pubs.acs.org/Langmuir © 2010 American Chemical Society
Effect of Ca2þ and Mg2þ Ions on Surfactant Solutions Investigated by Molecular Dynamics Simulation Hui Yan, Shi-Ling Yuan,* Gui-Ying Xu, and Cheng-Bu Liu Key Lab of Colloid and Interface Chemistry, Shandong University, Jinan 250100, China Received August 13, 2009. Revised Manuscript Received May 17, 2010 The effect of Ca2þ and Mg2þ on the H-bonding structure around the headgroup of the surfactants sodium dodecyl sulfate (SDS) and sodium dodecyl sulfonate (SDSn) in solution has been studied by molecular dynamics simulation. Our results show that binding between the headgroup of the surfactant and Ca2þ or Mg2þ is prevented by a stabilizing solvent-separated minimum formed in the potential of mean force (PMF) between the interacting ion-pair. Among the contributions to the PMF, the major repulsive interaction is due to the rearrangement of the hydration shell after the ions enter into the original H-bonding structure of water around the headgroup, leading to a decrease in the number of H-bonds and an increase in their lifetimes. In the second hydration shell around the headgroup, additional water molecules are bound to the headgroup oxygen atoms either directly or bridged by Ca2þ and Mg2þ. The PMF shows that the energy barriers to ion-pairing between the headgroup and Ca2þ and Mg2þ in the SDSn system are higher than those in the SDS system, and the water coordination numbers for Ca2þ or Mg2þ in SDS solution are lower. This result indicates that SDS binds the ions easily compared with SDSn, and the ions have a strong effect on the original hydration structure. That is why sulfonate surfactants such as SDSn have better efficiency in salt solution with Ca2þ and Mg2þ for enhanced oil recovery.
1. Introduction Surfactants have been investigated extensively in pharmaceutical, industrial, and environmental applications because of their unique solution properties. When dissolved in water, surfactant molecules self-assemble into different micellar aggregates, with their hydrophobic tails shielded from water in the aggregate interior and their hydrophilic heads exposed to water at the aggregate surface.1 This self-assembly is driven by many interactions, such as van der Waals, hydrogen-bonding, and electrostatic interactions (in the case of charged surfactants or in the electrolyte solution), and they play important roles in determining how micellization occurs.2 To obtain information about the microscopic nature of the aggregates and to understand the formation of aggregates in the solution, different experimental techniques, including fluorescence, resonance Raman scattering, nuclear magnetic resonance, electron paramagnanetic resonance, light scattering, and small angle neutron scattering, have been used.3-13 Special attention has been paid to the structure and dynamic properties of the surfactants (extension of the chains, different hydrophilic heads, *Corresponding author. E-mail:
[email protected]. (1) Stephenson, B. C.; Beers, K.; Blankschtein, D. Langmuir 2006, 22, 1500. (2) Isralachvili, J. N. Intermolecular and Surface forces, 2nd ed.; Academic Press: New York, 1991. (3) Hedin, N.; Furo, I.; Eriksson, P. O. J. Phys. Chem. B 2000, 104, 8544. (4) Moren, A. K.; Nyden, M.; S€oderman, O.; Khan, A. Langmuir 1999, 15, 5480. (5) Conboy, J. C.; Messmer, M. C.; Richmond, G. J. Phys. Chem. B 1997, 101, 6724. (6) Van Gorkom., L. C.; Jensen, A. Surf. Sci. Ser. 1998, 73, 169. (7) Enrnshaw, J. C.; McCoo, E. Langmuir 1995, 11, 1087. (8) Kim, D. H.; Oh, S. G. Colloid Polym. Sci. 2001, 279, 39. (9) Vass, S. J. Phys. Chem. B 2001, 105, 455. (10) Shukla, A.; Rehage, H. Langmuir 2008, 24, 8507. (11) Golemanov, K.; Denkov, N. D.; Tcholakova, S.; Vethamuthu, M.; Lips, A. Langmuir 2008, 24, 9956. (12) Miyake, M.; Yamada, K.; Oyama, N. Langmuir 2008, 24, 8527. (13) Lin, Y.; Han, X.; Cheng, X.; Huang, J.; Liang, D.; Yu, C. Langmuir 2008, 24, 13918.
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etc.).12,13 For instance, Miyake et al.12 gave evidence from changes in the 1H NMR and IR spectra that an attractive force acts between guanidine groups of dodecylguanidine hydrochloride (C12G) molecules to facilitate their assembly before and after micelle formation by increasing hydrogen-bonding between the guanidine group of the surfactant and water molecules. Lin and co-workers13 used dynamic light scattering and rheology measurements to study pH-regulated molecular self-assembly in a cationic-anionic surfactant system. They suggested that the hydrated volume of the surfactant headgroup should be taken into consideration to better elucidate the self-assembly behavior of “1:2” cetyltrimethlyammonium bromide (CTAB) and n-decylphosphoric acid surfactant mixtures. These investigations in different systems help us to understand the structures and properties of surfactant aggregates in solution. Due to the substantial increase in computational power over the past few years, computer simulations such as Monte Carlo14,15 and molecular dynamics (MD)16-22 also have proven to be valuable tools to study the self-assembly of surfactants and can provide a detailed, atomistic level insight into the threedimensional structure of the studied model system. These kinds of studies allow us to extract information about dynamic and structural properties at a microscopic level which is not easy to get from experiments. Ordered morphology can be observed in simulations of spherical micelles, and the headgroup density profiles for different types of molecules have been calculated for (14) Zehl, T.; Wahab, M.; M€ogel, H. J.; Schiller, P. Langmuir 2006, 22, 2523. (15) Howes, A. J.; Radke, C. J. Langmuir 2007, 23, 1835. (16) Tummal, N. R.; Striolo, A. J. Phys. Chem. B 2008, 112, 1987. (17) Jang, S. S.; Goddard, W. A., III J. Phys. Chem. B 2006, 110, 7992. (18) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 3788. (19) Rakitin, A. R.; Pack, G. R. J. Phys. Chem. B 2004, 108, 2712. (20) Khurana, E; Nielsen, S. O.; Klein, M. L. J. Phys. Chem. B 2006, 110, 22136. (21) Shelley, J.; Shelley, M. Curr. Opin. Colloid Interface Sci. 2000, 5, 101. (22) Yuan, S. L.; Ma, L. X.; Zhang, X. Q.; Zheng, L. Q. Colloids Surf. A 2006, 289, 1.
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normal23 or reverse24 micelles. Some interesting results were obtained in the simulations. Chanda and Bandyopadhyay25,26 recently investigated the lifetime dynamics of hydrogen bonds between anionic surfactant Aerosol OT (AOT) and water using atomistic MD simulation. They observed that water molecules beyond the first hydration layer form weaker hydrogen bonds than pure bulk water. Rossky and co-workers27,28 reported MD simulation studies on a fluorocarbon surfactant. They noticed that water molecules penetrated the fluorocarbon surfactants to a lesser extent than hydrocarbon surfactants. In this work, we focus on the microscopic and dynamic properties of two anionic surfactants, sodium dodecyl sulfate (C12H25SO4Na, SDS) and sodium dodecyl sulfonate (C12H25SO3Na, SDSn), using atomistic MD simulation methods. The surfactants are well-known and widely used in both technological applications and fundamental research. They have the same chain length, and the only difference is the headgroup of the surfactant. The single surfactant systems of SDS and SDSn are quite similar in many physicochemical properties except for their Krafft points;29,30 for example, the critical micelle concentrations (cmc) of SDS and SDSn are 8.7 10-3 and 9.7 10-3 mol L-1, respectively, and the Γmax values at the solution-air interface31,32 are 3.1 10-3 and 2.9 10-3 mol L-1, respectively. However, many studies have shown striking differences in their interactions with polymers, cationic surfactants, or salt solutions, even including other alkyl sulfate and alkyl sulfonate surfactants. For example, for the polymer-surfactant complex, there are two possible structures:33 (a) the polymer wraps around the micelles (“necklace” structures) or (b) the micelles nucleate on the polymer hydrophobic sites (“bead” structures). Studies by Cabane34 and Hou35 et al. found that SDS-poly(ethylene oxide) (PEO) and SDSn-PEO complexes were “necklace” and “bead” structures, respectively. When both were mixed with the cationic surfactant CTAB in solution, SDSn-CTAB mixtures were much more soluble than SDS-CTAB mixtures, and they were quite different in their phase behavior and aggregate properties.29 These differences might be explained in terms of the total charge of the headgroup and the charge distribution of the molecules in addition to the hydrophobic effect of the alkyl chains.36 The key point is the different headgroups of the SDS and SDSn surfactants, especially considering solutions of these anionic surfactants with added cations. In enhanced oil recovery (EOR) experiments, the sulfonate surfactant is more efficient than the sulfate surfactant in the case of high salt concentration, which means the inorganic cations have less effect on the physical characteristics of sulfonate surfactants than those of sulfate surfactants. Thus, the sulfonate surfactant will maintain its surface activity in high salt solution. In other words, the salt tolerance (23) Bogusz, S.; Venable, R. M.; Pastor, R. W. J. Phys. Chem. B 2001, 105, 8312. (24) Abel, S.; Sterpone, F.; Bandyopadhyay, S.; Marchi, M. J. Phys. Chem. B 2004, 108, 19458. (25) Chanda, J.; Bandyopadhyay, S. J. Phys. Chem. B 2006, 110, 23443. (26) Bandyopadhyay, S.; Chanda, J. Langmuir 2003, 19, 10443. (27) da Rocha, S. R. P.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. B 2002, 106, 13250. (28) Stone, M. T.; da Rocha, S. R. P.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. B 2003, 107, 10185. (29) Chen, L.; Xiao, J. X.; Ma J. Colloid Polym. Sci. 2004, 282, 524. (30) Rosen, M. J. Surfactant and Interfacial Phenomena; Wiley: New York, 1989. (31) Tajima, K.; Muramatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1970, 43, 1991. (32) Janczuk, B.; Gonzalez-Martı´ n, M. L.; Bruque, J. M.; Dorado-Calasanz, C. Colloids Surf. A 1998, 137, 15. (33) Turro, N. J.; Lei, X. G.; Ananthapadmanabhan., K. P.; Aroson, M. Langmuir 1995, 11, 2525. (34) Cabane, B. J. Phys. Chem. 1977, 81, 1639. (35) Hou, Z.; Li, Z.; Wang, H. Colloid Polym. Sci. 1999, 277, 1011. (36) Yan, P.; Xiao, J. X. Colloids Surf. A 2004, 244, 39.
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of sulfonate surfactants is superior to that of sulfate surfactants. We believe that this is caused by the interaction between anion headgroup and cations in the solution, especially for the divalent cations Ca2þ and Mg2þ. Therefore, the effects of Ca2þ and Mg2þ on the surfactant solutions were simulated using MD in this work to find the reason for the different properties of SDS and SDSn at the molecular level. In the past decade, several groups37-40 have investigated aggregates of different systems containing sulfate or sulfonate surfactants using different simulation methods. Shang and coworkers37 performed atomistic MD simulation of an anionic SDS micelle and a nonionic PEO polymer in aqueous solution. They found that the association between SDS and PEO is mainly driven by hydrophobic interactions between the polymer and surfactant tails, while the interaction between the polymer and sulfate headgroups on the micelle surface is weak. Khandelia and Kaznessis38 investigated the configuration of peptides in SDS micelles using MD simulation. They concluded that the lack of cation-π interaction and the electrostatic binding of the terminal arginine residues to the sulfate groups lead to an extended peptide structure in the micelles, and the simulations are in excellent agreement with available experimental measurements.41 Sammalkorpi et al.42 studied SDS in saline solutions of NaCl or CaCl2, and they found that micellar properties were affected by the ions. Meanwhile, we note that many simulations were focused on sulfonate surfactants such as sodium dodecyl benzenesulfonate (SDBS)43 or AOT,44,45 but few have considered SDSn surfactant. In this paper, we study the different microscopic properties of SDS and SDSn in electrolyte solution using atomistic MD simulation methods. We focus on the effects of Ca2þ and Mg2þ on the surfactant aggregate solutions and find the different interactions between sulfate or sulfonate and cations. First the simulation and models are discussed in detail, and then the main results obtained from the simulations and their interpretations are given.
2. Computational Details 2.1. Potential Model. In this work, a standard molecular mechanics potential model was used with the following functional form: uðrN Þ ¼
X bonds
ki ðli - li, 0 Þ2 þ
X
ki ðθi - θi, 0 Þ2
angles
X Vn ð1 þ cosðnω - γÞÞ 2 torsions 0 2 1 !12 !6 3 N N X X σ σ q q ij ij i j @4εij 4 5þ A þ rij rij rij i¼1 j¼iþ1 þ
ð1Þ
where the first three terms are the bonded interactions, including bond, angle, and torsion interactions, and the second two terms are nonbonded interactions, including van der Waals and (37) Shang, B. Z.; Wang, Z. W.; Larson, R. G. J. Phys. Chem. B 2008, 112, 2888. (38) Khandelia, H.; Kaznessis, Y. N. J. Phys. Chem. B 2007, 111, 242. (39) Domı´ nguez, H.; Rivera, M. Langmuir 2005, 21, 7257. (40) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 10775. (41) Rozek, A.; Friedrich, C. L.; Hancock, R. E. W. Biochemistry 2000, 39, 15765. (42) Sammalkorpi, M.; Karttunen, M.; Haataja, M. J. Phys. Chem. B 2009, 113, 5863. (43) Li, Z.; Guo, X.; Wang, H.; Li, Q.; Yuan, S.; Xu, G.; Liu, C. Acta Phys.Chim. Sin. 2009, 25, 6. (44) Chanda, J.; Chakraborty, S.; Bandyopadhyay, S. J. Phys. Chem. B 2005, 109, 471. (45) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2001, 105, 11148.
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Scheme 1. Structure of Sodium Dodecyl Sulfate and Sodium Dodecyl Sulfonate (hydrogens are omitted for clarity)
Table 1. Force Field Parameters (1) Bond Interaction bond
r0 (A˚)
kb (kJ mol-1 A˚-2)
C-C C-O (in ester CH2-O-S) C-S C-H C-H (in -CRH2-) S-O (in SO3) O (in ester CH2-O-S)-S
1.5260 1.4100 1.8100 1.0900 1.0850 1.4420 1.5800a
1298.0 1339.8 950.4 1423.6 1422.6 2665.5 2510.4
(2) Angle Interaction
Coulombic interactions. Our simulation systems include the ionic surfactants SDS, SDSn, water molecules, Ca2þ, Mg2þ, and Clions. The structures of SDS and SDSn are shown in Scheme 1, with the hydrophobic and hydrophilic regions labeled. Water was described by the SPC/E model,46 which is known to give a good agreement between experimental radial distribution function (RDF) and diffusion coefficient for pure water at ambient temperature. In the bonding interactions, the key parameters should concern the atoms in the midstructure between the hydrophobic tail and hydrophilic head. We found that the torsion C-C-C-O or angle C-O-S in the SDS molecule is not shown in the AMBER99 force field; therefore, these parameters are carefully selected in our studies. The van der Waals interaction parameters for the ions are taken from earlier work, and they give good results in some dynamics properties, such as RDF, coordination number, etc., which will be discussed later. Other parameters used in the simulation are selected from the AMBER99 force field (Table 1). Atom charges are a significant part of Coulombic interaction parameters, and using electrostatic potential (ESP) charges rather than Mulliken charges has been very efficient and successful for a variety of systems.50,51 In this work, we optimize the structures of the two surfactants and calculate the ESP atomic charges at the B3LYP/6-31þG** level using the Gaussian 03 package.52 Minimized structures were used to set equilibrium bond lengths and angles. Once the optimized geometries were obtained, the vibration frequencies were checked to ensure no negative frequencies existed and to verify the energy of a true minimum. The atom charges of SDS listed in Table 2 are compared with the data derived from ref 53 (shown in parentheses). It can be seen that the differences between these atoms are very small. The atoms charges
(46) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, J. P. J. Phys. Chem. 1987, 91, 6269. (47) Lopes, J. N. C.; Deschamaps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038. (48) Lyubartsev, A. P.; Laaksonen, A. J. Phys. Chem. 1996, 100, 16410. (49) Larentzos, J. P.; Criscenti, L. J. J. Phys. Chem. B 2008, 112, 14243. (50) Liu, X. M.; Zhang, S. J.; Zhou, G. H.; Wu, G. W.; Yuan, X. L.; Yao, X. Q. J. Phys. Chem. B 2006, 110, 12062. (51) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179. (52) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03; Gaussian, Inc.: Wallingford, CT, 2004. (53) Domı´ nguez, H. J. Phys. Chem. B 2002, 106, 5915.
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angle
θ0 (deg)
kθ (kJ mol-1 rad-2)
H-C-H H-C-C H-C-H (in -CRH2-) C-C-H (in -CRH2-) C-C-C C-C-O (in ester CH2-O-S) C-C-S H-C-O (in ester CH2-O-S) H-C-S C-O-S O (in ester CH2-O-S)-S-O O (in SO3)-S-O (in SO3) C-S-O (in SO3)
109.5 109.5 109.5 109.5 109.5 109.5 114.7 109.5 109.5 112.6 102.6 115.3 102.6
146.5 209.3 146.5 209.3 167.5 209.3 209.3 209.3 209.3 520. 1a 426.8a 484.5b 435.0b
(3) Torsion Interaction torsion
γ (deg)
Vn (kJ/mol)
n
C-C-C-C C-C-C-H H-C-C-H C-C-C-O (in ester CH2-O-S) X-C-O-X C-C-S-O O-S-O-C
0 0 0 0 0 0 0
0.753 0.669 0.628 0.652 1.6 1.4 1.046
3 3 3 3 3 3 3
(4) van der Waals Interaction atom
εi (kJ/mol)
σi
C 0.4581 3.4000 H 0.0657 2.6500 0.0657 2.4714 H (in -CRH2-) 0.7118 3.0004 O (in ester CH2-O-S) S 1.0467 3.5640 0.8793 2.9603 O (in SO3) 0.4184 2.5860c Naþ Ca2þ 1.8815 2.3609d Mg2þ 3.6610 1.3976d Cl0.4187 4.4015c a Reference 16. b Reference 46. c Reference 48. d Reference 49.
of SDSn are also shown in Table 2. In order to show the difference between SDS and SDSn in terms of the electron charges, the total charge on the polar head and alkyl tail are listed together. 2.2. Simulated Systems. In this study, we concentrate on the effects of Ca2þ and Mg2þ on the hydration structure of the surfactants. For each of the two surfactants, two MD simulations were performed. One was for the surfactant solution, which contained 40 surfactant molecules and 2400 waters. The other was for the surfactant saline solution, which was prepared by adding 40 Ca2þ and 40 Mg2þ to the pure surfactant solution. In order to ensure electrical neutrality in the simulated system, 160 Cl- ions were added to the saline solution. For comparison, we performed two more simulations. One was for the pure water system, which contained 2400 water molecules, and the other was for a CaCl2 and MgCl2 solution that included 40 CaCl2, 40 MgCl2, and 2400 Langmuir 2010, 26(13), 10448–10459
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Table 2. Atomic Partial Charges for SDS and SDSn atom
charge of SDS headgroup (e)
charge of SDSn headgroup (e)
S 1.256 (1.284)a 1.307 -0.528 (-0.459)a O4 O1-3 atom -0.663 (-0.654)a -0.733 -1.261 (-1.319)b -0.893 (-0.750)b charge on headgroupa b a charge on R-CH2 0.301 (þ0.374) -0.158 (-0.214)b charge on alkyl taila -0.040 (-0.055)b 0.051 (-0.036)b a The table shows the atomic partial charge differences between SDS and SDSn surfactant headgroups. We define that a surfactant molecule contains three parts: headgroup atoms, R-CH2, and the remaining alkyl tail. The charges on other atoms in force field are omitted for clarity. a Reference 53. b Reference 36.
Table 3. Simulated Systems number of molecules system water Ca2þ, Mg2þ Cl- SDS SDSn
box sizea
A 2400 0 0 0 0 41.1 41.1 41.1 A˚3 B 2400 0 0 40 0 43.7 43.7 43.7 A˚3 C 2400 0 0 0 40 44.2 44.2 44.2 A˚3 D 2400 80 160 40 0 44.9 44.9 44.9 A˚3 E 2400 80 160 0 40 45.0 45.0 45.0 A˚3 F 2400 80 160 0 0 42.0 42.0 42.0 A˚3 a The box size was obtained after the NPT run for each system.
water molecules. The six simulated systems are summarized in Table 3. MD simulations were performed with the standard periodical boundary conditions using the M.DynaMix package.54 The package utilized the multiple time step method.55 For the longrange electrostatic potential, the Ewald method with a precision of 10-4 was used, and the interactions were cut off at 12.5 A˚. The N ose-Hoover method56 was employed to maintain the temperature and pressure fluctuating around desired constant values, with coupling relaxation times of ΓT = 100 fs and ΓP = 700 fs. All the simulations were started at a very low density of 0.02 g cm-3 from a face-centered-cubic lattice. A short NPT run of 100 ps was then performed for each system at 298 K under 1 atm, which brought the “actual” density of the system to around ∼1.0 g/cm3. After the NPT run, a 5 ns NVT simulation was carried out at 298 K as the equilibration ran, followed by another NVT production run of 5 ns. The trajectories were collected at intervals of 10 fs for further analysis.
3. Results and Discussion 3.1. Aggregation Structure and Equilibration. The macroscopic behavior of the surfactant molecules is obtained by investigating the aggregation structure. As an example of system E (SDSn in Ca2þ,Mg2þ solution), the snapshots of the configurations at the beginning of the initial NPT run and at the end of equilibrium NVT run are shown in Figure 1. The assembly structures for systems B, C, and D are provided in the Supporting Information, Figure S1. From the figures, it is found that the surfactants assembled into micelles after a long MD run, as expected. By monitoring the trajectories, the micelles are found to remain stable throughout the production run. The equilibration of the simulation systems is determined by monitoring the time-scaled potential energy and average distance of the headgroup S atom from the micelle center of mass (COM). Figure 2a shows that the potential energy profile reaches a stable (54) Lyubartsev, A. P.; Laaksonen, A. Comput. Phys. Commun. 2000, 128, 565. (55) Tuckerman, M.; Berne, B. J.; Martyna, G. J. J. Chem. Phys. 1992, 97, 1990. (56) Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117.
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equilibrium after about 5 ns of simulation time. It can be noted from Figure 2b that the distance between the S atom and the COM is around 16.2 ( 1.3 A˚ at the last 5 ns, and during the long MD run the distance is kept steady. This indicates that after the surfactants assemble, the micelle itself remains stable throughout the course of the production run. Next, further analysis will be done and the results compared over all simulation systems. 3.2. Interactions between Surfactants and Water or Ions. 3.2.1. Surfactant Solution in the Absence of Ca2þ and Mg2þ. To analyze the water-headgroup interaction, relevant RDFs of water molecules with different atoms of the surfactant are calculated over the last 5 ns. Three and two types of correlations are calculated for SDS and SDSn, respectively: g(rO1-3-Ow), g(rO4-Ow), and g(rCR-Ow) for SDS; g(rO1-3-Ow) and g(rCR-Ow) for SDSn. As shown in Figure 3, the two RDFs between headgroup O1-3 and water oxygens Ow are almost the same, and the first peaks are located at 2.78 A˚. Moreover, the first peak of g(rO4-Ow) is also located at 2.78 A˚ and extends to the same second minimum. This indicates that the atoms O1-3 and atom O4 have similar nonbonding interactions with water molecules in the solution, and so, the entire hydrophilic polar head (-SO4) can extend into the water phase. However, the difference in the magnitudes of the first peaks shows clearly that the interaction of water molecules with atom O4 was a little weaker compared to that with atoms O1-3. Although the strong H-bond can cause some interaction of the oxygen O4 in the chain with water molecules, the spatial effect of the hydrophobic chain is essential, and it holds back the oxygen atom O4 from interacting with water molecules in the solution.57 Thus, this interaction of atom O4 with water molecules is weaker than those of the other oxygen atoms, O1-3, in the polar head. The position of CR in a SDSn molecule corresponds to that of O4 in SDS, so the RDFs g(rCR-Ow) for SDS and SDSn are also checked. For SDS (system B), the first peak is around 3.83 A˚, and the weak peak disappears quickly until the second minimum at about 5.61 A˚, while for SDSn (system C), the first peak almost coincides with the second peak of g(rO1-3-Ow) at about 5.03 A˚, which means the hydration shell of CR in SDSn is similar to the second hydration shell of the headgroup. There is a good agreement between the location, depth, and width of the second minima of RDFs of CR-Ow and O1-3-Ow for the SDSn surfactant (system C); however, no similar agreement is observed for the SDS system (system B). We think that the charge on CR of a SDSn molecule performs a vital role in its interaction with water oxygens, leading us to expect that atom CR has a similar electrostatic interaction with atoms O1-3, although atom CR cannot form strong H-bonds with water. Atom CR in SDSn is also negatively charged (-0.158e), like atoms O1-3 (-0.773e), if we only consider the electrostatic interaction, while atom CR in SDS has a positive charge (0.301e). For the same reason, the location of the first peak of g(rOR-Ow) for SDS is shorter than that for SDSn. 3.2.2. Surfactant Solution in the Presence of Ca2þ and Mg2þ. In the surfactant saline solutions (systems D and E), an interesting change of the RDF g(rO1-3-Ow) is found. As shown in Figure 4, a small peak appears at a distance around 4.03 A˚ between the first and second peaks for both SDS and SDSn. Since the surfactants SDS and SDSn have the same headgroup oxygen atoms O1-3, we believe that the middle peak (i.e., the third peak) observed in the RDF of O1-3-Ow should be a universal
(57) Bruce, C. D.; Senapati, S.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 10902.
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Figure 1. Snapshots of the configurations of SDSn in Ca2þ,Mg2þ solution (system E) at (a) t = 0 ns (box size: 173.0 173.0 173.0 A˚3) and (b) t = 10 ns (box size: 45.0 45.0 45.0 A˚3). In panel b, sulfur, oxygen, and carbon that belong to the SDSn molecule are shown as yellow, red, and gray spheres, respectively; hydrogen atoms are omitted for clarity. Water is represented by small red and white lines. The other ions are shown as little green and pink dots which may not be very clear.
Figure 3. RDF of headgroup to water molecule in SDS and SDSn solutions.
Figure 2. Time profiles of the (a) total energy and (b) average distance of sulfur atoms from the micelle center of mass (COM) for SDSn in Ca2þ,Mg2þ solution (system E).
phenomenon for both surfactant solutions in the presence of Ca2þ and Mg2þ. The RDFs g(rO1-3-Ca2þ) and g(rO1-3-Mg2þ) can help us to determine the distribution of Ca2þ and Mg2þ around the headgroup 10452 DOI: 10.1021/la100310w
Figure 4. RDF of headgroup to water molecules in the presence of divalent cations. M2þ represents the Ca2þ,Mg2þ (systems D and E).
(Supporting Information, Figure S2). Both of the RDFs show two peaks, indicating that there are two locations for divalent ions around the headgroup. Furthermore, the two distances are close Langmuir 2010, 26(13), 10448–10459
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Figure 5. Scheme of H-bond structure around the polar head. (a) The original water structure in the absence of Ca2þ,Mg2þ. (b) The structure
when the ions enter into the first water shell. (c) The structure when the ions enter into the second water shell. The unit on the numbers is A˚.
to those in the RDF of O1-3-Ow. It is possible that Ca2þ or Mg2þ ions are located in the first and second water shells when they enter into the water shells to interact with the headgroup oxygen atoms. Their positions can disturb the original water orientation around the polar head, which changes the interaction between the polar head and the water molecules. The third peak in the RDF reflects this change in the water structure around the polar head when Ca2þ or Mg2þ enters into the first and second water shells. Based on the analysis discussed above, a scheme of H-bond structure around the headgroup is presented in Figure 5. As shown in Figure 3, water molecules assemble at the first (2.78 A˚) and the second water shells (5.03 A˚) around the headgroup. Since the headgroup oxygen atom (O1-3) is the acceptor atom forming H-bonds between the headgroup oxygen and water, the water oxygen in the first shell should be the donor atom of H-bonds. Correspondingly, most of the water molecules in the second shell are still considered as donors and form H-bonds between the first and second water shells (Figure 5a). Considering Mg2þ, for example: when Mg2þ exists, the strong electrostatic interaction between Mg2þ and the headgroup oxygen atoms can pull Mg2þ into the water shell. We envisaged two possible structures among the polar head, cations, and water molecules after divalent ions entered into the hydration shells that might explain why the middle peaks appear. In one structure the ions enter into the first hydration shell around the polar head (Figure 5b), and in the other the ions enter into the second hydration shell (Figure 5c). In the first case, Mg2þ enters into the first shell, and the original water orientation around the headgroup changes. As shown by the white arrows pointing up in Figure 5b, the neighboring water molecules around Mg2þ change their orientations; that is, the water oxygen points toward Mg2þ. Meanwhile, some water molecules proceed close to the first shell, either by H-bonding interactions from water in the first shell or by the Coulomb attraction of the divalent ions. Thus, there will be another assembly water shell at 4.0 A˚ (Figure 5b), which is the third location between the first and second hydration shells of headgroup, as shown by the middle peak of RDF in Figure 4. In the other case, when Mg2þ enters into the second shell, a similar explanation can be given for the appearance of the middle peak. In conclusion, the middle peak appears whether the divalent ions enter into first or the second hydration shell of the headgroup. Figure 6 shows the H-bonds network around the headgroup of a single surfactant molecule, randomly selected in the simulation system. Three headgroup oxygen atoms form 5 H-bonds with 5 water molecules (ball-and-stick type in Figure 6a). We define the Langmuir 2010, 26(13), 10448–10459
first water shell as consisting of the 5 water molecules. All these water molecules are acceptors, forming H-bonds with the headgroup. There are another 11 water molecules in the second water shell (stick type in Figure 6a), forming 14 H-bonds with these 5 water molecules. The 11 water molecules can be divided into acceptors and donors according to their position around the first water shell. Figure 6b shows the molecular surface of SDS selected in Figure 6a, which represents the change of headgroup volume from the surface of the single molecule (without water molecules), to that with the first water shell (5 water molecules), to that with the second water shell (11 water molecules). With increasing number of water shells, the hydration volume of the headgroup increases significantly (Figure 6b). According to the number of H-bonds between the oxygen atoms O1-3 in the polar head and water in the first shell (Figure 6c,d), we can define three types of H-bonds: (i) 1:1, where one oxygen atom in the headgroup and one water form one H-bond; (ii) 1:2, with one oxygen atom in the headgroup and two water molecules; and (iii) 2:1, with two oxygen atoms and one water molecule. It is known that water molecules can be both double donors and double acceptors of hydrogen bonds. We note that the water molecules in the first shell are all donors for H-bonds with the headgroup oxygen, but they still remain one donor and two acceptors. Thus, one water molecule in the first shell can form at most three H-bonds with the water in the second shell. However, for the oxygen atom in the headgroup, the water molecules in the solution can only be considered as acceptors; therefore, more 1:2-type H-bonds form between the headgroup and water than 1:1-type, and only a few 2:1-type H-bonds form. We also note that very few n:1-type H-bonds form around the headgroup. 3.2.3. Interactions between the Headgroup and Ions. From the discussion above, we can conclude that Ca2þ and Mg2þ can enter into the hydration shell of the headgroup, and they can affect the orientation of water molecules surrounding the headgroup. In the simulation, we still have one question about the effect of Naþ on the structure of the headgroup and the water molecules: Since Naþ, like Ca2þ, has a positive charge, why does not Naþ affect the orientation of water molecules surrounding the headgroup? Since all the simulation systems contain a positive Naþ that belongs to the surfactant SDS or SDSn, the RDF of O1-3-Ow in systems B and C should reflect the effect of Naþ ions on the structure of the headgroup and water molecules. However, in Figure 3, the RDFs g(rO1-3-Ow) have only two peaks, and no clear middle peak is found. Naþ may have different effects on the DOI: 10.1021/la100310w
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Figure 6. H-bonds structure around the headgroup, drawn by selecting one surfactant molecule and some water randomly. (a) Five water molecules represent the first water shell around the headgroup (ball-and-stick type), and other 11 water molecules represent the second water shell (stick type). (b) Hydration volume of the headgroup with the first and second water shells for SDS molecules. (c) H-bonds around the SDS headgroup. (d) H-bonds around the SDSn headgroup. The green atom represents Ca2þ, and the violet Naþ.
H-bonding network of the headgroup and water molecules, compared to Ca2þ and Mg2þ. It is known that the cations Ca2þ, Mg2þ, and Naþ can bind to SDS or SDSn through electrostatic interactions. The binding energy should be related to the ability of the ions to interact with the headgroups. In this study, we defined a two-ion bond 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 PMF. In the simulation, the ion-pair PMF can be calculated by the pair distribution function g(r) through the equation58,59 E(r) = -kBT ln g(r), where kB is Boltzmann’s constant and T is the temperature of the simulation. Figure 7 shows the headgroup and ion PMFs in saline solutions obtained from the correlation g(r). Three representative cases are shown. Considering the headgroup-Mg2þ ion-pair, for instance (Figure 7a), we make the following observations: (i) The contact minimum (CM) in free energy is at rhead-Mg = 2.07 A˚, corresponding to direct contact between the headgroup and an ion, which means the headgroupion separation is 2.07 A˚. (ii) Another minimum is observed at a distance of 4.35 A˚, corresponding 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 solvent layer barriers show that the structures of water layers are found around the headgroup, and it connects with the first water shell and second shell around the headgroup. To bind with the headgroup, the ions should overcome the energy barrier between the two minima. The binding energy barrier for headgroup-ion-pair is related to SSM and BARR, ΔEþ = EBARR - ESSM. As shown in Figure 7a, it is clear that the order of the energy barriers þ þ is ΔEþ Head-Mg > ΔEHead-Ca > ΔEHead-Na. The energy barrier (58) Ghosh, T.; Garcı´ a, A. E.; GArde, S. J. Am. Chem. Soc. 2001, 123, 10997. (59) Ghosh, T.; Garcı´ a, A. E.; GArde, S. J. Phys. Chem. B 2003, 107, 612.
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between the headgroup and Mg2þ is the strongest, i.e., ΔEþ Head-Mg= 32.99 kJ/mol (i.e., 28.29 þ 4.70), which means that it is the most difficult for Mg2þ to enter into the first water shell of headgroup to form the ion-pair, while for Naþ it is the easiest. The energy barrier of Naþ with the headgroup is the lowest, i.e., ΔEþ Head-Na = 5.22 kJ/ mol (i.e., 2.70 þ 2.52). This indicates that Naþ can easily enter the first water shell to form one ion-pair. The same order is found þ in the SDSn saline solution, i.e., ΔEþ Head-Mg > ΔEHead-Ca > þ ΔEHead-Na (34.13, 21.60, and 4.84 kJ/mol, respectively). The dissociation energy barrier for the headgroup-ion-pair corresponding to CM and BARR, ΔE- = EBARR - ECM, also reflects the same order, which means the dissociation affinity of Mg2þ to the headgroup of either SDS or SDSn is the strongest. Because of the strong dissociation energy between the divalent ions and the headgroup, it is very difficult for Ca2þ and Mg2þ to escape from the headgroup if they are bound to the headgroup in the first hydration shell. On the other hand, Naþ ion easily dissociates from the headgroup because it has the smallest 2þ dissociation, ΔEand Mg2þ have stronHead-Na. Therefore, Ca ger effects on the H-bonds structure of the headgroup in the water shells than Naþ. It is possible that the RDF of O1-3-Ow in system B and C does not show the effect of Naþ, because no middle peak is found in Figure 3. For Ca2þ, we note that ΔE þ Head-Ca (21.60 kJ/mol) in SDSn solution is higher than that in SDS solution (17.13 kJ/mol), which means that it is more difficult for SDSn to bind to Ca2þ than SDS. For Mg2þ, since ΔE þ Head-Mg (or ΔE Head-Mg) is much higher than þ ΔEHead-Ca (or ΔEHead-Ca) and ΔE þ Head-Na (or ΔEHead-Na) for SDS or SDSn solution, it is difficult for Mg2þ to bind or dissociate with the headgroup. As the headgroups of the two surfactants SDS and SDSn are very similar, the potential models for the group -SO3- are identical, except for the atomic partial charge distribution on the headgroup. Therefore, the difference in the energy barrier for different systems is small; ΔEþ Head-Ca of SDS and SDSn is 17.13 and 21.60 kJ/mol, respectively. However, in our simulation, the energy barriers successfully report the trends Langmuir 2010, 26(13), 10448–10459
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Figure 7. Pair potential of mean force between headgroups and ions: (a) SDS saline solution (system D) and (b) SDSn saline solution (system E).
that reflect the level of difficulty in binding ions with headgroups using the potential model. It is also possible to consider the energy barrier as a measurement of efficiency for a variety of surfactants in saline solution conditions, such as in EOR experiments, by calculating the potential of mean force between a variety of surfactants’ headgroup and different ions. The long-range behavior of pair PMF between the headgroup and cations is important for the correct interpretation of the interaction. We note that, within statistical uncertainty, the PMFs shown in Figure 7 approach the correct long-range limit of zero beyond the ion-pair separations of ∼7 A˚. For a solution of surfactant, stronger hydrophilic interactions between the headgroup and water molecules cause ordering of the water layers around the headgroup through H-bonds and electrostatic interactions, leading to nonzero PMF at smaller separations. The pair corrections can be used to interpret the importance of the headgroup in the solution. 3.2.4. Spatial Distributions of Water Molecules and Ions around the Headgroup. To obtain visual insight around the headgroup, the spatial distribution functions (SDFs), which stand for the three-dimensional probability distributions of the headgroup and water molecules, have been studied. SDF is a useful Langmuir 2010, 26(13), 10448–10459
tool to measure the distribution of neighboring molecules of a specific type of atoms around a central molecule60 and can give a detailed description of the immediate environment around a molecule. The SDFs can help us to understand the positions and orientations of water molecules around the headgroup. In Figure 8, the SDFs of salt-free surfactant solutions are shown. Figure 8a,c displays several isoprobability surfaces and the same information recast in the form of a cut along a plane consisting of O1, O2, and S atoms in the headgroup. The smaller the value, the more hydration shells will be shown. When the value is less than 2.0, the corresponding second hydration shell will be presented (contour cut-line in Figure 8a,c). The neighboring water molecules around the headgroup are drawn at a value of 3.5 A˚, which corresponds to the first hydration shell (Figure 8b,d). For O1-3 of the SDS or SDSn headgroup, three circular rings are observed which represent the probability distribution of water molecules around atoms O1-3. The headgroup oxygens of SDS or SDSn can only accept hydrogen bonds, and the H-bonds are related to the electrons on the atoms O1-3, so more water molecules in the first water shell locate around the pair (60) Svishchev, I. M.; Kusalik, P. G. J. Chem. Phys. 1993, 99, 3049.
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Figure 9. Isoprobability surfaces around the headgroup of SDS (a) and SDSn (b) molecules in saline solutions. The contour level is the same as that in Figure 8.
Figure 8. Isoprobability contours around the headgroup of SDS and SDSn molecule in salt-free solution. (a,c) Different contour levels of the corresponding SDF isosurface. (b,d) SDFs of water oxygens (blue) which are set at a contour level of 3.5 times the average atomic density of oxygen atoms in water. (e) Scheme of water distribution around the headgroup. We define the angle O1-3-H-Ow as more than 135°, and the length of H-bonds is in the range of 2.5-3.4 A˚.
electrons, forming a circle (Figure 8e). Thus, the centers in the density rings along the direction of the S-O1-3 bond are empty. SDS and SDSn have similar SDFs of water molecules around the headgroup O1-3. However, water also distributes beside O4 of SDS in the first hydration shell (one blue ribbon indicated by arrow I in Figure 8b). This distribution results from the hydrogen bond formed between a water molecule and O4, indicating that packing and steric effects have a great influence on the arrangement of water molecules around the headgroup. The water molecules around the atoms O1-3 locate in important positions for strong H-bonding interactions, while water molecules near atom O4 would be squeezed out. It is interesting to find more water distributed in the first hydration shell when analyzing systems containing saline CaCl2 and MgCl2 (systems D and E). As indicated by the black arrows in Figure 9, three distinguishable lobes appear beside the circular distribution when Ca2þ and Mg2þ exist in solution. It is possible that these lobes appeared due to divalent ions entering into the first hydration shell. These invasive ions attract water molecules to form a head-ions-water structure. This process also illustrates how the middle peaks of RDF g(rO1-3-Ow) occurred (shown in Figure 4) vividly. Figure 10 illustrates the distribution of divalent ions in the first hydration shell of surfactant headgroup. As presented in Figures 8 and 9, the water molecules around the headgroup are distributed beside the three atoms O1-3 (contour plane in Figure 10a,b). A notable feature in Figure 10 is that Ca2þ and Mg2þ occupy the center of the circular ring formed by the 10456 DOI: 10.1021/la100310w
Figure 10. SDFs of ions around the headgroup of SDS (a) and
SDSn (b): Ca2þ, yellow; Mg2þ, green; the light blue line represents the contour plane of SDF (solid style shown in Figure 9) for water molecules around teh headgroup. (c) Scheme of water distribution around the headgroup. The contour levels are set at 100 times the average counterion density in the simulation for Ca2þ and Mg2þ.
distributions of water molecules around the headgroup. This shows that water molecules bind to the headgroup oxygen atoms either directly or bridged by the divalent ions, as depicted in Figure 10c. Although there is little distribution of Ca2þ along two of the three S-O bond directions for SDS (Figure 10a), the lobes still appear, so we imagine that water molecules can be bound to the headgroup oxygen atoms either directly or bridged by Mg2þ rather than Ca2þ. Moreover, different contributions of Ca2þ and Mg2þ to the headgroup hydration shell have been studied by considering Ca2þ and Mg2þ separately, and the hypothesis has been confirmed (the work is in process). To further compare the effects of different ions on the headgroup hydrogen-bond network, the average coordination numbers of ions in the first hydration shell are calculated via the integral of the RDFs for ions-headgroup from zero to the first minimum. The numbers are shown in Table 4 for the four systems. Langmuir 2010, 26(13), 10448–10459
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Table 4. Coordination Numbers of Cations around the Headgroupa system
Naþ
Ca2þ
Mg2þ
B 0.36 (3.175) C 0.36 (3.175) D 0.27 (3.175) 0.01 (3.125) 0.39 (2.525) E 0.24 (3.125) 0.12 (3.125) 0.39 (2.475) a Numbers in parentheses after each value represent the extent (A˚) of the first coordination shell around the headgroup of the surfactant.
The coordination number of Ca2þ around SDS headgroup is less than that of SDSn, corresponding to the SDF illustrated in Figure 10a, making the distribution of Ca2þ less compact. That is, unlike Mg2þ, Ca2þ evidently distributes beside only one oxygen atom of the SDS headgroup. This mainly results from the steric exclusion of O4 in SDS. Moreover, the effective Born radii differ greatly, i.e., Ca2þ (1.89 A˚) > Mg2þ (1.56 A˚),61 which may be another reason for the smaller distribution of Ca2þ in the first hydration shell of the SDS headgroup. The decreased coordination number of Naþ compared to that in salt-free solution indicates that, when present, Ca2þ and Mg2þ ions displace some Naþ ions from the vicinity of the headgroup. In order to find what role the Cl- ions play in the first hydration shell of the headgroup, the RDF g(rO1-3-Cl-) has also been investigated and is shown in the Supporting Information (Figure S2). A small peak was observed at 3.3 A˚, indicating the weak presence of Cl- in the hydration shell of the headgroup; thus, a few Cl- ions may accompany the cations. A similar phenomenon was found for SDSn as for the SDS system. Salt bridges can be a plausible explanation for the binding between positive ions and negative headgroup. To study this aspect, the probability of a salt bridge between nearest neighbor headgroup pairs has been assessed. We defined a salt bridge to exist when two headgroups’ S atoms were bridged by one Naþ, Mg2þ, or Ca2þ ion. The fact that the g(rS-Mg2þ) shows two peaks between 2.68 and 2.90 A˚ (Supporting Information, Figure S3c) suggests that Mg2þ may form ion bridges between two headgroups. It is clear that Naþ also formed ion bridges between two headgroups (Figure S3a).18,42 As for Ca2þ, the first peak (shown in Figure S3b) is weak because the Mg2þ distribution is more compact at the surfactant micelle, as discussed in Figure 10. Based on the analysis above, we have checked the MD configurations of SDS in saline solution (system D) to study these cases. Figure 11 illustrates one Mg2þ bridging between two surfactant headgroups, which is selected randomly. The percentages of the different cations forming the salt bridges are calculated. We define a salt bridge to exist when two headgroups’ S atoms were bridged by one Naþ, Mg2þ, or Ca2þ ion. If one cation resides within a distance of 7.2 A˚ from two nearest neighbor headgroup pairs, the salt bridge is formed between the headgroups.42 Of the sodium ions that are in the first shell of the headgroup, about 90% are interacting with only one headgroup, whereas 10% are bridging two headgroups. As for Ca2þ and Mg2þ, the percentages of the ions forming salt bridges are somewhat higher than that of Naþ, about 30% and 33% for Ca2þ and Mg2þ, respectively. For SDSn, very similar results are found. These results indicate that the contact ion-pairs exist and that interactions between a single ion and two headgroups occurred. 3.2.5. H-Bonds around the Headgroup. Hydrogen bond lifetimes can be used to represent the stability of the hydrogen bond around the headgroup. In this work we calculate hydrogen bond lifetime in terms of residence times for oxygen atoms (61) Jiao, D; King, C; Grossfield, A; Darden, T. A.; Ren, P. J. Phys. Chem. B 2006, 110, 18553.
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Figure 11. Salt bridging observed within the SDS surface aggregate. The case shown here corresponds to the binding of two headgroups and a Mg2þ. The color code is the same as that of Figure 1. The upper-right inset shows the area highlighted by the blue circled area on an enlarged scale. The distances between Mg2þ and the sulfur atom of two adjacent surfactants were 3.57 and 3.73 A˚. Table 5. Summary of H-Bond Information system B
C
D
E
H-bond lifetime (ps) 8.24 8.97 10.96 12.23 3.45 3.91 4.14 energy barrier (kJ/mol), -a 2.40 1.88 2.42 2.29 energy barrier (kJ/mol), þa 1.33 no. of H-bonds 6.07 (þ 0.88)b 6.63 5.34 (þ0.89)b 5.52 a “-” represents the dissociated energy, and “þ” is the bound energy. b The number in the parentheses refers to the H-bonds number of O4 in the SDS headgroup.
according to the previous approach.62,63 Table 5 shows that the presence of Ca2þ and Mg2þ (systems D and E) influences the residence times of H-bonds around the headgroup, and the times increase notably compared with those of the salt-free solutions (systems B and C), especially for the SDSn solution. It increases from 8.97 to 12.23 ps when Ca2þ and Mg2þ are added to the SDSn solution, indicating that Ca2þ and Mg2þ can affect the H-bond structure. We are still unsure of the reason for the increment of residence time. The residence time of H-bond should be related to the PMF between the headgroup and water. Table 5 shows the energy barrier between the headgroup oxygen atoms O1-3 and the water oxygen atom between the contact minimum and the barrier of solvent layer (defined the dissociated energy, symbol “-”), and the energy barrier between the solvent-separated minimum and the barrier of solvent layer (defined the bound energy, symbol “þ”). For instance, we note that the energy barrier increases when Ca2þ and Mg2þ are added to the SDSn solution: the dissociated energy increases from 3.45 to 4.14 kJ/mol. These changes are consistent with that of the residence time. It shows that when the energy barrier is higher, the dissociation of ion-pairs is more difficult, and therefore the residence time is longer, and vice versa. We note that the residence times of H-bond between atoms O1-3 and water in SDSn solution are longer than those in SDS solution both in the absence and in the presence of Ca2þ and Mg2þ. From Table 2, we note that each atom O1-3 in an SDSn (62) Koneshan, S.; Rasaiah, J. C.; Lynden-Bell, R. M.; Lee, S. H. J. Phys. Chem. B 1998, 102, 4193. (63) Vishnyakov, A.; Neimark, A. V. J. Phys. Chem. B 2000, 104, 4471.
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Figure 12. RDF between Ca2þ or Mg2þ and water molecules.
molecule approximately has more negative charges than in an SDS molecule (>0.07e). Because of the electropositive hydrogen atom (þ0.41e) in the water molecule, the electrostatic interaction between the headgroup of SDSn and water is stronger than that of SDSn and water. Consequently, the strong interaction between SDSn and water results in a long residence time of the H-bond. The organization of the bulk liquid can be analyzed by examining the coordination numbers via the integrals of RDFs from zero to the first minimum. Integration of g (rOHead-Hw) up to the first minimum, 2.43 A˚, gives approximately 6.07 H-bonds for SDS solution (see Supporting Information, Figure S4). This is slightly higher than Vishnyakov’s simulated result, 5.1.63 We note that the H-bond number decreases clearly after Ca2þ and Mg2þ are added to the solution (Table 5). It is possible that Ca2þ or Mg2þ occupies the original location of water molecules around the headgroup, so that the number of water molecules decreases, and the corresponding H-bond will be reduced. We also note that the number of H-bonds in SDSn systems is more than that in SDS systems. There are 6.63 and 6.07 H-bonds for systems C and B, 10458 DOI: 10.1021/la100310w
respectively. Maybe the atom O4 has a competitive impact on the atoms O1-3 when forming H-bonds with water molecules. However, when the whole polar head is considered, the number of H-bonds in the SDS head is still a small increase comparing to that in SDSn head. There are 6.95 (i.e., 6.07 þ 0.88) and 6.63 H-bonds for the SDS and SDS molecules, respectively. We also note that the H-bond number of O4 in SDS surfactant is the same both in the presence and in the absence of Ca2þ and Mg2þ, 0.89 and 0.88 (data shown in parentheses in Table 5). This indicates that the divalent cations weakly affect the H-bond between the atom O4 and water. On the other hand, Ca2þ and Mg2þ strongly affect the headgroup oxygen atoms O1-3. It is likely that this can be attributed to the spatial effect of the alkyl chain of the surfactant molecule. 3.3. Hydration Structure of Ca2þ and Mg2þ. It is important to study the hydration structure of Ca2þ and Mg2þ, as the hydration shell plays an important role in preventing divalent ions from bonding with anionic surfactants, so the RDFs g(rCa2þ-Ow) and g(rMg2þ-Ow) have been checked (Figure 12). All RDF curves Langmuir 2010, 26(13), 10448–10459
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exhibit two peaks. The sharp peaks indicate the highly ordered water structure around the ions. Moreover, the first valleys of Ca2þ-Ow and Mg2þ-Ow RDF are wide and flat, showing that the first and second solvation shells are clearly separated. In system F (the saline solution in the absence of surfactants), for example, the first maximum of the RDF is at 2.43 A˚ for Ca2þ and 1.98 A˚ for Mg2þ, consistent with the effective Born radii (Ca2þ > Mg2þ). The result is in excellent agreement with the previous work: 2.45 A˚ from simulation62 and 2.46 A˚ from experiment64,65 for Ca2þ; 2.07 A˚61 and 1.98 A˚49 from simulation for Mg2þ. The number of water molecules in the first coordination shell around Ca2þ is 7.1, which means the first coordination shell of Ca2þ ions consists of 7 water molecules. This is close to the X-ray experimental value of 7.2 ( 1.2,61 the SPE/C model value of 7.9,62 and ab initio MD simulation of 6.2 or 7.0,66 depending on the flexibility of the water molecules used. For Mg2þ, the coordination number is calculated to be 5.2, which is slightly lower than the experimental67 and ab initio MD results (6.0).68 According to the contrast above, we believe that the force field parameters about Ca2þ, Mg2þ, and others selected in our simulation are appropriate, and our simulated model can describe the difference between Ca2þ and Mg2þ in various solutions conditions. The strong first peak indicates that the dense water cluster formed around Ca2þ, which can diffuse with Ca2þ in the solution. There are about 7 water molecules in the dense cluster. It is difficult for ions to exchange this hydration water with bulk water. The weak second peak represents one loose water cluster around Ca2þ. Water molecules in this loose cluster can diffuse into the bulk water in the solution. Considering the two water shells, we define the hydration radius of Ca2þ as 4.58 A˚, close to the previous experiment (4.1269), and the hydration radius of Mg2þ as 4.28 A˚, identical to the experiment .69 In the surfactant saline solutions, we note that the first and second maxima of RDF g(rCa2þ-Ow) and g(rMg2þ-Ow) locate at the same distance for systems D, E and F. Therefore, it is difficult to describe the impact of surfactant molecules on the hydration structure of ions in the solution using only the RDF. On the other hand, the surfactant molecules affect the hydration structure of ions in the solution only weakly. However, in the surfactant saline solutions, water coordination numbers decrease. It is possible that Ca2þ or Mg2þ will bind the headgroup under the electrostatic interaction, and this ion-pair will destroy the original hydration structure of ions through the diffusion of ions in the solution, leading to the decrease of water coordination number for the ions. In order to further investigate the cation environment near the surfactant headgroups, we defined two kinds of cations in the simulation systems. One is the cations in the hydration shell of the headgroup, which is within 5.0 A˚ from the headgroup. (The distance is decided according to the corresponding RDFs, (64) Megyes, T.; Grosz, T.; Radnai, T.; Bako, I.; Palinkas, G. J. Phys. Chem. A 2004, 108, 7261. (65) Yamagouchi, T.; Hayashi, S.; Ochiai, H. Inorg. Chem. 1989, 18, 2434. (66) Lightstone, F. C.; Schwegler, E.; Allesch, M.; Gygi., F.; Galli, G.. ChemPhysChem 2005, 6, 1745. (67) Caminiti, R.; Licheri, G.; Piccaluga, G..; Pinna, G. Chem. Phys. Lett. 1977, 47, 275. (68) Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi., F.; Galli, G.. Chem. Phys. Lett. 2001, 343, 549. (69) Nightingale, E. R., Jr. J. Phys. Chem. 1959, 63, 1381.
Langmuir 2010, 26(13), 10448–10459
Article
see Figure 5.) The other kind is in the bulk water. The RDFs between the two kinds of divalent ions and water are calculated separately, and they are shown in the Supporting Information (Figure S5, only the data of system D supported). It can be noted from Figure S5 that only for the ions which enter into the hydration shell of the headgroups do the hydration coordination numbers have an obvious decrease. However, the coordination numbers of ions in bulk water are very close to those in system F shown in Figure 12. The loss of the hydrated water of ions makes the ions easy to bind to the headgroups, even to form ion-pairs with the anionic surfactants, resulting in surfactants precipitating from the solution.
4. Conclusions Atomistic MD simulations have been performed to study the effects of divalent ions Ca2þ and Mg2þ on the headgroup hydration shell of two surfactants, SDS and SDSn. The results show that Ca2þ and Mg2þ can affect the H-bond structure around their headgroups in the self-assembly solutions. Binding between the headgroup and Ca2þ or Mg2þ is prevented by a deep stabilizing minimum in the potential of mean force between the interacting ion-pair. Both RDF and SDF show that Ca2þ and Mg2þ can enter into the hydration structure around the headgroup, and they can disturb the original H-bond structure, leading a decrease of the H-bond number and an increase of H-bond lifetime. Compared with Ca2þ, Mg2þ has much greater difficulty to enter into the first hydration shell of the headgroup, and once entered into the shell, Mg2þ has a stronger effect on the hydrogen network. When the divalent ions are present, water molecules can bind to the headgroup oxygen atoms either directly or bridged by the ions; meanwhile, the cations, including Naþ, may form ion bridges between two headgroups. But in most conditions, the cation binds to one headgroup on the surface of the micelle. The PMF shows that the energy barriers of ion-pair between the headgroup and Ca2þ and Mg2þ in the SDSn system are higher than those in the SDS system. It can be explained that sulfonate surfactant (such as SDSn) is more efficient in saline solution containing Ca2þ and Mg2þ in EOR experiments. By investigating the hydration structure of Ca2þ and Mg2þ, it is found that the water coordination numbers around Ca2þ or Mg2þ in SDS solution are lower, which means that SDS surfactant binds the ions more easily than the SDSn surfactant. Acknowledgment. We are sincerely indebted to Prof. Aatto Laaksonen and Prof. Alexander P. Lyubartsev at Stockholm University for the helpful discussion about the M.DynaMix package. This work was financially supported by the National Science Foundation (20873074) and National Basic Research program (2009CB930104) of China. We also thank Dr. Pamela Holt for editing the manuscript. Supporting Information Available: Assembly structures, radial distribution functions of ions to headgroups, H-bond information around the headgroup, and coordination numbers of divalent ions at different locations. This material is available free of charge via the Internet at http://pubs. acs.org.
DOI: 10.1021/la100310w
10459
