Equilibrium and dynamic surface properties of cationic/anionic surfactant mixtures based on alcohol ether sulfate

Abstract The equilibrium and dynamic surface properties of anionic surfactant alcohol ether sulfate with different EO distribution(C-AE2S and N-AE2S) and cationic surfactant tetradecyltrimethylammonium bromide (TTAB) mixtures under different molar ratios were investigated. Their surface activities, adsorption, and spreading performances were investigated by static/dynamic surface tension measurements, molecular dynamics simulation, and dynamic contact angle techniques at 298 K. The static surface tension analysis reveals that the critical micellization concentration (cmc) values and the surface tension at cmc (γcmc) of the binary systems are much lower than that of the individual component. Compared with C-AE2S/TTAB, N-AE2S/TTAB systems have higher cmc and lower γcmc. It was found from the molecular dynamics simulation that negative charges of C-AE2S were drastically neutralized by the positively-charged TTAB at the interface in the system of C-AE2S/TTAB. The dynamic surface tension results indicate that the adsorption process of aqueous solutions for both C-AE2S/TTAB and N-AE2S/TTAB are mixed diffusion-kinetic adsorption mechanisms. From the dynamic contact angle measurements, it could be obtained that the mixtures exhibit better spreading behavior than that of the individual component and N-AE2S/TTAB systems have lower contact angles than that of C-AE2S/TTAB at the same mixing ratios. Graphical abstract


Introduction
Surfactants are chemical compounds commonly used in different industrial and daily life products, [1][2][3] from froth flotation and fire-fighting foams [4,5] to laundry detergents and cosmetics, [2,6,7] from dietary products [8,9] to coronavirus pandemic combatting. [10,11][14][15] The interactions such as cohesive forces and hydrogen bonding that work for the mixed system, lead to the synergistic effect. [16,17][23][24] Li et al. [25] investigated the equilibrium and dynamic surface properties of cationic/anionic surfactant mixtures based on bisquaternary ammonium salt.The results indicate that the cmc values of mixtures are two orders of magnitude lower than that of each component.Dynamic surface tension results demonstrate that the mixtures exhibit a faster reduction in surface tension than either of the component.Wang and coworkers [26] studied the vesicle formation in a mixture of cationic cetyltrimethylammonium chloride (CTAC) and anionic sodium dodecyl sulfate (SDS).It was found that a series of morphologies was obtained as the mixed ratio changed, when the ratio of SDS was equal to that of CTAC, a vesicle was formed by disklike bilayer curling and the entropy was the driving force.Zhang et al. [27] reported that the combustible matter recovery of low-rank coal flotation was improved using the mixed dodecyltrimethylammonium bromide and sodium dodecyl sulfate (DTAB/SDS) and the synergistic effect of the mixed surfactant was confirmed by contact angle test and wetting rate test.
Fatty alcohol polyoxyethylene ether sodium sulfates (AES) are ionic alkoxy-based surfactants, they have been studied extensively because their molecular contain both nonionic and anionic groups, which make them possess advantages of both nonionic and anionic surfactants, and they were widely used in various personal care products, detergents, oil recovery, and other practical field. [3]Number of ethylene oxide (EO) and EO distribution of AES products directly affects their properties.Experiments by Wang and coworkers [28] indicated that the properties of AE m S (m ¼ 3, 5, 7, and 9) with narrow ethylene oxide distribution vary with the number of EO.Michael and Dewey reported that Peaked AES is easier to salt-thicken, potentially more mild and posses lower content of 1,4-dioxane than conventional AES. [29,30]These are advantages that can translate directly into dollars and cents when they are used in the practical application process.Zhou applied molecular dynamics simulations to explore the mechanisms and interfacial behaviors of the binary mixture of AES and dodecyltrimethylammonium chloride (DTAC) at oil-water interface.They found that the number of EO of AES has a great influence on the behaviors of interface.An increase of EO number could cause AES molecules to exhibit varying degrees of bending. [31]Despite the extensive application of AES, investigations on the influences of the EO distribution on properties of its mixtures, especially the dynamic surface properties are still rarely addressed.
In this article, the equilibrium, dynamic surface tension, molecular dynamics simulation, and dynamic contact angle of the mixtures of AE 2 S (N-AE 2 S and C-AE 2 S with different EO distribution, number of EO is 2) and tetradecyltrimethylammonium bromide (TTAB) were investigated to study the effect of EO distribution on the properties of the mixture and provide some basic data and guides for practical application.

Materials
Fatty alcohol polyoxyethylene ethers with different ethylene oxide distributions were supplied by Sinolight Surfactants Technology Co., Ltd.The EO distributions obtained from gas chromatography using internal standard method were also provided in Figure 1.N-AE 2 S and C-AE 2 S were synthesized in our laboratory by the method described in our previous article. [32]As can be seen from Figure 1

Equilibrium surface tension
Surface tension was determined using a KRUSS K12 Processor Tensiometer (Sigma 700, Biolin, Sweden, accuracy ±0.01 mN�m À 1 ) with a platinum ring by the continuous method at 25.0 ± 0.1 � C. All the solutions were aged for at least 24 hour before the surface tension measurements were carried out.For each concentration, the recorded values for surface tension were averaged over three measurements.

Molecular dynamics simulation
All molecular dynamics simulations were performed in the GROMACS 4.6.7 package.The C-AE 2 S and TTAB monomers were generated by the automated force field topology builder (ATB) with optimized geometry configuration.[35][36] To perform the simulation, the system was constructed as such a structure that one �4 nm water slab sandwiched between two �8 nm air slabs.Such a dimension was large enough to overcome the finite size effect.A simulation box with the dimension of 5 � 5 � 20 nm (Lx ¼ Ly ¼ Lz) was adopted, then the molecules were inserted into the box with the corresponding numbers listed in Table S1 for the different systems.Duo to the total 100 molecules and the two interfaces (sandwiched structure) in the box, the average concentration of C-AE 2 S and C-AE 2 S/TTAB was 2/nm 2 .Number of different EO adducts in C-AE 2 S used for simulation was shown in Table S2.Water molecules were described by the simple point charge (SPC) model.The steepest descent method was used to minimize the energies of the initial configurations.The initial configurations were shown in Figure S2.Furthermore, 200 ps MD simulations in 1 atm and 298 K were performed to keep the system in the appropriate volume, and the last 20 ns trajectory was used for analysis.Electrostatic interactions were calculated using the Particle Mesh Ewald (PME) algorithm.

Dynamic surface tension (DST)
The dynamic surface tension was performed by a KR € USS BP100 bubble pressure tensiometer (Kr€ uss Company, Germany, accuracy ±0.01 mN�m À 1 ) at 25.0 ± 0.1 � C. The effective surface ages were ranging from 0.01 to 200 s.The diameter of the capillary was approximately 0.21 mm.

Dynamic contact angle
The spreading abilities were measured by the contact angle of droplet on paraffin film using a drop shape analyzer DAS-100 (Kr€ uss Company, Germany, accuracy ± 0.1 � ) at 25.0 ± 0.1 � C.

Equilibrium surface tension
Equilibrium surface tension measurement directly revealed the surface activity of the surfactants.Figure 2 displays the plots of surface tension (c) versus lgC for AE 2 S, TTAB, and AE 2 S/TTAB mixtures with different mixing molar ratios.It is noteworthy that as the surfactant concentration increases, the surface tension decreases, which suggest the molecules tend to adsorb at the air/liquid interface.And then the surface tension reaches a plateau at a certain concentration that indicates the saturated adsorption and the formation of aggregates.The inflection points are defined as the critical micelle concentration (cmc) of surfactants. [37]he parameters obtained from the surface tension curves are shown in Table 1.As can be seen, the cmc values for C-AE 2 S/TTAB at molar ratios of 2:8, 5:5, and 8:2 were 2.84 � 10 À 5 mol/L, 1.20 � 10 À 5 mol/L and 1.67 � 10 À 5 mol/L, respectively, which were 10 times and 100 times lower than that of the individual surfactant of C-AE 2 S for 1.50 � 10 À 4 mol/L and TTAB for 3.57 � 10 À 3 mol/L, respectively.A similar phenomenon was observed in the binary system of N-AE 2 S/TTAB.This indicates that the AE 2 S/TTAB mixtures possess better surface tension reduction efficiency than the single surfactant does.The synergistic interactions between the anionic and cationic head groups and the hydrophobic effects between the hydrocarbon chains greatly promote the association between the two kinds of surfactant ions leading to forming micelles easier in  solution. [24]It is worth mentioning that the cmc values for C-AE 2 S/TTAB were lower than N-AE 2 S/TTAB at the same mixing molar ratio.This suggests that C-AE 2 S/TTAB has greater efficiency in reducing the surface tension of water as compared to N-AE 2 S/TTAB.On the one hand, in an aqueous solution, EO groups become somewhat electrically positive, [38] and the lower content of fatty ether sulfates in C-AE 2 S results in the stronger electrostatic interaction between the opposite charges in C-AE 2 S/TTAB than in N-AE 2 S/TTAB.On the other hand, because the EO groups are hydrophilic, the lower content of fatty ether sulfates in C-AE 2 S, leading to the stronger hydrophobicity interaction between hydrocarbon chains in C-AE 2 S/TTAB than in N-AE 2 S/TTAB.The stronger electrostatic interaction and the stronger hydrophobic interaction synergistically make C-AE 2 S/TTAB has the lower cmc.
The surface tension at cmc (c cmc ) of AE 2 S/TTAB mixtures can be reduced to about 25 mN/m, which is lower than that of either component.It is explained that the formation of surfactant mixtures will reduce the electrostatic repulsion between hydrophilic head groups of surfactant molecules, which leads to a denser monomolecular adsorption layer at the air/liquid interface. [39]Figure 3 shows the charge density distribution of surfactants at the air/liquid interface calculated by the simulation.It can be seen that the negative charges of C-AE 2 S (see Figure 3a) were drastically neutralized by the positively-charged TTAB at the interface in the system of C-AE 2 S/TTAB (see Figure 3b).Moreover, the c cmc of N-AE 2 S/TTAB is a little lower than that of C-AE 2 S/TTAB at the same mixing molar ratio, which means that N-AE 2 S/TTAB has greater ability for reducing the surface tension of water.It can be interpreted that N-AE 2 S contains more fatty ether sulfates, especially posses more high EO adducts, this introduces EO groups into surfactant molecules formed a curling structure, which leads to more surface active methylene groups exposing to the air in N-AE 2 S/TTAB than in C-AE 2 S/TTAB.
For ideal mixing solution of a binary system, the ideal cmc (cmc ideal ) values of surfactant mixtures can be calculated by Clint's equation [40] : where a 1 and a 2 are the molar fraction of surfactant 1 and 2, respectively.The effects of mixing ratios on the values of experimental cmc (cmc exp ) and cmc ideal for C-AE 2 S/TTAB and N-AE 2 S/TTAB mixtures are shown in Figure S3.From Figure S3, it can be seen that both the values of cmc exp for C-AE 2 S/TTAB and N-AE 2 S/TTAB mixtures are lower than those of the cmc ideal , which implies the non-ideal mixing behavior of AE 2 S and TTAB.When mixing AE 2 S and TTAB, there is a strong electrostatic interaction between the oppositely charged head groups improving the formation of mixed micelle.
The surface excess concentration (C max , mol/cm 2 ) and the minimum area per molecule (A min , nm 2 /molecule) can reflect the arrangement of surfactant molecule at the air/liquid interface, and are calculated by the Gibbs adsorption equation [41] : where R is the gas constant (8.314J�mol À 1 �K À 1 ), T is the absolute temperature, N A is the Avogadro ' s constant, and @c=@lgC is the slope below the cmc, n ¼ 2 for the pure AE 2 S and TTAB, and n ¼ 1 for the binary systems because the surface adsorption of the non-1:1 mixture is equal to that of the 1:1 mixture.The C max and A min obtained are listed in Table 1.As shown in Table 1, the higher C max and lower A min of the mixtures indicate that the molecular arrangement in the binary systems at the air/liquid interface is denser than the case of the single surfactant.This could because of the stronger attraction between the oppositely charges and weaker repulsion between the same charges.As compared to C-AE 2 S/TTAB, N-AE 2 S/TTAB systems have the smaller C max and larger A min values at the same mixing ratios.It may be explained by the higher content of fatty ether sulfates in N-AE 2 S leading to the larger molecular size.

Interaction parameters
In the binary system, the values of interaction parameters between two components in the adsorbed layers (b s ) and the micelles (b m ) can be used to characterize the nature and strength of two components.If b < 0, it indicates that two components are attracted to each other, while if b > 0, it indicates that two components are exclusive mutually.When b ¼ 0, it indicates that the binary system is an ideal solution in micelle or surface layer. [42]The interaction parameter for mixed adsorbed layers (b s ) can be calculated by Equations ( 5) and (6): where X 1s is the molar fraction of component 1 in mixed adsorbed layers.c 1 , c 2 , and c 12 are the molar concentrations of component 1, component 2, and their mixture under a specified surface tension (c ¼ 40 mN/m), respectively.Here, a is the molar fraction of component 1 in the solution system.
The interaction parameter for mixed micelles (b m ) can be obtained by Equations ( 7) and (8): where X 1m is the molar fraction of component 1 in mixed micelle.c 1m , c 2m and c 12m are the critical micelle concentration of component 1, component 2, and their mixture, respectively.Here, a is the molar fraction of component 1 in the solution system.The corresponding interaction parameters of AE 2 S/TTAB mixtures with different mixing ratios are listed in Table 2.As shown in Table 2, b s and b m values for both C-AE 2 S/TTAB and N-AE 2 S/TTAB mixtures with different mixing ratios are negative, indicating the attraction effect in the surface layer and micelle.When at the same mixing ratio, both b s and b m for N-AE 2 S/TTAB are less negative than those for C-AE 2 S/TTAB, which shows the weaker attraction between the components.The oxygen atom of EO group are positively charged in aqueous solution, and the higher concentration of fatty ether sulfates in N-AE 2 S than in C-AE 2 S results in the weaker electrostatic attraction in the binary systems.
The driving force of mixed micelles formation and the factors affecting the interaction between the surfactants can be further understood by the thermodynamic parameters. [43]he activity coefficients of the anionic and cationic surfactant in mixed micelles f 1m and f 2m can be obtained by Equations ( 9) and (10).The Gibbs free energy of micellization and adsorption (DG mic and DG ads ), excess enthalpy of micellization (DH mic ) and entropy of micellization (DS mic ) can be calculated from Equations ( 11)-( 14).Where Q is the surface pressure (c 0À c ), and C Q refers to molar concentration of the surfactant in the aqueous phase at a surface pressure Q .
DG ads ¼ DG mic À 6:022C P A min � 10 À 3 ( 12) The thermodynamic parameters of micellization for AE 2 S/TTAB mixtures with different mixing ratios are shown in Table 3.All the mixtures show negative �G mic , indicating that the formation of mixed micelles is spontaneous.Meanwhile, the �G ads for each system is more negative than the corresponding �G mic , and therefore adsorption is the primary process. [44]Furthermore, the negative �H mic and positive �S mic demonstrate that the interactions of a mixed system are controlled by the electrostatic and hydrophobic forces.Due to the absolute values of the ratio T�S mic /�G mic are lower than 0.5, both the micellization of C-AE 2 S/TTAB and N-AE 2 S/TTAB mixtures are enthalpically driven processes. [45]

Dynamic surface tension
Dynamic surface tension (DST) at the air/liquid interface plays an important role in a wide scope of applications.DST measurements with a maximum bubble pressure technique are highly suitable for investigating the kinetics of surfactant adsorption at the air/liquid interface. [46]It is generally believed that the adsorption on the fresh surface needs to go through two processes, that is, the surfactant monomer diffuses from the bulk into the subsurface, and then it adsorbs or desorbs at the interface until the dynamic equilibrium is reached.Figure 4 shows the DST of AE 2 S/TTAB mixtures with different mixing ratios at 0.01 (Figure 4a, b) and 10 mmol/L (Figure 4c, d).It can be seen from Figure 4 that at the initial stage of adsorption, the surface tension of both C-AE 2 S/TTAB and N-AE 2 S/TTAB systems decrease rapidly at different molar ratios and different total concentrations.When a new air/liquid interface is created, the surface concentration of unimers in adsorption layer is much less than that in bulk phase, which drives in a flow of unimers from bulk solution to the adsorption layer, and thus leading to a rapid drop in the surface tension.As the progress goes on, the concentration of unimers in adsorption layer gradually increases, and the speeds of diffusion and adsorption gradually decrease, therefore, the trend of dynamic surface tension decreasing with the increase of adsorption time gradually becomes gentle.Noticeably, both the rate of surface tension and the time required to attain adsorption equilibrium decrease obviously with an increase in the concentration of AE 2 S/TTAB.Toward the end of adsorption, the interface has been occupied by a considerable number of unimers to form an adsorption film.At this time, the interface has been relatively crowded.There is certain repulsion between surfactant molecules with the same charge, which hinders the diffusion and adsorption of new unimers from the subsurface to the interface to strike an "empty site".The higher the concentration of the bulk solution, the more unimers occupy the interface of the solution, and the more difficult it is for the surfactant molecules to carry out further diffusion adsorption.In the mixed surfactant system, strong attraction between the oppositely charged molecules can reduce the mutual repulsion and contribute new unimers to strike an "empty site" at the interface, thus promotes the further diffusion and adsorption of the surfactant molecules.The higher concentrations of the bulk, the more favorable it is for the molecules to diffuse further.And this may be the reason that the surface tension of the binary systems decrease faster than that of the single surfactant systems at the higher concentration of 10 mmol/L in Figure 4c, d than at the lower one of 0.01 mmol/L in Figure 4a, b.However, the ability to reduce the surface tension is due to a combination of various effects, such as the concentration, surfactant type, hydrophobic nature, area per molecule at the interface and temperature.In the dilute solutions (Figure 4a, b), especially for N-AE 2 S/TTAB at 0.01 mmol/L (Figure 4b), the surface tension of single surfactant system of N-AE 2 S decrease faster as the surface age increase than the binary systems, this is the result of combined effect of the electrostatic attraction and steric hindrance, and in this case, the steric hindrance plays a major role.
For the aqueous solutions at pre-CMC concentrations, The diffusion-controlled adsorption model is used to investigate the diffusion process of surfactant molecules by following Word-Tordai equation [47] : The former part refers to the molecules migration from bulk phase to subsurface, and the latter denotes that molecules diffusion from subsurface back to bulk phase with the increase of subsurface concentration.Due to the integral of back diffusion is hard to calculate, this equation cannot be solved.A asymptotic method for solving this Word-Tordai equation is put forward [48,49] : where C 0 is the bulk concentration, p ¼ 3.142, c(t) and c eq refer to the surface tension at time and at infinite time respectively, U eq is the equilibrium surface excess concentration.Equations ( 16) and ( 17) allow us to calculate the apparent diffusion coefficient from the slope of the DST data plots against t 1/2 (short-time) andt À 1/2 (long-time).
Figure 5 shows the DST as a function of t 1/2 and t À 1/2 for the AE 2 S/TTAB systems at 0.01 mmol/L.In Figure 5a, c, the plots show a linear behavior on the short time scale, and the values of the intercept are about the surface tension of pure solvent.In Figure 5b, d, the plots also exhibit a linear behavior on the long time scale, and the intercept are close to the surface tension of the systems at equilibrium.The values of the diffusion coefficients estimated at short-time (D s ) and long-time (D L ) obtained from the gradients of the plots in Figure 5 are summarized in Table 4.The ratio of D L /D s for AE 2 S/TTAB is far less than 1 that means D L is lower than D s , so the adsorption process for both C-AE 2 S/TTAB and N-AE 2 S/TTAB are mixed diffusion-kinetic adsorption mechanism.

Dynamic contact angle
Wetting is an essential property in practice, such as lubrication, coating, and painting. [50]Dynamic contact angle measurement is a useful method to understand the spreading of surfactant solution on the low-energy solid interface. [51]It is well-known that the smaller the angle is, the better the wettability is. Figure 6 shows dynamic contact angles of 10 mmol/L AE 2 S/TTAB as a function of time on paraffin film at 298 K.It is obvious that wetting (h � 90 � ) was observed on the paraffin film at the concentration above CMC.The dynamic contact angles of the binary systems are significantly lower than the single surfactant, and both the contact angle at the initial stage and the time taken to reach the final equilibrium contact angle decrease with the increase of the content of AE 2 S in the binary systems, which indicates that the composite systems have the synergistic interactions and the higher content of AE 2 S the stronger the synergistic effects during the spreading process.Contact  angle can be calculated by Young's formula that shown in Equation ( 18), where c sg , c sl , and c lg , are solid/air interface, solid/liquid, and liquid/air interface tension, respectively.c sg of the paraffin surface is 26 mN/m, and it does not change with surfactant concentration and time.According to Young's formula, the value of c lg cosh increases with the decreases of c sl .In this case, the concentration of the surfactant systems used for the experiment was 10 mmol/L, which is much higher than the cmc of AE 2 S/TTAB systems, at this stage saturated adsorption film at liquid/air interface has been formed, therefore, the value of c lg for each system keeps constant.Thus, cosh increases with the decreases of c sl .As paraffin is low energy surface, surfactant molecules adsorb onto the solid with its nonpolar hydrophobic group oriented toward the paraffin surface and its hydrophilic group oriented toward the solution, which makes the solid more hydrophilic and would reduce the solid/liquid interface tension (c sl ).For AE 2 S/TTAB at molar ratios of 2:8, 5:5, and 8:2, as the content of AE 2 S increases, at the same time the degree of hydrophilic modification of the solid surface is higher that leading to a more decrease of c sl .As h is lower than 90 � , an increase in cosh causes decreased contact angle.Therefore, the system for AE 2 S/TTAB ¼ 8:2 has better spreading wettability than AE 2 S/TTAB ¼ 2:8 and AE 2 S/TTAB ¼ 5:5.It can also be seen in Figure 6 that the dynamic contact angles of the binary systems for N-AE 2 S/TTAB are lower than that of C-AE 2 S/TTAB.This may be attributed to the high content of fatty ether sulfates, especially possess more high EO adducts in N-AE 2 S/TTAB than in C-AE 2 S/TTAB, permitting more hydrophilic modification of the paraffin surface and leading to lower c sl .

Conclusion
In this study, the equilibrium and dynamic surface properties of AE 2 S/TTAB mixtures with different mixing molar ratios were investigated.30] in the Supporting Information, the free alcohol and low mole horologes in the ethoxylate mixture of N-AE 2 O is much lower than that of C-AE 2 O, which results in the lower content of fatty ether sulfates and low EO adducts in N-AE 2 S than in C-AE 2 S. Tetradecyltrimethylammonium bromide (TTAB) was supplied by Shanghai Aladdin Bio-Chem Technology Co., Ltd.Liquid paraffin was purchased by Tianjin Kermel Chemical Reagent Co., Ltd.The structural formulas of AE 2 S and TTAB were shown in Figure S1.All reagents were analytical-reagent grade.The deionized water with a resistivity of 18.25 MX�cm was prepared by a UPD-II ultrapure water purifier in all experiments.

Figure 1 .
Figure 1.EO distribution in C-AE 2 O and N-AE 2 O.

Figure 2 .
Figure 2. Surface tension curves of mixtures with different mixing molar ratios at 298 K (a) C-AE 2 S/TTAB and (b) N-AE 2 S/TTAB.

Figure 3 .
Figure 3. Charge density distribution of surfactants at the interface calculated by the simulation (a) C-AE 2 S and (b) C-AE 2 S:TTAB ¼ 2:8.
surfactant mixtures exhibit strong synergistic effects in the reduction of surface tension, the formation of micelles and enhance wettability.C-AE 2 S/TTAB has greater efficiency for reducing the surface tension of water, while N-AE 2 S/TTAB has a better ability to reduce the surface tension at the same mixing molar ratio.The adsorption models for both C-AE 2 S/TTAB and N-AE 2 S/TTAB systems are confirmed to be diffusion-kinetic adsorption model.Moreover, Compared with C-AE 2 S/TTAB and N-AE 2 S/TTAB systems exhibit better spreading behavior than that of C-AE 2 S/TTAB.

Table 1 .
Parameters of surface properties for AE 2 S/TTAB mixtures with different mixing ratios at 298 K.
aThe uncertainty limits of the values are ±3%.

Table 3 .
Thermodynamic parameters of AE 2 S/TTAB mixtures with different mixing ratios at 298 K.
aThe uncertainty limits of the values are ±3%.

Table 2 .
Interaction parameters of AE 2 S/TTAB mixtures with different mixing ratios at 298 K.

Table 4 .
Effective diffusion coefficients of AE 2 S/TTAB with different molar ratios at 298 K.
aThe uncertainty limits of the values are ±4%.