Article pubs.acs.org/Langmuir
Synergistic Adsorption of MIBC/CTAB Mixture at the Air/Water Interface and Applicability of Gibbs Adsorption Equation Chi M. Phan,*,† Cuong V. Nguyen,† Shin-ichi Yusa,‡ and Norifumi L. Yamada§ †
Department of Chemical Engineering, Curtin University, Perth, WA 6845, Australia Department of Materials Science and Chemistry, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan § Institute of Material Structure Science, High Energy Accelerator Research Organization (KEK), Tokai, Naka, Ibaraki 319-1106, Japan ‡
S Supporting Information *
ABSTRACT: The synergistic adsorption of a binary surfactant mixture was investigated by tensiometry and neutron reflectometry. The results directly contradicted the conventional Gibbs adsorption equation. The accompanied molecular simulation demonstrated a multilayer arrangement at the synergic conditions, with three distinctively oriented water layers. The positive synergism can be explained by considering the relationship between water orientation and surface tension, in a similar manner to Langmuir’s proposal in 1920s. In spite of the supporting evidence, the relationship has not been quantified in literature. The molecular orientation and arrangement are not included in the current theoretical framework, which simplifies the adsorbed zone into a single monolayer. A new theoretical framework is needed to properly quantify the interfacial adsorption for the mixed surfactant systems.
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INTRODUCTION The adsorption of surfactants at the air/water interface plays an important role in various technological and biological processes such as mineral flotation, lubrication, corrosion, foaming, and detergency. Despite a wealth of previous literature into adsorption of surfactant at air/water interface, the nature of the adsorption zone is not well-described. In most of these studies, the Gibbs adsorption equation has been used as an irreplaceable foundation as reviewed in the literature.1,2 The equation is particularly useful for single surfactant systems, which shows a monotonic reduction in surface tension with increasing concentration. However, the validity of the equation remains questionable.3 Moreover, industrial and natural processes often employed mixed surfactants systems, which can demonstrate a synergistic adsorption, namely, the net adsorption is different to the sum of individual adsorption.4,5 Most of the reported synergism was negative; that is, the net reduction of surface tension was lower than the sum of the individual effects.6−9 Recently, the surface tension of methyl isobutyl carbinol (MIBC) and cetyltrimethylammonium bromide (CTAB) mixtures were investigated using Wilhelmy plate method.10 Unexpectedly, the results showed a positive synergism at the air−water interface: the increasing CTAB concentration increased the net surface tension. The two available theoretical models, which were developed from the conventional analysis, for binary mixtures11,12 failed to describe the positive peak. The positive synergism was apparently related to the branching structure of MIBC, which is a superior frother in mineral flotation.13 © 2014 American Chemical Society
To explore the adsorbed layer at the interface, one needs to employ a direct measurement method, such as radioactive tracers14,15 or neutron reflectometry (NR).16 Although both methods require isotopic substitution, neutron reflection has become a routine procedure for the air/water interfacial adsorption. This study combined tensiometry and NR to direct measure the surface excess of one component of the above mixture to shed new insights into synergism. Furthermore, molecular dynamics was also applied to investigate the molecular arrangement of mixed adsorption zone.
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EXPERIMENTAL SECTION
For effective NR measurement, deuterated CTAB (d-CTAB) was employed. Null reflecting water (NRW), consisting of 8% D2O and 92% H2O, was used as solvent.17 Both tensiometry and neutron reflectometry followed the routine procedures in literature (details are provided in the Supporting Information). The pendant drop method with ADSA software18 was applied to measure the surface tension of eight samples: constant MIBC concentration (7.5 mM) and different d-CTAB concentrations (from 0 to 0.14 mM). SOFIA reflectometer19−21 at Japan Accelerator Research Complex (J-PARC) was applied to obtain the reflectivity profiles of four samples (d-CTAB at 0.05, 0.25, 0.4, and 0.144 mM). The reflectivity profiles were fitted by MOTOFIT22 to obtain the surface excess of d-CTAB. All experimental studies were carried out at 25 °C with the results depicted in Figure 1. The surface excess of d-CTAB at the air/water interface gradually increased with the increment of the bulk concentration of d-CTAB as expected.17 The surface tension showed a positive synergistic peak Received: November 20, 2013 Published: May 7, 2014 5790
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Figure 1. Surface tension and surface excess of d-CTAB/MIBC in NRW. before falling down. The deviations in surface tension (over five measurements) were less than 0.25 mN/m for all data. The surface tension of MIBC/NRW was measured at 54.32 mN/m (not showing in logarithmic scale). In other words, the peaked surface tension was ∼6 mN/m higher than that in the absence of d-CTAB, which was significant for interfacial tensiometry. The synergistic d-CTAB concentration was around 0.03−0.04 mM, which was slightly higher than the positive peak of CTAB/MIBC mixture in water.10 There are two reasons for the variation: CTAB has been replaced by d-CTAB and water has been replaced by the H2O/D2O mixture. Nevertheless, the positive synergism was clearly confirmed. It is noteworthy that the surface tension of pure d-CTAB in NRW following the normal single surfactant behavior: a monotonic reduction from 72 to 39 mN/m (Supporting Information Figure S1).
dγ = −2RT Γ1* d ln c1
It is noteworthy that eqs 1−3 are not practical for surfactant studies. Consequently, eq 4, which is often referred to as the Gibbs adsorption equation, has been used extensively in the literature. Equation 4 indicates that an increasing concentration monotonically leads to a decreasing surface tension, as observed with most single surfactant systems. However, the behavior on the left of the peak in Figure 1 directly defies eq 4: both c1 and Γ*1 increased, yet γ increased. No mathematic manipulation can match eq 4 to the experimental data. There are numbers of ways to mathematically describe the positive synergism using eq 2 or 3. For instance, one might argue that Γ*2 is negative with a larger magnitude than Γ*1 so that eq 3 can describe the increasing γ. The adsorption of inorganic anions depends on ion type25 and thus Γ1* is not necessarily equal to Γ*2 . However, an effective model would have Γ*1 /Γ*2 following a nonmonotonic relationship. Alternatively, the activities coefficients can be assumed nonunity. Again, the positive synergism would require a nonmonotonic relationship between concentration and activity coefficient. As far as we are aware, there are no such equations in the literature. Moreover, such a model would require a comprehensive description of the interfacial layers, with varying spatial arrangement. In summary, the results directly contradicted the conventional Gibbs adsorption equation, eq 4. To use the conventional framework, one needs to combine eq 2 or 3 with new and nonmonotonic relationship(s) between adsorbed quantities. There is no basis for such nonmonotonic relationship, which require few additional parameters, in the literature. We are cautious about applying a complicated mathematical model with new parameters, many of which cannot be independently verified. Instead, molecular simulation was applied to provide insights into the synergism.
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RE-EVALUATING THEORETICAL FRAMEWORK Following the conventional analysis, the change in surface tension is given as23 dγ = −
∑
Γi dμi
i = 0,1,2,3
(1)
where γ is the surface tension, and Γi and μi (i = 0 for water, 1 for CTA+, 2 for Br−, and 3 for MIBC) are surface excess and chemical potential, respectively. The chemical potential is given by μi = RT(ln ci + ln f i), where ci and f i are the bulk concentration and activity coefficient, respectively. By selecting the Gibbs dividing plane so that Γ0 = 0, eq 1 is reduced to dγ = −RT
∑
Γ*i d(ln ci + ln fi )
i = 1,2,3
(2)
The superscripts in Γi* indicate that the surface excesses are defined relatively to the position of the dividing plane. For the low concentrations, such as in this study, all activity coefficients can be assumed unity.23 As MIBC concentration remains constant, eq 2 is reduced to24 dγ = −RT (Γ1* + Γ*2 ) d ln c1
(4)
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(3)
MOLECULAR SIMULATION Molecular dynamics (MD) simulation has been advanced significantly and become a useful tool in investigating the
Following the conventional assumption, Γ1* = Γ2*, one can get the following form:23,24 5791
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Figure 2. Density distribution of surfactants at the air/water interface: 14 MIBCs (a); 10 MIBCs and 2 CTA+ (b); 4 MIBCs and 6 CTA+ (c); 6 CTA+ (d). The reference position, z = 0, was located at the Gibbs dividing plane.
Figure 3. Accumulative average surface tension29 of the investigated systems.
interfacial properties.26−29 Recently, MD can reveal some insights into the molecular interactions between adsorbed surfactants, ions, and water at the liquid/vapor interface.30,31 The simulations32 (details in the Supporting Information) were applied to four combinations of MIBC and CTAB: (i) 14 MIBCs; (ii) 10 MIBCs and 2 CTA+ Br−; (iii) 4 MIBCs and 6 CTA+ Br−; and (iv) 6 CTA+ Br−. The density profiles of the absorbed molecules (average over 10 ns) are plotted in Figure 2. As shown in Figure 2, both surfactants were located stably at the interface. While MIBCs were located further outside, with
their head groups were close to the Gibbs diving plane, the ionic heads were located further inside the aqueous phase. The results were consistent with the arrangement of single surfactant system at the air/water interface for alcohols30 and ionic surfactants.33,34 The surface tension of the investigated systems were calculated by using the accumulative average tension29 and plotted in Figure 3. The tension was fluctuated and could not reveal any definitive difference between the four systems. It should be noted that a similar level of fluctuation has been observed with pure water simulations as well.26,27 5792
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Figure 4. Profiles of water dipole order, cos(θ), over 10 ns. The reference position, z = 0, was located at the Gibbs dividing plane.
However, an effective quantification of the relationship is not available in the literature. Remarkably, the only quantitative approach for the relationship was proposed by Langmuir in the 1920s, in his “principle of independent surface action”.37 According to Langmuir’s elegant analysis, each part of molecules should have an independent surface energy, which can be calculated. Using the concept, Langmuir systematically calculated the optimal orientation of surface molecules as well as the surface tension, among other properties, of various solutions. Although his method and values appear primitive comparing to nowadays molecular simulations (for instance, the “surface energy” of −OH and −CH3 were calculated as 190 and 50 mN/m, respectively), the basis remains valid and unfortunately has not been developed further. The force associated with a single oriented water layer is obviously small and difficult to quantify separately. Nevertheless, the studies between two interfacial water layers, albeit water/solid interface, has revealed some interesting results on the short-range “hydration” force.39 As the two interfaces were pressed closer, within 2 nm, the interactive force oscillated with the decreasing distance. Since there were no surfactants in those systems, the force oscillation obviously comes from water reorientation.40 The periodicity of oscillation was almost constant, ∼0.25 nm,41 and equal to water molecule diameter. Hence, it is conceivable that as the two surfaces were pressed together, water layers were reoriented one-by-one. The reported measurements indicated that the force associated with reorientation of a single layer can be as high as 10 mN/m. Using the same basis, we hypothesize that any water layer, with a specific orientation, has a certain contribution to the overall air/water surface tension. Consequently, the adsorbed surfactants reduce surface tension via disrupting the water arrangements, which was suggested in our previous study with cationic surfactant systems.42 The positive synergism is evidently explained by the accumulative effects of multiple oriented water layers, for instance at 10 MIBC/2 CTAB combination. On either side of the combination (either more MIBC or more CTAB), there are less orientated layers and consequently the surface tension is lower. Finally, the radial distribution functions of water molecules around surfactants, which correspond to hydration shells,43 are
Consequently, the water orientation in the interface region was analyzed by the water dipole order parameter, cos(θ) where θ is defined as the angle between the water dipole and the positive z-axis (Figure 4). The profiles of water dipole angle indicated complicated but well-structured arrangements near the interface, with different peaks. Further inside the liquid phase, water molecules are randomly oriented so that the average angle is zero.35 For single surfactant systems, the simulations revealed a single peak in dipole angle: near the Gibbs dividing plane for MIBC and 0.6 nm inside the liquid for CTA+. Surprisingly, the intermediate combination (10 MIBC and 2 CTAB) showed multiple layers of water orientation. The combination corresponding to Γ1* = 0.4 × 10−6 mol/m2 and Γ3* = 1.8 × 10−6 mol/m2, which was within the estimated synergistic zone.10 From the distribution with single surfactants, the outer and inner peaks can be designated to MIBC and CTA+ heads, respectively. With increasing concentration of CTAB, that is, four MIBC and six CTAB, the outer peak was overlapped by the inner peak and the whole layer reduced to a single peak. We believe this is the underpinning mechanism of the positive synergism.
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THE RELATIONSHIP BETWEEN WATER ORIENTATION AND SURFACE TENSION It has been recognized that the interfacial molecules should orient themselves to provide the “most gradual transition from one phase to another”, or to “maximize their mutual interaction energy”.23 For pure water, it has been well accepted that the surface molecules have H-bonds pointing to the vapor phase.36 Yet, the average angle (orientation) of this bond is not exactly 90°.37 The two-layer interfacial structure has also been revealed.35 The second layer is oriented in a specific way, which might be considered it as a transition from the outmost layer to the bulk. The simulations have indicated that the interfacial structure was determined by the optimal energy state: that is, maximizing the number of H-bonds and minimizing the exposed partial charge. The interfacial water layer also has a lower H-bonds switching rate than that in the bulk.38 Hence, it is conceivable that the interfacial water arrangement and surface tension follows a deterministic relationship. 5793
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Figure 5. Radial distribution functions of water oxygen around: (a) oxygen atom of MIBC, (b) N atom, and (c) Br− ions.
shown in Figure 5. It clearly shows that the heads of MIBC, CTA+ and Br− have a hydration shell around them: with 6, 4, and 11 water molecules for −O (in MIBC), N (in CTA+), and Br−, respectively. The distribution functions are the same for the all concentration combinations, which indicate that the interactions between adsorbed molecules do not alter the hydration shells. Hence, the interactions between these molecules and water interfacial structure should be fully accounted for by the water reorientation. It has been shown that the outer layer of water surface has 25% dangling Hbonds,44 which is equivalent to 67 mN/m. Hence, the disruption of the outer layer should account for most of the tension reduction. It is noteworthy that location of CTA+ head was 0.6 nm inside the liquid phase, which was physically consistent with the long chain. Consequently, at least four layers of water, with multiple possibilities of reorientations, are disrupted by CTA+. Further calculation to relate the orientation profile to surface energy is being developed.
Using the hypothesized role of water reorientation, one might be able to explain the discrepancy for single ionic surfactant system. Evidently, ionic surfactants and their counterions do not form a monolayer at the interface.33,34,42 Hence, complicated water interfacial arrangements are formed, as demonstrated for alcohol/electrolyte solutions.30,48 Since most of water surface energy is associated with the outmost layer, the tension reduction is directly proportional to adsorbed surfactants at low concentrations. At high concentrations, however, the relative positions between surfactant and counterion can vary, which results in variation of water arrangement. Although the change in water arrangement could be a small factor, 80% of CMC. Our previous study also highlighted the unreliability of applying the Gibbs equation to cationic surfactants.42 5794
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Holland, P. M., Rubingh, D. N., Eds.; American Chemical Society: Washington, DC, 1992; Vol. 501, pp 114−125. (5) Sugihara, G.; Nagadome, S.; Oh, S. W.; Ko, J. S. A Review of Recent Studies on Aqueous Binary Mixed Surfactant Systems. J. Oleo Sci. 2008, 57, 61−92. (6) Wüstneck, R.; Miller, R. The Adsorption Behavior of Solutions Containing Sodium Dodecyl Sulfate and Different n-Alkanols. Colloids Surf. 1990, 47, 15−21. (7) Iyota, H.; Motomura, K. Miscibility of Ethanol and 2(Octylsulfinyl)ethanol in the Adsorbed Film at the Water/Air Interface and in the Micelle. J. Colloid Interface Sci. 1992, 148, 369−374. (8) Zdziennicka, A.; Jańczuk, B. Adsorption of Cetyltrimethylammonium Bromide and Propanol Mixtures with Regard to Wettability of Polytetrafluoroethylene. I. Adsorption at Aqueous Solution−Air Interface. J. Colloid Interface Sci. 2008, 317, 44−53. (9) Fainerman, V. B.; Aksenenko, E. V.; Lylyk, S. V.; Petkov, J. T.; Yorke, J.; Miller, R. Adsorption Layer Characteristics of Mixed Sodium Dodecyl Sulfate/CnEOm Solutions 1. Dynamic and Equilibrium Surface Tension. Langmuir 2009, 26, 284−292. (10) Le, T. N.; Phan, C. M.; Nguyen, A. V.; Ang, H. M. An Unusual Synergistic Adsorption of MIBC and CTAB Mixtures at the Air− Water Interface. Miner. Eng. 2012, 39, 255−261. (11) Siddiqui, F. A.; Franses, E. I. Surface Tension and Adsorption Synergism for Solutions of Binary Surfactants. Ind. Eng. Chem. Res. 1996, 35, 3223−3232. (12) Fainerman, V. B.; Miller, R.; Aksenenko, E. V. Simple Model for Prediction of Surface Tension of Mixed Surfactant Solutions. Adv. Colloid Interface Sci. 2002, 96, 339−359. (13) Pearse, M. J. An Overview of the Use of Chemical Reagents in Mineral Processing. Miner. Eng. 2005, 18, 139−149. (14) Nilsson, G. The Adsorption of Tritiated Sodium Dodecyl Sulfate at the Solution Surface Measured with a Windowless, High Humidity Gas Flow Proportional Counter. J. Phys. Chem. 1957, 61, 1135−1142. (15) Tajima, K.; Muramatsu, M.; Sasaki, T. Radiotracer Studies on Adsorption of Surface Active Substance at Aqueous Surface. I. Accurate Measurement of Adsorption of Tritiated Sodium Dodecylsulfate. Bull. Chem. Soc. Jpn. 1970, 43, 1991−1998. (16) Lyttle, D.; Lu, J.; Su, T.; Thomas, R.; Penfold, J. Structure of a Dodecyltrimethylammonium Bromide Layer at the Air/Water Interface Determined by Neutron Reflection: Comparison of the Monolayer Structure of Cationic Surfactants with Different Chain Lengths. Langmuir 1995, 11, 1001−1008. (17) Lu, J. R.; Hromadova, M.; Simister, E. A.; Thomas, R. K.; Penfold, J. Neutron Reflection from Hexadecyltrimethylammonium Bromide Adsorbed at the Air/Liquid Interface: The Variation of the Hydrocarbon Chain Distribution with Surface Concentration. J. Phys. Chem. 1994, 98, 11519−11526. (18) Zuo, Y. Y.; Ding, M.; Bateni, A.; Hoorfar, M.; Neumann, A. W. Improvement of Interfacial Tension Measurement Using a Captive Bubble in Conjunction with Axisymmetric Drop Shape Analysis (ADSA). Colloids Surf., A 2004, 250, 233−246. (19) Mitamura, K.; Yamada, N. L.; Sagehashi, H.; Seto, H.; Torikai, N.; Sugita, T.; Furusaka, M.; Takahara, A. Advanced Neutron Reflectometer for Investigation on Dynamic/Static Structures of Soft-Interfaces in J-PARC. J. Phys.: Conf. Ser. 2011, 272, 012017. (20) Mitamura, K.; Yamada, N. L.; Sagehashi, H.; Torikai, N.; Arita, H.; Terada, M.; Kobayashi, M.; Sato, S.; Seto, H.; Goko, S.; Furusaka, M.; Oda, T.; Hino, M.; Jinnai, H.; Takahara, A. Novel Neutron Reflectometer SOFIA at J-PARC/MLF for in-Situ Soft-Interface Characterization. Polym. J. 2013, 45, 100−108. (21) Yamada, N. L.; Torikai, N.; Mitamura, K.; Sagehashi, H.; Sato, S.; Seto, H.; Sugita, T.; Goko, S.; Furusaka, M.; Oda, T.; Hino, M.; Fujiwara, T.; Takahashi, H.; Takahara, A. Design and performance of horizontal-type neutron reflectometer SOFIA at J-PARC/MLF. Eur. Phys. J. Plus 2011, 126, 1−13. (22) Nelson, A. Co-Refinement of Multiple-Contrast Neutron/X-ray Reflectivity Data Using MOTOFIT. J. Appl. Crystallogr. 2006, 39, 273−276.
Figure 6. Schematic representation of positive (this study) and negative (with anionic surfactant) synergism.
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CONCLUSION The adsorption layer of the mixture between d-CTAB and MIBC demonstrated a positive synergism, which cannot be quantified by the conventional Gibbs adsorption equation. The molecular simulations identified multiple layers of oriented water, which apparently corresponds to the positive synergism in surface tension. The results revive the significance of the relationship between molecular arrangement and surface energy, which was attempted by Langmuir and has been largely ignored since the 1920s. The molecular orientation and arrangement are not included in the current theoretical framework, which simplifies the adsorbed zone into a single monolayer. A successful quantification of the relationship would appropriately describe the surface energy of binary surfactant systems as well as other industrial surfactant systems.
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ASSOCIATED CONTENT
S Supporting Information *
Details of experimental and molecular simulations. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS The neutron scattering experiment was approved by the Neutron Science Proposal Review Committee of J-PARC/MLF (Proposal No. 2012B0050) and supported by the InterUniversity Research Program on Neutron Scattering of IMSS, KEK. The simulation was supported by iVEC (Western Australia) through the use of advanced computing resources. C.V.N. was supported by the 322 scholarship, Ministry of Education and Training (Vietnam).
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REFERENCES
(1) Eastoe, J.; Dalton, J. S. Dynamic Surface Tension and Adsorption Mechanisms of Surfactants at the Air-Water Interface. Adv. Colloid Interface Sci. 2000, 85, 103−144. (2) Chang, C. H.; Franses, E. I. Adsorption Dynamics of Surfactants at the Air/Water Interface: A Critical Review of Mathematical Models, Data, And Mechanisms. Colloids Surf., A 1995, 100, 1−45. (3) Menger, F. M.; Rizvi, S. A. A. Relationship between Surface Tension and Surface Coverage. Langmuir 2011, 27, 13975−13977. (4) Holland, P. M. Modeling Polydispersity in Multicomponent Nonideal Mixed Surfactant Systems. In Mixed Surfactant Systems; 5795
dx.doi.org/10.1021/la500721d | Langmuir 2014, 30, 5790−5796
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(23) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; John Wiley & Sons: New York, 1997. (24) Rosen, M. J.; Kunjappu, J. T. Surfactants and Interfacial Phenomena, 4th ed.; Wiley: Hoboken, NJ, 2012. (25) Jungwirth, P.; Tobias, D. J. Specific Ion Effects at the Air/Water Interface. Chem. Rev. 2005, 106, 1259−1281. (26) Chen, F.; Smith, P. E. Simulated Surface Tensions of Common Water Models. J. Chem. Phys. 2007, 126, 221101. (27) Yuet, P. K.; Blankschtein, D. Molecular Dynamics Simulation Study of Water Surfaces: Comparison of Flexible Water Models. J. Phys. Chem. B 2010, 114, 13786−13795. (28) Mountain, R. D. An Internally Consistent Method for the Molecular Dynamics Simulation of the Surface Tension: Application to Some TIP4P-Type Models of Water. J. Phys. Chem. B 2009, 113, 482−486. (29) Vega, C.; de Miguel, E. Surface Tension of the Most Popular Models of Water by Using the Test-Area Simulation Method. J. Chem. Phys. 2007, 126, 154707. (30) Krisch, M. J.; D’Auria, R.; Brown, M. A.; Tobias, D. J.; Hemminger, C.; Ammann, M.; Starr, D. E.; Bluhm, H. The Effect of an Organic Surfactant on the Liquid−Vapor Interface of an Electrolyte Solution. J. Phys. Chem. C 2007, 111, 13497−13509. (31) Pang, J.; Wang, Y.; Xu, G.; Han, T.; Lv, X.; Zhang, J. Molecular Dynamics Simulations of SDS, DTAB, and C12E8 Monolayers Adsorbed at the Air/Water Surface in the Presence of DSEP. J. Phys. Chem. B 2011, 115, 2518−2526. (32) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, And Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (33) Rideg, N. A.; Darvas, M.; Horvai, G.; Jedlovszky, P. Immersion Depth of Surfactants at the Free Water Surface: A Computer Simulation and ITIM Analysis Study. J. Phys. Chem. B 2013, 117, 8733−8746. (34) Rideg, N. A.; Darvas, M.; Varga, I.; Jedlovszky, P. l. Lateral Dynamics of Surfactants at the Free Water Surface: A Computer Simulation Study. Langmuir 2012, 28, 14944−14953. (35) Fan, Y.; Chen, X.; Yang, L.; Cremer, P. S.; Gao, Y. Q. On the Structure of Water at the Aqueous/Air Interface. J. Phys. Chem. B 2009, 113, 11672−11679. (36) Shen, Y. R.; Ostroverkhov, V. Sum-Frequency Vibrational Spectroscopy on Water Interfaces: Polar Orientation of Water Molecules at Interfaces. Chem. Rev. 2006, 106, 1140−1154. (37) Langmuir, I. Distribution and Orientation of Molecules. Colloid Symp. Monogr. 1925, 48−75. (38) Ni, Y.; Gruenbaum, S. M.; Skinner, J. L. Slow Hydrogen-Bond Switching Dynamics at the Water Surface Revealed by Theoretical Two-Dimensional Sum-Frequency Spectroscopy. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 1992−1998. (39) Israelachvili, J. N.; McGuiggan, P. M. Forces Between Surfaces in Liquids. Science 1988, 241, 795−800. (40) Israelachvili, J. Solvation Forces and Liquid Structure, As Probed by Direct Force Measurements. Acc. Chem. Res. 1987, 20, 415−421. (41) Pashley, R. M.; Israelachvili, J. N. Molecular layering of water in thin films between mica surfaces and its relation to hydration forces. J. Colloid Interface Sci. 1984, 101, 511−523. (42) Phan, C. M.; Le, T. N.; Nguyen, C. V.; Yusa, S.-i. Modeling Adsorption of Cationic Surfactants at Air/Water Interface without Using the Gibbs Equation. Langmuir 2013, 29, 4743−4749. (43) Grossfield, A. Dependence of Ion Hydration on the Sign of the Ion’s Charge. J. Chem. Phys. 2004, 122, 024506. (44) Du, Q.; Freysz, E.; Shen, Y. R. Surface Vibrational Spectroscopic Studies of Hydrogen Bonding and Hydrophobicity. Science 1994, 264, 826−828. (45) Menger, F. M.; Shi, L. Electrostatic Binding among Equilibrating 2-D and 3-D Self-Assemblies. J. Am. Chem. Soc. 2009, 131, 6672− 6673. (46) Li, P. X.; Li, Z. X.; Shen, H.-H.; Thomas, R. K.; Penfold, J.; Lu, J. R. Application of the Gibbs Equation to the Adsorption of Nonionic Surfactants and Polymers at the Air−Water Interface: Comparison
with Surface Excesses Determined Directly using Neutron Reflectivity. Langmuir 2013, 29, 9324−9334. (47) Xu, H.; Li, P. X.; Ma, K.; Thomas, R. K.; Penfold, J.; Lu, J. R. Limitations in the Application of the Gibbs Equation to Anionic Surfactants at the Air/Water Surface: Sodium Dodecylsulfate and Sodium Dodecylmonooxyethylenesulfate Above and Below the CMC. Langmuir 2013, 29, 9335−9351. (48) Nguyen, C. V.; Phan, C. M.; Ang, H. M.; Nakahara, H.; Shibata, O.; Moroi, Y. Surface Potential of 1-Hexanol Solution: A Comparison with Methyl Isobutyl Carbinol. J. Phys. Chem. B 2013, 117, 7615− 7620. (49) McBain, J. W.; Mills, G. F. The Adsorption Theorem of J. Willard Gibbs. Anomalies in Applying It to Surface Tension Curves That Exhibit Minima in Dilute Solution. Rep. Prog. Phys. 1938, 5, 30. (50) Mysels, K. J. Surface Tension of Solutions of Pure Sodium Dodecyl Sulfate. Langmuir 1986, 2, 423−428. (51) Hines, J. D. The Preparation of Surface Chemically Pure Sodium n-Dodecyl Sulfate by Foam Fractionation. J. Colloid Interface Sci. 1996, 180, 488−492.
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