Micellization of Binary Mixture of Amino Sulfonate Amphoteric

Jan 27, 2017 - The micellization behaviors of binary mixtures constituted by an amphoteric surfactant, sodium 3-(N-dodecyl ethylenediamino)-2-hydropro...
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Micellization of Binary Mixture of Amino Sulfonate Amphoteric Surfactant and Octylphenol Polyoxyethylene Ether (10) in Aqueous Solution: Different Electrolyte Effect Zhao Hua Ren,*,† Jing Huang,‡ Yan Cheng Zheng,† Lu Lai,† Lin Li Hu,† and Yan Ling Chang† †

College of Chemistry and Environmental Engineering, Applied Chemistry Research Centre for Oil and Gas Fields, Yangtze University, Jingzhou 434023, China ‡ College of Management, Yangtze University, Jingzhou 434023, China ABSTRACT: The micellization behaviors of binary mixtures constituted by an amphoteric surfactant, sodium 3-(N-dodecyl ethylenediamino)-2-hydropropyl sulfonate, and a nonionic surfactant octylphenol polyoxyethylene ether (10), OP-10, in aqueous solutions containing seven inorganic salts were investigated. The values of mixed critical micelle concentration (cmcM) were determined by both the tensiometry and the UV−vis spectroscopy method using pyrene as a probe. The dependence of cmcM on inorganic salt was established. According to different theoretical models, the components in mixed micelle, interaction parameters between two surfactants, etc. were obtained. Upon adding inorganic salt, the component in real mixed micelle is inferior to the ideal case, indicating nonideal mixing. Different inorganic salts result in the variation of component in mixed micelle. For all mixed surfactant systems, a negative interaction parameter between surfactants shows synergistic effect. Thermodynamic parameters show that the process of micellization is spontaneous, and the addition of inorganic salt promotes the process of micellization. The contribution of micellization may result from three effects: salting-out effect, electrostatic shielding effect, and steric effect. And thermodynamic stability was also discussed. These results will help with understanding the micellization behavior between surfactants and to design surfactant formulations applied in many fields, especially relative to aqueous salt solutions. salinity. For example, in oil fields there sometimes exist the large amount of inorganic ions (even over the concentration of 1 mol/L) in a water body, and the valences of these ions are not single, such as, besides univalent Na+, K+, etc., including divalent Ca2+ or trivalent Fe3+, etc.12 Considering the high concentration of inorganic ions and their different valences, the investigation about the interacting behavior between surfactant molecules may be so complicated. The high salinity (usually near 1 mol/L and even smaller) may result in the decrease of solubility of surfactants or their mixtures and even the presence of precipitate in aqueous solution, and the relationship of the cmc of mixed surfactants with the concentration of inorganic ions or counterion may not be easy to describe with a specific mathematical equation, at least which may be not fulfill the Corrin−Harkins equation for ionic surfactants or the Tori− Nakagawa equation for nonionic or zwitterionic surfactants.8,13 Although the Tori−Nakagawa equation can describe the case of individual nonionic surfactant in the range of low salt concentration where the salting-out effect is not significant, few investigations show that the relationship holds for the

1. INTRODUCTION Surfactant mixtures are of importance from the fundamental as well as technological point of view. In the last decades, they have had wide attention because of their excellent properties, e.g., strong surface/interfacial activities, lower critical micelle concentration (cmc) values, low cost, etc., relative to single surfactant.1−5 In view of this, many binary and ternary combinations of ionic/ionic, ionic/nonionic, nonionic/nonionic, ionic/ionic/ionic, ionic/ionic/nonionic, and ionic/nonionic/nonionic surfactant mixtures have been investigated with respect to their mixed micelle and other surface/interfacial behaviors.1,4−7 Among these investigations, some thermodynamic models,1−5 e.g., Rubingh’s model, Rosen’s model, and so on, have been extensively adopted to focus on the interaction between the compositions of surfactant mixtures and to predict their mixed micellar compositions and other behaviors of micellization. Through these investigations, they help with understanding some interacting behaviors between amphiphiles. However, most of these investigations have been performed in aqueous solutions in absence of salt. Of course, some literature has considered the effect of inorganic salts on the interacting behaviors between molecules.8−11 Even so, dilute or low salinity reported in some literature may not match with the cases in many application occasions relative to high © 2017 American Chemical Society

Received: August 4, 2016 Accepted: January 16, 2017 Published: January 27, 2017 938

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use. In addition, pyrene was purified by recrystallizaiton from the mixed cosolvents of ethanol and DTD water. Solutions of C12AS, OP-10, or their mixtures were prepared in specific salt water obtained with DTD water, respectively. For all the binary mixtures of C12AS and OP-10, the molar fractions of C12AS were uniformly designated to 0.561, which was an optimum mixing fraction in the synergistic properties in aqueous solution.2 The pH values of all the surfactant solutions were found to near 6.2 within the range of isoelectric point for C12AS, which agrees with our previous investigation.14,15 The stock solution of pyrene was prepared as follow: a 3.0 μmol/L solution of pyrene was prepared using ethanol as a cosolvent and the ethanol concentration was diluted to about 0.1 wt %, where a small concentration of ethanol would not affect the spectral and self-aggregation behavior of amphiphiles.3 2.2. Methods. Compatibility of Surfactants in Aqueous Salt Solutions. To observe the solubility phenomena of surfactants in aqueous salt solutions, the 1.00g/L surfactant solution with different salinities were prepared. After thorough mixing, the solutions were held in sealed tubes at ambient pressure and then allowed to stand in a water bath of 298.15 ± 0.20 K for 24 h. For some specimens, the occurrence of precipitates in solutions can be visible to the naked eye, while for the other specimens, the turbidimetry12−14 can help us to judge whether or not the precipitates or a haze occur. If the difference between the turbidities before and after the test is more than 2% in turbidity, the precipitate phenomena seemed to happen.12−14,16 The experimental results show that for unvalent ion, e.g., Na+, K+, the concentration range of ions is lower than 1.20 mol/L, and while for divalent ion, e.g., Mg2+, Ca2+, and Ba2+, or for a trivalent ion, e.g., Al3+ and Fe3+, its concentration range is lower than 1.0 mol/L. On the basis of the solubility experiment, all of the investigations in this paper were conducted within the allowable range of surfactant or salt ion concentration. Tensiometry and Determinations of cmc. Surface tension (γ) of the solutions was measured with a JK99C automatic surface tensiometer (made in China) by the Wilhelmy plate method. Measurements were made after thorough mixing in an oscillator and temperature equilibration. To obtain the scheduled temperature, all solutions in the conical flasks sealed with a rubber plug were allowed to stand in water bath of 298.15 ± 0.20 K for over 50 min. The readings were taken in four times to ensure the reproducibility and accuracy of measurements within ±0.20 mN/m. The cmc values for all the surfactant solutions can be determined from the break point in the curve of variation of surface tension with the logarithm of surfactant concentration.2,3 Method of UV−vis Spectrum and Determinations of cmc. The absorbance measurements for solutions containing C12AS and OP-10 were taken in a UV-2450 UV−vis spectrophotometer made by Shimadzu using 5 mL quartz cuvettes. The spectra were recorded in the 200−400 nm wavelength range, in the intermediate scanning speed, and in the sample interval of 0.5 nm. Before the absorbance was measured, all of these surfactant solutions added a stock solution of pyrene of 3.0 μmol/L were fully mixed and then were allowed to stand in water bath of 298.15 ± 0.20 K for over 50 min. The values of cmc for all the surfactant systems can be obtained from the inflection point in the plot of the absorbance at the wavelength of about 275 nm versus the logarithms of surfactant concentration.2,3

mixtures containing ionic surfactants, much less for those cases with respect to high salt concentration. The addition of inorganic salt is known to modify the properties of surfactant solutions, such as solubility, shape and size of micelles, etc. In general, for the systems containing ionic surfactants, the electrostatic repulsion between ionic heads of surfactants will be lowered by the salt effect, resulting in the formation of micelles at lower surfactant concentration and then decreasing the cmc. While for systems containing nonionic surfactants, the inappreciable decrease of cmc may be attributed significantly to the salting-out or salting-in effect to the hydrophobic chain.8 In many practical applications, the presence of inorganic salts, the change of their concentrations, and their ionic types may influence the properties of previously designed surfactant formulations and even decide the success or failure of work. Then, in this paper, the micellization behavior of a binary mixture of an amphoteric surfactant, sodium 3-(N-dodecyl ethylenediamino)-2-hydropropyl sulfonate (C12AS) developed by our group,2,3 and a nonionic surfactant octylphenol polyoxyethylene ether (10), OP-10, was investigated in aqueous solution in the presence of different inorganic salts such as sodium chloride (NaCl), magnesium chloride (MgCl2), etc. The purpose of investigation is to discover the salt effect on the interaction between surfactant components in binary mixtures, especially, the salt effect on optimum components. The final aim is to design a suitable component of mixture for optimal behavior for a specific application, e.g., oil-displacing agent. To obtain information regarding the interaction between molecules as well as the component in mixed micelles, different theories and thermodynamic models were adopted and the results are theoretically discussed.

2. EXPERIMENTAL SECTION 2.1. Materials and Solutions. The C12AS treated by drying in a vacuum at 318.15 ± 0.20 K has a purity of over 99 wt % in mass fraction, measured with a Vario EL III automatic elementary analyzer made by Germany Elementar Co. The nonionic OP-10 is a chemically pure reagent, and all inorganic salts (including NaCl, KCl, MgCl2, CaCl2, BaCl2, AlCl3, and FeCl3) are analytical reagents, all of which have the purity of >99 wt % from Sinopharm Chemical Reagent Co., Ltd. Pyrene with a purity of 98 wt % is purchased from Aldrich Chemical Reagent Co. The chemical structure formulas of C12AS and OP-10 are depicted in Figure 1. C12AS and OP-10 were used as supplied, while all of these inorganic salts were recrystallized three times using deionized triple distilled (DTD) water before

Figure 1. Chemical structures for C12AS and OP-10 and their diagrammatic representations. 939

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3. RESULTS AND DISCUSSION 3.1. Effect of Inorganic Salts on cmc. The values of cmc for all the surfactants containing individual (C12AS or OP-10) or mixed surfactants in salt solutions were measured by both the tensiometry and the UV−vis spectroscopy method. Figure 2 showed the variation of surface tension or the ratio of

in Table 1 that the cmc of nonionic OP-10 or amphoteric C12AS decreased slightly with the addition of inorganic salt, which is in good agreement with the cases of nonionic or zwitterionic surfactants reported in some literature.16−20 It is different obviously from the cases of conventional ionic surfactants, where their cmc values always decrease largely with the addition of electrolyte.16,17,21,22 The cause can be explained by the interactions between salt and surfactant. For ionic surfactants, the counterions result mainly in the decrease of electrostatic repulsion between their ionic headgroups,8,16,17,21,22 promoting the formation of micelle. While, for nonionics, the salting-out effect to the hydrophobic group of surfactant plays a vital role in the process of micellization, which has been reported in some literature.8,13,17 For amphoteric surfactant, upon adding inorganic salt, the decrease of cmc may be attributed to the salting-out effect and the electrostatic effect. The contribution of the salting-out effect can be easily understood as described above. The amphoteric C12AS in salt solution may be viewed as a slightly charged anionic molecule because of the headgroup structure of C12AS.16 The similar viewpoints have been reported by Kroflic et al.19 and Qin et al.20 As a result, the presence of inorganic cations can shield the electrostatic repulsion between slightly charged anionic headgroups of C12AS, promoting the formation of micelle. In the 1960s, the relationship of cmc with concentration of inorganic salt [S] has been established by Tori et al.23 For amphoterics as well as nonionic surfactants, the relationship is satisfied empirically as follow: log cmc = K[S] + C([S] < 1 mol/L)

(1)

where K is a constant relating to the nature of surfactant, electrolyte, temperature, solvent, and so on, and C is a constant term in this linear relationship. Equation 1 is based on the case of the individual surfactant but is seldom used to describe the case of surfactant mixtures. In this investigation, it was observed from Figure 3 that the logarithm of mixed cmc almost decreases linearly with the addition of inorganic salt. These linear fitting equations were well obtained like the form of eq 1, as listed in Table 2. The good linear dependence of mixed cmc on [S] like the form of eq 1 may result from the nature of both nonionic OP-10 and amphoteric C12AS. Herein, we focus on the salt effect on mixed cmc, especially the inorganic cation effect. As indicated in Table 2, the negative coefficient K in eq 1 suggests that the addition of inorganic salt is favorable to decrease the mixed cmc, and the small value of K implies that the addition of inorganic salt does not largely influence the process of micellization, which can be also observed from the variation of mixed cmc with inorganic salt in Table 2, and then it can be found that the valences of cations can cause some slight differences in values of K, for example, −0.0663, −0.0767, and −0.0940 for the cases of NaCl, MgCl2, and AlCl3, respectively. Inorganic ions can hydrate in aqueous solution. However, the formation of the hydrated ion was to destroy the original hydrated structure of hydrophobic group of amphiphile, that is, the salting-out effect.13,16 These ions with large ratios of ionic charge versus radius, Z/R, are highly hydrated and are water structure makers.13,16,17 They salt out the hydrophobic groups of the monomeric form of surfactant and decrease the cmc. Relative to those ions with smaller Z/R, these ions with larger Z/R can be more effective to salt out the hydrophobic group of surfactant and decrease the cmc. Therefore, the salting-out effect may

Figure 2. Dependence of solution properties on surfactant concentration in CaCl2 solutions (T = 298.15 ± 0.20 K; p = 0.101 ± 0.006 MPa). (a) Variation of surface tension with the logarithm of surfactant concentration (c), log c. (b) Variation of the ratio (A/c) of absorbance at the wavelength of about 275 nm and concentration with log c.

absorbance at the wavelength of about 275 nm and concentration (A/c) with the logarithm of surfactant concentration, log c, for the binary mixture of C12AS and OP-10 in CaCl2 solutions, which are typical for all surfactant mixtures in different salt solutions. In parts a and b of Figure 2, the inflection point for each set of data can be observed and was used to determine the value of cmc. In our previous investigation,3 the tensiometry and the UV−vis spectrometry have also been adopted to obtain the cmc values of surfactant mixtures. In this investigation, there was a little difference in the cmc values obtained from two measuring methods. For example, when the concentration ([CaCl2]) of CaCl2 is 0.250 mol/L, the mixed cmc value measured by the tensiometry is about 1.875 × 10−4 mol/L, while an adjacent value of mixed cmc (about 1.971 × 10−4 mol/L) was obtained from the UV− vis spectrometry. For the sake of calculation’s convenience, the mean values of cmc obtained from two measuring methods were adopted to estimate the corresponding parameters in the text below. These mean values are listed in Table 1. It is found 940

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Table 1. Micellization Parameters for C12AS, OP-10, and Their Mixture in Aqueous Salt Solution According to Rubingh’s Treatment (T = 298.15 K; p = 0.101 MPa)a cmc/(10−4 mol·L−1) −1

[S]/(mol·L ) NaCl 0.125 0.250 0.500 0.750 1.000 KCl 0.125 0.250 0.500 0.750 1.000 MgCl2 0.125 0.250 0.500 0.750 CaCl2 0.125 0.250 0.500 0.750 BaCl2 0.125 0.250 0.500 0.750 AlCl3 0.125 0.250 0.500 FeCl3 0.125 0.250 0.500

C12AS

OP-10

mixed

Xideal 1

X1

f1

f2

β12

2.761 2.703 2.607 2.494 2.372

3.287 3.285 3.173 3.115 3.043

2.103 2.056 1.973 1.892 1.841

0.602 0.607 0.608 0.614 0.620

0.560 0.561 0.563 0.566 0.570

0.760 0.758 0.754 0.751 0.762

0.641 0.636 0.626 0.616 0.620

−1.417 −1.438 −1.480 −1.516 −1.470

2.722 2.645 2.543 2.407 2.284

3.242 3.214 3.181 3.077 2.983

2.061 2.014 1.912 1.847 1.802

0.603 0.607 0.614 0.619 0.624

0.562 0.563 0.565 0.569 0.574

0.755 0.757 0.745 0.754 0.771

0.630 0.630 0.608 0.612 0.624

−1.463 −1.455 −1.558 −1.517 −1.435

2.657 2.573 2.454 2.312

3.221 3.174 3.088 3.021

2.003 1.941 1.854 1.791

0.607 0.611 0.616 0.624

0.562 0.564 0.566 0.574

0.752 0.750 0.747 0.756

0.624 0.618 0.609 0.601

−1.490 −1.516 −1.548 −1.546

2.604 2.522 2.385 2.237

3.181 3.125 3.012 2.965

1.981 1.923 1.832 1.775

0.609 0.612 0.616 0.628

0.564 0.565 0.568 0.576

0.757 0.756 0.758 0.772

0.628 0.624 0.619 0.620

−1.465 −1.478 −1.485 −1.440

2.552 2.474 2.311 2.174

3.142 3.074 2.961 2.907

1.944 1.892 1.806 1.732

0.610 0.613 0.620 0.630

0.564 0.566 0.571 0.577

0.755 0.757 0.765 0.774

0.624 0.624 0.623 0.621

−1.481 −1.474 −1.454 −1.433

2.481 2.382 2.224

3.101 3.013 2.894

1.902 1.841 1.753

0.614 0.617 0.624

0.567 0.568 0.573

0.757 0.762 0.770

0.622 0.623 0.624

−1.479 −1.463 −1.434

2.411 2.304 2.152

3.041 2.954 2.841

1.850 1.782 1.700

0.616 0.620 0.627

0.568 0.570 0.575

0.757 0.760 0.770

0.619 0.618 0.620

−1.487 −1.483 −1.447

Standard uncertainty u are u(T) = 0.20K, u(p) = 0.006 MPa, u([S]) = 0.010 mol/L, u(cmc) = 0.008 × 10−4 mol/L, u(Xideal 1 ) = 0.006, u(X1) = 0.003, u( f1) = 0.003, u(f 2) = 0.003, and u(β12) = 0.002 (0.68 level of confidence); [S] represents the concentration of inorganic salt; The subscript 1 of parameters (e.g., X1) represents the component C12AS in binary mixture of C12AS/OP-10. a

Table 2. Dependence of the Mixed cmc on the Concentration ([S]) of Inorganic Salt (T = 298.15 K; p = 0.101 MPa)a inorganic salt Univalent Cationic Salt PrNaCl log cmc = KCl log cmc = Bivalent Cationic Salt MgCl2 log cmc = CaCl2 log cmc = BaCl2 log cmc = Trivalent Cationic Salt AlCl3 log cmc = FeCl3 log cmc =

linear fitting equation

R2

−0.0663[S] −3.671 ([S] ≤ 1 mol/L) −0.0685[S] −3.680 ([S] ≤ 1 mol/L)

0.990 0.970

−0.0767[S] −3.692 ([S] < 1 mol/L) −0.0775[S] −3.696 ([S] < 1 mol/L) −0.0798[S] −3.703 ([S] < 1 mol/L)

0.979 0.979 0.995

−0.0940[S] −3.710 ([S] ≤ 0.5 mol/L) −0.0954[S] −3.723 ([S] ≤ 0.5 mol/L)

0.992 0.961

a

Standard uncertainty u are u(T) = 0.20 K, u(p) = 0.006 MPa, and u(R2) = 0.004 (0.68 level of confidence).

Figure 3. Variation of the logarithm of mixed cmc with the concentration of inorganic salt (T = 298.15 ± 0.20 K; p = 0.101 ± 0.006 MPa).

result mainly in a large absolute value of K for these ions with large Z/R. For example, it is found in Table 3 that the absolute 941

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Table 3. Relationship of Nature of Inorganic Salt with Coefficient K in eq 1 (T = 298.15 K; p = 0.101 MPa)a cation of inorganic salt (MClx, where x = Z) univalence (Z = 1) Na R (nm) Z/R (nm−1) K

+

0.230 4.348 0.0663

bivalence (Z = 2) +

K

0.268 3.731 0.0685

Mg

2+

Ca

0.208 9.615 0.0767

2+

0.246 8.130 0.0775

trivalence (Z = 3) Ba

2+

0.272 7.353 0.0798

Al

3+

Fe3+

0.207 14.470 0.0940

0.222 13.514 0.0954

a Standard uncertainty u are u(T) = 0.20 K, u(p) = 0.006 MPa, u(R) = 0.008 nm, and u(K) = 0.0004; R is the mean value of van der Waals atom radius (from the literature24); Z is the valence of cation.

Figure 4. Mixed micelle structure in the presence of inorganic cation.

value of K (0.0776) of Mg2+ with larger Z/R (9.615) is larger than that 0.0663 of Na+ with smaller Z/R (4.348). In this investigation, this conclusion seems to be true for ions with different valences. However, it is not suitable to ions with the same valences. For example, although the Z/R value (7.353) of Ba2+ is smaller than 9.615 of Mg2+, the absolute value of K (0.0798) of Ba2+ is slightly larger than 0.0767 of Mg2+. The similar cases are also found in other ions with same valences, such as both Na+ and K+ and both Al3+ and Fe3+. Besides the salting-out effect, the addition of an inorganic cation can shield the electrostatic repulsion between slightly charged anionic headgroups of C12AS, promoting the process of micellization.16 The hydration of ions with different atom radii may bring different contributions in the process of micellization. In these cations with same valences, an ion with a small atom radius holds a large value of Z/R and then is highly hydrated.13,16,17 As shown from Figure 4, the large hydrated radius may result in a large space between headgroups of C12AS in a mixed micelle. Meanwhile, the large hydrated radius may lead to a low binding to the ionic headgroup of C12AS, which is not favorable to the shielding of electrostatic repulsion by the ionic atmosphere around each charged site.13,16,17,24 Consequently, in solution in the presence of cation with small atom radius, the curvature of a mixed micelle may be small, then disfavoring the formation of a mixed micelle. Therefore, regarding the above-mentioned, the formation of a mixed micelle should be attributed to three main contributions, namely the salting-out effect, the electrostatic effect, and the hydration of inorganic ion in aqueous solution. Of course, it should be noted that the added chloride anion may also partly

influence the formation of a mixed micelle by three effects mentioned above. 3.2. Effect of Inorganic Salt on Compositions of Mixed Micelle and Micellization. In an ideal state, the molar fraction (Xideal 1 ) of component i in mixed micelles for binary surfactant mixtures can be expressed as2,3,14−17 X1ideal =

x1C2 x1C2 + (1 − x1)C1

(2)

where x1 is the molar fraction of component 1 in bulk solution and C1 and C2 are the cmc of individual components 1 and 2, respectively, while for nonideal mixing systems, Rubingh’s treatment2,3,14−17,26 introduced the activity coefficients (f i) of component i in a mixed micelle. On the basis of the regular solution theory (RST), f1 and f 2 for binary surfactant mixtures can be obtained as follows, f1 = exp β12(1 − X1)2 = exp β12X 22

(3a)

f2 = exp β12(1 − X 2)2 = exp β12X12

(3b)

where β12 is an interaction parameter and X1 and X2 are the molar compositions of components 1 and 2 in a real mixed micelle, respectively. Combining the mixed cmc (CM) with the activity coefficients of single components of eq 3, it can be easy to deduce the following equation X12 ln[x1C M /(X1C1)] (1 − X1)2 ln{(1 − x1)C M /[(1 − X1)C2]} 942

=1 (4)

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Then, the value of X1 can be obtained iteratively from eq 4. β12 can be calculated by the relationship β12 =

of their higher hydration, the salting-out effect may not again be a main factor to lead to the difference in components (X1) of C12AS in a mixed micelle. Relatively speaking, the electrostatic repulsion may result mainly in the difference in components (X1) in real mixed micelles in solutions containing different salts. Then, because the cations with smaller atom radii have lower binding to the ionic headgroup of C12AS,25 they cannot be effective to shield the electrostatic repulsion between headgroups of C12AS. As a result, a value of X1 is larger in solution in the presence of a cation with larger atom radius. A previous investigation reported by Khimani et al.27 indicated that in anions with same valences, an ion with a larger atom radius caused a larger value of X1 in real mixed micelle, which is a similar result to the case in this investigation. It can be found in Table 1 that in a given salt solution, the X1 value of C12AS in a real mixed micelle is slightly smaller than that in an ideal case, showing some disadvantageous factors (e.g., electrostatic effect, steric effect, etc.) to form a real mixed micelle in this case of enriched C12AS in aqueous solution.2,14−16 In addition, it can be found in Table 1 that the activity coefficient of C12AS is always larger than that of OP-10 in a given salt solution due to the stronger micellization ability of C12AS relative to OP-10 in this investigation. However, it should be noted that there is not nearly a significant difference in the value of activity coefficient in different electrolyte solutions. The result seems to mean that the electrolyte or its type does not affect the degree of participation of amphiphile. Really, it is not the fact. The Rubingh’s treatment may be not suitable to the calculation of activity coefficient for the case in this investigation, which has been explained in some investigations.25,28,29 Even so, the discussion about the composition of a mixed micelle (X1) in this section is not restricted by activity coefficient. The value of β12 demonstrates the extent of interaction between two surfactants that leads to the deviation from ideality. A negative value of β12 indicates attractive interaction between two surfactants in mixed micelle (synergism) more than the self-attraction of two surfactants before mixing. It can be found from the data of β12 in Table 1 that all of them are negative and their absolute values are larger than |ln(C1/C2)| for all the mixed systems, indicating synergism between C12AS and OP-10 according to the criterion of Rosen,2,14,17 and negative values of β12 in the presence of an inorganic salt are also smaller than −1.403 in the absence of an inorganic salt.2 This indicates that the addition of an inorganic salt promotes the attractive interaction between C12AS and OP-10. 3.3. Thermodynamics. Thermodynamics plays an important role in understanding the process of micellization, which has been widely used to elucidate the mechanism of micelle formation.1−4,11,17,28−30 On the basis of RST, thermodynamic parameters of micellization, including free M energy change (ΔGM ideal on ideal state and ΔG on real state), M enthalpy change (ΔH ), and entropy change (ΔSM), can be obtained respectively by the following equations2,3,30

M ln[x1C12 /(X1C1)]

(1 − X1)2

(5)

Different parameters were calculated and are listed in Table 2. It is found from the data of Xideal and X1 in Table 1 that the 1 ideal values of components in a mixed micelle are always larger than the real values, suggesting nonideal mixing. In salt solution, the presence of an inorganic salt is favorable to form a compact mixed micelle by the salting-out effect and the electrostatic shielding effect.2,13−15 Consequently, small amounts of C12AS can form a mixed micelle on a real case. Figure 5 shows that the value of X1 in a real mixed micelle

Figure 5. Variation of molar fraction of mixed micelle with inorganic salt (T = 298.15 ± 0.20 K; p = 0.101 ± 0.006 MPa).

increased slightly with the addition of inorganic salt and the valence of cation. This cause can be explained mainly by the salting-out effect and the electrostatic repulsion. In salt solution, the salting-out effect may be contributive largely to the formation of a mixed micelle. Herein, it should be noticed that the salting-out effect to a hydrophobic group of C12AS may be stronger than that to the OP-10 because of the longer hydrophobic chain of C12AS. The salting-out effect and the shielding of electrostatic repulsion between the headgroups of C12AS increase with the ionic strength in aqueous solution. Then the addition of inorganic salt partly promotes the intercalation of C12AS into the mixed micelle, resulting in an slight increase of the component (X1) of C12AS in mixed micelle. As is observed in Table 2, the cations with high valences have a large value of Z/R, can be highly hydrated, and are water structure makers,13,15−17 favoring the salting-out effect to hydrophobic group. Furthermore, the cations with high valences are also beneficial partly to the formation of a compact mixed micelle by the electrostatic shielding to slightly charged headgroups of C12AS in salt solution. Consequently, in aqueous solution containing a cation with high valence, the component (X1) of C12AS in a mixed micelle is larger than the case in the presence of cation with low valence. For example, in salt solution at [S] = 0.25 mol/L, the X1 value of AlCl3 in a real mixed micelle is 0.568, which is slightly larger than 0.564 of MgCl2 and 0.561 of NaCl. For the cations with same valences, although cations with smaller atom radii may have a larger salting-out contribution to the process of micellization because

M ΔGideal = RT[X1 ln X1 + (1 − X1) ln(1 − X1)]

(6)

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

(7)

ΔH M = RT[X1 ln f1 + (1 − X1) ln f2 ]

(8)

ΔS M = 943

ΔH M − ΔGM T

(9) DOI: 10.1021/acs.jced.6b00699 J. Chem. Eng. Data 2017, 62, 938−946

Journal of Chemical & Engineering Data

Article

Table 4. Free Energy of Micellization and Thermodynaimic Stability According to Meada’s Treatment (T = 298.15 K; p = 0.101 MPa)a thermodynamic stability [S] (mol·L−1) NaCl 0.125 0.250 0.500 0.750 1.000 KCl 0.125 0.250 0.500 0.750 1.000 MgCl2 0.125 0.250 0.500 0.750 CaCl2 0.125 0.250 0.500 0.750 BaCl2 0.125 0.250 0.500 0.750 AlCl3 0.125 0.250 0.500 FeCl3 0.125 0.250 0.500

ΔG (kJ·mol−1)

B0

B1

B2

ΔGmic (kJ·mol−1)

−30.227 −30.282 −30.375 −30.482 −30.604

−5.718 −5.718 −5.753 −5.772 −5.795

−1.591 −1.633 −1.676 −1.738 −1.719

1.417 1.438 1.480 1.516 1.470

−15.281 −15.324 −15.438 −15.542 −15.610

−30.263 −30.337 −30.433 −30.573 −30.700

−5.732 −5.740 −5.751 −5.784 −5.815

−1.638 −1.650 −1.782 −1.763 −1.702

1.463 1.455 1.558 1.517 1.435

−15.344 −15.388 −15.517 −15.606 −15.664

−30.328 −30.404 −30.522 −30.668

−5.738 −5.753 −5.780 −5.802

−1.682 −1.726 −1.778 −1.813

1.490 1.516 1.548 1.546

−15.401 −15.478 −15.593 −15.700

−30.375 −30.452 −30.594 −30.755

−5.751 −5.768 −5.805 −5.821

−1.665 −1.692 −1.718 −1.722

1.465 1.478 1.485 1.440

−15.427 −15.499 −15.622 −15.703

−30.423 −30.502 −30.668 −30.823

−5.763 −5.785 −5.822 −5.841

−1.689 −1.691 −1.702 −1.724

1.481 1.474 1.454 1.433

−15.479 −15.542 −15.666 −15.760

−30.492 −30.594 −30.766

−5.776 −5.805 −5.845

−1.702 −1.698 −1.697

1.479 1.463 1.434

−15.531 −15.610 −15.733

−30.563 −30.679 −30.846

−5.796 −5.825 −5.864

−1.719 −1.732 −1.725

1.487 1.483 1.447

−15.597 −15.690 −15.807

a

Standard uncertainty u are u(T) = 0.20 K, u(p) = 0.006 MPa, u([S]) = 0.010 mol/L, u(ΔG) = 0.012 kJ/mol, u(B0) = 0.001, u(B1) = 0.002, u(B2) = 0.002, and u(ΔGmic) = 0.012 (0.68 level of confidence).

As mentioned above, Rubingh’s treatment failed to predict the values of activity coefficient,25,28,29 and then thermodynamic parameters were not calculated effectively from eqs 7−9 containing the term of activity coefficient. Herein, the free energy change of micellization (ΔG) proposed by Molyneux et al. can be approximately calculated by the relationship below15−17 ΔG = 2.3RT (log cmc − log ω)

(10)

where cmc is the value in the mixed micelle and ω is the number of moles of water per liter of water at the absolute temperature T (55.3 at 298.15 K). The values of ΔG calculated from eq 10 are listed in Table 4, and their variations with electrolytes are depicted in Figure 6. It can be found from the data in Table 4 that the free energy change of micellization (ΔG) for all surfactant mixtures is negative, indicating the spantaneous process of micellization, and the addition of inorganic salt can result in the increase of the absolute value of ΔG, implying the benefit of the formation of a mixed micelle.

Figure 6. Effect of inorganic salt on the free energy of micellization (ΔG) (T = 298.15 ± 0.20 K; p = 0.101 ± 0.006 MPa).

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DOI: 10.1021/acs.jced.6b00699 J. Chem. Eng. Data 2017, 62, 938−946

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In salt aqueous solutions, the dependence of mixed cmc on the concentration of inorganic salt has been established as a linear relationship. The effect of inorganic salt on the mixed cmc may result from several aspects. The nature of inorganic ions including their valences and their atom radius, the hydration of inorganic ion, the salting-out effect, and the electrostatic repulsion between the slightly charged headgroups of C12AS in the formation of mixed micelle may influence the value of mixed cmc. The components in mixed micelles are always inferior to the ideal case, indicating nonideal mixing. The components (X1) in a real mixed micelle are dependent partly on inorganic salt. The valence and atom radius of inorganic ion can largely influence the value of X1. The addition of inorganic salt promotes the synergistic effect of surfactant mixed systems. The free energy change of micellization (ΔG) shows that the process of micellization is spontaneous and the addition of inorganic salt promotes the formation of mixed micelle. Thermodynamic stability obtained by Meada’s treatment shows that the presence of inorganic salt is favorable to the formation of stable mixed micelle, and the cations with high valence and large atom radius can more effectively facilitate the stability of mixed micelle. As a result, the above conclusions help with understanding the micellization behavior of a surfactant mixture in aqueous salt solution, especially to obtain some information about effect of inorganic salt on the mixing behavior. Then these are helpful to describe the synergistic effect between surfactants and to design the surfactant formulations applied in many fields, especially relating to aqueous salt solution.

Other approaches were also adopted to thermodynamically describe the process of micellization. Herein, on the basis of the pseudophase separation model, th Maeda model2,14−16,31 involved thermodynamic stability (ΔGmic) as follows ΔGmic = RT (B0 + B1X1 + B2 X12)

(11a)

where B0, B1, and B2 are independent terms in eq 11a, respectively. They can be calculated from the relationships below B0 = ln C2

(11b)

B2 = −β12

(11c)

ln(C1/C2) = B1 + B2

(11d)

It can be found from both Figures 6 and 7 that the addition of inorganic salt can result in an increase of the absolute value of

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AUTHOR INFORMATION

Corresponding Author

*Tel(Fax): +86-716-8060650. E-mail: [email protected].

Figure 7. Effect of inorganic salt on the thermodynamic stability of micellization (ΔGmic) (T = 298.15 ± 0.20 K; p = 0.101 ± 0.006 MPa).

ORCID

Zhao Hua Ren: 0000-0002-9796-8039 Funding

ΔG and ΔGmic, respectively, suggesting the formation of stable mixed micelle. Also, the similar tendency in both Figures 6 and 7 can be found and these tendencies are more obvious in aqueous solutions in the presence of cations with high valence, which is in accordance with the cases of NaCl and MgCl2 in the previous investigation.27 These results can be explained rationally by the salting-out effect, the electrostatic shielding effect, and the decrease of steric effect. It is also observed in Table 4 that the values of ΔGmic have obvious deviations from the values of ΔG. It can be attributed to the fact that Maeda’s treatment like eq 11a has a different theoretical background and model from eq 10 proposed by Molyneux et al.15−17 Even so, both the free energy change of micellization (ΔG) and the thermodynamic stability (ΔGmic) can be used to thermodynamically elucidate the effect of electrolytes on the process of micellization.

Funding for this work was provided by the National Natural Science Foundation of China (51304029), the Natural Science Foundation of Hubei Province (2016CFB477), China, and the Training Program for Youth Scientific Research Team of Colloge of Chemistry & Environmental Engineering, Yangtze University, China. Notes

The authors declare no competing financial interest.

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