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water interface using dissipative particle dynamics simulations
Journal of Colloid and Interface Science 361 (2011) 573–580
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Investigation of interfacial and structural properties of CTAB at the oil/water interface using dissipative particle dynamics simulations Yiming Li ⇑, Yingyan Guo, Mutai Bao, Xueli Gao Key Laboratory of Marine Chemistry Theory and Technology, Ocean University of China, Ministry of Education, Qingdao 266100, PR China
a r t i c l e
i n f o
Article history: Received 14 March 2011 Accepted 26 May 2011 Available online 13 June 2011 Keywords: Spatial structure Interfacial density Interfacial thickness Interfacial tension Area compressibility modulus End-to-end distance Order parameter
a b s t r a c t We have used dissipative particle dynamics (DPD) to simulate the system of cetyltrimethylammonium bromide (CTAB) monolayer at the oil/water interface. The interfacial properties (interfacial density, interfacial thickness, and interfacial tension), structural properties (area compressibility modulus, end to end distance, and order parameter), and their dependence on the oil/water ratio and the surfactant concentration were investigated. Three different microstructures, spherical oil in water (o/w), interfacial phase, and water in oil (w/o), can be clearly observed with the oil/water ratio increasing. Both the snapshots and the density profiles of the simulation show that a well defined interface exists between the oil and water phases. The interface thickens with CTAB concentration and oil/water ratio. The area compressibility modulus decreases with an increase in the oil/water ratio. The CTAB molecules are more highly packed at the interface and more upright with both concentration and oil/water ratio. The root mean square end-to-end distance and order parameter have a very weak dependence on the oil/water ratio. But both of them show an increase with CTAB concentration, indicating that the surfactant molecules at the interface become more stretched and more ordered at high concentration. As CTAB concentration increases further, the order parameter decreases instead because the bending of the interface. At the same time, it is shown that CTAB has a high interfacial efficiency at the oil/water interface. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Studies of surfactant molecules at the liquid/liquid interfaces have been the subject of investigations for a long time, not only for their scientific interest but also for their applicability in industry, such as pharmaceutical, food technology, plastic, and petroleum industries [1–4]. A typical surfactant molecule consists of the ‘‘head’’ part having a polar or ionic functional group and the ‘‘tail’’ part having a hydrocarbon chain. Owing to possess of both the hydrophilic and hydrophobic character, they can adsorb at the oil/water interface forming a surfactant monolayer, which can effectively reduce the interfacial tension. Today, microemulsions are receiving ever-increasing attention from both practical and theoretical points of view [5,6]. Especially, because of their ability to encapsulate droplets of one material in another; micellar microemulsions may be useful in many applications, from nanoparticle self-assembly to drug delivery. Thus, an important first step to understand microemulsion is to have a molecular level understanding of the surfactant monolayer at the interface. Hence, it is instructive to understand the structure, interfacial properties, ⇑ Corresponding author. Fax: +86 532 66782480. E-mail address: [email protected] (Y. Li). 0021-9797/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2011.05.078
and dynamics of surfactants at the oil/water interface. A deeper investigation of interfacial properties of surfactant monolayer at the oil/water interface is crucial for understanding the workings of surfactant systems from fundamental interests of colloid and interface science, as well as practical applications. In the past decades, a vast number of experimental techniques have been used to investigate the dynamical and structural properties of surfactant systems such as fluorescence [7–10], resonance Raman scattering [11,12], neutron reflection [13–16], second harmonic generation [17,18], nuclear magnetic resonance spectrum [19–21], and vibrational sum-frequency spectroscopy [22]. However, only a few techniques are available for the investigation of oil/water interface, such as nonlinear vibrational sum-frequency spectroscopy and second harmonic generation. So it is difficult to obtain detailed information on the behavior of the surfactant molecules at the interface experimentally. The interfacial molecules typically form only a small fraction of a fluid, and perturbations from bulk structure and dynamics are difficult to measure and distinguish experimentally [23]. Therefore, computer simulations are an attractive alternative to provide additional information on dynamics, distributions, and ordering of surfactants, enhancing the understanding of interfacial properties of surfactants. With the aid of the increase in computational power, computer
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simulations have become a potential method to address the limitations of analytical approaches. To explore the interfacial structure and properties at the molecular level, MD simulation techniques have been widely applied to the study of structure and dynamics of surfactants at the liquid/ liquid interface [24–27]. For instance, Mu et al. studied the interfacial behavior of surfactin methyl ester derivatives at the n-decane/ water interface at low surface coverage by MD simulation. Molecular orientations, structural variability of the peptide ring backbones, interfacial molecular areas, and the motion activities of surfactin derivatives were determined [28]. Dai et al. reported the MD simulation of the in situ self-assembly of nanoparticles and SDS surfactants at a water/trichloroethylene (TCE) interface, highlighting the potential of using the liquid/liquid interface to produce novel nanomaterials [29]. Rivera et al. simulated alkane/water systems containing methanol and reported the surfactant behavior of methanol molecules as they are preferably adsorbed at the interface and reduce the interfacial tension through a rearrangement of the molecules at the interface [30]. All of these studies provide detailed insight into the microscopic structure of surfactant monolayers at the interface between the binary immiscible fluids. However, the time scales accessible to ordinary MD simulations are too short to observe diffusion to the interface and formation of micelles. Simulation at atomic resolution is also computationally very expensive. An alternative approach is to simulate the oil/water/surfactant system at a mesoscopic level. Dissipative particle dynamics (DPD) is a technique that has been developed to simulate fluids at a mesoscopic level [31–33]. Compared with usual dynamics simulations, for example all-atom simulation, the major advantage of DPD is its soft interactions [34,35]. The particles represent molecules or liquid elements rather than atoms, and the soft potential allows for a much larger time step and length scales than which is commonly used in usual dynamic simulations [36]. Although less detailed than MD, it still enables a systematic study of the interfacial properties of surfactant and can point out the mechanisms and surfactant properties that determine the interfacial properties of surfactant at the oil/water interface. However, research on the surfactants at the oil/water interface by DPD simulation is relatively scarce. Live Rekvig et al. have ever used DPD to investigate how variations in size and structure of surfactants influence their ability to reduce the interfacial tension at the oil/water interface [37]. Their simulations reveal that the branching of the hydrophobic tail has a positive effect on the efficiency at the interface only if the head group is hydrophilic enough to maintain a compact layer. Recently, the adsorption of sodium dodecylbenzene sulfonate and sodium oleate at the oil/water interface was simulated [38]. The results show that it is beneficial to decrease interfacial tension if the structure of hydrophobic chain of surfactant and the oil was similar; in addition, the presence of inorganic salts causes the surfactant molecules to form more compact and ordered arrangement and helps to decrease the interfacial tension. Hence, from a practical view, it is instructive to have an understanding of the structure, interfacial properties, and dynamics of surfactant at the liquid/liquid interface. Cetyltrimethylammonium bromide (CTAB) is an important cationic surfactant and is widely used in both fundamental research and many industrial applications. It is well-known that self-assembly of CTAB molecules at liquid/liquid interfaces is essential for the preparation and stabilization of microemulsions, as well as of particular interest for various natural and industrial applications. The structural and dynamic properties of CTAB monolayer formed at the air/water interface have been investigated by Yuan et al. using MD simulation [39]. However, the interfacial behavior of CTAB at the oil/water interface is still not fully understood, and it is of practical value for making further study on this. Taking a panoramic view of the situation, little is known about the stability and dynamics of the CTAB monolayer at the oil/water interface, espe-
cially the effect of oil/water ratio on its interfacial and structural properties, which is very important in the enhanced recovery of crude oil [40]. For this purpose, we take CTAB as an example to investigate the structural and interfacial properties of surfactant at the oil/water interface using DPD simulation. In the present work, the interfacial properties (interfacial density, interfacial thickness and interfacial tension), structural properties (area compressibility modulus, end to end distance and order parameter), and their dependence on the surfactant concentration and the oil/water ratio were investigated in detail. More importantly, these DPD studies conducted here can throw more light on the interfacial behavior of CTAB at the oil/water interface and thereby obtain a more detailed picture of the monolayers. 2. Computational methods 2.1. Dissipative particle dynamics In DPD, conservative, random, and dissipative forces act between two particles i and j which are a distance rij apart.
fi ¼
X
F Cij þ F Rij þ F Dij
ð1Þ
i–j
The first term in the above equation represents a conservative force, which is usually soft repulsive of the form
F Cij ¼
aij ð1 rij =Rc Þ^rij ðrij < Rc Þ 0
ðr ij > Rc Þ
ð2Þ
where aij is a maximum repulsion between particles i and j, rij is the distance between them, with the corresponding unit vector ^rij ; and Rc is a cutoff radius which gives the extent of the interaction range. The other two forces in Eq. (1) are a random force (F Rij ) and a dissipative force (F Dij ).
F Rij ¼ rwR ðr ij Þhij^r ij
ð3Þ
F Dij ¼ gwD ðrij Þð^r ij v ij Þ^r ij
ð4Þ
Here, vij is the velocity difference for the two particles, h is a random number between 0 and 1, and w is the weight function. g is the friction coefficient and r is the noise amplitude. The combined effect of these two forces is a thermostat, which conserves momentum and, hence, gives the correct hydrodynamics at sufficient long time and length scales. aij, r and g determine the amplitude of the conservative, random, and dissipative forces, respectively. The values r = 3 and g = 4.5 are used in this study. The DPD method was described in detail by Groot and Warren [41]. 2.2. Computational models Each molecular bead in the system has equal mass, meaning that the molecular mass of hydrophilic bead (H) and hydrophobic bead (T) are equal. In order to make the molecular mass of tail and head group approximate possible, the surfactant CTAB is divided into two DPD beads that are tied together by a harmonic spring, as shown in Fig. 1. Water and oil are represented by one bead W and O for simplicity. All DPD beads belonging to the same molecule are connected by a loosely bounded spring with a spring force constant K = 4.0 according to Groot’s work [41]. This spring constant controls the stiffness of the molecule, but it is not very sensitive to the simulation result. There are several methods suggested in the literatures to evaluate the interaction parameters for DPD simulation [41]. The quantitative structure–property relationship (QSPR) is based only on the solubility parameter [42]. It is not appropriate for the present
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Fig. 1. DPD model of CTAB molecule, ‘‘H’’ denotes the hydrophilic head group and ‘‘T’’ denotes the hydrophobic tail.
Table 1 Interaction repulsion parameters aij in oil/water/CTAB systema.
H T W O a
H
T
W
O
25.00 177.82 25.34 143.61
177.82 25.00 151.52 25.94
25.34 151.52 25.00 103.24
143.61 25.94 103.24 25.00
sary to illustrate that all the simulation concentration used in this paper is the molar fraction of various molecules in the cube. 3. Results and discussion 3.1. Spatial structure of oil/water/CTAB system
H = head group bead, T = tail group bead, W = water bead and O = oil bead.
system because of a partial charge in CTAB molecular. So we use the interaction repulsion parameters aij in Table 1 calculated by Chen et al. [43] .The calculated interaction energy is very sensitive to these partial charges. The averaged interaction energy is calculated based on the fragments as described above. 2.3. Computational details The size of simulated box is set to 20 10 10 nm (Lx Ly Lz), which contains a total of 6000 beads. Periodic boundary conditions were applied in all three directions. The bead density of systems is set to 3.0. As Hoogerbrugge and Koelman do [34,35], we set the temperature of the system as kBT = 1.0, which effectively specifies pffiffiffia unit of time since root mean square velocity of the particles is 3 from the Maxwell–Boltzmann distribution. A time step of Dt = 0.05 is used for the DPD simulations. The 20,000 DPD steps are adopted in this research in order to obtain the steady and balanceable results. As can be seen from the diffusion plot of the simulation (Fig. 2), equilibrium is reached before 12,000 time steps, so 20,000 time steps per simulation is sufficient for the simulation. It is neces-
One way of characterizing the structure of CTAB molecules at the oil/water interface is to observe the snapshots of the simulation system. The structures of CTAB molecules at the interface with different oil/water ratios and different concentrations are shown in Fig. 3. Three different microstructures, spherical oil in water emulsion (o/w), interfacial phase, and water in oil emulsion (w/o), are observed with the oil/water ratio increasing. It goes the following structure transitions: o/w ? interfacial phase ? w/o. When oil/ water ratio <0.5, o/w microstructure is formed, and when oil/water ratio >5, w/o microstructure is formed. Well defined interfaces are obtained at the oil/water ratio range from 0.5 to 3 as seen in Fig. 3b–f. It is clearly shown that the head groups of CTAB are immersed in the water phase and the tail groups are located close to the oil phase. Also it is shown from Fig. 3h–j, the number of CTAB molecules at the interface and the thickness of the interface increase obviously with CTAB concentration. The instability of the supersaturated CTAB monolayer at the oil/water interface leads to monolayer collapse. At first, the monolayer increases its interfacial area by the development of curvature (Fig. 3k) and with concentration further enhanced the buckling deformations grow in amplitude (Fig. 3l). Note that the CTAB monolayer curves toward the aqueous phase, which allows penetration of the water into the head group region. Buckling deformation of the CTAB monolayer results in the formation of o/w microstructure (Fig. 3m) and the increase of interfacial area. Analysis of structural variance reveals that electrostatic repulsion interactions between head groups give a positive curvature of the CTAB monolayer. When CTAB concentration is high enough, a liquid crystalline phase is formed as shown in Fig. 3n. These 3D structures bear resemblance to key features of a collapse mode proposed by Milner et al. [44]. They argued that for an oil/water interface in the limit of vanishing, the monolayer collapse may result in the dispersion of oil in water or of water in oil and thereby lead to the formation of a micellar microemulsion. In order to have an insight into the characteristics of the interfacial behavior of CTAB, the interfacial phase in Fig. 3b–f is focused in the following sections. 3.2. Interfacial density
Fig. 2. Diffusion versus simulation time steps for different beads where oil/ water = 1, cCTAB = 0.053.
The density profiles can be obtained according to the snapshot of the simulation, and an example is shown in Fig. 4. The average numbers of water, oil, head, and tail beads per volume unit are plotted across the box. According to the density profiles, the interfacial thickness was calculated by the ‘‘90–10’’ criterion, which is
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Fig. 3. Snapshots of the simulation of oil/water/CTAB system at different oil/water ratios of (a) 0.25, (b) 0.5, (c) 0.75, (d) 1, (e) 2, (f) 3, (g) 5 for cCTAB = 0.053, and at different CTAB concentrations of (h) 0.005, (i) 0.026, (j) 0.053, (k) 0.086, (l) 0.099, (m) 0.176, (n) 0.250 for oil/water = 1. Oil beads are shown in pink, water beads in blue, head group in red and tail group in green. The symbols defined above are also used in the following figures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
defined as the distance along the interface over which the densities of oil from 90% to 10% of their bulk values [29]. To analyze the interfacial density of CTAB molecules at the interface, the density profiles of the oil/water/CTAB ternary system were investigated. Typical mass density profiles for the ternary systems at different CTAB concentrations and oil/water ratios are shown in Fig. 5. In these density profiles, it is clearly shown that the oil and water bulk phases have their own bulk densities, indicating that the system size is fairly large enough to describe the interface between bulk phases and CTAB molecules. CTAB molecules are located mainly at the interface with the head groups in water phase and tail groups in oil phase. A well defined interface exists between the oil and water phases in the system. As we can see, density profiles for the head group and tail group of CTAB obviously grow higher with CTAB concentration, indicating that the monolayer is more highly packed at higher interfacial coverage. The width of the interfacial region becomes obviously wider with CTAB concentration, suggesting that the tails are straighter at higher CTAB concentration. It exhibits the same tendency as the interfacial thickness in Fig. 6a. It is also found that water molecules penetrate into the region up to the head group of the monolayer, which results in the maximum solvation of head groups. Oil molecules mostly permeate into the surfactant tails. With the increase of CTAB concentration, the penetration of oil into the tail region becomes weaker due to the smaller interfacial area per CTAB molecule. With oil/water ratio increasing, the peak height of density profiles for the head group or tail group keeps invariable. This indicates that the packing degree of CTAB molecules at the interface is not influenced by the oil/water ratio. The width of the interfacial region becomes obviously larger with oil/water ratio, suggesting that the surfactant tails are straighter and the angle between the interface normal and the surfactant axis becomes smaller at higher oil/water ratios. It is consistent with the variance of interfacial thickness in Fig. 6a inset that the interface thickens with oil/water ratio.
3.3. Interfacial thickness Interfacial thickness is an important interfacial physical property that provides a quantitative measure for the size of the interface. To understand how the width of the oil/water interface is affected by the presence of CTAB monolayer, we calculate the interfacial thickness at different CTAB concentrations and oil/water ratios. As shown in Fig. 6a, two distinct phase regions are observed. In each, the interfacial thickness has a different dependence on CTAB concentration. In the first region, the interfacial thickness is weakly varied with the increase of CTAB concentration. While in the latter region, the increased CTAB concentration leads to a pronounced expansion of the interfacial thickness. The growth of thickness suggests that surfactant molecules want to be more upright at high concentration. A slightly more detailed analysis of Fig. 6a inset where cCTAB is 0.053 shows that the interface thickens slightly with oil/water ratio increase. This is attributed to the more stretch of hydrophobic tails with the percentage of oil enhanced according to the rule of similarity. It is in agreement with Guo et al.’s results that the interfacial thickness is more dependent on surfactant tail [45]. But at higher CTAB concentration (i.e., cCTAB = 0.086, Fig. 6a inset), one peak of interfacial thickness with oil/water ratio increase is shown because some CTAB molecules are repulsed into the water phase to form o/w swollen micelles. This can be clearly seen in the snapshots in Fig. 6b. So the interfacial thickness decreases instead. 3.4. Interfacial tension A key challenge for the oil industry is to separate oil from the water phase. In the process of separating oil from water, surfactant is very important especially its properties at the oil/water interface. The adsorption of surfactant at the oil/water interface can lower the interfacial tension and promote the mixing of oil and
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Fig. 4. A snapshot of the simulation of oil/water/CTAB system (a) and the average density profile of different beads (b) at oil/water = 1, cCTAB = 0.053.
water. When choosing surfactants available used in enhancing crude oil recovery, one would often like surfactants that reduce the interfacial tension efficiently by adding as little surfactant as possible. So, investigating the interfacial tension of surfactant at the oil/water interface is very valuable for understanding the mechanism of surfactant efficiency in the enhanced crude oil recovery. Therefore, we calculate the entire interfacial tension versus concentration isotherm for different oil/water ratios. The interfacial tension is calculated by dividing the simulation box into a lot of slabs parallel to the interface and calculating the pressure tensor in each slab:
c¼
1 2
Z 0
Lz
1 pzz ðzÞ ðpxx ðzÞ þ pyy ðzÞÞ dz 2
ð5Þ
Here, Lz is the box size in the z direction (the direction normal to the oil/water interface) and pij is the ij component of the pressure tension [43]. The first factor of 1/2 is to account for the two interfaces in the simulation box. Fig. 7a presents the interfacial tension values as a function of CTAB concentration. The overall efficiency of a surfactant depends on two factors: the tendency to adsorb at the interface and its efficiency at the interface. It shows that the interfacial efficiency is enhanced by increasing CTAB concentration. This is in agreement with the experiments and other molecular simulations [37,46]. The interfacial tension shows a rapid decrease with CTAB concentration initially, and then a plateau is reached. The increase of surfactant concentration from 0.004 to 0.1 corresponds to a 90% reduction of the interfacial tension. It shows that CTAB has a high
Fig. 5. Density profiles for water (blue), oil (black), the head groups (red) and the tail groups (green) of surfactants normal to the monolayer interface for different CTAB concentrations at oil/water = 1 (a), and for different oil/water ratios at cCTAB = 0.053 (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
interfacial efficiency at the oil/water interface. At higher concentration, the interfacial tension almost does not depend on CTAB concentration because the interface has been saturated by CTAB molecules and excessive CTAB molecules go into forming swollen micelles rather than to the interface as shown in Fig. 3l. The interfacial tension decreases with the oil/water ratio increasing, as presented in Fig. 7a inset. In other words, the interfacial tension
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Fig. 6. (a) Interfacial thickness versus CTAB concentration for different oil/water ratios. The inset shows the variation of the interfacial thickness against the oil/water ratio at different CTAB concentrations; (b) snapshot of the simulation of oil/water/CTAB system at different oil/water ratios for cCTAB = 0.086.
decreases with the water percentage decreasing. It has the same trend with Chen et al.’s experimental result that the water percentage ranges from 26% to 54%, in which the oil and water phases interpenetrate with each other in the role of surfactant, the interfacial tension increases quickly and then keeps one constant [43]. To characterize the monolayer material properties, we calculate mesoscopic continuum properties such as area compressibility modulus KA according to the following formula [47]
c ¼ K A ðA A0 Þ=A0
ð6Þ
where A is the area per molecule at the interfacial tension of c. At low CTAB concentration, we observe that c displays a roughly linear behavior. We perform the linear fit to all interfacial tension isotherms. From the intersection of each straight fitting line with the horizontal line at zero tension, we can determine the area per surfactant molecule at the tensionless state, which is called the saturated area per molecule (A0). From the slope of c versus (A A0)/ A0 isotherms shown in Fig. 7b, KA can be obtained. We note that
the calculated KA value decreases with an increase in oil/water ratio, which indicates that the higher oil/water ratio, the more compressible the CTAB monolayer is. Unfortunately, there are no experimental or theoretical data to compare the predicted KA values. 3.5. End-to-end distance of CTAB Root mean square (RMS) end-to-end distance (hh2i1/2) is a concept derived from polymer, which describe the degree of curliness in polymer chain [48]. In this paper, hh2i1/2 is quoted to show the orientation of CTAB at the oil/water interface. And the variations of hh2i1/2 might give some information about the structure of CTAB at the interface. To better understand how the arrangement of CTAB molecules is influenced by the concentration and the oil/ water ratio, we discuss the variance of hh2i1/2, as presented in Fig. 8. It is found that hh2i1/2 shows very weak dependence on the oil/ water ratio. But all the curves demonstrate the same trend with
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Fig. 8. hh2i1/2 of CTAB versus concentration for different oil/water ratios.
Fig. 7. (a) Interfacial tension versus CTAB concentration for different oil/water ratios. The inset shows the interfacial tension versus oil/water ratio at cCTAB = 0.053. (b) The variation of the interfacial tension against the reduced relative area change per molecule (A A0)/A0. The area compression modulus KA can be extracted from the slope.
CTAB concentration. An increase in hh2i1/2 is observed obviously with CTAB concentration increase, and after that a plateau is reached. The increase in hh2i1/2 suggests the increase in the orientation of CTAB, and the CTAB chains become straighter at the interface. This is in agreement with Conboy et al.’s experimental results that the conformation of surfactant alkyl chains could be a function of the number density of surfactants at the interface [49,50]. As the interfacial density increases, the degree of conformational mobility within alkyl chains decreases, leading to more ordering. Therefore, CTAB molecules are in somewhat straighter compared to the low concentration. When the interface is saturated by CTAB, the excess molecules cluster together to form a micelle-like structure as shown in Fig. 3k, which has more interfacial areas. 3.6. Order parameter Another quantity used in determining the conformational order of surfactants at the oil/water interface is the orientation order parameter. The order parameter is given in the form
Fig. 9. The order parameter S = h3cos2 h 1i/2 where h is the angle between the bond that connects the head group and the tail group and the normal to the interface.
S¼
1 h3 cos2 h 1i 2
cos h ¼
zij r ij
ð7Þ
ð8Þ
where h is the angle between the interface normal and the molecular axis defined as the united vector from the first to the last bead of the surfactant. The brackets denote the average over all such bonds. Here, rij = ri rj = |rij|, and it is the vector between beads i and j in the surfactant [29]. The quantity S measures the extent to which surfactant molecules stand up along the interface normal. With this definition of the angle h, we can compute the order parameter for a vector between two beads in the surfactant. A value of S = 1 is interpreted as a perfect orientation along the interface normal, while S = 1/2 as an orientation fully parallel to the interface but S = 0 as a random orientation with respect to the interface normal. The variance of S with CTAB concentration and oil/water ratio is shown in Fig. 9 and it helps to obtain more information about the interfacial behavior of CTAB molecules at the interface.
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From Fig. 9, we notice that S is always nonzero. This may be explained by the fact that the molecular orientation is biased toward the interface normal. Another possibility is due to the small size of the system (only a small concentration of molecules, i.e., 0.005, 0.025 and 0.053 were employed), which leads to a poor statistical average. At the same time, we found that S has very weak dependence on oil/water ratio, exhibiting the same trend as observed in the end-to-end distance. However, the order parameter monotonically increases with CTAB concentration increase, thus suggesting that the chain stands up and becomes more ordered. When the surfactant concentration is further increased, the interface begins to bend in order to obtain more areas for more surfactants. It leads to larger angles between the interface normal and the surfactant axis. So the value of S decreases instead with CTAB concentration as seen in Fig. 9. 4. Conclusions In this paper, we perform a series of DPD simulations on the CTAB monolayer at the oil/water interface. The interfacial properties, structural properties, and their dependence on CTAB concentration and the oil/water ratio are investigated in detail. Despite a number of extensive studies of monolayer at the liquid/liquid interface [45,51], to our knowledge, the effect of oil/water ratio on the interfacial properties of CTAB as described here has not been reported in the literature. The simulation results contribute to a better understanding of the interfacial and structural properties of CTAB at the oil/water interface, especially their dependence on the oil/water ratio. This will pave the way for further studies on how surfactants improve flushing efficiency in the enhanced recovery of crude oil. From the snapshots of the system, three different microstructures are observed with the oil/water ratio increasing, spherical oil in water (o/w), interfacial phase, and water in oil (w/o). The number of CTAB molecules at the interface and the interfacial thickness increase obviously with CTAB concentration. This clearly suggests that CTAB molecule is more upright at high concentration. The result is consistent with the interfacial properties of SDS-type surfactant monolayers at the water/trichiloroethylene interface [45]. The interface thickens slightly with oil/water ratio, which is attributed to the more stretch of hydrophobic tails of CTAB according to the rule of similarity. The CTAB molecule is more compressible with the increase in oil/water ratio. CTAB molecules also become straighter with oil/water ratio. They are more highly packed at the interface as the concentration increases, but it is not influenced by the oil/water ratio. The variance of end-to-end distance demonstrates the trend that an increase first, and then a plateau with CTAB concentration. This further shows that with concentration increase, the space available for each CTAB molecule at the interface decreases and the surfactant molecules have to be more ordered and more upright. The order parameter illustrates that at higher concentration, the interface begins to bend even to form a sphere to obtain more areas for extra surfactants, resulting in the decrease in order parameter. At the same time, we can clearly see that CTAB has a high interfacial efficiency with the CTAB concentration and oil/water ratio increasing. In conclusion, the successfully application of DPD simulation method to investigate the properties of CTAB at the oil/water interface, especially the effect of oil/water ratio on the properties, is of great importance for the positive use of surfactant. And it is helpful to advance the development of the colloid and interface science. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 20803069) and the Science Foundation for Excel-
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Contents lists available at ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Investigation of interfacial and structural properties of CTAB at the oil/water interface using dissipative particle dynamics simulations Yiming Li ⇑, Yingyan Guo, Mutai Bao, Xueli Gao Key Laboratory of Marine Chemistry Theory and Technology, Ocean University of China, Ministry of Education, Qingdao 266100, PR China
a r t i c l e
i n f o
Article history: Received 14 March 2011 Accepted 26 May 2011 Available online 13 June 2011 Keywords: Spatial structure Interfacial density Interfacial thickness Interfacial tension Area compressibility modulus End-to-end distance Order parameter
a b s t r a c t We have used dissipative particle dynamics (DPD) to simulate the system of cetyltrimethylammonium bromide (CTAB) monolayer at the oil/water interface. The interfacial properties (interfacial density, interfacial thickness, and interfacial tension), structural properties (area compressibility modulus, end to end distance, and order parameter), and their dependence on the oil/water ratio and the surfactant concentration were investigated. Three different microstructures, spherical oil in water (o/w), interfacial phase, and water in oil (w/o), can be clearly observed with the oil/water ratio increasing. Both the snapshots and the density profiles of the simulation show that a well defined interface exists between the oil and water phases. The interface thickens with CTAB concentration and oil/water ratio. The area compressibility modulus decreases with an increase in the oil/water ratio. The CTAB molecules are more highly packed at the interface and more upright with both concentration and oil/water ratio. The root mean square end-to-end distance and order parameter have a very weak dependence on the oil/water ratio. But both of them show an increase with CTAB concentration, indicating that the surfactant molecules at the interface become more stretched and more ordered at high concentration. As CTAB concentration increases further, the order parameter decreases instead because the bending of the interface. At the same time, it is shown that CTAB has a high interfacial efficiency at the oil/water interface. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Studies of surfactant molecules at the liquid/liquid interfaces have been the subject of investigations for a long time, not only for their scientific interest but also for their applicability in industry, such as pharmaceutical, food technology, plastic, and petroleum industries [1–4]. A typical surfactant molecule consists of the ‘‘head’’ part having a polar or ionic functional group and the ‘‘tail’’ part having a hydrocarbon chain. Owing to possess of both the hydrophilic and hydrophobic character, they can adsorb at the oil/water interface forming a surfactant monolayer, which can effectively reduce the interfacial tension. Today, microemulsions are receiving ever-increasing attention from both practical and theoretical points of view [5,6]. Especially, because of their ability to encapsulate droplets of one material in another; micellar microemulsions may be useful in many applications, from nanoparticle self-assembly to drug delivery. Thus, an important first step to understand microemulsion is to have a molecular level understanding of the surfactant monolayer at the interface. Hence, it is instructive to understand the structure, interfacial properties, ⇑ Corresponding author. Fax: +86 532 66782480. E-mail address: [email protected] (Y. Li). 0021-9797/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2011.05.078
and dynamics of surfactants at the oil/water interface. A deeper investigation of interfacial properties of surfactant monolayer at the oil/water interface is crucial for understanding the workings of surfactant systems from fundamental interests of colloid and interface science, as well as practical applications. In the past decades, a vast number of experimental techniques have been used to investigate the dynamical and structural properties of surfactant systems such as fluorescence [7–10], resonance Raman scattering [11,12], neutron reflection [13–16], second harmonic generation [17,18], nuclear magnetic resonance spectrum [19–21], and vibrational sum-frequency spectroscopy [22]. However, only a few techniques are available for the investigation of oil/water interface, such as nonlinear vibrational sum-frequency spectroscopy and second harmonic generation. So it is difficult to obtain detailed information on the behavior of the surfactant molecules at the interface experimentally. The interfacial molecules typically form only a small fraction of a fluid, and perturbations from bulk structure and dynamics are difficult to measure and distinguish experimentally [23]. Therefore, computer simulations are an attractive alternative to provide additional information on dynamics, distributions, and ordering of surfactants, enhancing the understanding of interfacial properties of surfactants. With the aid of the increase in computational power, computer
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simulations have become a potential method to address the limitations of analytical approaches. To explore the interfacial structure and properties at the molecular level, MD simulation techniques have been widely applied to the study of structure and dynamics of surfactants at the liquid/ liquid interface [24–27]. For instance, Mu et al. studied the interfacial behavior of surfactin methyl ester derivatives at the n-decane/ water interface at low surface coverage by MD simulation. Molecular orientations, structural variability of the peptide ring backbones, interfacial molecular areas, and the motion activities of surfactin derivatives were determined [28]. Dai et al. reported the MD simulation of the in situ self-assembly of nanoparticles and SDS surfactants at a water/trichloroethylene (TCE) interface, highlighting the potential of using the liquid/liquid interface to produce novel nanomaterials [29]. Rivera et al. simulated alkane/water systems containing methanol and reported the surfactant behavior of methanol molecules as they are preferably adsorbed at the interface and reduce the interfacial tension through a rearrangement of the molecules at the interface [30]. All of these studies provide detailed insight into the microscopic structure of surfactant monolayers at the interface between the binary immiscible fluids. However, the time scales accessible to ordinary MD simulations are too short to observe diffusion to the interface and formation of micelles. Simulation at atomic resolution is also computationally very expensive. An alternative approach is to simulate the oil/water/surfactant system at a mesoscopic level. Dissipative particle dynamics (DPD) is a technique that has been developed to simulate fluids at a mesoscopic level [31–33]. Compared with usual dynamics simulations, for example all-atom simulation, the major advantage of DPD is its soft interactions [34,35]. The particles represent molecules or liquid elements rather than atoms, and the soft potential allows for a much larger time step and length scales than which is commonly used in usual dynamic simulations [36]. Although less detailed than MD, it still enables a systematic study of the interfacial properties of surfactant and can point out the mechanisms and surfactant properties that determine the interfacial properties of surfactant at the oil/water interface. However, research on the surfactants at the oil/water interface by DPD simulation is relatively scarce. Live Rekvig et al. have ever used DPD to investigate how variations in size and structure of surfactants influence their ability to reduce the interfacial tension at the oil/water interface [37]. Their simulations reveal that the branching of the hydrophobic tail has a positive effect on the efficiency at the interface only if the head group is hydrophilic enough to maintain a compact layer. Recently, the adsorption of sodium dodecylbenzene sulfonate and sodium oleate at the oil/water interface was simulated [38]. The results show that it is beneficial to decrease interfacial tension if the structure of hydrophobic chain of surfactant and the oil was similar; in addition, the presence of inorganic salts causes the surfactant molecules to form more compact and ordered arrangement and helps to decrease the interfacial tension. Hence, from a practical view, it is instructive to have an understanding of the structure, interfacial properties, and dynamics of surfactant at the liquid/liquid interface. Cetyltrimethylammonium bromide (CTAB) is an important cationic surfactant and is widely used in both fundamental research and many industrial applications. It is well-known that self-assembly of CTAB molecules at liquid/liquid interfaces is essential for the preparation and stabilization of microemulsions, as well as of particular interest for various natural and industrial applications. The structural and dynamic properties of CTAB monolayer formed at the air/water interface have been investigated by Yuan et al. using MD simulation [39]. However, the interfacial behavior of CTAB at the oil/water interface is still not fully understood, and it is of practical value for making further study on this. Taking a panoramic view of the situation, little is known about the stability and dynamics of the CTAB monolayer at the oil/water interface, espe-
cially the effect of oil/water ratio on its interfacial and structural properties, which is very important in the enhanced recovery of crude oil [40]. For this purpose, we take CTAB as an example to investigate the structural and interfacial properties of surfactant at the oil/water interface using DPD simulation. In the present work, the interfacial properties (interfacial density, interfacial thickness and interfacial tension), structural properties (area compressibility modulus, end to end distance and order parameter), and their dependence on the surfactant concentration and the oil/water ratio were investigated in detail. More importantly, these DPD studies conducted here can throw more light on the interfacial behavior of CTAB at the oil/water interface and thereby obtain a more detailed picture of the monolayers. 2. Computational methods 2.1. Dissipative particle dynamics In DPD, conservative, random, and dissipative forces act between two particles i and j which are a distance rij apart.
fi ¼
X
F Cij þ F Rij þ F Dij
ð1Þ
i–j
The first term in the above equation represents a conservative force, which is usually soft repulsive of the form
F Cij ¼
aij ð1 rij =Rc Þ^rij ðrij < Rc Þ 0
ðr ij > Rc Þ
ð2Þ
where aij is a maximum repulsion between particles i and j, rij is the distance between them, with the corresponding unit vector ^rij ; and Rc is a cutoff radius which gives the extent of the interaction range. The other two forces in Eq. (1) are a random force (F Rij ) and a dissipative force (F Dij ).
F Rij ¼ rwR ðr ij Þhij^r ij
ð3Þ
F Dij ¼ gwD ðrij Þð^r ij v ij Þ^r ij
ð4Þ
Here, vij is the velocity difference for the two particles, h is a random number between 0 and 1, and w is the weight function. g is the friction coefficient and r is the noise amplitude. The combined effect of these two forces is a thermostat, which conserves momentum and, hence, gives the correct hydrodynamics at sufficient long time and length scales. aij, r and g determine the amplitude of the conservative, random, and dissipative forces, respectively. The values r = 3 and g = 4.5 are used in this study. The DPD method was described in detail by Groot and Warren [41]. 2.2. Computational models Each molecular bead in the system has equal mass, meaning that the molecular mass of hydrophilic bead (H) and hydrophobic bead (T) are equal. In order to make the molecular mass of tail and head group approximate possible, the surfactant CTAB is divided into two DPD beads that are tied together by a harmonic spring, as shown in Fig. 1. Water and oil are represented by one bead W and O for simplicity. All DPD beads belonging to the same molecule are connected by a loosely bounded spring with a spring force constant K = 4.0 according to Groot’s work [41]. This spring constant controls the stiffness of the molecule, but it is not very sensitive to the simulation result. There are several methods suggested in the literatures to evaluate the interaction parameters for DPD simulation [41]. The quantitative structure–property relationship (QSPR) is based only on the solubility parameter [42]. It is not appropriate for the present
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Fig. 1. DPD model of CTAB molecule, ‘‘H’’ denotes the hydrophilic head group and ‘‘T’’ denotes the hydrophobic tail.
Table 1 Interaction repulsion parameters aij in oil/water/CTAB systema.
H T W O a
H
T
W
O
25.00 177.82 25.34 143.61
177.82 25.00 151.52 25.94
25.34 151.52 25.00 103.24
143.61 25.94 103.24 25.00
sary to illustrate that all the simulation concentration used in this paper is the molar fraction of various molecules in the cube. 3. Results and discussion 3.1. Spatial structure of oil/water/CTAB system
H = head group bead, T = tail group bead, W = water bead and O = oil bead.
system because of a partial charge in CTAB molecular. So we use the interaction repulsion parameters aij in Table 1 calculated by Chen et al. [43] .The calculated interaction energy is very sensitive to these partial charges. The averaged interaction energy is calculated based on the fragments as described above. 2.3. Computational details The size of simulated box is set to 20 10 10 nm (Lx Ly Lz), which contains a total of 6000 beads. Periodic boundary conditions were applied in all three directions. The bead density of systems is set to 3.0. As Hoogerbrugge and Koelman do [34,35], we set the temperature of the system as kBT = 1.0, which effectively specifies pffiffiffia unit of time since root mean square velocity of the particles is 3 from the Maxwell–Boltzmann distribution. A time step of Dt = 0.05 is used for the DPD simulations. The 20,000 DPD steps are adopted in this research in order to obtain the steady and balanceable results. As can be seen from the diffusion plot of the simulation (Fig. 2), equilibrium is reached before 12,000 time steps, so 20,000 time steps per simulation is sufficient for the simulation. It is neces-
One way of characterizing the structure of CTAB molecules at the oil/water interface is to observe the snapshots of the simulation system. The structures of CTAB molecules at the interface with different oil/water ratios and different concentrations are shown in Fig. 3. Three different microstructures, spherical oil in water emulsion (o/w), interfacial phase, and water in oil emulsion (w/o), are observed with the oil/water ratio increasing. It goes the following structure transitions: o/w ? interfacial phase ? w/o. When oil/ water ratio <0.5, o/w microstructure is formed, and when oil/water ratio >5, w/o microstructure is formed. Well defined interfaces are obtained at the oil/water ratio range from 0.5 to 3 as seen in Fig. 3b–f. It is clearly shown that the head groups of CTAB are immersed in the water phase and the tail groups are located close to the oil phase. Also it is shown from Fig. 3h–j, the number of CTAB molecules at the interface and the thickness of the interface increase obviously with CTAB concentration. The instability of the supersaturated CTAB monolayer at the oil/water interface leads to monolayer collapse. At first, the monolayer increases its interfacial area by the development of curvature (Fig. 3k) and with concentration further enhanced the buckling deformations grow in amplitude (Fig. 3l). Note that the CTAB monolayer curves toward the aqueous phase, which allows penetration of the water into the head group region. Buckling deformation of the CTAB monolayer results in the formation of o/w microstructure (Fig. 3m) and the increase of interfacial area. Analysis of structural variance reveals that electrostatic repulsion interactions between head groups give a positive curvature of the CTAB monolayer. When CTAB concentration is high enough, a liquid crystalline phase is formed as shown in Fig. 3n. These 3D structures bear resemblance to key features of a collapse mode proposed by Milner et al. [44]. They argued that for an oil/water interface in the limit of vanishing, the monolayer collapse may result in the dispersion of oil in water or of water in oil and thereby lead to the formation of a micellar microemulsion. In order to have an insight into the characteristics of the interfacial behavior of CTAB, the interfacial phase in Fig. 3b–f is focused in the following sections. 3.2. Interfacial density
Fig. 2. Diffusion versus simulation time steps for different beads where oil/ water = 1, cCTAB = 0.053.
The density profiles can be obtained according to the snapshot of the simulation, and an example is shown in Fig. 4. The average numbers of water, oil, head, and tail beads per volume unit are plotted across the box. According to the density profiles, the interfacial thickness was calculated by the ‘‘90–10’’ criterion, which is
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Fig. 3. Snapshots of the simulation of oil/water/CTAB system at different oil/water ratios of (a) 0.25, (b) 0.5, (c) 0.75, (d) 1, (e) 2, (f) 3, (g) 5 for cCTAB = 0.053, and at different CTAB concentrations of (h) 0.005, (i) 0.026, (j) 0.053, (k) 0.086, (l) 0.099, (m) 0.176, (n) 0.250 for oil/water = 1. Oil beads are shown in pink, water beads in blue, head group in red and tail group in green. The symbols defined above are also used in the following figures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
defined as the distance along the interface over which the densities of oil from 90% to 10% of their bulk values [29]. To analyze the interfacial density of CTAB molecules at the interface, the density profiles of the oil/water/CTAB ternary system were investigated. Typical mass density profiles for the ternary systems at different CTAB concentrations and oil/water ratios are shown in Fig. 5. In these density profiles, it is clearly shown that the oil and water bulk phases have their own bulk densities, indicating that the system size is fairly large enough to describe the interface between bulk phases and CTAB molecules. CTAB molecules are located mainly at the interface with the head groups in water phase and tail groups in oil phase. A well defined interface exists between the oil and water phases in the system. As we can see, density profiles for the head group and tail group of CTAB obviously grow higher with CTAB concentration, indicating that the monolayer is more highly packed at higher interfacial coverage. The width of the interfacial region becomes obviously wider with CTAB concentration, suggesting that the tails are straighter at higher CTAB concentration. It exhibits the same tendency as the interfacial thickness in Fig. 6a. It is also found that water molecules penetrate into the region up to the head group of the monolayer, which results in the maximum solvation of head groups. Oil molecules mostly permeate into the surfactant tails. With the increase of CTAB concentration, the penetration of oil into the tail region becomes weaker due to the smaller interfacial area per CTAB molecule. With oil/water ratio increasing, the peak height of density profiles for the head group or tail group keeps invariable. This indicates that the packing degree of CTAB molecules at the interface is not influenced by the oil/water ratio. The width of the interfacial region becomes obviously larger with oil/water ratio, suggesting that the surfactant tails are straighter and the angle between the interface normal and the surfactant axis becomes smaller at higher oil/water ratios. It is consistent with the variance of interfacial thickness in Fig. 6a inset that the interface thickens with oil/water ratio.
3.3. Interfacial thickness Interfacial thickness is an important interfacial physical property that provides a quantitative measure for the size of the interface. To understand how the width of the oil/water interface is affected by the presence of CTAB monolayer, we calculate the interfacial thickness at different CTAB concentrations and oil/water ratios. As shown in Fig. 6a, two distinct phase regions are observed. In each, the interfacial thickness has a different dependence on CTAB concentration. In the first region, the interfacial thickness is weakly varied with the increase of CTAB concentration. While in the latter region, the increased CTAB concentration leads to a pronounced expansion of the interfacial thickness. The growth of thickness suggests that surfactant molecules want to be more upright at high concentration. A slightly more detailed analysis of Fig. 6a inset where cCTAB is 0.053 shows that the interface thickens slightly with oil/water ratio increase. This is attributed to the more stretch of hydrophobic tails with the percentage of oil enhanced according to the rule of similarity. It is in agreement with Guo et al.’s results that the interfacial thickness is more dependent on surfactant tail [45]. But at higher CTAB concentration (i.e., cCTAB = 0.086, Fig. 6a inset), one peak of interfacial thickness with oil/water ratio increase is shown because some CTAB molecules are repulsed into the water phase to form o/w swollen micelles. This can be clearly seen in the snapshots in Fig. 6b. So the interfacial thickness decreases instead. 3.4. Interfacial tension A key challenge for the oil industry is to separate oil from the water phase. In the process of separating oil from water, surfactant is very important especially its properties at the oil/water interface. The adsorption of surfactant at the oil/water interface can lower the interfacial tension and promote the mixing of oil and
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Fig. 4. A snapshot of the simulation of oil/water/CTAB system (a) and the average density profile of different beads (b) at oil/water = 1, cCTAB = 0.053.
water. When choosing surfactants available used in enhancing crude oil recovery, one would often like surfactants that reduce the interfacial tension efficiently by adding as little surfactant as possible. So, investigating the interfacial tension of surfactant at the oil/water interface is very valuable for understanding the mechanism of surfactant efficiency in the enhanced crude oil recovery. Therefore, we calculate the entire interfacial tension versus concentration isotherm for different oil/water ratios. The interfacial tension is calculated by dividing the simulation box into a lot of slabs parallel to the interface and calculating the pressure tensor in each slab:
c¼
1 2
Z 0
Lz
1 pzz ðzÞ ðpxx ðzÞ þ pyy ðzÞÞ dz 2
ð5Þ
Here, Lz is the box size in the z direction (the direction normal to the oil/water interface) and pij is the ij component of the pressure tension [43]. The first factor of 1/2 is to account for the two interfaces in the simulation box. Fig. 7a presents the interfacial tension values as a function of CTAB concentration. The overall efficiency of a surfactant depends on two factors: the tendency to adsorb at the interface and its efficiency at the interface. It shows that the interfacial efficiency is enhanced by increasing CTAB concentration. This is in agreement with the experiments and other molecular simulations [37,46]. The interfacial tension shows a rapid decrease with CTAB concentration initially, and then a plateau is reached. The increase of surfactant concentration from 0.004 to 0.1 corresponds to a 90% reduction of the interfacial tension. It shows that CTAB has a high
Fig. 5. Density profiles for water (blue), oil (black), the head groups (red) and the tail groups (green) of surfactants normal to the monolayer interface for different CTAB concentrations at oil/water = 1 (a), and for different oil/water ratios at cCTAB = 0.053 (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
interfacial efficiency at the oil/water interface. At higher concentration, the interfacial tension almost does not depend on CTAB concentration because the interface has been saturated by CTAB molecules and excessive CTAB molecules go into forming swollen micelles rather than to the interface as shown in Fig. 3l. The interfacial tension decreases with the oil/water ratio increasing, as presented in Fig. 7a inset. In other words, the interfacial tension
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Fig. 6. (a) Interfacial thickness versus CTAB concentration for different oil/water ratios. The inset shows the variation of the interfacial thickness against the oil/water ratio at different CTAB concentrations; (b) snapshot of the simulation of oil/water/CTAB system at different oil/water ratios for cCTAB = 0.086.
decreases with the water percentage decreasing. It has the same trend with Chen et al.’s experimental result that the water percentage ranges from 26% to 54%, in which the oil and water phases interpenetrate with each other in the role of surfactant, the interfacial tension increases quickly and then keeps one constant [43]. To characterize the monolayer material properties, we calculate mesoscopic continuum properties such as area compressibility modulus KA according to the following formula [47]
c ¼ K A ðA A0 Þ=A0
ð6Þ
where A is the area per molecule at the interfacial tension of c. At low CTAB concentration, we observe that c displays a roughly linear behavior. We perform the linear fit to all interfacial tension isotherms. From the intersection of each straight fitting line with the horizontal line at zero tension, we can determine the area per surfactant molecule at the tensionless state, which is called the saturated area per molecule (A0). From the slope of c versus (A A0)/ A0 isotherms shown in Fig. 7b, KA can be obtained. We note that
the calculated KA value decreases with an increase in oil/water ratio, which indicates that the higher oil/water ratio, the more compressible the CTAB monolayer is. Unfortunately, there are no experimental or theoretical data to compare the predicted KA values. 3.5. End-to-end distance of CTAB Root mean square (RMS) end-to-end distance (hh2i1/2) is a concept derived from polymer, which describe the degree of curliness in polymer chain [48]. In this paper, hh2i1/2 is quoted to show the orientation of CTAB at the oil/water interface. And the variations of hh2i1/2 might give some information about the structure of CTAB at the interface. To better understand how the arrangement of CTAB molecules is influenced by the concentration and the oil/ water ratio, we discuss the variance of hh2i1/2, as presented in Fig. 8. It is found that hh2i1/2 shows very weak dependence on the oil/ water ratio. But all the curves demonstrate the same trend with
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Fig. 8. hh2i1/2 of CTAB versus concentration for different oil/water ratios.
Fig. 7. (a) Interfacial tension versus CTAB concentration for different oil/water ratios. The inset shows the interfacial tension versus oil/water ratio at cCTAB = 0.053. (b) The variation of the interfacial tension against the reduced relative area change per molecule (A A0)/A0. The area compression modulus KA can be extracted from the slope.
CTAB concentration. An increase in hh2i1/2 is observed obviously with CTAB concentration increase, and after that a plateau is reached. The increase in hh2i1/2 suggests the increase in the orientation of CTAB, and the CTAB chains become straighter at the interface. This is in agreement with Conboy et al.’s experimental results that the conformation of surfactant alkyl chains could be a function of the number density of surfactants at the interface [49,50]. As the interfacial density increases, the degree of conformational mobility within alkyl chains decreases, leading to more ordering. Therefore, CTAB molecules are in somewhat straighter compared to the low concentration. When the interface is saturated by CTAB, the excess molecules cluster together to form a micelle-like structure as shown in Fig. 3k, which has more interfacial areas. 3.6. Order parameter Another quantity used in determining the conformational order of surfactants at the oil/water interface is the orientation order parameter. The order parameter is given in the form
Fig. 9. The order parameter S = h3cos2 h 1i/2 where h is the angle between the bond that connects the head group and the tail group and the normal to the interface.
S¼
1 h3 cos2 h 1i 2
cos h ¼
zij r ij
ð7Þ
ð8Þ
where h is the angle between the interface normal and the molecular axis defined as the united vector from the first to the last bead of the surfactant. The brackets denote the average over all such bonds. Here, rij = ri rj = |rij|, and it is the vector between beads i and j in the surfactant [29]. The quantity S measures the extent to which surfactant molecules stand up along the interface normal. With this definition of the angle h, we can compute the order parameter for a vector between two beads in the surfactant. A value of S = 1 is interpreted as a perfect orientation along the interface normal, while S = 1/2 as an orientation fully parallel to the interface but S = 0 as a random orientation with respect to the interface normal. The variance of S with CTAB concentration and oil/water ratio is shown in Fig. 9 and it helps to obtain more information about the interfacial behavior of CTAB molecules at the interface.
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From Fig. 9, we notice that S is always nonzero. This may be explained by the fact that the molecular orientation is biased toward the interface normal. Another possibility is due to the small size of the system (only a small concentration of molecules, i.e., 0.005, 0.025 and 0.053 were employed), which leads to a poor statistical average. At the same time, we found that S has very weak dependence on oil/water ratio, exhibiting the same trend as observed in the end-to-end distance. However, the order parameter monotonically increases with CTAB concentration increase, thus suggesting that the chain stands up and becomes more ordered. When the surfactant concentration is further increased, the interface begins to bend in order to obtain more areas for more surfactants. It leads to larger angles between the interface normal and the surfactant axis. So the value of S decreases instead with CTAB concentration as seen in Fig. 9. 4. Conclusions In this paper, we perform a series of DPD simulations on the CTAB monolayer at the oil/water interface. The interfacial properties, structural properties, and their dependence on CTAB concentration and the oil/water ratio are investigated in detail. Despite a number of extensive studies of monolayer at the liquid/liquid interface [45,51], to our knowledge, the effect of oil/water ratio on the interfacial properties of CTAB as described here has not been reported in the literature. The simulation results contribute to a better understanding of the interfacial and structural properties of CTAB at the oil/water interface, especially their dependence on the oil/water ratio. This will pave the way for further studies on how surfactants improve flushing efficiency in the enhanced recovery of crude oil. From the snapshots of the system, three different microstructures are observed with the oil/water ratio increasing, spherical oil in water (o/w), interfacial phase, and water in oil (w/o). The number of CTAB molecules at the interface and the interfacial thickness increase obviously with CTAB concentration. This clearly suggests that CTAB molecule is more upright at high concentration. The result is consistent with the interfacial properties of SDS-type surfactant monolayers at the water/trichiloroethylene interface [45]. The interface thickens slightly with oil/water ratio, which is attributed to the more stretch of hydrophobic tails of CTAB according to the rule of similarity. The CTAB molecule is more compressible with the increase in oil/water ratio. CTAB molecules also become straighter with oil/water ratio. They are more highly packed at the interface as the concentration increases, but it is not influenced by the oil/water ratio. The variance of end-to-end distance demonstrates the trend that an increase first, and then a plateau with CTAB concentration. This further shows that with concentration increase, the space available for each CTAB molecule at the interface decreases and the surfactant molecules have to be more ordered and more upright. The order parameter illustrates that at higher concentration, the interface begins to bend even to form a sphere to obtain more areas for extra surfactants, resulting in the decrease in order parameter. At the same time, we can clearly see that CTAB has a high interfacial efficiency with the CTAB concentration and oil/water ratio increasing. In conclusion, the successfully application of DPD simulation method to investigate the properties of CTAB at the oil/water interface, especially the effect of oil/water ratio on the properties, is of great importance for the positive use of surfactant. And it is helpful to advance the development of the colloid and interface science. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 20803069) and the Science Foundation for Excel-
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