Molecular insight into interfacial tension modulated by mixed cationic and anionic surfactants

Abstract The oil/water interfacial tension plays a crucial role in tertiary oil recovery, and the low interfacial tension facilitates oil emulsification and stripping. Here, anionic surfactant sodium dodecyl sulfate and cationic surfactant hexadecyltrimethylammonium bromide were employed to study their ability to reduce the oil/water interfacial tension (IFT). Experimental results show that the mixed cationic and anionic surfactants could produce lower IFT than that of individual cationic or anionic surfactant, and the lowest IFT could be obtained at molar ratio of CTAB:SDS = 2:1. Employing molecular dynamics simulation method, the oil/water IFT was calculated and gave same changing trend with that of the experiment. The underlying mechanism of IFT modulated by mixed cationic and anionic surfactants was unveiled from the insight of interfacial structure, interfacial energy, interaction energy between different molecules and interface roughness, and so on. We found the hydration radius of counterion as well as the charge distribution of polar headgroup of surfactant together play crucial role determining the ion distribution inside water phase and surfactant/water interface, and further influencing the IFT. Our study provides an atomic-level understanding of the IFT modulated by cationic and anionic surfactants, and our results might have some references for enhanced oil recovery.


Introduction
In enhanced oil recovery (EOR) techniques, the oil/water interfacial tension (IFT) is significantly important because it affects the crude oil emulsification, capillary number Nc, etc.For example, it was found that the larger the capillary number Nc, the higher oil recovery efficiency (Shah and Schechter 1977;Cai et al. 2022).Since Nc is inversely proportional to IFT (Bera, Mandal, and Guha 2014), the reduction of oil/water IFT is an effective way to improve Nc and oil recovery efficiency (Zolghadr, Ghatee, and Zolghadr 2014;Zhao et al. 2016).
Chemical EOR methods are widely exploited by injecting chemical substances in chemical flooding to strengthen the interaction between oil and water (Kamal 2016;Mahmoud, Attia, and Al-Hashim 2017).Chemical flooding mainly includes alkaline water flooding, surfactant flooding, polymer flooding, combined flooding, and so on (Dong, Liu, and Li 2012;Olajire 2014;Bera et al. 2020;Khayati et al. 2020).Surfactants are widely employed in EOR operations because of their ability to reduce oil-water interfacial energy and alter rock-wetting characteristics (Pal, Hoteit, and Mandal 2021;Xu et al. 2022).The hydrophilic headgroup inserts into the water phase and the hydrophobic tail chain enters into the oil phase, and an orderly self-assembly film forms at oil/water interface.Consequently, the interaction between water phase and oil phase is strengthened and the oil/ water miscibility happens, leading to the decrease of IFT (Zarbakhsh et al. 2005;Zarbakhsh, Webster, and Eames 2009).The anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant hexadecyltrimethylammonium bromide (CTAB) are two kinds of widely used surfactants to modulate the IFT.Bera, Mandal, and Guha (2014) reported the experimental IFT value between crude oil (India) and water was 48 mN/m.Once the SDS and CTAB were added, the IFT decreased to 1-2 and 10 À1 mN/m, respectively.Rashmi Kumari et al. (Kumari et al. 2019) found that the SDS or CTAB could decrease the IFT to 2.9 and 0.12 mN/m at the critical micellar concentration (CMC), respectively.Similar results were also validated by other researchers (Xu et al. 2013;Esmaeilzadeh et al. 2014;Jia et al. 2019).
In recent years, mixed anionic and cationic surfactants were often adopted to decrease the IFT.Benefited from the strong electrostatic attraction between the positively charged headgroup of cationic surfactant and negatively charged headgroup of anionic surfactant, a tight self-assembly surfactant film could form at the oil/water interface and largely reduce the IFT (Hajibagheri et al. 2017;Li et al. 2019).Hajibagheri et al. (2017) have investigated the mixed systems with different molar ratio of SDS and CTAB.They found that the combination of SDS and CTAB yields optimized interface activity and their synergistic effect greatly decreases the CMC compared to that of individual surfactant.Meanwhile, the IFTs of 1.3, 0.19, and 5.021 mN/m were obtained at molar ratio of SDS:CTAB ¼ 3:7, 5:5, and 7:3, respectively.Li et al. (2017) designed a lipophilic surfactant by mixing a hydrophilic anionic (nonylphenyl ethoxylate carboxylate) and cationic (quaternary ammonium chloride) surfactant and yielded a lower IFT, which was used for EOR at low salinities.And they found by tuning the molar ratio of anionic surfactant to cationic surfactant, the surface charge will be changed, and other properties, such as adsorption on reservoir rock and aggregation behavior will be correspondingly influenced.Guo et al. (2021) proposed a mixed surfactant system containing anionic surfactant SDB and cationic surfactant SDY, which could reduce the oil viscosity, reduce the IFT and change the wettability of the rock surface.Such mixed surfactant system could improve the oil recovery to approximately 10% and has excellent properties for high-temperature and high-salinity reservoir.
Molecular dynamics (MD) simulation method has been fully developed and exhibited great advantages in investigating various interface and intermolecular interaction phenomena at atomic level, such as the interface structure, interface thickness, thickening mechanisms, dynamical properties, and so on (Yan et al. 2017;Jia et al. 2020;Han et al. 2021).However, the MD simulation study on oil/water interface modulated by mixed anionic and cationic surfactants is scarce.Jia et al. (2020) investigated the interfacial assembly process and interface configuration of the pseudogemini surfactant using MD simulations.Jia et al. (2019) employed MD simulation to explore the surface/interfacial activity of the mixed cationic surfactant M12 and anionic surfactants SDS, and tell us that the mixed surfactants give more adsorption at oil/water interface, yielding lower IFT, emulsification, and wettability alteration capability.Su et al. (2021) used MD simulation to research the photoinduced emulsification and demulsification processes of mixed cationic surfactant AzoTAB and anionic surfactant SDS in n-octane/water emulsions.They found SDS inhibited the desorption of AzoTAB from the oil/water interface and investigated the influence of trans-and cis-AzoTAB molecules on interfacial stability.
In this article, combined experiment and MD simulation methods, the oil/water IFT modulated by mixed CTAB and SDS with different molar ratio were investigated.The interface configuration, interface energy, interaction energy, interface roughness, and so on, were analyzed to give an atomic level insight for IFT reduction mechanism.

Experiment details
The surfactants, SDS, CTAB, and n-dodecane were purchased from Sinopharm Chemical Reagent Co., Ltd.(Shanghai, China).The mole fraction purities of SDS and CTAB are 0.97 and 0.99, respectively.The IFT was measured by the spinning-drop technique using a Tex-500C interfacial tensiometer.The instrument has a wide measurement region from 10 À6 to 10 2 mN/m.Thirteen different surfactant solutions were prepared, that is, SDS, CTAB, and their mixture with molar ratio of CTAB:SDS ¼ 8:1, 5:1, 4:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:4, 1:5, and 1:8.For CTAB or SDS surfactant solution, the surfactant was added directly into the distilled water.For the mixed surfactant solution, first, the surfactant CTAB was dissolved in distilled water, then the surfactant SDS was added and dissolved in the CTAB solution.The molar concentration of SDS or CTAB in these solutions is listed in Table S2 in supplementary materials.The concentration of CTAB surfactant is greater than their CMC and the concentration of SDS is lower than their CMC (Wu et al. 2016).The temperature of solution was first increased to 353 K, and then dropped to 313 K.This process could increase the surfactant activity for its quick adsorb at the oil/water interface to avoid the precipitation of mixed surfactant originating from their strong electrostatic interaction.The solution was stirred vigorously at 1000 rpm for 1 hr to obtain a completely dissolved surfactant solution.The oil/water IFT was measured using the Tex-500C dynamic interfacial tensiometer at 40 ± 0.1 C. The solution was injected into the tube and kept rotated at speed of 5000 r/min for about 5 min to produce pre-equilibrium before injection of dodecane (C12, acted as oil).

Molecular dynamics simulation details
All MD simulation calculations were performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package (Plimpton 1995).The simulation system contains dodecane, water, and surfactant molecules.The CVFF force field (Dauber-Osguthorpe et al. 1988) was used for oil and surfactant molecules.The SPC model (Berendsen, Grigera, and Straatsma 1987) was used to describe the water molecule.Atomic charge for dodecane molecules and surfactant molecules are extracted from the COMPASS force field (Sun, Ren, and Fried 1998).For the bonded potential, it includes bond stretching, angular bending, and dihedral angle torsion.The non-bonding interactions between molecules include the short-range van der Waals (vdW) and long-range electrostatic interaction.The vdW and electrostatic interactions are represented by Lennard-Jones 12-6 potentials and Coulombic potentials, respectively, as shown in Equation (1).
where e ij and r ij are potential well depth and collision diameter, r ij is the distance between atoms i and j. q i represents the charge of atom i, e 0 ¼ 8.8542 Â10 À12 C 2 N À1 m À2 is permittivity of vacuum.The Nos e-Hoover thermostat (Nos e 1984) was used to control the temperature during all above MD simulations.The long-range electrostatic interactions were calculated by the particle-particle-particle-mesh (PPPM) method (Hockney and Eastwood 1988).All force field parameters e ij , r ij and q i for SDS, CTAB, dodecane and water could be found in Table S1 in supplementary materials.
According to previous reports (Xu et al. 2013), a symmetric model (40 Â 40 Â 182 ÅÞ with periodic boundary conditions was built, as shown in Figure 1a.The middle slab is water phase with thickness of 30 Å. Thirtysix surfactant molecules are aligned on two water surfaces with headgroups toward the water phase.Their headgroups are organized in an appropriate 6Â6 square lattice in xy plane, and hydrocarbon chains are perpendicular to xy plane.The average occupied area of headgroup is 42.44 Å based on experimental results (Jang and Goddard 2006).Then two oil slabs with thickness of 30 Å are placed on two sides.The top view of arranged surfactant on oil/water interface could be seen in Figure 1c.
Initially, the structure was optimized using the steepest descent method.Subsequently, a 1 ns equilibrium MD simulation was performed under the NVT ensemble at 313 K. Finally, a 6 ns NVT MD simulation was performed at 313 K.In all calculations, a cutoff of 12.0 Å and a time step of 1 fs were used.Full coordinates were saved and output every 2 ps for the analysis of the results.Snapshots of the interfacial configurations were rendered using visual molecular dynamics (VMD) software (Humphrey, Dalke, and Schulten 1996).The MD simulation results showed that when simulation time t > 5.5 ns, the change of system configuration and the total energy is slight, which indicate the simulation systems reach equilibrium.

Interfacial tension
The experimental and MD simulated oil/water IFTs modulated by different ratio of CTAB:SDS were listed in Table 1.In order to save computational cost, not all molar ratios of CTAB:SDS considered in experiment were investigated in MD simulation.The IFT of the systems was calculated by subtracting mean tangential stress tensors from the normal one (Zhang et al. 1995).
where c represents the IFT, L z is the length of the simulation box in the z-axis; p xx , p yy , and p zz are the stress tensors in the x-axis, y-axis, and zaxis, respectively.From the experimental results, the pure oil/water IFT is 50.23 mN/m.Our experimental IFT values are in agreement with previous experimental results (52.55 mN/m) (Zeppieri, Rodriguez, and Ramos de 2001).Individual adding of CTAB and SDS yield oil/water IFTs of 5.2 and 10.7 mN/m, respectively.Interestingly, both CTAB and SDS are added together, a significant decrease of IFT could be obtained, even at the molar ratios of CTAB:SDS of 8:1 or 1:8.The minimum IFT emerges at molar ratio 2:1.As for the MD simulated results, the oil/water IFT is 46.35 mN/m and is close to the experimental value, which validates the reasonability of our MD simulation.From Table 1, it could be found that when the molar ratio of CTAB is larger than SDS, the MD calculation results are consistent with the experimental results.When the molar ratio of CTAB is less than SDS, the MD calculation results are quite different from the experimental results.However, the changing trend of IFT with the molar ratio of CTAB:SDS is the same in experimental and MD simulated IFT.The addition of surfactant could decrease the oil/water IFT values, and the minimum MD simulated IFT is found at the molar ratio of CTAB:SDS ¼ 2:1, which is consistent with experimental result.Furthermore, with the decrease of molar ratio of CTAB:SDS, the IFT first decreases and reach minimum value at 2:1, and then increases, which is agreement with the experimental results.

Interface structure
Figure 2 shows the snapshot of the final equivalent configuration.It can be seen that the headgroup of surfactant insert into water phase, and the tail chain inserted into oil phase.The surfactant formed a self-assembly film at the oil/water interface.As known, in pure oil/water system, the oil phase and water phase have perfect interface, and their interaction is weak.Once the surfactant emerges at oil/water interface, there are strong electrostatic attraction between the hydrophilic headgroup of surfactant and water phase.Meanwhile, there are Van der Waals interaction between hydrophobic tail chain and oil phase.As a result, the introduce of surfactant could intensify the interaction between water phase and oil phase, facilitating the decrease of IFT.
According to previous experiments and theoretical research studies, SDS or CTAB surfactant with their counterions would accumulate at the air-water or oil-water interface and form an electrical double layer structure (Stern layer) (Wojciechowski et al. 2010, Warszy nski, Lunkenheimer, and Czichocki 2002, Bruce et al. 2002, Wu et al. 2016).The formation of double layer will exhibit electrostatic screening effect to weaken the interaction between surfactant and water phase, resulting in increase of IFT.In our simulation, Figure 2 shows that in the case of CTAB:SDS ¼ 0:1, that is, only SDS is added, nearly all Na þ ions distribute around the SDS/water interface.While in the case of CTAB, besides those Br -ions accumulating around the headgroups, there are also some Br -ions distribute inside the water phase.
The different distribution phenomenon of Na þ in SDS solution and Br - in CTAB solution could be explained from the hydration radius of ion and electrostatic interaction between ion and surfactant's polar headgroup.The hydrated radius of Br -and Na þ are 3.30 and 3.58 Ð, respectively.Therefore, compared to Br -and Na þ should has weaker migration capability to combine with surfactant's polar headgroup.While our MD calculation results show that some Br -ions distribute in water phase and nearly all Na þ ions accumulate around SDS headgroups, meaning Na þ has stronger combination capability with headgroup than Br -.In order to explain above result, the atomic charge distribution of surfactant's headgroup is considered.As shown in Figure 3, for SDS headgroup, S is surrounded by four O atoms, and the total charge of the headgroup is À1.339.For CTAB headgroup, N is surrounded by three C and nine H atoms, and the total charge of the headgroup is 0.5929.Therefore, there is stronger electrostatic interaction between Na þ and SDS's headgroup than that between Br -and CTAB's headgroup.Combined the hydration radius and electrostatic interaction, the strong electrostatic interaction will dominant the interaction between ion and surfactant's polar headgroup, and the distribution of Na þ and Br -in our model could be understood.Consequently, Na þ ion in SDS case has stronger electrostatic screening effect than that of Br -in CTAB case, yielding a higher IFT.In other cases, both CTAB and SDS are added together.There are some dissolved Br -ions in water phase, which could attract some Na þ ions and make them distribute inside the water phase.As a result, the number of Na þ ions adsorbed around the headgroup of surfactant decreases, leading to weakened electrostatic screening effect, which is beneficial to decrease the IFT. Figure 4a gives Na þ distribution perpendicular to the oil/water interface and Figure 4b shows the number of Na þ in water phase in different surfactant systems.It can be seen that, in the case of CTAB:SDS ¼ 2:1, the number of dissolved Na þ ions inside water phase reaches maximum, yielding a lowest IFT.Meanwhile, the electrostatic attraction between positively charged ammonium and negatively charged sulfonate facilitates a dense alignment of surfactant molecules on oil/water interface, leading to a decrease of IFT.

The interfacial energy
The decrease of the interfacial energy with the introduction of the surfactant (IFE) is one important parameter to reveal the interface stability.The IFE of single surfactant molecule is defined as (Xu et al. 2013): where E total , E surfactant, single , and E oilÀwater denote the energy of the whole system, one single surfactant molecule (the average energy of all surfactant molecules) and pure oil/water system, respectively, n is the number of surfactant molecules.Figure 5 depicts the IFEs of all MD cases.
From Figure 5, it can be seen that all IFEs are negative values, which indicates that the introduction of surfactant could decrease the system energy, yielding a more stable oil/water interface and a lower IFT.With the increase of molar ratio of CTAB:SDS, the absolute value of IFE increases and reach maximum at the molar ratio of CTAB:SDS ¼ 2:1, and then decreases.Therefore the most stable interface and lowest IFT could be obtained at molar ratio of CTAB:SDS ¼ 2:1, which is consistent with the experimental and MD simulated IFTs.

Interface interaction
The interface interaction is another important parameter for interface stability.Using the molar ratio of CTAB:SDS ¼ 2:1 as example, the interaction energy between CTAB (SDS) and water, CTAB (SDS) and oil, CTAB, and SDS were calculated as depicted in Figure 6.The interaction energy of other cases can be found in Figure S1 in supplementary materials.
From Figure 6, it can be seen that there is ultra-strong interaction between CTAB and SDS, which is originated from the electrostatic attraction between positively charged ammonium and negatively charged sulfonate.Consequently, a dense aligned surfactant film forms, and more surfactant molecules adsorbed at oil/water interface intensify the interface interaction, yielding lower IFT.The interaction between surfactant and water is larger than that between surfactant and oil.This is because the interaction between surfactant and water mainly comes from the strong electrostatic interaction between charged headgroup of surfactant and the polar water, while the interaction between surfactant and oil mainly comes from the weak hydrophobic association interaction between tail chain of surfactant and oil.Therefore, the interaction between surfactant and water is given more attention in following discussion.Using the system of CTAB:SDS ¼ 2:1 as example, Figure 6 presents that the interaction energy E CTAB/water is larger than two times of E SDS/water .Based on this point, it can be inferred that the single CTAB molecule has stronger interaction with water than that of SDS, and CTAB surfactant has stronger ability to reduce IFT, which is consistent with the experimental and MD-calculated IFT.The radial distribution function (RDF) g(r) presented in Figure 7a and b could provide convincing evidence for the interaction.It can be seen that g(r) between nitrogen of ammonium and oxygen of water in Figure 7a gives higher density peak than that of g(r) between OSO 3 À of sulfonate and oxygen of water in Figure 7b, meaning that the CTAB has stronger interaction with water.The electrostatic screening effect could be introduced to explain these results.Figure 7c give the g(r) between nitrogen of ammonium and Br À , and Figure 7d gives the g(r) between OSO 3 À of sulfonate and Na þ .The high g(r) density peak of OSO 3 À -Na þ indicates that the negatively charged sulfonate of SDS is surrounded by a large number of cation Na þ , and the intensive electrostatic screening effect would largely decrease the interaction between SDS and water.On the contrary, the low g(r) density peak of N-Br À indicates the positively charged ammonium of CTAB is surrounded by fewer anions, and the weak electrostatic screening effect yields stronger interaction between CTAB and water than the interaction between SDS and water.
In order to investigate the influence of molar ratio of CTAB:SDS on interaction between surfactant and water, the area of first density peak of g(r) of N-O w , OSO 3 À -O w and (N þ OSO 3 À )-O w , that is, the area of the first hydration layer was calculated as depicted in Figure 8.The area could be used to assess the interaction strength between headgroup of surfactant and water.The larger the area is, the stronger the interaction between surfactant and water phase.It can be seen that CTAB have dominant contribution to the interaction of surfactant and water over that of SDS.The area of the first g(r) peak of (N þ OSO 3 À )-O w exhibits largest area at molar ratio of CTAB:SDS ¼ 2:1, inferring strongest surfactant-water interaction and lowest IFT.

Interface roughness
Interface roughness is another parameter closely related with the IFT (Zhao et al. 2016;Zhang et al. 2017).The molecular penetrations and capillary waves due to thermal fluctuations at the interface are known as the interfacial roughness (Zhao et al. 2016).Interface roughness could reflect the miscibility of oil and water phase.A large interface roughness means that the water and oil phases have a large contacting area and a high miscible degree, yielding a low IFT. Figure 9 shows the interface roughness of different surfactant systems using the QuickSurf method in VMD.For clarity, the surfactant molecules, Na þ and Br -are not displayed.From Figure 9, it can be seen that the red water and cyan oil form interlocked interface, and a clear miscible oil/ water interface is exhibited.A careful comparison indicates that it shows more oil molecule distribution at the interface at molar ratio of CTAB:SDS ¼ 2:1, which indicates the interface of molar ratio of CTAB:SDS ¼ 2:1 gives a largest interface roughness, meaning a highest miscibility and lowest IFT.

Conclusion
In this work, the interface activity modulated by mixed cationic surfactant CTAB and anionic surfactant SDS were investigated via experiment and MD simulation.
(1) Experimental results show that the mixed addition of CTAB and SDS could effectively decrease the IFT than that of individual addition of CTAB or SDS.Though the experiment IFT and MD simulation IFT give different value, they show same changing trend.The experimental and MD IFT both experiences minimum at molar ratio of CTAB:SDS ¼ 2:1.(2) Interface structure indicates that the addition of surfactant could disorder the regular oil/water interface and make oil and water phases miscible, therefore addition of surfactants could decrease the oil/ water IFT.(3) Na þ could produce strong electrostatic screening effect on SDS's polar headgroup and weaken the interaction between the SDS and water molecules, yielding a higher IFT.Whereas, Br À gives weak electrostatic screening effect on CTAB's polar headgroup, yielding a lower IFT.In the case of the mixed CTAB and SDS surfactant systems, because of the electrostatic attraction between Br À ions and Na þ ions, the electrostatic screening effect of Na þ to SDS's polar headgroup become attenuated, and the interaction between CTAB's headgroup and SDS's headgroup increases, which is helpful to form denser self-assembly surfactant film, facilitating the decrease of IFT.In the case of CTAB:SDS ¼ 2:1, the number of dissolved Na þ ions inside water phase reaches maximum and leading to a weakest electrostatic screening effect, and yields a lowest IFT, which is in agreement with the experimental and MD IFT results.(4) The interfacial energy decreases with the introduction of the surfactant, and the RDF of (N þ OSO 3 À )ÀO w and interface roughness are analyzed and gives maximum value at molar ratio of CTAB:SDS ¼ 2:1, meaning a highest oil/water miscibility and a lowest IFT, which is in agreement with the experimental and MD IFT results.
Our study provides an atomic level understanding of IFT modulated by mixed cationic and anionic surfactant, and our results might have some meaning for enhanced oil recovery in surfactant flooding.

Figure 1 .
Figure 1.(a) Original configuration of the IFT model.(b) Molecular structure of SDS and CTAB surfactants, atom color codes: O, red; H, white; C, gray; S, yellow; N, blue; Na, purple; Br, blue.(c) The top-view of the headgroup of arranged surfactants at oil/water interface with different molar ratios of CTAB:SDS.H atoms in headgroup of CTAB are not shown.Atom color codes: O, red; C, green; S, yellow; N, blue.

Figure 2 .
Figure 2. Snapshots of the equilibrated configuration of different oil/water/CTAB/SDS systems.Cyan sticks denote C atoms in oil molecules.Red sticks denote O atoms in water molecules.White sticks denote H atoms in oil and water molecules.Purple sticks denote tail chains of SDS molecule, and green sticks denote tail chains of CTAB molecules.Green balls denote the headgroup of CTAB molecules.Purple balls denote the headgroup of SDS molecules.Red balls and yellow balls denote Br À and Na þ ions, respectively.Headgroups of surfactants, Br À and Na þ ions are all denoted by VDW (van der Waals radii of atoms) style.

Figure 3 .
Figure 3.The charge of each atom of (a) SDS and (b) CTAB headgroup.

Figure 4 .
Figure 4. (a) Na þ distribution in different surfactant system along z-axis, which is perpendicular to oil/water interface.: Na þ ; : range of the headgroups of SDS molecules; (b) Number of Na þ in water phase in different surfactant systems.

Figure 5 .
Figure 5.The decrease of the interfacial energy with the introduction of the surfactant (IFE) of different systems.

Figure 8 .
Figure 8.The area of the first g(r) peak of N-O w , OSO 3 À -O w and (N þ OSO 3 À )-O w .

Figure 9 .
Figure 9. Equilibrated snapshot of the oil/water interfaces with different molar ratio of CTAB:SDS.Red and cyan colors denote the water and oil molecules, respectively.The surfactant molecules, Na þ and Br -are not shown.Ratio denote the molar ratio of CTAB:SDS.

Table 1 .
Experimental and MD simulated oil/water IFT modulated by different molar ratio of CTAB: SDS.