Thermodynamics of Mixed Surfactant Solutions of N,Nâ²-Bis

Article pubs.acs.org/JPCB

Thermodynamics of Mixed Surfactant Solutions of N,N′‑Bis(dimethyldodecyl)-1,2-ethanediammoniumdibromide with 1‑Dodecyl-3-methylimidazolium Bromide Changfei Du,† Dongxing Cai,‡ Miao Qin,† Peizhu Zheng,‡ Zhiguo Hao,‡ Tianxiang Yin,† Jihua Zhao,‡ and Weiguo Shen*,†,‡ †

School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China

‡

ABSTRACT: Mixed surfactant solutions are studied to understand their synergistic effects. Here we report the micellization properties of mixed surfactant solutions of the gemini surfactant N,N′-bis(dimethyldodecyl)-1,2ethanediammoniumdibromide (12−2−12) with the imidazolium ionic liquid 1-dodecyl-3-methylimidazolium bromide (C12mimBr) investigated by isothermal titration calorimetry (ITC), conductometry, fluorimetry, and dynamic light scattering (DLS). A two-parameter Margules model was successfully used to correlate the cmc values and calculate the compositions and activity coefficients of the two components in the mixed micelle phase for 12−2−12/ C12mimBr aqueous solutions with different overall surfactant compositions. The dissociation degree of counterion, the thermodynamic quantities of micellization, and the excess thermodynamic quantities for the mixed micelle were calculated and discussed. The ITC experiment in the low overall surfactant composition region showed a second phase transition. A thermodynamic model was proposed to explore phase behaviors of two different types of micelle and their solution, which was further confirmed by fluorescence and DLS studies.

1. INTRODUCTION The mixed surfactant solution has been extensively studied due to its importance in both practical applications and theoretical interest. By mixing appropriate surfactants, the mixed micelle system with better performance than single micelle solutions can be obtained,1,2 which results from the nonideal mixing behavior of the micelles. When the critical micelle concentration (cmc) is lower than the ideal mixing, the so-called synergism is generated.3,4 In recent years, studies on nonideal mixing surfactant solutions have been widely reported. Some thermodynamic models have been proposed to analyze the nonideal behavior of mixing.2 The most popular model among them is the Rubingh model,5 where only one parameter was used to describe the nonideal behavior of mixed surfactant solutions. The Rubingh equation has been successfully applied in many mixed surfactant solutions;2 however, when the system is complex, the equation with only one parameter does not satisfy the requirement for describing the mixing behavior2 and the parameter was usually found to be dependent on the mole fraction of the mixed micelle. With the Rubingh equation, a large number of studies have been focused on the cmc and excess free energy of mixed surfactant solutions; however, studies on other excess properties such as excess enthalpy6 and excess volume are scarce. As in normal solutions, excess enthalpy should be an important thermodynamic property to reflect the differences of the interactions between the like and © XXXX American Chemical Society

unlike molecules in the mixed micelle. It impels us to look for the possibility to deduce the excess enthalpy from the micellization enthalpies of a mixed micelle system at various compositions determined from isothermal titration calorimetry (ITC) measurements. It has been reported that mixed cationic surfactant solutions were prone to form two types of micelle corresponding to two cmcs, which has been detected by ITC and conductometry.7−10 The interpretation of this phenomenon provided by most authors was that the first type of micelle undergoes structural transition to form the second type,10 however, no evidence has been provided to confirm the coexistence of two types of micelle by ITC experiment. This kind of coexistence of two types of micelle with different sizes and structures was found and investigated by measurements of surface tension,11 gel filtration,12 NMR, time-resolved fluorescence quenching, and cryo-TEM.13 It would be interesting to exploit the capacity of ITC in studying the coexistence of the three phases, namely, two different micelle phases and their monomer solution in the mixed micellar system. In order to detect the ITC signals from the three-phase separation, it requires a larger difference in cmc between two surfactants constituting a mixed surfactant solution. Received: December 26, 2013 Revised: January 6, 2014

A

dx.doi.org/10.1021/jp412640m | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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h under the protection of argon. After evaporation, the residue was recrystallized with ethanol−ethyl acetate 6 times and then dried under vacuum at 55 °C for 48 h. The purity of the product was ascertained by 1HNMR (300 MHz, CDCl3: δ = 0.86 (t, 6H), 1.17−1.30 (m, 36H), 1.81 (m, 4H), 3.47 (s, 12H), 3.70 (m, 4H), 4.70 (s, 4H)). The structures of 12−2−12 and C12mimBr are shown in Figure 1.

The gemini surfactant is a special class of surfactants which is composed by connecting two amphiphiles with a spacer. In comparison to conventional surfactants, gemini surfactants have a series of unique properties such as very low cmc, high detergency, high solubilization, and high surface wetting capability, possessing a wide range of applications in mining, petroleum, chemical, and pharmaceutical industries.14−19 Ionic liquids (ILs) are a class of organic molten electrolytes processing particular properties such as insignificant vapor pressure, high ion conductivity, outstanding catalytic property, nonflammability, and stability as a result of their unique composition and structure.20−23 They are considered to be potential green solvents which have been applied in organic synthesis, catalysis, lubricants, etc.20,21 Long-chain ILs which consist of a charged hydrophilic head group and hydrophobic tail(s) have the properties of amphiphiles, behaving as conventional surfactants which can self-assemble in a solvent.20 Investigations of the aggregation behaviors of gemini/IL mixed solutions and the synergic effect are of importance to extend the knowledge about how the mixing and micellization of the surfactants occur.24 Because the difference of cmc values of the gemini surfactant and the IL with the same hydrophobic tails is as large as 10-fold, it is a presumable system in which we may be able to detect the ITC signals of the coexistence of two types of micelle and reveal the thermodynamic behaviors of multiplephase equilibrium. In this work, we study the micellization behavior of the mixed micelle of N,N′-bis(dimethyldodecyl)-1,2-ethanediammoniumdibromide (12−2−12)/1-dodecyl-3-methylimidazolium bromide (C12mimBr) at various compositions. The cmc, the enthalpy of micellization, and the degree of dissociation of the conterion for each single surfactant and their mixtures with different compositions of the surfactants at 298.15 K are determined by ITC and conductometry. The experimental results are used to determine the thermodynamic properties of micellization, the micelle compositions, and the activity coefficients of the surfactants in the mixed micelle based on a two-parameter Margules model.25,26 An approach for determination of the excess enthalpy of the mixed micelle is proposed and used to calculate the excess quantities for the 12−2−12/ C12mimBr mixed surfactant system. Moreover, the three-phase coexistence is investigated in mixed surfactant solutions with low 12−2−12 compositions by ITC, analyzed by a thermodynamic model, and confirmed by fluoremetry and light scattering studies.

Figure 1. Chemical structures of the surfactants studied: (a) 12−2− 12, (b) C12mimBr.

2.2. Isothermal Titration Microcalorimetry. The isothermal titration data were obtained by using a TAM 2277-201 microcalorimetric system (Thermometric AB, Järfäfla, Sweden), which has a 4 mL sample and reference cells. The sample and reference cells were initially filled with 2.20 and 2.70 mL double-distilled water, respectively. The titration was carried out at (298.15 ± 0.02) K by injecting surfactant solution with a certain concentration from a 1000 μL syringe into the sample cell. The volume of each injection was (15−20) μL, and the total titration volume was 0.9 mL. The injection schedule was automatically controlled by the Digitam 4.1 software after setting up the number of injections, volume of each injection, and interval between each injection. The stirring speed in the sample cell was set at 60 rpm. 2.3. Conductometry. The conductivity measurements were performed by using a 150A+ conductometer (Thermo Orion, U.S.) with a temperature sensor. The conductometer was initially calibrated by standard KCl solutions with the concentrations of 0.01 and 0.1 mol·L−1. The conductivities at various concentrations of surfactants were determined using a titration method. A certain amount of water was weighed into a sample cell which was placed in the water bath where the temperature was maintained at (298.15 ± 0.1) K. A surfactant solution with a required overall mole fraction α1 of 12−2−12 (the mole fraction of 12−2−12 in the total surfactants) and the total surfactant concentration being about 12 mmol·L−1 for α1 > 0.3 or 24 mmol·L−1 for α1 ≤ 0.3 was prepared by weighing and titrated into the sample cell using a buret; after each titration, the sample cell was shaken and then kept undisturbed for at least 10 min before the conductivity measurement. 2.4. Fluorimetry. The fluorescence measurements were carried out using a fluorimeter (Model FLS 920, Edinburgh Instrument), equipped with a R928P Hamamatsu PMT detector, a 450 mW Xe arc lamp for the steady-state measurement, and a nanoflash lamp for the time-resolved measurement. The temperature in the measurements was maintained at (298.15 ± 0.1) K.

2. EXPERIMENTAL SECTION 2.1. Materials. The 1-dodecyl-3-methylimidazolium bromide (C12mimBr, ≥ 99% mass fraction) was purchased from Cheng Jie Chemical Co. LTD (Shanghai, China) and dried under vacuum for 48 h before use. 1-Bromododecane (97% mass fraction), N,N,N′,N′-tetramethylethylenediamine (99% mass fraction), pyrene (>98% mass fraction), and 1,6-diphenyl1,3,5-hexatriene (DPH, > 98% mass fraction) were purchased from Sigma-Aldrich Chemical Co. Cetylpyrid bromide (CPB, > 98% mass fraction) was purchased from Sinopharm Chemical Reagent Co. Ltd. Double-distilled water was used in preparation of the samples throughout the experiments. The conductivity of the water was in the range of 1−2 μS·cm−1. The gemini surfactant 12−2−12 was synthesized according to the procedure reported in the literature.27 N,N,N′,N′Tetramethylethylenediamine and 1-bromododecane with the molar ratio of 1:2.4 were refluxed in dry ethanol at 80 °C for 48 B



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The micropolarity of the micelle was measured using pyrene as the probe with a concentration of 5 × 10−7 mol·L−1. The samples were excited by the light with the wavelength of 335 nm, and the emission spectra were scanned from 360 to 500 nm at a step of 1 nm with the split of the monochromator being set at 1.2 nm. To investigate the microenvironment in the micelle, the steady-state anisotropy (r) of the probe DPH with a concentration of 5 × 10−6 mol·L−1 in the micelle system was measured. The sample was excited with vertically polarized light at a wavelength of 360 nm and fluorescence polarized components, and the light intensities of the emission parallel and perpendicular to the direction of the excitation light were automatically recorded by the instrument from 440 to 500 nm at a step of 1 nm and with a split of 20 nm. All measurements were corrected for instrumental polarization bias using the Gfactor correction. The fluorescence lifetime of a probe in the micelle and the aggregation number of the micelle was determined using a time-correlated single photon counting technique and a nanoflash lamp. For the measurement of lifetime, the DPH was used as a probe with a concentration of 5 × 10−6 mol·L−1. The sample was excited at a wavelength of 360 nm, and the fluorescence emission intensity at 430 nm was collected in a period of time to obtain the fluorescence intensity decay profile. For measurement of the aggregation number, pyrene and CPB were used as a probe and a quencher with the concentrations in the system being 5 × 10−7 and 1 × 10−4 mol·L−1, respectively. The sample was excited at a wavelength of 335 nm, and the fluorescence emission intensity at 373 nm was collected in a period of time to obtain the fluorescence intensity decay profile. 2.5. Dynamic Light Scattering. Hydrodynamic diameters of the aggregates were measured by dynamic light scattering using a Malvern Zetasizer Nano ZS instrument (Southborough, MA) with a backscattering detector (173°) and a laser of 633 nm wavelength. Measurements were taken in a batch mode at 298.15 K using a quartz cuvette with a path length of 10 mm. All sample solutions were filtered through a 0.22 μm filter before measurements.

Figure 2. Enthalpy curves of 12−2−12/C12mimBr aqueous solutions for α1 > 0.1; α1 is the overall mole fraction of 12−2−12 in the mixed surfactants.

Figure 3. Enthalpy curves of 12−2−12/C12mimBr aqueous solutions for α1 < 0.1; α1 is the overall mole fraction of 12−2−12 in the mixed surfactants.

3. RESULTS AND DISCUSSION 3.1. Cmc and Enthalpy of Micellization of Mixed Surfactants. We first studied the micellization behaviors of the mixed 12−2−12/C12mimBr solutions with different values of α1 by ITC at 298.15 K and the ambient pressure. The total surfactant concentration (Ctot) in the syringe was 20 mmol·L−1 for α1 ≥ 0.1 and 65 mmol·L−1 for α1 < 0.1 except for α1 = 0.04, which was 30 mmol·L−1 and used to confirm that the determination of cmc (also named as the first cmc) is independent of Ctot in the syringe. The values of the observed differential molar enthalpy (ΔHobs) of various surfactant solutions were determined from the integral of the areas under the calorimetric peaks and normalized by the amounts of injected surfactants. By plotting ΔHobs against the total concentration in the sample cell, the enthalpy curves of titration were obtained and are shown in Figure 2 for α1 ≥ 0.1 and Figure 3 for α1 < 0.1. All the enthalpy curves in Figure 2 are sigmoidal shape, while all the enthalpy curves except for that of α1 = 0 in Figure 3 show three platforms and two break points, indicating multiple phase transition behaviors, which we shall discuss later. Each of the enthalpy curves in Figure 2 and the left parts of the curves in Figure 3 can be classified into three concentration ranges.

When Ctot is lower than cmc, ΔHobs represents the sum of the enthalpy changes for dilution of the micelles, demicellization of the micelles, and dilution of the resultant monomers; when the surfactant in the sample cell starts to aggregate, ΔHobs changes sharply; after the micelles are formed, it levels off and the slow change in ΔHobs represents the contribution of varying micelle concentration.28,29 Figure 4 illustrates the determinations of cmc and ΔHmic obs on an enthalpy curve for a C12mimBr aqueous solution as an example. The values of cmc can be obtained from the location of the extreme value of the first derivative of the enthalpy curve29 (see Figure 4B). The molar enthalpy of micellization (ΔHmic obs ), which is defined as the enthalpy change of 1 mole surfactant entering the micelle phase from the aqueous phase, can be determined by the enthalpy difference between the two extrapolated lines at cmc29 (see Figure 4A). As it is shown in Figure 3, the second platform on the enthalpy curve for the solution with α1 being 0.01 is narrow and unclear; thus, we were unable to locate its cmc by the method described above. We estimated it from the midvalue between the first platform and the second narrow platform on the enthalpy curve and obtained the corresponding ΔHmic obs . In the titration process, the amount of the injected micelle solution from the syringe contains both micelle and monomer, C



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Figure 4. Illustration of determinations of cmc and observed molar enthalpy of micellization for the C12mimBr aqueous solution: (A) enthalpy curve, (B) the first derivative curve of the enthalpy curve. The value of cmc is defined as the extreme value of the first derivative curve.

Table 1. Values of Cmc, Degree of Counterion Dissociation β, Enthalpy of Micellization ΔHmic, Gibbs Free Energy of Micellization ΔGmic, and Entropy of Micellization TΔSmic for 12-2−12/C12mimBr Mixed Aqueous Solutions with Various α1 at 298.15 K cmc/mmol·L−1 α1 0 0.01 0.02 0.04 0.06 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 1.00 a

calorimetry 10.05 6.40 5.50 4.45 3.90 3.22 2.35 1.90 1.71 1.48 1.34 1.19 1.11 0.93

± ± ± ± ± ± ± ± ± ± ± ± ± ±

conductometry a

0.07, 9.56 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02, 0.937b

10.07 − − − − 3.17 2.34 1.97 1.70 1.50 1.31 1.23 1.14 0.94

± 0.12

± ± ± ± ± ± ± ± ±

0.05 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.02

ΔHmic (kJ·mol−1)

β

0.352 − − − − 0.806 0.677 0.617 0.516 0.475 0.436 0.404 0.383 0.348

± 0.007

± ± ± ± ± ± ± ± ±

−3.28 −0.30 −0.77 −1.13 −1.73 −3.00 −5.05 −7.14 −8.66 −10.10 −12.08 −13.63 −14.63 −17.42

0.006 0.006 0.009 0.007 0.007 0.005 0.005 0.007 0.006

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.04, −3.51 0.22 0.19 0.07 0.12 0.07 0.14 0.20 0.30 0.34 0.26 0.42 0.45 0.29

ΔGmic (kJ·mol−1) a

−18.79 − − − − −21.49 −25.33 −27.29 −30.27 −31.88 −33.53 −34.69 −35.59 −37.56

± 0.09

± ± ± ± ± ± ± ± ±

0.10 0.13 0.12 0.11 0.13 0.15 0.17 0.18 0.24

TΔSmic (kJ·mol−1) 15.50 − − − − 18.49 20.29 20.15 21.60 21.78 21.45 21.06 20.96 20.14

± 0.10

± ± ± ± ± ± ± ± ±

0.12 0.19 0.23 0.32 0.36 0.30 0.45 0.49 0.37

From ref 20. bFrom ref 19.

agreement with that reported by other authors. The micellization enthalpies ΔHmic of the surfactants studied here are all negative, suggesting that all micellization processes are exothermic. 3.2. Mole Fractions and Activity Coefficients of Mixed Micelles. According to the pseudo phase separation model, the chemical potentials of the ith component in the micelle phase and solution phase should be equal at the cmc, which yields5,30 αi cmc = γixi cmci (2)

and only the surfactant in the form of micelle can contribute to the enthalpy of demicellization;28 thus, a correction to the molar enthalpy ΔHmic obs of micellization determined by the way described above is required. The molar enthalpy ΔHmic of micellization after correction has the form: mic ΔHmic = ΔHobs

Csyringe Csyringe − cmc

(1)

where Csyringe and cmc are the concentration in the syringe and the cmc value of the mixed surfactants or pure surfactant, respectively. Table 1 lists the cmc values and the molar enthalpy of micellization at 298.15 K for the micelle solutions of 12−2−12, C12mimBr, and 12−2−12/C12mimBr with various α1, and compares with the literature values. Considering that the experimental values of cmc and ΔHmic are somewhat dependent on the method used in determination, the values of cmc and ΔHmic obtained in this work are in fairly good

where αi, cmci, γi, and xi are the overall composition of surfactant, the cmc value, the activity coefficient in the micelle, and the molar fraction in the micelle for component i (i = 1 for 12−2−12 and i = 2 for C12mimBr), respectively. In order to calculate the micelle composition, we need to know the relation between the activity coefficient γi and the mole fraction xi. A simplest expression of the dependence of γi on xi is the Rubingh model with only one adjust interaction parameter A:6 D



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ln γ1 = Ax 22

α1 α2 1 = + cmc cmc1 cmc 2

(3)

ln γ2 = Ax12

(4)

For comparison, we plot the predicted cmc from the Margules model and the Clint ideal model for 12−12−12/C12mimBr in Figure 5.

This equation has been widely used to fit cmc data for mixed micelle systems; however, it failed to describe the mixing behavior of complex mixed micelle systems. Thus additional interaction parameters were introduced to include the contributions of the long-range electrostatic and nearestneighbor interactions such as the effects of differences in size and shape of two surfactant components or packing condition of nonpolar chains.2 On the other hand, it was well-known that a semiempirical equation, namely the Margules equation, has been successfully used to correlate the activity coefficient γi and the mole fraction xi for many classical binary solutions. The Margules equation has selectable forms with corresponding selectable number of the adjusting parameters and satisfies the thermodynamic consistency, among which the simplest form has the same expression as the Rubingh equation. This equation has been extended to fit the cmc data for surfactant mixture more recently.25,26 It was found that a two-parameter Margules equation was required for our data analysis: ln γ1 = Ax 22 + Bx 23

(5)

⎛ 3 ⎞ ln γ2 = ⎜A + B⎟x12 − Bx13 ⎝ 2 ⎠

(6)

Figure 5. Comparison of the predicted and experimental cmc values of 12−2−12/C12mimBr aqueous solutions at 298.15 K. The solid line represents the predicted values of the Margules model, the dotted line represents the predicted values of the ideal mixing model, and squares are experimental data. α1 is the overall mole fraction of 12−2−12 in the mixed surfactants.

Combination of eqs 2, 5, and 6 yields α1cmc =

exp(Ax 22

+

Bx 23)x1cmc1

As it can be seen from Figure 5, the two-parameter Margules model is reasonably well fitted with the experimental data, and the mixing behavior of the systems we studied significantly departs from the ideal mixing, showing a synergetic effect; i.e., cmc values are lower than that of ideal mixing. 3.3. Dissociation Degree of Counterion, Gibbs Free Energy, and Entropy of Micellization for Mixed Surfactants. A typical plot of conductivity κ against the total surfactant concentration for 12−2−12/C12mimBr solutions with α1 being 0.3 is shown in Figure 6, from which one can clearly see a break point between two almost straight lines with different slopes, indicating the existence of the cmc. The values of κ were fitted by eq 10 with the nonlinear least-squares

(7)

⎤ ⎡⎛ 3 ⎞ (1 − α1)cmc = exp⎢⎜A + B⎟x12 − Bx13⎥x 2cmc 2 ⎠ ⎦ ⎣⎝ 2

(9)

(8)

The cmc values for various α1 listed in column 2 of Table 1 were fitted to eqs 7 and 8 to obtain the values of x1 and the parameters A and B. The values of A and B are 1.16 ± 0.17 and −4.01 ± 0.20, respectively, and the optimized values of x1 are listed in column 2 of Table 2. If two surfactants are ideally mixed in a micelle, then cmc may be related to cmc1 and cmc2 by an ideal mixing model of Clint31 Table 2. Values of x1, Excess Enthalpy HE, Excess Gibbs Free Energy GE, and Excess Entropy TSE for 12-2-12/C12mimBr Mixed Micelle with Various α1 at 298.15 K α1 0.01 0.02 0.04 0.06 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

HE (kJ·mol−1)

x1 0.22 0.28 0.35 0.39 0.46 0.57 0.65 0.72 0.78 0.85 0.90 0.94

± ± ± ± ± ± ± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

6.11 6.48 7.10 7.07 6.78 6.28 5.32 4.78 4.18 3.19 2.34 1.90

± ± ± ± ± ± ± ± ± ± ± ±

0.32 0.28 0.20 0.21 0.17 0.19 0.22 0.31 0.35 0.27 0.42 0.45

GE (kJ·mol−1) −1.03 −1.14 −1.21 −1.22 −1.19 −1.04 −0.87 −0.70 −0.55 −0.36 −0.23 −0.14

± ± ± ± ± ± ± ± ± ± ± ±

0.09 0.10 0.11 0.11 0.12 0.14 0.14 0.14 0.13 0.11 0.08 0.05

TSE (kJ·mol−1) 7.13 7.62 8.31 8.29 7.97 7.32 6.19 5.48 4.73 3.55 2.57 2.04

± ± ± ± ± ± ± ± ± ± ± ±

0.33 0.30 0.23 0.24 0.21 0.23 0.26 0.34 0.37 0.29 0.43 0.45

Figure 6. Typical plot of κ against the Ctot for 12−2−12/C12mimBr aqueous solutions with α1 being 0.3. E



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method to obtain the cmc values32 for 10 systems with different α1 κ = κ0 + S1C tot + p(S2 − S1) ⎧ 1 + exp[(C tot − cmc)/p] ⎫ ⎬ ln⎨ 1 + exp( −cmc/p) ⎭ ⎩

HE = ΔHmic,mix − x1ΔHmic,1 − (1 − x1)ΔHmic,2 + Hmon,mix − x1Hmon,1 − (1 − x1)Hmon,2

(16)

where [Hmon,mix − x1Hmon,1 − (1−x1)Hmon,2] is the enthalpy of mixing of the two monomer solutions at cmc whose composition is the same as that in the mixed micelle phase. We carried out the measurements of the mixing enthalpy for the dilute mixed surfactant solutions with various compositions and total surfactant concentrations below cmc and found that the heats generated were undetectable as compared with a blank titration, i.e., titrating water to water, which generates a heat less than 70 μJ. Neglecting [Hmon,mix − x1Hmon,1 − (1 − x1) Hmon,2] yields

(10)

where κ0 is the conductivity when Ctot = 0; S1 and S2 are the slopes below and above the cmc, respectively; p is a parameter related to the width of the transition between two linear dependencies. The degree of counterion dissociation (β) is calculated by S2/S1. The values of cmc and β are listed in Table 1. The comparison of cmc values from the conductivity and ITC measurements in Table 1 shows good agreement with each other. For mixed surfactant solutions, the value of β measured by experiment is the average dissociation degree of the counterion. The micellization of the mixed surfactants with one component being gemini ionic surfactant and the other being the ionic surfactant with single tail can be interpreted as x1 mole cation of gemini surfactant and (1 − x1) mole cation of the surfactant with a single tail reacting with [2(1 − β)x1 + (1 − β)(1 − x1)] mole counterion to form 1 mole aggregation. The standard Gibbs free energy (ΔGmic) of such micellezation may be calculated by

HE = ΔHmic,mix − x1ΔHmic,1 − (1 − x1)ΔHmic,2

(17)

The excess Gibbs free energy is expressed by GE = RT[x1ln γ1 + (1 − x1)ln γ2]

(18)

and the excess entropy can be calculated through

S E = (HE − GE)/T

(19)

The excess quantities of the mixed micelle phase at various overall surfactant compositions at 298.15 K are listed in Tables 2 and shown in Figure 7, where the solid lines represent the results of fitting the experimental values of HE, GE, and TSE with the Redlich−Kister equation:33

ΔGmic = RT {x1ln(α1cmc) + (1 − x1)ln[(1 − α1)cmc]

n

+ (1 + x1)(1 − β)ln[2α1cmc + (1 − α1)cmc]}

GE( or H E or S E) = x1(1 − x1) ∑ Bi (2x1 − 1)i

(11)

i=0

(20)

The entropy of micellization (ΔSmic) can be calculated by ΔSmic = −

ΔGmic − ΔHmic T

(12)

The calculated values of ΔGmic and TΔSmic together with ΔHmic are listed in Table 1. It may be seen in Table 1 that all the values of ΔGmic and ΔHmic are negative and all the values of TΔSmic are positive, indicating that the micellization in the 12− 2−12/C12mimBr mixed surfactant solutions is driven by both enthalpy and entropy. 3.4. Excess Properties of Mixed Surfactants. The excess molar enthalpy of mixed surfactants in the micelle phase is defined by HE = Hmic,mix − x1Hmic,1 − (1 − x1)Hmic,2

(13)

Figure 7. β, TSE, HE, and GE for 12−12−12/C12mimBr mixed micelles at various x1; the solid lines are the results calculated by the Redlich− Kister equation.

where Hmic,mix, Hmic,1, and Hmic,2 are the molar enthalpies of the surfactant in the mixed micelle, the micelle 1, and the micelle 2, respectively. The molar enthalpy ΔHmic, i of micellization of pure component i is defined as ΔHmic, i = Hmic, i − Hmon, i

Table 3 lists the values of Bi for 12−12−12/C12mimBr mixed micelles with various α1. There are no experimental data being determined for x1 < 0.22 in this work, because even though the overall composition α1 of 12−2−12 is as low as 0.01, the mole fraction x1 of 12−2−12 in the micelle is as high as 0.22 due to significant larger surface activity of 12−2−12 as compared with C12mimBr. However, for the solution with α1 being 0.01, the second platform of the enthalpy curve almost disappears as shown in Figure 3, resulting in the difficulty to determine excess quantities in a further lower x1 region, which we shall discuss later.

(14)

where Hmon,i is the molar enthalpy of the monomer of component i in the solution; ΔHmic,i can be determined by experiment. The molar enthalpy of micellization of the mixed micelles Hmon,mix is expressed by ΔHmic,mix = Hmic,mix − Hmon,mix

(15)

where Hmon,mix is the molar enthalpy of mixed surfactants in the monomer state. Combination of eqs 13, 14, and 15 gives F



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Table 3. Fitting Results of the Redlich−Kister Equation −1

B0 (kJ·mol ) B1 (kJ·mol−1) standard deviation (kJ·mol−1)

HE

TSE

GE

28.0 ± 0.5 −8.3 ± 1.5 0.4

32.6 ± 0.5 −10.8 ± 1.5 0.4

−4.580 ± 0.001 2.485 ± 0.001 0.001

Table 4. Experimental Second Critical Micelle Concentration Cmc2nd and the Calculated Cmc2nd, the Optimized Values of the Concentrations Cmon,1 and Cmon,2 for 12−2−12 and C12mimBr in the Solution and the Mole Fraction x1 of the Micelle in the Three-Phase Region, and the Total Micelle Concentration Cmic at the Second Cmc α1

Cmon,1 (mmol·L−1)

Cmon,2 (mmol·L−1)

x1

0.01 0.02 0.04 0.06

0.049 ± 0.012

6.87 ± 0.35

0.198 ± 0.019

Cmic (mmol·L−1) 0.15 0.58 1.27 2.13

The dependences of HE, TSE GE, and β on x1 are shown in Figure 7, from which it can be seen that HE and SE are all positive and the compensation between the enthalpy and the entropy results in negative GE for the mixed micelle in all concentrations we investigated. It is also can be found in Figure 7 that the tendency of variations of HE, TSE, and β with x1 is very similar, which indicates that the positive HE and TSE are probably dominated by the change of the degree of counterion dissociation. 3.5. Three-Phase Equilibrium of Mixed Surfactant Solutions. The enthalpy curves of 12−2−12/C12mimBr with α1 < 0.1 in Figure 3 significantly differ from the curves with α1 ≥ 0.1 in Figure 2, revealing the second phase transitions. When Ctot increases to a certain value, the second break point can be observed for each of the enthalpy curves except for α1 = 0 in Figure 3, which is defined as the second critical micelle concentration cmcsecond with the value cmcsecond. Analysis of the difference of the enthalpy curves shown in Figures 2 and 3 suggests that the emerging of the second phase transition in two-surfactant mixed aqueous solutions in this system should satisfy two conditions: (1) the difference of surface activities or the cmc values between two surfactants should be relatively large for the separation of two ITC signals corresponding to two-phase transitions; (2) the overall composition α1 of the component with the larger surface activity is low enough. The second condition may be explained as follows. When a mixed surfactant solution such as 12−12− 12/C12mimBr with a certain overall composition α1 is titrated into water, the micelle with a higher composition x1 is generated at very low Ctot due to the higher surface activity of 12−2−12. With the titration continually being conducted, the total surfactant concentration Ctot increases, and x1 decreases and approaches the value of α1 but is always higher than it. If two types of micelle may coexist when the composition x1 of a binary mixed micelle is less than a particular value x1*, then only when α1 < x1* can the second critical micelle concentration possibly be detected by ITC during the titration. Our ITC experiment evidenced that the titrations of 12−2−12/ C12mimBr mixed solutions with α1 ≥ 0.1 did not show the second phase transition, indicating that the value of x1* is quite low, which requires more thermodynamic analysis and experimental evidence. 3.5.1. Thermodynamic Model for Three-Phase Equilibrium. Based on the pseudo phase separation model, when Ctot exceeds the first cmc, the surfactants are partitioned in both forms of monomer and micelle. Let ntot and nmic be the total

± ± ± ±

0.08 0.13 0.21 0.33

calcd cmcsecond (mmol·L−1) 7.07 7.51 8.19 9.05

± ± ± ±

0.36 0.38 0.41 0.49

exptl cmcsecond (mmol·L−1) 7.9 8.2 7.5 8.1

± ± ± ±

0.6 0.5 0.6 0.5

mole of surfactants and the mole of surfactants in the form of the micelle, respectively, and Cmic be the total micelle concentration in the system; according to the material balance and eq 2, we can obtain Cmon,1 = C totα1 − Cmicx1 = x1γ1cmc1

(21)

Cmon,2 = C tot(1 − α1) − Cmic(1 − x1) = (1 − x1)γ2cmc 2 (22)

With known cmc1, cmc2, α1, and A and B in eqs 5 and 6, we can obtain Cmon,1, Cmon,2, x1, and Cmic by solving eqs 5, 6, 21, and 22 for various Ctot. It was found that x1 decreases and Cmic increases with increase of Ctot. The second break point indicates that the second type of micelle is generated and three forms of surfactants coexist: the monomer, the first type of micelle, and the second type of micelle. According to the Gibbs phase rule, the degree of the freedom of the system is zero in the three-phase region at constant temperature and pressure. Thus once the second type of micelle is generated, the compositions in the three phases, namely, Cmon,1, Cmon,2, and the mole fractions in the two coexisting micelles, should not change with the variation of Ctot or α1 up to the first type of micelle disappearing, while the total micelle concentration Cmic in the system continuously increases with Ctot and α1. The values of the second cmcs at various α1 were determined and are listed in column 7 of Table 4, which were used to replace Ctot in eqs 21 and 22 and fitted by the expressions on the right sides of eqs 21 and 22 together with eqs 5 and 6 to obtain the optimized constant value of x1 and the four optimized values of Cmic corresponding to different α1 at the second cmc by a least-squares method. The optimized values of x1 and four Cmic then were used to calculate Cmon,1 and Cmon,2 by expressions Cmon,1 = x1γ1cmc1 and Cmon,1 = (1 − x1)γ2cmc2, respectively, and cmcsecond by material balance. All the results are listed in Table 4. The calculated values of the second cmc listed in column 6 are in good agreement with the experimental ones listed in column 7 within the experimental uncertainties. After the second type of micelle is generated, with increase of Ctot, the enthalpy curve drops continuously because the titrated surfactant enters into the second micelle phase, and the quantity ratio of the second micelle phase to the first micelle phase increases. It was found that the enthalpy curves with three different values of α1 merged with each other with that of the pure C12mimBr solution at the total surfactant concentrations being about 17 mmol·L−1, and the titration curves behave as that in a pure C12mimBr aqueous solution after G



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mergence. This point is referred as the third critical micelle concentration cmcthird with the values cmcthird, at which the first micelle phase disappears and the second micelle phase is similar to the pure C12mimBr micelle. After cmcthird all the titrated surfactants enter the second micelle phase. At the third cmc, the first micelle just disappears, while Cmon,1, Cmon,2 still keep at constant values of 0.049 ± 0.012 and 6.87 ± 0.35 in the threephase region, respectively. According to the material balance, the mole fraction of C12mimBr in the second micelle phase y2 was calculated by using the values of cmcthird and α1, which was found to be 0.99 for the system of α1 = 0.01, or 0.97 for the system of α1 = 0.02, or 0.90 for the system of α1 = 0.06. Averaging the three values gave y2 = 0.95 ± 0.04, which is close to 1, indicating that the second micelle phase should be similar to the pure C12mimBr micelle. According to the above analysis, the composition of the first micelle phase x1 is about 0.20, and the composition of the second micelle phase y1 is about 0.05 in the three-phase region at 298.15 K and constant pressure. Thus no second-phase transitions being observed in our ITC measurements for all systems whose enthalpy curves are shown in Figure 2 are expected except for α1 = 0.10, because for α1 ≥ 0.20, the overall micelle composition of 12−2−12 in the ampule is always higher than 0.20 and only the first type of micelle can be generated. For the system of α1 = 0.10, it was found, from the calculation based on eqs 21 and 22, that only when Ctot is higher than 13.36 mmol·L−1 may the second micelle be generated. In our ITC experiment, Ctot was limited in the range of less than 6 mmol·L−1; thus, no second cmc for the system of α1 = 0.10 being observed is expected. For the system of α1 = 0.01, the value 0.22 of x1 at the first cmc is slightly larger than x1 = 0.20 and close to the three-phase region; thus, the two-phase region (the first type of the micelle coexisting with its monomers in the solution) is narrow, reflected by a narrow second platform of the enthalpy curve, and just after entering the two-phase region, the system almost immediately reaches the region of coexistence of two types of micelle. It suggests that the excess quantities determined by the method described in section 3.4 are limited in the concentration range of x1 > 0.20. It may also be predicted that in a very low region of the overall surfactant composition of 12−2−12 in the micelles (possibly lower than 0.05 ± 0.04 in the mole fraction), the first micelle phase would disappear. 3.5.2. Fluorescence Studies of Three-Phase Equilibrium. Three-phase equilibrium behaviors of 12−2−12/C12mimBr surfactant solutions with α1 being 0.06 were investigated by the fluorimetry. The microenvironmental polarity, the fluorescence anisotropy of the probe, the fluorescence lifetime of the probe, and the aggregation number of the mixed micelle were measured to study the phase behaviors of the mixed surfactant system. 1. Microenvironmental Polarity. The fluorescence emission spectrum of pyrene in each of the 12−2−12/C12mimBr surfactant solutions with various compositions was measured, and the intensity ratio (I1/I3) of the first peak (373 nm) to the third peak (384 nm) of vibration was calculated. A lower I1/I3 value stands for the higher hydrophobicity of the microenvironment. The plot of I1/I3 against Ctot is shown in Figure 8. As can be seen from Figure 8, I1/I3 is almost independent of Ctot at first, then sharply decreases with increase of Ctot, and finally reaches an almost constant value independent of the further increase of Ctot. The values of cmc can be obtained from location of the extreme value of the first derivative curve of the

Figure 8. Variation of the pyrene fluorescence intensity ratio I1/I3 with Ctot in mixed 12−2−12/C12mimBr aqueous solutions.

dependence of I1/I3 on Ctot. The value of cmc was determined to be 3.59 mmol·L−1, which is in good agreement with 3.90 mmol·L−1 obtained by ITC. As we discussed above, besides the phase transition near cmc, a second phase transition has been observed at Ctot ≈ 8.5 mmol·L−1 by ITC measurement. However, the polarity measurement of pyrene did not show notable changes in the polarity as can be seen from Figure 8, suggesting that the second phase transition involves only the formation of the second micelle. Because the polarities in the two micelles are little different, the second phase transition could not be detected by the micropolarity experiment. 2. Fluorescence Anisotropy. The fluorescence anisotropy (r) of the DPH probe significantly changes as the molecular packing alters in the hydrophobic domains of self-assemblies. Thus it may be used in study of structure changes of the pure micelles and the mixed micelle. The fluorescence anisotropy of the DPH probe in each of the 12−2−12/C12mimBr surfactant solutions with various Ctot above the cmc was measured. The dependence of r on Ctot is illustrated in Figure 9. Figure 9 shows that the value of r is larger at low Ctot and decreases fast with increase of Ctot, while in the high Ctot region, the value of r is smaller and slowly decreases with increase of Ctot; the variation rate changes in the region of 9.4 mmol·L−1 < Ctot < 18.5 mmol·L−1. It was reported that 12−2−12 formed

Figure 9. Variation of anisotropy of DPH with Ctot in mixed 12−2− 12/C12mimBr aqueous solutions. H



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threadlike micelle in its aqueous solution and the value of r for DPH in this micelle was 0.111,34 while C12mimBr forms spherical micelles in aqueous solution35 with a lower r value of 0.061 measured in this work. This may be attributed to the less restriction of DPH in the C12mimBr spherical micelle as compared with that in 12−2−12 threadlike micelle. According to our thermodynamic analysis in section 3.5.1, the composition increases for C12mimBr and decreases for 12− 2−12 with increase of Ctot in the first type of the mixed micelle. Thus, the fast decrease of r with increase of Ctot characterizes the microenvironment of the first type of the mixed micelle. In the higher Ctot region (Ctot ≥ 18.5 mmol·L−1), smaller value of r and slow decrease with increase of Ctot indicate the disappearance of the first micelle; because the second C12mimBr dominant micelle microenvironment is similar to that of the pure C12mimBr micelle as we discussed in section 3.5.1, it is less affected by the change of Ctot. The dependences of r on Ctot in above two regions are almost liner with different slopes, and a slope-change occurs in the region between them, which may be attributed to the three-phase coexistence of the two types of micelle and the monomer surfactant solution. The values of cmcsecond and cmcthird obtained by the DPH anisotropy measurement were 9.4 and 18.5 mmol·L−1, respectively, which were consistent with the values 8.5 and 17.3 mmol·L−1 obtained by ITC measurement, indicating the accordance between the thermodynamic analysis and the fluorescence anisotropy measurement. 3. Fluorescence Lifetime of DPH Probe. The fluorescence lifetime measurements were carried out using the timecorrelated single photon counting technique. The timedependent fluorescence intensity was fitted to a model with one or two exponentials using the Marquardte−Levenberg algorithm f (t ) =

∑ aiexp(−t /τi) i

Figure 10. Variation of lifetime of DPH with Ctot in mixed 12−2−12/ C12mimBr aqueous solutions.

literature34 and 3.9 ns for C12mimBr in this work. As shown in Figure 10 for mixed micelles, the lifetime decreases linearly with increase of Ctot and accordingly with increase of mole fraction of C12mimBr in the first type of the micelle after the first cmc. This linear relationship ends at Ctot = 10.1 mmol·L−1 (cmcsecond, τ1 = 4.77 ns), indicating the formation of the C12mimBr dominant second type of the micelle and the coexistence of two types of micelles in the system. At the concentration above 18.18 mmol·L−1 (cmcthird, τ2 = 4.28 ns), the first type of micelle disappears and only the second type of micelle coexists with the solution phase, and the fluorescence lifetime remains almost unchanged. In the two-micelle coexisting region, at Ctot being 12.12 and 15.15 mmol·L−1, two lifetimes of 4.77 ns at Ctot = 10.1 mmol·L−1and 4.28 ns at Ctot = 18.18 mmol·L−1 should be coexisting; thus, the fluorescence intensity decay profiles at Ctot = 12.12 mmol·L−1 and Ctot = 15.15 mmol·L−1 were used to fit eq 24 with τ1 being 4.77 ns and τ2 being 4.28 ns to obtain the values of a1 and a2

(23)

where f(t) is the fluorescence intensity at time t, τi is the fluorescence lifetime of DPH, and ai is related to the portion of the DPH in the ith microenvironment. The goodness-of-fit criterion (χ2) and the residual curve were checked in order to obtain reliable lifetime values. As the χ2 value was in the range of 0.99−1.3036 and the residual data looked like random noise distributed around 0, the results were accepted. The fluorescence lifetimes τ of DPH in the 12−2−12/ C12mimBr surfactant solutions for various Ctot were obtained by fitting the fluorescence intensity decay profiles of the DPH probe by eq 23 with one exponential. The dependence of τ on Ctot is plotted in Figure 10. It is known that the fluorescence lifetime of DPH is reduced with increasing water content in its immediate environment.37 When Ctot is low, DPH is dispersed in the aqueous phase and has a small lifetime. As the concentration increases to cmc, micelle forms in the system and DPH molecules are adsorbed at the interface of the micelle; thus, the lifetime significantly increases due to the lower polarity at the interface than that in water. As can be seen from Figure 10, a rapid increase of lifetime occurred at the concentration of no more than 5 mmol· L−1, which suggests the formation of the first type of the micelle. The cmc value of no more than 5 mmol·L−1 observed in this experiment is close to 3.9 mmol·L−1 obtained by ITC measurement. The lifetime of DPH in micelles formed by single surfactant was measured to be 7.85 ns for 12−2−12 reported in the

f (t ) = a1exp( −t /τ1) + a 2exp(−t /τ2)

(24)

where the subscripts 1 and 2 represent the first and the second micelle phases, respectively. The values of χ2 were calculated to be 1.07 and 1.01, respectively, which supports the coexistence of two fluorescence lifetimes corresponding to two types of micelle. The quantity ratios of the first type of micelle to the second type of micelle were calculated by a1/a2 and found to be 2.84 at Ctot = 12.12 mmol·L−1 and 0.35 at Ctot = 15.15 mmol· L−1, respectively, which indicates a decrease of the ratio with increase of Ctot until Ctot = 18.18 mmol·L−1, at which it is supposed to be null. The above analysis is consistent with ITC measurement, anisotropy measurement, and the thermodynamic model. 4. Aggregation Number of the Mixed Micelle. The aggregation numbers (Nagg) of the mixed micelle at various surfactant concentrations above cmc were determined by timeresolved fluorescence quenching (TRFQ). The dependence of Nagg on Ctot is plotted in Figure 11, which shows that the aggregation number is almost independent of the concentration in the regions of Ctot being below 9 mmol·L−1 and above 15 mmol·L−1, corresponding to the first micelle phase region and the second micelle phase region, respectively. When Ctot is greater than 9 mmol·L−1 and less than 15 mmol·L−1, the two micelles coexist in the system. According to the analysis of the thermodynamic model, the amount of the first type of micelle decreases and the amounts of the second type of micelle I



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aggregates decreases continually with increase of Ctot, but the rate of the variation changes significantly. A sharp decrease of the size with increase of Ctot is observed and corresponds to the region of the first type of micelle; for 8 mmol·L−1 < Ctot < 15 mmol·L−1, the size decrease becomes slower corresponding to the region that two micelles coexist in the system; when Ctot > 15 mmol·L−1, the size decreases further slowly and characterizes the second micelle region. The above analysis is consistent with the thermodynamic model described in section 3.5.1 and the experimental results from the other techniques used in this work. By comparing Figures 11 and 12, we may see that the aggregation number does not change significantly in the regions of the first and the second micelle phases, while the micelle size does, which may be attributed to that changes of the composition in the mixed micelles possibly do not significantly influence the aggregation number but result in the change of the arrangement of the head groups and the charge density on the micelle interface, causing the significant changes in the surface area and hence the micelle size. The values of the critical concentrations for the 12−2−12/ C12mimBr surfactant solutions with α1 = 0.06 determined by various methods are summarized and compared in Table 5. It can be seen from Table 5 that the values of three kinds of cmc obtained by different methods used in this work are consistent with each other, which supports the thermodynamic analysis proposed in section 3.5.1.

Figure 11. Variation of aggregation number with Ctot in mixed 12−2− 12/C12mimBr aqueous solutions.

increase with increase of Ctot in the coexistence region of the two types of micelle. Since the aggregation number of the first type of micelle is larger than that of the second one, the average aggregation number in the two-micelle coexisting region decreases with increase of Ctot. The above analysis is consistent with the results from measurements of the ITC, the anisotropy, and the fluorescence lifetime and is also consistent with the thermodynamic analysis in section 3.5.1. 3.5.3. Dynamic Light Scattering. The sizes of the mixed micelles formed in aqueous solutions were determined by dynamic light scattering measurement, and the dependence of the hydrodynamic diameter on Ctot above cmc is shown in Figure 12. As it can be seen from Figure12, the size of the

4. CONCLUSION In present study we determined the cmc values, the dissociation degree of counterion β, and the enthalpies ΔHmic of micellization for 12−2−12/C12mimBr mixed surfactant solutions with different overall mole fractions α1 of 12−2−12 in mixed surfactants by ITC and conductometry. A two-parameter Margules model was successfully used to fit the experimental cmc values and to calculate the compositions and activity coefficients of two components in the mixed micelle phase for the mixed surfactant solutions. All mixed surfactant systems showed the synergistic effects. The entropies ΔSmic and the Gibbs free energies ΔGmic of micellization were calculated, and it was found that ΔGmic and ΔHmic were negative while ΔSmic was positive, indicating that the micellization in the 12−2−12/ C12mimBr mixed surfactant solutions was driven by both enthalpy and entropy. An approach for determination of the excess enthalpy was proposed and the excess thermodynamic quantities HE and SE and GE were calculated. It was found that HE and SE were positive, while GE was negative, which were attributed to the domination of change in β as mixed micelle formed. A thermodynamic model was proposed to explore the phase behaviors in these complex mixed surfactant solutions, based on

Figure 12. Variation of micelle size with Ctot in mixed 12−2−12/ C12mimBr aqueous solutions.

Table 5. Critical Concentrations for Mixed 12−2−12/C12mimBr Aqueous Solutions with α1 = 0.06 Determined by Various Methods method of determination

cmc (mmol·L−1)

cmcsecond (mmol·L−1)

cmcthird (mmol·L−1)

ITC micropolarity (I1/I3) anisotropy (r) fluorescence lifetime (⟨τ⟩) aggregation number (Nagg) hydrodynamic diameter (d)

3.90 3.59

Thermodynamics of Mixed Surfactant Solutions of N,Nâ²-Bis

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