hexane interface by molecular dynamics simulation

Chemical Engineering Science 134 (2015) 813–822

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Effect of surfactant SDS on DMSO transport across water/hexane interface by molecular dynamics simulation Yao-Feng Hu a, Wen-Jie Lv b, Shuangliang Zhao a,n, Ya-Zhuo Shang c, Hua-Lin Wang b,n, Hong-Lai Liu a,c,nn a

State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China State Environmental Protection Key Laboratory of Environmental Risk Assessment and Control on Chemical Process, East China University of Science and Technology, Shanghai 200237, China c Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China b

H I G H L I G H T S








Both DMSO and SDS molecules compete to occupy the water/hexane interfacial region. The interfacial tension decreases linearly with the increase of SDS concentration. Higher SDS concentration results in a lower self-diffusion coefficient for DMSO. The addition of SDS facilitates DMSO moving out of the interfacial region. The orientation of DMSO molecule gradually changes in passing the interface.

art ic l e i nf o

a b s t r a c t

Article history: Received 3 January 2015 Received in revised form 27 May 2015 Accepted 30 May 2015 Available online 12 June 2015

Solute transport behavior across liquid–liquid interfaces plays important roles in many chemical engineering processes and usually occurs in the presence of surfactants. In this work, we report a full all-atom molecular dynamics simulation study of dimethyl sulfoxide (DMSO) crossing a water/hexane interface in different concentrations of sodium dodecylsulfate (SDS). By analyzing various properties, ranging from the configuration and energetic behaviors to the dynamic characteristics, we conclude that the presence of SDS has multiple non-trivial effects: (1) the association of SDS at the interface drives the interfacial region wider and decreases the interfacial tension with an almost linear dependence on SDS concentration; (2) higher SDS concentrations result in both a lower self-diffusion coefficient for DMSO and a smaller resistance force to DMSO moving out of the interfacial region, causing the exchange of DMSO between the interface and bulk region to become more frequent; and (3) the transition of the orientation preference of DMSO molecules passing from the interface to the water-rich phase vanishes. Current simulation studies examining the molecular level provide helpful insights for understanding the influence of surfactants on solute transport. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Transport Dimethyl sulfoxide Interface Sodium dodecylsulfate Simulation

1. Introduction Most chemical engineering processes address multi-phase systems in which interfacial reactions and mass transportations across interfaces are usually involved. Although the interfacial region is fairly narrow and covers a width of only several molecules (ranging

n

Corresponding author's. Coressponding author at: State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China. E-mail addresses: [email protected] (S. Zhao), [email protected] (H.-L. Wang), [email protected] (H.-L. Liu). nn

http://dx.doi.org/10.1016/j.ces.2015.05.068 0009-2509/& 2015 Elsevier Ltd. All rights reserved.

from a few angstroms to several nanometers), the physicochemical properties of this region are significantly different from those in the bulk phase due to the sharp changes in both concentration and density. Such differences are neglected in many studies when the interfacial volume is small compared to the volume of the continuous phase. However, when the volume of the continuous phase is on the nano- or micro-scale and the interfacial area becomes relatively large, the interfacial properties play a pivotal role. This feature has been exploited in practice for designing engineering processes. For example, because amphiphilic molecules tend to associate at interfaces and form dense molecular films with specific structures, they are commonly employed to inhibit mass

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transportation across the interface, allowing the addition of those species to become a control step in multi-phase chemical engineering processes. Despite the importance of the interfacial problems in chemical engineering processes, basic understanding in the formation of interfaces at the nano/micro-scale, the intrinsic relations between interfacial structure and properties, and the mechanism of interfacial interactions are still lacking. This mainly arises from the absence of precise in situ experimental observation techniques. In many chemical systems, the interface problems are associated with the presence of surfactants. Although the amount of surfactants may be small, they can cause a noticeable impact on mass transportation. For instance, it has been reported that surfactants can dominate the transport of a single drop across a liquid–liquid interface (Mao and Chen, 2004; Wegener et al., 2007; Liang and Slater, 1990) and hinder solutes crossing the interface through the resultant hydrodynamic effect (Lee et al., 1998; Arendt and Eggers, 2007) or extra interfacial barriers (Chen and Lee, 2000; Ahn et al., 2011; Gupta et al., 2008). In general, ionic surfactants can induce interfacial convection and strengthen interfacial mass transport, while non-ionic surfactants have the opposite effect (Ahn et al., 2011; Wang et al., 2011). In addition, the presence of surfactants at the interface can lead to the Marangoni effect in mass transport systems (Wegener et al., 2007; Arendt and Eggers, 2007; Wang et al., 2011; Wegenera et al., 2009). To investigate the impact of surfactants, molecular dynamics (MD) simulations are an ideal method because the interfacial region is too narrow for common experimental techniques to explore and the chemical system is too complicated for liquid state theories (Gray and Gubbins, 1984) to handle. By using MD simulations, Gupta and his coworkers studied solute transport together with an energy barrier effect across an interface covered with surfactant molecules. They showed that the presence of non-ionic surfactant increases the free energy barrier when solute is transferring from one continuous phase to the other (Ahn et al., 2011; Gupta et al., 2008). Ghaemi et al. (2012) applied a novel procedure to investigate the process of molecule permeation across a lipid bilayer and found that many factors, including correlations among ingredients, play important roles in the transport process. On the other hand, surface active solutes have attracted significant interest from both simulation and experimental viewpoints (Karpovich and Ray, 1998; Autrey et al., 2004; Allen et al., 1999). The free energy profile of the transport of surface active solutes exhibits a minimum near the interface (Garrett et al., 2006). Interfacial activity suggests that these solutes tend to associate in the interfacial area. Therefore, their transport behavior is different from other solutes. Dimethyl sulfoxide (DMSO) is an important interface active solute, and its aqueous solution has been widely used as the medium for various reactions (Lee, 1991; Tidwell, 1990; Manusco et al., 1979) and separations (Foucault and Chevolot, 1998). DMSO aqueous solutions display interesting thermodynamic properties. For instance, adding DMSO to water results in a significant freezing point depression. The freezing points of water and DMSO are 273 K and 291 K, respectively, whereas for water/DMSO mixtures, the freezing temperature is reduced to 203 K (Rasmussen and Mackenzie, 1968; Havemeyer, 1966). In the presence of DMSO, the hydrogen bond network among water molecules (Luzar and Chandler, 1993) is disrupted, leading to the depression of the freezing point. Another interesting property of water/DMSO solutions is that DMSO molecules tend to self-associate when the mole fraction of DMSO exceeds 0.1 (Shin et al., 2001, 2002; Katalin et al., 2010). This self-association causes microcosmic phase separation, which decreases the mobility of the DMSO molecules. In addition, the DMSO molecule presents strong interfacial activity and tends to associate in the interfacial area (Katalin et al., 2010). This association results in a redistribution of DMSO molecules both at the interface and in the

continuous aqueous phase. Consequently, the concentration in the interfacial region is higher than that in the continuous phase. Due to these properties, DMSO is regarded as a typical interface active solute in many chemical processes. In the present work, we investigate the transport process of DMSO from a light linear paraffin phase to an aqueous phase by simulation. Such a process occurs in aromatic extractions in which the low fraction extractant DMSO is usually removed from paraffin by water. In industry, contamination is inevitable in many facilities. Most of these contaminants are surfactants. Therefore, in the current study, the effect of the surfactant sodium dodecylsulfate (SDS) on DMSO transport is investigated. Regarding solute transport across an interface, a few studies (Ahn et al., 2011; Gupta et al., 2008; Garrett et al., 2006) have contributed to the understanding of the mechanism, but most of them addressed infinite dilutions, i.e., only one solute molecule was considered. While such assumptions can greatly simplify the study and supply helpful physical insights, it ignores correlations among solute molecules. Those correlation effects may play an important role during the transport process when the solute concentration is high. Indeed, in our recent work (Hu et al., 2013), we showed that the concentration of DMSO was crucial to its transport. Here, we focus on the effect of adding surfactant SDS on the transport process of DMSO at finite concentrations. By performing a full atom MD simulation, we investigate in particular the interfacial interaction among various components and then explore the influence of SDS surfactant on DMSO transport across a water/hexane interface from configurational, energetic and dynamic perspectives. The remainder of this work is organized as follows: In Section 2, we present the simulation details and review or explain the methods by which the energetic and dynamic properties are addressed. Those properties are analyzed and discussed in Section 3, and the conclusions are presented in Section 4.

2. Simulation and calculation methods 2.1. Modeling and simulation details Several systems with a variety of SDS concentrations are simulated. Each system contains 8720 water molecules and 1200 hexane molecules. The number of DMSO molecules in the systems is 392, corresponding to a finite solute concentration of 4.3% in water. For the purpose of comparison, we also perform simulations for infinitely dilute solutions, i.e., only one DMSO solute molecule is considered. The number of SDS molecules is set to 0, 36, 56 or 80. We follow the reduced definition for the concentration of surfactant (Dominguez and Berkowitz, 2000) to represent the corresponding concentration of SDS at the interface, i.e., by introducing the ratio between the interfacial area each SDS molecule occupies and the corresponding area at the water/vapor interface in the critical micelle concentration (CMC) condition, i.e., 45 Å2/molecule from neutron reflection experiment (Lu et al., 1993), the concentration of SDS can be expressed as CSDS ¼0%, 25% CMC, 40% CMC and 56% CMC. The simulation systems are set up as follows: first, water and hexane molecules are filled into two individual boxes of same size LX  LY  LZ (LX ¼ LY ¼8 nm, LZ ¼4 nm). For the bulk system in each box, we run 10 ns NPT simulations to reach equilibrium. Second, three copies of these boxes (one for water and two for hexane) are placed in line along the z-direction with a gap of 1.5 nm and the water box in the middle. With this setup, we can generate a system with two water/hexane interfaces perpendicular to the z-direction. Afterwards, a specific amount of SDS is introduced into the gaps with favorable orientations (for instance, all heads toward the water phase). Finally, DMSO molecules are added into the vacant space in

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the gaps. Periodic boundary conditions are applied in three directions for each simulation system. When the system is set up, we run the initial MD simulation with an NPT ensemble for 5 ns. During this process, the simulation system shrinks slightly along the z-direction and the box length of the entire system in this direction decreases. After 100 ps this length becomes nearly constant. Afterwards, another 20 ns NPT simulation is performed for the entire system to reach equilibrium. To ensure that we have the final equilibrium system, we sample the number density profile of each component every 1 ns and find that there are no apparent density deviations after approximately 15 ns. At equilibrium, an NVT production run has been conducted for 5 ns to sample the properties of interest. The time step is set to 2 fs in the above simulation processes. Our MD simulations are performed with the GROMACS v4.5.4 program (Hess, 2008). Force-field parameters from the OPLS allatom (OPLS-AA) model (Zheng and Ornstein, 1996) are used to describe both hexane and DMSO molecules and the extended simple point charge (SPC/E) model is employed for water molecules (Berendsen et al., 1987). Unfortunately, parameters for the SDS head are missing in the OPLS force field and are therefore manually included following Dominguez’s work (Dominguez and Berkowitz, 2000). The tail of SDS is an alkane chain. The temperature is maintained at 298 K using a Hoover–Nose thermostat (Hoover, 1985) with a relaxation time of 0.5 ps. All simulation processes in the above-mentioned NPT ensemble are imposed with a semi-isotropic Parrinello–Rahman barostat (Parrinello and Rahman, 1981) along the z-direction, allowing size variation only in this direction; equivalently, the interfacial area (8  8 nm2) is fixed throughout all simulations. Long-range electrostatic interactions are calculated by the particle mesh Ewald method (Darden et al., 1993; Essmann et al., 1995) with a cutoff of 1 nm. All covalent bonds involving hydrogen atoms are kept constrained with the LINCS algorithm (Hess et al., 1997).

In our simulation, the PMF is sampled within 6 nm across the interface, which is sufficiently long to cover the whole path from the aqueous phase to the hexane-rich phase. Three probe molecules are settled at three separate positions along the z-axis at 2 nm intervals. Larger intervals were tested and no different results were obtained. Each interval is divided with a grid width of 0.05 nm, resulting in 40  3 grid points for each PMF curve. Finally, all of the data obtained from the umbrella sampling are corrected by the weighted histogram analysis method (Kumar et al., 1992) (WHAM). All other properties are sampled without using any bias potential. 2.3. Self-diffusion coefficient The self-diffusion coefficient D is a vital quantity for understanding transport properties. In a homogeneous system, the selfdiffusion coefficient can be determined either from the slope of the mean-square displacement (MSD) versus long time τ using the Einstein relation or evaluated from the temporal integration of the velocity autocorrelation function (VAF) using the Green–Kubo formula. However, in an interface system the calculation of D is more difficult due to the inaccurate long-term MSD sampling at the inhomogeneous interfacial region. Different methods have been proposed to overcome this problem (Liu et al., 2004; Wick and Dang, 2005). In this study, an alternative algorithm by revising the Langevin equation Pedro and López, 2009 is employed. The extension of the Langevin equation has been detailed in our previous work (Hu et al., 2013), and here we only review the major calculation procedure. The interfacial region is divided into a few parallel zones along the z-direction so that in each zone, the PMF gradient is almost constant. However, these zones should have enough DMSO for reliable sampling. Then, the so-called survival probability inside the zone za is calculated from a separate set of simulations by Pðt; za Þ ¼

2.2. Energetics of solute transport The potential of mean force (PMF) of the solute is our starting point to study the transport and has been widely investigated in many simulations involving mass transport processes (Ahn et al., 2011; Gupta et al., 2008; Ghaemi et al., 2012; Garrett et al., 2006). While PMF cannot directly describe dynamic properties, it indicates the transport trend. The PMF of the solute along the z-direction, i.e., Wðzs Þ, can be calculated in an MD simulation by Z zs   Wðzs Þ ¼ f z ðz0s Þ zs dz0s ð1Þ z0

where f z is the z-component of the total force acting on the solutes and o : 4 zs represents the ensemble average with zs fixed. z0 is a reference position where Wðz0 Þ is zero. Usually, we can take z0 at a position remote from the interface. Eq. (1) is the definition for PMF, and to calculate it several methods are available, including the constrained mean approach (McQuarrie, 1976), umbrella sampling method (Pohorille and Wilson, 1993; Chandler, 1987) and statistical perturbation theory (Zwanzig, 1954). Similar to our previous work (Hu et al., 2013), we apply the umbrella sampling method here. To guarantee sufficient sampling in high energy regions (corresponding to the low probabilities of finding solute molecules), a bias potential is introduced to trap the solute at a certain position: UðzÞ ¼ Kðz  z0s Þ2 ;

ð2Þ 2

where K is a constant  set to 800 kJ/(mol∙nm ). Statistically, this bias force balances f z ðz0s Þ zs in Eq. (1). After taking the integral over the reaction coordinate z0s , the PMF can be obtained.

815

Nj ðtÞ 1 XJ 1 XJ ; P j ðtÞ ¼ j ¼ 1 j ¼ 1 N ð0Þ J J j

ð3Þ

where J is the total number of samples, N j ð0Þ is the number of DMSO molecules initially in a specific layer, and N j ðtÞ is the number of DMSO molecules that never move out of the layer within time t. A relaxation time τðza Þ can be obtained by fitting Pðt; za Þ with Pðt; za Þ ¼ e  t=τðza Þ :

ð4Þ

The effect of the zone width on the survival probability is analyzed in (Pedro and López, 2009), and it has been showed that Eq. (4) can fit the simulation result of an anisotropic fluid very well in a wide range of zone width. Dzz is a component of the self-diffusion coefficient matrix D, and here it is equal to the self-diffusion coefficient Dz in the zdirection. The self-diffusion coefficient is calculated with the combination of the following equations:   mv2F mvF ðv0  vF Þ B RðtÞ þ SðtÞ; ð5Þ ½ΔzðtÞ2 ¼ f z ðtÞ þ kB T kB T   where ½ΔzðtÞ2 is the mean-square displacement (MSD) normal to the interface, and a ðω½1  ω½aÞ; 1a

ð6Þ

a ðω½a  aω½1Þ; 1a

ð7Þ

 a  ð1  aÞω½a þ ð2 þ aÞω½1 þ a  2ω½1 þ 2a : 1þa

ð8Þ

B

f z ðtÞ ¼ 2Dzz t RðtÞ ¼ 2Dzz t SðtÞ ¼ 2Dzz t

Here, a ¼ αz τ; αz ¼ kB T=Dzz m; vF ¼ FðzÞ=mα. FðzÞ is the external force stemmed from PMF in the z-direction (Hu et al., 2013), and in

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each calculation window it’s a constant of individual value.

τ ω½λ ¼ 1 þ ðe  λt=τ  1Þ λt

ð9Þ

where λ takes values of 1, a, 1 þa, or 1 þ2a. Note that the selfdiffusion coefficient is the diffusion which takes place in the absence of a chemical potential gradient, describing the uncorrelated movement of a solute particle (Liu et al., 2013; Babarao and Jiang, 2008), and it’s generally different to the transport diffusion coefficient which combines the self-diffusion coefficient and the chemical potential gradient as detailed in the literature (Rolando, 2007). The self-diffusion coefficient reflects the friction among particles, i.e., kB T=Dz gives the solute friction coefficient along the z-direction.

3. Results and discussion 3.1. Interface properties Fig. 1 plots the density distributions of different components at the interfacial region. The solute concentration is fixed at CDMSO ¼4.3% and the surfactant concentration CSDC takes three representative values, i.e., CSDS ¼0, CSDS ¼ 25%CMC and CSDS ¼56% CMC. The aqueous phase is located in the region of zo0, and the hexane-rich phase is in the region of z 40. Fig. 1 indicates that an increase in SDS concentration has a gradual impact on interfacial properties. First, the addition of SDS increases the total density of all components at the interfacial zone. When the SDS concentration is high, a noticeable density barrier emerges at the interface as shown in Fig. 1C. Such a density barrier may increase the energy cost of solute transferring from one continuous phase to the other, which has been reported elsewhere (Gupta et al., 2008). However, the density barrier in our systems is small because the addition of SDS also increases the interfacial width. The density at the cross point of the dashed line (representing the water density) and the dotted line (representing the hexane density) has a decreasing value with increasing SDS concentration, and the hexane-rich phase is more and more remote from the interfacial center. This indicates that the interfacial width becomes larger when more SDS molecules are introduced, while the density peak of the DMSO distribution within the interfacial region significantly decreases due to the volume exclusion of SDS molecules. From the viewpoint of dynamics, a wider interface means a longer distance for the solute to transfer through in passing from one continuous phase to the other. Second, we also analyze the density distributions of the surfactant head and tail at the interface. The SDS hydrophilic head is similar to the DMSO molecule; thus, in the interfacial region, the density peaks of the SDS head (short dotted line) and DMSO (solid line) are located at almost the same position as shown in Fig. 1A–C. The SDS tail is hydrophobic, and thus its density peak is located close to the hexane-rich phase. The distance between the peaks of density distributions for the SDS head and tail reflects the average extension of surfactant molecules along the z-direction. This distance slightly increases with SDS concentration, indicating that when more SDS is added, the enhanced excluded volume effect drives the SDS chain molecule to be more extended along the z-direction. It should be noted that the chemical potential of SDS is a constant throughout both bulk phases and the interface at equilibrium according to the theory of phase equilibrium, and thus some amounts of SDS molecules are supposed to be desorbed from the interface and enter the bulk phases. This is well captured by our simulation. Indeed, the inset of Fig. 1C shows that the SDS concentrations in bulk phases are small but finite, and especially

Fig. 1. Density distributions of different components across the water/hexane interface at three typical SDS concentrations: (A) CSDS ¼ 0 (B) CSDS ¼25%CMC and (C) CSDS ¼ 56%CMC. The DMSO concentration is fixed at CDMSO ¼ 4.3%. In (C), the inset shows the zoom-in density distribution of SDS.

the SDS density is around 2.8 kg/m3 in the water-rich phase and less than 0.5 kg/m3 in the hexane-rich phase. The interfacial tension can be calculated in MD simulations through

γ ¼ ð1=2ÞL½P zz  ðP xx þP yy Þ=2:

ð10Þ

Here, L is the length of the simulation box and P xx , P yy and P zz are the elements of the pressure tensor. The interfacial tension versus the SDS concentration at C DMSO ¼ 4:3% is plotted in Fig. 2, and for comparison we also plot the distributions of interfacial

Y.-F. Hu et al. / Chemical Engineering Science 134 (2015) 813–822

817

tension with the presence of DMSO is larger than in the absence of DMSO.

3.2. Energetics of solute transport

Fig. 2. Interfacial tensions versus SDS concentration in the water/hexane system with and without DMSO. The experimental result is from Pradines et al. (2009), and the concentration of DMSO is set zero or C DMSO ¼ 4:3%. Curves are drawn to guide the eye.

tensions in the absence of DMSO from both the current simulation and available experimental results (Pradines et al., 2009). First, at zero DMSO concentration, the overall simulation curve agrees well with experimental results at various SDS concentrations. While the simulation result is generally slightly larger, the agreement confirms the validity of our calculation. Second, at zero SDS concentration, the interfacial tension with DMSO is noticeably smaller than without DMSO because DMSO is an interface active solute that behaves as a weak surfactant, and thus its presence at the interface lowers the interfacial tension. Third, when the surfactant concentration is very large (0.6 cmc  1), the concentration of DMSO at the interface significantly decreases as discussed in Fig. 1. Consequently, the presence of DMSO has little impact on surfactant efficiency (Rekvig et al., 2003), i.e., the surfactant efficiency is dominated by SDS, and the interfacial tension becomes nearly insensitive to the presence of DMSO. In that limit, the simulation predictions for the interfacial tension in the absence and presence of DMSO become comparable and both agree with experimental data. Finally, the experimental curve satisfies the Frumkin rule, which presents logarithmic dependence on surfactant concentration (Fainerman et al., 2003). Because DMSO behaves as a weak surfactant, one would expect the surfactant efficiency of SDS is enhanced when mixed with DMSO and this results in smaller interfacial tension. However, the opposite occurs, and the interfacial tension presents an almost linear dependence on SDS concentration. Similar trends have been found in experiment (Moya et al., 2006). Indeed, this phenomenon can be explained by combining the density distributions of various components as shown in Fig. 1 and the discussion above. Although the addition of surfactant SDS drives the DMSO molecules into the water-rich phase as shown in Fig. 1, Fig. 2 indicates that the addition of DMSO can also drive a small amount of SDS molecules into the continuous phases because DMSO behaves as weak surfactant. In other words, we conjecture that both DMSO and SDS compete to occupy the interfacial region, and although SDS is more competitive, such competition finally leads to the local SDS concentration at the interfacial region becoming smaller than in the case with pure SDS surfactant, i.e., the total amount of added SDS molecules in the systems with and without DMSO are the same, but their local concentrations at the interface are different. In particular, due to the volume exclusion from DMSO molecules, the local concentration of SDS at the interface is smaller than that without the presence of DMSO, and accordingly, the interfacial

The sampling of PMF in solutions with finite solute concentration is difficult due to the frequent solute exchanges within interface, and thus a sufficiently long simulation time is required to reach sampling precision. Because we are interested in the gradient of the PMF distribution rather than the absolute values, we simply set the PMF value of DMSO in the hexane-rich phase with zero SDS concentration to zero. In other word, during each individual calculation of PMF the reference position z0 is always placed in hexane-rich phase. Fig. 3A shows the PMF distributions of DMSO at a typical concentration (CDMSO ¼4.3%) with various SDS concentrations. Because of its amphiphilic properties, each PMF of DMSO exhibits a minimum in the interfacial region regardless of the concentration of surfactant SDS. The position of the PMF minimum is set as the interface center (z ¼ 0), and as before, the hexane-rich phase is located in the area of z 4 1 and the aqueous phase is in z o  1. DMSO is more hydrophilic, and thus the PMF values at the interface and in the aqueous phase are negative. We find that with the addition of SDS the changes in the depth of the PMF well are small, but the PMF value in the water-rich phase apparently

Fig. 3. PMF distributions of DMSO along the z-direction at various SDS concentrations: (A) CDMSO ¼ 4.3%, (B) infinitely dilute systems. The minimum of PMF (the interface center) is defined at z ¼0. The relative PMF is defined as the residual value by subtracting the PMF in the hexane-rich phase.

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decreases as the SDS concentration increases. This is because, on one hand, the addition of SDS drives the DMSO molecules into the water-rich phase (see Fig. 1) which leads to a considerably improved solubility of DMSO in the water-rich phase, and on the other hand, the increase of SDS concentration in entire system gives rise to an increased concentration of SDS in the water-rich phase, and this results in a variation of the PMF value. The free energy difference of solute in both continuous phases depending on surfactant concentration coincides with the experiment observation (Pandit and Basu, 2004) and other similar simulation studies (Ahn et al., 2011; Wardle et al., 2005), and can be exploited to improve the extraction sufficiency as discussed in our recent work (Shi et al., 2015). As for the PMF value at the interface, an increase of SDS concentration causes competition between the attraction between DMSO and surfactant and the excluded volume effect, and thus the depth of the PMF well hardly changes. For comparison, we also plot the PMF curves of DMSO in an infinitely dilute solution in Fig. 3B. Generally the PMF curves present the same shape as those for the system with finite DMSO concentration. However, in contrast to Fig. 3A, the PMF well of DMSO at the interface significantly decreases in an infinitely dilute system when SDS in introduced because the attractive interaction between the SDS head and DMSO tends to attract DMSO to the interface. The comparison of Fig. 3A and B confirms that the correlation effect among DMSO molecules is important when surfactant is present. 3.3. Dynamic properties of the transport process The self-diffusion coefficient is related to DMSO distribution, and thus is position-dependent along the z-direction at the interface. Fig. 4 plots the calculated self-diffusion coefficients of different sets of DMSO and SDS concentrations. Because the selfdiffusion coefficient Dz is a constant in the continuous phase, it is not shown Fig. 4. At DMSO concentration of 4.3% and zero surfactant, the calculated Dz with the conventional MSD method in the water-rich and hexane-rich phases are 0.29 A2/ps and 0.285 A2/ps, respectively. During our calculation, we divide the interfacial region into five zones according to both the gradient of the PMF curves and the solute sufficiency in each zone for sensible sampling. The survival probability of DMSO in each zone is computed with the algorithm introduced above. As in the PMF distributions displayed in Fig. 3, the interface center is located at z ¼ 0. The diffusivity of DMSO in the bulk phase should be insensitive to SDS concentration, while within the interfacial zone, as showed in Fig. 4, the diffusion

Fig. 4. Self-diffusion coefficients Dz at the interface for different sets of DMSO and SDS concentrations. The position scale ( 0.6 nm to 0.6 nm) is within interface range.

coefficient in the interface is position- and SDS-concentration dependent. One may note that the interface range in Fig. 4 is smaller compared to that for PMF displayed in Fig. 3, and the remote considered distance from the interface is only 0.6 nm which is still within the interface zone. The information of selfdiffusion coefficient at the anisotropic intermediate region (i.e., in distance between 0.6 nm and 2 nm) is absent due to the lack of sufficient DMSO molecules for reliable simulation sampling. To calculate the self-diffusion coefficient in this region a combined interface mode proposed by Gupta et al. (2008) may be helpful. We conjecture that the self-diffusion coefficient gradually recovers to the values in the continuous phases on both sides as the distance increases. Normally, the PMF gradient is the main driving force for the transport of DMSO at the interfacial region. However, at the center of the interface where the PMF gradient is zero, DMSO molecules exhibit a high self-diffusion coefficient Dz. These self-diffusion coefficients reflect the friction between a DMSO molecule and the molecules in its surroundings. When the friction is smaller, the self-diffusion coefficient is higher. Fig. 4 suggests the friction that DMSO encounters at the interface center is much smaller than those in both sides, probably because of its amphiphilic nature. The presence of SDS affects the mobility of solutes at the interface. The comparison of the various curves in Fig. 4 demonstrates that the self-diffusion coefficient of DMSO at the interface decreases when SDS is added into the system. The self-diffusion coefficient in the middle is affected the most because the accumulation of SDS at the interfacial region greatly increases the friction for the self-diffusion of the DMSO molecule. It has been shown (Gupta et al., 2008) that the apparent friction coefficient significantly increases in the region of strong solute-interface coupling which is opposite to the solute friction coefficient, and this discrepancy is well explained by the influence of soluteinterface coupling. However, the calculated self-diffusion coefficient in present work should be compared to the solute friction coefficient in Gupta et al. (2008) because the solute-interface coupling is not included in the random force during the calculation. Although both model systems are very different, we find that our calculated self-diffusion coefficient is quantitatively comparable to the solute friction coefficient in Fainerman et al. (2003) by noting the inverse relation between two quantities. Specifically, both self-diffusion coefficients present a maximum at the interfaces and overall decrease after the addition of surfactant. While the association of DMSO with itself or with the solvent molecule in bulk phase has been extensively reported from experiment (Shin et al., 2001, 2002) and simulation (Skaf, 1999; Borin and Skaf, 1999), little information is known about its association behavior at interfaces (Katalin et al., 2010). In the current study, although the average concentration of DMSO is low (i.e., 4.3%), the local proportion of DMSO at the interfacial region is high. The local concentration can be reflected by the radial distribution of DMSO molecules and is depicted in Fig. 5. Because it is hard to define the mean solute density at the interfacial region, we plot only the absolute density instead of the normalized one. During the calculation, we sample all DMSO pairs within the interfacial region. Specifically, the DMSO molecule is counted when its center of mass is located within  0.5 nmozo0.5 nm. From Fig. 5, a density maximum located approximately 5.2 Å away from a target DMSO is found. At further distances, the density of DMSO diminishes quickly. In addition, when the concentration of SDS increases, Fig. 5 shows the first peak of DMSO RDF falls down and the second peak moves to a further distance. This trend agrees with our analysis in Fig. 1: the addition of surfactant occupies the space, and the enhanced excluded volume effect competes with the attraction, causing the average distance among DMSO to become slightly larger. Because the integral of density distribution yields the total molecule

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Fig. 5. Radial distribution function of DMSO at the interfacial region at four representative SDS concentrations. The DMSO molecule is counted when its center of mass is located within  0.5 nmo z o0.5 nm. The black dashed curve corresponds to the number density profile of DMSO at water–vapor (W–V) interface with CDMSO ¼5.0% from Katalin et al. (2010), and all other curves are from this work with CDMSO ¼ 4.3% at various surfactant concentrations.

Fig. 6. (A) Orientation distributions of DMSO molecules at different surfactant SDS concentrations. The DMSO concentration is fixed at 4.3%. The water phase is located on the left and the hexane phase is located on the right. The center of the interface is marked with a dashed line. (B) Illustration of the orientation of a DMSO molecule. Z is the direction normal to the interface pointing from the water phase to the hexane phase.

number of DMSO, the overall decrease of density distribution with the increase in surfactant concentration indicates that the DMSO molecule number at the interface reduces after the addition of more surfactants, suggesting that some amount of DMSO molecules are pushed always from the interface and go into the continuous phases. The characterization of the self-association behavior of DMSO at the interface is not a straightforward task. With a combined

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method Pojjak et al. studied the association behaviors of the like components at the liquid–vapor interface of water-DMSO mixtures with various compositions (Katalin et al., 2010), and they found that the DMSO molecules form self-aggregates at the interface of the 5% DMSO system in comparison to 10% in the water-DMSO mixture (Shin et al., 2001, 2002). After a translational shift their number density profile of the DMSO molecules in the water–vapor interface is depicted in Fig. 5 (with the black dashed curve). While the density profile (referring to one-body density distribution) is different to the RDF (referring to two-body density distribution) (Chandler, 1987), the peak height in both quantities has the same physical meaning of telling the value of maximum density. Generally, the peak is sharper when the system is more compact (Gray and Gubbins, 1984). Indeed, Pojjak showed that the peak in the number density profile of DMSO at the interface was sharper when the DMSO mole fraction in the water-mixture was higher. Whereas the DMSO mole fraction in water-DMSO mixture is 4.3%, a value less than 5%, the RDF of DMSO at the water-hexane interface presents a comparable peak to the black dashed curve from Katalin et al. (2010), indicating the DMSO molecules selfassociate in the water-hexane interfacial region. Moreover, while the self-association degree cannot be determined simply from DMSO RDF, Fig. 5 shows that it should be influenced by the concentration of SDS. Interaction with SDS can also affect the orientation of DMSO when it approaches the interface. The orientation of DMSO is defined by the angle θ between the vector SO (from the sulfur atom pointing to the oxygen atom) and the z-direction, as illustrated in Fig. 6B. For convenience, cosθ instead of the angle θ is used. When cos θ is greater than zero, the DMSO molecule heads to the hexane-rich phase; otherwise, it heads to the water-rich phase. Additionally, when the absolute value of cos θ is larger, the orientations of all DMSO molecules are more regular. The distributions of the averaged orientations of the DMSO molecules at different SDS concentrations are plotted in Fig. 6A. When DMSO stays in the continuous phase remote from the interface, it adopts all orientations with equal probability, and the average value for cosθ should be 0. This is confirmed in our calculation when DMSO is in the water-rich phase. In the hexane-rich phase, because the solubility of DMSO is too small, credible sampling cannot be achieved. Fig. 6A shows that the orientation distribution of DMSO changes significantly when the surfactant SDS is added into the system. In particular, without SDS, in passing from the interface to the water-rich phase, DMSO molecules first head to the water-rich phase and then gradually rotate and slightly head to the hexanerich phase at the edge of the interface. When they move farther into the water-rich phase, the average orientation goes to zero. During this process, an apparent transition of orientation, or orientation jump, is observed. However, when SDS is introduced, this orientation jump disappears, i.e., during the same transport process DMSO molecules always head to the water-rich phase, and the average orientation value vanishes when they reach the water continuous phase. When more SDS is introduced, the orientations of the DMSO molecules within the interface become more regular. The characteristics of the DMSO orientation along the z-direction are closely associated with its interaction with other components. In the absence of SDS, the orientation of DMSO is determined by the orientation distribution of water or hexane in the vicinity of interface, depending on which side the DMSO molecule is located. As reported by Xiao et al. (2010), in a water/n-alkane interface system, the water molecules (more specifically, the dipole axis of water) presented a slight orientation preference of cos θ ¼0.03 at the interfacial center (z ¼ 0), which was gradually reduced to a minimum value of cos θ ¼  0:03 at z ¼  0:3 nm (i.e., a position within the interfacial region while close to water-rich phase) and thereafter increased and became zero when z o  1:0 nm (i.e., in

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the water-rich phase). The orientation profile of DMSO at C SDS ¼ 0 in our work is consistent with that of water molecules near the interface as reported by Xiao et al., considering our definition of orientation here is opposite to theirs. When SDS is added at the interface, its interaction with DMSO impacts the orientation of water. As discussed above, the SDS chain extends itself along the z-direction, forming an array-like structure at the interface and forcing DMSO to distribute at the interface more regularly to achieve a minimized free energy. When DMSO moves to the edge of the interface, the restraint from SDS vanishes. As a result, the average orientation of DMSO gradually goes to zero, as shown in Fig. 6A. We also calculate the residual probability of DMSO at the central region of the interface (  0.25 nmoz o 0.25 nm). The calculation of the residual probability is similar to that of survival probability, and the involved residual number is the amount of DMSO molecules that belong to a specific zone at t ¼0 still remaining after a given time regardless of where they have been during the sampling period. In other words, a DMSO molecule which escaped from the specific zone is still counted as long as it returns. The residual probability only reflects the exchange frequency of DMSO within different zones. The combination of Figs. 3 and 4 suggests that with more SDS, DMSO presents a lower self-diffusion coefficient while encountering a smaller PMF gradient when moving away from the interface. Additionally, the association among DMSO molecules gradually diminishes with increasing SDS concentration, as indicated by the RDF in Fig. 5. The integrated effect can be explained with the residual probability. As shown in Fig. 7, the residual probabilities at different SDS concentrations descend quickly at first and then in moderate slopes after approximately 200 ps. We compare the residual probabilities of DMSO at three representative SDS concentrations and show that an increase in SDS concentration significantly reduces the residual probability. This means that the addition of SDS facilitates the exchange of DMSO molecules between the interface center and other zones. Mass transport is usually coupled with interface deformation, which itself is associated with the formation of a capillary wave. The existence of capillary waves in liquid–liquid interfaces was first observed by simulation (Toxvaerd and Stecki, 1995a, 1995b) and then confirmed by liquid state theories (Iatsevitch and Forstmann, 1995; Napari et al., 1995). One of the characteristics of interface deformation is the slow damping autocorrelation of random forces acting on the solute. The autocorrelation can be

fitted by an exponential decay function, C F ðtÞ ¼ a1 e

 τt

1

þ a2 e

 τt

2

ð11Þ

τ1 (τ1 o τ2) is the characteristic time of the delta correlated noise, and τ2 is the characteristic time of the autocorrelation time reflecting the degree of interface coupling at a certain position z. The correlation between the solute and the interface can be strong, and the autocorrelation time depends on the distance between them (Ban et al., 2011). Generally, a prolonged simulation is necessitated to properly capture the interface coupling during the mass transport. With a coarse-grained model containing around 9000 Lennard–Jones-type beads to study the transport of a small solute across water-hexadecane interface covered by H3T3 surfactant, Gupta et al. (2008) demonstrated that an approximately 500 ns production run is needed to analyze the interface coupling. Such a large time scale is hardly reachable for a simulation of interface system with all-atom force field. On the other hand, the impact of the solute-interface coupling is very important, and it’s directly related to the mean transport time. To analyze the mean transport time of DMSO molecules across water/ hexane interface covered by SDS surfactant, an individual coarsegrained molecule dynamics simulation study should be performed. Nevertheless, we emphasize that the simulation time in present study is sufficiently long for the properties discussed above, and an all-atom simulation study is also very helpful to provide distinctive molecule feature on the solute transport across interface. Finally, it is interesting to compare DMSO behavior at a water/ oil interface and at a water/air interface. It has been shown that competitive adsorption at the interface plays different roles in the water/air and water/oil interfaces (Pradines et al., 2009). Specifically, when amphiphilic surfactants such as SDS are adsorbed at the water/air interface, despite an increase in the interfacial width, the hydrophobic tails of SDS are repelled from both sides, forming a disordered structure at the interface (Dominguez and Berkowitz, 2000). This is different from the situation at the water/oil interface, where an ordered structure is formed as explained above. In this case, if the transport of DMSO across the interface is considered, the resistance forces from the water/oil and water/ air interfaces are different, even though the surfactant concentrations at both interfaces are the same. However, the transport efficiency is the integrated result of multiple effects, and to have a quantitative comparison of the transport efficiency of DMSO along this line, a specific study should be performed. 4. Conclusions

Fig. 7. DMSO residual probabilities at different surfactant concentrations within the region of  0.25 nmo z o0.25 nm. The DMSO concentration is fixed at 4.3%.

DMSO is a representative interface active solute, and its transport across interfaces is of great importance in understanding the mechanism of many chemical engineering processes involving interfaces. From a practical point of view, the transport of DMSO is usually accompanied by the presence of surfactants. By using molecular dynamics simulations we investigated the effect of SDS surfactant on DMSO transport across a water/hexane interface. In our system, all components, including water, hexane, DMSO and SDS, are described with full all-atom force fields and the concentration of SDS varies from zero to high values while the concentration of DMSO remains finite. By investigating various properties from configurational, energetic and dynamic perspectives, we find that the presence of SDS brings non-trivial effects. First, the study of the interfacial structure shows that the SDS molecules tend to associate at the interface, and due to the attraction between SDS and DMSO the total number density of all components in the interfacial region is slightly larger than in the continuous phase. In addition, SDS in water/hexane

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increases the interfacial width and reduces the DMSO concentration in the interfacial region. Second, we investigated the interfacial tension and compared its distributions as a function of SDS concentration in the presence and absence of DMSO, concluding that at zero SDS concentration the interfacial tension with DMSO is smaller than without it because it behaves as a weak surfactant. At moderately finite SDS concentrations, the opposite phenomenon is observed because the local SDS concentration at the interface becomes smaller due to the exclusion of DMSO molecules, while at high SDS concentration the interfacial region is nearly occupied by SDS molecules and the interfacial tensions for both systems become comparable. For interface systems without DMSO, we also compared our predicted interfacial tensions with experimental results at various SDS concentrations, and good agreement was found. Third, dynamic characteristics were considered. When more SDS molecules are introduced into the system, the self-diffusion coefficient of DMSO decreases due to the blocking effect of SDS. However, we found that the resistance force from the PMF gradient for DMSO moving out of the interfacial region also decreases. The final integrated effect depends on the competition between these two effects, and as a result the exchange of DMSO between the interface and other regions becomes more frequent. Finally, we studied the configuration of the DMSO molecule during its transport across the water/hexane interface and found that the average orientation of DMSO presents an apparent transition in the system without SDS during the transport process from the interfacial region to the water-rich phase, which vanishes with the addition of SDS. Most of the analysis in this work is made based on equilibrium sampling with molecular dynamics simulations and supplies basic insights from different perspectives toward the understanding of solute transport. The real-time influence of surfactant on solute transport should be an integrated result of various competitive factors, including those from the non-equilibrium perspective, and the gradients of mass distribution, chemical potential distribution and pressure distribution should all be considered. To obtain a more comprehensive understanding, non-equilibrium dynamics studies on solute transport with the presence of surfactant, probably with a coarse-grained model, should be performed.

Acknowledgments This work is supported by the National Natural Science Foundation of China (Projects nos. 20990224, 51125032, 21076073), the 111 Project of the Ministry of Education of China (no. B08021) and the Open Project of State Key Laboratory of Chemical Engineering of China (SKL-ChE-13C04). SZ also acknowledges the support of the Shanghai Science and Technology Committee Rising-Star Program (no. 14QA1401300). References Ahn, Y.N., Gupta, A., Chauhan, A., Kopelevich, D.I., 2011. Molecular transport through surfactant-covered oil–water interfaces: role of physical properties of solutes and surfactants in creating energy barriers for transport. Langmuir 27 (7), 2420–2436. Allen, H.C., Gragson, D.E., Richmond, G.L., 1999. Molecular structure and adsorption of dimethyl sulfoxide at the surface of aqueous solutions. J. Phys. Chem. B 103 (4), 660–666. Arendt, B., Eggers, R., 2007. Interaction of Marangoni convection with mass transfer effects at droplets. Int. J. Heat Mass Transfer 50 (14), 2805–2815. Autrey, T., Brown, A.K., Camaioni, D.M., Dupuis, M., Foster, N.S., Getty, A., 2004. Thermochemistry of aqueous hydroxyl radical from advances in photoacoustic calorimetry and ab initio continuum solvation theory. J. Am. Chem. Soc. 126 (12), 3680–3681. Babarao, R., Jiang, J., 2008. Diffusion and separation of CO2 and CH4 in silicalite, C168 Schwarzite, and IRMOF-1: a comparative study from molecular dynamics simulation. Langmuir 24 (10), 5474–5484.

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