11942
J. Phys. Chem. B 2008, 112, 11942–11949
Mixtures of Monomeric and Dimeric Surfactants: Hydrophobic Chain Length and Spacer Group Length Effects on Non Ideality Amalia Rodrı´guez,‡ Marı´a del Mar Graciani,‡ Antonio Jose´ Moreno-Vargas,† and Marı´a Luisa Moya´*,‡ Departamento de Quı´mica Orga´nica, UniVersidad de SeVilla, C/ Profesor Garcı´a Gonza´lez 1, 41012 SeVilla, Spain and Departamento de Quı´mica Fı´sica, UniVersidad de SeVilla, C/ Profesor Garcı´a Gonza´lez 1, 41012 SeVilla, Spain ReceiVed: March 14, 2008; ReVised Manuscript ReceiVed: June 26, 2008
Critical micelle concentrations of the CmTAB+12-s-12 (s ) 3, 4, 5 and m ) 10, 12, 14, 16) binary systems have been determined, through conductivity and fluorescence measurements, at 298 K. Application of different theoretical approaches to explain mixed micellization shows that non-ideality of the binary systems follows the trend C16TAB+12-3-12 < C14TAB+12-3-12 < C12TAB+12-3-12 < C10TAB+12-3-12, and C12TAB+125-12 ≈ C12TAB+12-4-12 < C12TAB+12-3-12. Literature data corresponding to the C12TAB+12-2-12, C12TAB+m-s-m (s ) 2, 4, 6 and m ) 12, 14, 16) and TritonX-100+12-s-12 (with s ) 3, 6, 12) mixtures were considered in order to investigate the hydrophobic chain length and the spacer group length roles on the observed non ideal behavior. It was found that the capacity of the mixture components to form micelles of similar or different shapes plays a major role in non-ideality. SCHEME 1
Introduction Solution properties of mixed surfactants are more interesting than pure surfactants, from both physicochemical and application points of view. By virtue of the better performances in solubilization, transportation, and so forth, mixed surfactants have gained importance in the industrial, pharmaceutical, and biological fields.1,2 Surfactant mixtures are also of interest in the investigation of micellar catalysis.3-9 Binary combinations of different types of surfactants such as anionic/non-ionic,10-16 cationic/non-ionic,10,17-21 anionic/anionic22,23 and cationic/cationic24-29 have been studied, and the nature of mutual interaction of monomers in the mixed micelles has been quantitatively analyzed by using different theories.30 Dimeric surfactants are made of two hydrophobic chains and two polar head groups covalently linked through a spacer group, which significantly influences their properties.31-34 These surfactants have been drawing increasing attention due to their unique properties that are superior to those of conventional single-chain (monomeric) surfactants. Owing to the widespread applications of surfactant mixtures and the substantial differences between mixed surfactants and individual components, insight into the mixtures of dimeric and single-chain surfactant properties is of particular interest. Several investigations have been focused on micelle size and microstructure of mixtures of dimeric and monomeric surfactants,35-44 but analyses of the applicability of different theoretical approaches in order to explain the behavior of these binary mixtures are less frequent.45-47 In this work, different theoretical treatments have been used to rationalize the behavior of alkanediyl-R-ωbis(dodecyldimethylammonium) bromide, 12-s-12, and alkyltrimethylammonium bromide, CmTAB, binary mixtures. With the scope of elucidating the hydrophobic chain length and spacer * To whom correspondence should be addressed. E-mail: moya@ us.es. Homepage: www.grupo.us.es/coloides. ‡ Departamento de Quı´mica Fı´sica, Universidad de Sevilla. † Departamento de Quı´mica Orga ´ nica, Universidad de Sevilla.
group length roles on binary systems behavior, data corresponding to the mixtures of m-s-m dimeric surfactants with cationic and non-ionic surfactants were taken from the literature.41,42,45 Discussion of the results shows that the capacity of the mixture components to form micelles of similar or different shapes plays a major role on non-ideality. Experimental Section Materials. Pyrene was from Aldrich and it was purified before use by methods reported in the literature.48 Decyltrimethylammonium bromide, C10TAB ) DeTAB, dodecyltrimethylammonium bromide, C12TAB ) DTAB, tetradecyltrimethylammonium bromide, C14TAB ) TTAB, and hexadecyltrimethylammonium bromide, C16TAB ) CTAB, were from Fluka and used as received. The synthesis of the dimeric surfactants (see Scheme 1) was done as described in ref 49. The surfactants were characterized by 1H NMR, 13C NMR and elemental analysis (CITIUS, University of Seville), the results being in agreement with those previously reported. Conductivity Measurements. Conductivity was measured with a Crison GLP31 conductimeter, connected to a water-flow cryostat maintained at 298 K. A dispenser Crison Burette 1S was programmed to add the adequate quantities of a concentrated surfactant solution in order to change the [surfactant] from concentrations well below the cmc, up to at least two to three times the cmc concentration. This method allows one to obtain a large number of experimental conductivity data, the estimation
10.1021/jp802243f CCC: $40.75 2008 American Chemical Society Published on Web 09/03/2008
Mixtures of Monomeric and Dimeric Surfactants
J. Phys. Chem. B, Vol. 112, No. 38, 2008 11943
TABLE 1: Mixed Critical Micelle Concentrations, cmcexp, of Alkyltrimethylammonium Bromides + Didoceyl Dibromides Binary Systems at 298 Ka solution mole 103 × cmcexp/mol dm-3 fraction of monomeric CTAB+ TTAB+ DTAB+ DeTAB+ DTAB+ DTAB+ surfactant, R1 12-3-12 12-3-12 12-3-12 12-3-12 12-4-12 12-5-12 0.00 0.10 0.20 0.40 0.60 0.80 0.90 0.95 0.98 1.00
0.97 0.97 0.96 0.96 0.96 0.97 0.98
0.97
0.99
3.6
1.1 1.3 1.6 2.1 2.6 3.0
0.97 1.1 1.3 1.7 2.4 3.2 4.4 8.4 15
0.97 1.1 1.3 1.6 2.4 3.3 13 8.8 67
1.1
1.2
1.3 1.7 2.2 3.0 4.3 5.8
1.4 1.7 2.0 3.0 4.2 6.2 9.4 15
15
CTAB ) hexadecyltrimethylammonium bromide; TTAB ) tetradecyltrimethylammonium bromide; DTAB ) dodecyltrimethylammonium bromide; DeTAB ) decyltrimethylammonium bromide; 12-s-12 ) alkanedyil-R-ω-bis(didodecyldimethylammonium) bromide. a
Figure 1. Dependence of the specific conductivity on surfactant concentration for DTAB+12-3-12 binary systems, with solution mole fraction of DTAB equal to 0.8, at 298 K. Inset: Application of the Carpena method to the experimental conductivity data.
of the cmc being more accurate. The conductimeter was calibrated with KCl solutions of the appropriate concentration range. Steady-State Fluorescence Measurements. Fluorescence measurements were made by using a Hitachi F-2500 fluorescence spectrophotometer. The temperature was kept at 298 K by a water flow thermostat connected to the cell compartment. Cmc′s Determination by Using Pyrene As Probe: The 1 × 10-6 M pyrene surfactants solutions were prepared in twice distilled water. The excitation wavelength was 335 nm and the fluorescence intensities were measured at 373 nm (band 1) and 384 nm (band 3). Excitation and emission slits were 2.5 nm and a scan speed of 60 nm/min was used. The intensity ratio of the vibronic bands (1:3) is called the pyrene 1:3 ratio. Introduction of pyrene in the surfactant solutions was done as in ref.50 Results Table 1 summarizes the critical micelle concentration values, cmcexp, obtained for the different dimeric+monomeric surfactant binary mixtures. These values were obtained through conductivity measurements (see Figure 1), cmcexp values being determined from inflections in plots of conductivity, κ, against the surfactant concentration (Williams′ method51), as described in ref 52 (see solid lines in Figure 1). Cmcexp values corresponding to pure
Figure 2. Effect of surfactant concentration on pyrene II/IIII ratio in DTAB+12-3-12 binary systems, with DTAB mole fraction equal to 0.9, at 298 K.
aqueous 12-s-12 solutions are in agreement with literature data.53 The authors also used a method recently proposed by Carpena et al.54 in order to calculate the cmcexp values from the conductivity data. This method is based on the fitting of the experimental raw data to a simple non-linear function obtained by direct integration of a Boltzmann type sigmoidal function. This method applied well to real systems that present a gradual transition from the premicellar to the postmicelar region, for which the break in the conductivity-surfactant concentration plots are difficult to determine. An example of the application of Carpena′s method is shown in the inset of Figure 1. The cmcexp values obtained from the Williams and Carpena methods were in good agreement. However, since criticism has arisen about the use of conductivity data for the determination of critical micelle concentrations,55 the authors also used a fluorescent method, based on the variations of the pyrene intensity ratio II/IIII following the micellization process, to check the reliability of the cmcexp data. All II/IIII plots show a rapid decrease as the total surfactant concentration increases, associated with the formation of micelles (see Figure 2). The cmcexp was taken as the concentration at the intercept of the rapidly varying part and the nearly horizontal part at high concentration of the II/IIII plot.56 This procedure yields cmcexp values in agreement with those obtained by means of conductivity measurements. Discussion In order to investigate the ideality of the mixed micelles, we studied the Clint equation, based on the pseudophase thermodynamic model.57 This equation can be written as follows:
R1 R2 1 ) + id cmc1 cmc2 cmc
(1)
where R1 and R2 are the mole fractions of the monomeric and the dimeric surfactant in the solution, respectively. The cmcid is the theoretical ideal mixed cmc and cmc1 and cmc2 are the critical micelle concentrations of the pure monomeric and dimeric surfactants, respectively. Figure 3 shows that the experimental cmc′s, cmcexp, deviate negatively from the cmcid values for all of the binary mixtures investigated. The negative deviation indicates that attractive interactions between the components are at work in the mixed micelles. For dimeric surfactants, the spacer group significantly affects the electrostatic
11944 J. Phys. Chem. B, Vol. 112, No. 38, 2008
Rodrı´guez et al.
Figure 3. Critical micelle concentrations for CmTAB+12-s-12 binary systems at 298 K. Solid circles are experimental data, the dash lines were calculated from the ideal mixing and the solid lines were calculated from the non ideal mixing models.
interactions at the micellar surface.58 Its presence also influences the shape and size of the micellar aggregates formed by the dimeric surfactants,59-61 which, in turn, can affect the hydrophobic interactions within the micelle core. It is known that for short spacer groups 12-s-12 surfactants form thread-like or rodlike micelles, whereas for long spacer groups spherical micelles are observed. However, the CmTAB surfactants with m ) 10, 12, 14 form spherical micelles, while for m ) 16, spherocylindrical micelles are observed at moderately high surfactant concentrations.62 When the two components of a binary mixture tend to form micelles of different shape and size, hydrophobic as well as electrostatic interactions between the two components of the mixtures investigated are expected to contribute to nonideality. With this in mind, and in order to investigate the role of the hydrophobic chain length and the spacer group length on the non ideal behavior of the monomeric+dimeric mixtures, literature data corresponding to the CTAB+m-s-m (with m ) 12, 14, 16 and s ) 2, 4, 6, 12)41,45 and Triton X-100+12-s-12 (with s ) 3, 6, 12)42 binary systems were considered. These data are summarized in Table 1 of the Supporting Information. The authors found that the Clint theory could not explain the mixed cmc values of these binary systems. A quantitative interpretation of the experimental results can be carried out by considering Rubingh′s treatment,63 based on
the regular solution theory. This theory allows for the calculation of the micellar mole fractions as well as the interaction parameter, β, by using the equations:
X 21ln(cmcexpR1 /cmc1X1) (1 - X1)2ln(cmcexp(1 - R1)/cmc2(1 - X1)) β)
ln(cmcexpR1 /cmc1X1) (1 - X1)2
)1
(2)
(3)
where X1 is the micelle mole fraction of the monomeric surfactant in the mixed micelles. β indicates the magnitude of the interactions operating between the two components in the mixed micelle state, and it is expected to remain constant for the whole composition range. The activity coefficients of the monomeric, f1, and the dimeric, f2, surfactants can be obtained by using the equations:
f1 ) exp[β(1 - X1)2] f2 )
exp(βX 21)
(4) (5)
The values of the micelle mole fraction of the monomeric surfactant, X1Rubingh, for some of the mixtures investigated
Mixtures of Monomeric and Dimeric Surfactants
J. Phys. Chem. B, Vol. 112, No. 38, 2008 11945
TABLE 2: Mole Fraction of the Monomeric Surfactant in the Mixed Micelles According to Rubingh′S Model, XRubinngh, j 1, and Rodena′s Model, XRodenas, for Motomura′s Model, X Some of the Binary Mixtures Investigated Rmonomeric 0.10 0.20 0.40 0.60 0.80 0.90 0.20 0.40 0.60 0.80 0.90 0.95 0.98 0.181 0.521 0.674 0.888 0.956 0.10 0.20 0.30 0.40 0.60 0.80 0.90 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 a
X Rubingh
X¯1
CTAB+12-3-12 (T ) 298 K) 0.105 0.104 0.206 0.206 0.401 0.402 0.592 0.591 0.788 0.786 0.893 0.891 DTAB+12-3-12 (T ) 298 K) 0.082 0.081 0.150 0.134 0.227 0.231 0.347 0.335 0.444 0.423 0.525 0.520 0.658 0.620 DTAB+12-2-12a (T ) 298 K) 0.074 0.042 0.215 0.225 0.275 0.230 0.370 0.433 0.469 0.469 Triton X-100+12-3-12b (T ) 298 K) 0.357 0.369 0.460 0.431 0.529 0.458 0.593 0.496 0.725 0.628 0.873 0.800 0.934 0.900 CTAB+12-2-12c (T ) 319.5 K) 0.142 0.122 0.258 0.234 0.355 0.300 0.454 0.391 0.539 0.503 0.623 0.592 0.705 0.689 0.802 0.790 0.889 0.882
X Rodenas 0.105 0.206 0.400 0.591 0.788 0.891 0.079 0.154 0.221 0.321 0.455 0.538 0.631 0.047 0.212 0.232 0.441 0.473 0.367 0.400 0.444 0.502 0.649 0.818 0.908 0.155 0.244 0.330 0.419 0.511 0.605 0.701 0.799 0.899
Ref 42. b Ref 41. c Ref 45.
in this work as well as in previous studies are listed in Table 2. The interaction parameter, β, for the binary systems CmTAB+12-s-12 (s ) 3, 4, 5) and Triton X-100+12-s-12 (with s ) 3, 6, 12, taken from ref 41) were calculated and are summarized in Table 3. This Table shows that β remains constant only for the CTAB+12-3-12 mixtures, the interaction parameter showing a tendency to increase upon increasing the mole fraction of the monomeric surfactant in the solution (errors in the cmc affect the interaction parameter values, but they do not alter the observed tendency in β). The non-constancy of β with mixture composition have been found previously,22,64-68 showing the shortcomings of the Rubingh′s approach for binary mixtures. Interaction parameters were calculated by Alargova et al.41 and Zhao et al.45 by using the Rubingh treatment for the CTAB+12-2-12 and CTAB+m-s-m (m ) 14, 16 and s ) 2, 4, 6) mixtures and the average β values, βaverage, given in refs 41 and 45 are listed in Table 3. For the sake of comparison, βaverage values were also calculated for the CmTAB+12-s-12 and Triton X-100+12-s-12 binary mixtures, in spite of β not being constant upon mixture composition. As it will be seen below, βaverage values are going to be useful in the discussion of results. All βaverage values were negative, pointing out the
existence of synergistic interactions between the monomeric and the dimeric components in the mixed micelle formation. Motomura et al.69 have shown that the process of micelle formation can be treated from the viewpoint of thermodynamics and takes into account dissociation of ionic surfactants (which is important since most of the monomeric and all the dimeric surfactants taken into account in this work are ionic). According to this approach, micellization is considered similar to a macroscopic bulk phase, and energetic parameters associated with the process are expressed by excess thermodynamic quantities. Composition of the mixed micelles can be determined by using the equations:
X1 ) R1 - (R1R2 /δcmc)(δcmc/δR1)T,Px ×
[
1-
δcdν1,cν2,d ν1,cν2(1 - R1) + ν2,dν1R1
]
(6)
and
cmc ) (ν1R1 + ν2R2)cmcexp
(7)
j 1 is the micelle mole fraction of the monomeric where X surfactant, R j 1 is the bulk mole fraction, and δdc is the Kronecker delta. R j 1 is given by the following:
R1 )
R1ν1 R1ν1 + R2ν2
(8)
where ν1 and ν2 are the number of ions produced by the surfactant upon dissociation. The variable ν1 is given by 1 for non-ionic surfactants, by 2 for monomeric ionic surfactants, and j 1 obtained by 3 for dimeric ionic surfactants.70 The values of X for some of the mixtures studied are listed in Table 2. One can see that the micelle mole fractions of the monomeric surfactants calculated by using Rubingh and Motomura′s treatments are similar. A new treatment for mixed micelles was recently proposed by Rodenas et al.71 It was based on Lange′s model72 and it uses the Gibbs-Duhem equation to relate the activity coefficients of the surfactants in the mixed micelles. It does not introduce any restrictions on the activity coefficients of the surfactants in the mixed micelles and the micelle mole fraction of the monomeric surfactant, X1Rodenas, can be obtained by using eq 9:
X Rodenas ) -(1 - R1)R1(∂lncmcexp /∂R1)P,T + R1 (9) 1 Values of X1Rodenas calculated for some of the mixtures are listed in Table 2. This Table shows that micelle mole fractions of the monomeric surfactants obtained through the three treatments considered are similar. The same result was found for the rest of the monomeric+dimeric binary mixtures examined. Quantitatively, deviation from ideal mixing can be estimated by the excess Gibbs energy of micelle formation, GE, where GE ) RTΣ XiMicelle ln Σfi and eqs 10 and 1173 allow one to calculate the activity coefficients. The GE values estimated by,
X Micelle f1cmc1 ) R1cmcexp 1
(10)
f2cmc2 ) R2cmcexp X Micelle 2
(11)
considering Motomura and Rodena′s approaches are summarized in Table 4, together with the excess Gibbs energy of micelle formation values estimated by using Rubingh′s theory (from f1 and f2 values estimated by using eqs 4 and 5). One can see that the trends of GE with mixture composition are the same for the three sets of GE values. Therefore, in spite of the shortcomings of Rubingh′s theory and the non-constancy of β, βaverage values
11946 J. Phys. Chem. B, Vol. 112, No. 38, 2008 TABLE 3: Interaction Parameter, β, and the Average β Value, βaverage, Obtained for the Monomeric-Dimeric Binary Mixtures by Using Rubingh′s Theory CTAB+12-3-12 (298 K) Rmonomeric 0.10 0.20 0.40 0.60 0.80 0.90 -β 0.09 0.10 0.09 0.10 0.09 0.10 βaverage ) -0.095 TTAB+12-3-12 (T ) 298 K) Rmonomeric 0.20 0.40 0.60 0.80 0.90 0.95 -β 0.09 0.17 0.39 0.36 0.39 0.36 βaverage ) -0.29 DTAB+12-3-12 (T ) 298 K) Rmonomeric 0.20 0.40 0.60 0.80 0.90 0.95 0.98 -β 0.74 0.87 0.88 1.0 1.2 1.2 1.5 βaverage ) -1.0 DeTAB+12-3-12 (T ) 298 K) Rmonomeric 0.20 0.40 0.60 0.80 0.90 0.95 0.98 -β 1.6 1.6 1.9 1.9 2.2 2.8 3.7 βaverage ) -2.2 DTAB+12-4-12 (T ) 298 K) Rmonomeric 0.20 0.40 0.60 0.80 0.90 0.95 0.98 -β 0.10 0.59 0.69 0.83 0.80 0.89 1.3 -βaverage ) -0.74 DTAB+12-5-12 (T ) 298 K) Rmonomeric 0.20 0.40 0.60 0.80 0.90 0.95 0.98 -β 0.46 0.57 0.80 0.85 0.85 0.93 1.3 -βaverage ) -0.82 Triton X-100+12-3-12b(T ) 298 K) Rmonomeric 0.10 0.20 0.30 0.40 0.60 0.80 0.90 -β 1.9 2.0 1.8 1.5 1.2 0.90 0.84 -βaverage ) -1.5 Triton X-100+12-6-12b(T ) 298 K) Rmonomeric 0.10 0.20 0.30 0.40 0.60 0.80 0.90 -β 2.0 2.1 2.0 1.8 1.2 0.90 1.1 -βaverage ) -1.6 Triton X-100+12-12-12b(T ) 298 K) Rmonomeric 0.10 0.20 0.30 0.40 0.60 0.80 0.90 -β 0.41 0.32 0.34 0.19 0.16 0.20 0.36 DTAB+12-2-12a (T ) 298 K) -βaverage ) -0.28 CTAB+14-2-14c (T ) 319.5 K) -βaverage ) -2.2 CTAB+16-2-16c (T ) 319.5 K) -βaverage ) -4.2 ( 0.5 CTAB+16-4-16c (T ) 319.5 K) -βaverage ) -3.6 ( 0.4 CTAB+16-6-16c (T ) 319.5 K) -βaverage ) -3.7 ( 0.4 a
Ref 42. b Ref 41. c Ref 45.
will be considered for all of the binary mixtures in order to emphasize some interesting features in relation to the role of the hydrophobic chains length and the spacer group length on the non-ideal behavior. This would be equivalent to consider Rubingh′s treatment adequate for rationalizing experimental results, without the restriction that the β interaction parameter was independent of the mixture composition. (1) The CmTAB+12-3-12 mixtures are more ideal the longer the hydrophobic chain of the monomeric surfactant is. (2) The non ideality of the DTAB+12-s-12 binary systems seems to increase when s (the spacer group length) decreases, although for s ) 4 and 5, the average β value is similar. (3) The non-ideality of the CTAB+16-s-16 mixtures with s ) 4 and 6 is practically the same, these mixtures being somewhat less ideal for s ) 2. (4) The mixed systems CTAB+m-2-m are more ideal the shorter the hydrophobic chain length of the dimeric surfactant becomes. (5) The non ideality of the Triton X-100+12-s-12 binary systems with s ) 3 and 6 were similar, these systems being more ideal when s ) 12. Interactions between the surfactants in binary mixtures are usually considered the result of two contributions,23 one
Rodrı´guez et al. TABLE 4: Excess Gibbs Energy of Micelle Formation, GE, for CmTAB+12-s-12 Binary Systems at 298 K solution mole fraction of monomeric surfactant 0.10 0.20 0.40 0.60 0.80 0.90 0.20 0.40 0.60 0.80 0.90 0.95 0.20 0.40 0.60 0.80 0.90 0.95 0.98 0.20 0.40 0.60 0.80 0.90 0.95 0.98 0.20 0.40 0.60 0.80 0.90 0.95 0.98 0.20 0.40 0.60 0.80 0.90 0.95 0.98
GE(Rubingh)/ kJ mol-1
GE(Motomura)/ kJ mol-1
CTAB+12-3-12 (T ) 298 K) -0.85 -0.022 -1.3 -0.077 -1.7 -0.054 -1.3 -0.072 -1.3 -0.040 -0.87 -0.020 TTAB+12-3-12 (T ) 298 K) -0.60 -0.10 -1.2 -0.10 -1.4 -0.21 -1.9 -0.22 -1.9 -0.21 -1.4 -0.14 DTAB+12-3-12 (T ) 298 K) -0.72 -0.34 -1.3 -0.58 -1.7 -0.92 -2.2 -1.5 -2.4 -1.7 -2.5 -2.0 -0.89 -1.0 DeTAB+12-3-12 (T ) 298 K) -0.97 -0.74 -1.4 -1.5 -2.1 -2.1 -2.4 -2.8 -2.9 -3.4 -3.5 -3.5 -2.9 -2.9 DTAB+12-4-12 (T ) 298 K) -0.36 -0.2 -0.52 -0.50 -1.0 -0.82 -2.0 -1.1 -2.2 -1.3 -2.2 -1.3 -1.2 -0.90 DTAB+12-5-12 (T ) 298 K) -0.54 -0.16 -0.91 -0.48 -1.7 -0.95 -2.1 -1.3 -2.2 -1.3 -1.0 -1.1 -0.70 -0.80
GE(Rodenas)/ kJ-1 mol-1 -0.023 -0.040 -0.054 -0.058 -0.038 -0.020 -0.13 -0.10 -0.21 -0.22 -0.21 -0.14 -0.26 -0.69 -1.2 -1.6 -1.7 -1.9 -1.1 -0.83 -1.2 -2.6 -3.4 -3.5 -3.4 -2.6 -0.10 -0.31 -0.78 -1.0 -1.1 -1.2 -0.92 -0.17 -0.53 -0.94 -1.2 -1.2 -1.1 -0.82
associated with interactions between the hydrophobic moieties of the two surfactants in the micellar core and the other with electrostatic interactions between the head groups of both surfactants at the interface. In the case of the binary systems Triton X-100+12-s-12, Wang et al.42 explained non-ideality by considering that the intercalation of the Triton X-100 surfactant molecules among the dimeric surfactant molecules within the micelle results in a diminution of the electrostatic repulsions at the interface, this promoting micellization. However, the reduction is expected to be more important for low RTriton X-100 than for high RTriton X-100, since in the former electrostatic repulsions between dimeric surfactants head groups is strong. For high RTriton X-100, the repulsions have been screened markedly and the micellization would be less obviously promoted by further increase in RTriton X-100. With regard to the influence of the spacer group length, it was explained on the basis of the hydrophobic interactions between the dimeric surfactants molecules. The 1212-12 dimeric surfactant shows a cmc lower than those corresponding to 12-3-12 and 12-6-12 pure surfactants (see
Mixtures of Monomeric and Dimeric Surfactants
J. Phys. Chem. B, Vol. 112, No. 38, 2008 11947
TABLE 5: Structural Parameters for Several Pure Monomeric, CmTAB, and Dimeric Surfactants, 12-s-12, and Packing Parameters for CmTAB+12-s-12 Binary Mixtures surfactant
lc/nm
V/nm3
Amin/nm2a
CTAB TTAB DTAB DeTAB 12-2-12 12-3-12 12-4-12 12-5-12 12-6-12 12-12-12 TritonX-100
2.178 1.925 1.672 1.419 1.672 1.672 1.672 1.672 1.672 1.672 2.914
0.4578 0.4040 0.3502 0.2964 0.3502 0.3502 0.3502 0.3502 0.3502 0.3502 0.973
0.55 0.62 0.66 0.75 0.30 0.35 0.38 0.42 0.51 0.75 0.91
Peff 0.382 0.338 0.317 0.278 0.698 0.598 0.544 0.493 0.410 0.279 0.367
Peff fraction of CmTAB, R1 0.00 0.181 0.20 0.40 0.521 0.60 0.674 0.80 0.888 0.90 0.95 0.986 1.00 a
TTAB + 12-3-12
DTAB + 12-3-12
DeTAB + 12-3-12
DTAB + 12-2-12
DTAB + 12-4-12
DTAB + 12-5-12
0.598
0.598
0.598
0.598
0.544
0.493
0.585 0.564 0.563
0.565 0.525
0.549 0.528
0.698 0.641 0.532
0.501
0.473 0.495
0.456
0.454
0.435
0.434
0.412
0.410 0.392
0.394
0.317
0.317
CTAB + 12-3-12
0.555 0.448
0.480
0.490
0.451 0.525
0.413
0.428
0.458
0.401 0.483
0.397
0.394
0.429 0.488
0.384 0.321
0.382
0.338
0.317
0.278
0.447 0.317
Ref 59 for CmTAB, Ref 78 for 12-s-12, Ref 79 for Triton X-100.
Table 1 of the Supporting Information). This is so because the looped conformation of the 12-12-12 surfactant molecules within the micelles results in stronger hydrophobic interactions of 1212-12 molecules themselves than those between 12 and 3-12 and 12-6-12 surfactant molecules. As a consequence, the influence on the micellization from electrostatic screening induced by the addition of Triton X-100 may not be important and the interaction parameter values for these mixtures are smaller than those for Triton X-100+12-3-12 and Triton X-100+12-6-12 mixtures. For the CmTAB+m-s-m binary mixtures examined, with the exception of the CTAB+12-3-12 system which can be considered almost ideal, cmcexp values are close to that of the pure dimeric surfactant. Only when the CmTAB mole fraction in the solution is close to 0.9, cmcexp starts to increase substantially. This result points out that m-s-m molecules can easily partition into the CmTAB micelles, but the CmTAB molecules do not partition well into the pure m-s-m micelles. Tables 3 and 4 show that the non ideality of the CmTAB+12-3-12 systems increases when m decreases, whereas the non-ideality of the CTAB+ms-m ones increases when m increases. This result may be related to the tendency of the components of the mixtures to form micelles with different shapes. The nature of amphiphilic packing in micelles and their structural geometry was predicted by Israelachvili in terms of a packing parameter, P, defined by the relation P ) V/Alc74 where lc is the maximum effective length of the hydrophobic chain of a monomer, A is the surface area of the headgroup, and V is the volume of the hydrophobic chain considered to be fluid and incompressible. Both lc and V can be obtained for saturated hydrocarbon chains from the proposed formulas of Tanford.75 The other parameter required to calculate P was A and, as an approximation,68 the authors used Amin (the
headgroup cross-sectional area at cmc), obtained by tensiometry, in order to calculate P. Since Amin instead of A was used for all the surfactants investigated, differences between these two areas will not affect the qualitative discussion of the results. Table 5 summarizes the values of lc, V, and A () Amin) for those CmTAB and m-s-m surfactants for which Amin is available in the literature. One can see that for CmTAB+123-12 binary systems, the difference between the packing parameters of the two components increases when m decreases. With respect to the DTAB+12-s-12 binary systems, the difference in the packing parameter of the pure surfactants, that is, in the shape of the micelles formed by the pure components of the mixture, increases when s decreases. The authors did not find the Amin values for 142-14 and 16-s-16 surfactants. However, as in the case of the monomeric surfactants, P is expected to increase when m increases, for a given s value. Therefore, the difference in the packing parameters of the two pure components of the CTAB+m-2-m systems will increase when m increases. Finally, and following the same reasoning, the difference in the shape of the micelles formed by CTAB and 16-s-16 surfactants will increase upon increasing s. It is worth noting that one of the Gibbs energy contributions to micellization is the deformation Gibbs energy of the surfactant tail.76 This contribution, which is positive, increases when the packing parameter increases for a given hydrophobic chain length. Therefore, a decrease in P favors micellization. It is interesting to point out that differences in the shape of micelles not only affect the hydrophobic interactions between the two components of the mixtures within the micellar core, but also the electrostatic interactions at the mixed micelles surface (among other contributions to the Gibbs energy of micellization).
11948 J. Phys. Chem. B, Vol. 112, No. 38, 2008
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This would mean that the non-ideality observed when the difference in the packing parameter of the components increases, will be the result of hydrophobic as well as electrostatic interactions between the two surfactants present in the mixed micelles. For mixed micelles, equation 12 can be used in order to calculate the effective packing parameter:20
Peff )
( ) V Alc
) eff
ΣVi Xi (ΣAi Xi)(Σ1ci Xi)
(12)
Table 5 shows the values of the packing parameter for the binary mixtures studied in this work and those of DTAB+122-12 binary systems. P values corresponding to the DTAB+122-12 mixtures show that the incorporation of DTAB into the 12-2-12 micelles results in a decrease in P; that is, the addition of a spherical micelle-forming surfactant to a threadlike micelleforming surfactant would be expected to inhibit progressively the capacity of the latter to form such micelles when the surfactants comicellized. This is in agreement with cryoTEM measurements carried out with DTAB+12-2-12 mixtures,77 which indicate that in fact DTAB and 12-2-12 do comicellize. When the P values corresponding to the pure components of the system differ substantially, comicellization will result in significant P variations. Changes in the deformation Gibbs energy contribution will follow and, as a consequence, nonideal behavior is expected for these binary systems. Taking this into account, one would expect that the non-ideality of the binary systems would increase when difference in the packing parameters of the two components of the mixture increases. Table 5 shows that variations in Peff for the CmTAB+12-3-12 mixtures augment when the hydrophobic chain length, m, decreases. The non-ideality of these systems follows the same trend. For the DTAB+12-s-12 binary systems changes in Peff follow the trend DTAB+12-5-12 < DTAB+12-4-12 < DTAB+12-3-12 < DTAB+12-2-12, in approximated agreement with the tendency shown by the average β value. Consideration of tendencies of the two surfactants, present in the mixed micelles, to form aggregates of different shapes could also explain approximately the trend shown by the average β values for CTAB+m-s-m mixtures. For Triton X-100+12-s-12 mixtures, the tendency of the two components of the binary system to form micelles with different shapes can also contribute to their non-ideal behavior. Triton X-100 forms preferentially spherical micelles (see Table 5). The packing parameter of the dimeric surfactant 12-12-12 is substantially lower than that for 12-3-12 and 12-6-12 due to the looped conformation of the spacer group. This indicates that 12-12-12 molecules show a stronger tendency to form spherical micelles than 12-3-12 and 12-6-12, and it would explain the more ideal behavior of the Triton X-100 + 12-12-12 systems as compared to Triton X-100 + 12-312 and Triton X-100+12-6-12. Conclusions In this work, the influence of the hydrophobic chain length and the spacer group length on non-ideality of binary monomeric-dimeric surfactant mixtures was investigated. Several mixtures were examined and it was found that non-ideality, as determined by the average -β value and the excess Gibbs energy of micellization, -GE, follows the trends CTAB+123-12 < TTAB+12-3-12 < DTAB+12-3-12 < DeTAB+12-312, DTAB+12-5-12 ≈ DTAB+12-4-12 < DTAB+12-3-12, Triton X-100+12-12-12 < Triton X-100+12-3-12 ≈ Triton X100+12-6-12,CTAB+12-2-12
