Water System by Adjusting Mesoscopic

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J. Phys. Chem. B 2009, 113, 8854–8859

Description of Ionic Surfactant/Water System by Adjusting Mesoscopic Parameters Baogen Duan, Xiongfei Zhang, Baofu Qiao, Bin Kong, and Xiaozhen Yang* Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Science and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ReceiVed: December 10, 2008; ReVised Manuscript ReceiVed: May 8, 2009

Dissipative particle dynamics simulations were utilized to simulate a model surfactant solution-air system. Amphiphilic surfactant molecules were modeled as dimers composed of a hydrophilic head and a hydrophobic tail. With a simple model, the influence of conservative interaction parameters on the surfactant’s properties, including surfactant efficiency and critical micelle concentration (CMC), was investigated in the present research. It is not the surfactant total concentration, but the bulk concentration, that should be employed to achieve the right surfactant properties. It is found that the adjustment of interaction between water and head or air and tail (aWH or aAT) will result in the obvious change in surfactant efficiency. The parameter that affects CMC the most significantly is the interaction between water and tail (aWT). On the basis of the findings about the relationship between conservative interaction parameters and surfactant behaviors, we varied the interaction parameters and simulated a real ionic surfactant system with different tail lengths. Introduction Surfactants are widely used in both industry and everyday life. When applied in a phase-separated system, surfactant molecules absorb on the interface between oil and water, lowering the surface tension and promoting mixing.1,2 To improve the quality and efficiency of surfactants, extra components are usually added, thus making molecular interactions within the system extremely complex. Since the details of the interactions and how they affect the macroscopic properties are unknown, it is difficult to predict the surfactant effect with empirical methods.3-5 Furthermore, experiments can hardly provide any insight into the complex interactions. Computer simulation, a powerful tool to investigate the dynamics in microscopic scale, can be employed here to correlate the thermodynamic properties and the microstructure of the surfactant system. Quantum mechanics simulation has been used to calculate interactions such as the hydrogen bond between water and other molecules and their distributions.6,7 Molecular dynamics simulation, which is based on atomic scale calculations, could be applied to yield information on the surface energy of the system,8 the structure of a single micelle,9,10 the relaxation of a molecular chain,11 and so on. However, the time and length scales of these simulation methods limit their application in simulating larger-scale behaviors, such as the molecules’ diffusion to the interface and the formation of micelles.12 As an alternative method, mesoscopic simulation dissipative particle dynamics (DPD) has made it possible to investigate the mesostructure of complex fluid and surfactant systems up to the microsecond range.13-16 The simulation strategy is to regard a cluster of atoms or molecules as a single, coarse-grained particle or bead whose motion is governed by Newton’s motion equation. Groot and Madden17 first applied DPD to examine the microphase separation behavior of block copolymers and much research has been devoted to the exploration of the application of DPD simulation method ever since. The success* Corresponding author. Phone: 86-10-82618423. E-mail: yangx@ iccas.ac.cn.

ful DPD simulation of a mesoscopic system lies in the appropriate selection of conservative interaction parameters. Since Groot and Warren established an important link between conservative interaction parameters and the Flory-Huggins χ parameter for polymer solutions in 1997,18 a great amount of work has been focused on the approximation of conservative interaction parameters from the χ parameter.18-21 Maiti et al.19 used discrete bead sizes to obtain a series of elementary χ parameters and interfacial tensions for immiscible binary systems. Comparing with experimental interfacial tensions, suitable χ parameters were selected, and thus, a set of conservative interaction parameters were obtained. At that moment, the system was still without the surfactants. In the work of He2 and Yuan,22 the blends module in Cerius 2 was applied to study the system with surfactants in the calculation of χ parameters from the mixing energy between DPD particles. Rekvig et al.16 combined DPD and Monte Carlo simulation methods to obtain the correlation between surfactant structure and surfactant efficiency. To the best of our knowledge, there has been no DPD research on the critical micelle concentration (CMC) of surfactant systems. At the mesoscopic level, the microinteractions, including van der Waals forces, electrostatic interactions, hydrogen bond, etc., cannot be individually observed. DPD conservative interaction parameters should cover all of these interactions. However, until now, there has been no theory to quantitatively correlate these interactions with conservative interaction parameters. Surface tension is an overall description of the interactions between molecules in two phases.23-25 Consequently, we adjusted conservative interaction parameters directly and chose surface tension to qualitatively correlate microinteractions of small molecule surfactants in aqueous solution with mesoscopic conservative interaction parameters in the present research. In addition, the variation of surface tension was used to monitor the effect caused by the adjustment of repulsion interactions among surfactant head and tail, water, and air. The concentration dependence of the surfactant efficiency and CMC has been discussed, and factors which play the most significant role in

10.1021/jp8108545 CCC: $40.75  2009 American Chemical Society Published on Web 06/09/2009

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affecting surfactant efficiency and CMC were found. The present work will probably open the door for correlating conservative interaction parameters with the behaviors of a surfactant/water system. Methodology Introduction of the DPD Method. In the DPD method, the forces between two particles, i and j, consist of repulsive conservative forces (FijC), pairwise dissipation forces (FDij ), and pairwise random forces (FRij ). The force acting on a particle i is given by

Fi )

TABLE 1: Conservative Interaction Parameters aij

∑

(FijC

+

FijD

+

FijR)

(1)

j*i

W A H T

where the forces are of the form

FijC ) aijωCrˆij

(2)

FijD ) -ηωD(rij)(rˆijνij)rˆij

(3)

FijR ) σωR(rij)ζijrˆij

(4)

Here, Vij is the velocity difference for the two particles, and r∧ij is the unit vector pointing from particle i to particle j. ζij is a random number between 0 and 1. Rij, σ, and η determine the amplitude of the conservative, random, and dissipative forces, respectively, and ωC, ωD and ωR are weight functions. To obey the fluctuation-dissipation theorem,26 ωC, ωD, ωR, η, and σ must have a relationship as follows:

ω (r) ) ω (r) ) √ω (r) ) ω(r), σ ) 2ηκBT C

R

D

2

{

10

r r < rc rc for for r g rc

∫ [pzz

(6)

1 - (pxx + pyy) dz 2

]

(7)

where pxx, pyy, and pzz are the three diagonal components of the pressure tensor. The interface is parallel to the x-y plane. In terms of the interparticle forces, eq 7 is transformed as

γ)

1 A

[∑ i,j

]

1 Fijzrijz - (Fijxrijx + Fijyrijy) i > j 2

A

H

T

25 90 15 67

90 25 90 25

15 90 35 67

67 25 67 15

The summation is carried out all over the pairwise particles. A is the surface area. Dimer Models. In the DPD method, a number of atoms are taken together into one simulation bead that is regarded as a simulation element. In the current study, the hydrophilic headgroup and hydrophobic tail part are denoted as H and T, respectively, and water beads and air beads are denoted as W and A. Kong et al.28 adopted a liquid to be the gas phase to study contact angle hysteresis on a patterned solid/air composite surface. The same method is applied in the present study. The model surfactants investigated are shown in Figure 1. A surfactant molecule consists of a hydrophilic group and a hydrophobic group connected by harmonic springs.16

(9)

(5)

Throughout this paper, we use reduced units. rc is the unit of length; kT (the temperature of the thermostat) is the unit of energy; and the mass unit is the mass of a DPD bead. The random and dissipative parameters were taken as σ ) 3.0 and ζ ) 4.5, respectively.16 In simulations, the surface tension is calculated using the Irving-Kirkwood equation27

γ)

W

Fijbond ) -ks(rij - r0)rˆij

where

ω(r) )

Figure 1. Molecular structures of alkylsulfonate-type ionic surfactants.

(8)

(Fijx, Fijy, Fijz) and (rijx, rijy, rijz) are the x, y, and z components of the force and the vector between particles i and j, respectively.

We chose ks ) 100 and r0 ) 0.7.29 The conservative interaction parameters were taken from the literature.15,16 Each parameter has been adjusted to determine its influence on properties such as surfactant efficiency, CMC etc. A set of interaction parameters employed in the simulation is listed in Table 1. DPD simulation was completed through modifying the MYDPD source code.30 Dimensions of the simulation box are Lx ) 10 by Ly ) 10 by Lz ) 30, where the z-direction is perpendicular to the liquid/air interface. It contains 9000 beads (F ) 3), and periodic boundary conditions are applied in all three directions. The amphiphiles were placed in the water phase initially close to (but not at) the interfaces according to Smit.31 The simulation runs 400 000 steps with a time step of 0.05. The surface tensions were averaged after 200 000 steps. Results and Discussion The Bulk Concentration and the Total Concentration. The surfactant concentration used in experiments is usually the total concentration (Ctotal), which is defined as the ratio of total surfactant molecules to the volume. Due to the relatively large system size accessible to experiments, the surface layer occupies a very small part of the system and can be neglected. In this situation, the total concentration is nearly equivalent to the bulk concentration (Cbulk is the ratio of the surfactant molecules in bulk to the volume). As system depth shrinks, the proportion of surface layer to the total volume becomes larger and larger. When the depth has a magnitude of micrometerssin other words, the system becomes a thin filmsthe total concentration

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Figure 2. Relative surface tension versus surfactant bulk concentration (a) and total concentration (b) with different water-tail/head-tail repulsion parameters (aWT/aHT).

Figure 3. Relative surface tension versus surfactant bulk concentration (a) and total concentration (b) with different water-head repulsion parameters (aWH).

and the bulk concentration might have a huge discrepancy. In the present work, the dependence of surface tension and CMC on concentration, both the bulk concentration and the total concentration, has been intensively discussed. Effect of DPD Parameters on Surfactant Efficiency and CMC. In the present study, we tried to develop a set of DPD parameters that are reasonable for a real ionic surfactant/water system. At the beginning of the study, we selected the initial conservative parameters in combination with that in the literature15,16 for aWW, aAA, aHH, aTT, aWH, aAT and that in our estimation for aWA, aAH, and aWT ) aHT, as shown in Table 1. On the basis of the initial parameters, we started parameter adjustment as mentioned below. The first two conservative interaction parameters adjusted are the water-tail and head-tail repulsion parameters (aWT and aHT). It is reported that these two parameters have the same value;16 therefore, they are adjusted simultaneously in the present work. The variation of aWT (aHT) corresponds to molecular chains with the same hydrophilic headgroup, but with different tail lengths.32 In the present research, we set the water-air repulsion parameter (aWA) to be 90 and varied aWT (aHT) from 40 to 67. A set of conservative interaction parameters (aWT ) aHT ) 67) is shown in Table 1. The concentration dependence of relative surface tension simulated with different interaction parameters is shown in Figure 2. In Figure 2a and b (i.e., relative surface tension versus Cbulk and Ctotal respectively), CMCs are clearly identified in Figure 2a that the surfactant corresponding to an aWT (aHT) value of 67 has the lowest CMC value. The larger the aWT (aHT) is, the lower the CMC is. Such an observation cannot be found in Figure 2b; that is, the plot of relative surface tension versus Ctotal. In the present article, the definition of surfactant efficiency is consistent with Rekvig et al.,16 -dγ/d ln(c). From both figures,

it can be found that the surfactant with a higher aWT (aHT) value has a higher efficiency. From an experimental point of view, the surfactant with the longer alkyl chain is more difficult to dissolve in water and, thus, has a lower CMC and a higher efficiency.33,34 The surfactant with a longer hydrophobic chain has poorer solubility in water; thus, the interaction parameter is larger. Therefore, Figure 2a matches experimental observations qualitatively, but only the surfactant efficiency in Figure 2b is consistent with the experimental results. The second conservative interaction parameter adjusted here is the water-head repulsion parameter (aWH). The variation of aWH can be used to present surfactant systems with different hydrophilic head parts; for example, ionic surfactants and nonionic surfactants that have the same hydrophobic tail groups. It is reported that if containing the same hydrophobic groups, ionic surfactants have much higher CMCs than nonionic surfactants do in the aqueous medium.35 Comparing with nonionic surfactants, ionic surfactant has a much more hydrophilic headgroup. Therefore, the repulsion between their head groups and water is much weaker; in other words, ionic surfactants have a smaller aWH. It can be seen from Figure 3a that the curve corresponding to the smallest aWH value, 5, has the highest CMC. The curve with aWH ) 25 has the lowest CMC. Thus, Figure 3a matches reported results qualitatively. In the simulation, for the surfactant model with a smaller aWH, surfactant molecules tend to stay in water and are more difficult to migrate from the bulk to the surface. Therefore, the surfactant efficiency is lower, which can also be observed in Figure 3a. If the relative surface tension is plotted against Ctotal, as shown in Figure 3b, a larger aWH corresponds to a curve with a higher CMC, which is opposite to the truth. On the other hand, it can also be found from Figure 3b that the surfactant with aWH ) 25 has the highest efficiency; aWH ) 15, the next;

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Figure 4. Relative surface tension versus surfactant bulk concentration with (a) different air-tail repulsion parameters (aAT) and (b) different air-head repulsion parameters (aAH).

Figure 5. Influence of each conservative interaction parameter on surfactant efficiency by using the bulk concentration (Cbulk).

and aWH ) 5, the worst. The relationship between surfactant efficiency and aWH is the same as that shown in Figure 3a, which is similar to the situation shown in Figure 2. The effect of the air-tail interaction parameter (aAT) on surfactant behavior is also investigated. Similar to aWH, the variation of aAT can be used to describe surfactants with the same hydrophilic head but different hydrophobic tails. Longer hydrophobic tails means elevated solubility in hydrophobic phase but poorer solubility in water. Therefore, surfactant molecules with longer hydrophobic tails are able to migrate from the bulk phase to the surface easily and decrease surface tension effectively. As shown in Figure 4a, the surfactant with aAT ) 15, which corresponds to the surfactant molecule with the longest hydrophobic tail, has the highest surfactant efficiency. Furthermore, the surfactant with the smaller aAT value has a lower CMC. This can be explained by the fact that surfactant molecules with more hydrophobic tails come out of water phase more easily and are able to form micelles at lower concentra-

tions. Nevertheless, CMCs are not very well separated in Figure 4a as compared with those in Figures 2a and 3a. Surfactants in those two figures have aAT values of 25, which are equivalent to the maximum aAT value in this series of simulations. Surfactants in this series of simulations are more hydrophobic and form micelles more easily. Therefore, the CMCs are lower ( aAH ) 70 > aAH ) 90, but the CMCs are poorly separated. The reason may be the poor water solubility of the surfactants, since aAH ) 50 and 70 are for more hydrophobic surfactants than aAH ) 90 in this series of simulations. This result indicates that variation of aAH has a smaller effect on the CMC than aWH does. Surfactant Efficiency and CMCs Obtained from Cbulk and Ctotal. The influence of conservative interaction parameters on surfactant efficiency obtained from Cbulk is illustrated in Figures 5. We can find that the increase in aWT or aWH will raise the surfactant efficiency. On the other hand, the surfactant efficiency decreases when aAT or aAH increases. When surfactants are added to the air/water system, they are adsorbed at the interface, hydrophilic groups are immersed in water, and hydrophobic parts are organized into the air. The presence of surfactants at

Figure 6. Influence of each conservative interaction parameter on the logarithm of the CMC by using (a) Cbulk and (b) Ctotal.

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Figure 7. (a) Experimental results. C8S: sodium octylsulfonate; C10S: sodium decylsulfonate; C11S: sodium undecylsulfonate (with the permission from Luigi Paduano); (b) simulation results of relative surface tension versus surfactant bulk concentration.

the air/water interface lowers the surface tension.36 The increase in aWT or aWH will strengthen the surfactant’s tendency to migrate from the bulk to the surface, then the surfactant efficiency is improved. But the increase in aAT or aAH means that the surfactant has to overcome the larger energy barrier to migrate from the bulk to the surface. Figure 5 shows the result that the surfactant efficiency decreases. It is thus concluded that whether the surfactant efficiency increases with the repulsion parameter depends on the phase type involved in the interaction. To be specific, if one increases the interaction between the water phase and part of surfactant, regardless of head or tail, which means increasing the repulsion parameters, the surfactant efficiency will go up, and if one increases the interaction between the air phase and the part of surfactant, the surfactant efficiency will come down. Furthermore, in Figure 5, the surfactant efficiency is more sensitive to aWH and aAT than to aWT and aAH. When water and air molecules are replaced by surfactant molecules at the interface, the surface interaction is divided into two parts: one is the interaction between the hydrophilic group and water, the other is the interaction between the hydrophobic group and air. These two interactions lead to the decrease in the surface tension. Therefore, it is the interaction between the hydrophobic group and air or the hydrophilic group and water in the system that affects the surfactant efficiency the most significantly. The relationship between the logarithm of the CMCs and the interaction parameters obtained from Cbulk and Ctotal is summarized in Figure 6a and b, respectively. In Figure 6b, reasonably sensitive aWT, as shown in Figure 6a, becomes insensitive, and aWH and aAT behave in a manner opposite that expected. When aWH increases, then the hydrophobic nature should increase. This, thus, results in a lower CMC, but the line there goes in the opposite direction. aAT does the same thing. The variation trend of the CMCs in Figure 6b is either inconspicuous, such as the situation corresponding to the variation of aWT and aAH, or opposite the truth, such as the situation corresponding to the variation of aWH and aAT. Once again, this validates the use of Cbulk when measuring CMCs. Figure 6a shows that the interaction parameter that affects the CMC the most significantly is aWT. The value of the CMC is directly correlated to the solubility of the surfactant in water, and the solubility is determined by the interaction between a water molecule and the surfactant molecule, both the head and the tail. Comparing with the headgroup, the tail part has a higher tendency to separate from the water phase and to promote the formation of a micelle. Therefore, CMCs are the most sensitive to the variation of aWT. Consequently, Cbulk has to be employed in a system of the simulations where the surface layer cannot be neglected when

Figure 8. Snapshots of the simulation system (Cbulk ) 0.028) with interaction parameters (aWT ) 67). Head groups are in red; tail groups, in yellow. For clarity, water and air particles are not shown.

investigating properties such as surface tension, CMC, surfactant efficiency, and so on. Simulation of Real Surfactant System. Figure 7a shows the data of the surface tension versus the concentration for real ionic surfactants: sodium octylsulfonate, sodium decylsulfonate, and sodium undecylsulfonate from experimemts.34 To simulate such behaviors on a mesoscale, we have to adjust the DPD parameters. As analyzed above, within all the conservative interaction parameters, aWT affects the CMC of the surfactant the most. Therefore, a series of surfactant models that are based on the same interaction parameters, except aWT, are set up to allow the comparison with real surfactant systems. The relative surface tension versus surfactant bulk concentration for surfactants with different aWT’s is shown in Figure 7b. The CMCs of

DPD Parameters Adjustment three surfactants with an aWT of 51, 60, and 67 are 0.0224, 0.0111, and 0.0096, respectively. Since in the simulation, CMC is in Cbulk (dimensionless) and in the experiments CMC is in mol/L, which are 0.13, 0.04, and 0.017 in Figure 7a, it is hard to make a quantitative comparison between the behaviors of the simulated and the observed, but obtained results show that both the simulated and the observed results for the surfactant efficiency and CMC are very similar. The surfactant structure of sodium alkylsulfonate systems is shown in Figure 1. Therefore, it is safe to draw the conclusion that the adjustment of aWT is efficient in the DPD method to simulate at least ionic surfactants of sodium alkylsulfonate type with different alkyl chain lengths. A snapshot of a surfactant system (Cbulk ) 0.028, aWT ) 67), that corresponds to the sodium undecylsulfonate system is shown in Figure 8. Conclusions The DPD method is employed to simulate low molecular weight surfactant molecule behaves, including surfactant efficiency and CMC in water. It is proved that the bulk concentration (Cbulk) has to be employed to achieve the right trend of the surfactant efficiency and the CMCs. The plot of the relative surface tension versus surfactant total concentration (Ctotal) always yields the wrong trend for the CMC variation. The surfactant efficiency obtained from the relative surface tension versus Ctotal is an order of magnitude lower than that based on Cbulk. The influence of variation of each conservative interaction parameter on surfactant efficiency was disclosed. If one increases the interaction parameter between water and the surfactant (aWH and aWT), regardless of head or tail, the surfactant efficiency will increase. This is because the increase in aWT or aWH will strengthen the surfactant’s tendency to migrate from the bulk to the surface. On the other hand, if one increases the interaction parameter between air and the surfactant (aAH and aAT), the surfactant efficiency will decrease. This can be explained by the elevated energy barrier that the surfactant molecules have to overcome when migrating from the bulk to the surface. Furthermore, the surfactant efficiency is more sensitive to aWH and aAT than to aWT and aAH. At the surface, the interaction is composed of water-head interaction and air-tail interaction. It is these two kinds of interaction that cause the reduction in the surface tension. Therefore, the surfactant efficiency is more sensitive to aWH and aAT. The relationship between the CMCs and conservative interaction parameters is also investigated. It is found that the interaction parameter that affects the CMC the most significantly is aWT because the CMC is closely related to the water solubility of the surfactant molecules, which relies heavily on the repulsion between water and the hydrophobic tail group of the surfactant molecule. On the basis of the relationship between an individual interaction parameter and the surfactant behavior, we adjust aWT

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8859 to simulate real ionic surfactant molecules with different tail lengths. From the results on both the CMC and surfactant efficiency, it is found that the simulation results match experimental observations very closely. The findings in the present research can serve as a basis to investigate mixed-surfactant system behaviors in the near future. Acknowledgment. This research is supported by NSFC 20674090. References and Notes (1) Howes, A. J.; Radke, C. J. Langmuir 2007, 23, 11580. (2) Li, Y.; He, X. J.; Cao, X. L.; Shao, Y. H.; Li, Z. Q.; Dong, F. L. Mol. Simul. 2005, 31, 1027. (3) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294. (4) Hoff, E.; Nystrom, B.; Lindman, B. Langmuir 2001, 17, 28. (5) Sakai, K.; Torigoe, K.; Esumi, K. Langmuir 2001, 17, 4973. (6) Zeng, X. G.; Yang, X. Z. J. Phys. Chem. B 2004, 108, 17384. (7) Fonseca, T. L.; Coutinho, K.; Canuto, S. J. Chem. Phys. 2008, 129, 034502. (8) Yoshii, N.; Okazaki, S. J. Chem. Phys. 2007, 126, 096101. (9) Ryjkina, E.; Kuhn, H.; Rehage, H.; Muller, F.; Peggau, J. Angew. Chem., Int. Ed. 2002, 41, 983. (10) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 3788. (11) Tieleman, D. P.; van der Spoel, D.; Berendsen, H. J. C. J. Phys. Chem. B 2000, 104, 6380. (12) Marrink, S. J.; Tieleman, D. P.; Mark, A. E. J. Phys. Chem. B 2000, 104, 12165. (13) Koelman, J.; Hoogerbrugge, P. J. Europhys. Lett. 1993, 21, 363. (14) Hoogerbrugge, P. J.; Koelman, J. Europhys. Lett. 1992, 19, 155. (15) Groot, R. D. Langmuir 2000, 16, 7493. (16) Rekvig, L.; Kranenburg, M.; Vreede, J.; Hafskjold, B.; Smitt, B. Langmuir 2003, 19, 8195. (17) Groot, R. D.; Madden, T. J. J. Chem. Phys. 1998, 108, 8713. (18) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423. (19) Maiti, A.; McGrother, S. J. Chem. Phys. 2004, 120, 1594. (20) Akkermans, R. L. C. J. Chem. Phys. 2008, 128, 244904. (21) Case, F. H. Predicting Dynamic Mesoscale Structure of Commercially ReleVant Surfactant Solutions; John Wiley & Sons: New York, 2007. (22) Yuan, S. L.; Cai, Z. T.; Xu, G. Y.; Jiang, Y. S. Chem. Phys. Lett. 2002, 365, 347. (23) Abbas, S.; Ahlstrom, P.; Nordholm, S. Langmuir 1998, 14, 396. (24) Li, Z. B.; Lu, B. C. Y. Chem. Eng. Sci. 2001, 56, 6977. (25) Korochkova, E. A.; Boltachev, G. S.; Baidakov, V. G. Russ. J. Phys. Chem. 2006, 80, 445. (26) Espan˜ol, P.; Warren, P. Europhys. Lett. 1995, 30, 191. (27) Irving, J. H.; Kirkwood, J. G. J. Chem. Phys. 1950, 18, 817. (28) Kong, B.; Yang, X. Z. Langmuir 2006, 22, 2065. (29) Goicochea, A. G.; Romero-Bastida, M.; Lopez-Rendon, R. Mol. Phys. 2007, 105, 2375. (30) de Fabritiis, G.; Serrano, M.; Espan˜ol, P.; Coveney, P. V. Physica A 2006, 361, 429. (31) Smit, B. Phys. ReV. A 1988, 37, 3431. (32) Sun, H. Y.; Xu, G. Y.; Li, Y. M.; Chen, Y. J. J. Fluorine Chem. 2006, 127, 187. (33) Tarter, H. V.; Wright, K. A. J. Am. Chem. Soc. 1939, 61, 539. (34) Roscigno, P.; Paduano, L.; D’Errico, G.; Vitagliano, V. Langmuir 2001, 17, 4510. (35) Rosen, M. J. Surfactants and Interfacial Phenomena, 3rd ed.; Wiley: New York, 2004. (36) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997.

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