Surfactant Structure on Bending Moduli of Monolayers. J. Chem. Phys. 2004, 120, 4897. (31) Shi, W.-X.; Guo, H.-X. Structure, Interfacial Properties, and Dynamics of the Sodium Alkyl Sulfate Type Surfactant Monolayer at the Water/Trichloroethylene Interface: A Molecular Dynamics Simulation Study. J. Phys. Chem. B 2010, 114, 6365−6376. (32) Chacón, E.; Fernández, E.; Duque, D.; Delgado-Buscalioni, R.; Tarazona, P. Comparative Study of the Surface Layer Density of Liquid Surfaces. Phys. Rev. B 2009, 80, 195403.

ASSOCIATED CONTENT

S Supporting Information *

Force field parameters for intermolecular interactions. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Mailing address: State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering, Nanjing University, 163 Xianlin Road, Nanjing 210023, China. E-mail: [email protected]. Fax: +86-25-83686016. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We acknowledge the China National Science and Technology Major Project 2011ZX05010-005 and National Basic Research Program (973) of China (No.2012CB214803). We are grateful to the High Performance Computing Center of Nanjing University for using the IBM Blade cluster system.

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Specific Counterion Effects on the Atomistic Structure and Capillary

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