Synergism and aggregation behaviour in an aqueous binary mixture of cationic–zwitterionic surfactants: physico-chemical characterization with molecular simulation approach

Abstract

Aqueous interactions between a cationic surfactant benzyl dimethylhexadecylammonium chloride (BDHAC) and alkyldimethylammoniopropane sulfonates (C_nDAPS) based three zwitterionic surfactants n = 10, 12, and 14 (abbreviated as C₁₀DAPS, C₁₂DAPS and C₁₄DAPS, respectively) were studied using tensiometry, and fluorescence spectrophotometry techniques. The critical micelle concentration degree of synergism and various other parameters such as interaction parameter (β), activity coefficients (f^m) and interfacial parameters such as surface pressure (π_CMC), packing parameter (P), surface excess concentration (Γ_max), surface tension at CMC (γ_CMC), and minimum area per molecule (A_min) were evaluated using the Regular Solution Theory (RST) of mixed systems. The results indicate a strong dependency on the mixed system and their composition. For the quantitative prediction, the molecular architecture of the surfactants in mixed systems and their synergistic interactions were investigated by computational simulation using Spartan’14 V1.1.8. The structural optimization results obtained were found to be in good agreement with the estimations made using RST. The reduction in surface tension indicates a certain efficiency in mixed micelle formation owing to electrostatic attraction between the cationic and zwitterionic surfactants. In addition, the binary surfactant systems evaluated by Maeda's approach infer the mixed micelles are thermodynamically stable. The aggregation number (N_agg) appeared to be larger at the composition point where the efficiency of mixed micelle formation is greatest. The strength of the interaction between BDHAC and C_nDAPS followed the order: C₁₄DAPS > C₁₂DAPS > C₁₀DAPS indicating a greater synergism at 0.25 molar ratio of zwitterionic surfactants to cationic surfactants in the aqueous solution at 303.15 K.

---

Introduction

Cationic surfactants, which are frequently encountered ionic surfactants, consist at a minimum of a nonpolar, hydrophobic long alkyl chain and a positively charged hydrophilic head group.^1–3 These groups could be modified further to tune their solution behaviour for various industrial and commercial applications.^4,5 One common surfactant with a strong antibacterial activity of this type is benzyldimethylhexadecylammonium chloride (BDHAC).⁶ Zwitterionic surfactants are often desirable due to their mildness and their electrically neutral nature, which clearly distinguishes them from other classes of surfactants. As solutions in pure water, their behaviour is similar to that of the ionic surfactants.⁷ We choose alkyldimethylammonium propane sulfonate, because these zwitterionic surfactants are not only insensitive to pH, but also remain zwitterionic at any pH in aqueous solutions.⁸ However, reported studies have shown that the solution behaviour and physicochemical properties of zwitterionic surfactants are greatly influenced by the length and number of hydrophobic tail chain and charged head groups.^9,10 As a consequence, these zwitterionic surfactants are becoming more desirable and widely applicable because of their good solubility in water and reduced sensitivity towards temperature and salts.^11,12

Generally, the interfacial characteristics and colloidal properties of a mixture of two or more surfactants are unique and significantly better than their individual components. Such surfactant blends are less expensive and have therefore been applied widely in detergency, enhanced oil recovery, cosmetics, textiles, and pharmaceuticals.^13–15 Recent studies on mixed surfactant systems pay special attention to the synergism observed in micellization upon mixing of various ionic/non-ionic surfactants. Several models and theories have been proposed to describe the micellization phenomenon in mixed surfactant systems.^16,17 Studies have reported that if the mixture shows a greater surface activity, for example, low critical micelle concentration (CMC) compared to the individual components, then the mixture exhibits synergism.^18,19 Synergism is often modelled in the literature by employing the regular solution theory (RST) with a negative interaction parameter.^20,21 Reports on such binary surfactant systems have revealed a strong interaction. Therefore, it is interesting and useful to design a mixed ionic-zwitterionic surfactant system in which the advantages of the surfactant can be exploited.^22–25

In line with this interest, herein, we report the interfacial and bulk properties in a mixed system of a cationic surfactant (benzyldimethylhexadecylammonium chloride, BDHA⁺Cl⁻) with three zwitterionic surfactants, 3-(N,N-dimethyl decylammonium) propane sulfonate (C₁₀DAPS), 3-(N,N-dimethyldodecylammonio) propane sulfonate (C₁₂DAPS), 3-(N,N-dimethyltetradecyl-ammonio) propane sulfonate (C₁₄DAPS). In this study, the head group–head group and chain–chain interactions are considered important because both the surfactants in mixed systems are ionic, which could underline the synergistic mechanism. Several mixed systems have been well discussed and presented in terms of CMC, surface excess concentration (Γ_max), minimum area per molecule (A_min), surface pressure at CMC (π_CMC), aggregation number (N_agg), interaction parameters in the monolayer (β⁰) and in the micelle (β^m), standard Gibbs free energy of adsorption (ΔG_ads), excess free energy of micellization (ΔG_ex), and standard Gibbs free energy of micellization (ΔG_M) for the mixtures of C_nDAPS + BDHAC. Compared with the experimental methods, it is important to design the molecular architecture of surfactants for the purpose of optimizing the synergistic performance of the mixtures of zwitterionic–cationic surfactants in which we are interested, as such study is very limited. Thus, the experimental observations were rationalized with a computer based quantum mechanical study to provide atomistic or molecular details and to understand the behaviour of mixed surfactants at the interfaces, which could prove highly beneficial from a commercial and industrial point of view.

Experimental

Materials

Benzyldimethylhexadecylammonium chloride (BDHAC), and alkyldimethylammoniopropane sulfonate (C_nDAPS) (n = 10, 12, 14), the fluorescent probe: pyrene, and N-cetylpyridinium chloride (CPC) were purchased from Sigma-Aldrich (purity > 99.5%) and used without further purification. To ensure removal of surface active contaminants, all glassware was cleaned in chromic acid and rinsed with double distilled water. All solutions were prepared in water with a specific conductance and pH in the range of 1–2 μS cm⁻¹ and ∼6.5, respectively. The entire experimental study was performed at 303.15 K.

Methods

Surface tension. Surface tension of the air–water was measured at 303.15 ± 0.1 K using the “du Noüy” ring method (Kruss tensiometer, Kruss K9, Germany). Surface tension was measured as a function of surfactant concentration (C_s in mol L⁻¹) over a wide range within the accuracy of ±0.1 mN m⁻¹ and the CMCs were determined from the inflections in γ versus the logarithm of C_s isotherms.

The surface parameters such as π_CMC, Γ_max, A_min and P were calculated using an appropriate form of the Gibb's adsorption equation:

π_CMC = γ_water − γ_CMC (1)

where γ is the surface tension in mN m⁻¹ and ∂γ/∂ ln C is the maximum slope, R is the gas constant (8.314 J mol⁻¹ K⁻¹); T is the absolute temperature in Kelvin, C is surfactant concentration in mol L⁻¹, N_A is the Avogadro number, Γ_max represents the maximum surface excess concentration at the CMC, V₀ is volume of hydrocarbon chain and n_c is the number of carbon atoms in hydrocarbon chains, given by Tanford formula. Here, A_min is the cross-sectional area occupied by the hydrophilic head group.^26–30

Aggregation. For the determination of the micellar aggregation number (N_agg) at various mole ratios of the binary C₁₄DAPS + BDHAC mixture, the solutions were prepared using the fluorescence probe and quencher. The probe pyrene concentration was kept constant (∼2 × 10⁻⁶ M) while the quencher concentration was varied within the range 0–9 × 10⁻⁶ M. The total surfactant concentration was prepared as 4 mM, well above the CMC.

The fluorescence intensities of the obtained peaks decreased with an increase in the quencher concentration without the appearance of any new peaks.

According to the theory proposed by Turro and Yekta,³¹ the relationship between the steady state fluorescence intensities with (I₀) and without (I₁) quencher is determined by the total surfactant concentration (C) and the quencher concentration (Q) in micelles as:

Thus, using the slope of the straight line from the plot of ln(I₀/I) versus [Q] shown in Fig. 3 for the C₁₄DAPS + BDHAC system in various ratios the aggregation number, N_agg can be obtained. The fluorescence intensities I₀ and I also can be used to calculate the Stern–Volmer binding constants (K_sv) by using the following equation:

I(t) = A₀ exp(−A − A₁t − A₂(1 − exp(−A₃t))) (7)

where A₀ is the intensity at time zero, A₁ 1/τ₀, A₂ = (X) = Q/M, and A₃ = k_q.

Results and discussion

Synergism in the mixed surfactant system

Reported studies have shown that there is correlation between the concentration and activity for binary mixtures at a given temperature, considering their mole fractions in mixed solution system. Rubingh was apparently the first to use this correlation to fit the mixture CMC data for binary surfactant systems.⁷ Thus it was more profound to employ Rubingh's activity coefficient relationship for our investigation, which earlier was addressed as a one-parameter Margules equation for describing the nonideality in aqueous mixed surfactant systems.^32,33

According to Rubingh's nonideal solution theory, the mixed CMC, when more than one surfactant is mixed, is evaluated using eqn (8):

where α₁ is the mole fraction of a conventional BDHAC surfactant in the total mixed solvents, and C₁ and C₂ are the CMC values of the pure surfactants.

After measuring the CMC of the aqueous solution of mixed surfactants and the CMC of the individual surfactants, the value of the interfacial composition (X^m₁) in the aqueous phase can be calculated from the equation:

where X^m₁ is the mole fraction of the BDHAC surfactant in the total surfactant in the mixed micelle, α₁ is the mole fraction of surfactant 1 (BDHAC surfactant) in the total surfactant C in solution. C₁, C₂ and C₁₂ are the CMCs surfactant 1, surfactant 2 (zwitterionic surfactant) and their mixture at a mole fraction of α, respectively.

After determining X^m₁ from eqn (9), we can obtain the interaction parameter (β^m) according to the equation:

where β^m measures the extent of the interaction between the surfactants resulting in the deviations from the ideality on mixing behaviour, with negative values indicating synergism, positive values antagonism and a zero value indicating no interactions between the two surfactants, respectively.³⁴

The interaction parameter (β^m) is related to the activity coefficient (f^m) of surfactant within the micelle by the following relations:

ln f^m₁ = βⁿ(1 − X₁)² (11)

ln f^m₂ = β^m(X₁)² (12)

where f₁ and f₂ are the activity coefficients.

Studies have reported the chain–chain and head group–head group interactions as a driving force in mixed micellar systems depicting the stability of mixed micelles.^35,36 The free energy of micellization (ΔG_Maeda) in the mixed micelle is given by:

ΔG_Maeda = RT(B₀ + B₁X₁ + B₂X₁²) (13)

where B₀ = ln C₂ (C₂ is the CMC of C_nDAPS); B₁ + B₂ = ln (C₁/C₂) (C₁ is the CMC of surfactant BDHAC) and B₂ = −β^m.

For the air–water interface study, solutions of both the surfactants (C_nDAPS + BDHAC) were prepared in varying mole fractions of 0.25, 0.50 and 0.75. Plots of the surface tension versus logarithm C_s for pure surfactants and their mixtures depict the CMC with sharp break points (Fig. 1). The evaluated CMC of BDHAC and C_nDAPS is in harmony with the reported values from the literature.³⁷ Mixed CMC data along with the computed results for the mixed micellar composition, interaction parameter (β) and activity coefficients (f^m) are presented in Table 1.

Fig. 1 Variation of the surface tension versus total surfactant concentration in different mole ratios of cationic surfactant BDHAC with different zwitterionics (a) C₁₀DAPS (b) C₁₂DAPS (c) C₁₄DAPS, respectively, at 303.15 K.

Table 1 CMC's (ideal and experimental), mole fraction in micelle (X^m₁), interaction parameter (β), and activity coefficients (f^m) at 303.15 K

α BDHAC	CMC (mM)		X ^m1	β ^m	f ^m1	f ^m2
	Ideal	Experimental
BDHAC + C10DAPS
0	19.00	16.80	—	—	—	—
0.25	1.73	6.20	0.35	5.25	9.33	1.89
0.50	0.91	5.31	0.40	7.24	14.33	3.06
0.75	0.62	3.12	0.46	8.17	10.73	5.67
1.0	0.50	0.47	—	—	—	—
BDHAC + C12DAPS
0	2.50	2.40	—	—	—	—
0.25	1.18	0.93	0.58	−1.01	0.84	0.71
0.50	0.73	0.86	0.89	0.68	1.01	1.71
0.75	0.52	0.70	0.98	1.81	1.00	5.63
1.0	0.50	0.47	—	—	—	—
BDHAC + C14DAPS
0	0.31	0.27	—	—	—	—
0.25	0.30	0.16	0.35	−3.26	0.25	0.67
0.50	0.34	0.22	0.43	−1.84	0.55	0.71
0.75	0.40	0.24	0.56	−2.08	0.67	0.52
1.0	0.50	0.47	—	—	—	—

---

An almost linear decrease in surface tension was observed in the pre-micellar region until CMC; however, beyond CMC in the post-micellar region, the surface tension appeared more or less constant. The CMCs for the mixed systems presented revealed the CMC values lie between those of the pure single conventional components. It can be seen from our findings that the micellization behaviour of zwitterionic–cationic mixed surfactants significantly differs from their pure surfactants. The CMC values decrease correspondingly with the addition of the zwitterionic to a cationic surfactant with varying ratios. The interaction parameter (β) value appeared to be positive for the mix systems containing C₁₀DAPS and C₁₂DAPS, thereby indicating antagonism while it appeared negative for C₁₄DAPS indicating synergism. It can be seen from Fig. 2 that out of the three different mix systems only one, C₁₄DAPS + BDHAC, has a β value as more negative, indicating the plausible interaction between them.

Fig. 2 Comparison between ideal and experimental CMC's for BDHAC + C₁₄DAPS system.

Fig. 2 show a comparison between the ideal and experimental CMCs for the C₁₄DAPS + BDHAC system, where the three mix ratios exhibit a negative deviation from its ideal behaviour, thereby indicating a synergistic interaction between the binary surfactant system. The negative deviation is also supported by a negative value of β^m which also indicates an attractive interaction. Such behaviour could be attributed to the electrostatic interaction between C₁₄DAPS and BDHAC.

Adsorption of mixed surfactants at the air–water interface

The adsorption efficiency at the interface is an important criterion for the surfactant in order to understand its solution.³⁸ The value of surface pressure at CMC (π_CMC) of the binary surfactant mixtures is presented in Table 2. It can be observed that in all surfactant mixtures, the (π_CMC) values are lower than their respective pure surfactants. While (π_CMC) of the binary mixtures decreases gradually with an increase in the mole fraction of the cationic surfactant, the formation of mixed micelles is due to the favoured hydrophobic effect.

Table 2 Interfacial composition (X⁰₁), interaction parameter (β⁰), effectiveness (γ_CMC), surface excess (Γ_max), minimum area per molecule (A_min), packing parameter (P), and surface pressure (π_CMC) of binary surfactant mixture at 303.15 K

α BDHAC	X ^01	β ^0	f ^01	f ^02	γ CMC mN m^−1	Γ max (× 10^6 mol m^−2)	A min (Å^2)	P	π CMC
BDHAC + C10DAPS
0	—	—	—	—	38.92	1.88	88.5	0.48	32.48
0.25	0.35	5.20	8.94	1.90	42.94	1.41	117.6	0.36	28.46
0.50	0.40	7.15	12.90	3.18	41.85	1.12	148.0	0.29	29.55
0.75	0.46	8.10	10.62	5.56	42.63	1.42	116.6	0.36	28.77
1.0	—	—	—	—	39.79	1.14	145.5	0.29	31.61
BDHAC + C12DAPS
0	—	—	—	—	40.88	1.13	146.6	0.15	30.32
0.25	0.58	−1.25	0.80	0.66	44.4	1.12	148.6	0.14	26.80
0.50	0.75	−0.81	0.95	0.63	44.79	1.03	161.5	0.13	26.41
0.75	0.72	0.4	1.00	1.45	44.01	1.28	129.3	0.16	27.19
1.0	—	—	—	—	39.99	1.14	145.5	0.15	31.21
BDHAC + C14DAPS
0	—	—	—	—	39.31	1.40	118.4	0.18	31.89
0.25	0.35	−3.54	0.22	0.65	41.56	0.92	179.8	0.12	29.64
0.50	0.44	−2.66	0.43	0.60	43.02	1.03	161.5	0.13	28.18
0.75	0.56	−2.88	0.57	0.40	43.01	1.08	153.9	0.14	28.19
1.0	—	—	—	—	39.99	1.14	145.5	0.15	31.21

---

The minimum area per molecule (A_min) suggests the assembly of the surfactant molecule at the air–water interface was observed to be higher for pure BDHAC as compared to C_nDAPS, which may be ascribed to the greater electrostatic repulsions between similarly charged head groups at the surface monolayer. The entire mole fraction, except 0.5 mole fraction, of the three systems shows low A_min values due to strong electrostatic interactions between cationic and zwitterionic surfactants, while in the 0.5 mole fraction the value appears higher which indicates the packing expansion at the air–water interface. However, the correct reason for the packing expansion at the 0.5 mole fraction is not known. This expansion may be due to the dissimilarity in the nature of the interaction amongst the hydrophobic and hydrophilic groups in the mixed adsorbed layer. The packing parameter P which gives information about the size of the micelle was found to be low, where the A_min was more.^39,40

Thermodynamic and interfacial adsorption study of surfactants in aqueous binary mixtures

The thermodynamic parameter for the evolution of synergism in the mixed system at equilibrium is described as follows:⁴¹

ΔG_min = A_minγ_CMCN_A (14)

The excess free energy of micellization, ΔG_ex:

ΔG_ex = [X₁ ln f₁ + (1 − X₁)ln f₂]RT (15)

The free energy of micellization can be given by:

ΔG_M = [X₁ ln X₁f₁ + X₂ ln X₂f₂]RT (16)

The last term in eqn (17) expresses the work involved in transferring the surfactant molecule from a monolayer at a zero surface pressure to the micelle. Here, for all the binary mixtures, the last term of eqn (16) is very small as compared to ΔG_M, which suggests that work involved in transferring the surfactant molecule from the monolayer at zero surface pressure to the micelle is negligible.

RST assumes that the excess entropy of mixing and ideal enthalpy of mixing are zero. According to RST, the relation between the excess free energy of micellization, excess enthalpy and the enthalpy of micellization can be written as:

ΔG_ex = ΔH_ex = ΔH_M = [X₁ ln f₁ + (1 − X₁)ln f₂]RT (18)

Using eqn (16) and (17), the entropy of micellization can be calculated as:For any selected mix surfactant systems, if both the components are ionic in nature, then head group–head group and chain–chain interactions play an important role. Maeda's approach is widely considered for such charged species involved.³⁶ In this approach, the free energy of micellization (ΔG_Maeda) is calculated as a function of the mole fraction of the ionic component in the mixed micelle as given in eqn (13).

In Table 3(a) the value of B₁ appears to be negative in only the 0.25 mole ratio, indicating that the chain–chain interaction plays an important role in mixed micellization. When a hydrocarbon chain is dissimilar, the chain–chain interaction gives a more negative value of B₁.⁴²

Table 3 (a) Chain–chain interaction parameters (B₀, B₁, and B₂) for surfactant mixtures at 303.15 K. (b) Thermodynamic parameters (free energy micellization by Maeda's approach (ΔG_Maeda)), surface free energy (ΔG_min), free energy of micellization (ΔG_M), free energy of adsorption (ΔG_ads), excess free energy (ΔG_ex) and entropy of micellization (ΔS_M) of surfactant mixtures at 303.15 K

(a)
α BDHAC	B 0	B 1	B 2
BDHAC + C10DAPS
0	—	—	—
0.25	2.82	1.67	−5.25
0.50	2.82	3.66	−7.24
0.75	2.82	4.59	−8.17
1.0	—	—	—
BDHAC + C12DAPS
0	—	—	—
0.25	0.87	−2.64	1.01
0.50	0.87	−0.95	−0.68
0.75	0.87	0.16	−1.80
1.0	—	—	—
BDHAC + C14DAPS
0	—	—	—
0.25	−1.30	−2.70	3.26
0.50	−1.30	−1.24	1.84
0.75	−1.30	−1.53	2.08
1.0	—	—	—

---

(b)
α BDHAC	ΔGMaeda (KJ mol^−1)	ΔGmin (KJ mol^−1)	ΔGM (KJ mol^−1)	ΔGads (KJ mol^−1)	ΔGex = ΔHM (KJ mol^−1)	ΔSM (J mol^−1 K^−1)
BDHAC + C10DAPS
0	—	20.73	—	—	—	—
0.25	6.97	30.40	1.37	−18.81	2.99	5.37
0.50	7.91	37.31	2.66	−23.72	4.35	5.57
0.75	8.07	29.93	3.37	−16.89	5.11	5.74
1.0	—	34.88	—	—	—	—
BDHAC + C12DAPS
0	—	36.10	—	—	—	—
0.25	−0.80	39.73	−2.33	−26.31	−0.62	5.65
0.50	−1.23	43.57	−0.705	−26.40	0.17	2.88
0.75	−1.73	34.28	−0.158	−21.33	0.08	0.81
1.0	—	35.06	—		—	—
BDHAC + C14DAPS
0	—	28.03	—		—	—
0.25	−4.68	45.00	−3.45	−35.59	−1.86	5.38
0.50	−3.83	41.86	−2.86	−30.28	−1.14	5.68
0.75	−3.81	39.87	−3.02	−29.15	−1.30	5.70
1.0	—	35.05	—		—	—

---

Another thermodynamic parameter presented in Table 3(b) describes the transition of a solution component from the bulk phase to the surface in the mixed study at equilibrium.^43,44 It is known that the lower the value of Gibb's free energy (ΔG_Maeda, ΔG_M, and ΔG_ads) the surface is more thermodynamically stable or more surface active. In our case, C₁₄DAPS + BDHAC attain clear surface activity thereby indicating good synergism. Similarly, the extent of synergism in our mixed surfactant system depends on the lowering of the measured free energy. ΔG_M and ΔG_ads values are negative and reveal that the latter is more spontaneous; implying that the adsorption of surfactants and their mixtures at the air/solution interface is more favourable than that of micelle formation. The negative value of excess free energy (ΔG_ex) of micellization indicates the energetic stabilization accompanied by the mixed micelle formation. The positive values for entropy (ΔS_M) contribution must be the driving force of micellization. This means that the mixed micelle formation is an entropically favourable process.^45–47

Synergism

The order of interaction between the individual surfactants in the mixture and CMC plays a vital role in predicting synergism. However, it obeys certain conditions: (a) β⁰ and β^m must be negative, (b) |β⁰| > |ln(C⁰₁/C⁰₂)|, where C⁰₁ and C⁰₂ are the molar concentrations of the individual surfactants in a binary mixture and (c) |β^m| > |ln(C^m₁/C^m₂)|, where C^m₁ and C^m₂ are the CMCs of the individual surfactants. The terms: and were evaluated using eqn (20) proposed by Liu and Rosen⁴⁸ where the value must be a maximum of 1 and which determines the degree of synergism in reducing the surface tension efficiently.where C_12,min is the minimum concentration of mixed surfactant and C⁰₁ is the concentration required for the more efficient surfactant. When the CMC of the mixture is less than the individual surfactants, it indicates synergism in the mixed micelles. The degree of synergism possible in mixed micelle formation in a mixture is determined as follows.⁴⁸where C^m_12,min the lowest CMC of the mixed surfactant systems and C^m₁ is the lower CMC of the two surfactants constituting the mixture. The greater the value of (maximum = 1), the greater the degree of synergism. Values are given in Table 4. All the values are close to 1 for all three systems indicating synergism.

Table 4 Parameters predicting molecular interaction and synergism in a binary surfactant mixture at 303.15 K

Mixture	β ^0			β ^m
BDHAC + C14DAPS	−9.08	0.43	0.92	−7.18	0.55	0.88

---

The zwitterionic surfactants studied here, alkyldimethylammoniopropane sulfonates, are not sensitive to pH in the solution. Although there is no net charge, many physical properties of these surfactants are quite different from those of non-ionic surfactants and very similar to those of ionic surfactants and they can have a synergistic effect with BDHAC by means of a electrostatic attraction between the N⁺(CH₃)₂ group in the zwitterionic surfactants and the aryl chloride group in the BDHAC.

Computational study

Recent studies have shown the intensive applications of the computational approach can offer an insight into the atomic studies of structure and dynamics phenomena in surfactants, inorganic/organic complexes and biomolecules etc. at different interfaces.^49–51 Based on our experimental findings for the binary BDHAC + C_nDAPS systems in aqueous solution, the quantum molecular simulations were performed by applying the Spartan’14 V1.1.8 program in the gas phase to understand the interactions in the formation of various stable adducts (synergism) between the two surfactants in the mixed surfactant system. It was reported that the interfacial structure of the mixed surfactant complex depends on the surfactant concentration at the interface. Furthermore, it was determined that the electrostatic interaction and hydrophobic interaction are the driving forces between surfactants that exhibit the degree of synergism. In the case of homogeneous mix surfactant systems (BDHAC and C_nDAPS) with no phase separation, it could be depicted that an adsorption monolayer of BDHAC and C_nDAPS at the air/water surface is formed, with their headgroups extending into the water solvate (i.e. the head groups are hydrated in the water phase), and the carbon chains are stretching towards air. However, a small portion of the carbon chains penetrates into the water. Based on our findings, it could be concluded that mixed BDHAC + C_nDAPS surfactant systems display adequate surface activity in mix molar ratios with n = 14 as the maximum, compare to 10 and 12.

The optimized structure obtained by the Spartan’14 V1.1.8 for the individual surfactants, as well as for the surfactant mixtures in a 1 : 1 molar ratio is shown in Fig. 3. As can be seen in Fig. 3c, the hydrophobic carbon tails stretch into the plane with a length of 19.71 Å and 17.77 Å in the case of BDHAC and C₁₄DAPS, respectively. The headgroups of these two surfactants are found to be localized in such a way that the negative O⁻ atom of the sulphonic group in C₁₄DAPS becomes bonded with the H atom of the BDHAC head group leading to a hydrogen bond formation of length ∼1.912–1.940 Å. Here the tapering tail ends of both surfactants appear a little closer due to hydrophobic interactions. Furthermore, the significant fractions of the counterions are found to exist in the interfacial area, near to the headgroups of these surfactants. The binding forces of BDHAC and C₁₄DAPS molecules at the air/water interface could be attributed to two types of interactions: the electrostatic interaction between the ionic headgroups, and the hydrophobic interaction between the carbon chains. The top view of the 1 : 1 adducts of BDHAC and C₁₄DAPS clearly indicates the slight conformational changes due to the hydrophobic interaction between the carbon chains. The association process between the two surfactants: BDHAC (area = 520.52 Ų; volume = 483.63 ų) and C₁₄DAPS (area = 453.10 Ų; volume = 414.63 ų) resulted in the decrease in the area and volume upon close contact between the two surfactants in the BDHAC:C₁₄DAPS adduct (area = 904.99 Ų; volume = 890.04 ų).

Fig. 3 The two views (side and top) of the optimized structure of (a) BDHAC, (b) C₁₄DAPS and (c) the 1 : 1 adduct of BDHAC + C₁₄DAPS.

Considering the experimental data, the structural simulations were performed exclusively for the surfactants BDHAC and C₁₄DAPS by keeping the molar ratio at 1 : 3 (Fig. 4a) and 3 : 1 (Fig. 4b). The results showed that the ratio of 1 : 3 exhibited better synergistic behaviour. The bond position of these two headgroups at a molar ratio of 1 : 3 is nearly overlapping resulting in a compact spatial arrangement, thereby indicating a large interaction between these two surfactants, as could be seen in the optimized space-filling model structure. The plausible explanation for such behaviour could be that the head groups of C₁₄DAPS have more sulphonic groups, for example an O⁻ atom on the surface which is responsible for forming a H-bond with the ammonium head group of BDHAC, as a result all the surfactant molecules are packed closely to each other thereby remaining intact or compact with a surface area of 1669.89 Ų and volume of 1697.83 ų. The molecules of both surfactants exhibit an electrostatic interaction between the ionic head groups of BDHAC and C₁₄DAPS instead of repelling each other which rationalizes the high surface activity obtained by the surface tension and other results. In contrast, the optimized structure of the mixed surfactants BDHAC + C₁₄DAPS for the ratio 3 : 1 with several ammonium groups on the surface with a single sulphonic group leads to the formation of the limited non-covalent interactions between the head groups of the adjacent surfactant. As a result, the head group of one of the BDHAC molecules is free from the 3 : 1 adduct, and therefore the compactness is found to be less than the 1 : 3 adduct, as shown in the 3D space-filling model. In addition to the interactions with BDHAC, the C₁₄DAPS molecule yields a repulsive force with its head group, therefore, the cluster shows a depurative formation that leads to an increased surface area of 1786.48 Ų and volume of 1836.22 ų. Thus our findings suggest that the presence of a lower number of O⁻ ions in the adduct plays a decisive role for synergism in mixed surfactants at the surface.

Fig. 4 Three views (side, top and 3D ball) of the optimized structure of BDHAC + C₁₄DAPS in varying ratios (a) 1 : 3 and (b) 3 : 1.

The synergism of the mixed surfactants in the adducts (1 : 3 and 3 : 1 ratio) was also analysed by comparing the band gap (ΔE) between the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbital energies (Fig. 5). The band gap of BDHAC + C₁₄DAPS (1 : 3) was ∼8.09 eV which is lower than BDHAC + C₁₄DAPS (3 : 1) ∼ 8.19 eV due to the better compactness that promotes the charge transfer within the four surfactants in the respective set of the mixture. In addition, the larger dipole moment μ = 17.58 Debye of BDHAC + C₁₄DAPS (1 : 3) compared to μ = 10.14 Debye of the BDHAC + (3 : 1) system indicates the former showed a higher polarity that facilitates the interaction of the surfactant with water molecules leading to a thermodynamic stable system.

Fig. 5 The HOMO and LUMO diagrams of BDHAC + C₁₄DAPS in (a) 1 : 3 and (b) 3 : 1 mix ratios at 303.15 K.

Aggregation (N_agg) in mixed micellar systems

Micelle aggregation number (N_agg) is determined by using fluorescence spectroscopy. The representative Stern–Volmer plot of ln(I₀/I₁) versus quencher concentration [Q] shown in Fig. 6a depicts the linear characteristics indicating that the individual surfactant in the mixture is accessible to [Q] and the slope value gives N_agg, as shown in Table 5. The N_agg values for the pure zwitterionic surfactant have been found to be close to the literature values.^52,53 The decay profile for pyrene quenching by CPC is presented in Fig. 6b for the mix ratio of the binary surfactants in aqueous solution. It can be seen that the fluorescence decay was observed to be parallel for a long time thereby implying that the quencher could move freely between the micelles and the water pseudo-phase.

Fig. 6 Plot of (a) ln(I₀/I₁) versus (b) [Q] for the BDHAC + C₁₄DAPS system at 303.15 K.

Table 5 CMC and N_agg of binary BDHAC + C₁₄DAPS mixtures in aqueous solution at 303.15 K

Surfactant	CMC (mM)	N agg	K sv/10^5 (M^−1)
	Fluorescence spectroscopy
C14DAPS	0.28, 0.27^52	48	2.37
0.25	0.19	35	1.26
0.50	0.23	46	1.53
0.75	0.25	40	1.40
BDHAC	0.41, 0.46^7	29	1.01

---

It was observed that the N_agg values for the mixed surfactant ratio are larger than for pure BDHAC, but lower than pure C₁₄DAPS. The decrease in N_agg is observed in the mixture when the ratio of BDHAC was 0.25 and 0.75. Such behaviour is associated with an increase in the average repulsive interaction between the head groups with decreasing C₁₄DAPS; as zwitterionic surfactant molecules are progressively replaced by the cationic surfactant. The smallest aggregation number corresponds to the highest surface charge density, when the ratio of pure zwitterionic surfactant is more than the cationic BDHAC surfactant. However, for the molar ratio of 50 : 50 the N_agg was found to be higher because the head group–head group charge density increases between the cationic and zwitterionic surfactant. Also, in terms of the electrostatic charges, the negative charge of the sulfonate of C₁₄DAPS faces towards the positive charge of the ammonium head group of BDHAC, since the micelles are stabilized, resulting in a high aggregation number.^54,55 It was also observed that the high K_sv values suggest that an increase in quenching is due to the presence of both the pyrene and quencher in the strong hydrophobic environment.

Conclusions

Our work offers a better understanding of the adsorption at the air–water interface, the thermodynamics of micellization, and the aggregation behaviour obtained using tensiometry and fluorescence spectroscopy techniques for conventional surfactants and their binary mixtures at different mole fractions in aqueous solution. The results obtained are well explained and provide an insight into the nature of the individual surfactants alone and also in mixtures of zwitterionic surfactants C_n (n = 10, 12 and 14) with the cationic surfactant benzyldimethylhexadecylammonium chloride (BDHAC). The mixed surfactant system, BDHAC + C₁₄DAPS exhibited better solution properties as compared to C₁₀DAPS + BDHAC and BDHAC + C₁₂DAPS. The CMC's in the mixed surfactant systems at any mole ratio lies between those of their single surfactants, thereby indicating the values of CMC strongly depend on the composition of the mixture. Using RST, deviations from ideal behaviour were observed which implied the molecular interaction parameter (β), activity coefficients, and the excess Gibbs energy of the mixed micelle formation are close to the ideal behaviour. The chain–chain interactions indicated a fair level of the stability of mixed micelles. The interactions at micelles (β^m) are more attractive and reflect more synergistic behaviour than at the monolayer (β⁰) in mixed systems. Aggregation data obtained using fluorescence measurements highlighted the accumulation of compact packing of monomers in the micelle, which was found to be clearly delineated with the optimization results. Such behaviour could be attributed to the electrostatic interactions, for example hydrogen bond formation in BDHAC + C₁₄DAPS leading to the fair adsorption and thereby resulting in a strong affinity in the mixed surfactants. The addition of BDHAC leads to a great increase in the total charge and generally makes the surfactants arrange themselves more loosely, resulting in a decrease of the micellar aggregation number in the mixture. Furthermore, it was also found that the values of the standard Gibb's energy of micellization for the mixture of these two surfactants confirms the synergetic effect, thereby predicting the mixed micellar system to be more spontaneous. Considering these findings, we anticipate that such a study may prove more beneficial to design a mixed ionic-zwitterionic surfactant system and tune the interfacial and micellar properties in which the advantages of either surfactant can be exploited.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Authors acknowledge Technical Education Quality Improvement Programme-II (TEQIP-II) Credit No.: 4685-0IN for financial aid and Sardar Vallabhbhai National Institute of Technology (SVNIT), Surat, Gujarat-INDIA for providing the central instrumentation facility for analysis.

References

1. R. Atkin, V. Craig, S. J. Wanless and E. J. Biggs, Mechanism of cationic surfactant adsorption at the solid–aqueous interface, Adv. Colloid Interface Sci., 2003, 103, 219–304.
2. P. Somasundaran and U. L. Huang, adsorption/aggregation of surfactants and their mixtures at solid/liquid interfaces, Adv. Colloid Interface Sci., 2000, 88, 179–208.
3. K. Lunkenheimer, A. Lind and M. Jost, Surface tension of surfactant solutions, J. Phys. Chem. B, 2003, 107, 7527–7531.
4. T. Farías, L. C. de Ménorval, J. Zajac and A. Rivera, Solubilization of drugs by cationic surfactants micelles: conductivity and ¹H-NMR experiments, Colloids Surf., A, 2009, 345, 51–57.
5. J. L. Trompette, J. Zajac, E. Keh and S. Partyka, Scanning of the cationic surfactant adsorption on a hydrophilic silica Surface at low surface coverages, Langmuir, 1994, 10, 812–818.
6. Z. Grenoble and S. Baldelli, Adsorption of benzyldimethylhexadecylammonium chloride at the hydrophobic silica-water interface studied by total internal reflection Raman spectroscopy: effects of silica surface properties and metal salt addition, J. Phys. Chem. B, 2013, 117, 9882–9894.
7. D. López-Díaz, I. García-Mateos and M. M. Velazquez, Synergism in mixtures of zwitterionic and ionic surfactants, Colloids Surf., A, 2005, 270, 153–162.
8. K. Singh and D. G. Marangoni, Synergistic interactions in the mixed micelles of cationic gemini with zwitterionic surfactants: the pH and spacer effect, J. Colloid Interface Sci., 2007, 315, 620–626.
9. M. J. Rosen, Synergism in mixtures containing zwitterionic surfactants, Langmuir, 1991, 7, 885–888.
10. T. Iwasaki, M. Ogawa, K. Esumi and K. Meguro, Interactions between betaine-type zwitterionic and anionic surfactants in mixed micelles, Langmuir, 1991, 7, 30–35.
11. Y. Konodo, H. Uchiyama, N. Yoshino, K. Nishiyama and M. Abe, Spontaneous vesicle formation from aqueous solutions of didodecyldimethylammonium bromide and sodium dodecyl sulfate mixtures, Langmuir, 1995, 11, 2380–2384.
12. J. Marignan, F. Gauthier-Fournier, J. Appell and F. Akoum, Size and shape of micelles in the ternary system n-dodecylbetaine/water/1-pentanol, J. Phys. Chem., 1988, 92, 440–445.
13. G. Ran, Y. Zhang, Q. Song and D. C. Wang, The adsorption behavior of cationic surfactants onto human hair fibers, Colloids Surf., B, 2009, 68, 106–110.
14. Z. Grenoble and S. Baldelli, Adsorption of Benzyldimethylhexadecylammonium Chloride at the Hydrophobic Silica–Water Interface Studied by Total Internal Reflection Raman Spectroscopy: Effects of Silica Surface Properties and Metal Salt Addition, J. Phys. Chem. B, 2013, 117, 9882–9894.
15. (a) P. Somasundaran and L. Zhang, Adsorption of surfactants on minerals for wettability control in improved oil recovery processes, J. Pet. Sci. Eng., 2006, 52, 198–212; (b) B. Adibhatla, K. K. Mohanty, P. Berger and C. Lee, Effect of surfactants on wettability of near-wellbore regions of gas reservoirs, J. Pet. Sci. Eng., 2006, 52, 227–236.
16. T. R. Desai and S. G. Dixit, Interaction and viscous properties of aqueous solutions of mixed cationic and nonionic surfactants, J. Colloid Interface Sci., 1996, 177, 471–477.
17. M. Prasad, S. P. Moulik and R. Palepu, Self-aggregation of binary mixtures of alkyltriphenylphosphonium bromides: a critical assessment in favor of more than one kind of micelle formation, J. Colloid Interface Sci., 2005, 284, 658–666.
18. N. El Kadi, F. Martins and D. Clausse, Critical micelle concentration of aqueous hexadecyltrimethylammoniumbromide-sodium oleate mixtures, Colloid Polym. Sci., 1998, 281, 353–362.
19. (a) O. Owoyomi, J. Ige and O. Soriyan, Mixed micelles of tetradecyltrimethylammonium and N-alkyltriphenylphosphonium bromides, J. Dispersion Sci. Technol., 2014, 35, 826–831; (b) T. Joshi, B. Bharatiya and K. Kuperkar, Micellization and Interaction Properties of Aqueous Solutions of Mixed Cationic and Nonionic Surfactants, J. Dispersion Sci. Technol., 2008, 29, 1–7.
20. M. S. Bakshi, I. Kaur, R. Sood, J. Singh, K. Singh, S. Sachar, K. J. Singh and G. Kaur, Mixed micelles of benzyldimethyltetradecylammonium chloride with tetradecyltrimethylammonium and tetradecyltriphenylphosphonium bromides: a head group contribution, J. Colloid Interface Sci., 2004, 271, 227–231.
21. S. Ghosh, Surface chemical, and micellar properties of binary and ternary surfactant mixtures (cetyl pyridinium chloride, Tween-40, and Brij-56) in an aqueous medium, J. Colloid Interface Sci., 2001, 244, 128–138.
22. A. Avranas, E. Malasidou and E. I. Mandrazidou, Adsorption of cetyl dimethyl benzyl ammonium chloride on octane emulsions droplets: the effect of the presence of Tween 80, J. Colloid Interface Sci., 1998, 207, 363–370.
23. R. K. Mahajan and R. Sharma, Analysis of interfacial and micellar behavior of sodium dioctyl sulphosuccinate salt (AOT) with zwitterionic surfactants in aqueous media, J. Colloid Interface Sci., 2011, 363, 275–283.
24. T. R. Desai and S. G. Dixit, Interaction and viscous properties of aqueous solutions of mixed cationic and nonionic surfactants, J. Colloid Interface Sci., 1996, 177, 471–477.
25. (a) M. Prasad, S. P. Moulik and R. Palepu, Self-aggregation of binary mixtures of alkyltriphenylphosphonium bromides: a critical assessment in favor of more than one kind of micelle formation, J. Colloid Interface Sci., 2005, 284, 658–666; (b) K. Glenn, A. van Bommel, S. C. Bhattacharya and R. Palepu, Self aggregation of binary mixtures of sodium dodecyl sulfate and polyoxyethylene alkyl ethers in aqueous solution, Colloid Polym. Sci., 2005, 283, 845–853; (c) A. Al-Wardian, K. Glenn and R. Palepu, Thermodynamic and interfacial properties of binary cationic mixed systems, Colloids Surf., A, 2004, 247, 115–123.
26. C. Minero, E. Pramauro, E. Pelizzetti, V. Degiorgio and M. Corti, Micellar properties of sodium dodecylpoly(oxyethy-1-ene) sulfates, J. Phys. Chem., 1986, 90, 1620–1625.
27. Q. Zhou and M. J. Rosen, Molecular interactions of surfactants in mixed monolayers at the air/aqueous solution interface and in mixed micelles in aqueous media: the regular solution approach, Langmuir, 2003, 19, 4555–4562.
28. G. Bai, J. Wang, H. Yan, Z. Li and R. K. Thomas, Thermodynamics of molecularself assembly of cationic gemini and related double chain surfactants in aqueous solution, J. Phys. Chem. B, 2001, 105, 3105–3108.
29. C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Wiley, New York, 1980.
30. J. N. Israelachvili, D. J. Mitchell and B. W. Ninham, Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers, J. Chem. Soc., Faraday Trans. 2, 1976, 72, 1525–1568.
31. N. J. Turro and A. Yekta, Luminescent probes for detergent solutions. A simple procedure for determination of the mean aggregation number of micelle, J. Am. Chem. Soc., 1978, 100, 5951–5952.
32. (a) P. Letellier, A. Mayaffre and M. Turmine, Thoughts on the ideal behavior of mixed micelles and the appropriate application of regular solution theory (RST), J. Colloid Interface Sci., 2011, 354, 248–255; (b) P. Letellier, A. Mayaffre and M. Turmine, Thermodynamics of mixed micelles: determination of aggregate composition, J. Colloid Interface Sci., 2008, 327, 186–190.
33. S. D. Christian, E. E. Tucker and J. F. Scamehorn, Terminology for Describing Thermodynamic Properties of Nonideal Mixed Micellar Systems, in Mixed Surfactant Systems, ACS Symposium Series, American Chemical Society, Washington, DC, 1992, ch. 3, pp. 46–51.
34. K. Kuperkar, L. Abezgauz, K. Prasad and P. Bahadur, Formation and Growth of Micelles in dilute aqueous CTAB solutions in the presence of NaNO₃ and NaClO₃, J. Surfact Deterg., 2010, 13, 293–303.
35. P. M. Holland and D. N. Rubingh, Mixed Surfactant Systems, Am. Chem. Soc., Washington DC, 1992.
36. H. Maeda, A simple thermodynamic analysis of the stability of ionic/non-ionic mixed micelles, J. Colloid Interface Sci., 1995, 172, 98–105.
37. C. C. Ruiz and J. Aquiar, Interaction, stability, and microenvironmental properties of mixed micelles of Triton X100 and n-alkyltrimethylammonium bromides: influence of alkyl chain length, Langmuir, 2000, 16, 7946–7953.
38. T. Oida, N. Nakashima, S. Nagadome, J. Ko, S. Oh and G. Sugihara, Adsorption and micelle formation of mixed surfactant systems in water. III. A comparison between cationic gemini /cationic and cationic gemini/nonionic combinations, J. Oleo Sci., 2003, 52, 509–522.
39. Z. Lin, Y. Zheng, H. T. Davis, L. E. Scriven, Y. Talmon and J. L. Zakin, Unusual effects of counterion to surfactant concentration ratio on viscoelasticity of a cationic surfactant drug reducer, J. Non-Newtonian Fluid Mech., 2000, 93, 363–373.
40. P. Parekh, D. Varade, J. Parikh and P. Bahadur, Anionic–cationic mixed surfactant systems: micellar interaction of sodium dodecyl trioxyethylene sulfate with cationic Gemini surfactants, Colloids Surf., A, 2011, 385, 111–120.
41. R. K. Mahajan and R. Sharma, Analysis of interfacial and micellar behavior of sodium dioctyl sulphosuccinate salt (AOT) with zwitterionic surfactants in aqueous media, J. Colloid Interface Sci., 2011, 363, 275–283.
42. F. Li, G. Z. Li and J. B. Chen, Synergism in mixed zwitterionic–anionic surfactant solutions and the aggregation numbers of the mixed micelles, Colloids Surf., A, 1998, 145, 167–174.
43. Y. Kadam, T. Patel, G. Ghosh and P. Bahadur, Mixed micellization of n-alkyltrimethylammonium bromides and dodecyl polyoxyethylene ethers, J. Dispersion Sci. Technol., 2009, 30, 843–851.
44. T. Oida, N. Nakashima, S. Nagadome, J. Ko, S. Oh and G. Sugihara, Adsorption and micelle formation of mixed surfactant systems in water. III. A comparison between cationic Gemini/cationic and cationic Gemini/nonionic combinations, J. Oleo Sci., 2003, 52, 509–522.
45. A. A. Dar, B. Chatterjee, G. M. Rather and A. R. Das, Mixed micellization and interfacial properties of dodecyltrimethylammonium bromide and tetraethyleneglycol mono-n-dodecyl ether in absence and presence of sodium propionate, J. Colloid Interface Sci., 2006, 298, 395–405.
46. S. Paria, The mixing behavior of n-alkylpyridinium bromide–NP-9 mixed surfactant systems, Colloids Surf., A, 2006, 281, 113–118.
47. E. Rodenas, M. Valiente and M. S. Villafruela, Different theoretical approaches for the study of the mixed tetraethylene glycol mono-n-dodecyl ether/hexadecyltrimethylammonium bromide micelles, J. Phys. Chem. B, 1999, 103, 4549–4554.
48. L. Liu and M. J. Rosen, The interaction of some novel diquaternary gemini surfactants with anionic surfactants, J. Colloid Interface Sci., 1996, 179, 454–459.
49. S. H. Chun, J. W. Kim, J. Kim, H. Zheng, C. C. Stoumpos, C. D. Malliakas, J. F. Mitchell, K. Mehlawat, Y. Singh, Y. Choi, T. Gog, A. Al-Zein, M. Moretti Sala, M. Krisch, J. Chaloupka, G. Jackeli, G. Khaliullin and B. J. Kim, Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na₂IrO₃, Nat. Phys., 2015, 11, 462–466.
50. J. Wang, X. Xu, S. Ding, J. Zeng, R. Spurr, X. Liu, K. Chance and M. Mishchenko, A numerical testbed for remote sensing of aerosols, and its demonstration for evaluating retrieval synergy from a geostationary satellite constellation of GEO-CAPE and GOES-R, J. Quant. Spectrosc. Radiat. Transfer, 2014, 146, 510–528.
51. T. Wang, K. Birsoy, N. W. Hughes, K. M. Krupczak, Y. Post, J. J. Wei, E. S. Lander and D. M. Sabatini, Identification and characterization of essential genes in the human genome, Science Express Report, 2015, 350, 1096–1101.
52. G. B. Behera, B. K. Mishra, P. K. Behera and M. Panda, Fluorescent probes for structural and distance effect studies in micelles, reversed micelles and microemulsions, Adv. Colloid Interface Sci., 1999, 82, 1–42.
53. K. Thakkar, B. Bharatiya, D. O. Shah and P. Bahadur, Investigations on zwitterionic alkylsulfobetaines and nonionic Triton X-100 in mixed aqueous solutions: effect on size, phase separation and mixed micellar characteristics, J. Mol. Liq., 2015, 209, 569–577.
54. J. R. Rodríguez, A. González-Pérez, J. L. Castillo and J. Czapkiewicz, Thermodynamics of Micellization of Alkyldimethylbenzylammonium Chlorides in Aqueous Solutions, J. Colloid Interface Sci., 2002, 250, 438–443.
55. K. S. Sharma, P. A. Hassan and A. K. Rakshit, Self-aggregation of binary surfactant mixtures of a cationic dimeric (Gemini) surfactant with nonionic surfactants in aqueous medium, Colloids Surf., A, 2006, 289, 17–24.

---