Molecular Structure Inhibiting Synergism in Charged Surfactant

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

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Molecular Structure Inhibiting Synergism in Charged Surfactant Mixtures: An Atomistic Molecular Dynamics Simulation Study Gözde Ergin, Mária Lbadaoui-Darvas, and Satoshi Takahama* Atmospheric Particle and Research Laboratory, School of Architecture, Civil and Environmental Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: Synergistic and nonsynergistic surfactant−water mixtures of sodium dodecyl sulfate (SDS), lauryl betaine (C12B), and cocoamidopropyl betaine (CAPB) systems are studied using molecular simulation to understand the role of interactions among headgroups, tailgroups, and water on structural and thermodynamic properties at the air−water interface. SDS is an anionic surfactant, while C12B and CAPB are zwitterionic; CAPB differs from C12B by an amide group in the tail. While the lowest surface tensions at high surface concentrations in the SDS−C12B synergistic system could not be reproduced by simulation, estimated partitioning between surface and bulk shows trends consistent with synergism. Structural analysis shows the influence of the SDS headgroup pulling C12B to the surface, resulting in closely packed structures compared to their respective homomolecular-surfactant systems. The SDS−CAPB system, on the other hand, is nonsynergistic when the surfactants are mixed on account of the tilted structure of the CAPB tail. The translational excess entropy due to the tailgroup interactions discriminates between the synergistic and nonsynergistic systems. The implications of such interactions on surfactant effects in complex, multicomponent atmospheric aerosols are discussed.

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compound mixtures studied in laboratories,12 also exhibiting concentrations far exceeding the apparent CMC level.13 Hypotheses regarding the discrepancy between the magnitude of surface tension reduction studied in the laboratory and ambient aerosols can be attributed to the existence of particular types of molecules in atmospheric particles which lower the surface tension significantly (e.g., biosurfactants),14 synergistic interactions among the molecules which are present,15 or both. In this work, we investigate properties leading to the second hypothesis. Recent speciation of the surface-active molecules from atmospheric aerosols indicates the presence of anionic, neutral, and cationic mixtures.13 Researchers have previously studied the synergism among charged and uncharged surfactants through experiments16−26 and chemical thermodynamic modeling.27−29 Synergism between charged and uncharged surfactants are mainly attributed to the electrostatic interaction between ionic and ion-dipole interaction between ionic−noninoic hydrophilic headgroups.17,18,27−29 On the other hand, steric interactions between hydrophobic tailgroups occupying increasingly large volumes, for instance, when branched structures are present, can reduce instances of synergism.1,29,30 Given the large number geometries and interactions that regulate these relationships, many approaches are needed to predict how different combination of surfactants

INTRODUCTION Synergism among surfactant mixtures at the air−water interface leads to surface properties that are not easily predicted from the behavior of their individual components. Synergism is caused by nonideal interactions and can be categorized by how they alter the relationship between the concentration of surfactant molecules in the bulk solution and its apparent surface tension: positive synergism describes cases in which the surface tension of the mixed system is elevated with respect to each of its homomolecular-surfactant counterparts, while negative synergism describes cases in which the surface tension of the mixed system is depressed.1 The effect of surfactant mixtures on surface tension reduction can be described in terms of its efficiency, lowering the surface tension at a given bulk-phase concentration, or its effectiveness, lowering of the surface tension at the threshold of its saturation point, or critical micelle concentration (CMC).1 Understanding such phenomena is important for selecting surfactants for industrial processes or predicting cloud droplet formation behavior of atmospheric aerosols. For instance, field studies repeatedly show that surface-active organic molecules are prevalent in atmospheric particles.2−5 Surfactant partitioning between the bulk and surface affects solution activity and surface tension, altering the supersaturation of water vapor in rising updrafts required to “activate” these aerosols into cloud droplets.6−10 New methods for extraction of surface-active molecules from atmospheric aerosols collected in field studies11 have revealed lower surface tension (∼30 mN/m) than most © XXXX American Chemical Society

Received: September 23, 2017 Revised: November 17, 2017 Published: November 21, 2017 A

DOI: 10.1021/acs.langmuir.7b03346 Langmuir XXXX, XXX, XXX−XXX

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which introduces both a hydrophilic component and tilt to the tail structure. Even while these exact molecules have not been discovered in atmospheric aerosol particles, their structures capture many essential characteristics of environmentally surface-active molecules and a comparative analysis provide additional insights into parameters regulating synergism among complex surfactants. After describing our general approach of simulation, we report structural differences resulting from surfactant− surfactant and surfactant−water interactions for the SDS− C12B system and their relationship to surface tension and bulksurface partitioning. Corresponding descriptors relevant for characterizing the SDS−CAPB system are then presented. A qualitative discussion of thermodynamic properties leading to divergent behavior between the two mixtures follows. Summarizing our findings regarding the nature of synergistic and nonsynergistic systems, we discuss possible implications of mixing surfactants on the surface tension in atmospheric aerosols.

affect surface tension and concentrations in the bulk. For instance, a semiempirical parameter derived from regular solution theory can be used to characterize the strength of interaction between two surfactants relative to their homomolecular-surfactant systems. Models relating bulk concentrations of surfactants to surface tensions often comprise adsorption isotherms (relating bulk and surface concentrations or activity) and surface equations of state (relating surface concentrations to surface pressure).31,32 Electrostatic headgroup interactions are often modeled as an electrical multilayer configuration combined with a diffuse charging region at the interface, which has yielded successful results in past studies.28,33−35 In principle, these relationships can be obtained using molecular simulation of classical statistical mechanics36 governed by the same underlying set of physics (i.e., molecular interactions parametrized by semiempirical force fields). For instance, Phan et al.37 analyzed the adsorption of a ternary surfactant−water mixture by molecular simulations and explained its positive synergism through the change in water orientation over their single-surfacant counterparts. Molecular simulations have been used to investigate aggregation in related micellar structures. Given the size of typical surfactant molecules, simplification of molecular representation is sometimes used to reduce the computational burden. In this approach, molecules are discretized by their functional units rather than their constituent atoms (resulting in “united-atom” or “coarse-grained” parametrizations of their interaction potentials38,39) to reduce the number of interactions that must be evaluated during simulation. While such simplifications can provide insights into the overall behavior of the system, some detail regarding hydrogen bonding is lost and the dynamics of the system can be different from that expected from real systems.40,41 All-atom representations are computationally expensive and are more limited with respect to system size or length scales that it can access, but preserve atomistic details such as hydrogen bonding which can play an important role in water−water and organic−water interactions. In this study, we perform all-atom molecular dynamics (MD) simulations to investigate the synergism in surface tension reduction efficiency in zwitterionic−anionic mixed systems. To evaluate our capability to reproduce this type of behavior with MD simulation and explore key parameters governing synergistic behavior, we consider systems for which experimental measurements have been previously reported. We first study in detail the binary (surfactant−water) and ternary (surfactant−surfactant−water) systems containing sodium dodecyl sulfate (SDS) and lauryl betaine (C12B) at several fixed surface concentrations. SDS is a well-studied,33,42−44 commonly used surfactant in industry (mainly used in detergents for laundry with many cleaning applications) and serves as a model surfactant in atmospheric studies.10 C12B is a widely used surfactant in commercial shampoos and hair conditioners because of its propensity to stabilize foams and reduce eye and skin irritation.16,21 Previous studies have consistently shown that the SDS−C12B mixture exhibits marked deviations from ideality in both surface tension reduction efficiency and effectiveness, providing a model system for our initial study and evaluation of its molecular interactions.17,20,28 For contrast, we present simulations for a nonsynergistic system of SDS and cocoamidopropyl betaine (CAPB)16 at one surface concentration. CAPB differs from C12B only by a secondary amide group in the skeletal tail,

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METHODS

The systems studied include water with several surfactants: anionic sodium dodecyl sulfate (SDS), zwitterionic lauryl betaine (C12B), and zwitterionic cocoamidopropyl betaine (CAPB; Figure 1). We label our

Figure 1. Schematic representation of the simulated surfactants (a) SDS (NaC12H25SO4), (b) C12B (C16H33NO2), and (c) CAPB (C19H38N2O3). binary systems surfactant and water as SDS_W, C12B_W, and CAPB_W and our ternary systems (mixture of two different surfactant types and water) as MIX_W and MIX2_W for %50 SDS + %50 C12B and %50 SDS + %50 CAPB in mole fraction, respectively. Simulations are performed using Gromacs 5.045 MD software. The CHARMM3646 force field is applied to specify the all-atom intramolecular and intermolecular potentials between surfactant− water and surfactant−surfactant molecules. Water molecules are modeled by the rigid TIP3P47 potential. All bond lengths are constrained to their equilibrium values using LINCS48 linear constraint solver. To treat short-range interactions we use a spherical atom centered cutoff of 1.2 nm, beyond which Lennard-Jones interactions are truncated to zero. Long-range electrostatic interactions are taken into account by the Particle Mesh Ewald (PME) method beyond the same cutoff. We use NVT ensemble for the interfacial surface and NPT ensemble for bulk simulations. The Parrinello−Rahman barostat49 is used to control the pressure at 1 atm. The temperature (300 K) is implicitly handled by the leapfrog stochastic dynamics integrator50 which is used to solve the equations of motion with a time step of 2 fs. The initial configurations are generated by randomly placing the molecules in the specified regions of the simulation boxes and subjected to two minimization processes: steepest descent and low-memory Broyden−Fletcher−Goldfarb−Shanno (L-BFGS) approach.45 The simulations are sampled for 4 ns after 6 ns of equilibration. We estimate the partitioning of surfactant from surface to bulk by calculating the chemical potential differences between surfactant B


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Figure 2. y−z projection of the (i) surface and (ii) bulk simulation box for C12B_W. Green, blue, red, and white colors indicate carbon, nitrogen, oxygen, and hydrogen atoms, respectively. Water molecules are shown in dark gray. molecules on the surfactant-covered water surface and in bulk water. The surfactant bilayer is modeled with a rectangular box with dimensions of 5 × 5 × 40 nm3. Two surfaces are separated by a 14 nm water layer, and the surfactant molecules occupy an approximately 3 nm wide region on each surface. There is a 10 nm layer of vacuum space on each surface. The simulations are performed for SDS_W and C12B_W systems with the surface concentrations from 0.26 × 10−6 to 2.92 × 10−6 mol/m2 (0.16 to 1.76 molecules/nm2). Additionally two extra surface concentrations, 4.40 × 10−6 mol/m2 and 5.44 × 10−6 mol/m2, are simulated for MIX_W. These surface concentrations for binary and ternary systems encompass liquid-expanded (LE) to liquidcondensed (LC) states.17,19,25 For CAPB_W and MIX2_W systems, only one surface concentration (Γ = 1.99 × 10−6 mol/m2 or 1.19 molecules/nm2) is simulated. This surface concentration is the closest surface concentration to the saturated surface concentration value for CAPB_W.51 For bulk simulation, one surfactant molecule is placed in a 5 × 5 × 5 nm3 water box in order to represent the infinitely dilute condition. The biggest surfactant (CAPB) length is 2.4 nm and the size of the box is large enough to avoid interactions between the surfactant and its periodic images. Snapshot of the surfactant and bulk simulation boxes can be seen in Figure 2. We briefly summarize the method for estimating surface-bulk partitioning detailed by Shen and Sun,52 which we apply in this work. The free energy change for each region α is written as

ΔGα = μα ,surfactant − nμα ,water

The primary challenge in applying eq 3 remains in numerical estimation of the excess chemical potentials. μsex and μbex are determined from thermodynamic integration (described below) and the ideal part of the surface chemical potential [RT ln xs/(1 − xs)] is analytically calculated. For a given surfactant mole fraction in the surface region xs, the mole fraction in the bulk region xb is given by

xs =

Cs Cw + Cs − Cexch,s

xb =

Cb . Cw + C b − Cexch,b

(4)

Cs and Cb are the molar concentration of surfactants on the surface and in the bulk, Cw is the molar concentration of pure water, Cexch,s and Cexch,b are molar concentrations of water that are occupied by surfactants in the surface and in the bulk, respectively. Cexch,s and Cexch,b can be written as Cexch,s = nCs and Cexch,s = nCb, where Aw is the number of water molecules that can fill the equivalent volume of one surfactant: 18 for SDS, 30 for C12B, and 40 for CAPB. Thermodynamic integration55 (TI) is used to calculate the excess chemical potential of surfactant on the surface and in the bulk. One surfactant molecule is decoupled during the simulation and chemical potentials are calculated by Zwanzig relationship:56

(1)

where α can be either the interfacial region, s, or the bulk phase, b. n indicates the number of water molecules whose volume of these water molecules equals the volume of one surfactant. At surface-bulk equilibrium, the chemical potential of surface molecules on the surface must be equal to its chemical potential in the bulk:52−54 μs ,surfactant − nμs ,water = μb ,surfactant − nμb ,water (2)

μiex ,i+1

⎡ ⎢ exp = − RT ln⎢ ⎢ ⎢⎣ exp

( (

−ΔUi , i + 1 / RT 2

ΔUi , i + 1 / RT 2

)

⎤ ⎥ i ⎥ ⎥ ⎥ i+1 ⎦

)

(5)

ΔUi,i+1 is the potential energy differences between states at the different coupling factor, λ from 0 to 1. μex i,i+1 is estimated by taking the average of forward (numerator of eq 5) and reverse (denominator of eq 5) potential energy differences. TI is a free energy perturbation approach similar to Widom’s particle insertion method57 but does not require changing the number of molecules or atoms in the system. λ = 0 is the initial and λ = 1 is the final state where the target molecule is decoupled. λ is linearly turning off with an interval of 0.1 for the electrostatic interactions and turning off by using soft-core potential58 with an interval of 0.05 for the van der Waals interactions. The equilibration time of 6 ns of the TI simulations have been verified by checking the convergence of forward and reverse chemical potentials (Figure S1). The errors, σsim(λ), at each λ are calculated using block average method by dividing the trajectory into blocks and computing the standard error of the observable for each block.59 The error in the estimated excess chemical potentials difference is calculated by

The chemical potential μ can be decomposed into its ideal and excess contributions52 μα = μidα + μex α . Separating eq 2 to its excess and ideal parts leads to the following expression for the surfactant: xs xb μsex + RT ln = μ bex + RT ln 1 − xs 1 − xb (3) ex where μex s and μb represent the excess chemical potential differences for the process of replacing same volume of water by one surfactant molecule. Chemical potentials of the surface and bulk are estimated in two uncoupled TI simulations; consequently, the water contribution on the free energy changes of moving one surfactant between surface and bulk is considered. If a surfactant is moved from surface to bulk the same volume of water is moved in reverse direction.

C


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Table 1. Surface Tension Values from Simulations (γMD ′ = γMD + 15) and Experiments (γexp.; mN/m) as a Function of Surface Concentrations Γ (×106 mol/m2)a γMD ′ Γ

SDS_W

0.26 1.06 1.99 2.92 4.40 5.44 a

69.7 68.2 58.1 50.1

[1.3] [2.0] [1.0] [1.3]

C12B_W 71.0 68.7 56.0 49.3

[1.5] [1.3] [3.3] [1.6]

γexp. MIX_W 68.9 69.0 68.8 69.8 66.8 61.0

[1.2] [2.4] [2.0] [3.2] [1.3] [4.4]

SDS_W25

C12B_W19

MIX_W17

70 68 58 50

71 67 60 47

70 69 68 67 45 30

Errors are shown in square brackets.

Figure 3. Area distribution of the Voronoi polyhedra of the projections of (a) water oxygens and central atoms of the headgroups (sulfur and nitrogen for SDS and C12B respectively), (b) only water oxygens, and (c) only headgroup central atoms.

σΔμex =

∫0

1

σsim(λ)2 dλ

NVT ensemble by relaxing the surface area to 5 × 5 nm2. Convergence time is also estimated to be within 6 ns (Figure S3). Uncertainties in the surface tension are calculated by using the block average method. The surface tension of pure water as estimated with the TIP3P potential is 57 mN/m, and the difference between experiment and simulation (72−57 = 15 mN/m) is added to the surface tension estimates reported for the SDS_W, C12B_W, and MIX_W systems in Table 1. For the CAPB_W and MIX2_W systems, bias-corrected surface tensions are estimated as 68.4 ± 1.3 and 68.2 ± 1.5. The existence of bias with respect to experimentally determined values of pure water surface tension is known and may arise from specific phenomena not fully accounted for by eq 7.61,62 However, the derivative of surface tension with respect to surfactant molecules is largely governed by the surface equation-of-state (the relationship between surface concentration and surface pressure), which the MD simulations appear to reproduce well except at the highest surface concentrations in the mixed system (which we largely attribute to organic− organic interactions as described below). While we cannot rule out the varying contribution of water−surfactant interactions to the surface tension, we empirically find that the bias can be assumed to be constant in most cases and is therefore added to the estimated values estimated (a common convention for molecular simulation).63,64 In order to compare experimental and simulated surface tension for the MIX_W system at lower surface concentrations,

(6)

A flat-bottomed position restraint45 is used to restrain surfactants on the surface with a spring constant of 418.4 kJ mol−1 nm2. Boltzmann exponential reweighting method52 is used to remove the effect of flatbottomed position restraints on excess chemical potentials. However, the preferred position of the surfactants is observed to be the surface layer, and the effect of the potential on the overall energy is negligible and less than the average energy of degrees of freedom (3kBT/2; Figure S4).

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RESULTS AND DISCUSSION Surface Tension. The surface tension values of surfactant systems for different surface coverages are compared with experimental results in this section. The average surface tension is calculated from the difference between the normal and lateral pressure60 γ (t ) =

Lz (PN(t ) − PL(t )) n

(7)

where Lz is the height of the box and n is the number of surfaces. The similar equilibration (6 ns) and production (4 ns) time is also used for surface tension calculation as TI simulations. In order to ensure the calculated values are converged, the MIX_W system with Γ = 5.44 mol/m2 surface concentration is also simulated by using the NγT ensemble by fixing the surface tension at 30 mN/m. The last configuration of the NγT ensemble simulation is then simulated under the D


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Langmuir we extrapolate the surface tensions from experimental data17 using a linear fit. The simulation results for the binary surfactant systems are in good agreement to reported results in the literature,19,25 but deviations are observed for the ternary systems especially at high surface concentrations.17 This inconsistency may be due to the lack of nonbonded interaction parameters (NBFIX) between charged groups, nonoptimized charge distribution and/or insufficient simulation times.62,65−70 However, the concentration dependence is estimated correctly by simulation. Using different force field parametrizations (Tables S1 and S2) can lead to lower surface tension values, down to 48 mN/m at the highest concentrations in our simulations, but have no impact on structural parameters examined in our system. Therefore, we discuss results obtained using our standard force fields described in the Methods section above. The surface tensions for the ternary system at lower surface concentrations are more similar to that of the pure water than those of the binary systems (Table 1), which is explained by the lateral arrangement of surfactans on the surface. The lateral structure of the interface is obtained by means of Voronoi analysis in two dimensions corresponding to the plane of the interface.71,72 We calculate the distribution of the size of the Voronoi cells for the set of points created by projecting the position of water oxygens, sulfur atoms (S) of SDS and nitrogen atoms (N) of C12B on the macroscopic plane of the interface. Then we repeat the analysis disregarding waters and keeping only surfactants and vice versa. One characteristic of these curves is that at a nearly uniform distribution of points in the curve provide a nearly Gaussian distribution, whereas any self-organization or clustering is represented by a tail appearing at larger sizes in the curve. Size distributions of Voronoi cells are shown in Figure 3. When representative atoms from both water and surfactants are considered indiscriminately, we obtain rather Gaussian-like distributions for the single-surfactant as well as the mixedsurfactant surfaces (Figure 3a), showing that the lateral spread of atoms across the surface is quite even. Examining water and surfactants separately for the binary system, we find that surfactants are evenly distributed within a matrix of water molecules as evidenced by the similar Voronoi cell size profiles (Figure 3b,c). The greater size of surfactant headgroups than water molecules is reflected by larger Voronoi cluster sizes and higher peak locations (near 100 Å2 for SDS_W and 150 Å2 for C12B_W in Figure 3c). The tail toward larger areas signifies the presence of small clusters of surfactants embedded in the uniform water matrix. The cell area profiles for the ternary system show more striking features. The appearance of a tail in both the water oxygen (ranging up to ∼75 Å2, Figure 3b) and the headgroup central atoms indicate clustering of water molecules that collectively occupy a greater surface area than in the binary system. The strongly asymmetric surfactant distribution (Figure 3c) suggests an uneven distribution of surfactants. Some surfactants are closely packed and isolated, while larger clusters emerge to cover a larger area (up to 500 Å2 in the distribution). This uneven distribution results in the presence of a surfactant-free portion of the aqueous interface, which likely explains the increasing surface tension at moderate surface coverage by the synergistic surfactants. Surface-Bulk Partitioning. The surface-to-bulk partitioning of anionic and zwitterionic surfactants are estimated by calculating the chemical potential differences using the two

uncoupled simulation boxes. The surface concentration is analytically calculated and included to excess chemical potential of surface in eq 3, and the results are shown in Table 2. The Table 2. Surface Chemical Potentials, μs = μsex + RT ln

xs 1 − xs

(kcal/mol) of Surfactants on the Surface as a Function of Surface Concentrations, Γ (×106 mol/m2)a μs SDS in SDS_W

Γ

−83.88 −83.66 −83.24 −83.05

0.26 1.06 1.99 2.92 4.40 5.44 a

[0.09] [0.13] [0.12] [0.21]

C12B in C12B_W −68.75 −67.70 −65.45 −64.67

SDS in MIX_W

[0.11] [0.18] [0.19] [0.24]

−84.53 −84.00 −84.75 −84.23 −83.61 −83.20

[0.09] [0.17] [0.18] [0.23] [0.39] [0.24]

C12B in MIX_W −68.80 −69.75 −69.49 −70.10 −66.99 −63.64

[0.11] [0.18] [0.19] [0.30] [0.33] [0.29]

Errors are shown in square brackets.

surface chemical potential, μs, increases with the surface concentrations as expected. While the surface concentration reaches the saturation point, more molecules partition to the bulk as consistent with Gibbs adsorption theory.73,74 The chemical potential of the bulk is estimated as −75.20 and −59.75 kcal/mol for SDS_W and C12B_W, respectively, within the assumption of infinite dilution52,54,75 and treated as a constant. Equilibrium bulk concentrations are obtained by using eq 3 from the simulated chemical potentials and analytically calculated ideal contribution of surface concentrations. These results are compared to experimental equilibrium concentrations of the SDS_W,76 C12B_W,19 and MIX_W17 systems. While discrepancies between simulated and experimental results are evident in Figure 4, trends along the concentration range are similar to those obtained from experiments. For the mixed system, we have experimental surface concentrations17 down to 2 × 10−6 mol/m2; thus, we could not compare the partitioning at 0.26 × 10−6 and 1.06 × 10−6 mol/m2. Corresponding simulated bulk concentration values for SDS_W are in agreement with Purcell et al.,76 C12B_W with Hines et al.,19 and MIX_W composition with Hines et al.17 In comparing results from the binary and the ternary system (Table 2 and Figure 4), we find that μs values are lower for the mixed surfactant systems, and consequently, the partition from surface to bulk is lower. This comparison indicates that it is more favorable for the surfactants to reside on the surface in the ternary system than in the binary ones. While experimental surface tensions in the MIX_W system at high surface concentrations are not reproduced (Table 1), the simulated trends in partitioning are consistent with a synergistic system when evaluating surface tension reduction efficiency along the Gibbs isotherm:1,77 dγ = −nRT Γd(ln C)

∫γ

γwater

surfactant

dγ = Π = −nRT

∫C

0

Γ d(ln C) (8)

Π is the surface pressure and n is the number of solute species whose concentration at the interface changes with change in the value of molar concentration, C. For SDS, nSDS = 2 and for C12B, nC12B = 1 since there is no counterion adsorption is expected. For their mix, n = nC12BXC12B + nSDSXSDS where XC12B E


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Figure 4. Surfactants equilibrium concentrations between surface and bulk of simulated systems compared with experiments. Red lines on simulation points show the error bars and continuous lines are fitted curves to simulation results for Gibbs isotherm theory.

and XSDS are the mole fraction of species at the MIX_W interface. Additionally since both the bulk and surface mole fractions for SDS and C12B in the MIX_W system remain constant with total concentration, ΓMIX_W = ΓSDS in MIX_W + ΓC12B in MIX_W and CMIX_W = CSDS in MIX_W + CC12B in MIX_W.78,79 To obtain the relationship Γ = Γ(C), ln C is fitted to a secondorder polynomial function of Γ (since the residual to be minimized is along the simulated quantity, ln C) and inverted to obtain the inverse relation, which is then integrated for the concentrations below CMC (Figure 5). For the same surface

surface tension value (∼68 mN/m), the bulk concentration in MIX2_W is higher than CAPB_W, which indicates that the MIX2_W system is nonsynergistic. Structural Analysis. We next present particular structural features of the surface that arise from synergistic and nonsynergistic interactions among mixed surfactants. We present detailed structural results for the same concentration (1.99 × 10−6 mol/m2) for synergistic and nonsynergistic systems. More detailed structural analysis on the synergistic system (i.e., water dipole order (Figures S10 and S11), hydrogen bond number, and radial distribution functions (RDF; Figure S12)) can be found in the Supporting Information. While different force fields result in different surface tension values for the MIX_W system, structural arrangements described below are insensitive with respect to choice of this parametrization (Figures S6−S8). Therefore, our structural descriptions explain how efficient surface packing is permitted in the mixed systems rather than how they affect the surface tension directly. In the following sections, we present relevant descriptors of mesoscale surface arrangement (i) and surfactant orientation (ii−iv) that result from synergistic and nonsynergistic mixing of surfactants. In summary, for synergistic system, SDS and C12B prefer to stay closer to each other in the mixed system than homomolecular-surfactant systems of the same surface concentration, with SDS exerting a pulling force on C12B in the MIX_W system both in the vertical and lateral directions. In the nonsynergistic system, the hydrophilic amide group in the tailgroup reorients the vertical distribution of CAPB and leads to inhibited interaction with SDS. Analysis of the minimum distance between headgroups with headgroup and tail orientations reveals preferred interactions of the headgroups and their effect on molecular orientation both in the MIX_W and MIX2_W systems. Depth Profile of Surfactants. The relationship between surface arrangement and synergism is analyzed with the aid of ITIM (identification of the truly interfacial molecules),80 which is a method that balances computational cost and accuracy for extracting the behavior of only the dynamically changing and molecular rugged surface from a simulation trajectory. ITIM defines interfacial molecules as those being first touched by a probe sphere of a given radius approaching a surface along gridlines perpendicular to the macroscopic plane of the interface. Since this algorithm finds not only the covering surface but also

Figure 5. Surface pressure with errors as a function of the bulk concentration, estimated from simulated surface and bulk concentrations and Gibbs adsorption isotherm.

pressure, the mixed system bulk concentration is always lower than the SDS and C12B binary surfactant systems, consistent with negative synergism in surface tension reduction efficiency. Chemical potentials for CAPB in bulk, CAPB in the surface CAPB_W, and in the MIX2_W surface systems are −65.4, −76.17, and −77.73 kcal/mol, respectively. The chemical potential of bulk and surface values for SDS in the binary system are reported in Table 2, and in the MIX2_W system, the chemical potential of SDS is −84.16 kcal/mol. Since the simulated CAPB_W and MIX2_W surface tensions are almost similar (68.4 and 68.2) and these results are consistent with experimental studies,16,51 we can directly compare the bulk concentrations of binary and ternary systems to understand the existence or nonexistence of synergism. The bulk concentrations of the binary system and the ternary systems are estimated as 2.2 × 10−4, 1.1 × 10−6, and 1.6 × 10−5 mol/L for SDS_W, CAPB_W, and MIX2_W, respectively. At the same F


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Figure 6. Schematic representation of the percentage of surfactant headgroups in four surface layers for (a) synergistic and (b) nonsynergistic systems. Dots are added for illustration.

Figure 7. Probability distribution of the angle of N−O for (a) synergistic and (b) nonsynergistic systems.

For nonsynergistic system, CAPB penetrates deeper into the bulk than C12B (Figure 6b) due to the amide group in the chain preferring closer proximity to the water. Even though the presence of SDS increases the percentage of CAPB headgroups in the first layer, there are more CAPB headgroups in the second layer that cannot interact with SDS. This lack of interaction reduces the synergistic effects between charged headgroups. In the following section we focus our structural analysis on the first layer. Headgroup Association. Minimum distances between headgroups of sulfate−sulfate for SDS_W, betaine−betaine for C12B_W and CAPB_W, and sulfate−betaine for MIX_W and MIX2_W are estimated to further examine surfactant headgroup interactions. Headgroups are represented by their center of mass. For SDS_W, C12B_W, and MIX_W these values are found to be 0.455, 0.435, and 0.285 nm, respectively. In MIX_W, C12B and SDS preferentially stay closer due to the attractive headgroup forces, leading to increased free area on the surface to which more surfactants can adsorb. This result is consistent with the increased partitioning toward the surface simulated for the MIX_W system, and the free water surface revealed by Voronoi analysis for the MIX_W system at lower surface concentrations. The minimum distance among headgroups in the CAPB_W and MIX2_W surfactant systems are found to be 0.3 and 0.29 nm. Adding anionic SDS surfactant to zwitterionic CAPB does not decrease significantly the minimum distance between betaine and sulfate head groups. The charged interactions between SDS and CAPB in this case are not strong enough to increase the packing on the surface as for SDS and C12B mixed system. More information about the effect of minimum distance on the structure of the surfactant is gained by analyzing the head and tail orientation.

the full list interfacial molecules, it allows investigation of several molecular layers of the same system. This analysis provides both horizontal and perpendicular distributions of surface molecules, which are related to surface tension. The radius of the probe sphere is a free parameter which has to be chosen a priori based on the size of atoms in the interfacial system, and implications of its selection have been thoroughly assessed by Jorge et al.81 For our case, we use a probe sphere of radius 0.2 nm and 50 × 50 grid, with a grid spacing of 0.1 nm. We carry out the analysis for four consecutive molecular layers in order to obtain an in-depth distribution of the surfactant molecules. We only consider surfactant headgroups and water molecules; alkyl chains are disregarded from the analysis. We characterize the depth distribution of surfactants by summing the number of headgroups found in each molecular layer of water from the ITIM analysis. Our results in Figure 6a show that in the binary systems both SDS and C12B headgroups stay preferentially in the first two atomic layers, with a small but non-negligible contribution in the third layer. For the ternary synergistic system, the distribution is clearly narrower and shifted toward the first layer. In particular, the percentage change in layers for C12B_W is more visible than for SDS_W. The presence of SDS molecules forces the C12B headgroup out of its vertical orientation, thus, compensating the configurational entropy gain deriving from being spread across several molecular layers. This finding is in agreement with the experimental results of Hines et al.17 The density distribution of charged headgroups (Figure S13) also shows the alignment of the oppositely charged groups effectively within the same layer. Based on this vertical profile, we attribute the synergistic effect in the MIX_W system mostly to the behavior of the molecules in the first molecular layer. G


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Figure 8. Carbon order parameters from head to tail of (a) SDS and C12B and (b) SDS and CAPB both in the binary and in the ternary systems, respectively.

Headgroup Orientation. To further elaborate structural reasons behind favorable and unfavorable surfactant−surfactant interactions, we calculate the probability distribution of the angle of N−O (nitrogen−oxygen) vectors defining the orientation of the C12B and CAPB headgroup with respect to the unit vector parallel to the macroscopic plane of the interface. The two N−O vectors belonging of each molecule are averaged when calculating the angle distribution. The angle distribution turns out to be very similar in C12B_W and in the MIX_W system (Figure 7a). The probability of assuming a specific angle decreases toward larger angles; that is, configurations where the headgroup points close to perpendicularly toward the interface are in general less frequented than the close-to-parallel orientation. The only striking feature of the otherwise decreasing distribution is a large peak centered at 45°, which shows the preference of the betaine headgroup to assume a tilted orientation. Such an arrangement minimizes the contact of the hydrophobic oxygen atoms with the surface while increasing repulsion between the negatively charged oxygen atoms to a smaller extent than the closely packed perpendicular orientation would. The addition of SDS does not change the distribution significantly, as at this concentration there is enough space for the sulfate headgroups without altering the favorable orientation for the C12B molecules. To complete the analysis of the headgroup orientation, we determine whether the headgroup is “stretched” or “bent”. We address this question by calculating the distance between the N atom and the midpoint of the segment defined by the two oxygen atoms. The estimated distance of 0.32 nm corresponds to a fully stretched headgroup; thus, we can conclude that the C−C bond of the headgroups prefers to be in the trans conformation, and no bending of the headgroup is observed. Similarly, the headgroup orientation of the CAPB betaine group reveals fewer changes between the binary and ternary systems where the orientation of the N−O peaks remain at 45° (Figure 7b); SDS does not reorder the headgroup of CAPB. The only non-negligible difference between the synergistic and the nonsynergistic mixed systems is the sharpening of the peak at 45° in the case of MIX2_W. This enhanced preference for the tilted orientation can be explained considering that in this system CAPB headgroups are much less constrained to reside in the first molecular layer than C12B molecules are in MIX_W. Thus, SDS headgroups in the first layer interact rather with the first few atoms of the tails of CAPB molecules, fixing them in the tilted orientation.

All things considered, the headgroup orientation does not appear to be the feature responsible for the ability to pack more or less molecules on the surface in the mixed systems. Tail Orientation. The order parameters per atom for carbon tails of the binary and the mixed systems are obtained from head to tail of the surfactant. The order parameter, Sz′z′, for the nth carbon atom is estimated as82 (S z′z′)n =

1 ⟨3 cos2(θ z′) − 1⟩n 2

(9)

θz′ is the angle between a hypothetical line adjoining two neighboring carbon atoms (indexed as n − 1 and n + 1) and the vector normal to the monolayer surface. A minimum value of −0.5 corresponds to orientation that is flat in the plane of the surface, and a maximum value of unity corresponds to the orientation that is normal to the surface. The carbon order parameter of the hydrocarbon tails of SDS and C12B in MIX_W is higher than in each of their respective singlesurfactant systems (Figure 8a), indicating that the tails are more ordered (vertically oriented). The minimum headgroup distance and carbon order of the tail are not independent; they both explain the increased packing efficiency at the surface and its effect on bulk-surface partitioning in synergistic system, consistent with the experimental results.17 The order parameters in MIX2_W for both SDS and CAPB are higher than their binary cases as seen in Figure 8b. However, the difference in order parameter for the binary CAPB and the ternary CAPB system is not as pronounced as for the binary C12B and the ternary C12B system. This is again due to the effect of the hydrophilic amide group in the CAPB tail. This group stays tilted and does not permit CAPB and SDS tail or headgroups to come in close proximity to each other. The difference in the order parameters for n ≥ 5 between C12B and CAPB is due to the presence of the amide group. Upon further inspection, we find no bonded interactions (i.e., hydrogen bonding between H and O of neighboring amide groups) influencing the order parameter of the tailgroups, suggesting that close packing in CAPB is inhibited as a consequence of inherent tail chain geometry, rather than specific interactions induced by the amide group. This suggests that synergism that may otherwise occur on account of strong headgroup interactions can be broken more generally by nonstraight-chain tail groups in one of the surfactants. However, we cannot rule out the indirect influence of the amide group on headgroup interactions through its vertical displacement of CAPB (in comparison to C12B) in water. H


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Figure 9. Entropic and enthalpic contributions to the free energy of mixing. The length of the arrows is indicative and not strictly proportional to the values.

Thermodynamics of Synergism. To consolidate our understanding of mixing and structural rearrangement on synergistic behavior within a thermodynamic framework, we provide a qualitative comparison of the enthalpy together with the translational (two-body excess), configurational (tail orientation), and conformational terms of the entropy of mixing. Calculation of each term is described in the Supporting Information. Estimates for each term can be compared meaningfully between MIX_W and MIX2_W but not within each system on account of approximations made. While our simulations are performed in the canonical ensemble, the open periodic boundaries in the vertical direction in our system establishes an isothermal−isobaric system with zero pressure83,84 which is aptly described by the Gibbs free energy. Figure 9 illustrates the relative magnitude of the enthalpic and entropic contributions of the Gibbs free energy of mixing (determined here by the chemical potential). This quantity is negative for both the synergistic and the nonsynergistic system, indicating that the mixed surface is preferred over the pure surfaces, although to a smaller extent for the nonsynergistic system. The enthalpy of mixing determined from the system internal energy is positive in both cases, indicating that the preference of both systems for mixing arises from entropic reasons. The positive sign of ΔmixH is counterintuitive and is partially (approximately 0.22 kcal mol−1) attributed to the fact that sodium ions in the mixed systems are pushed from the subsurface layer toward the bulk aqueous phase (which is confirmed by the ITIM analysis), with remaining contributions likely due to changes in bonded interactions and nonbonded interactions with water molecules. Enthalpic contributions from tailgroup−tailgroup interactions are −10.8 and −5.7 kcal mol−1 for the MIX_W and MIX2_W systems, respectively, and 1 order of magnitude larger than the corresponding headgroup contributions of −1.03 and −0.50 kcal mol−1. The polar headgroups should in principle have stronger interactions with each other than the apolar tails. Nevertheless, headgroups are found in an aqueous environment where their nearest neighbors are mostly water, and thus their interactions are shielded by their hydration shell. The amide−amide interaction gives a very small repulsive contribution (0.24 kcal mol−1) to the tailgroup interactions in the CAPB_W system, which vanishes upon mixing with SDS when the nonsubstituted hydrocarbon chains of the latter intercalate among the tails of CAPB.

From the three different entropic contributions, we estimate that two have the same number signs. The ideal contribution to the conformational entropy trivially favors mixing, which can be explained by basic combinatorial rules ensuring that the ternary phase has simply more conformational degrees of freedom than the binary one, regardless of the physicochemical properties of the systems in question. The configurational term describes the extent of order in individual molecules and is estimated from the position of its atoms; this value suggests mixing is disfavored due to reorientation and repulsion85 as evidenced by the increasing trend in −TΔmixSconf in Figure 9. The difference between synergistic and nonsynergistic behavior is evident in the two-body excess or local translational term of the entropy. In a synergistic system, −TΔmixStr shows an apparent decrease upon mixing, while in a nonsynergistic system the two-body excess entropy of a mixed system turns out to be lower than that of the corresponding pure systems (TΔmixStr greater than 0). Consequently, the two-body excess entropy of the hydrocarbon tails (which has also been used to estimate the tendency of a system to aggregate86) discriminates between synergistic and nonsynergistic behavior in the systems examined in this work.

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SUMMARY AND CONCLUSIONS Using MD simulations with TI, we study the structural properties related to synergism in zwitterionic C12B and anionic SDS surfactant systems and nonsynergism in a closely related CAPB and SDS surfactant system. For a set of surface concentrations, the bulk-surface partitioning and surface tensions are calculated for each of the binary systems and also a system with a 50% mixture of the two surfactants. With a correction for a constant bias in surface tension, the binary system (SDS_W and C12B_W) surface tensions for all concentrations studied and the ternary system (MIX_W) for low surface concentrations (Γ < 2.92 × 106 mol/m2) agreed with experimental values within 3 mN/m. Deviation of up to ∼31 mN/m from experiments are observed at higher surface concentrations (Γ = 4.4−5.4 × 106 mol/m2) for the mixed SDS−C12B system on account of uncertain force field parametrizations or insufficient simulation times, but the simulated increased partitioning toward the surface is consistent with a synergistic system following the Gibbs adsorption isotherm. Analysis of structural parameters in the SDS−C12B system shows that the oppositely charged interactions results in SDS I


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drawing C12B closer to the surface, with upright alignment permitting dense packing (approximately twice as much) compared to their binary component configurations. At low surface coverage, this dense packing of surfactants leads to pockets of exposed water, which explains higher surface tensions, closer to that of water, estimated for MIX_W system over pure for the same surface concentrations. The mixed surfactant interactions that enables dense packing also favors increased adsorption of molecules to the air−water interface, leading to higher surface concentrations for the same bulkphase concentration than in the binary systems. Therefore, the enhanced partitioning of molecules to the surface in the MIX_W leads to efficiency in surface tension reduction relative to bulk concentrations, in spite of the higher surface tensions obtained for the same surface concentrations in their respective homomolecular−surfactant systems. While changes to the hydrogen bonding and orientation of water dipoles in the ternary system are also observed in contrast to the binary systems configuration, it appears these are incidental changes that are not required to explain the synergistic effects for the mixture studied in this work. Our results are generally consistent with experimental17 and modeling studies27,87 in which synergistic effects are mostly attributed to surfactant− surfactant interactions and increased packing density. CAPB naturally resides deeper in the water than C12B (CAPB differs from C12B only by an amide group in the tailgroup chain) in its homomolecular−surfactant system on account of the amide oxygen−water interaction. In a mixture with SDS surfactants, CAPB is not necessarily pulled toward the surface as with C12B, and interactions of ionic headgroups do not dictate the structural geometry that leads to synergism. The tilt in the backbone caused by the nonmethylene heterogroup appears to prevent close packing and leads to an increase in the translational entropy over the C12B−SDS mixture. The low surface tensions observed in atmospheric particles remain an active area of inquiry. While we did not focus on the interactions and surface structure near the CMC level in great detail, mechanisms responsible for efficiency in surface tension reduction are also likely to increase effectiveness in reduction. In atmospheric systems where there are many more types of surfactants likely to be present at the surface simultaneously, synergistic interactions among charged and possibly uncharged species can potentially remain significant. For instance, Mulqueen and Blanckstein27 report that addition of a neutral species to a binary, synergistic mixture consisting of straightchain surfactants does not diminish the effect of synergism, which further supports the viability of this hypothesis. However, the importance of the surfactant tail in reducing synergism requires further investigation. Tilted or branched structures are likely found in atmospheric mixtures88,89 and can reduce the magnitude or occurrence of these synergistic interactions. Even the addition of a minority percentage (∼20%) of branched surfactants can significantly reduce the close-packing of surface monolayers as evidenced by increase molecular transfer across the air−surfactant interface.90 The role of the tailgroup in controlling surfactant aggregation in micelles and emulsions is characterized with quantitative consideration for geometric and thermodynamic aspects of tail structure.91,92 Further study of molecular details of aggregation at the air−water interface is likely to provide useful insights for a mechanistic prediction of synergism in complex mixtures of surface-active molecules.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b03346. Additional simulation results and methods including figures, tables, and references as discussed in the text. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: satoshi.takahama@epfl.ch. Phone: +41 21 6935777. ORCID

Gözde Ergin: 0000-0002-1955-3022 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the Swiss National Science Foundation (200021_169506) and EPFL for funding. We also deeply acknowledge Dr. Zhe Shen for his advice and helpful discussion regarding the simulation methods and Prof. Pál Jedlovszky for providing the codes for the Voronoi and water orientation analysis.

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REFERENCES

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