Strong synergistic effect of cationic hydrocarbon surfactant and novel nonionic tri-block short-chain fluorocarbon surfactant mixtures on surface activity, wettability and solubilization

Mixing hydrocarbon surfactants with fluorocarbon surfactants is still an important strategy to improve the economic benefits and performances of fluorocarbon surfactants and expand their range of application. Herein, we prepared a novel kind of hydrocarbon-fluorocarbon surfactant mixtures via mixing a cationic surfactant, cetyltrimethylammonium bromide (CTAB), with a tri-block nonionic short-chain fluorocarbon surfactant (F9EG13F9) in aqueous solution. The results showed that adding a small CTAB amount to F9EG13F9 (the molar fraction of CTAB in the mixture (x1) was 0.2) could greatly reduce its critical micelle concentrations (cmc) from 0.408 mmol/L to 0.191 mmol/L. At this x1, the contact angle of the mixture was the minimum (57.7 °) at 100 s on polytetrafluoroethylene film, which was even lower than that of F9EG13F9. Besides, CTAB/F9EG13F9 mixtures possessed better colloidal stability and solubilization ability toward hydrophobic dye (Sudan І) than F9EG13F9. The outstanding performances of binary surfactant mixtures benefited from the non-ideal mixing and strong synergistic effect evidence that CTAB/F9EG13F9 surfactant mixtures could be used in practical applications instead of individual F9EG13F9, thereby reducing the used cost of F9EG13F9.


Introduction
Fluorocarbon surfactants can be used in leather production to improve the performances and quality of leather due to their outstanding properties, including the wet and dry finishing process of leather production [1][2][3]. Conventional fluorocarbon surfactants usually have long fluorocarbon chains (C x F 2x + 1 , x > 7). Although them possess many advantages, their serious toxicity and high bioaccumulation in the environment greatly limit their future development [4][5][6][7]. For example, a typical finishing agent based on perfluorooctanoic acid (3 M Scotch-guard™ FC-805) [8] has been banned. An effective method to decrease the harm to the environment is reducing the number of perfluorinated carbon atoms in a hydrophobic tail from C8-C10 to C4-C6 [9]. Heretofore, a great amount of short-chain fluorocarbon surfactants with low bioaccumulation have been prepared and studied [10][11][12][13][14][15][16]. However, the complex synthesis steps and expensive raw materials lead to the high cost of these surfactants, which vastly reduced their range of application. So, how to effectively reduce the used cost of these fluorocarbon surfactants is still a hot topic. In fact, a lot of studies have disclosed that binary hydrocarbon surfactant mixtures possessed strong synergistic effect and presented better performances than individual hydrocarbon surfactant such as lower cmc [17], stronger solubilization ability and emulsifying ability [18,19]. Therefore, researchers expect to improve the performances of fluorocarbon surfactants and reduce their high cost by mixing cheap hydrocarbon surfactants with fluorocarbon surfactants [20][21][22].
Some efforts have been made in recent years to achieve the above objectives. For instance, Wang et al. prepared a kind of fluorocarbon surfactant mixtures with good surface activity by mixing sodium perfluoropolyether carboxylate (PFPE-Na) with cetyltrimethylammonium bromide (CTAB), where the minimum cmc of mixtures was 100 times lower than the cmc of CTAB and more than 1000 times below that of PFPE-Na [23]. Zhang et al. found that introducing sodium lauryl sulfate (K12) to perfluoropolyether (3) amide propyl dimethyl ammonium iodide (PFPE-A) could effectively decrease the cmc of PFPE-A [24]. Jiang et al. reported the foaming ability of mixtures of an amphoteric short-chain fluorocarbon surfactant (FS-50) and sodium dodecyl sulfate (SDS) where the adding of SDS could improve their respective residual foam ratio due to the interaction between two surfactants [25]. Above researches showed the synergistic effect of fluorocarbon and hydrocarbon surfactant mixtures on surface activity and foam ability, ect., which effectively reduced the used cost of fluorocarbon surfactants and improved their performances. However, most of the researches only referred to ionicionichydrocarbon-fluorocarbon surfactant mixtures due to the stronger interaction between oppositely charged hydrophilic groups. There was little research on ionicnonionichydrocarbon-fluorocarbon surfactant mixtures although nonionic fluorocarbon surfactants exhibited the advantages of lower toxicity, stronger salt resistance and stronger acid and alkali resistance [13,14]. Designing a kind of ionic-nonionichydrocarbon-fluorocarbon surfactant mixture with a strong synergistic effect and good performances is still a challenge.
In this work, we reported a novel class of fluorocarbon surfactant mixtures consisted of cetyltrimethylammonium bromide (CTAB) and a tri-block nonionic fluorocarbon surfactant with two short fluorocarbon chains (F 9 EG 13 F 9 ). Their micellization, adsorption and thermodynamic behaviors were researched via using various theoretical models. Meanwhile, the wettability, colloidal stability and solubilization towards hydrophobic dye of binary mixtures were also investigated. CTAB served as a commercial surfactant commonly is widely used in mixed surfactant systems, and F 9 EG 13 F 9 possesses the special tri-block structure that means an adjustable molecular chain spacing [13]. So, the properties of mixtures of CTAB and F 9 EG 13 F 9 are intriguing. The results reveal that CTAB/F 9 EG 13 F 9 mixtures possess strong synergistic effect, and the performances of binary surfactant mixture with a specific proportion are superior to individual F 9 EG 13 F 9 including cmc, wettability, colloidal stability and solubilization capacity. We believe that the studying of CTAB/F 9 EG 13 F 9 mixtures could provide new insights into the development of fluorocarbon surfactant mixtures with low cost, low bioaccumulation and high performances, which is beneficial to expand the application range of fluorocarbon surfactants in leather and other fields.

Surface tension measurements
Surface tension measurements were performed using an automatic tension meter (BZY-1, Shanghai Hengping Instruments Factory) at 25.0 ± 0.1°C. The curve of surface tension varying with the logarithm concentration could be obtained via measuring the surface tension of 8-10 different concentrations of sample. Before the measurements of samples with different molar fractions of CTAB, the surface tension of water should also be measured and maintain at about 72.0 mN/m to minimize the experimental error.

Conductivity measurements
Conductivities of CTAB and its mixtures solutions were measured by using a conductivity analyzer (DDS-11A, Shanghai INESA & Scientific Instrument Co., Ltd., China) at 25°C. Each sample shall be measured at least six times.

Contact angle measurements
Dynamic contact angle of individual surfactant or binary mixtures was measured on a DSA 25 contact angle goniometer (Krüss Company, Germany) at 25.0 ± 0.1°C where the surfactant concentration was 1 mmol/L. The polytetrafluoroethylene (PTFE) film and parafilm were used as base plates.

Transmittance measurements
Transmittance of CTAB, F 9 EG 13 F 9 and their mixture was measured by a Hitachi UV-1900UV-Visible spectrophotometer in the range of visible light range (380 nm-800 nm). The surfactant solutions with a certain concentration (2.5 mmol/L) were prepared and placed in water bath at 25°C. 2 ml of supernatant was taken for each test.

Solubilization of hydrophobic dye
To assess the solubilization ability of binary surfactant mixtures towards hydrophobic dye, a series of experiments were carried out by adding an excess of Sudan I to the surfactant solutions with different concentrations to ensure maximum solubility. Subsequently, these samples were stirred for 24 h at 25°C. Then the excess nonsolubilized portion of Sudan I was separated using syringe filters with a Nylon Membrane (pore size of 0.22 μm) and the filtrate (5 mL) was diluted with an equal volume of ethanol. The absorbance of the diluent was measured by a Hitachi UV-1900UV-Visible spectrophotometer at λ max (485 nm) [26]. Besides, the molar absorption coefficient of the Sudan I in ethanol-water (50% v/v) was obtained and its value was 1.1656 × 10 4 L·mol − 1 ·cm − 1 .

Micellization behavior of binary mixtures
The curves of surface tension as a function of the logarithm concentration of individual CTAB, F 9 EG 13 F 9 and their mixtures were obtained by the surface tension measurements. As depicted in Fig. 2, every curve has an obvious break point which indicates that the micelle has been formed in aqueous solution. And the concentration of surfactant at this point is called critical micelle concentration (cmc).
In Table 1, the cmc values of CTAB/F 9 EG 13 F 9 mixtures are presented. For individual surfactant, the cmc value of F 9 EG 13 F 9 is 0.408 mmol/L which is consistence with our previous reported date [13]. Whereas, the cmc value of CTAB is 0.429 mmol/L which is higher than F 9 EG 13 F 9 , indicating that F 9 EG 13 F 9 is easier to form micelle in a low surfactant concentration. When adding F 9 EG 13 F 9 to CTAB, the cmc value of CTAB decreases a lot and is even lower than that of F 9 EG 13 F 9 . It is related to the electrostatic interaction and steric effect between ionic surfactants and nonionic surfactants [27][28][29]. In our work, the addition of F 9 EG 13 F 9 can decrease the electrostatic repulsion effect of cationic hydrophilic head groups of CTAB, meanwhile, the presence of CTAB also decreases the steric hindrance effect of nonionic hydrophilic head groups of F 9 EG 13 F 9 . With the decrease of molar fraction of CTAB in mixed solution (x 1 ) from 0.8 to 0.2, the cmc values of binary mixtures decrease from 0.314 mmol/L to 0.191 mmol/L indicating that the increase of F 9 EG 13 F 9 favors the formation of mixed micelle. Actually, similar phenomenon can be also found in other literatures [30,31]. This can be ascribed to that the increase of F 9 EG 13 F 9 composition enhances the electrostatic screen effect resulting in the weaker electrostatic repulsive force between the cationic hydrophilic head groups of CTAB. Besides, the fluorocarbon surfactant possesses stronger hydrophobicity so that the mixed system with a lower x 1 is more efficient to proceed micellization. The cmc values of binary surfactant mixtures with x 1 = 1, 0.8, 0.6, 0.4 and 0.2 measured by conductivity measurements are 0.428, 0.326, 0.298, 0.251 and 0.164 mmol/L, respectively (as represented in Fig. 3), which coincides with those obtained from the surface tension method and indicates the accuracy of the cmc values of binary surfactant mixtures. In addition, the conductivity measurements also manifest that the conductivities of solutions decrease with the decrease of x 1 , further confirming the electrostatic screen effect of F 9 EG 13 F 9 .
The cmc value of CTAB/F 9 EG 13 F 9 mixture on an ideal state can be given by the Clint equation [32].
where cmc ideal is the ideal cmc value of binary surfactant mixture; cmc 1 and cmc 2 are the cmc value of individual CTAB and F 9 EG 13 F 9 , respectively. Table 1 lists the calculated cmc ideal values and Fig. 4 reveals the difference between the ideal and experimental cmc values. As illustrated in Fig. 4, the experimental cmc values have an obvious negative deviation from the ideal cmc values, suggesting the formation of non-ideal mixtures and the presence of strong interaction between two surfactants due to the decrease of steric hindrance effect and electrostatic repulsion effect.
To further understand the non-ideal behavior for binary surfactant mixtures, Rubingh [33] proposed the wellknown regular solution theory (RST). On a basis of RST, the interaction parameter (β 12 ) between CTAB and F 9 EG 13 F 9 is given by following equation: where X 1 is the molar fraction of CTAB in the non-ideal mixed micelle, which can be deduced by using Eq. (3) Table 1 Values of cmc and micellization parameters for CTAB/F 9 EG 13 F 9 mixtures at different CTAB proportions at 25°C Additionally, the molar fraction of CTAB in the ideal mixed micelle (Χ ideal 1 ) can be obtained by: The calculated results of above parameters (β 12 , X 1 and Χ ideal 1 ) are given by Table 1. As illustrated in Table 1, the values of X 1 have the deviation from the values of Χ ideal 1 further indicating the formation of non-ideal mixtures. Notably, the negative deviation can be found when the x 1 is in the range of 0.6-0.8 but the positive deviation is presented when the x 1 is less than 0.6. This diffidence can be ascribed to the fact that no matter for CTAB or F 9 EG 13 F 9 , the high content components always provide an unfavorable factor (the electrostatic repulsion effect or the steric hindrance effect) to hinder the formation of mixed micelles. Therefore, the mixed micelles tend to vary the molar ratio of two surfactants, thereby reducing the hindrance provided by high content components. Subsequently, the interaction degree between CTAB and F 9 EG 13 F 9 is estimated by the β 12 . The negative values of β 12 are found in all binary mixtures with different x 1 , which suggests the presence of strong synergistic effect. At x 1 = 0.2 , the value of β 12 reaches the minimum which is − 3.662 and means the strongest synergistic effect. The result is consistent with the measured value of cmc.
Moreover, the activity coefficient of CTAB and F 9 EG 13 F 9 (denoted as f 1 and f 2 , respectively) for the binary mixtures in aqueous solutions can be expressed as Eqs. (5a) and (5b), which describes the degree of participation of two surfactants in the micellization.
The calculated values of f 1 and f 2 are given in Table 1. It can be observed that f 1 and f 2 are lower than 1.0, further suggesting the non-ideal behavior of binary mixtures. Specially, the f 1 is greater than the f 2 when the x 1 is 0.6-0.8, indicating the formation of the mixed micelles governed by CTAB. Conversely, with the decrease of x 1 , F 9 EG 13 F 9 replaces CTAB to govern the formation of the mixed micelles. This means that the reduction of adverse factors coursed by high content components is a key point to promote the formation of mixed micelles in CTAB/F 9 EG 13 F 9 mixtures.

Adsorption behavior of binary mixtures
Surfactants possess special amphiphilic structure which enables them to arrange at air-water interface, hydrophilic head in aqueous-phase and hydrophobic tail in air, resulting in the decrease of surface tension of water. Therefore, the measurement of surface tension of surfactant aqueous solution is an important method to characterize its adsorption ability on the water surface. The variation of surface tension with the logarithm concentration of individual CTAB, F 9 EG 13 F 9 or their mixtures in aqueous solution was measured by surface tension measurements as depicted in Fig. 2. Table 2 records the critical surface tension (γ cmc ) values of CTAB/F 9 EG 13 F 9 mixtures with different x 1 . These values mean the surface tension of surfactants aqueous solutions at cmc and indicate the saturated molecular arrangement at air-water interface. It can be found in Table 2 that the γ cmc value of F 9 EG 13 F 9 (21.4 mN/m) is lower than that of CTAB (30.2 mN/m) because of the strong hydrophobicity of fluorocarbon surfactant. When adding a small F 9 EG 13 F 9 amount of to CTAB (x 1 = 0.8), the γ cmc value dramatically decreases from 30.2 mN/m to 24.3 mN/m. It can be attributed to the fact that the special tri-block structure of F 9 EG 13 F 9 endows it with an adjustable chain spacing, which means that F 9 EG 13 F 9 can screen more cationic head groups of CTAB as depicted in Fig. 5. With further increasing F 9 EG 13 F 9 , the γ cmc values decrease from 24.3 mN/m to 22.7 mN/m because F 9 EG 13 F 9 possesses higher surface activity. Although these binary mixed systems display the strong synergistic effect, their surface activity was hardly on a par with F 9 EG 13 F 9 . Some possible reasons are implicit in Fig. 5. On the one hand, the exceeded length of hydrocarbon chains may bend and lead to the decrease of interfacial density of fluorocarbon chains. On the other hand, the mutual immiscibility of hydrocarbon and fluorocarbon chains decreases the number of surfactant molecules at air-water interface. Thus, the ability of binary mixtures to reduce surface tension of water is slightly inferior to that of F 9 EG 13 F 9 .
To further understand the absorption state of individual CTAB, F 9 EG 13 F 9 and binary surfactant mixtures on the water surface, two important parameters, the surface  (7).
where R is the gas constant (8.314 J·mol − 1 ·K − 1 ) and T is the absolute temperature and taken as 298.15 K; ∂γ/ ∂logC is determined from the maximum slope in Fig. 2; N A is the Avogadro's constant; the value of n is 1 for nonionic F 9 EG 13 F 9 or 2 for cationic CTAB and their mixtures [34,35]. It can be clear seen the Γ max and A min values of different surfactant systems in Table 2. The higher Γ max values, the lower A min values and the more closely molecular arrangement at air-water interface. Obviously, the Γ max values of binary mixtures are larger than that of CTAB indicating the denser molecular arrangement at air-water interface. With the increase of molar fraction of F 9 EG 13 F 9 from 0.2 to 0.4, the Γ max values decrease and A min values increase anomalously due to the increasing repulsive effect between hydrocarbon and fluorocarbon chains adverse to the dense molecular arrangement. Further increasing the molar fraction of F 9 EG 13 F 9 , the Γ max values increase and the A min values decrease due to the lower A min value of nonionic F 9 EG 13 F 9 . However, the A min values of CTAB/ F 9 EG 13 F 9 mixtures are larger than that of F 9 EG 13 F 9 , which also explains why F 9 EG 13 F 9 has better surface activity than its mixtures with CTAB. Moreover, the adsorption efficiency of CTAB/ F 9 EG 13 F 9 mixtures with different x 1 is characterized by pC 20 which is the negative logarithm of surfactant concentration required to reduce the surface tension of water by 20 mN/m [36]. As described in Table 2, the pC 20 values of CTAB and F 9 EG 13 F 9 are 4.83 and 4.67, respectively. Interestingly, the adsorption efficiency of CTAB is slightly superior to that of F 9 EG 13 F 9 although F 9 EG 13 F 9 possesses stronger hydrophobicity. The reason may be that the nonionic polyoxyethylene chains of F 9 EG 13 F 9 are easily twined together, thereby hindering the migration of F 9 EG 13 F 9 from solution to air-water interface. For mixed surfactant systems, their pC 20 values are larger than individual surfactant no matter for CTAB or F 9 EG 13 F 9 . This is because the presence of CTAB can avoid the entanglement of polyoxyethylene chains and enable F 9 EG 13 F 9 to faster adsorb to water surface resulting in the enhancement of interfacial hydrophobicity.

Thermodynamics of binary mixtures
Thermodynamic behavior of CTAB/F 9 EG 13 F 9 mixtures is analyzed via using a series of parameters. For example, the standard free energy of micelle formation (ΔG mic ) and adsorption (ΔG ads ) for the mixed systems can be calculated from Eq. (8) and Eq. (9) [37,38], respectively.
where γ 0 is the surface tension of pure water (72.0 mN/ m). In addition, to further prove the interaction of CTAB and F 9 EG 13 F 9 mixtures, the non-ideal free energy change (ΔG) and ideal free energy change (ΔG ideal ) of micellization for binary surfactant mixtures are given by following equations based on the RST [33].
The calculated values of thermodynamic parameters are presented in Table 3 that display all negative values indicating the spontaneous micellization and adsorption process of binary surfactant mixtures. Fig. 6 discloses the difference between ΔG mic and ΔG ads values. As shown in Fig. 6, the values of ΔG ads are all lower than the values of ΔG mic , which indicates that the surfactant molecules tend to adsorb at air-water interface rather than form micelles in aqueous solution no matter for individual CTAB, F 9 EG 13 F 9 or their mixtures. For the micellization process, the variation trend of ΔG mic values with the decrease of x 1 is consistence with that of cmc values. When x 1 is 0.2, the ΔG mic has the minimum value that is − 31.14 KJ/mol. As for adsorption process, ΔG ads values of surfactant mixtures are also lower than those of CTAB (− 61.11 KJ/mol) and F 9 EG 13 F 9 (− 41.31 KJ/mol) due to the synergistic effect between two surfactants and the strong hydrophobicity of fluorocarbon surfactant. The calculated results of ΔG and ΔG ideal display the obvious deviation, further suggesting the non-ideal behavior of mixtures.
Furthermore, on a basis of Maeda model proposed in 1995 [39], the thermodynamic stability (ΔG M ) of binary ionic/nonionic surfactant mixtures can be obtained by following equation.
where B 0 , B 1 and B 2 can be calculated in terms of above dates from the Eqs. (12b) to (12d).
where B 0 is a constant taken as − 7.80; the calculated values of B 1 , B 2 and ΔG M can be obtained in Table 3. With the decrease of x 1 in the mixed systems, the values of ΔG M are decrease correspondingly as visualized in Fig. 6, that is, forming the stable mixed micelles. The minimum ΔG M value is − 21.42 KJ/mol when x 1 is 0.2, due to the interaction between CTAB and F 9 EG 13 F 9 . Adding a small CTAB amount to F 9 EG 13 F 9 can favor the formation of compact mixed micelles owing to the decrease of steric hindrance effect. But with the increase of CTAB component, the mutual immiscibility between the hydrocarbon and fluorocarbon surfactants increases, which is adverse for the closely arrangement of surfactant molecules in the mixed micelles.

Wettability of binary mixtures
Wettability is a significant property for surfactants, which enables them to be widely used for industrial production and daily life [40][41][42]. Generally speaking, the wettability of surfactants is directly related to their contact angle on a solid surface, that is, the smaller contact angle and the better wettability. Therefore, the contact angle measurements were conducted to evaluate the wettability of individual CTAB, F 9 EG 13 F 9 and their mixtures on PTFE film and parafilm, respectively.
It is described in Fig. 7a and b that the contact angles of CTAB/F 9 EG 13 F 9 mixtures on PTFE and parafilm decrease with the increase of time. Figure 7c and d present the variation images of solution droplet of binary mixture (x 1 = 0.6) within 100 s. From Fig. 7a, it can be found that introducing F 9 EG 13 F 9 to CTAB effectively decreases the contact angle of CTAB and the more composition of F 9 EG 13 F 9 , the smaller contact angle of surfactant solution. This is caused by the low surface energy of F 9 EG 13 F 9 and the synergistic interaction between two surfactants. When the x 1 decreases from 1 to 0.6, the surfactant mixtures possess lower contact angle than F 9 EG 13 F 9 before about 35 s, indicating that these surfactant mixtures easier migrate from solution to liquid-solid surface due to the decrease of steric hindrance effect and electrostatic repulsion effect. Surprisingly, the contact angle of binary surfactant mixture at x 1 = 0.2 can reduce to 57.7°at 100 s which is lower than that of F 9 EG 13 F 9 (73.8°), that is, the wettability of binary surfactant mixtures is even better than that of F 9 EG 13 F 9 at a low x 1 . Similar results can be found in Fig. 7b, further suggesting the superior wettability of CTAB/ F 9 EG 13 F 9 mixtures. However, for parafilm, the wettability of binary mixtures is preferable to that of F 9 EG 13 F 9 when the x 1 reaches 0.4. This difference may be related to the property of parafilm whose higher surface energy enables binary surfactant mixtures to easily spread on the solid surface.

Colloidal stability of binary mixtures
Colloidal stability is another important factor that determines the commercial value of these surfactant mixtures. Fig. 8 is the visualized image of samples and unveils the difference between CTAB/F 9 EG 13 F 9 mixtures with x 1 = 1, 0.6 and 0 on the colloidal stability. For CTAB (x 1 = 1), its solution is very transparent and there is almost no Tyndall effect due to the small size of aggregates [43].
With the increase of time, the solution properties have no obvious change. For CTAB/F 9 EG 13 F 9 mixture (x 1 = 0.6), its solution is transparent blue and the Tyndall effect can be seen obviously. After 7 days, there is no significant change in the red beam path and transparency of solution, verifying the good colloidal stability of surfactant mixture. As for F 9 EG 13 F 9 (x 1 = 0), its solution is slightly cloudy and the incident light cannot pass through the solution well indicating the formation of large aggregates. After 3 days, the transparency of solution increases and the red beam path can also be found but not obvious. After a week, the transparency of the solution further increases and the red beam path basically disappears. Figure 9 unveils the transmittance spectra of these samples. It can be found that the variation trend of transmittance of solutions agree well with the above description. A possible explanation for the transmittance variation of F 9 EG 13 F 9 solution is the weak interaction between the aggregates. Because of the hydrophilic shell of aggregates constituted by the nonionic polyoxyethylene chains, these aggregates of F 9 EG 13 F 9 are easy to further gather together and turn into white precipitate at the bottom of the vial (as exhibited in Fig. 8). The addition of CTAB provides a certain positive charge for the hydrophilic shell of aggregates and increases the electrostatic repulsion effect between the aggregates favoring the stable dispersion of the aggregates in solution.

Solubilization of hydrophobic dye
Solubilization effect of surfactants on hydrophobic organic compounds is important because these organic compounds are usually harmful and difficult to remove from environment. Surfactants can form micelles in aqueous solution, when the concentration is larger than cmc. The micelle has a hydrophilic shell and hydrophobic core which can incorporate these hydrophobic organic compounds in water, thereby improving their solubility. Generally speaking, resulting in the lack of solubilization ability towards hydrocarbons of fluorocarbon surfactants, these hydrophobic substances are hydrocarbons which have poor compatibility with fluorocarbon surfactants [44].
Mixing hydrocarbon surfactants with fluorocarbon surfactants may be an effectively method to solve this problem due to the formation of mixed micelles. Herein, the solubilization of CTAB/F 9 EG 13 F 9 mixtures towards hydrophobic dye (Sudan I) was investigated by a UV-Visible spectrophotometer. The absorbance curves of Sudan I versus concentration of binary surfactant mixtures with different x 1 are depicted in Fig. 10 inset. It can be obviously seen that the absorbance increases with the increase of surfactant concentration. When the concentration exceeds a specific value, the absorbance increases shapely due to the formation of micelle. To further assess the solubilization ability of binary surfactant mixtures, the concentration of solubilized Sudan I is calculated according to the molar absorption coefficient and disclosed in Fig. 10. The molar solubilization power (SP M ) of different mixed systems can be obtained according to the following relationship [45].
where S dye and S cmc are the solubility of Sudan I in the solution at a particular surfactant concentration or at critical micelle concentration, respectively; C s is the concentration of CTAB/F 9 EG 13 F 9 mixtures. The calculated results can be found in Table 4. It points out that CTAB has a larger SP M value (0.00913) than that of F 9 EG 13 F 9 (0), which means a better solubilization ability. Compared with CTAB, F 9 EG 13 F 9 hardly solubilizes Sudan I due to the mutual immiscibility of hydrocarbon and fluorocarbon compounds. In fact, some similar results can be found in other literatures. For example, Takata et al. [46] found individual fluorocarbon surfactant hardly solubilizes Sudan III and Matsuoka et al. [44] reported that a series of fluorocarbon surfactants had no solubilization ability towards naphthalene. As a result, fluorocarbon surfactants are unlikely to have applications in the solubilization of hydrocarbons. In our experiment, when adding a small CTAB amount, the solubilization ability of F 9 EG 13 F 9 is effectively improved. For example, the SP M value of CTAB/ F 9 EG 13 F 9 mixture at x 1 = 0.2 is 0.00883, which is close to that of CTAB. This is caused by the fact that the formation of mixed micelle improves the compatibility of heterogeneous system and favors the insertion of Sudan I. Besides, the lower cmc value of this binary mixture also endows it with a stronger solubilization ability than F 9 EG 13 F 9 . With further increasing x 1 , the SP M values increase correspondingly. The maximum SP M is 0.01195 when x 1 = 0.8, which is even larger than that of CTAB. Above results further indicate that mixed surfactant systems possess a better solubilization ability than individual CTAB or F 9 EG 13 F 9 .
For an ideal mixed surfactant system, their SP M values can be calculated by following relationship [47].
where SP ideal is the ideal SP M value of binary surfactant mixture; SP 1 M and SP 2 M denote the SP M value of individual CTAB and F 9 EG 13 F 9 , respectively. The SP ideal values of CTAB/F 9 EG 13 F 9 mixtures with different x 1 are presented in Table 4. A positive deviation of the experimental value from the ideal one can be found in Fig. 11, further suggesting the non-ideal behavior of mixtures and verifying the strong synergistic effect between CTAB and F 9 EG 13 F 9 .
In addition, the partition coefficient of Sudan I between mixed micelle phase and aqueous phase (K m ) and the standard free energy of solubilization (ΔG s ) can be used to estimate the trend of solubilization [48,49].
The lnK m and ΔG s values are listed in Table 4. Specially, the lnK m and ΔG s values of F 9 EG 13 F 9 cannot be given in this work due to the S cmc = 0. From Table 4, the lnK m values increase with the decrease of x 1 and the maximum lnK m value is 5.42 at x 1 = 0.2. This is because the cmc value reach minimum when x 1 = 0.2, which favors the insertion of Sudan I. However, this is not consistent with the SP M indicating that the solubilization ability is related to not only cmc but also micellar composition. The calculated ΔG s values are all negative suggesting the spontaneous solubilization process. In conclusion, the micellization, adsorption, thermodynamics, wettability, colloidal stability and solubilization towards Sudan І of CTAB/F 9 EG 13 F 9 mixtures were investigated successively based on different theoretical models and experimental methods. The results manifested that mixing CTAB with F 9 EG 13 F 9 is non-ideal and a strong synergistic effect exists in these mixtures. Among them, CTAB/F 9 EG 13 F 9 mixture at x 1 = 0.2 had the strongest synergistic effect (β 12 = − 3.662). Its cmc and surface tension could reach 0.191 mmol/L and 22.7 mN/m, respectively. Besides, the contact angle of this surfactant mixture could reduce to 57.7°at 100 s, which is even lower than F 9 EG 13 F 9 . Compared with F 9 EG 13 F 9 , CTAB/F 9 EG 13 F 9 mixtures also presented a better colloidal stability. In addition, introducing CTAB into F 9 EG 13 F 9 effectively improved the solubilization ability towards Sudan І of F 9 EG 13 F 9 where the SP M value of CTAB/F 9 EG 13 F 9 mixture at 0.4 (0.01068) even exceeded that of CTAB (0.00913). Based on the results mentioned above, CTAB/F 9 EG 13 F 9 mixtures could be widely used in practical applications as a feasible alternative for individual F 9 EG 13 F 9 because of their better performances and lower used cost.