Jule Ma,Peiwen Xiao,Pingmei Wang,Xue Han,Jianhui Luo,Ruifang Shi,Xuan Wang,Xianyu Song,Shuangliang Zhao,5,*

1 State Key Laboratory of Chemical Engineering and School of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

2 Research Institute of Petroleum Exploration &Development (RIPED),PetroChina,Beijing 100083,China

3 Key Laboratory of Nano Chemistry (KLNC),CNPC,Beijing 100083,China

4 Key Laboratory of Water Environment Evolution and Pollution Control in Three Gorges Reservoir,School of Environmental and Chemical Engineering,Chongqing Three Gorges University,Chongqing 404100,China

5 Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology and School of Chemistry and Chemical Engineering,Guangxi University,Nanning 530004,China

Keywords:Surfactants Interface Interfacial tension π-π stacking Microemulsion Molecular simulation

ABSTRACT Whereas the π-π stacking interactions at oil/water interfaces can affect interfacial structures hence the interfacial properties,the underlying microscopic mechanism remains largely unknown.We reported an all-atom molecular dynamics(MD)simulation study to demonstrate how the Gemini surfactants with pyrenyl groups affect the interfacial properties,structural conformations,and the motion of molecules in the water/n-octane/surfactant ternary systems.It is found that the pyrenyl groups tend to be vertical to the interface owing to the π-π stacking interaction.Besides,a synergistic effect between the π-π interaction and steric hindrance is found,which jointly affects the coalescence of liquid droplets.Therefore,the existence of aromatic groups and a moderate number of surfactants helps to form microemulsion.This work provides a molecular understanding of Gemini surfactants with aromatic groups in microemulsion preparation and applications.

1.Introduction

Gemini surfactants,endowed with double chains consisting of two hydrophilic heads and two hydrophobic tails,have attracted increasing attentions from both industry and academy [1].Compared with conventional single-chain surfactants,Gemini surfactants have high interfacial efficiency [2],and thus are widely utilized in many fields including soil remediation[3],soap[4],pigment industries [5],and enhanced oil recovery [6,7].

A well-studied category of Gemini surfactants is theN,N-bis[(dimethyl alkyl)-α,ω-alkanediammonium dibromide] surfactants,usually designated asm-s-mtype Gemini surfactant.Here,mrepresents the number of carbon atoms in the hydrophobic tails andsmeans the number of carbon atoms in the polymethylene spacer area [8].For instance,the molecular formula,C12H25N+(CH3)2-C3H6-N+(CH3)2C12H25,can be designated as 12-3-12.In recent decades,this category of surfactants has been comprehensively investigated through fundamental experimental and/or theoretical methods.Khuranaet al.[9]explored the structural effect of Gemini surfactant by increasing the length of the spacer,and they found that the surfactant molecules with long spacer could penetrate into the aqueous phase and form a rippled surface.Wanget al.[10]performed coarse-grained molecular dynamics simulations for studying the formation mechanism of wormlike micelle from the selfassembly of Gemini surfactants,and they showed that a directional micellar transformation was favorable to encapsulate the hydrophobic parts of surfactants as well as to decrease the system total energy.Besides,Chenet al.[11]and Tuet al.[12]investigated the photoresponsive behaviors of wormlike micelles constructed bym-s-mtype Gemini surfactants,and explored the effects of chemical groups on macrophenomena and micro-interaction in these micellar systems.In addition,Fenget al.[13] synthesized a series of sulfate Gemini surfactants with different lengths of the hydrophobic tails and spacer groups for testing the foam stabilization performance in their individual systems,and they concluded that increasing the length of hydrophobic tail or reducing the length of the spacer is favorable for foam stability.

Besides the aliphatic groups in Gemini surfactants,the aromatic groups such as phenyl,naphthyl and pyrenyl groups are also examined.For example,Muslimet al.[14,15]prepared a series of asymmetric Gemini surfactants by introducing pyrenyl groups in the hydrophobic tails,and they investigated the properties including the critical micelle concentration (CMC) and surface tension (γ),and found that a low CMC can be obtained for the system with π-π stacking among the surfactants.

The π-π stacking represents one of the noncovalent interactions[16].The π-π stacking,synergizing with other noncovalent interactions such as electrostatic interaction and hydrophobic attraction,can provide a more convenient way to regulate the microtopology of the system.Therefore,the Gemini surfactants with ππ stacking display versatile self-assembled behaviors and superior properties owing to their unique molecular structure.The π-π stacking has been studied in a series of complex systems including carbon nanotube,graphene oxide and components with aromatic groups [17-19].However,there still remains largely unknown regarding the underlying mechanism by which the π-π interactions affect the interfacial structure and thus the associated properties of an oil/water interface.

MD simulation represents a powerful approach to explore the microscopic structural characteristics [20],and thus has been widely employed to study interfacial properties in emulsion/microemulsion systems[21-24].Herein,we consider the Gemini surfactants with pyrenyl groups in the hydrophobic tails,and explore how the pyrenyl groups influence the interfacial accumulation through π-π stacking by using MD simulation.

The remainder of this work is organized as follows: the system modeling together with the details of MD simulations are laid out in the next section.Subsequently,the validation of the model interfacial system is discussed in Section 3,and the interfacial properties and coalescence of droplets are investigated in the biphasic interface systems and droplet systems,respectively.Finally,a brief conclusion is given in Section 4.

2.Computational Methodology

2.1.Modeling and molecular structure

The simulation systems are composed of three components,viz.n-octane,water and surfactant.Herein,three kinds of surfactants are considered,and their structures are depicted in Fig.1,along with the molecular structures of water and octane.For clarity,the conventional molecular formula,i.e.,them-s-ntype,and the abbreviation of these surfactants are listed in Table 1.

The simulation systems can be divided into two categories: (1)surface systems for validating the constructed model system;and(2) interfacial systems for analyzing the interfacial properties and droplets interaction.Therefore,four types of model systems are considered and exhibited in Fig.2.Specifically,in Fig.2(a),the water phase is located at the middle zone with one-layer surfactants at the top and bottom in order to simulate the surface tension of water with presence of different types of surfactants.Moreover,the water and oil phases are located in the box to form an interface system to analyse the surface tension between water and octane in Fig.2(b).Besides,the interfacial tension (γ) between water and octane is also measured when replacing the surfactant by octane.These two model systems are called interface systems.The initial biphasic interface systems with five layers (water/surfactant/octa ne/surfactant/water) alongZdirection are built as intuitively displayed in Fig.2(c),in which the surfactant number varies.Finally,two water-in-oil(W/O)droplets with a radius of 6 nm are also constructed as shown in Fig.2(d)in the cross-sectional view.The numbers of different components are listed in Table 2.It should be pointed out that the numbers in the table represent the initial values during the setup of the simulation systems,and a tiny fraction of water molecules is replaced by chlorine ions in the subsequent simulation.

Table 1 Three kinds of surfactants with their molecular formula,type,abbreviation

Table 2 Details of simulation systems including box size,system components and molecular numbers in the interface systems,biphasic interface systems and droplet systems

2.2.Simulation details

Molecular dynamics simulations are all performed by using the Groningen machine for chemical simulation (GROMACS) software(version 2019.4 and 2019.5) [25].The GROMOS54A7 all-atoms force field [26,27] are used to describe the surfactants andnoctane molecules,while the water molecules are described with the simple point charge extended(SPC/E)model[28].The topology files of the above molecules are generated from the Automated Topology Builder (ATB,version 3.0) website [29],on which the ATB ids of the three kinds of surfactants and octane molecule can be found as follows: DCC12(id: 246970),DPC12(id: 605263),DPP(id: 478986),and octane (id: 463018).After structural optimization,the addition of the components into systems is achieved through the Packmol Program [30,31].The chloride ions are additionally added to maintain the electrical neutrality of the systems.

The constructed systems are firstly optimized by using the steepest descent minimization [32].The further NVT and NPT stabilization steps are performed until the maximum forces of the entire system reaches a threshold value of 100 kJ·mol-1·nm-1[33],which is beneficial to the integration of the equations of motion and form a stable system.For the interface systems,the sequent simulation under the NVT ensemble with 5 ns is carried out to analyze the surface tension.For the biphasic interface systems,the simulations are performed for 1 ns under the NVT ensemble and then for 20 ns under the NPT ensemble.For droplet system,the simulation is performed for 40 ns in the NPT ensemble.The timestep is 2 fs for the interface and biphasic systems[34]and 1 fs for the droplet systems [35],as a smaller timestep provides a more accurate description of droplet movement.The periodic boundary conditions (PBC) are employed in three directions in all simulations [36].The temperature is maintained at 300 K with a time constant of 0.1 ps[37]by using the modified Berendsen thermostat(namely the V-rescale thermostat)under both the NVT and NPT ensembles [38].The pressure coupling is used in the NPT stabilization step using the Berendsen barostat [39] to keep the system pressure as 1 × 105Pa with the compressibility of 4.5×10-10Pa-1[40].All bonds are constrained with the LINCS algorithm[41].Furthermore,the particle-mesh Ewald summation is used for calculating long-range electrostatic interactions [42],which are truncated with a cutoff distance of 1.2 nm.The same cutoff distance is applied in the calculation of van der Waals interactions[43].All simulations are visualized in the visual molecular dynamics (VMD) software (version 1.9.2) [44].

3.Results and Discussion

3.1.Validation of model systems

Fig.1.All-atom molecular models for three kinds of surfactants (a) DCC12,(b) DPC12,(c) DPP,and for (d)n-octane and (e) SPC/E water.The hydrogen,carbon,nitrogen and oxygen are represented in white,cyan(or light cyan),blue and red colors.In(b)and(c),the bonds in the pyrenyl groups are displayed as single bonds instead of partial double bonds for clarity,and the carbon atoms in the pyrenyl groups are highlighted in light cyan color.

Considering that all kinds of surfactants possess two nitrogen atoms in their hydrophilic groups,the interfacial coverage (IC) of nitrogen atoms is employed to quantify the surfactant coverage at the oil/water interface.One can calculate the IC by using the following equation:whereNNis the number of nitrogen atoms at the interface,LxandLyrepresent the box length in theXandYdirections.It is noteworthy that all nitrogen atoms are taken into account although some of them may locate outside the interfacial zone when a large number of surfactants aggregate at the interface.For convenience,we introduce three regions according to the degree of IC in the biphasic interface systems,i.e.,low IC,moderate IC,and high IC regions.Specifically,the low IC region is defined by Γ＜1.60 μmol·m-2,which equivalently elucidates that the interfaces are covered by less than 80 nitrogen atoms.The moderate IC region is defined by 1.60＜Γ＜3.50 μmol·m-2,which corresponds to the interfaces covered by 80-180 nitrogen atoms.The high IC region is defined by Γ＞3.50 μmol·m-2for the interfaces covered by more than 180 nitrogen atoms.

Fig.2.Schematic illustration for (a) interface system with water and surfactant,(b) interface system with water and oil,(c) biphasic interface system and (d) W/O droplet system in the cross-sectional view.In (a),the box in the blue line is shown to illustrate the existence of the vacuum layer on both sides of the surfactants.The surfactant molecules are highlighted in light cyan color in (a),(c) and (d).

The surface tension,interrelated with phase behavior,is one of the essential properties in the dispersed system.The average surface tension γ(t) can be calculated from the difference between the normal and the lateral pressures,viz.[45,46]:

where theLzrepresents the box length in theZdirection andnis the number of surfaces.Ifnequals to 2,then Eq.(2)can be further simplified as [47]:

where the pressure components in each direction are represented byPx,PyandPz,respectively.The surface tensions of water involving surfactants DCC12/DPC12are computed,which are shown in Fig.3(a).The simulation results at the saturated concentration (?！?.6 μmol·m-2) are also compared with the experimental data in the right panel.

As increasing the interfacial coverage to Γ=1.60 μmol·m-2,the surface tension decreases and gradually approaches to their individual stable values in both interface systems.The comparisons in Fig.3(b) show that the calculated surface tensions are in good agreement with experimental data in the CMC condition.Additionally,the interfacial tension betweenn-octane and water is calculated and compared with the relevant experimental value [49],with a deviation less than 4%.Specifically,the calculated interfacial tension is 52.8 mN·m-1,close to 51.7 mN·m-1in the MD simulation by Xiaoet al.[50],while the experimental data are 52.5 mN·m-1at 295 K[49]and 51.0 mN·m-1at 300 K[51].These overall agreements validate the constructed model systems.

3.2.Interfacial properties in biphasic interface systems

3.2.1.Density distribution

The density distributions reflect the spatial distributions of different systems components[52].Fig.4 illustrates the density distributions of three kinds of surfactants under the condition of different ICs,as well as the density distributions of water and octane,and the total density.We can see that the water density near the bulk phase maintains at(999.5±3.7)kg·m-3,while the octane density keeps at(738.9 ± 3.1) kg·m-3.These results are in good agreement with experimental values,viz.,997 kg·m-3at 300 K for water [53] and 698.5 kg·m-3at 298.15 K for octane[54],respectively.

From the density distributions,a common trend can be noted that as the IC increases,the width of the interfacial zone is enlarged.At the low and moderate ICs,several density peaks can be found in the surfactant density curves,and the peak values rise as the IC increases.However,this situation becomes complicated when the IC is high.The density curves of surfactants (red lines)present secondary peaks in Fig.4(b3) and (c3),which may relate to the accumulation of pyrenyl groups caused by the π-π stacking.Indeed,as shown in Fig.S1 of Supplementary Material,the density distribution of pyrenyl groups shows a similar trend.The aggregation of pyrenyl groups is discussed in the next section.The density distributions of the system components in other cases are displayed in Fig.S2-S4.

3.2.2.Interfacial thickness and interfacial tension

Fig.3.(a)Surface tension varying with interfacial coverage of surfactant DCC12 or DPC12.(b)Comparison of simulation and measured surface tensions for the systems with surfactant DCC12 or DPC12.The experimental values for the surface tension involving DCC12 or DPC12 are extracted from Ref.[48] and Ref.[14],and the interfacial tension between the water/octane is from Ref.[49].

As indicated by the density distributions,the aggregation of surfactants at the interfaces can enlarge the interfacial zone.To further explore the mechanism,the interfacial thickness is calculated and analyzed.The interfacial thickness can be readily accessible through simulationand/ortheoreticalcalculations[55],inwhichthe‘‘90-90”criterion can be utilized.In the criterion,the interfacial thickness refers to the distance between two positions in theZ-axis,at which the density of water or oil is 90% of the individual bulk value[56,57].Followingthisdefinition,thecalculatedinterfacialthickness varying with interfacial coverage is displayed in Fig.5(a).

Fig.4.Density distribution of components along the z axis in the biphasic interface systems with three types of surfactants:(a)DCC12,(b)DPC12,and(c)DPP.The surfactant number in each interface layer is:36 in the first column(low IC,Γ=(1.36±0.01)μmol·m-2);81 in the second column(moderate IC,Γ=(2.92±0.02)μmol·m-2);121 in the third column (high IC,Γ= (4.21 ± 0.04)μmol·m-2).

Fig.5.(a)Interfacial thickness and(b) interfacial tension in terms of interfacial coverage for the systems involving three different types of surfactants.The colors shown in color bar present different interfacial thicknesses with unit nm in (a) and interfacial tensions with unit mN·m-1 in (b).

As increasing the IC,the variation of the interfacial thickness displays two ascent stages,namely slowly growing at low IC and rapidly increasing at high IC.This variation trend has been discovered in previous studies [57].At low IC,the surfactants molecules tend to straighten themselves,and thus the interfacial thickness display a slow growth when increasing the IC.However,the interface becomes uneven while continuing to increase the IC.At high IC,anomalous aggregation occurs at the interface,which can also be observed in density distribution profiles in Fig.4 and Fig.S2-S4.This interfacial aggregation results in a rapid increase in interfacial thickness as well as a miscible mixing between the aqueous and oil phases,which is consistent with the previous study [58].

On the other hand,three curves of interfacial thickness present similar trends and values due to the similar size of the surfactants.However,it is apparent to see that the interfacial thickness of the system involving DPC12or DPP is less than 1.5 nm at low IC (the first three points in red color in Fig.5(a)),but the thickness for the DCC12system is beyond 1.5 nm at the same IC.This phenomenon is also related to the relatively high interfacial tension of systems with DPC12and DPP at low IC.

The calculation of interfacial tensions is based on Eq.(3).Fig.5(b) displays the interfacial tension varying with IC.It is found that at high IC the interfacial tension tends to vanish even approaching a negative value.However,at low IC the situation is slightly different.The interfacial tension for the systems containing pyrenyl-based surfactants (i.e.DPC12and DPP) does not change much when increasing the surfactant concentrations at low IC,but the interfacial tension of DCC12system decreases rapidly.This suggests that the π-π stacking can maintain a high interfacial tension,thus it leads to a small interfacial thickness.Moreover,the DPC12and DPP systems possess relatively low interfacial tensions compared to the DCC12system.Therefore,it is concluded that the π-π stacking allows the system to have a high and stable interfacial tension at low IC,and a tiny interfacial tension at high IC.

3.2.3π-π.stacking and order parameter

The aggregation of the pyrenyl-based surfactants at the interfaces is investigated.Considering that the pyrenyl groups account for a large mass fraction in the surfactants and affect the interfacial morphology through the π-π stacking interaction,the statistics of π-π stacking pairs are calculated.Technically,each pyrenyl group at the end of the hydrophobic chain is treated as a plane,determined by three selected atoms in the pyrenyl group.Thereafter,the atomic coordinates are substituted to the plane equation to calculate the dihedral angle of two pyrenyl group formed planes.We consider that the π-π stacking is formed when the dihedral angle of these two planes approximately equals to 0 and the distance in-between is less than a specific value (0.45 nm).In other words,two pyrenyl groups parallel with each other and staying not far apart constitutes a π-π stacking pair.The detailed calculations about the π-π stacking are supplied in the Supplementary Material,including the determination of plane,and the distance between a pair of pyrenyl groups.The threshold distance for the π-π stacking pair is obtained by a parallel simulation study of a pure system composed of two pyrene molecules,which is calculated as 0.35 nm,close to the simulation result by Sharmaet al.[59].According to this mathematical method of plane calculation,the π-π stacking pairs can be obtained from the selected atomic coordinates of the pyrenyl groups.

The average π-π stacking numbers are shown in Fig.6(a) and(b).The stacking number shows a rising tendency as the IC increases.However,it should be noted that the π-π stacking number in the interfacial system covered with DPP surfactant is nearly 5-7 times higher than the counterpart with DPC12surfactant,despite that the DPP surfactant has only twice number of pyrenyl groups than the DPC12.The enhancement in the π-π stacking number is intuitively indicated by the green shaded area in Fig.6(a).This area shows the π-π interaction process is significantly promoted if the surfactant contains two pyrenyl groups.

The same phenomenon can be found in Fig.6(b) and (d).Fig.6(b)displays the π-π stacking ratio in the biphasic interface systems with different ICs.The π-π stacking ratio is defined as the number of π-π pairs divided by the total number of pyrenyl pairs.Interestingly,the ratio for the system involving DPP surfactants is higher than that containing DPC12.Besides,the ratio reaches a plateau when the IC is high(approximately Γ＞3.50 μmol·m-2in both systems),indicating that the π-π stacking ratio has a saturated value.In other words,even more surfactants are added into the interface,the π-π stacking ratio no longer increases after Γ=3.50 μmol·m-2.This is likely because the orientation of the pyrenyl groups tends to become ordered as the IC reaches a certain high value.As shown in Fig.6(c),the order parameter profile first increases and then reaches a plateau,and the presence of a plateau indicates an ordered distribution of the adsorbed monolayer.And then the percentage of π-π stacking is not varied.

Conventionally,the order parameter is used to describe the interfacial aggregation behavior.Considering each pyrenyl group has a planar structure at the ends of both DPC12and DPP surfactants,we investigate the order parameter of the pyrenyl groups here.Towards this end,the order parameter is defined as [60]:

where the angular bracket ＜·＞indicates the ensemble average.The angle θpmeans the tilt angle between the normal vector of the pyrenyl plane and the normal vector of the interface.When the order parameter has the value ofSθ=1,the pyrenyl groups are all perpendicular with the interface;whenSθ=-1/2,the pyrenyl groups are fully parallel with the interface [61].The schematic diagram is depicted in Fig.S6.

Fig.6(c) shows that the order parameter increases with the IC increasing in both biphasic systems,indicating the pyrenyl groups tend to be vertical to the interface at high IC.A similar phenomenon is also reported by Coasneet al.[62],and they found benzene molecules present a preferable orientation with their rings perpendicular to the pore surface.The orientational distribution of pyrenyl groups enables the multi-layer aggregation of the surfactants at the interface as shown in Fig.6(d),which therefore brings secondary peaks in the density distribution profile as discussed in Fig.4.

Except for the order parameter,the critical packing parameter(Cpp) is widely used for predicting the geometry of molecular aggregation.Cppis usually defined as follows [63]:

whereVrepresents the volume of the hydrocarbon chain,a0is the effective headgroup area,andlcis the chain length.In this work,the effective surface areaa0of the headgroup is calculated by an indirect method,which is obtained by replacing the effective headgroup area with the solvent accessible surface area(SASA)[64],as it’s difficult to directly evaluatea0with computational tools [65,66].In this case,the accessible volume (AV) can also be used to replace the hydrocarbon chain volume.Considering that the Gemini surfactants own two hydrocarbon chains,the value of anlccannot fully represent the chain length of the entire surfactant.Therefore,the ratio of SASA:AV is now used to describe molecular aggregation[67].Herein,the ratios of SASA:AV for all biphasic systems are collected in Table 3.

As shown in Table 3,SASA:AV ratios display an upward trend as the IC increases.Obviously,increasing the concentration of surfactants,namely the IC in these systems,promotes the aggregation process.Meanwhile,systems containing DPP and DPC12surfactants have a larger SASA:AV ratio than that in systems involving DCC12surfactant at a similar IC.This shows that the π-π stacking formed by pyrenyl groups in DPP and DPC12surfactants also helps the surfactants aggregate together at the oil/water interface.

Fig.6.π-π stacking in the biphasic interface systems:(a)Relative number of π-π stacking pairs,(b)π-π stacking ratio and(c)order parameter of pyrenyl groups as a function of interfacial coverage;(d)representative snapshots of pyrenyl groups at the interfaces.In(a)and(b),the green area represents the difference between the value of DPP and the double value of DPC12.In(d),surfactant species are(d1)DPC12(Γ=4.21 μmol·m-2)and(d2)DPP(Γ=4.16 μmol·m-2)in each biphasic interface system,respectively,and for clarity only the pyrenyl groups are displayed.

Table 3 SASA:AV ratios in DCC12,DPC12 and DPP biphasic systems with different ICs

3.3.Droplet interaction in droplet systems

3.3.1.Center of mass motion

In order to investigate the interaction of emulsified droplets in the microemulsion systems,the center of mass (COM) of the surfactants in each droplet is calculated as [68]:

wheremiand riare the mass and the coordinate position of thei-th atom of the surfactants,respectively;Nrepresents the total number of atoms in each droplet.Given the surfactants distribute at the surface of spherical droplet,the calculated COM of surrounding surfactant molecules is virtually the COM of the droplet,ignoring the water and octane molecules.Thus,based on Eq.(6),the evolution of the COM distance between two droplets containing different kinds of surfactants is displayed in Fig.7.For better interpretation,the COM trajectories of the DPC12surfactants are exhibited in Fig.8 and Fig.9,and the COM trajectories of the other kinds of surfactants are supplied in Fig.S7-S10.

The COM distance between two droplets is approximately 13 nm in the deliberate enlargement of the initial simulation stage.Then,the droplet shrinks itself to form a more stable structure,and thereby the COM distance rapidly decreases.Afterward,the surfactant molecules start to attract each other and fill in the structural holes at the surface of droplets during this process.Once the droplets are stable,the COM trajectory motion moves gently and the droplets undergo a randomly irregular motion.Fig.8(b) and Fig.9(b) give corresponding views from all three directions.

As simulation time elapses,the end groups in the surfactants begin to attract each other.However,the situations become quite different when the species or number of the involved surfactants is different.Fig.7(a)shows the evolution of COM distance between two droplets in the microemulsion system containing 200 DCC12,DPC12or DPP surfactants in each droplet.The curves corresponding to the DPC12and DPP surfactants present similar trends,and namely they gradually decline over time,yet the COM distance of the two DCC12droplets presents a relatively high value.Confirmed by the snapshots,the two droplets in the DCC12system are still not in contact at the end of the simulation,while the DPC12and DPP droplets approach each other and finally coalesce together.In this case,the π-π sticking causes attraction,assisting two droplets coalesce together.

Fig.7.Evolution of the COM distance between two droplets in each system including three individual types of surfactants:(a)200 surfactants(Γ=1.77 μmol·m-2)in each droplet and(b)300 surfactants(Γ=2.65 μmol·m-2)in each droplet.The topologies of both droplets at initial(t=0 ns)and final(t=40 ns)time moments are also displayed for guidance in (c) and (d).

Nevertheless,the results are rather different if increasing the number of surfactants in each droplet.As shown in Fig.7(b) in which 300 surfactants are contained in each droplet,the DCC12droplets tend to coalesce together to form a large droplet after the shrinking process,revealing that increasing the number of surfactants in each droplet enhances the interaction between both droplets and thus leads to the proximity of two droplets.But the coalescence progress of droplets with DPC12and DPP surfactant slows down as the number of surfactants increases.The curves of surfactant containing pyrenyl groups show a monotonic trend in the COM distance value,and more pyrenyl groups lead to a bigger COM distance,thus it is hard for the droplets to coalesce together.This phenomenon denotes that increasing the number of the surfactants (mainly the pyrenyl groups) at the surface of the droplet,the attraction evolves to repulsion,and two droplets cannot coalesce together easily as before.Therefore,among the pyrenyl groups,a synergistic relationship between the π-π attraction and the steric hindrance jointly affects the coalescence of droplets[69].

3.3.2.π-πstacking in emulsified droplets

The π-π stacking ratio is calculated in the droplet systems,as displayed in Fig.10(a)and(b).Accompanied by the overall motion of the droplets,the π-π stacking ratio decreases during the droplet shrinking process.Afterward,all four curves maintain a stable value and the ratios change little with the motion of the droplets.At the same time,the π-π stacking ratio increases with the increment in the number of surfactants in each droplet.Nevertheless,the COM motion of the droplet is still hindered,which can be obtained by comparing Fig.10(c1) and (c2),or Fig.10(d1) and(d2).Comparing the trajectory diagrams in Fig.8 and Fig.9,it is not difficult to find that the increment in the surfactant number makes the moving range of droplets smaller,especially in theZdirection.

Fig.8.Trajectory of the COM of 200 DPC12 surfactants in each droplet:(a)3D mobile trajectory,(b1)2D mobile trajectory at the X-Y plane,(b2)2D mobile trajectory at the X-Z plane and (b3) 2D mobile trajectory at the Y-Z plane.The color bar denotes the simulation time axis.

Fig.9.Trajectory of the COM of 300 DPC12 surfactants in each droplet:(a)3D mobile trajectory,(b1)2D mobile trajectory at the X-Y plane,(b2)2D mobile trajectory at the X-Z plane and (b3) 2D mobile trajectory at the Y-Z plane.The color bar denotes the simulation time axis.

When the surfactant number in each droplet changes from 200 to 300,the stacking ratio in the system involving DPP surfactants does not increase significantly (increasing from～ 0.103 to 0.128).In contrast,the ratio of systems involving DPC12is increased by approximately 35%,namely from～ 0.035 to～0.047.On the other hand,the droplets containing DPP possess a relatively large topology compared to the systems involving DPC12,which also can be observed in Fig.10(c)-(d).The π-π interaction synergies with the steric hindrance,determining the coalescence of droplets in these systems.

Fig.10.Evolution of π-π stacking in the droplet systems within 40 ns:(a)π-π stacking ratio of DPC12 and(b)π-π stacking ratio of DPP.Representative snapshots of pyrenyl groups in (c) DPC12 and (d) DPP on the droplet surface.The numbers of surfactants in each droplet are 200 in (c1) and (d1),and 300 in (c2) and (d2),respectively.

4.Conclusions

By performing molecular dynamics simulations,we investigate the properties ofn-octane/water interfacial systems with the presence of three different kinds of surfactants.In the biphasic interface system,we find that the π-π stacking among the surfactants appears when the surfactants have pyrenyl groups,and this results in a secondary peak in the local density distribution of surfactant at high IC and an ordered orientation of the pyrenyl groups at the oil/water interface.Besides,due to the π-π interaction,the biphasic systems containing surfactants with the pyrenyl groups have a narrow interfacial thickness at the low IC.

As for the droplet systems,it is discovered that the coalescence of droplets depends on the species and the number of surfactants.On the one hand,the π-π stacking formed by the pyrenyl groups can promote the attraction of the droplets.On the other hand,the irregular orientation of the pyrenyl groups may also cause steric hindrance.Consequently,a synergistic relationship between the π-π interaction and the steric hindrance jointly affects the coalescence of droplets.In other words,the existence of aromatic groups in surfactants and a moderatenumber of surfactants are beneficial,both of which can improve the formation of microemulsion in their respective systems.The present study casts guidance towards the preparation and applications of the surfactants relevant to chemicals containing aromatic groups such as phenyl,naphthyl,anthryl,etc.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by National Natural Science Foundation of China (21878078,and 22108022),and by PetroChina Scientific Research and Technology Development Project (2018A-0907).The authors thank computing resources supported by Chengdu Supercomputing Center.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2022.06.010.