Journal of Molecular Liquids 142 (2008) 136–142

Contents lists available at ScienceDirect

Journal of Molecular Liquids

j ourna l homepage: www.e lsev ie r.com/ locate /mol l iq

Non-ideal behavior of mixed micelles of cationic gemini surfactants with varyingspacer length and anionic surfactants: A conductimetric study

Yujie Wang, Eduardo F. Marques ⁎Centro de Investigação em Química, Department of Chemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre, no. 687, P-4169-007 Porto, Portugal

⁎ Corresponding author. Tel.: +351 22 0402 535; fax:E-mail address: efmarque@fc.up.pt (E.F. Marques).

0167-7322/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.molliq.2008.06.001

A B S T R A C T

A R T I C L E I N F O

Article history:

Mixtures of cationic and a Received 27 February 2008Received in revised form 2 June 2008Accepted 3 June 2008Available online 8 June 2008

Keywords:Gemini surfactantsCatanionic mixturesNon-idealConductivity

nionic surfactants (catanionic mixtures) are often highly non-ideal, exhibitingstrong synergism in their interfacial properties, manifested for instance in significant reduction of themixture critical micelle concentration (cmc) and enhanced adsorption onto surfaces. The magnitude of sucheffects is of fundamental interest and has important application-related uses (e.g. in detergent formulation).In this work, the micellization process of mixtures of cationic gemini surfactants of the alkanediyl-α,ω-bis(alkyl dimethylammonium bromide) type, denoted by 12–n–12 (where n is the spacer length), with severalcommon anionic surfactants has been investigated by electric conductivity. For the purpose of comparison,cationic–cationic mixtures, where dodecyltrimethylammonium bromide is the second cationic surfactant,have also been investigated. The cationic/anionic mixtures show relatively significant deviations from idealbehavior, depending on the structure of the gemini surfactant and the anionic surfactant. The interactionparameter β12, within Rubingh's non-ideal model for mixed micelles, has been calculated for each mixture,as well as the mixed micelle composition as a function of mixture composition. The observed synergism inthe different mixtures is interpreted in terms of the molecular structure of the surfactants and correspondinghead–head and chain–chain interactions.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Gemini or dimeric surfactants consist of two amphiphilic moieties,charged or uncharged, covalently linkedbya spacer group, usually at theheadgroup level. The chemical nature, length and conformationalflexibility of the spacer may vary considerably and thus a wide class ofamphiphiles is formed. Over thepast 10–15 years, these surfactants havebeen subject to intensive scrutiny, in view of their versatile and efficientphysico-chemical properties in aqueous solution [1–3]. Gemini surfac-tants exhibit lower values for the critical micelle concentration (cmc)and higher surface activity than their parentmonomeric surfactants [3].Furthermore, the spacer length can considerably affect the interfacialand aggregation properties. For instance, for geminis of them–n–m, 2Xtype, where m is the alkylquaternary ammonium chain length, X thecounterion and n the length of a polymethylene chain, it is seen that forconstant m=12 and varying n in the range 2–18, the cmc attains amaximum at n=6. Concomitantly, the aggregation structures varygradually from long micelles to small micelles and then lamellar ag-gregates (vesicles) as n increases [4].

The investigation of aqueousmixtures of geminiswith other types ofamphiphiles has been much less explored [5,6]. However, the funda-mental and technical interest of surfactant mixtures is obvious, sinceuponmixing some interfacial and colloidproperties (e.g. surface activity,

+351 22 0402 559.

l rights reserved.

foaming, wetting, viscosity, self-assembly) are drastically changed, andthus may be enhanced or, at least, advantageously manipulated [7–12].

From a thermodynamic viewpoint, mixed surfactant systems oftenshow non-ideal behavior in their interfacial properties. Non-idealitymay be particularly significant when there are strong intermolecularinteractions (leading to strong association), as is clearly the case ofcationic–anionic mixtures [5,8,9,13]. However, the details of thechemistry of the surfactants also play a role in the degree of synergism.It is a challenging task to relate the synergistic properties, e.g. largereduction of the mixture cmc, with the molecular structure of the co-solutes. For the case of geminis, some theoretical work has been donerelating molecular architecture and phase behavior in a broad sense[14,15], but more experimental data is needed.

In this work, we have investigated the micellization behavior ofseveral cationic–anionic mixtures (often designated as catanionicmixtures) involving several alkanediyl-α,ω-bis(alkyl dimethylammo-nium bromide) geminis, 12–2–12, 12–6–12 and 12–10–12. The anionicsurfactants comprise sodium dodecylsulphate (SDS), sodium dodecano-ate (SD) and the bile salt sodium taurodeoxycholate (STDC). Themolecular structures of all the amphiphiles can be seen in Fig. 1. Oneof our main goals has been to measure the extent of synergism forcatanionic mixtures comprising gemini cationic amphiphiles andcommon monomeric anionic surfactants. Further information is to beobtained on the influence of spacer length (n=2, 6 and 10) and anionicsurfactant chemistry (sulphate and carboxylate headgroups) on themixture cmc and micellar composition. We also point out the choice of

Fig. 1. Molecular structure of the surfactants used in this study: (a) gemini alkanediyl-α,ω-bis(dodecydimethylammonium bromide), where n=2, 6 and 10, abbreviated hereas 12–2–12, 12–6–12 and 12–10–12; (b) sodium taurodeoxycholate, STDC; (c) sodiumdodecylsulphate, SDS; (d) sodium dodecanoate, SD; and (e) dodecyltrimethylammo-nium bromide, DTAB.

137Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

the bile acid salt STDC in this study. Bile acid salts are physiologicallyrelevant amphiphiles with a peculiar structure, consisting of a rigidhydrophobic portion (a cholic ring systemwith2 or 3OHgroups), and anunusual aggregation behavior [16–18]. A common feature of reportedmixtures of bile salts with various surfactants is the formation of largemicellar solutionphases, as exemplifiedby the STDC/didodecyldimethy-lammonium [19] and sodium deoxycholate/DTAB mixtures [20];however, quantitative studies on the extent of synergism–and itsrationalization, especially in comparison with flexible-chained anionicsurfactants–are scarce, if non-existent, in the literature.

The interaction parameter within Rubingh's model for non-idealmixtures has been thus determined for these catanionic systems.Furthermore, for the purpose of comparison, cationic–cationicmixtures of geminis with dodecyltrimethylammonium bromide(DTAB) have also been investigated.

2. Experimental section

2.1. Materials

The gemini surfactants were synthesized and purified according tothe method described by Menger [21]. The following materials wereused for the synthesis, without further purification: N,N,N′,N′-tetra-methylethylenediamine (99%, Aldrich), 1-bromododecane (97%,Aldrich),1,6-dibromohexane (96%, Aldrich), 1,10-dibromodecane (97%,Aldrich), 1-dimethylaminododecane (97%, Fluka). The high purity of theproducts was confirmed by NMR, elemental analysis, surface tensionand DSC. The surfactants sodium taurodeoxycholate, STDC (N97%),sodium dodecylsulphate, SDS (N99%), sodium dodecanoate, SD (99–100%), and dodecyltrimethylammonium bromide (DTAB, 9%) werepurchased from Sigma and used without further purification, since theobtained cmcvalues checkedby surface tensionwere in good agreementwith tabulated values. All solutionswere preparedwithwater producedby a Milli-Q system.

2.2. Conductivity measurements

The electrical conductivity of single andmixed surfactant solutionswas measured with a CDM210 Conductivity Meter (CDC641Telectrode, France) in a double-wall vessel with flowing thermostatedwater at T=(303.1±0.1) K. The conductimeter was initially calibratedwith standard solutions of KCl 0.01 and 0.1 mol dm−3

. Themeasurement for single surfactants was carried out by graduallyadding small aliquots of concentrated surfactant solution into a dilute

solution. For mixed surfactant systems the measurement was carriedout by adding successive aliquots of two concentrated solutions ofeach individual surfactant into the conductivity cell to form a dilutecatanionic solution. For the measurements, the equilibration timesvaried between 5 and 30min and the conductivitywas recordedwhenits fluctuation was less than 1% for at least 2 min.

3. Non-ideal mixing model: brief description

Several theoretical models have been developed which account fornon-ideal mixing in binary surfactant mixtures [9,22–26]. In thissection we briefly review the relevant expressions and their physicalmeaning for Rubingh's model [22], used in this paper.

The mixtures have an approximately ideal behavior if the surfactantheadgroups are chemically similar and differences reside only in chainlength. For ideal mixing, the cmc of the mixture arises from the con-tributionof the respective surfactants,1 and2, in themicelle according to:

cmc12 ¼ xm1 d cmc1 þ 1−xm1� �

d cmc2 ð1Þ

where cmc12, cmc1 and cmc2 are the cmc of the mixture, of surfactant1 and of surfactant 2, respectively, and x1

m is the mole fraction ofsurfactant 1 in the micelle. From Eq. (1) one can easily obtain, by massconservation, Eqs. (2) and (3),

1=cmc12 ¼ x1=cmc1 þ 1−x1ð Þ=cmc2 ð2Þ

xm1 ¼ x1d cmc2= x1d cmc2 þ 1−x1ð Þd cmc1f g ð3Þ

which relate cmc12 and x1m with x1, the mole fraction of surfactant 1 in

themixture. Since the cmc and themole fraction for each surfactant inthe mixture are known, one can readily predict the mixture cmc12 andthe micellar composition from the single surfactant parameters.

However, nonionic/ionic and cationic/anionic surfactant mixturesdeviate considerably from ideal mixing, in particular the latter [10].Rubingh's non-ideal model is based on the pseudo-phase separationmodel for micellization and the regular solution approximation,having been successfully tested with experimental data for severalsurfactant mixtures [22]. Activity coefficients are introduced forsurfactants 1 and 2 in the mixture, f1 and f2 respectively, and so Eq.(2) is modified to yield:

1=cmc12 ¼ x1=f1cmc1 þ 1−x1ð Þ=f2cmc2: ð4Þ

The model introduces also a dimensionless interaction parameterβ12,which reflects themagnitudeof thenet interactionbetween the twosurfactants and is constant for a given temperature. β12 is also anestimation of the excess enthalpy of mixingHE, since the excess entropySE is assumed to be zero (regular solution approximation), according to:

HE ¼ β12d xm1 d 1−xm1

� �RT: ð5Þ

For ideal systems (no net interaction), β12=0; for systems with anet attraction (synergistic), β12b0; for systems with a net repulsion(antagonistic), β12N0. Further development of the model yields thefollowing central expressions:

x1d cmc12 ¼ xm1 d cmc1d exp β12 1−xm1� �2h i

ð6Þ

1−x1ð Þd cmc12 ¼ 1−xm1� �

d cmc2d exp β12 xm1� �2h i

: ð7Þ

Eqs. (6) and (7) can be solved iteratively to yield x1m and β12 from

the experimental values of critical micelle concentrations of surfactant1 (cmc1), of surfactant 2 (cmc2) and of the mixture (cmc12).

Fig. 2. Specific conductivity vs. concentration for the single surfactants, atT=303.1K: (a)DTAB(□); SDS (○); SD (△); (b) 12–2–12 (■); 12–6–12 (▲); 12–10–12 (▽) the bile salt STDC (⋄).

138 Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

It should be noted that there are mixtures for which theassumptions of the regular solution approximation do not hold.Rubingh's model has been originally developed for nonionic mixturesbut it has been shown to provide very useful descriptions of non-ideality in a wide range of mixtures containing ionic surfactants,including cationic–anionic mixtures [7–10].

4. Results and discussion

4.1. cmc determination of single and mixed surfactants

Fig. 2(a) shows the curves of specific conductivity vs. concentrationfor the surfactants SDS, SD and DTAB and Fig. 2(b) for the gemini

Table 1The cmc and degree of counterion dissociation, α, of surfactants measured withconductivity

Surfactant 103cmc/(mol dm−3) α

This worka Literatureb This worka Literatureb

12–2–12 0.93 0.90 [28] 0.19 0.22 [34]12–6–12 0.99 1.03 [34] 0.37 0.33 [34]12–10–12 0.61 0.63 [34] 0.52 0.54 [34] ·DTAB 15.5 15.5 [28] 0.29 0.25 [33], 0.24 [35]STDC 2.0 2.3 [27] 0.95 –

SDS 7.9 8.1 [27] 0.39 0.27 [30]SD 15.6 – 0.63 –

a Values for 303.1 K.b Values for 298.1 K.

surfactants and the anionic surfactant STDC. The cmc values can bedetermined by the intersection of the two straight lines above andbelow the inflection point, and as can be seen in Table 1, they are ingood agreement with reported values from the literature. Table 1 alsoshows the degree of counterion dissociation from the micelles, α, forthe single surfactants, measured as the ratio between the post-micellization slope and pre-micellization slope.

For the cationic–cationic mixtures 12–n–12/DTAB, the cmc valuesand α could also be determined by this simple method, in somecompositions, due to the clear inflection region, as shown in Fig. 3(a).However, the conductivity curves show an increasingly weakerchange in slopes before and after micellization, as the molar fractionof DTAB increases. Also, for SD, STDC (Fig. 2a and b, respectively) andthe 12–n–12/anionic mixtures, as exemplified by 12–6–12/SDS inFig. 4, the difference of slopes of the two straight lines is small. Thismeans that the cmc obtained by this method has a relatively largeuncertainty and it has to be determined with other methods. For suchsystems with small slope difference in the two regions, severalapproaches have been previously discussed [27–32]. Here we plot theconductivity change between every two determinations vs. totalsurfactant concentration, so as to make the inflection evident, Fig. 3(b). Thismethodwas used in combinationwith the one above, in orderto obtain more reliable average cmc values.

Fig. 3. Conductivity data for the 12–6–12/DTAB mixtures, at T=303.1 K: (a) the specificconductivity vs. total surfactant concentration for the different molar fractions of DTAB,increasing from 0 to 1 with the arrow including 0.05 and 0.95; (b) the change of specificconductivity between every two determinations vs. total surfactant concentration for 12–6–12/DTAB mixtures, with different molar fractions of DTAB. Legend: (■), x12–2–12=0.20;(▲) x12–2–12=0.40; (●) x12–2–12=0.60; (▼) x12–2–12=0.80.

Fig. 4. The specific conductivity (■), the specific conductivity change between everytwo determinations (●, inner right-hand axis), and the specific conductivity changeafter interaction of oppositely charged surfactants (▲, outer right-hand axis), vs. thetotal concentration of a 12–6–12/SDS mixture with x12–6–12=0.70, at T=303.1 K.

Fig. 5. The degree of counterion dissociation, α, for the gemini–DTAB and gemini–SDSmixtures as a function of molar fraction of gemini surfactant 12–n–12 (with n=2, 6, 10),at T=303.1 K. Legend: (■), 12–2–12/DTAB; (●), 12–6–12/DTAB; (▲), 12–10–12/DTAB;(▼), 12–2–12/SDS; (♦), 12–6–12/SDS. The lines are guides for the eyes only.

139Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

For the cationic/anionic surfactant mixtures, a third method wasused (Fig. 4). Concentrated cationic surfactant and anionic surfactantsolutions are sequentially titrated into the conductivity cell withoutprevious mixing. For example, for the 12–6–12/SDS mixture, after bothsurfactants are added to the cell, the equilibrium conductivity ismeasured at the total concentration of the mixture (Fig. 4, shown assolid squares), and used to obtain the cmc andα, asmentioned for Fig. 2,even though there are relatively large errors. The difference of specificconductivity corresponding to two consecutive determinations is shownas a solid circle, asmentioned for Fig. 3(b). It is interesting to observe therespective conductivity after adding 12–6–12 or SDS. When concen-trated 12–6–12 is added into the cell, the conductivity rises to a certainvalue, but once some SDS is added into it, the conductivity drops downdue to the interaction of SDS with excess of 12–6–12. The differencebetween the conductivities after and before adding SDS is plotted vs.concentration (Fig. 4, shown as solid triangles). The magnitude of thedifference before and after the interaction decreases with the totalsurfactant concentration. Interestingly, the slopes of the two sections(linear or non-linear) above and below cmc are different, and the twosections are linked by a short line (with a near-zero slope). To be noted isthat the short line always appears for every mixture at different molefractions, in the whole mixing range, except for xSDS=0.55. Bycomparison with the methods in Figs. 2 and 3, this far end of the shortline corresponds to the cmc.

This is a new approach for cmc determinations in mixed systemswith cationic/anionic surfactants. It appears to be more suitable thanother methods, according to the present results. The cmc valuesobtained from the three methods in Fig. 4 are 0.60 mM (●), 0.57 mM(■), and 0.56 mM (▲), respectively.

The phenomenon in Fig. 4 can be interpreted by consideringinteractions between surfactants and between surfactant and counter-ions in the system. Counterions are the main contribution to theconductivity of the solutions due to their larger ionic mobility. The totalconcentration of the counterions increases with increasing surfactantconcentration, so that the conductivity always increases with the totalconcentration. The slope difference before and after cmc arises fromchanges of counterion association. Because the ionic pairs in the mixedsurfactants are formed before the cmc, the slope difference (shown assolid square) is much smaller than that of the single surfactant. The plotof specific conductivity change between every determination extractsthe conductivity change from the total conductivity, which makes theinflection at the cmc more evident (shown as a solid circle).

The case of the specific conductivity after interaction of oppositelycharged surfactants is more complex. First, some amount of 12–6–12

is added into the solution, so it is reasonable to picture the excessmolecules of 12–6–12 as free cationic surfactant and Br−, stronglyincreasing the conductivity of the solution. Then some SDS is added,and the dissociated SD−, as a Lewis base, reacts with the 12–6–12cation, as a Lewis acid, to form a catanionic pair with head-to-head, oreven head-to-head plus tail-to-tail, pairing, which causes lower ionicstrength and then lower conductivity of the solution. Above the cmc,the dissociation of counterions decreases and the slope becomessmaller. Near the cmc, the surfactants may form mixed pre-micellaraggregates with small aggregation number and the slope differs fromthe slopes before and after cmc. In this case, the mid section shouldnot be a real level line but have a small slope (due to decreasingconductivity), but the present measurements might not be sensitiveenough to detect this effect. With this treatment the plot shows threesections and not two like the former ones. It should be emphasizedthat the specific conductivity difference after interaction of cationic/anionic surfactants changes from positive to negative, with thenegative value meaning an increase of specific conductivity.

4.2. Determination of the degree of counterion dissociation

The values of the degree of counterion dissociation calculated for thegemini–DTAB and the gemini–SDS mixtures, as a function of molarfraction of gemini surfactants, are shown in Fig. 5. For the gemini–DTABsystems, a common trend can be observed. As DTAB is added into neatgemini or gemini-rich solutions, α increases gradually up to 0.80 atxi≈0.95. Then it decreases steeply to the value of neat DTAB (α=0.29). Asimple explanation for this effect is the following. As DTAB is added tothe mixed micelle, the cmc does not change much but the headgrouprepulsions in the micellar surface should decrease gradually, due to the“dilution” effect provided by the DTABmolecules.Moreover, since DTABis a single-chained surfactant, compared to the double-chained gemini,packing effects should also act as to increase the average area perheadgroup. Hence,more counterions can be released gradually from thesurface as xDTAB increases. At the DTAB-rich side, a small addition ofgemini induces a large decrease in themixture cmc; this effect should bebehind the significant increase in dissociation as one goes from neatDTAB micelle to the mixed micelle at xDTAB=0.95.

For the gemini–SDS mixtures the ratio between post-micellar andpre-micellar slopes in the conductivity plots has small values, even forsmall molar fractions of the minority surfactant. This means that thecalculated α has large values and the error associated is somewhatlarge (we estimate it at about ±0.1). There are only a few studies of

140 Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

counterion dissociation in catanionic mixtures, for comparisonpurposes. For the DTAB/SDS catanionic mixture, for xSDS=0.10 theobtained α was 0.50 [33], whereas in the 12–2–12/SDS for xSDS=0.10,α is about 0.90. Assuming that the α values represent the true degreeof ion dissociation of the micelles, the high values could simply reflectthe large electrostatic interactions between the gemini and SDS, dueto the high charge density of the gemini headgroups.

Fig. 7. The cmc of the mixtures 12–2–12/SD, 12–2–12/SDS, and 12–2–12/STDC vs. molefraction of SD, SDS, and STDC, respectively, at T=303.1 K. Legend: mixture of 12–2–12and: (●) SD; (□) SDS; (×) STDC. Dotted lines a, b and c are, respectively, the cmc of 12–2–12/SD, 12–2–12/SDS, and 12–2–12/STDC, calculated with the ideal mixing model. Thefull line represents the fitting of the non-ideal model to the 12–2–12/SDS mixture (theothers were omitted for clarity of picture). Note: phase separation occurs in thefollowings ranges, 0.07≤xSD≤0.85, 0.35≤xSTDC≤0.95, 0.63≤xSDS≤0.77.

Fig. 6. The cmc of themixtures of DTABwith (a) 12–2–12, (b) 12–6–12 and (c) 12–10–12as a function of mole fraction of DTAB, at T=303.1 K. The solid points representexperimental results; the dotted line with no point represents values calculated fromthe ideal mixing model.

4.3. Comparisons between mixture cmcs

Fig. 6 shows the cmc12 of the mixtures of Gemini surfactants andDTAB obtained from conductivity measurements and calculated withthe ideal mixingmodel, according to Eqs. (1) and (2). For the three pairsof surfactants, the molecules of gemini surfactants and DTAB haveidentical hydrophobic chains and similar headgroups. However, eachmolecule of gemini surfactants has two headgroups connected with apolymethylene spacer that has 2, 6, and 10 carbon atoms (Fig.1a).WhenxDTABb0.4, the experimental cmc12 for the three pairs of surfactants arevery close to the ideal mixing ones, which means the componentsexhibit practically ideal behavior in themixedmicelle.When xDTABN0.4,the experimental cmc12 values are below ideal values because moreDTABmolecules are incorporated in themicelle and synergistic behaviorconcomitantly arises.

In Figs. 7 and 8, it can be seen that the cmc12 values of themixturesof 12–n–12/SD, 12–n–12/SDS, and 12–n–12/STDC are smaller thanthose of the unmixed surfactants in a large composition range. For themixtures of the cationic gemini surfactants, 12–n–12, and the anionicsurfactants, electrostatic interactions are very strong, so that largesynergistic effects are exhibited. Thus cationic/anionic mixtures oftenform insoluble catanionic surfactant complexes or large aggregates(such as vesicles), for which the definition of a cmc has no meaning atthat mixing ratio range. So, when inspecting Figs. 7 and 8, one shouldnote that there is an insolubility (two-phase) region for each mixture.For the case of 12–2–12 (Fig. 7), the two-phase regions occur for0.07≤xSD≤0.85; 0.35≤xSTDC≤0.95; 0.63≤xSDS≤0.77. For 12–6–12 mix-tures (Fig. 8), the two-phase regions occur for: 0.50≤xSDb0.90;0.45≤xSTDC≤0.90; the 12–6–12/SDS mixture shows no phase separa-tion. For the case of 12–10–12/anionic mixtures, also investigated inthis work, a precipitate region is found for a very wide compositionrange, roughly 0.1≤xanionic≤0.9, irrespective of anionic surfactant,suggesting that when the spacer is long and flexible enough acatanionic solid is largely stabilized compared to mixed micelles.

When comparing 12–2–12/anionic and 12–6–12/anionic mixtures,the two-phase regions are wider for the former, possibly due to thestronger attractive interactionsowing to thehigher charge densityof the12–2–12 headgroup (short spacer). For the same gemini surfactant, theinsoluble region of the SD mixture is always the largest, followed bySTDC and then SDS. Thus, for the shorter spacer geminis there is a strongdependence of the insolubility of the catanionic complex upon thechemical nature of the anionic surfactant.

Fig. 9.Mole fraction of SDS in the mixed micelle vs. mole fraction of SDS in the mixture,for the 12–2–12/SDS system, at T=303.1 K. Dotted line: ideal model. Full line and (□):non-ideal model.

Fig. 8. The cmc of the mixtures 12–6–12/SD, 12–6–12/SDS, and 12–6–12/STDC vs. molefraction of SD, SDS, and STDC, respectively, at T=303.1 K. Signs: mixture of 12–6–12 and:(●) SD; (□) SDS; (×) STDC. Dotted lines a, b and c are, respectively, the cmcs of 12–6–12/SD, 12–6–12/SDS, and 12–6–12/STDC, calculated with the ideal mixing model. The fullline represents the fitting of the non-ideal model to the 12-6-12/SDS mixture (theothers were omitted for clarity of picture). Note: phase separation occurs in thefollowings ranges, 0.50≤xSDb0.90; 0.45≤xSTDC≤0.90; the 12–6–12/SDS mixture showsno phase separation.

141Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

The anionic dodecanoate is a stronger Lewis base than taurodeoxy-cholate and dodecylsulphate, so it tends to interact with geminisurfactants to form ionic pairs or large aggregates with lower solubility.STDCandSDShave similarheadgroupsbut utterlydifferenthydrophobicparts. Since the hydrophobic chains of SDS and the gemini surfactantshave the same type of structure, they easily mix together, due tohydrophobic interactions, to form the core of a mixed micelle. But thehydrophobic part of STDC consists of a rigid slightly non-planar cholicacid ring (Fig. 1b), so that it is more difficult to assemble into a mixedmicelle with the alkyl chains of gemini surfactants than to form aninsoluble catanionic complex. Therefore, the different molecularstructures of SD, STDC and SDS (Fig. 1) contribute to the differentphase behavior of their mixtures with gemini surfactants. Figs. 7 and 8also show the calculated cmc12 according to ideal mixing. They presentlarge deviations from the real behavior, confirming the strong interac-tions between the oppositely charged surfactants.

4.4. Rubingh's interaction parameter and molecular interactions

With the experimental cmc12 data, Rubingh's interaction para-meter, β12, can be obtained from Eqs. (6) and (7) through an iterativecalculation method. Average β12 values of the oppositely chargedsurfactant pairs are shown in Table 2. For the surfactant pairs with thesame gemini surfactant, the order of interaction strength isSDNSDSNSTDC. Furthermore, the interaction strength of the pairswith 12–2–12 is always stronger than that with 12–6–12, for the sameanionic surfactant. These results coincide with the qualitativeinterpretation of the existence range of the insoluble region asdiscussed above. For the 12–10–12/anionic surfactant systems a widetwo-phase region (precipitate and solution) was always obtained and,thus, no interaction parameter can be obtained.

The β12 values for cationic–anionic mixtures are typically in therange −10 to −25 [10], reflecting the strong headgroup attractionsleading to significant non-ideal effects. For the cationic gemini/anionic

Table 2The pair interaction parameter β12 for gemini–anionic surfactant mixtures

Gemini Gemini/STDC Gemini/SDS Gemini/SD

12–2–12 −4.1 −6.2 −9.812–6–12 −1.4 −6.2 −6.2

Typical uncertainty in β12: ±10%.

mixtures studied here the values are somewhat lower in magnitude(Table2). This suggests that the spacer in thegemini amphiphile (Fig.1a),which tends to lie flat in the water–hydrocarbon interface when nb10[3], weakens the attractive interaction with the monomeric anionicsurfactant, as there should be some unfavorable packing constraints inthemixedmicelle. For 12–2–12, since it has a shorter spacer than 12–6–12, the constraints may be slightly weaker and, together with a highercharge density of the headgroup region, this should lead to morefavorable attractive interactions with anionic surfactants; hence, toslightly more negative β12 values, as effectively seen with SD and STDC(Table 2). Neat 12–2–12 is known to form micelles with largeaggregation numbers already at the CMC, that quickly grow withconcentration to long threadlike micelles [3,28]. It is therefore reason-able to assume that these large micelles would easily accommodate theanionic amphiphile and grow even more, due to partial chargeneutralization, while keeping the elongated shape. On the other hand,neat 12–6–12 formsmuch smaller, spheroidal micelles [3]. Upon uptakeof the anionic amphiphile theywill also grow, buthere onecan speculatethat the growth is likely more limited in view of the packing constraintsimposed by the gemini, presumably resulting in slightly non-spheroidalshapes. For 12–10–12, the long spacerhashigh conformationalflexibilityand can more easily bend toward the hydrophobic core. This allows forless hindered headgroup attractions in the mixtures and, at the same

Fig. 10.Mole fraction of anionic surfactant i in the mixed micelle vs. mole fraction of i inthe mixture, at T=303.1 K, for the 12–6–12/surfactant i systems, where i stands forSTDC, SDS or SD in the specific mixture. Dotted lines: ideal model; full lines andsymbols: non-ideal model. Legends: curve (a) and symbol (×), mixture 12–6–12/STDC;curve (b) and symbol (□), 12–6–12/SDS; curve (c) and symbol (●), 12–6–12/SD mixture.

142 Y. Wang, E.F. Marques / Journal of Molecular Liquids 142 (2008) 136–142

time, enhanced hydrophobic interactions. Thus, a solid phase can bestabilized for a very wide cationic/anionic mixing ratio, in detriment ofmixed micelles in solution.

The β12 values of the gemini/DTAB systems are not constant butdecrease monotonically as the molar fraction of DTAB increases (datanot shown here). This indicates that Rubingh's treatment does notapply to these particular mixtures. Even though the exact explanationfor this is not known, one could in principle deduce that the regularsolution approximation (negligible SE compared to HE) should nothold for these mixtures in view of the weak gemini/DTAB headgroupinteractions.

4.5. The composition of the mixed micelles

The mole fraction of surfactant 1 in the mixed micelle can beobtained simultaneously with β12 through iterative calculations basedon Eqs. (6) and (7) and it is now designated as x1m,R (where R stands forRubingh's model). The mole fraction of 1 in the micelle with idealmixing behavior, designated as x1m,I (where I stands for ideal), can becalculated from Eq. (1). For the systems of gemini/DTAB mixtures,since non-constant β12 values were obtained, as stated above, thederived micelle compositions are not meaningful. For the case ofgemini/anionic mixtures, however, the results are interesting.

The deviations of x1m,R from x1m,I, apparent in Figs. 9 and 10, are

generally very pronounced. Fig. 9 shows the mole fraction of SDS inthe micelle as function of its mole fraction in the mixture with 12–2–12. Fig. 10 shows the mole fraction of anionic surfactant component inthemixedmicelle as a function of its mole fraction in themixture with12–6–12.

For an ideal mixture, the component with a smaller cmc has alarger molar ratio xi

m in the micelle than xi in the solution according toEq. (2). This implies that for ideal gemini/anionic surfactant mixtures,the mixed micelle bears a net positive charge for a wide bulkcomposition range, evenwhen there is excess anionic surfactant in thebulk. This statement is still valid for non-ideal mixing. However, in thiscase, xim dependents simultaneously on the difference of cmcs of thetwo components and the interaction parameter β12 (Eqs. (6) and (7)).The interaction between the two components enhances the incor-poration of anionic surfactant into the mixed micelles, resulting in alarger x1m,R than x1

m,I, as can be seen in Figs. 9 and 10. Hence for both12–2–12 and 12–6–12 geminis, the mole fraction of SDS or SD in themixed micelles is much larger than that predicted by the ideal model.For the case of the STDC/12–6–12 mixture the deviation x1

m,R from x1m,I

is relatively smaller, which is in agreement with the small absolutevalue of β12.

5. Conclusions

The cmc values of surfactant mixtures involving cationic 12–n–12(n=2 and 6) and anionic surfactants have been measured byconductivity methods as function of the mixing ratio. All mixturesshow synergistic effects, with negative values for the interactionparameter, β12. However, the latter is somewhat lower in magnitudethan what is observed for cationic/anionic mixtures involving

monomeric surfactants (e.g. DTAB/SDS). For the mixtures containing12–2–12, the interaction increases in the order SDNSDSNSTDC, whilefor 12–6–12 the order goes as SD≈SDSNSTDC. For the same anionicsurfactant, the interaction with 12–2–12 is always stronger than thatwith 12–6–12. These results have been qualitatively interpreted interms of interaction constraints imposed by the gemini architecture.For the 12–10–12/anionic surfactant systems, the phase behavior isdominated by a very wide two-phase region (precipitate andsolution).

Acknowledgments

Y.W. is grateful to Fundação para a Ciência e Tecnologia (F.C.T.),Portugal, for a post-doc scholarship, ref. SFRH/BPD/6979/2001. Wekindly acknowledge financial support from F.C.T., Portugal, and FEDERFunds, through the research project POCTI/QUI/44296/2002, and C.I.Q.(U.P.)-linha 5, F.C.T., Portugal.

References

[1] F.M. Menger, C.A. Littau, J. Am. Chem. Soc. 115 (1993) 10083.[2] F.M. Menger, J.S. Keiper, Angew. Chem. Int. Ed. 39 (2000) 1906.[3] R. Zana, Adv. Colloid Interface Sci. 97 (2002) 205.[4] L. Grosmaire, M. Chorro, C. Chorro, S. Partyka, S. Lagerge, Thermochim. Acta 379

(2001) 255.[5] Y. Wang, G. Bai, E.F. Marques, H. Yan, J. Phys. Chem B 110 (2006) 5294.[6] Y. Wang, E.F. Marques, J. Phys. Chem. B 110 (2006) 1151.[7] J.F. Scamehorn (Ed.), Phenomena in Mixed Surfactant Systems, A.C.S., Washington,

D.C., 1986.[8] K. Ogino, A. Masahiko (Eds.), Mixed Surfactant Systems, Marcell Dekker, New York,

1993.[9] P.M. Holland, in: P.M. Holland, D.N. Rubingh (Eds.), Mixed Surfactant Systems, A. C. S.,

Washington D. C., 1992.[10] A. Khan, E. Marques, in: I.D. Robb (Ed.), Specialists surfactants, Blackie Academic

and Professional, an imprint of Chapman & Hall, London, 1997, pp. 37.[11] E. Marques, O. Regev, A. Khan, M. Miguel, B. Lindman, J. Phys. Chem. B 102 (1998)

6746.[12] E.F. Marques, O. Regev, H. Edlund, A. Khan, Langmuir 16 (2000) 8255.[13] A. Khan, E.F. Marques, Curr. Opin. Colloid Interface Sci. 4 (2000) 402.[14] K.M. Layn, P.G. Debenedetti, R.K. Prud’homme, J. Chem. Phys. 109 (1998) 5651.[15] T.A. Camesano, R. Nagarajan, Colloids Surf. A 167 (2000) 165.[16] M.C. Carey, D.M. Small, Arch. Intern. Med. 130 (1972) 506.[17] E.F. Marques, H. Edlund, C.L. Mesa, A. Khan, Langmuir 16 (2000) 5178.[18] B. Lindman, N. Kamenka, B. Brun, J. Colloid Interface Sci. 56 (1976) 238.[19] E.F. Marques, O. Regev, H. Edlund, A. Khan, Langmuir 16 (2000) 8255.[20] C.L. Mesa, A. Khan, K. Fontell, B. Lindman, J. Colloid Interface Sci. 103 (1985) 373.[21] F.M. Menger, C.A. Littau, J. Am. Chem. Soc. 113 (1991) 1451.[22] P.M. Holland, D.N. Rubhing, J. Phys. Chem. 87 (1983) 1984.[23] A. Graciaa, B.G.M., G. Marion, J. Lachaise, J. Phys. Chem. 93 (1989) 4167.[24] Z.-J. Yu, G.-X. Zhao, J. Colloid Interface Sci. 156 (1993) 325.[25] E. Haque, A.R. Das, A.K. Rakshit, S.P. Moulik, Langmuir 12 (1996) 4084.[26] E. Rodenas, M. Valiente, M.S. Villafruella, J. Phys. Chem. B 103 (1999) 4549.[27] P.J. Jana, S.P. Moulik, J. Phys. Chem. 95 (1991) 9225.[28] R.G. Alargova, I.I. Kochijaskhky, M.L. Sierra, R. Zana, J. Colloid Interface Sci. 235

(2001) 119.[29] J. Zhao, S.D. Christian, B.M. Fung, J. Phys. Chem. B 102 (1998) 7613.[30] F.H. Quina, P.M. Nassar, J.B.S. Bonilha, B.L. Bales, J. Phys. Chem. 99 (1995) 17028.[31] N. Jalsenjak, D. Tezak, Chem. Eur. J. 10 (2004) 5000.[32] M.S. Bakshi, J. Singh, K. Singh, G. Kaur, Colloids Surf. A 237 (2004) 61.[33] K.L. Herrington, E.W. Kaler, D.D. Miller, J.A. Zasadzinski, S. Chiruvolu, J. Phys. Chem.

97 (1993) 13792.[34] R. Zana, M. Benrraou, R. Rueff, Langmuir 7 (2001) 1072.[35] R. Zana, J. Colloid Interface Sci. 78 (1980) 330.