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Temperature-Dependent Phase Transition and Desorption Free Energy of Sodium Dodecyl Sulfate at the Water/Vapor Interface: Approaches from Molecular Dynamics Simulations Meng Chen,† Xiancai Lu,*,† Xiandong Liu,† Qingfeng Hou,‡ Youyi Zhu,‡ and Huiqun Zhou† †

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

ABSTRACT: Adsorption of surfactants at the water/vapor interface depends upon their chemical potential at the interface, which is generally temperature-dependent. Molecular dynamics simulations have been performed to reveal temperature influences on the microstructure of sodium dodecyl sulfate (SDS) molecule adsorption layer. At room temperature, SDS molecules aggregate at the interface, being in a liquidexpanded phase, whereas they tend to spread out and probably transit to a gaseous phase as the temperature increases to above 318 K. This phase transition has been confirmed by the temperature-dependent changes in two-dimensional array, tilt angles, and immersion depths to the aqueous phase of SDS molecules. The aggregation of SDS molecules accompanies with larger immersion depths, more coordination of Na+ ions, and less coordination of water. Desorption free energy profiles show that higher desorption free energy appears for SDS molecules at the aggregate state at low temperatures, but no energy barrier is observed. The shapes of desorption free energy profiles depend upon the distribution of SDS at the interface, which, in turn, is related to the phase state of SDS. Our study sheds light on the development of adsorption thermodynamics and kinetics theories.

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INTRODUCTION The adsorption ability of surfactants at the water/vapor interface is crucial for foam production, which is valuable in a lot of fields, including producing pharmaceutical and personal care products, mineral separation processes, and petroleum recovery.1 The relation between adsorption of surfactant (Γ) at the water/vapor interface and concentration in solution (c) can be described by the equation μ − μ0(s) Γ = δ exp 0 c RT

Because sodium dodecyl sulfate (SDS) is one of the most commonly used surfactants, the structure of the water/vapor interface with a SDS adsorption monolayer have been wellinvestigated by multiple techniques, including neutron reflection technique,8,9 infrared external reflection spectroscopy (IERS), 10−12 vibrational sum frequency spectroscopy (VSFS),13−16 and Brewster angle microscopy (BAM).17−19 However, there are still contradictions in experimental results. IERS studies show that the conformational order of the hydrocarbon chains of the adsorbed SDS monolayer is higher than those of monomers and micelles at room temperature, and the monolayer is maintained in liquid crystal state even below the Krafft temperature.10,12 However, an infrared reflection absorption spectroscopy study indicates that the hydrocarbon chains of the SDS monolayer are disordered with a large number of gauche conformers,11 which is also supported by a VSFS study.14 BAM studies have shown that condensed phase domains cannot be formed for highly purified SDS even above the critical micelle concentration (cmc) and at low temperature, but the dodecanol/SDS mixture can form a condensed phase with the lattice structure.18,19

(1)

μ(s) 0

where δ is the interface thickness and and μ0 are the standard parts of chemical potentials of surfactants at the interface and in solution, respectively.2 This equation is based on dilute adsorption layer and ideal solution approximations. As interactions between surfactants are taken into account, μ(s) 0 depends upon Γ, and therefore, no linear relationship between Γ and c can be found, which is confirmed by experimental observations.3−6 On the basis of different hypotheses on surfactant adsorption states, many adsorption models, including well-known Langmuir isotherm, van der Waals isotherm, etc., have been built in the past 100 years. Comparisons between them can be found in refs 4 and 7. Details about the atomistic structure of the surfactant-covered interface are needed to verify those adsorption models. © 2014 American Chemical Society

Received: May 1, 2014 Revised: August 11, 2014 Published: August 15, 2014 10600

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The water phase is a slab with a thickness of 6 nm parallel to the x−y plane, comprising 22 521 water molecules. It was positioned in the middle of the box, sandwiched by two vapor phases, which were initially set to vacuum for simplicity (Figure 1). Two SDS monolayers

Molecular dynamics (MD) simulations have also been employed to study the structure of SDS adsorbed at the water/vapor interface.20−24 It is found that the tails of SDS molecules prefer to bend at the water/vapor interface and are less ordered than those at the water/CCl4 interface.20,21 However, the size of the model they built (Lx = Ly = 4.0249 nm; 36 SDS molecules at the interface)21 was too small to consider SDS two-dimensional distributions and interface roughness. Using a capillary-wave-based algorithm for characterization of surface roughness,25 Martinez et al. depicted the solvation structure of water around SDS in detail and obtained the bending modulus of the monolayer.22 A comparison study reveals that SDS molecule aggregates at the water/vapor interface show more compact structures compared to non-ionic hexaethylene glycol monododecyl ether (C12E6) and discloses a transition of C12E6 from gaslike to liquidlike phases as the C12E6 surface density increases. However, the collected data are insufficient for approaching the entire phase diagram for SDS in that study.23 Phase transitions in Langmuir monolayers, characterized by the tilt order of amphiphilic molecules at the interface, have long been reported via experiments and molecular simulations.26 The monolayer can form liquidcondensed, liquid-expanded, and gaseous phases. The liquidcondensed phase characterizes the monolayer with well-aligned amphiphilic molecules, which are parallel to each other. Those molecules in the liquid-condensed phase can be tilted to the interface or perpendicular to it, whereas in liquid-expanded and gaseous phases, the chains of amphiphilic molecules are disordered.26 Recently, a number of atomic and coarse-grained MD simulations have been performed to study phase structures of lipid and surfactant monolayers, revealing the dependence of the tilt order of amphiphilic molecules on surface density, temperature, and molecular structure.27−32 According to those studies, increasing surface density or decreasing temperature generally leads to a more ordered phase structure. For a Gibbs monolayer (adsorption monolayer), liquid−gas phase transitions characterized by the clear configuration change of the adsorbed amphiphilic molecules from compact aggregation to much loose state have also been observed in experiments33 and MD simulations.34 According to eq 1, adsorption of surfactants depends upon the temperature T, chemical potential difference μ0 − μ(s) 0 , and adsorption layer thickness δ. μ(s) 0 is sensitive to the structure of the adsorption layer, especially the phase structure of the monolayer.19 Therefore, MD simulations have been employed to investigate the changes in the phase structure of adsorbed SDS molecules at the water/vapor interface as the temperature increases from 298 to 348 K in this study. Alkyl chain structure, relation between sulfate groups and aqueous species, and their variation with the temperature have been revealed. It is disclosed that SDS molecules are in the liquid-expanded phase and aggregate locally at low temperatures, and they transit to the gaseous phase at high temperatures. From integration of the calculation of desorption free energy of SDS from the interface to the inner aqueous phase, the influences of adsorption states on thermodynamics and kinetics of surfactant adsorption are further discussed.

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Figure 1. Initial configuration of simulated models. The cyan bonds stand for alkyl chains; yellow balls stand for sulfur atoms; red balls stand for oxygen atoms; blue balls stand for Na+ ions; and red points stand for water molecules.

with 256 molecules each were placed at the water/vapor interfaces. The distance between two monolayers (about 6 nm in this study) is large enough to ignore their interaction. Counterions of SDS (Na+) were inserted into the water phase randomly. The area per SDS molecule is approximately 0.44 nm2, corresponding to a neutron reflection-based measurement of SDS solution with cmc at 298 K.8 Because the temperature dependence of the area per molecule is not apparent,8 we employed the same MD box at different temperatures to investigate the temperature dependence of the SDS adsorption structure. We also simulate systems with approximately 0.35 nm2 per SDS molecule for comparison (the system size is the same), to test the sensitivity of SDS adsorption to the temperature-dependent phase structure. The initial configuration was constructed using Packmol.35 Periodic boundary conditions were applied for all three directions. GROMACS 4.0 package36−39 was used to perform MD simulations. Force fields are the same as those in our previous study.40 The SPC/E model41 and the force field by Berkowitz et al.20,21 were used to describe water molecules and sulfate groups separately. On the basis of the comparison to the L-OPLS-AA force field42 (see the Supporting Information), the optimized potential for liquid simulations with all atoms (OPLS-AA) force field43 was selected to describe alkyl chains because of its good performance for monolayers. The cutoff distance for Lennard−Jones potential was as long as 1.6 nm. The particle-mesh Ewald (PME) method44,45 was used to describe long-range electrostatic interactions. In each MD simulation, an energy minimization was carried out to relax the system at first. Then, the LINCS algorithm46 was applied to constrain bonds with H atoms. We performed simulations in NVT canonical ensemble for six systems, with adoption of the velocityrescaling thermostat47 to control the temperature. The equations of motion are integrated with a time step of 1.0 fs. Systems were set to 348 K at first and then annealed to target temperatures in 0.5 ns, to

SIMULATION DETAILS

Six simulations of the water/vapor interface with SDS as surfactants at different temperatures (298, 308, 318, 328, 338, and 348 K) were performed from the same initial configuration. The simulation model is an orthogonal box with Lx = Ly = 10.613 nm and Lz = 16.000 nm. 10601

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Figure 2. Tilt azimuth of each SDS molecule on the x−y plane in the final snapshot. The tilt azimuth is defined as the projection of the vector from the nearest carbon atom to the sulfate group to the furthest carbon atom on the x−y plane. overcome possible local energy minima.48 We carried out 12 ns simulation for each, in which the last 5 ns was for property evaluation.

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they might be in the gaseous phase. The transition of SDS molecules from the aggregate state to scattered distribution with the temperature increasing seems to be a liquid−gas phase transition. In density maps of sulfur atoms on the x−y plane (see Figure S4 of the Supporting Information), remarkable heterogeneity in density can be identified at a low temperature. However, the densities become relatively uniform as the temperature increases to higher than 318 K. The probability distribution of two-dimensional density was calculated and shown in Figure 3. It is clear that, as the temperature increases, the distribution

RESULTS AND DISCUSSION

SDS Distribution at the Water/Vapor Interface. According to the simulation snapshots, at low temperatures (e.g., 298 and 308 K), SDS molecules tend to aggregate together at the interface (see panels a and b of Figure S3 in the Supporting Information), which is consistent with previous studies.23,49 However, at relatively higher temperatures (e.g., 338 and 348 K), SDS molecules almost randomly distribute all over the interface (see panels e and f of Figure S3 in the Supporting Information). Local ordered structure can be noticed in the snapshots at a low temperature; therefore, we analyzed the tilt azimuth of SDS molecules. The tilt azimuth is defined as the projection of the vector from the nearest C atom to the sulfate group to the furthest C atom on the x−y plane. Results show that local organization of tilt azimuths is obvious at low temperatures (e.g., 298 and 308 K) but hardly found at high temperatures (e.g., 338 and 348 K) (Figure 2). However, this organization of tilt azimuths is distinct from that found in the liquid-condensed phase of the Langmuir monolayer, in which rod-like amphiphilic molecules are well-aligned and parallel with each other in a long range.26 Previous simulation studies on ca. 100 amphiphilic molecules at ca. 0.2 nm2/ molecule at the interface have a well-reproduced ordered liquidcondensed phase structure.26 The local order in the SDS monolayer cannot develop into long-range order, and the monolayer should be in the liquid-expanded phase. Coarsegrained MD simulations of a dipalmitoylphosphatidylcholine monolayer showed that, while the area per molecule is low, the monolayer in the liquid-expanded phase coexists with pores (parts of the water/vapor interface uncovered by amphiphilic molecules).27 This is similar to the situation at low temperatures in our study that aggregate SDS molecules in the liquidexpanded phase coexist with the “naked” water surface (panels a−c of Figure 2). The scattered distribution of SDS molecules at high temperatures (panels e and f of Figure 2) implies that

Figure 3. Probability distribution of two-dimensional density of sulfur atoms in the x−y plane. Two-dimensional densities were calculated by dividing the x−y plane into grids with area of 0.965 × 0.965 nm2. The lines show the fitted Gaussian distributions. The inset shows the relationship between the temperature and height of the Gaussion distribution of the fitting.

becomes sharp and the probability of the average density (2.27 nm−2) increases (Figure 3), which reveals that the surfactants tend to spread out at the interface as the temperature increases. When the distribution is fit with a Gaussian function, the relationship between the height of the Gaussian distribution and the temperature is derived (inset in Figure 3). It is clear 10602

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Experiments8 and MD simulations24 have shown that alkyl chains of SDS partly immerse into the aqueous phase. By comparing density profiles of sulfur atoms and carbon atoms at different temperatures (298 and 348 K; Figure 6), we find that

that a sudden large increment of the height appears between 318 and 328 K. Such a transition can also be found in the radial distribution function (RDF) between sulfur atoms (Figure 4).

Figure 4. RDFs between sulfur atoms at different temperatures. Figure 6. Number density profiles of oxygen atoms of water (marked as Ow), sulfur and carbon atoms of SDS, and Na+ ions perpendicular to the water/vapor interface. The middle of the water slab is set as the 0 point.

The peak at about 0.5 nm is weakened as the temperature increases, particularly from 318 to 328 K, which implies a structure transition. While the temperature increases, thermal expansion appears for SDS aggregations; as the temperature increases from 318 to 328 K, a large expansion appears probably because of the liquid−gas phase transition. Meanwhile, the mean tilt angle of SDS molecules, the angle between the vector of the alkyl chain and the interface normal vector,48 increases with the temperature (Figure 5). Such an

surfactant molecules are immersed deeper into the aqueous phase at 298 K than at 348 K. The density profile of oxygen atoms of water (Ow) can be fitted with a hyperbolic tangent function, ρ(z) = 0.5ρ0 − 0.5ρ0 tanh(2(z − z0)/d),50 where ρ0 refers to the bulk phase density, z0 is the position of the Gibbs dividing surface, and d is a parameter related to the interfacial thickness. The density profile of sulfur atoms was fitted using a Gaussion with z1 as the average position.51 The distance difference between z0 and z1, Δ, (i.e., Δ = z0 − z1), is used to characterize the immersion depth of the SDS molecule. Figure 5 shows that Δ decreases with increasing the temperature, and a sudden drop occurs between 318 and 328 K. This phenomenon recalls the finding by Striolo et al. that, as C12E6 molecules transit from a liquidlike phase to a gaslike phase, their immersion depths into the aqueous phase suddenly become shallower.23 Now, we find that the aggregation and immersion of SDS are well-coupled, as shown by the antidependence of the immersion depth and mean tilt angle in Figure 5. An aggregation state is accompanied by a large immersion depth of SDS. As the liquid−gas transition occurs, segregation of SDS molecules leads to the fact that they immerse shallower to the aqueous phase. Interactions between SDS and Other Species. The aggregation of SDS molecules is inherently controlled by hydrogen bridges52 and salt (Na+) bridges53 between hydrophilic ionic groups at the interface. At the interfaces, because of hydrogen bonds between hydrophilic groups and water,53−55 hydration shells are formed around hydrophilic groups, as shown by RDFs between oxygen atoms of the sulfate groups (Os) and oxygen atoms of water (Ow) (see Figure S7 of the Supporting Information). The peaks in RDFs increase as the temperature increases, and an obvious increment is seen between 318 and 328 K. The coordination number of hydrogen atoms of water also slightly increases (Figure 7). The increment between 318 and 328 K is the largest (inset in Figure 7), probably corresponding to the phase transition of surfactant monolayers. However, the RDFs and the coordination number of Na+ ions show an opposite trend, i.e., the coordination number decreases as the temperature increases, with the largest

Figure 5. SDS immersion depth Δ and mean tilt angle of SDS molecules as a function of the temperature T.

increase reflects that SDS molecules become less compact as the temperature increases, which is consistent with the increase in gauche probability of alkyl chains (see the Supporting Information). The tilt angle is also a measure characterizing the aggregation level of surfactants. A steep increment also occurs between 318 and 328 K, probably corresponding to the phase transition. The liquid−gas phase transition induced by increasing the temperature appears for SDS molecules partially covering the interface. Because of the imperfection of force fields, the force field produced area per molecule is not necessarily the experimental area per molecule at cmc. If more SDS molecules are adsorbed to the interface, the situation may be different. Therefore, we simulate SDS monolayers of ca. 0.35 nm2/ molecule. Although the adsorption is largely improved, the liquid−gas phase transition for SDS molecules still occurs between 318 and 328 K (see the Supporting Information). Therefore, we deduce that the temperature-dependent liquid− gas phase transition is not sensitive to the adsorption of SDS. 10603

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SDS molecules, and aggregate structure on the x−y plane all reflect the liquid−gas phase transition. Desorption Free Energy of SDS. Because the partition of SDS between bulk aqueous and adsorbed phases is determined by μ0 − μ(s) 0 in eq 1, the desorption free energy profile of a SDS molecule from the adsorbed monolayer to the aqueous phase was calculated. Both monolayers in liquid-expanded and gaseous phases are considered. The desorption free energy of SDS molecules from the interface may vary with the instantaneous local density at the interface. The average distance between every surfactant and its six nearest neighbors, represented by distances between sulfur atoms, was calculated first. Then, the atoms with the shortest and longest average distances were selected for exactly representing surfactants in the highest and lowest surface density zones (panels a and b of Figure 9). The selected

Figure 7. Coordination numbers of hydrogen atoms from water around charged oxygen atoms from sulfate groups. The inset shows the relationship between coordination numbers with the distance of 0.25 nm and the temperature.

decrement between 318 and 328 K (Figure 8 and see Figure S9 of the Supporting Information).

Figure 8. Coorination numbers of Na+ around charged oxygen atoms from sulfate groups. The inset shows the relationship between coordination numbers with the distance of 0.32 nm and the temperature.

As the temperature increases, the stability of hydrogen bonds decreases (see the Supporting Information) and the mobility of Na+ increases (see Figure S10 of the Supporing Information), both of which are in favor of the dissociation of SDS aggregations. Because of the space limitation, aggregate SDS molecules are less coordinated by water than the dissociated molecules. The bridges of less hydrated Na+ ions in the deep zones of the monolayer56 between nearby SDS molecules are coupled to the aggregation of SDS molecules. As the temperature increases, the decrement in the coordination number of Na+ ions accompanies the segregation of SDS molecules. According to the above analyses, the interaction between SDS and aqueous species, the aggregation, and the SDS immersion into the aqueous phase are interdependent. At low temperatures, hydrogen bridges and Na+ bridges accompany a compact structure of SDS molecules, so that alkyl tails are more surrounded by hydrophobic alkyl tail neighbors and less by water molecules, leading to deep immersion into the aqueous phase. As the temperature increases, breakdown of bridges accompanies segregation of SDS molecules; as a result, the high energy between alkyl tails and surrounding water leads to the shallower immersion of SDS. The sudden large changes in coordination numbers of aqueous species, immersion depth of

Figure 9. (a) Final snapshots (down view) of monolayers at 298 K. The representations of colors are the same as in Figure 1. Molecules are shown in lines in this case. (A) Picked surfactant in the highest surface density zone. (B) Picked surfactant in the lowest surface density zone. (b) Same as in panel a, except that the temperature is 348 K. (c) Potential of mean force along the z axis. The coordination of the end of the pulled trajectory, which is in the aqueous phase, is set as 0. The PMF at position z = 0 is set as 0. The broken line shows the 0 value of PMF, to reflect the existence of energy barriers.

surfactants were pulled from the surface monolayer into the aqueous phase along the z axis using the umbrella pulling method with a spring constant of 1000 kJ/mol and a pull rate of 0.001 nm/ps, which is similar to the study by Lemkul et al.57 Frames of the pulling trajectory were extracted every 0.2 ns, forming 26 starting configurations for the umbrella sampling windows.58 MD (1 ns) was performed for each umbrella sampling window. The weighted histogram analysis method (WHAM)59 was used to analyze the data and derive the potential of mean force (PMF) along the reaction coordinate (Figure 9c). The PMF curves of surfactants show that an isolated SDS molecule should overcome a free energy barrier as it desorbs from the interface into the aqueous phase, which is 10604

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energy barrier or lower energy well corresponds to a lower desorption rate constant. At low temperatures, the PMF curve shapes for SDS molecules in different zones are different; therefore, the adsorption rates of SDS molecules at the subsurface layer must be position-dependent. However, as the temperature increases, the adsorption rates tend to be positionindependent. Understanding the relationship between the spatial distribution and adsorption rates of surfactants calls for future development of adsorption kinetics theories.

similar to the study on a decanol molecule at the water/vapor interface.60 At 348 K, the PMF of surfactants in different zones is almost the same because SDS molecules are in the gaseous phase and each SDS molecule is almost isolated from each other. However, at 298 K, the PMF of the surfactant is clearly dependent upon the position where it is adsorbed. At 298 K, the PMF curve of the isolated SDS molecule is very similar to that at 348 K, showing that the desorption free energy profile of an isolated SDS molecule is almost independent of the temperature. However, the PMF curve of the SDS molecule in the zone with a high density at 298 K is obviously different from that of isolated SDS molecules, and the desorption free energy is about 20 kJ/mol higher. In the high surface density zone, where surfactants aggregate, hydrophobic attraction from nearby alkyl chains, hydrogen bridges, and Na+ bridges are all unfavorable for the desorption, thus leading to higher desorption free energy. There are plateaus observed in the PMF curve, showing a relaxation response of the system, while the SDS molecule is pulled into the aqueous phase. No energy barrier is observed in that curve for aggregate SDS molecules, while there are energy barriers for those isolated SDS molecules. This energy barrier may be caused by reorganization of water around the hydrophobic part of the surfactant molecule as it enters the aqueous phase.60 Because aggregate SDS molecules are immersed deeper into the aqueous phase and are well-hydrated, the reorganization of water during the SDS desorption process is not so significant and no energy barrier occurs. Because higher desorption free energy appears for surfactants in the aggregate state, the exponential term (μ0 − μ(s) 0 )/RT in eq 1 should decrease as SDS molecules transit from the liquidexpanded phase to the gaseous phase. However, the surface roughness should increase as the temperature increases,61 implying an enlarged vertical room of surfactant; i.e., the interface thickness δ increases. Therefore, according to eq 1, the adsorption of SDS (Γ) should vary under the counter influences of decreased (μ0 − μ(s) 0 )/RT and increased δ as the temperature increases. Thermodynamics theories have been proposed to study the adsorption of surfactant molecules, but many of them are based on the hypothesis that each surfactant molecule at the interface is equal.4 This hypothesis corresponds exactly to the case at high temperatures in our study but fails at low temperatures because surfactant molecules aggregate in the liquid-expanded phase. Fainerman and Miller proposed an adsorption isotherm considering the capability of surfactant molecules forming twodimensional aggregates at the interface,62 but their suggestion of a dimer formation in adsorption layer is certainly not the case found in our study. At low temperatures, the SDS molecules mostly isolated from others show obviously different desorption free energy compared to those in aggregation. It is necessary to reconsider the adsorption thermodynamics theories, in which surfactant distribution, temperature influences, and adsorption layer thickness should be taken into account. Combining detailed molecular simulations in verifying and/or developing thermodynamics theories by fitting experimental data are topics for further studies. The desorption free energy profile not only contains information about adsorption thermodynamics but also adsorption kinetics.60,63 According to the transition-state theory,64 the desorption rate constant is closely related to the free energy barrier and well in the PMF curve; i.e., a higher

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CONCLUSION MD simulations have been performed to study the microscopic structures of SDS adsorption monolayer and SDS desorption free energy at different temperatures. The results show that SDS molecules aggregate as the liquid-expanded state at low temperatures and tend to spread out with increasing the temperature. A probable liquid−gas phase transition occurs at the temperature range from 318 to 328 K, which is confirmed by the changes in two-dimensional structures, tilt angles, and immersion depths of SDS molecules. At higher temperatures, because SDS molecules are in the gaseous phase, the desorption free energy is independent of the adsorbed position of certain SDS molecules. At low temperatures, because SDS molecules are in the liquid-expanded phase, certain SDS molecules might be in aggregate or isolated states at specific times. The sulfate groups of SDS molecules are more bridged by Na+ ions and less coordinated by water while they are aggregated. The desorption free energy varies with the local density of SDS molecules. The finding of the phase transition of surfactants at the interface and the position-dependent adsorption behavior shed light on improving traditional adsorption thermodynamics4,7 and kinetics theories.63

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ASSOCIATED CONTENT

S Supporting Information *

Force field comparison, additional data about the twodimensional structure of surfactants, the relationship between sulfate groups and aqueous species, and the diffusion of Na+ ions. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +86-25-83686016. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the China National Science and Technology Major Project 2011ZX05010-005 and the National Basic Research Program (973) of China (2012CB214803). The authors are grateful to the High Performance Computing Center of Nanjing University for using the IBM Blade cluster system.

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