Journal of Colloid and Interface Science 361 (2011) 573–580

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Journal of Colloid and Interface Science

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Investigation of interfacial and structural properties of CTAB at the oil/waterinterface using dissipative particle dynamics simulations

Yiming Li ⇑, Yingyan Guo, Mutai Bao, Xueli GaoKey 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 2011Accepted 26 May 2011Available online 13 June 2011

Keywords:Spatial structureInterfacial densityInterfacial thicknessInterfacial tensionArea compressibility modulusEnd-to-end distanceOrder parameter

0021-9797/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.jcis.2011.05.078

⇑ Corresponding author. Fax: +86 532 66782480.E-mail address: liym@ouc.edu.cn (Y. Li).

a b s t r a c t

We have used dissipative particle dynamics (DPD) to simulate the system of cetyltrimethylammoniumbromide (CTAB) monolayer at the oil/water interface. The interfacial properties (interfacial density, inter-facial thickness, and interfacial tension), structural properties (area compressibility modulus, end to enddistance, and order parameter), and their dependence on the oil/water ratio and the surfactant concen-tration 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 andthe density profiles of the simulation show that a well defined interface exists between the oil and waterphases. The interface thickens with CTAB concentration and oil/water ratio. The area compressibilitymodulus decreases with an increase in the oil/water ratio. The CTAB molecules are more highly packedat the interface and more upright with both concentration and oil/water ratio. The root mean squareend-to-end distance and order parameter have a very weak dependence on the oil/water ratio. But bothof them show an increase with CTAB concentration, indicating that the surfactant molecules at the inter-face become more stretched and more ordered at high concentration. As CTAB concentration increasesfurther, 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.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

Studies of surfactant molecules at the liquid/liquid interfaceshave been the subject of investigations for a long time, not onlyfor their scientific interest but also for their applicability in indus-try, such as pharmaceutical, food technology, plastic, and petro-leum industries [1–4]. A typical surfactant molecule consists ofthe ‘‘head’’ part having a polar or ionic functional group and the‘‘tail’’ part having a hydrocarbon chain. Owing to possess of boththe hydrophilic and hydrophobic character, they can adsorb atthe oil/water interface forming a surfactant monolayer, whichcan effectively reduce the interfacial tension. Today, microemul-sions are receiving ever-increasing attention from both practicaland theoretical points of view [5,6]. Especially, because of theirability to encapsulate droplets of one material in another; micellarmicroemulsions may be useful in many applications, from nano-particle self-assembly to drug delivery. Thus, an important firststep to understand microemulsion is to have a molecular levelunderstanding of the surfactant monolayer at the interface. Hence,it is instructive to understand the structure, interfacial properties,

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and dynamics of surfactants at the oil/water interface. A deeperinvestigation of interfacial properties of surfactant monolayer atthe oil/water interface is crucial for understanding the workingsof surfactant systems from fundamental interests of colloid andinterface science, as well as practical applications.

In the past decades, a vast number of experimental techniqueshave been used to investigate the dynamical and structural proper-ties of surfactant systems such as fluorescence [7–10], resonanceRaman scattering [11,12], neutron reflection [13–16], second har-monic generation [17,18], nuclear magnetic resonance spectrum[19–21], and vibrational sum-frequency spectroscopy [22]. How-ever, only a few techniques are available for the investigation ofoil/water interface, such as nonlinear vibrational sum-frequencyspectroscopy and second harmonic generation. So it is difficult toobtain detailed information on the behavior of the surfactant mol-ecules at the interface experimentally. The interfacial moleculestypically form only a small fraction of a fluid, and perturbationsfrom bulk structure and dynamics are difficult to measure anddistinguish experimentally [23]. Therefore, computer simulationsare an attractive alternative to provide additional information ondynamics, distributions, and ordering of surfactants, enhancingthe understanding of interfacial properties of surfactants. Withthe aid of the increase in computational power, computer

574 Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580

simulations have become a potential method to address the limita-tions of analytical approaches.

To explore the interfacial structure and properties at the molec-ular level, MD simulation techniques have been widely applied tothe study of structure and dynamics of surfactants at the liquid/liquid interface [24–27]. For instance, Mu et al. studied the interfa-cial behavior of surfactin methyl ester derivatives at the n-decane/water interface at low surface coverage by MD simulation. Molecu-lar orientations, structural variability of the peptide ring backbones,interfacial molecular areas, and the motion activities of surfactinderivatives were determined [28]. Dai et al. reported the MD simu-lation of the in situ self-assembly of nanoparticles and SDS surfac-tants at a water/trichloroethylene (TCE) interface, highlighting thepotential of using the liquid/liquid interface to produce novelnanomaterials [29]. Rivera et al. simulated alkane/water systemscontaining methanol and reported the surfactant behavior of meth-anol molecules as they are preferably adsorbed at the interface andreduce the interfacial tension through a rearrangement of the mol-ecules at the interface [30]. All of these studies provide detailedinsight into the microscopic structure of surfactant monolayers atthe interface between the binary immiscible fluids. However, thetime scales accessible to ordinary MD simulations are too short toobserve diffusion to the interface and formation of micelles. Simula-tion at atomic resolution is also computationally very expensive. Analternative approach is to simulate the oil/water/surfactant systemat a mesoscopic level. Dissipative particle dynamics (DPD) is a tech-nique that has been developed to simulate fluids at a mesoscopiclevel [31–33]. Compared with usual dynamics simulations, forexample all-atom simulation, the major advantage of DPD is its softinteractions [34,35]. The particles represent molecules or liquid ele-ments rather than atoms, and the soft potential allows for a muchlarger time step and length scales than which is commonly usedin usual dynamic simulations [36]. Although less detailed thanMD, it still enables a systematic study of the interfacial propertiesof surfactant and can point out the mechanisms and surfactantproperties that determine the interfacial properties of surfactantat the oil/water interface. However, research on the surfactants atthe oil/water interface by DPD simulation is relatively scarce. LiveRekvig et al. have ever used DPD to investigate how variations insize and structure of surfactants influence their ability to reducethe interfacial tension at the oil/water interface [37]. Their simula-tions reveal that the branching of the hydrophobic tail has a positiveeffect on the efficiency at the interface only if the head group ishydrophilic enough to maintain a compact layer. Recently, theadsorption of sodium dodecylbenzene sulfonate and sodium oleateat the oil/water interface was simulated [38]. The results show thatit is beneficial to decrease interfacial tension if the structure ofhydrophobic chain of surfactant and the oil was similar; in addition,the presence of inorganic salts causes the surfactant molecules toform more compact and ordered arrangement and helps to decreasethe interfacial tension. Hence, from a practical view, it is instructiveto have an understanding of the structure, interfacial properties, anddynamics of surfactant at the liquid/liquid interface.

Cetyltrimethylammonium bromide (CTAB) is an important cat-ionic surfactant and is widely used in both fundamental researchand many industrial applications. It is well-known that self-assem-bly of CTAB molecules at liquid/liquid interfaces is essential for thepreparation and stabilization of microemulsions, as well as of par-ticular interest for various natural and industrial applications. Thestructural and dynamic properties of CTAB monolayer formed atthe air/water interface have been investigated by Yuan et al. usingMD simulation [39]. However, the interfacial behavior of CTAB atthe oil/water interface is still not fully understood, and it is of prac-tical value for making further study on this. Taking a panoramicview of the situation, little is known about the stability anddynamics of the CTAB monolayer at the oil/water interface, espe-

cially the effect of oil/water ratio on its interfacial and structuralproperties, which is very important in the enhanced recovery ofcrude oil [40]. For this purpose, we take CTAB as an example toinvestigate the structural and interfacial properties of surfactantat the oil/water interface using DPD simulation. In the presentwork, the interfacial properties (interfacial density, interfacialthickness and interfacial tension), structural properties (area com-pressibility modulus, end to end distance and order parameter),and their dependence on the surfactant concentration and theoil/water ratio were investigated in detail. More importantly, theseDPD studies conducted here can throw more light on the interfacialbehavior of CTAB at the oil/water interface and thereby obtain amore detailed picture of the monolayers.

2. Computational methods

2.1. Dissipative particle dynamics

In DPD, conservative, random, and dissipative forces actbetween two particles i and j which are a distance rij apart.

fi ¼Xi–j

FCij þ FR

ij þ FDij

� �ð1Þ

The first term in the above equation represents a conservative force,which is usually soft repulsive of the form

FCij ¼

aijð1� rij=RcÞr̂ij ðrij < RcÞ0 ðrij > RcÞ

�ð2Þ

where aij is a maximum repulsion between particles i and j, rij is thedistance between them, with the corresponding unit vector r̂ij; andRc is a cutoff radius which gives the extent of the interaction range.

The other two forces in Eq. (1) are a random force (FRij) and a dis-

sipative force (FDij ).

FRij ¼ rwRðrijÞhij r̂ij ð3Þ

FDij ¼ �gwDðrijÞðr̂ij � v ijÞr̂ij ð4Þ

Here, vij is the velocity difference for the two particles, h is a randomnumber between 0 and 1, and w is the weight function. g is the fric-tion coefficient and r is the noise amplitude. The combined effect ofthese two forces is a thermostat, which conserves momentum and,hence, gives the correct hydrodynamics at sufficient long time andlength scales. aij, r and g determine the amplitude of the conserva-tive, random, and dissipative forces, respectively. The values r = 3and g = 4.5 are used in this study. The DPD method was describedin detail by Groot and Warren [41].

2.2. Computational models

Each molecular bead in the system has equal mass, meaningthat the molecular mass of hydrophilic bead (H) and hydrophobicbead (T) are equal. In order to make the molecular mass of tail andhead group approximate possible, the surfactant CTAB is dividedinto two DPD beads that are tied together by a harmonic spring,as shown in Fig. 1. Water and oil are represented by one bead Wand O for simplicity. All DPD beads belonging to the same moleculeare connected by a loosely bounded spring with a spring force con-stant K = 4.0 according to Groot’s work [41]. This spring constantcontrols the stiffness of the molecule, but it is not very sensitiveto the simulation result.

There are several methods suggested in the literatures to eval-uate the interaction parameters for DPD simulation [41]. The quan-titative structure–property relationship (QSPR) is based only onthe solubility parameter [42]. It is not appropriate for the present

Fig. 1. DPD model of CTAB molecule, ‘‘H’’ denotes the hydrophilic head group and ‘‘T’’ denotes the hydrophobic tail.

Table 1Interaction repulsion parameters aij in oil/water/CTAB systema.

H T W O

H 25.00 177.82 25.34 143.61T 177.82 25.00 151.52 25.94W 25.34 151.52 25.00 103.24O 143.61 25.94 103.24 25.00

a H = head group bead, T = tail group bead, W = water bead and O = oil bead.

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system because of a partial charge in CTAB molecular. So we usethe interaction repulsion parameters aij in Table 1 calculated byChen et al. [43] .The calculated interaction energy is very sensitiveto these partial charges. The averaged interaction energy is calcu-lated 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 conditionswere applied in all three directions. The bead density of systems isset to 3.0. As Hoogerbrugge and Koelman do [34,35], we set the tem-perature of the system as kBT = 1.0, which effectively specifies a unitof time since root mean square velocity of the particles is

ffiffiffi3p

fromthe Maxwell–Boltzmann distribution. A time step of Dt = 0.05 isused for the DPD simulations. The 20,000 DPD steps are adoptedin this research in order to obtain the steady and balanceable re-sults. As can be seen from the diffusion plot of the simulation(Fig. 2), equilibrium is reached before 12,000 time steps, so 20,000time steps per simulation is sufficient for the simulation. It is neces-

Fig. 2. Diffusion versus simulation time steps for different beads where oil/water = 1, cCTAB = 0.053.

sary to illustrate that all the simulation concentration used in thispaper is the molar fraction of various molecules in the cube.

3. Results and discussion

3.1. Spatial structure of oil/water/CTAB system

One way of characterizing the structure of CTAB molecules atthe oil/water interface is to observe the snapshots of the simula-tion system. The structures of CTAB molecules at the interface withdifferent oil/water ratios and different concentrations are shown inFig. 3. Three different microstructures, spherical oil in water emul-sion (o/w), interfacial phase, and water in oil emulsion (w/o), areobserved with the oil/water ratio increasing. It goes the followingstructure transitions: o/w ? interfacial phase ? w/o. When oil/water ratio <0.5, o/w microstructure is formed, and when oil/waterratio >5, w/o microstructure is formed. Well defined interfaces areobtained at the oil/water ratio range from 0.5 to 3 as seen inFig. 3b–f. It is clearly shown that the head groups of CTAB are im-mersed in the water phase and the tail groups are located close tothe oil phase. Also it is shown from Fig. 3h–j, the number of CTABmolecules at the interface and the thickness of the interface in-crease obviously with CTAB concentration. The instability of thesupersaturated CTAB monolayer at the oil/water interface leadsto monolayer collapse. At first, the monolayer increases its interfa-cial area by the development of curvature (Fig. 3k) and with con-centration further enhanced the buckling deformations grow inamplitude (Fig. 3l). Note that the CTAB monolayer curves towardthe aqueous phase, which allows penetration of the water intothe head group region. Buckling deformation of the CTAB mono-layer results in the formation of o/w microstructure (Fig. 3m)and the increase of interfacial area. Analysis of structural variancereveals that electrostatic repulsion interactions between headgroups give a positive curvature of the CTAB monolayer. WhenCTAB concentration is high enough, a liquid crystalline phase isformed as shown in Fig. 3n. These 3D structures bear resemblanceto 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 wateror of water in oil and thereby lead to the formation of a micellarmicroemulsion.

In order to have an insight into the characteristics of the inter-facial behavior of CTAB, the interfacial phase in Fig. 3b–f is focusedin the following sections.

3.2. Interfacial density

The density profiles can be obtained according to the snapshotof the simulation, and an example is shown in Fig. 4. The averagenumbers of water, oil, head, and tail beads per volume unit areplotted across the box. According to the density profiles, the inter-facial thickness was calculated by the ‘‘90–10’’ criterion, which is

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 differentCTAB 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 inred 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 isreferred to the web version of this article.)

576 Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580

defined as the distance along the interface over which the densitiesof oil from 90% to 10% of their bulk values [29].

To analyze the interfacial density of CTAB molecules at theinterface, the density profiles of the oil/water/CTAB ternary systemwere investigated. Typical mass density profiles for the ternarysystems at different CTAB concentrations and oil/water ratios areshown in Fig. 5. In these density profiles, it is clearly shown thatthe oil and water bulk phases have their own bulk densities, indi-cating that the system size is fairly large enough to describe theinterface between bulk phases and CTAB molecules. CTAB mole-cules are located mainly at the interface with the head groups inwater phase and tail groups in oil phase. A well defined interfaceexists between the oil and water phases in the system.

As we can see, density profiles for the head group and tail groupof CTAB obviously grow higher with CTAB concentration, indicatingthat the monolayer is more highly packed at higher interfacial cov-erage. The width of the interfacial region becomes obviously widerwith CTAB concentration, suggesting that the tails are straighter athigher CTAB concentration. It exhibits the same tendency as theinterfacial thickness in Fig. 6a. It is also found that water moleculespenetrate into the region up to the head group of the monolayer,which results in the maximum solvation of head groups. Oil mole-cules mostly permeate into the surfactant tails. With the increaseof CTAB concentration, the penetration of oil into the tail region be-comes weaker due to the smaller interfacial area per CTAB molecule.

With oil/water ratio increasing, the peak height of density pro-files for the head group or tail group keeps invariable. This indicatesthat the packing degree of CTAB molecules at the interface is notinfluenced by the oil/water ratio. The width of the interfacial regionbecomes obviously larger with oil/water ratio, suggesting that thesurfactant tails are straighter and the angle between the interfacenormal and the surfactant axis becomes smaller at higher oil/waterratios. It is consistent with the variance of interfacial thickness inFig. 6a inset that the interface thickens with oil/water ratio.

3.3. Interfacial thickness

Interfacial thickness is an important interfacial physical prop-erty that provides a quantitative measure for the size of theinterface. To understand how the width of the oil/water interfaceis affected by the presence of CTAB monolayer, we calculate theinterfacial thickness at different CTAB concentrations and oil/waterratios. As shown in Fig. 6a, two distinct phase regions are observed.In each, the interfacial thickness has a different dependence onCTAB concentration. In the first region, the interfacial thickness isweakly varied with the increase of CTAB concentration. While inthe latter region, the increased CTAB concentration leads to a pro-nounced expansion of the interfacial thickness. The growth ofthickness suggests that surfactant molecules want to be more up-right at high concentration. A slightly more detailed analysis ofFig. 6a inset where cCTAB is 0.053 shows that the interface thickensslightly with oil/water ratio increase. This is attributed to the morestretch of hydrophobic tails with the percentage of oil enhancedaccording to the rule of similarity. It is in agreement with Guoet al.’s results that the interfacial thickness is more dependent onsurfactant tail [45]. But at higher CTAB concentration (i.e.,cCTAB = 0.086, Fig. 6a inset), one peak of interfacial thickness withoil/water ratio increase is shown because some CTAB moleculesare repulsed into the water phase to form o/w swollen micelles.This can be clearly seen in the snapshots in Fig. 6b. So the interfa-cial thickness decreases instead.

3.4. Interfacial tension

A key challenge for the oil industry is to separate oil from thewater phase. In the process of separating oil from water, surfactantis very important especially its properties at the oil/water inter-face. The adsorption of surfactant at the oil/water interface canlower the interfacial tension and promote the mixing of oil and

Fig. 4. A snapshot of the simulation of oil/water/CTAB system (a) and the averagedensity profile of different beads (b) at oil/water = 1, cCTAB = 0.053.

Fig. 5. Density profiles for water (blue), oil (black), the head groups (red) and thetail groups (green) of surfactants normal to the monolayer interface for differentCTAB concentrations at oil/water = 1 (a), and for different oil/water ratios atcCTAB = 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.)

Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580 577

water. When choosing surfactants available used in enhancingcrude oil recovery, one would often like surfactants that reducethe interfacial tension efficiently by adding as little surfactant aspossible. So, investigating the interfacial tension of surfactant atthe oil/water interface is very valuable for understanding themechanism of surfactant efficiency in the enhanced crude oilrecovery.

Therefore, we calculate the entire interfacial tension versus con-centration isotherm for different oil/water ratios. The interfacialtension is calculated by dividing the simulation box into a lot ofslabs parallel to the interface and calculating the pressure tensorin each slab:

c ¼ 12

Z Lz

0pzzðzÞ �

12ðpxxðzÞ þ pyyðzÞÞ

� �dz ð5Þ

Here, Lz is the box size in the z direction (the direction normal to theoil/water interface) and pij is the ij component of the pressure ten-sion [43]. The first factor of 1/2 is to account for the two interfacesin the simulation box.

Fig. 7a presents the interfacial tension values as a function ofCTAB concentration. The overall efficiency of a surfactant dependson two factors: the tendency to adsorb at the interface and its effi-ciency at the interface. It shows that the interfacial efficiency isenhanced by increasing CTAB concentration. This is in agreementwith the experiments and other molecular simulations [37,46].The interfacial tension shows a rapid decrease with CTAB concen-tration initially, and then a plateau is reached. The increase of sur-factant concentration from 0.004 to 0.1 corresponds to a 90%reduction of the interfacial tension. It shows that CTAB has a high

interfacial efficiency at the oil/water interface. At higher concen-tration, the interfacial tension almost does not depend on CTABconcentration because the interface has been saturated by CTABmolecules and excessive CTAB molecules go into forming swollenmicelles rather than to the interface as shown in Fig. 3l. The inter-facial tension decreases with the oil/water ratio increasing, as pre-sented in Fig. 7a inset. In other words, the interfacial tension

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 atdifferent CTAB concentrations; (b) snapshot of the simulation of oil/water/CTAB system at different oil/water ratios for cCTAB = 0.086.

578 Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580

decreases with the water percentage decreasing. It has the sametrend with Chen et al.’s experimental result that the water percent-age ranges from 26% to 54%, in which the oil and water phasesinterpenetrate with each other in the role of surfactant, the inter-facial tension increases quickly and then keeps one constant [43].

To characterize the monolayer material properties, we calculatemesoscopic continuum properties such as area compressibilitymodulus KA according to the following formula [47]

c ¼ KAðA� A0Þ=A0 ð6Þ

where A is the area per molecule at the interfacial tension of c. Atlow CTAB concentration, we observe that c displays a roughly linearbehavior. We perform the linear fit to all interfacial tension iso-therms. From the intersection of each straight fitting line with thehorizontal line at zero tension, we can determine the area per sur-factant molecule at the tensionless state, which is called the satu-rated 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 compress-ible the CTAB monolayer is. Unfortunately, there are no experimen-tal 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 con-cept derived from polymer, which describe the degree of curlinessin polymer chain [48]. In this paper, hh2i1/2 is quoted to show theorientation of CTAB at the oil/water interface. And the variationsof hh2i1/2 might give some information about the structure of CTABat the interface. To better understand how the arrangement ofCTAB molecules is influenced by the concentration and the oil/water ratio, we discuss the variance of hh2i1/2, as presented inFig. 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

Fig. 7. (a) Interfacial tension versus CTAB concentration for different oil/waterratios. 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 changeper molecule (A � A0)/A0. The area compression modulus KA can be extracted fromthe slope.

Fig. 8. hh2i1/2 of CTAB versus concentration for different oil/water ratios.

Fig. 9. The order parameter S = h3cos2 h �1i/2 where h is the angle between thebond that connects the head group and the tail group and the normal to theinterface.

Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580 579

CTAB concentration. An increase in hh2i1/2 is observed obviouslywith CTAB concentration increase, and after that a plateau isreached. The increase in hh2i1/2 suggests the increase in the orien-tation of CTAB, and the CTAB chains become straighter at the inter-face. This is in agreement with Conboy et al.’s experimental resultsthat the conformation of surfactant alkyl chains could be a functionof the number density of surfactants at the interface [49,50]. As theinterfacial density increases, the degree of conformational mobilitywithin alkyl chains decreases, leading to more ordering. Therefore,CTAB molecules are in somewhat straighter compared to the lowconcentration. When the interface is saturated by CTAB, the excessmolecules cluster together to form a micelle-like structure asshown in Fig. 3k, which has more interfacial areas.

3.6. Order parameter

Another quantity used in determining the conformational orderof surfactants at the oil/water interface is the orientation orderparameter. The order parameter is given in the form

S ¼ 12h3 cos2 h� 1i ð7Þ

cos h ¼ zij

rijð8Þ

where h is the angle between the interface normal and the molecu-lar axis defined as the united vector from the first to the last bead ofthe 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 inthe surfactant [29]. The quantity S measures the extent to whichsurfactant molecules stand up along the interface normal. With thisdefinition of the angle h, we can compute the order parameter for avector between two beads in the surfactant. A value of S = 1 is inter-preted as a perfect orientation along the interface normal, whileS = �1/2 as an orientation fully parallel to the interface but S = 0as a random orientation with respect to the interface normal. Thevariance of S with CTAB concentration and oil/water ratio is shownin Fig. 9 and it helps to obtain more information about the interfa-cial behavior of CTAB molecules at the interface.

580 Y. Li et al. / Journal of Colloid and Interface Science 361 (2011) 573–580

From Fig. 9, we notice that S is always nonzero. This may be ex-plained by the fact that the molecular orientation is biased towardthe interface normal. Another possibility is due to the small size ofthe system (only a small concentration of molecules, i.e., 0.005,0.025 and 0.053 were employed), which leads to a poor statisticalaverage. At the same time, we found that S has very weak depen-dence on oil/water ratio, exhibiting the same trend as observed inthe end-to-end distance. However, the order parameter monotoni-cally increases with CTAB concentration increase, thus suggestingthat the chain stands up and becomes more ordered. When the sur-factant concentration is further increased, the interface begins tobend in order to obtain more areas for more surfactants. It leads tolarger angles between the interface normal and the surfactant axis.So the value of S decreases instead with CTAB concentration as seenin Fig. 9.

4. Conclusions

In this paper, we perform a series of DPD simulations on the CTABmonolayer at the oil/water interface. The interfacial properties,structural properties, and their dependence on CTAB concentrationand the oil/water ratio are investigated in detail. Despite a numberof extensive studies of monolayer at the liquid/liquid interface[45,51], to our knowledge, the effect of oil/water ratio on the inter-facial properties of CTAB as described here has not been reported inthe literature. The simulation results contribute to a better under-standing of the interfacial and structural properties of CTAB at theoil/water interface, especially their dependence on the oil/water ra-tio. This will pave the way for further studies on how surfactants im-prove flushing efficiency in the enhanced recovery of crude oil.

From the snapshots of the system, three different microstruc-tures are observed with the oil/water ratio increasing, sphericaloil in water (o/w), interfacial phase, and water in oil (w/o). Thenumber of CTAB molecules at the interface and the interfacialthickness increase obviously with CTAB concentration. This clearlysuggests that CTAB molecule is more upright at high concentration.The result is consistent with the interfacial properties of SDS-typesurfactant monolayers at the water/trichiloroethylene interface[45]. The interface thickens slightly with oil/water ratio, which isattributed to the more stretch of hydrophobic tails of CTAB accord-ing to the rule of similarity. The CTAB molecule is more compress-ible with the increase in oil/water ratio. CTAB molecules alsobecome straighter with oil/water ratio. They are more highlypacked at the interface as the concentration increases, but it isnot influenced by the oil/water ratio. The variance of end-to-enddistance demonstrates the trend that an increase first, and then aplateau with CTAB concentration. This further shows that withconcentration increase, the space available for each CTAB moleculeat the interface decreases and the surfactant molecules have to bemore ordered and more upright. The order parameter illustratesthat at higher concentration, the interface begins to bend even toform a sphere to obtain more areas for extra surfactants, resultingin the decrease in order parameter. At the same time, we canclearly see that CTAB has a high interfacial efficiency with the CTABconcentration and oil/water ratio increasing.

In conclusion, the successfully application of DPD simulationmethod to investigate the properties of CTAB at the oil/water inter-face, especially the effect of oil/water ratio on the properties, is ofgreat importance for the positive use of surfactant. And it is helpfulto advance the development of the colloid and interface science.

Acknowledgments

This work is supported by the National Natural Science Founda-tion of China (No. 20803069) and the Science Foundation for Excel-

lent Middle & Young Scientist of Shandong Province (BS2010CL050).

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