J. Phys. Chem. B 2008, 112, 14869–14876
14869
Molecular Interactions of Cationic and Anionic Surfactants in Mixed Monolayers and Aggregates Beheshteh Sohrabi,‡ Hussein Gharibi,*,† Behnoosh Tajik,‡ Soheila Javadian,† and Majid Hashemianzadeh‡ Department of Chemistry, Tarbiat Modares UniVersity, P.O. Box 14155-4838, Tehran, Iran, and Department of Chemistry, Iran UniVersity of Science and Technology, P.O. Box 16765-163, Tehran, Iran ReceiVed: April 10, 2008; ReVised Manuscript ReceiVed: September 16, 2008
The properties of anionic-rich and cationic-rich mixtures of CTAB (cetyltrimethylammonium bromide) and SDS (sodium dodecyl sulfate) were investigated with conductometry and surface tension measurements and by determining the surfactant NMR self-diffusion coefficients. The critical aggregate concentration (CAC), surface tension reduction effectiveness(γCAC), surface excess(Γmax), and mean molecular surface area (Amin) were determined from plots of the surface tension (γ) as a function of the total surfactant concentration. The compositions of the adsorbed films (Z) and aggregates (χ) were estimated by using regular solution theory, and then the interaction parameters in the aggregates (β) and the adsorbed film phases (βσ) were calculated. The results showed that the synergism between the surfactants enhances the formation of mixed aggregates and reduces the surface tension. Further, the nature and strength of the interaction between the surfactants in the mixtures were obtained by calculating the values of the following parameters: the interaction parameter, β, the size parameter, F, and the nonrandom mixing parameter,P*. These results indicate that in ionic surfactant mixtures the optimized packing parameter has the highest value and that the size parameter can be used to account for deviations from the predictions of regular solution theory. It was concluded that, for planar air/ aqueous interfaces and aggregation systems, this nonideality increases as the temperature increases. This trend is attributed to the increased dehydration of the surfactant head groups that results from increases in temperature. Further, our conductometry measurements show that the counterion binding number of mixed micelles formed in mixtures with a high CTAB content is different to those with a high SDS content. This difference is due to either their different aggregation sizes or the different interactions between the head groups and the counterions. 1. Introduction It has been well-known for a long time that among the various types of binary surfactant systems, anionic/cationic binary systems exhibit the strongest synergisms both in surface tension reduction and in mixed micelle formation.1-3 Such synergetic effects are important for a wide range of surfactant-based phenomena such as foaming, emulsification, solubilization, and detergency. Electrostatic repulsion between the head groups of ionic surfactants with the same charge is a major factor in increases in the free energy of micelle formation.4 Thus, if other surfactants with oppositely charged head groups are incorporated into the micelles, the micelle aggregation number is expected to increase, so in these systems stable vesicle phases form without the need for highly energetic methods such as sonication and extrusion.5 In general, mixed anionic/cationic surfactant systems exhibit various complex phase behaviors.6-11 For example, precipitation (liquid-solid separation), coacervation (liquid-liquid separation), and liquid crystal formation occur at extremely low surfactant concentrations.12-14 These phenomena originate from the strong interactions between the oppositely charged head groups of the surfactant molecules. It has been shown that the phase behaviors of cationic/anionic surfactant mixtures strongly depend on the molar ratio, the actual concentrations of the individual surfactants, the relative number * Corresponding author. E-mail:
[email protected]. † Tarbiat Modares University. ‡ Iran University of Science and Technology.
of alkyl chains per surfactant, and the temperature, resulting in a rich array of aggregates.15-22 For some compositions, two oppositely charged surfactants can form catanionic micelles.6,7,17,23-27 Therefore, the preparation of mixtures of two oppositely charged surfactants requires careful attention. Many researchers have determined the interaction parameters of mixed micelles by using Rubingh’s equations, which do not account for electroneutrality or the ionic atmosphere of micelles.28 Mixtures of alkyltrimethylammonium bromides have been reported to give positive or negative values of the interaction parameter or excess Gibbs energy.29-32 Some authors have suggested that the type of interactions, attractive or repulsive, depends on the mole fractions of surfactants.33-35 Several molecular thermodynamic theories have been developed for predicting the properties of and interactions in binary surfactant systems.36-38 In our previous study, cationic/anionic mixtures were investigated by using a capacitor model to determine the contributions of the electrostatic and translational free energies to the formation of vesicles and mixed micelles.6 Rosen and Hua have successfully extended Rubingh’s treatment of mixed micelle formation to the adsorption of binary mixtures of surfactants, including anionic/cationic systems.39-42,28 Rosen et al. derived the conditions for synergetic effects in the surface tension reduction efficiency, the surface tension reduction effectiveness, and mixed micelle formation.39,40,42-45 Although there have been many studies of micelles and the surface behavior of surfactant mixtures, the interactions between
10.1021/jp803105n CCC: $40.75 2008 American Chemical Society Published on Web 10/29/2008
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TABLE 1: SDS and CTAB Diffusion Coefficients, Viscosities, and Densities in Cationic-Rich CTAB/SDS Mixtures for Various Surfactant Concentrations at 25 °C
TABLE 2: SDS and CTAB Diffusion Coefficients, Viscosities, and Densities of Anionic-Rich SDS/CTAB Mixtures for Various Surfactant Concentrations at 25 °C
η × 103 d DCTAB × 1010 DSDS × 1010 CCTAB CSDS (mM) (mM) (kg m-1 s-1) (g cm-3) (m2 s-1) (m2 s-1)
η × 103 d DCTAB × 1012 DSDS × 1012 CCTAB CSDS (mM) (mM) (kg m-1 s-1) (g cm-3) (m2 s-1) (m2 s-1)
0.090 0.100 0.200 0.300 0.400 0.500 1.000 1.500 3.000 5.000 9.000 12.000
0.100 0.200 0.100 0.400 0.100 0.600 0.100 0.800 0.100 1.000 0.100 1.400 0.100 1.800 0.100 2.200 0.100 2.800 0.100 3.800 0.100 4.200 0.100 5.000 0.100 5.400 0.100 7.400 0.100 16.000 0.100 25.000
0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030
1.224 1.245 1.218 1.205 1.205 1.048 1.048 1.048 1.058 1.062 1.077 1.079
1.020 1.019 1.021 1.022 1.021 1.020 1.017 1.019 1.020 1.022 1.020 1.023
0.870 0.840 1.260 1.430 1.790 2.440 2.398 2.372 2.343 2.298 2.241 2.164
0.888 0.909 1.330 1.470 1.860 2.510 2.431 2.442 2.415 2.339 2.289 2.181
surfactant molecules on the surfaces of films and aggregates are still not fully understood. To the best of our knowledge, the nonrandom mixing of surfactants and the effects of headgroup size on their interactions have not been studied. In this study, we investigated the mixed aggregates and adsorption properties of binary surfactant systems containing the cationic surfactant cetyltrimethylammonium bromide (CTAB) and the anionic surfactant sodium dodecyl sulfate (SDS) in aqueous solution. The nature and strength of the interaction in the surfactant mixtures were characterized by calculating the values of the following parameters: the interaction parameter, β, the size parameter, F, and the optimized packing parameter, P*. The interaction parameter for mixed monolayer formation at the interface between the aqueous solution and air, βσ, was also calculated. 2. Experimental Section 2.1. Materials and Sample Preparation. SDS (>99%) and CTAB were obtained from Merck & Co. and Aldrich respectively. D2O (99.95%) was obtained from Merck & Co. Samples with less than 1 wt % total surfactant were prepared by combining the appropriate volumes of SDS and CTAB stock solutions and then mixed by weight depending on the desired composition; these samples were macroscopically homogeneous. All samples were equilibrated at 25 °C in a thermostated bath, and the measurements were carried out within 1 day of sample preparation. The surfactant concentration is specified in weight percent or, when convenient, as the total surfactant molar concentration, Ct ) CSDS + CCTAB, and the mixing ratio is specified as the molar fraction χSDS ) CSDS/(CSDS + CCTAB) of SDS in the surfactant mixture. We prepared cationic-rich mixed micelles or vesicles by mixing solutions of SDS and CTAB in which the concentration of SDS was maintained at 0.03 mM (∼0.0008% w/w) while the concentration of CTAB was varied from 0.09 to 12 mM (∼0.004 to 0.5% w/w). Anionic-rich solutions were also prepared by mixing solutions of SDS and CTAB in which the concentration of CTAB was maintained at 0.1 mM (∼0.003 65% w/w) while the concentration of SDS was varied from 0.2 to 25 mM (∼0.0058 to 0.72% w/w). Tables 1 and 2 show the concentrations, diffusion coefficients, viscosities, and densities of the cationic-rich and anionic-rich CTAB/ SDS mixtures at 25 °C. We also prepared aqueous solutions for surface tension measurements with concentration of 20 mM and 30 mM with compositions 99/1 and 1/99 for cationic-rich and anionic-rich regions, respectively. These solutions were prepared with doubly distilled water.
1.094 1.058 1.059 1.058 1.058 1.059 1.062 1.063 1.064 1.066 1.068 1.069 1.072 1.064 1.068 1.070
1.018 1.018 1.019 1.019 1.021 1.017 1.019 1.020 1.017 1.023 1.020 1.018 1.022 1.018 1.017 1.020
1.044 1.591 1.665 1.809 1.842 1.872 1.866 1.903 1.955 2.029 2.066 2.107 2.397 3.334 3.245 3.172
1.047 1.612 1.676 1.831 1.848 1.883 1.871 1.934 1.963 2.041 2.078 2.116 2.429 3.355 3.253 3.183
2.2. Methods. 2.2.1. NMR Self-Diffusion. The NMR selfdiffusion studies were performed at 25 °C on a Bruker 500 NMR spectrometer using an LED pulse program.6 The basic sequence had a pulsed field duration, δ, of 5 ms and a time interval, ∆, between the two gradient pulses of 120 ms. For all samples, a single-exponential decay of the echo amplitude was observed, indicating that only a single self-diffusion mode was present in each system. This finding is strong evidence for vesicle or mixed micelle formation. The peaks corresponding to the N-methyl proton and the methylene groups bonded to oxygen in CTAB and SDS respectively were selected, and the surfactant selfdiffusion coefficients were obtained from the decreases in the heights of these peaks with increasing pulse gradient strength. The self-diffusion coefficients were calculated using the Core program with a normalized global error squared sum of 0.1.46 When both vesicles and mixed micelles were present in the solution, the ILT (inverse Laplace transform) and Core programs were used to analyze the data.47 The viscosities of the mixed surfactant solutions were measured by using semimicro Cannon Ubbelohde capillary viscometers immersed in a water bath of temperature 25 ( 0.1 °C. The densities of the mixed surfactant solutions were measured using a 25 mL pycnometer at 25 °C.6 2.2.2. Surface Tension Measurements. Surface tension measurements were carried out with the ring method using a Kru¨ss K12 tensiometer under atmospheric pressure.48 The platinum ring was thoroughly cleaned and flame-dried before each measurement. To measure the surface tension, the vertically hung ring was dipped into the liquid and then removed; the maximum force required to pull the ring through the interface is then the surface tension, γ(mN/m). Measurements of the surface tension of pure water at 298 K were used to calibrate the tensiometer and to check the cleanliness of the glassware. In all cases, more than three successive measurements were carried out, and the standard deviation did not exceed (0.1 mN/m. The temperature was controlled to within (0.1 °C by circulating thermostated water through the jacketed glass cell. Each sample solution was stirred with a magnetic stirrer, and then the stirring of the sample was discontinued for 3 min and the surface tension was measured. 2.2.3. Electrical ConductiWity. Electrical conductivity measurements were carried out with a Metrohom conductometer (Model 771). The conductivity cell (Tacussel, France, type XE100) consists of two square platinum electrodes embedded
Properties of Mixtures of CTAB and SDS
J. Phys. Chem. B, Vol. 112, No. 47, 2008 14871
β)
Figure 1. Variation of the surface tension with the logarithm of the total concentration of mixed surfactants in anionic-rich mixtures for various temperatures.
in glass. This cell was immersed in the surfactant solution, which had been placed in a double-walled temperature-controlled glass container. 3. Theoretical Method for Determining the Interaction Parameter of Catanionic Mixed Monolayers and Mixed Aggregates 3.1. Regular Solution Method for Catanionic Mixtures. The nature and strength of the interaction between two surfactants in a binary system can be determined by calculating the values of their β parameters, which can be obtained by using the regular solution model developed by Rosen et al.41,49-51 The interaction parameter for mixed monolayer formation at the aqueous solution/air interface, βσ, can be calculated using the following equations:49-51
Z12 ln(R1Cσ12Z1Cσ1 ) (1 - Z1)2 ln[(1 - R1)]Cσ12/(1 - Z1)Cσ2
βσ )
)1
ln(R1Cσ12/Z1Cσ1 )
(1)
(2)
(1 - Z1)2
where Z1 is the mole fraction of surfactant 1 in the mixed monolayer (on a surfactant-only basis); and Cσ1 , Cσ2 , and Cσ12 are the molar concentrations in the solution phases of surfactant 1, surfactant 2, and their mixture, respectively, at the mole fraction, R1, of surfactant 1 required to produce a given γ value. In our experiments, Cσ1 , Cσ2 , and Cσ12 were determined, and correspond to a surface tension of γ ) 40 mN m-1 for the anionic-rich and cationic-rich mixtures (see Figures 1 and 2). Equation 1 can be solved numerically for Z1, which can then be substituted into eq 2 to calculate βσ. The interaction parameter β for mixed aggregate formation in an aqueous medium can be calculated with the following equations: 49-51
(χ1)2 ln(R1C12/χ1C1) (1 - χ1) ln[(1 - R1)]C12/(1 - χ1)C2 2
)1
(3)
ln(R1C12/χ1C1) (1 - χ1)2
(4)
where χ1 is the mole fraction of surfactant 1 with respect to the total surfactant in the mixed aggregate, and C1, C2, and C12 are the critical aggregate concentrations (CACs) for surfactant 1, surfactant 2, and their mixture, respectively, at the mole fraction R1. Since the value of the β parameter is proportional to the free energy of mixing of the system, a negative β value for catanionic mixtures indicates there is an attractive interaction between the two different surfactants with opposite charges. However, cationic/anionic surfactant mixtures exhibit large synergistic effects such as reductions in the critical micelle concentration and in the surface tension. In the present study, negative values of the β parameter measure the strength of the attractive interaction between the two different surfactants relative to the self-attraction of the individual surfactants. Intersurfactant interactions, and consequently the values of the β parameter, are usually dominated by the electrostatic interaction between the hydrophilic head groups of surfactants.52 The strength of the interaction between two surfactants on the surface of a mixed monolayer depends on the nature of the surface and the molecular environment (e.g., the temperature and the ionic strength of the solution phase). However, catanionic surfactants with strong attractive interactions between their charged head groups exhibit surface properties that are different to those of conventional surfactants. 3.2. Modification for Catanionic Mixtures of the Regular Solution Theory. We have previously modified the regular solution theory of ionic/nonionic surfactant mixtures: three additional parameters were introduced into the regular solution theory: a size parameter, a packing constraint parameter, and an interaction parameter.53 For a mixture of cationic and anionic surfactants, these parameters can be used to calculate the excess Gibbs free energy of the formation of mixed aggregates, GE
(
)(
)(
)
χ1 χ1 Fχ2 GE 1) β* RT χ1 + Fχ2 χ1 + Fχ2 (χ1 + Fχ2) f(R)P* (5) which on rearrangement can be expressed as
Figure 2. Variation of the surface tension with the logarithm of the total concentration of mixed surfactants in cationic-rich mixtures for various temperatures.
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GE 1 ) A(χ1)(1 - χ1)(Bχ1 + 1) RT (1 + Cχ1)3 A)
β* , F
B)
RP* - RFP* - 1 , RFP*
C)
TABLE 3: Values of the CAC Obtained from the Surface Tension, and the Degree of Counterion Dissociation Obtained with Conductometry for Various Temperatures and Compositions
1-F (6) F
compound CTAB
where β* is the modified interaction parameter of the aggregate; χ1 is the mole fraction of surfactant 1, which is the more surfaceactive (CTAB) surfactant in the mixed aggregate, and can be determined directly from PFG-NMR measurements; F is the size parameter; and P* is the optimized packing parameter.6 For binary surfactant mixtures, the packing parameter, P*, can be employed to account for the constraints on the packing in micelles of surfactant 1 that result from the presence of surfactant 2. The packing constraints are directly related to the nonrandom mixing in the system.54 The f(R) function is introduced to allow for possible variation in the packing parameter with R. As for the relationship between packing density and the mixing ratio for a system containing two different particle types, f(R)can be expressed as follows:54
f(R) )
{
R (R>0.5) 1 - R (R e 0.5)
This function is introduced to allow for possible variation with R in the packing parameter and is used in eq 5. This equation indicates that, when R approaches 0 or 1 for a constant total surfactant concentration, the packing ability in the mixed micelles is better than that when R is near 0.5. The possibility of surfactants A and B coming into contact is greatest when the overall mixing ratio is 0.5, and the packing constraints then become more significant. In the following section, this equation is fitted to experimental data by optimizing the values of the parameters, β*, F, and P*. 4. Results and Discussion 4.1. CAC (Critical Aggregation Concentration). The surface tensions of CTAB, SDS, and 99/1 CTAB/SDS cationicrich and anionic-rich mixtures were measured as a function of the surfactant concentration at various temperatures. Figures 1 and 2 show plots at various temperatures of the surface tensions versus the logarithm of the total surfactant concentration for cationic-rich and anionic-rich mixtures respectively. The values of CAC obtained from these figures are listed in Table 3. Further, the degrees of counterion dissociation, Ri, obtained with conductometry for CTAB, SDS, and the 99/1 CTAB/SDS cationic-rich and anionic-rich mixtures at various temperatures are listed in Table 3. These results show that the degrees of counterion dissociation for the pure surfactants and their mixtures increase monotonically with temperature. The observed increases in Ri are probably due to the decreases in the charge density at the micellar surface that result from decreases in the aggregation number of the micelles. Since Ri in the anionicrich mixed aggregates are higher than in cationic-rich aggregates, it can be assumed that the anionic-rich aggregates are larger. This result is consistent with those of previous studies, in which the diffusion coefficients for anionic-rich aggregates obtained with PFG-NMR were found to be smaller than those of cationicrich aggregates.6 This difference is due either to differences in aggregate size or in the interaction between SDS and CTAB pure micelles, which might be related to the differences between the interacting species: O-SO3- and Na+ in the former, and
SDS
CTAB/SDS cationic-rich
SDS/CTAB anionic-rich
temp (K)
CAC (mM)
Ri (i ) Br- or Na+)
298 308 318 328 298 308 318 328 298 308 318 328 298 308 318 328
0.997 0.979 0.953 0.86 8.910 8.736 8.383 7.663 0.910 0.895 0.861 0.772 1.910 1.821 1.760 1.691
0.180 0.291 0.321 0.371 0.240 0.312 0.341 0.395 0.374 0.378 0.380 0.381 0.502 0.526 0.595 0.625
TABLE 4: Results of Least-Squares Fitting of the Three-Parameter Asymmetric Regular Solution Model to Excess Free Energy at 25°C mixed surfactant
βAB
F
P/
SDS/CTAB CTAB/SDS
-8.785 -6.870
0.356 0.351
41.580 35.812
-N+(CH3)3 and Br- in the latter. The values of the interaction parameter presented in Table 4 confirm the differences between the interactions of SDS and CTAB. 4.2. Determination of the Micellar Composition and the Activity Coefficient. PFG-NMR data can be used to determine the concentrations of monomers and aggregates in mixed surfactant systems (Tables 1 and 2), and to determine the diffusion coefficients of monomers, micelles, and mixed aggregates. We have previously presented a three-site model, similar to that for micellar systems of catanionic mixtures of surfactants, as follows: 6
Dobs ) pDmon + qDves + rDmic
(7)
where Dobs is the measured surfactant diffusion coefficient, Dves is the diffusion coefficient of vesicles, Dmic is the diffusion coefficient of mixed micelles, Dmon is the diffusion coefficient of monomers, and p, q, and r are the fractions of monomers, vesicles, and mixed micelles inside the solution, respectively. In the specific concentration range examined in the PFG-NMR and conductivity measurements, the solution contains vesicles and mixed micelles and there is a dynamic equilibrium between these two types of aggregates.6 Since the exchange rate between vesicles and mixed micelles is high, only one diffusion coefficient was observed and the experimental measurements yield an average diffusion coefficient Dagg. Therefore, in the presence of aggregates, the mean values of the self-diffusion coefficients of free and aggregated surfactants can be expressed as
DCTAB )
f agg C CTAB CCTAB f DCTAB + D Ct,CTAB C t,CTAB agg
(8)
Properties of Mixtures of CTAB and SDS
DSDS
f agg C SDS C SDS f ) D + D Ct,SDS SDS Ct,SDS agg
J. Phys. Chem. B, Vol. 112, No. 47, 2008 14873
(9)
where DfCTAB and DfSDS are the diffusion coefficients of CTAB and SDS in the free state respectively, Dagg is the aggregate diffusion coefficient, Cf and Cagg are the concentrations of the free and aggregated surfactants, respectively, and Ct is the total surfactant concentration in the system. Dagg has been determined experimentally by carrying out the addition of TMS to the solution.53,55 We used eqs 8 and 9 to determine the values of Cf and Cagg for each surfactant. The activity coefficient f *i was calculated with the phase separation model:
C if ) f i*χiCACi
Figure 4. Excess Gibbs free energy as a function of the mole fraction of CTAB for CTAB/SDS (cationic-rich) and SDS/CTAB (anionic-rich) mixed aggregates at T ) 298 K.
(10)
where CACi and Cfi are the CACS and the monomer concentrations of the anionic-rich and cationic-rich mixtures respectively, which were obtained with PFG-NMR. 6 The symmetric regular solution model predicts that a plot of ln fi (i ) A or B) vs (χj)2 (j ) B or A) should give a straight line with slope β. Figure 3 shows these plots for the SDS/CTAB systems and indicates that these systems contain an asymmetry that the regular solution theory cannot account for. 4.3. Interaction of the Ionic Surfactants in the Micellar Phase. In the present study, the interaction between the two different ionic surfactants in mixed aggregates was analyzed with the two methods described in section 3. Since no structure of the aggregates was assumed in the derivation of the thermodynamics of mixed-micelle formation, and the phase separation model was adopted, this model is also applicable to the formation of other aggregates. Thus we have used the term CAC instead of CMC. In the regular solution model, the interaction parameter is calculated using eq 4. The obtained values of β for the 99/1 anionic-rich and cationic-rich mixtures at various temperatures are listed in Table 5. The values of β are negative, which indicates that after mixing the interaction between CTAB and SDS is more attractive or less repulsive than before mixing. These results show there is a strong synergism between the cationic and anionic surfactants. According to the data in Table 5, β is more negative in the anionic-rich mixtures than in the cationic-rich mixtures. The value of the β parameter depends on the steric self-repulsion and van der Waals attraction interactions. In the anionic-rich mixtures, the strength of the
Figure 3. Logarithm of the activity coefficient of surfactant i vs the square of the mole fraction of surfactant j for CTAB/SDS anionic-rich and cationic-rich mixed aggregates.
steric self-repulsion decreases but that of the van der Waals attraction increases with increases in the concentration of the SDS monomer, and so the van der Waals attraction has a greater effect on the β parameter. Further, the data show that β increases with increasing temperature in both anionic-rich and cationicrich mixtures, which is due to the resulting decreases in dehydration of the head groups and thus increases in the attractive interaction between surfactants. Since the regular solution model yields a composition-dependent interaction parameter, β, the values of β evaluated at the CAC cannot generally be used for other total surfactant concentrations. Therefore, the regular solution theory does not adequately describe the behavior of monomers in a surfactant solution, nor is it adequate for determining the activity coefficients and excess Gibbs free energies of catanionic mixtures. We used the model described in section 3.2 for catanionic mixtures. For nonideal mixtures, the excess Gibbs free energy was calculated as follows:
GE ) RT
∑ χi ln f i*
(11)
i
where f *i and χi are the activity coefficients and the mole fractions of the ionic surfactants in the catanionic mixture respectively. Figure 4 shows the variation of GE (determined using eq 11 and the experimental data) with the mole fraction of CTAB for the cationic-rich and anionic-rich mixtures at a temperature of 25 °C. It is obvious from the plot (Figure 4) that the excess Gibbs free energy is not symmetric with respect to the mole fraction; according to regular solution theory, the excess Gibbs free energy is symmetric and reaches a minimum at a surfactant mole fraction of 0.5. Next, we assessed the ability of eq 6 to describe the behavior of GE at 25 °C. The values of the modified interaction parameter, β*, the size parameter, and the nonrandom mixing parameter were obtained with leastsquares fitting to obtain the best possible fit of the variation of GE with the mole fraction of the surfactant. Therefore, this model successfully predicts the behavior of catanionic mixtures in aqueous solution. Table 4 shows that the interaction parameter β* increases with increases in the mole fraction of SDS, which results in increases in electrostatic repulsion. The size parameter is the ratio of the size of SDS molecules to the size of CTAB molecules and is almost the same for anionic-rich and cationicrich mixtures (Table 4). The optimized packing parameter P* is high in catanionic mixtures because of the strong tendency of ionic surfactants to form mixed aggregates. Therefore, this factor can be neglected in the modified equation. The initial
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TABLE 5: Effects of Temperature on the βσ and β Values of 99/1 Anionic-Rich and Cationic-Rich Mixtures for a Constant Surface Tension (γ ) 40 mN m-1) cationic-rich anionic-rich
temp (K)
-βσ
f σ1
f σ2
Z1
-β
f1
f2
χ1
β - βσ
308 318 328 308 318 328
15.5015 21.2113 18.9484 13.2362 10.9751 9.1956
0.1750 0.0605 0.1035 0.0071 0.0169 0.0289
0.0011 0.0002 0.0003 0.1354 0.1877 0.2665
0.6647 0.6363 0.6540 0.3887 0.3904 0.3792
5.8643 6.4565 6.6227 7.7247 8.9917 9.8233
0.9365 0.9030 0.8910 0.0493 0.0353 0.0286
0.0092 0.0072 0.0067 0.3359 0.2544 0.2103
0.8942 0.8743 0.8682 0.3758 0.3902 0.3984
-9.6372 -14.7548 -12.3257 -5.5115 -1.9834 0.6277
TABLE 6: Surface Excess Concentration (Γmax) and Minimum Area Per Molecule (Amin) for Pure CTAB, SDS, and 99/1 Anionic-Rich and Cationic-Rich Mixtures and Aideal for These Systems at Various Temperatures compound CTAB SDS CTAB/SDS Cationic-rich SDS/CTAB Anionic-rich
temp (K)
Z1
Γmax × 106 (mol/m2)
Amin (nm2)
Aideal (nm2)
Aexp - Aideal (nm2)
308 318 328 308 318 328 308 318 328 308 318 328
1 1 1 0 0 0 0.6647 0.6363 0.6540 0.3887 0.3904 0.3792
2.53 2.65 2.73 2.61 2.72 2.85 2.68 2.83 2.92 2.75 2.89 2.97
0.657 0.627 0.608 0.636 0.611 0.583 0.620 0.587 0.570 0.603 0.574 0.561
0.650 0.621 0.599 0.644 0.617 0.592
-0.030 -0.034 -0.029 -0.041 -0.043 -0.031
decrease in GE is attributed to synergistic effects between the two surfactants, and the increase in GE at higher fractions of surfactant is mainly attributed to a decrease in the stability of the mixed aggregates. These conclusions are in agreement with previous findings.53 4.4. Interactions in Catanionic Mixed Monolayers. For catanionic CTAB/SDS mixtures, the composition of an adsorbed mixed monolayer of SDS/CTAB in equilibrium with singly dispersed CTAB (species 1) and SDS (species 2) in the bulk phase was evaluated with eqs 1 and 2. The values of Cσ1 , Cσ2 , Cσ3 , and Cσ12, which correspond to a surface tension of γ ) 40 mN m-1 for the anionic-rich and cationic-rich mixtures (see Figures 1 and 2), and the calculated Z1, βσ, f1, f2, f σ1 , and f σ2 ,are listed in Table 5 for various temperatures. These results show that βσ is more negative than β, which was calculated with regular solution theory, which indicates that there is a stronger synergism in the mixed monolayer than in the mixed aggregates; this effect arises because the surfactant interaction is more favorable at the planar air/aqueous solution interface than at the curved aggregate surface. As shown in Table 5, the absolute values of both βσ and β increase with increasing temperature. The variations in βσ and β with temperature in the anionic-rich mixtures are larger than the corresponding variations in the cationic-rich mixtures because the dehydration of the head groups of the surfactants increases with increasing temperature. The headgroup of SDS can be hydrated via three oxygen atoms but the headgroup of CTAB can only be hydrated via one nitrogen atom, so SDS is more hydrated than CTAB. As a result, temperature increases result in greater increases in the electrostatic attraction between the anionic groups in anionic-rich mixtures than in cationic-rich mixtures. Furthermore, it has been shown that the value of βσ - β in the cationic-rich mixtures increases with increases in the temperature. This result suggests that increasing the temperature of the aqueous medium has a greater effect on the planar air/aqueous interface than on the convex aggregate surface. The surface excess (Γmax, mol/cm2) concentration of a surfactant is a measure of adsorption at the air/water interface. The surfactant concentration is always greater on the surface than in the bulk. The adsorption of a single surfactant molecule
at the air/solution interface was determined from the slope of the surface tension,, versus or ln CCTAB or ln CSDS with the concentration of the other surfactant being held constant. The maximum surface excess concentrations of the CTAB and SDS surfactants, Γmax(CTAB)and Γmax(SDS), respectively, were calculated with the following equations: 51
1 ( 2RT )( d lnd lnC γ )
(12)
1 ( 2RT )( d dlnlnCγ )
(13)
Γmax(CTAB) ) -
CTAB
Γmax(SDS) ) -
SDS
where C is the concentration, R is the gas constant, and T is the absolute temperature. The minimum area occupied by a surfactant molecule adsorbed at the air/solution interface, Amin (nm2), when Γmax is expressed in units of moles per centimeter squared, is
Amin )
1014 ΓmaxNA
(14)
where NA is Avogadro’s number. The maximum surface excess concentrations of each surfactant and their mixtures were obtained for anionic-rich and cationic-rich mixtures from the premicellar slopes of the surface tension concentration curves. Table 6 lists the surface excess concentration, Γmax, minimum area, Amin, and the ideal mixing value, Aideal, for anionic-rich and cationic-rich mixtures at various temperatures. According to the data in Table 6, since CTAB is more surface active than SDS, the surface excess concentration of SDS is less than that of pure CTAB, as expected. The minimum area per molecule of pure SDS is higher than that of pure CTAB. The minimum area per molecule is higher for mixed surfactant systems than for either of the pure surfactants (Table 6). The results in Table 6 show that in anionic-rich mixtures as well as in cationic-rich mixtures, the addition of a
Properties of Mixtures of CTAB and SDS surfactant with the opposite charge causes an increase in Γmax due to the reduction in the electrostatic repulsions between head groups. Table 6 shows that Γmax increases with increases in the temperature. Since the head groups are increasingly dehydrated with increases in the temperature, the number of monomers on the surface increases. Table 6 also lists the ideal mixing values, Aideal, calculated with the equation Aideal ) Z1A1 + (1 - Z1)A2, where Z1 is the molar fraction of component 1 in the mixed monolayer and A1 and A2 designate the minimum area per molecule of CTAB and SDS, respectively. The Aideal values are greater than the corresponding experimental (Aexp) values, which confirms the presence of synergism in these catanionic mixtures. 5. Conclusions The interfacial and aggregation behaviors of catanionic mixtures in aqueous media were studied. This investigation showed that the attractive interaction in mixed aggregates is weaker than in mixed monolayers at the air/solution interface. However, the results also show that there is a strong synergism in these catanionic mixtures in both the aggregate and monolayer states. Further, temperature increases result in greater increases in the electrostatic attraction between the anionic groups in anionic-rich mixtures than in cationic-rich mixtures. It was also shown that the value of βσ - β in cationic-rich mixtures increases with increases in the temperature. This result suggests that increases in the strength of the electrostatic interaction that result from increases in the temperature have a greater effect at the planar air/solution interface in an aqueous medium than at the convex aggregate surface. In addition, we determined the micelle interaction parameter (β), F, and P* for the modified version of the regular solution theory for cationic and anionic surfactants mixtures that we proposed in a previous study. The proposed model provides a good description of the behavior of binary surfactant mixtures. Our results indicate that in ionic surfactant mixtures, the interaction parameter, β, increases with increases in the mole fraction of SDS. Notation Aideal ) ideal mixing area Amin ) minimum area per molecule Cfi ) monomer concentration of an ionic surfactant Ci ) critical aggregate concentration of the ionic surfactants CT ) total surfactant concentration D ) diffusion coefficient d ) density f( ) mean activity coefficient fi ) activity coefficient of an ionic surfactant GE ) excess Gibbs free energy NA ) Avogadro’s number ni ) number of molecules in a mixed aggregate P* ) optimized packing parameter R ) gas constant T ) absolute temperature χi ) mole fraction of an ionic surfactant in a mixed aggregate χ/i ) modified mole fraction of an ionic surfactant in a mixed aggregate χ ) composition of a mixed aggregate Z ) composition of an adsorbed film R ) mole fraction of a surfactant in a mixture Ri ) degree of dissociation of a counterion β ) interaction parameter for a mixed aggregate βσ ) interaction parameter for an adsorbed film phase
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