J. Phys. Chem. B 2006, 110, 21735-21740
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Dissipative Particle Dynamics Simulation of Phase Behavior of Aerosol OT/Water System Chunjie Yang,† Xiao Chen,*,† Huayu Qiu,*,‡ Wenchang Zhuang,† Yongcun Chai,† and Jingcheng Hao† Key Laboratory of Colloid and Interface Chemistry, Shandong UniVersity, Ministry of Education, Jinan, Shandong, 250100, P. R. China, and Key Laboratory of Organosilicon and Material Technology, Hangzhou Teachers’ College, Ministry of Education, Hangzhou, Zhejiang, 310012, P. R. China ReceiVed: April 18, 2006; In Final Form: July 6, 2006
The phase behaviors of the binary mixture of an anionic surfactant aerosol OT (AOT) and water are investigated on a mesoscopic level using dissipative particle dynamics (DPD) computer simulations. With a simple surfactant model, various aggregation structures of AOT in water including the lamellar, viscous isotropic, and reverse hexagonal phases are obtained, which agree well with the experimental phase diagram. Special attention is given on the unusual lamellar regions. Water diffusivity shows much useful information to understand how the phase behaviors varied with concentration and temperature. It is proposed that the anomalous lamellar phenomena at intermediate AOT concentration (about 40%) are due to the formation of a defective structure, pseudoreversed hexagonal phase, which evidently decreases the water diffusivity. After increasing temperature above 328 K, the pseudoreversed hexagonal structure will be partly transformed to a normal lamellar phase structure and the system lamellar ordering is therefore enhanced.
Introduction AOT (bis(2-ethylhexy) sodium sulfosuccinate) is an important double-chain anionic surfactant that has been widely used in both technological applications and fundamental research such as material for the detergent industry and a model to simulate biological membranes.1 Depending on the temperature and concentration, it is capable of building diverse structures in water. As can be seen from the typical phase diagram of an AOT/water system (Figure 1),2-4 with AOT concentration increasing, a broad lamellar phase and a reverse hexagonal phase are formed with a narrow region of viscous isotropic cubic phase at 80% AOT between (all concentrations are in weight percent). The unusual phase behavior that the lamellar mesophase covers a wide concentration and temperature range has caused the properties of this particular phase to be intensely studied for several decades. A variety of experimental techniques such as X-ray diffraction,4 nuclear magnetic resonance,5,6 pulsed field gradient nuclear magnetic resonance,7 Raman spectroscopy,8 infrared spectroscopy,9 rheological, and optical methods10 have been used to investigate the structural and dynamical properties of AOT/water system. Although the obtained results have obviously improved understanding of the lamellar phase of this two-tail surfactant, the detailed ordering information inside this binary system is still ambiguous and the theoretical simulation research is also rarely reported. Recently, with the fast development of computers, such simulation has become a powerful tool for the study of surfactant systems on a molecular level, like molecular dynamics (MD) simulations.11-15 However, building a surfactant mesophase model with classical MD methods at atomic resolution is currently not possible because of the limit * To whom correspondence should be addressed. E-mail: xchen@ sdu.edu.cn (X.C.);
[email protected] (H.Q.). Telephone: +86-53188365420 (X.C.). Fax: +86-531-88564464 (X.C.). † Shandong University. ‡ Hangzhou Teachers’ College.
Figure 1. Phase diagram of aerosol OT/water system (refs 1-3).
of time and length scales at which these complex phase structures can be formed. As an alternative and effective mesoscopic dynamics technique, dissipative particle dynamics (DPD),16,17 introduced by Hoogerbrugge and Koelman in 1992, has been widely used to bridge the gap between the atomic and macroscopic simulation. It allows the simulation of hydrodynamic behavior in much larger systems that contain millions of atoms up to microsecond range.16-21 The parameters used for carrying out DPD simulation can be obtained from the Flory-Huggins type theory.19 Ryjkina et al.20 applied this method to study the phase behavior of a nonionic surfactant, dodecyldimethylamine oxide (DDAO), and got results in very good agreement with experimentally determined DDAO phase diagrams. Groot et al.22 investigated the diblock copolymer microphase separation by employing the DPD method, and their simulations qualitatively agreed with experiments and the existing mean-field theory. By combining DPD with the Monte Carlo method, Kranenburg et al.23 studied the phase behavior and the induced interdigitation of surfactant bilayers. All of these studies show that the DPD method is appropriate to obtain the phase structure information of complex systems on the mesoscale. The aim of present work is to study the phase behavior of an anionic surfactant AOT/water binary system by DPD simulations. Necessary interaction parameters between AOT molecules
10.1021/jp0623692 CCC: $33.50 © 2006 American Chemical Society Published on Web 10/04/2006
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and AOT-H2O molecules are developed using the blending method, which provides a way to predict the thermodynamics of mixtures directly from the chemical structures of the two components and, therefore, require only their molecular structures and a force field as input. Simulation results across the full range of AOT concentrations are presented. Analysis is focused on the anomalous structure found at 40% AOT concentration, which is supported by previous experimental results. Introduction of shear stress into the simulations is found to promote formation of the reverse hexagonal phase at high AOT concentrations, an effect that is also observed experimentally. Simulation Method and Computational Details Theory. In the DPD method, droplets or clusters of fluid molecules are regarded as soft particles (DPD particles or beads).16 Their dynamical evolution is governed by Newton’s laws, as given in eq 1:
∂ri ) Vi , ∂t
mi
∂Vi ) fi ∂t
(1)
where ri, Vi, and fi are the position vector, velocity, and total force, respectively, on the ith particle. All particle masses, mi, are assumed to be equal and set to unity for simplicity. The force between each pair of particles contains three terms: conservative (F Cij ), dissipative (F Dij ), and random (F Rij ) forces. The effective force fi acting on particle i is given by eq 2.
fi )
∑ i*j
F Cij
+
∑ i*j
F Dij
+
∑ i*j
F Rij
(2)
where the sum is over all particles within a distance rc of the ith particle. As this is the only length scale in the system, the cutoff radius is used as a unit of length, rc ) 1, so that all lengths are measured relative to the particle radius. The conservative force F Cij is a repulsive central force with a maximum magnitude aij, as given by following eq 3.
F Cij )
{
aij(1 - rij)rˆij rij < 1 rij g1 0
(3)
where rij is the magnitude of the particle-particle vector b rij, and rˆij is the unit vector joining particles i and j, b rij ) b ri - b rj, rij ) |r bij|, rˆij ) b rij/rij. The other two forces F Dij and F Rij are both responsible for the conservation of total momentum in the system and incorporate the effect of Brownian motion into the larger length scale. The Newton equations for the particles’ position and velocity are solved by a modified version of the velocity Verlet algorithm.19 The interaction parameters in DPD simulations are crucial and produced by considering both the accuracy and the computation time when we adopt the Monte Carlo method to calculate the mixing energy between DPD particles from their pair contact energies. The mixing energy of two particles i and j, E ijmix, can be obtained from eq 4,
E ijmix )
[Zij〈Eij(T)〉 + Zji〈Eji(T)〉 - Zii〈Eii(T)〉 - Zjj〈Ejj(T)〉] 2 (4)
where Zij, Zji, Zii, and Zjj are, respectively, the coordination numbers for each pair of particles, i.e., Zij is the number of particle j capable of surrounding particle i in space. 〈Eij(T)〉, etc. are the mean pair interaction energies. They have been
Figure 2. Schematic representation of the simulation model, which shows the fragmentation of the AOT molecule into three DPD particles. Particles H (red) and T (yellow) are connected together with a harmonic spring. Water is treated as a separate DPD particle W (blue).
obtained from Monte Carlo calculations according to eq 5.24,25
〈Eij(T)〉 )
∫ dEijP(Eij)Eij exp(-Eij/kT) ∫ dEijP(Eij) exp(-Eij/kT)
(5)
where P(Eij) represents the probability distribution of pair interaction energies. All of these calculations are carried out with the potential functions and parameters of the COMPASS force field by using CeriusII software on an SGI workstation. The relationship between Flory-Huggins interaction parameters χij(T) and E ijmix is described as eq 6,
χij(T) ) E ijmix(T)/RT
(6)
The χij(T) is used to determine the repulsion parameters aij (in kT units)19 and is given in eq 7,
aij(T) ) aii + 1.451χij(T)
for F ) 5
(7)
where the aii term is derived from the compressibility of water at room temperature (aii ) 75kBT/F). The parameters derived from Groot and Warren19 are used for the calculations of F Dij and F Rij , which the dissipative parameter is set to a value of 4.5kT. The spring force constant is chosen as 4. The detailed theory information can be found in ref 19. The Interaction Parameters. As for AOT molecular structure, it is difficult to distinguish the hydrophobic tails and hydrophilic parts because of the complex interactions between the -COO- ester groups (referred as the “elbow” regions between the polar head and apolar tails) and water molecules.21 In this study, both -SO3Na and the nearby -COO- ester groups are selected as the hydrophilic ones, and the remaining groups are selected as the hydrophobic tails. Therefore, the AOT molecule is represented by a coarse-grained model of H[T]T, the hydrophilic particle H ((COO)2SO3-Na+) and two hydrophobic particles T (CH2CH(C2H5)C4H9), which are connected together by harmonic springs, as shown in Figure 2. Water molecules are represented by the monomer particle W. In the blend module of CeriusII, one fragment of H, T, and a water molecule are chosen as three units to calculate the Emix and Z, in which several interactions are considered, such as electronic,
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Figure 3. Diffusivity plot of 30% AOT lamellar system as a function of simulation steps at room temperature.
TABLE 1: Interaction Parameters (in DPD units) of the Simulation System aij
H
T
W
H T W
15 77.3 7.9
77.3 15 80.5
7.9 80.5 15
van der Waals interactions, and so on. The calculated interaction parameters between different particles aij are given in Table 1. The dynamics of 40 000 DPD particles, starting from a random distribution, is simulated in a 20 × 20 × 20 cubic box under periodical boundary conditions. The step size for the integration of the Newton equation is ∆t ) 0.05. For each system, 20 000 time steps per simulation are carried out. The temperature is set at room temperature except where otherwise specified. Results and Discussion The diffusivity of a DPD particle is a parameter characterizing the fluid and can be interpreted as the ratio between the time for fluid particles to diffuse a given distance and the time for hydrodynamic interactions to reach steady state on the same distance.19 As an example, one diffusivity plot of the simulation results for 30% AOT system is shown in Figure 3. It can be seen that the diffusivity equilibrium is quickly reached for H and T particles before 10 000 steps, although there is a small drop for the water particle from the midpoint of the simulation to the end (Table S1, Supporting Information), longer time steps bringing little effect on the phase structure. Considering the DPD simulation quality and computation time cost, 20 000 time steps per simulation is sufficient for the phase structure study. The Phase Structures of AOT/Water System at Different Concentrations. Lamellar Phase. The lamellar mesophase of the studied system covers a wide concentration and temperature range. Many researchers have reported unusual experiment results, like the modification of the optical sign of the birefringence in the range between 30 and 40% AOT, the discontinuity of the electrical conductivity, and the anomalies from the X-ray data.4-7 The lamellar mesophase is therefore divided into three different ranges, low-concentration regime (LCR) (16-31%), intermediate-concentration regime (ICR) (32-42%), and highconcentration regime (HCR) (43-79%). Two of them (LCR and HCR) show an ideal swelling behavior and are separated by a nonswelling one (ICR), where more defective structures
are found than in the other two regimes. Figure 4 shows the calculated “ball-and-stick” models (series 1) and isodensity profiles of the water particle (series 2) for lamellar phases of the selected concentrations (30%, 40%, 50%, 60%, and 70% respectively) in thermodynamic equilibrium. To see clearly the arrangements of surfactant particles, water is not shown in series 1. H and T particles are presented in red and yellow, respectively. (The snapshots containing both surfactant and water particles can be referred to in Figure S1, Supporting Information.) The water particle isodensity surfaces are given in series 2, which link points with equivalent concentrations of the selected field. Except for the concentration at 40%, these results are in very good agreement with the experimentally observed phase structures. Comparatively, ideal lamellar structures, i.e., nearly parallel bilayers of AOT alternating with water layers, can be observed. The double layer of the AOT part arranges with hydrophobic groups aggregated inside and the hydrophilic groups oriented toward the water, with the lamellar ordering much improved at higher surfactant concentrations. What is the origin of the cause of the anomalous lamellar regions at about 40% concentration? Diffusivity results here are mainly used to illuminate this peculiar phase behavior. The water particles’ diffusivities in different lamellar systems are shown in Figure 5a. It can be seen that the water diffusivity decreased linearly with AOT concentration except at 40%, where the value is obviously below that from the linear fit relation of other lamellar systems. Also from Figure 4b, it is found that there exist nonideal lamellar structures in the ICR, which on a local scale shows the characters of a reversed hexagonal phase, i.e., rodlike micelles with the hydrophilic heads “H” particles facing toward water. We call it a pseudoreversed hexagonal phase structure, which is consistent with the nature of AOT. It is wellknown that AOT tends to form a reversed hexagonal phase at much lower amphiphile concentration than other surfactants, for example, phospholipids.7 Such a defective structure evidently decreases the water diffusivity in that the water particles meet a large number of walls of different domains. The pseudoreversed hexagonal structures might result in some changes on the mesophase properties, such as reduction of liquid crystalline long-range order. Moreover, the water diffusivities in three lamellar phases at different temperatures are shown in Figure 5b (1 DPD unit is equivalent to room temperature, 298 K). They all increase with temperature, and the plots can be divided into two sections at about 328 K (1.1 DPD units). Below 328 K, water diffusivity of 40% system is the lowest. Fluctuations are exhibited at room temperature for both 30% and 50% systems, but not for the 40% system. This indicates that the lamellar structures in LCR and HCR are flexible and sensitive to temperature in this range, while the pseudoreversed hexagonal structure in ICR is comparatively stable with temperature change. However, when the temperature is higher than 328 K, water diffusivities for all the three systems are almost linearly increased and the value of the 40% system has exceeded that of the 50% system in this temperature range. It indicates that there is normal lamellar structure formation (Figure S2, Supporting Information), but it also can be seen that the water diffusivity in the 40% system remains much closer to the 50% value than the 30% value, indicating a strong departure from the linear behavior observed at other concentrations, which show that water diffusivity still remains anomalously low in the high temperature range. Thus, the pseudoreversed hexagonal structure is dominant over all of the temperature range, which will be partly transformed to the
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Figure 4. Representation of AOT/water lamellar phases with “ball-and-stick” models (series 1, water particles are not shown for clear, H and T particles are presented in red and yellow, respectively) and water particles’ isodensity surfaces (series 2, in blue) at selected concentrations: (a1, a2) 30%, (b1, b2) 40%, (c1, c2) 50%, (d1, d2) 60%, and (e1, e2) 70%.
Figure 5. Water diffusivity in AOT/water lamellar phase as a function of AOT concentration (a) and temperature (b). (c) Measured small-angle X-ray scattering spectra at room temperature for three AOT concentrations: 30%, 40%, and 50% (reprinted from ref 27).
Figure 6. Calculated ball-stick model of viscous isotropic cubic phase (a) and isodensity surfaces of water particles (b and c). H, T, and W particles are presented in red, yellow, and blue, respectively.
normal lamellar phase with enhanced lamellar ordering at higher temperature.26 Our DPD simulation results therefore intuitively reproduce the anomalous peculiarity of the ICR lamellar phase of the AOT/ water system mentioned in previous studies.4-7 We have previously conducted small-angle X-ray scattering (SAXS) experiments (shown in Figure 5c),27 which give results in general agreement with the simulation results presented here. For 30% and 50% AOT concentrations, two scattering peaks can be distinguished easily and become sharper with increasing surfactant concentration, indicating a normal lamellar phase and enhanced structural ordering. The pseudoreversed hexagonal structure at 40% AOT concentration, however, only results in a very weak first peak in SAXS curve.
Isotropic Cubic Phase. By increasing the concentration of AOT further to 80%, a viscous isotropic cubic phase is built, which covers a very narrow range between the lamellar and reversed hexagonal phase. Such a situation in fact combines together the structural elements of two neighboring phases. The ball-and-stick model and isodensity surface of water particles of this phase are shown in Figure 6. Both the lamellar and reversed hexagonal phase character can be observed. ReVersed Hexagonal Phase. Another important phase of the AOT/water binary system is the reversed hexagonal phase, where highly ordered, rodlike reverse micelles are in hexagonally packed arrays. In the enlargement of a single rod, the micelle core composed of hydrophilic heads and hydrophobic tails are extended outside. The corresponding ball-and-stick
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Figure 7. Representation of the reversed hexagonal phase (a), water particles distribution (b), isodensity surface of AOT head particles (c), and the sheared reversed hexagonal phase, isodensity surfaces of AOT head particles (d), and water particles (e). H, T, and W particles are presented in red, yellow, and blue, respectively.
model is shown in Figure 7a. The water particles are specially set off for better observation (Figure 7b). Figure 7c indicates the isodensity surface of AOT head particles. Although there are some cross-linked defects, the reversed hexagonal phase structure is well present. Meanwhile, a shear effect study is also carried out. When a shear is imposed to the simulation box, the formation of reversed hexagonal phase proceeds rather quickly. This is in accord with the widespread experience when processing a high concentration phase formation of colloid and polymers.28-30 In our DPD simulations, the way to model the shear is by applying the Lees-Edwards sliding-brick boundary conditions.31 Under these conditions, there is a shear in the direction of the x-axis. As a molecule passes through the y ) 0 plane of the bounding box, it reappears on the other side, shifted by a fixed amount and with a given streaming velocity in the x direction. The value for the shear rate is set to 0.2 DPD reduced units, corresponding to quite large values of shear. The lower values, however, tend to result in slow phase evolution. Figure 7d,e show the results of the simulation box sheared for 5000 DPD time steps, as onefourth of the time of runs without shear. It takes relatively little time for the system developing into an almost perfect array of reversed hexagons in the direction of shear. Conclusions With a simple mesoscopic model, the different phase structures of an AOT/water system are reproduced by DPD simulations. The calculation results are in very good agreement with the experimental phase diagram. Water diffusivity results are used to illuminate the anomalous phase behavior in the lamellar phase. It is proposed that in the intermediate-concentration regime at about 40% concentration, a defective structure, pseudoreversed hexagonal phase, is formed to evidently decrease the water diffusivity, which might produce some mesophase property changes such as reduction of the liquid crystalline longrange order. Water diffusivity curves of three lamellar systems
as a function of temperature indicate that the pseudoreversed hexagonal structure in ICR will be partly transformed to a normal lamellar phase structure and enhanced system lamellar ordering after increasing temperature. Therefore, the DPD simulation results could provide us a new insight for better understanding of AOT/water phase behaviors. Acknowledgment. We thank the National Natural Science Foundation of China (20373035, 20573066, 20428101, 20533050), the Shandong Provincial Science Fund (Y2005B18), and the Distinguished Professor Fund of Zhejiang Province (200508) for financial support. Supporting Information Available: Snapshots of AOT/ water lamellar phases with “ball-and-stick” models containing both surfactant and water particles, 40% AOT phase structures at high temperature, and a table of water diffusivity for the 30% AOT system at different simulation time steps. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Porter, M. R. Handbook of Surfactants, 2nd ed.; Blackie: London, 1994. (2) Rogers, J.; Winsor, P. A. Nature 1967, 216, 477. (3) Winsor, P. A. Chem. ReV. 1968, 68, 1. (4) Fontell, K. J. Colloid Interface Sci. 1973, 44, 318. (5) Chidichimo, G.; Lamesa, C.; Ranieri, G. A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1987, 150, 221. (6) Coppola, L.; Muzzalupo, R.; Ranieri, G. A.; Terenzi, M. Langmuir 1995, 11, 1116. (7) Callaghan, P. T.; Soderman, O. J. Phys. Chem. 1983, 87, 1737. (8) Faiman, R.; Lundstrom. I.; Fontell, K. Chem. Phys. Lipids 1977, 18, 73. (9) Boissiere, C.; Brubach, J. B.; Mermet, A.; de Marzi, G.; Bourgaux, C.; Prouzet, E.; Roy, P. J. Phys. Chem. B 2002, 106, 1032. (10) Petrov, P. G.; Ahir, S. V.; Terentjev, E. M. Langmuir 2002, 18, 9133. (11) Alaimo, M. H.; Kumosinski, T. F. Langmuir 1997, 13, 2007. (12) Allen, R.; Bandyopadhyay, S.; Klein, M. L. Langmuir 2000, 16, 10547.
21740 J. Phys. Chem. B, Vol. 110, No. 43, 2006 (13) Bandyopadhyay, S.; Tarek, M.; Lynch, M. L.; Klein, M. L. Langmuir 2000, 16, 942. (14) Salaniwal, S.; Cui, S. T.; Cochran, H. D.; Cummings, P. T. Langmuir 2001, 17, 1784. (15) Abel, S.; Sterpone, F.; Bandyopadhyay, S.; Marchi, M. J. Phys. Chem. B 2004, 108, 19458. (16) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhys. Lett. 1992, 19, 155. (17) Koelman, J. M. V. A.; Hoogerbrugge, P. J. Europhys. Lett. 1993, 21, 363. (18) Espanol, E.; Warren, P. B. Europhys. Lett. 1995, 30, 191. (19) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423. (20) Ryjkina, E.; Kuhn, H.; Rehage, H.; Muller, F.; Peggau, J. Angew. Chem., Int. Ed. 2002, 41, 983. (21) Yuan, S. L.; Cai, Z. T.; Xu, G. Y.; Jiang, Y. S. Chem. Phys. Lett. 2002, 365, 347. (22) Groot, R. D.; Madden, T. J. J. Chem. Phys. 1998, 108, 8713.
Yang et al. (23) Kranenburg, M.; Venturoli M.; Smit, B. J. Phys. Chem. B 2003, 107, 11491. (24) Blanco, M. J. Comput. Chem. 1991, 12, 237. (25) Fan, C.; Olafson, B.; Blanco, M.; Hau, S. Macromolecules 1992, 25, 3667. (26) Simmons, B.; Irvin, G.; Agarwal, V.; Bose, A.; John, V. T.; McPherson, G. L.; Balsara, N. P. Langmuir 2002, 18, 624. (27) Zhuang, W. C.; Chen, X.; Yang, C. J.; Wang, L. Y.; Chai, Y. C. Acta Phys. Chim. Sin. 2005, 21, 1055. (28) Fredrickson, G. H.; Bates, F. S. Annu. ReV. Mater. Sci. 1996, 26, 501. (29) Jury, S.; Bladon, P.; Cates, M.; Krishna, S.; Hagen, M.; Ruddock, N.; Warren, P. Phys. Chem. Chem. Phys. 1999, 1, 2051. (30) Fraaije, J. G. E. M.; Zvelindovsky, A. V.; Sevink, G. J. A. Mol. Simul. 2004, 30, 225. (31) Wijmans, C. M.; Smit, B. Macromolecules 2002, 35, 7138.
