Synergistic effects in micellization and surface tension reduction in nonionic gemini S-10 and cationic RTAB surfactants mixtures

Accepted Manuscript Title: Synergistic effects in micellization and surface tension reduction in nonionic gemini S-10 and cationic rtab surfactants mixtures Author: A. Trawicka E. Hallmann K. M˛edrzycka PII: DOI: Reference:

S0927-7757(15)30268-5 http://dx.doi.org/doi:10.1016/j.colsurfa.2015.10.008 COLSUA 20216

To appear in:

Colloids and Surfaces A: Physicochem. Eng. Aspects

Received date: Revised date: Accepted date:

30-7-2015 5-10-2015 8-10-2015

Please cite this article as: A.Trawicka, E.Hallmann, K.M˛edrzycka, Synergistic effects in micellization and surface tension reduction in nonionic gemini S-10 and cationic rtab surfactants mixtures, Colloids and Surfaces A: Physicochemical and Engineering Aspects http://dx.doi.org/10.1016/j.colsurfa.2015.10.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

SYNERGISTIC EFFECTS IN MICELLIZATION AND SURFACE TENSION REDUCTION IN NONIONIC GEMINI S-10 AND CATIONIC RTAB SURFACTANTS MIXTURES A. Trawickaa, E. Hallmanna, K. Mędrzyckaa,* a

Gdańsk University of Technology, Chemical Faculty, Narutowicza str. 11/12, 80-952 Gdańsk, Poland *Corresponding author: [email protected], tel: (48) 583472469

1. Graphical abstract 1

Synergism in mixed micelle formation

0.02

0.8

0.015

S-10

XMRTAB

cmc [mol/dm3]

DTAB

Mixed micelles composition

0.01

0.6

0.4 0.005

S-10 : DeTAB S-10 : DTAB S-10 : TTAB S-10 : CTAB X= a

0.2 cmcid (ideal) cmcex (experimental)

0

0 0

0.2

0.4

aDTAB

0.6

0.8

1

0

0.2

0.4

aRTAB

0.6

0.8

1

2. 3. 4. 5. 6. 7. HIGHLIGHTS 8. 9. 10. We examined mixtures of nonionic gemini and classical cationic surfactants 11. Strong synergy in mixed micellization was stated in S-10+RTAB surfactants mixtures 12. Synergy in surface tension reduction efficiency is weaker than in cmc reduction 13. The alkyl chain length affect the composition of mixed film and mixed micelle 14. S-10 incorporate into mixed film preferably than into mixed micelle

Abstract. Mixtures of nonionic gemini surfactant S-10 ( α, α'-[2,4,7,9-tetrametyl-5-decyne4,7-diyl]bis[ω-hydroxy -polioxyetylene] with cationic alkyltrimethylammonium bromides of different alkyl chain length (RTAB) were investigated. Basing on surface tension measurements the cmc values and other adsorption parameters were found. The Clint, Rubing’s and Rosen theories were applied for evaluation of the synergistic effects in mixed films and mixed micelles formation. The molecular interaction parameters have negative values in all investigated mixtures, which confirm attractive forces between components. The magnitude of this forces depends on mixtures composition and in mixed micelles was higher than that in mixed films. It has been documented that in the process of micellization strong synergy exists, while in mixed film formation it is not so evident and was stated only in surface tension reduction efficiency. The composition of mixed films is different than the composition of mixed micelles, because a molar fraction of S-10 in monolayers is much higher than its contribution in mixed micelles at the same bulk composition. Keywords: gemini surfactant, alkyltrimethylammonium bromides, synergism, mixed micelles, mixed monolayers 1. INTRODUCTION Surfactants mixtures are widely investigated due to their possible synergistic behavior. Synergy is defined as the situation such that the properties of a mixture are better than those attainable by the single components separately [1]. Synergism in mixed surfactant system can be related to efficiency and effectiveness in surface tension reduction, mixed micelle formation, efficiency in decreasing cmc and C20 values [1-3], foaming and froth flotation [4,5] wetting and solubilizing power [6,7], detergency, dispergation and emulsification properties [7,8]. Recently the Gemini–type compounds have received a great attention because of their behavior in mixtures with other surfactants [9,10]. These compounds are much more surface active in comparison to their single head group homologues (conventional equivalents). A considerable number of investigations have reported their remarkable physicochemical properties like high surface activity, unusual micelle structure and strong interaction with other surfactants. Nowadays, the binary mixtures containing ionic gemini surfactants with other types of conventional surfactants are widely investigated because these systems exhibits synergistic behavior, sometimes even more prone than binary mixtures of conventional surfactants. Some reports relates to mixtures containing anionic Gemini surfactants [11-15]. For example Tsubone [15] studied molecular interactions between an anionic gemini surfactant (GA) having N,Ndialkylamide and carboxylate groups in a molecule with conventional anionic surfactants (SDS and AGS) and indicated that the GA/SDS mixture exhibits synergism in both, surface tension reduction efficiency and effectiveness, also in mixed micellization, while the GA/AGS mixture exhibits synergism only in surface tension reduction effectiveness. However, majority of investigations concentrate on mixtures with cationic gemini’s [16-28]. Wang and co-workers [17] indicated that mixtures of cationic gemini surfactants 12-n-12 (n = 2 and 6) with conventional anionic surfactants (SD, SDS, STDC) exhibits synergistic effects in mixed micelles formation, with negative values for the interaction parameter, β. Many other researchers also have been studying systems containing cationic gemini surfactants with other anionic [23, 27], cationic [19],

nonionic [13, 24, 26] and zwitterionic [19, 25] surfactants and they have found different types of synergism, especially in mixed micelle formation. It results also from many other publications, that the mixtures containing ionic gemini surfactants usually reveal synergy. However, it is not so evident in case of nonionic gemini’s. In the literature one can find only a few studies which focused on the properties of nonionic gemini surfactants [29-37], and even fewer on their mixtures with ionic conventional surfactants. Basing on reports about properties of conventional nonionic/ionic surfactants mixtures one can expect that synergistic behavior is possible also in case of nonionic gemini’s. Thus, the objective of the current study was to investigate the mixed nonionic gemini with conventional cationic surfactants systems behavior, and especially interesting seemed to be the evaluation of the interaction between different surfactants molecules, what may result in synergistic effects. Molecular interactions between two surfactants at the interface or in micelles are commonly measured by interaction parameters, β. The β parameter indicates degree of interaction between two components and also accounts for the deviation from ideality. The β value can be negative, positive or equal to zero, which indicate the synergistic, antagonistic or ideal mixing, respectively. The β is the interaction parameter for mixed monolayer formation at the aqueous solution/air interface and βM is the interaction parameter for mixed micelle formation. There are different theories and models, describing molecular interaction. In this research the obtained results were quantitatively evaluated on the basis of Rubingh’ regular solution theory (RST), which was developed for mixed films [38, 39] and similar theory relating to mixed micelles, described by Rosen [1]. According to Rosen theory [1, 39], the mole fraction of component 1 in the mixed film (X1) and regular solution interaction parameter (β) are computed using the following equations: 1=( =

⁄ )

(

)

⁄(

⁄ (

)

(1) (2)

)

where α1 – is the mol fraction of surfactant 1 in total mixed solute, , and the molar concentrations of components 1, 2 and their mixture at the mole fraction α1, respectively, required to produce a given surface tension  value.

are

The micellar mole fraction of component 1 (X1M) and interaction parameter for mixed micelle formation (βM) are computed from below equations, formulated by Rubingh [38]: 1=

(

=

)

(3)

(4)

where , and are the critical micelle concentrations (cmc) of components 1, 2 and their mixture at the mole fraction α1 , respectively. The interaction parameters values are a measure of probable synergism existance. However, when other prerequisite suggests the synergistic behavior, the interaction parameters are needed to confirm the synergy. In this paper three types of synergistic effects are considered and very shortly they are characterized below. Synergism in the mixed micelle formation exists when the cmc of the mixture is lower than that of each amphiphile of the mixture ( < ; ) and it is confirmed when the following conditions are fulfilled [1]: 1. βM is negative 2.  βM >  ln (C1M/C2 M)  Synergism in surface tension reduction efficiency is observed, when the total concentration of mixed surfactant solution required to reduce surface tension of water to a given value (e.g. by 20 mN/m) is less than that, of the individual component and it is confirmed when the following conditions are fulfilled [1, 39]: 1. β is negative 2. β  > ln (C1/C2 )  where C1 and C2 are the molar concentrations of surfactant 1 and 2, respectively, required to achieve the same surface tension. Synergism in effectiveness in surface tension reduction exists when the mixture of two surfactants reaches the surface tension value at its cmc (cmc ) lower than that, attained at the cmc of individual surfactants solutions [40]. An additional conditions for synergism in surface tension reduction effectiveness to exist are: 1. β - βM is negative 2. β - βM > [ln (C1 /C2 ) - ln (C1M/C2M)] In the current research the adsorption properties in mixed, nonionic gemini surfactant, Surfynol 465 (S-10) with classical cationic (RTAB) surfactants systems were investigated. The aim of the research was searching for synergism in mixed films as well, as in mixed micelles formation, and analysis of alkyl chain length effect on synergism extent.

2. EXPERIMENTAL 2.1 Materials Nonionic gemini surfactant S-10 ( α, α'-[2,4,7,9-tetrametyl-5-decyne-4,7-diyl]bis[ωhydroxy -polioxyetylene], Fig. 1) was obtained from Air Products and Chemicals, Inc. and it was used as received. ). This compound was earlier investigated in respect to its micellization [35-37], however, only one paper relates to its mixtures with other surfactants [41]. Fig.1. Molecular structure of nonionic gemini surfactant S-10 ( α, α'-[2,4,7,9-tetrametyl-5-decyne-4,7diyl]bis[ω-hydroxy -polioxyetylene]) where: R’ = (CH2CH2O)m – H; R” = (CH2CH2O)n – H; m + n = 10; [37]

Cationic surfactants used in experiments were alkyltrimethylammonium bromides (RTAB) with different alkyl chain length (from 10 to 16 carbon atoms). Decyltrimethylammonium bromide (DeTAB), dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB) and hexadecyltrimethylammonium bromide (CTAB) were purchased from Fluka and were recrystalized two times from acetone before application. The experiments were carried out for individual surfactants solutions and for four, independent series of mixed solutions of S-10 + RTAB. In the initial bulk solutions in each series the mole fractions of cationics (α 1) varied from 0.05 to 0.95. Aqueous solutions of surfactants were prepared using doubly distilled water (conductivity 5.4S/m). 2.2 Methods 2.2.1 Surface tension measurements The surface tension was measured using the drop shape analysis method (Krűss DSA 10 Mk2 tensiometer) at 298 K. The apparatus is controlled by a personal computer, equipped with image analysis software and a pendant drop shape analysis software. The time to achieve equilibrium was between 10 and 30 min. Time dependence of the surface tension was determined from evolution of the droplet shape. The reproducibility of the surface tension measurements was within 0.2 mN/m. The surface tension was measured for each solution and the obtained results were plotted as surface tension versus surfactants concentration dependences, separately for each series. 2.2.2 Micelle size determination The micelle size distribution was investigated by DLS method (dynamic light scattering), using Zetasizer Nano ZS apparatus (Malvern Instruments Ltd., Malvern, UK). From size distribution curves the mean diameter of the micelles was found. These investigations were carried out for solutions of concentrations above the cmc values.

3. RESULTS AND DISCUSSION 3.1 Adsorption at the air/water interface In Fig. 2 the surface tension isotherms for single surfactants and for their mixtures of selected compositions are presented. The isotherms for other compositions are not presented in the figure, due to the great similarity in runs of particular curves. However,all isotherms (those presented and not presented here) were used for calculation of adsorption parameters, collected in Tables 1-3.

Fig.2. Plots of surface tension () wersus concentration (logC scale) in solutions of pure surfactants (gemini S-10 and cationic DeTAB, DTAB, TTAB, CTAB) and their mixtures of different composition. Values in brackets (α1) denotes RTAB molar fraction in the mixture.

From Figure 2 it appears that the shape of curves for mixtures of α equal 0.5 or lower is similar to that for gemini S-10 rather, than to curves for RTAB (except for the mixture with CTAB, Fig.2d). The higher the α value, the closer to RTAB isotherm lie curves for mixtures. Each isotherm curve was used to find the cmc value and other adsorption parameters. The experimental critical micellar concentration (cmcex) was found from the dependence of surface tension, versus the logarithm of surfactant concentration at the intersection of two linear segments of the isotherm. The cmcex values are collected in Table 1 (also for mixtures not presented in Fig. 2). The Clint equation (eq. 5) describing the ideality in the mixed micelle formation was used to calculate the theoretical ideal mixed cmcid [42].

1 1 1  1   cmcid cmc 1 cmc 2

(5)

where α1 – is the mol fraction of surfactant 1 in total mixed solute, cmc1 and cmc2 are the critical micellar concentrations of components 1 and 2, respectively (identical with and in equations 1-4), and cmcid is the theoretical ideal mixed cmc. These values are also presented in Table 1. In our systems index 1 relates to cationic surfactants, RTAB, while index 2 refers to gemini S-10. From the experimental isotherms other parametrs like cmc , pC20, max and Amin were also found. The pC20 (the efficiency of the surfactant in reducing the surface tension of water) is the log of molar surfactant concentration, required to reduce the surface tension by 20 mN/m. The value of surface tension at the cmc, cmc , is defined as effectiveness in surface tension reduction. The cmc/C20 ratio is a measure of tendency of the surfactant to adsorb at the air/water interface, relative to its tendency to form micelles. The max (the maximum surface excess) was calculated from Gibbs equation and Amin (the minimum surface area per molecule) was calculated from max value. For the mixtures, if there is no interaction between the two components in the mixed monolayer, the ideal molecular area value, Aid , was calculated from equation 6. Aid = X1A1 + (1 - X1)A2

(6)

where X1 refers to the molar fraction of RTAB component in the mixed monolayers, and cross sectional areas A1 and A2 designate the cationic and nonionic gemini surfactants, respectively. All these data are collected in Table 1. As it can be seen from Table 1 the Amin values increase slightly as the alkyl group length in RTAB molecule rises from C10 to C16 (experimental Amin , Aex = 42.1; 47.4; 56.8 and 52.1, respectively). For S-10 the Amin value equals 59.3. For mixtures the Amin values depend on their composition (Table 1). In case of all mixtures with DeTAB and DTAB (except at DTAB = 0.95), the experimental Amin values (Aex ) are higher than those, for individual surfactants in the whole range of composition (Table 1). Mixing of gemini and above mentioned cationic surfactants causes that the package of molecules in the mixed monolayer is looser than that, in the film of single surfactant. A different situation we observe in mixtures with TTAB and CTAB, where the Aex values are higher than Aex for individual surfactants only at low content of RTAB in mixture (at 1 = 0.05; 0.1 or 0.3), while at their high content (1 = 0.7; 0.9 or 0.95), the Aex values are lower than that for single components, which is a result of stronger attraction (or weaker repulsion) when contribution of cationic component in the mixture is dominating (Table 1).

In table 2 the parameters of mixed films formation are presented and in Table 3 the parameters of mixed micellization are collected. As it is documented in Tables 2 and 3, the activity coefficients of surfactants in mixed films (f  ) and mixed micelles (f M) are lower than 1 in the whole investigated range of mole fractions, indicating attractive interactions between surfactants in mixed film as well, as in mixed micelles, which means that the state of surfactants in both is far from the ideal one. Activity coefficient values rise with the increase of particular surfactant mole fraction in the mixed solution. For cationic surfactants these values are the higher, the more surface active is compound (the longer is the alkyl chain in RTAB molecule). Thus, for CTAB they are the highest and for DeTAB are the lowest. The opposite relation is observed when analyze activity coefficient of gemini surfactant; its highest values are reached in mixtures with DeTAB, while the lowest – in mixtures with CTAB.

3.2 Molecular interactions The calculated β and βM values for all investigated systems are presented in Tables 2 and 3. In all investigated mixtures the interaction parameters β and βM have a negative values, what indicate that attractive interactions between molecules of S-10 and RTAB are stronger than the self-interaction of the two surfactants before mixing. Besides, the βM values are higher than the β values, which means that the attraction in the micelles are stronger than in the monolayer. However, analyzing the β parameter values one can state that generaly molecular interactions are not strong (as β  < 6), and the strongest were observed for the mixtures of S-10 + DTAB. As it can be seen in table 3, the higher the mole fraction of RTAB in the mixture, the lower the interaction parametr βM, which means that interactions in the micelles are weaker. Generally, interactions in the mixed micelles are stronger than interactions in the mixed films, as βM values are about 1.5-2 times higher than the values of β  (tables 2 and 3). This difference may be explained considering the distance between alkyl chains, which is greater in the flat monolayer than in the core of the spherical micelle. Thus, the hydrophobic attraction, stabilizing monolayers and micellar aggregates, is stronger in micelles, what results in higher βM values (comparing to β values). The length of the alkyl chain in the RTAB, do not affect the β value significantly, and only slightly stronger interaction is observed in mixtures of S-10 with DeTAB, while the weakest one, in mixtures with CTAB. It can be observed for mixed micelles as well, as for mixed films. The stronger interactions in case of DeTAB may result from the fact, that this cationic surfactant have alkyl chain of similar length to that in S-10 molecule, while in CTAB molecule the alkyl chain is much longer. When compare the interaction parameters for mixtures of S-10 with anionic surfactants presented by Rosen and Zhou [41] (β were –2.37 and –1.93, while βM equal –2.9 and –2.47 for mixtures with X1 = 0.19 of C12SO3Na and X1 = 0.04 of C12E2S, respectively), with those, obtained in the current research for S-10 mixtures with cationic RTAB’s, one can observe that in respect to β parameter the values are about 1.5 - 2 times higher and only in case of mixtures with DeTAB they are about three times higher (table 2). In respect to βM in all mixture with RTAB the values are about 2.5 to 3 times higher than those, obtained by Rosen for S-10 mixtures with anionics. It means that molecular interactions of gemini S-10 with RTAB cationics are stronger than interactions with mentioned anionics, especially in mixed micelles. The interaction of S-10, stronger with cationics than with anionics may result from oxyethylene group properties. Polyoxyethylene chain have a large number of oxygen

atoms with unpaired electrons, which may have a tendency to react coulombically with cationic surfactant, what causes the increase of interaction parameter [24].

3.3 The composition of mixed films and mixed micelles As it can be seen from Table 2 the mole fractions of cationic surfactants in mixed monolayers (X1 ) are lower than the stoichiometric mole fractions of these compounds in solution. This indicates that the transfer of gemini surfactant from the solution into the monolayer is preferential in comparison with transfer of cationics. The opposite situation (preferential transport of cationics) is observed only at low 1 value (1 < 0.1 for DeTAB and DTAB or 1 < 0.5 for CTAB). When analyze the X1 values from Table 2 one can see that they are the higher, the longer is the alkyl chain, R. This is in agreement with lower Aex values in mixed monolayers, which results from stronger attraction between longer chains. Thus, the longer the alkyl chain in the RTAB molecule, the more compact is the molecular package in mixed monolayer. In Fig. 3 the plots of mole fraction of RTAB (X RTAB ) in the mixed films, versus their bulk fraction (α RTAB ) in S-10 + RTAB mixtures are presented. It can be seen from this figure that mixed film composition (X ) depends on bulk composition (α) and is different for different RTAB in the mixtures. Comparing to bulk composition the mixed film is enriched in RTAB only at their lower bulk mole fraction, while at their high bulk mole fraction, the mixed film is more rich in nonionic gemini S-10. The mixed film composition similar to bulk composition (X = α) is observed at different bulk ratio, depending on cationic component. For CTAB it is attained at α value about 0.6. In case of TTAB, DTAB and DeTAB these values are about 0.25, 0.2, 0.1, respectively. So, except of mixtures with CTAB, the S-10 dominate in the mixed films within the wide range of bulk compositions. The preferential transfer of S-10 molecules to monolayer should be analyzed in the context of S-10 structure. S-10 molecule contains a triple bond between carbon atoms, which makes this molecule rigid and having a tendency to locate in a flat position at the interface. On the contrary, the RTAB molecules having longer and flexible linear alkyl chains have problem to compete with S-10 molecules in location at the flat free surface. Fig.3. Plots of mole fraction of RTAB (X RTAB ) in the mixed film, versus their bulk fraction (αRTAB ) in S-10 + RTAB mixtures. The solid lines are guides for the eyes. The dotted line represents similar composition in both, bulk and mixed film (X = α).

In Fig. 4 the variation in micellar mole fraction (XM) of alkyltrimethylammonium bromides (RTAB) versus their bulk mole fraction (αRTAB) is presented. The dotted line represents the systems, in which the composition of mixed micelles is the same as bulk composition (XM = α). Fig. 4. Plots of micellar mole fraction of RTAB (XM RTAB ), versus their bulk fraction (α RTAB) in S-10 + RTAB mixtures. The solid lines are guides for the eyes. The dotted line represents similar composition in both, bulk and mixed miceles (XM = α);

It can be seen from Fig. 4 that mixed micelles composition similar to bulk composition (XM = α) is observed at different bulk ratio, depending on cationic component, and for DeTAB, DTAB, TTAB and CTAB it is attained at αRTAB values about 0.35, 0.45, 0.67, and 0.78, respectively. For other values of αRTAB the micelles are enriched in one of the components, comparing to bulk composition. Thus, below mentioned α values the mole fractions of RTAB components in micelles are higher than their content in bulk, while above

these values the micelles contain more S-10 than its bulk fraction indicate. The longer the alkyl chain in cationic surfactant, the greater the range of molar fraction, where RTAB contribution in mixed micelle is higher than that in bulk. What is more, the range of RTAB bulk fraction at which they enrich mixed micelles is much greater than that, at which they enrich mixed monolayers. For example mixed micelles are more reach in TTAB comparing to bulk up to αTTAB value about 0.67 while mixed film only up to αTTAB value about 0.25 (Figs 5 and 6). So, considering the content of gemini S-10 in mixed films and mixed micelles one can state that it is higher in comparison with bulk above the αTTAB value of 0.25 and 0.67, respectively. Let’s analyze the systems with bulk composition of RTAB:S-10 = 9:1 (bulk fraction of S-10 equals 0.1). When compare the molar fraction of S-10 in mixed film (XS-10 ) and in mixed micelle ( XMS-10) one can observe that for mixtures with each RTAB, the fraction X is higher than XM. For mixtures with DeTAB they equal respectively 0.69 and 0.46, for mixtures with DTAB – 0.53 and 0.35, for mixtures with TTAB – 0.23 and 0.20, for mixtures with CTAB – 0.23 and 0.15. So, the biggest differences between X and XM are observed for mixtures of S-10 with DeTAB, and the smallest differences for mixtures with TTAB and CTAB. When analyze the system of α RTAB equal to 0.3 (α S-10 equal 0.7), the observed relations are similar. The values of XS-10 are higher than α S-10 for all mixtures, except those with CTAB (0.81, 0.78, 0.73 and 0.58 for mixtures with DeTAB, DTAB, TTAB and CTAB, respectively), while the values of XMS-10 are smaller than α S-10 (0.65, 0.59, 0.48 and 0.35, respectively). Summarizing, one can say that at higher fractions of RTAB surfactants in bulk, their contribution to mixed films and mixed micelles are smaller than in bulk, while contribution of S-10 is higher than its bulk fraction. And on the contrary, at lower bulk fractions of RTAB, their fractions in mixed films and mixed micelles are higher, while S-10 fractions are lower, than those in bulk. The above considerations have led us to conclusion that S-10 molecules accumulate in the mixed films preferably in comparison to incorporation into mixed micelle. On the contrary, the tendency of RTAB molecules to form mixed micelles is greater than their tendency to form mixed films. Thus, one can state that at big disproportion in bulk composition (e.g. α equal to 0.1 or 0.9) the dominating component contributes to smaller than α value fractions in both, mixed film and mixed micelle (X and XM are less than α ). At intermediate values of α fraction (e.g. 0.3 – 0.7) there are differences in preferential accumulation of surfactant molecules in mixed film and in mixed micelle and it depends on type of surfactant. It has been documented that S10 preferentially adsorb in the mixed film when compare with accumulation in mixed micelles, while RTAB oppositely, incorporate into the mixed micelle preferentially, comparing to adsorption in mixed film. From the literature report [41] it is known, that S-10 in mixtures with anionic surfactants behave similarly. For its high bulk fraction (αS-10 values equal to 0.812 and 0.959 in mixtures with C12SO3Na and C12E2S, respectively) the molar fraction in mixed films were higher (0.64) than the fraction in mixed micelles (0.50) and both were lower than α values). However, the differences between fraction in mixed films and mixed micelles were not so significant and were much smaller than that, observed in the current research for mixtures of S-10 with cationic RTAB. From many literature reports results that nonionic gemini surfactants usually incorporate into mixed micelles preferably in comparison with incorporation into mixed monolayers. Micelles are easier formed if the structure of surfactant molecule is flexible and linear. The opposite behavior of S-10 gemini surfactant is probably an effect of a rigid structure of its molecule, containing triple bond between carbon atoms, what makes formation a monolayer at a flat interface favorable in comparison with micelles formation.

3.4 Synergism In the current research the possible synergism in surface tension reduction efficiency and effectiveness, and in mixed micelle formation was considered. The calculated molecular interaction parameters, β and βM have negative values for all mole fractions of all investigated mixtures (Tables 1 and 2), which suggest that interactions in mixed films and mixed micelles are more attractive (or less repulsive) than that, in single components systems. Thus, one may expect that synergism in surface tension reduction as well, as in mixed micelle formation does exist. 3.4.1 Synergism in surface tension reduction efficiency Synergism in surface tension reduction efficiency exists when the concentration of surfactant mixture required to decrease surface tension of water by 20 mN/m (C20) is lower than concentrations required in individual surfactants solutions. The magnitude of the negative log of the C20 value (pC20) can be a measure of surface tension reduction efficiency. The values of pC20 for all investigated systems are collected in Table 1. It can be seen that C20 concentration for mixtures is lower (pC20 is higher) than C20 for single surfactants solutions only at low contribution of cationic surfactants in the mixtures (1 lower or equal to 0.5) (Table 1). Only for the mixtures of S-10 with CTAB lower C20 values (higher pC20) are observed almost in the whole range of bulk composition. For the confirmation of the synergistic effects in surface tension reduction efficiency the additional requirements (described above) were analyzed. They were the interaction parameter β and the value of expression: ln(C1/C2) calculated for  equal 40 mN/m. All these data are summarized in Table 2. The negative values of all β suggest that synergism in surface tension reduction efficiency may exist in mixtures of S-10 with all investigated RTAB, in the whole range of mixtures compositions (Table 2). On the other side, the second condition (β  >  ln (C1/C2 )  ) should be also fulfilled. It has been found that in case of mixtures with CTAB and TTAB this condition is fulfilled. In case of S-10 mixtures with other cationics such condition is not fulfilled entirely, as β  value is higher than  ln (C1/C2 )  only at high mole fraction of S10 (low t  = 0.5, 0.9 and 0.95 for mixtures with DTAB and at  0.7, 0.9 and 0.95 in the mixtures with DeTAB this condition is not fulfilled (Table 2). These results confirm the former conclusion, based on pC20 values, that at low aRTAB values (athe synergism in surface tension reduction efficiency exists in S-10 mixtures with all RTAB, while at higher aRTAB values (a> 0.5) it is observed only in mixtures with CTAB. The above analysis leads to conclusion that negative value of interaction parameter,  β , may only imply the synergism existence, but is not a definite proof. 3.4.2 Synergism in effectiveness in surface tension reduction Synergism in effectiveness in surface tension reduction exists when the mixture of two surfactants reaches cmc value lower than that attained at the cmc of individual surfactants. From the surface tension isotherms presented in Fig. 2 the values of surface tension at the cmc (cmc), have been found. In Fig.5 the cmc values for all investigated systems are presented. It is clearly visible that the surface tension value at cmc (cmc ) is the lowest for S-10 (27.17 mN/m) and the highest for RTAB (almost the same value for all RTAB - about 35 mN/m), while for mixtures the intermediate values are typical. Thus, one can conclude that synergism in effectiveness of surface tension reduction by mixtures of S-10 and RTAB surfactants is not

observed. Verification of this conclusion was based on analysis of molecular interaction parameters, presented in tables 2 and 3. The values of β are lower (table 2) than βM (table 3), so β - βM values are in all cases positive, but not negative. The second condition β - βM > [ln (C1 /C2 ) - ln (C1M/C2 M)] is also not fulfilled (see, values in tables 2 and 3), which means that synergism in surface tension reduction effectiveness, is not observed in the investigated systems. Fig. 5. Dependence of surface tension at the cmc (cmc) versus mole fraction of RTAB in surfactants mixtures. The solid lines are guides for the eyes.

3.4.3 Synergism in the mixed micelle formation This type of synergism exists when the cmc of the mixture is lower than the cmc of each component individually. Besides, as it was already mentioned, such synergism is confirmed when following conditions are fulfilled: βM is negative and βM >  ln (C1M/C2 M) . The experimental cmc values (cmcex ), obtained for all series of measurements are presented in Figs 6a – 6d as points and solid lines, while theoretical cmc (cmcid,) calculated from Clint model (eq.5) are presented as dashed lines. These values are also shown in Table 1. Fig. 6. Plots of cmc vs αRTMABr in the S-10 + RTAB mixtures. Experimental cmc - points and solid lines which are guides for the eyes; cmcid predicted from Clint model - dashed lines.

In spite of the fact that graphical forms of isotherms for all compositions reveal great similarity in runs (Fig. 2), the critical micellar concentrations for mixtures differ from that of single components and in all cases are lower than the cmc of single S-10 and RTAB. They are also lower than the ideal mixing cmc values (cmcid , dashed lines). However, the decrease of mixture’s cmc value depends on the difference between single components cmc. One can observe that the highest deviation of cmcex from cmcid occurs in case, when the difference in cmc values of individual components is the smallest. This takes place for mixtures of S-10 + DTAB (cmc = 11.0 and 15.4 mM/l, respectively, see, fig. 6b). For example the ideal cmcid value for equimolar composition is 12.8 mM/l, while experimental cmcex value was 4.4 mM/l (see also Table 1). And on the contrary, the smallest deviation was observed for mixtures of S-10 with CTAB, where the difference between cmc values for individual components is the highest (cmc =11 mM/l and 0.8 mM/l, respectively, see, Fig. 6d). In this case the ideal cmcid equals 1.5 mM/l and experimental cmcex was 0.8 mM/l for equimolar composition (Table 1). It can also be noticed that for smaller mole fractions of CTAB in the mixture (1 below 0.2) the experimental cmc ex values are only slightly higher than that, for equimolar solution, but the deviation from the ideal cmcid is much higher (Fig. 6d). Thus, summarizing one can state that in all series the negative deviation of experimental cmc values from ideal ones (cmcid), calculated from Clint equation is observed, what suggests the synergistic effects in mixed micelle formation. The calculated parameters of molecular interactions in mixed micelles, βM values, are presented in Table 3. All values are negative, which fulfil the second required condition for synergy. The final confirmation is evident when analyze the data from table 3, as the condition βM >  ln (C1M/C2 M)  is also fulfilled for all investigated mixtures. Thus, the synergism in mixed micelles formation in the systems: S-10 + RTAB is well documented. 3.5 Size of the micelles

In Fig. 7 the micelles diameter in micellar solutions (0.01mol/dm3 ) versus bulk composition is presented. The results relates to mixtures of gemini S-10 with DTAB, TTAB or CTAB. Fig.7. The mean diameter of micelles in the micellar solutions of S-10 and RTAB mixtures

From Fig.7 it results that the micelle size, observed for single components is the bigest for S-10 (about 5.0 nm) and much smaller for single DTAB, TTAB and CTAB (2.81, 2.22 and 1.71 nm, respectively). In case of surfactants mixtures the micelle size is smaller than that, for individual components. This may suggest that incorporation of any RTAB into S-10 micelle decreases its size, probably due to better spacial compaction of the aggregate, as RTAB molecules can fit to the vacances in the S-10 micelle structure. As it can be seen in Fig. 7 a very small addition of RTAB to gemini surfactant results in micelle size decreasing from 5 nm to 2.5 nm (at 0.1 bulk mole fraction of RTAB) and even to 1 nm (equimolar bulk composition). On the other side, the small addition of S-10 to the RTAB surfactants do not change the micellar size so much. These results indicate that RTAB surfactants molecules can easily partition into the micelles formed by S-10 molecules, but the S-10 molecules do not partition well into the micelles of RTAB surfactant. Considering the structure of RTAB and S-10 molecules one can see that it is evident that S-10 could not compete with RTAB in spherical micelles formation, due to the rigid structure of its hydrophobic part. The hydrophobic part of S-10 molecule consists of 10-carbon atoms chain, enlarged with attached 4 methyl groups. Thus, due to the length of alkyl chain, the best fiting could be expected for DTAB, and the worst for CTAB. Besides, comparing the values of interaction parameters βM one can state that the highest attractive forces are observed in mixed micelles of S-10 with DTAB, while the weakest attraction exists in mixed micelles of S-10 with CTAB (Table 3). This may suggest that the amount of DTAB molecules incorporated into mixed micelles is bigger than the amount of CTAB molecules in mixed micelles, what could result in bigger size of S-10+DTAB micelles, as it has been stated experimentally (Fig. 7). Another explanation may be based on the differences between magnitude of attractive and repulsive forces, when the length of alkyl chain in RTAB molecule increases. At the same ionic head groups, the resultant interaction becomes more attractive (or less repulsive), what causes that formed micelles are more compact. 3.6 Free energy of micellization Thermodynamic parameters of micellization are important properties and they are usefull in analysis of synergistic effects in micellization process. Free energy of micelle formation (ΔG0 Ma) has been calculated according to Maeda model [43] and in Fig. 8 versus RTAB mole fraction in the mixture (RTAB) it has been presented. In single-component systems the highest values of ΔG0Ma are observed for CTAB (- 17.69kJ/mol), while the lowest values for DeTAB (- 6.97 kJ/mol). Similar relation is observed for mixtures with S-10, the longer the alkyl chain in RTAB molecule, the lower the ΔG0Ma value. For example, in equimolar systems these values equal to -12.75, -13.48, -15.16 and -17.90 kJ/mol, for mixtures of S-10 with DeTAB, DTAB, TTAB and CTAB, respectively (table 3). Fig.8. Free energy of mixed micelle formation in air/water systems, versus RTAB

From figure 8 it results that the values of free energy of mixed micelle formation are lower (more negative) than the values of free energy of micelles formation by individual components. This was observed in all cases. For example in S-10 + TTAB system the ΔG0Ma values varied from -15.67 to -14.51 kJ/mol, while for single components they equal to -11.18 and -13.81 kJ/mol, respectively. The values of free energy of micellization, lower for

mixtures than for individual surfactants, prove that the mixed micelles formation is energetically preferable in comparison with individual components micellization and confirm the synergy in mixed micellization process. Besides, the excess free energy of mixing Gex has been calculated from equation 6 [16, 43]: Gex = RT(

ln

+

ln

)

(7)

where and refer to the molar fractions of RTAB and S-10, while and are activity coefficients of both surfactants within the mixed micelles. As it can be seen from Table 3 all Gex values are negative and their magnitude decreases with an increase in RTAB value. This suggests that the higher RTAB contribution, the less stable micelles are formed, which may be explained in terms of electrostatic repulsion between heads of ionic surfactants in the aggregate, stronger at higher micellar mole fraction.

4. CONCLUSIONS Commercial uses of dimeric surfactants is still limited because of high costs of their production, that’s why they are often used in combination with conventional surfactants. Such mixtures have many practical applications, as they often exhibit cooperative interactions or synergism in their effects on the properties of a system. In the current research the physicochemical properties of mixtures, containing nonionic gemini and classical cationic surfactants were investigated and synergism in some practical aspects was expected. It has been shown that S-10 (Surfynol 465), nonionic gemini surfactant, reveal strong synergistic effects in mixed micelle formation with cationic surfactants, alkyltrimethylammonium bromides (RTAB). In the wide range of bulk mole fractions (from 0.05 up to 0.95 for RTAB) the cmc values are lower (even 1.56 mM/l), than those, for individual components (11.0 and 9.2 mM/l for S-10 and CTAB, respectively). They are also lower than cmcid calculated from ideal mixing model. The deviation from cmcid depends on the difference between single components cmc, and is the higher, the smaller is this difference. It has been stated strong synergistic effect in mixed micelle formation in case of all systems. The free energy of micellization has more negative values for mixtures than for individual surfactants, which confirm the synergy in mixed micellization process. The β and βM values for all mole fractions of investigated mixtures are negative with evidently higher values at lower content of RTAB, which indicates stronger intermolecular interactions in case of mixtures with dominating fraction of S-10. Besides, these interactions are stronger in mixed micelles comparing to that, in mixed monolayers ( βM > β ). In respect to mixed films formation the synergistic effects are not so evident, in spite of the fact that all β values are negative. The synergy has been found in surface tension reduction efficiency only in a certain range of mixtures composition, depending on alkyl chain length in cationic surfactant molecule. In respect to surface tension reduction effectiveness, the synergism is not observed in any case. Thus, summarizing, one can state that in the investigated systems synergism is quite strong in respect to mixed micelle formation (due to high values of interaction parameter) and what more, it is stronger than the synergism in surface tension reduction efficiency (β  is less than βM). Considering the composition of mixed films and mixed micelles (the molar fractions of particular components) one can conclude that S-10 molecules accumulate in the mixed films preferably in comparison to incorporation into mixed micelles. This tendency is an

effect of rigid structure of its molecule. On the contrary, the tendency of RTAB molecules to form mixed micelles is greater, than their tendency to form mixed monolayers.

ACKNOWLEDGMENT: The authors are grateful to Air Products and Chemicals, Inc. for delivery of gemini surfactant S-10. Aleksandra Trawicka is thankful to Chemical Faculty of TUG for financial assistance.

REFERENCES: 1. Rosen M. J. , Surfactants and Interfacial Phenomena, 3ed ed., John Wiley, New York, (2004). 2. Rosen M. J., Gu B., Synergism in binary mixtures of surfactants. 6. Interfacial tension reduction efficiency at the liquid/hydrophobic solid interface, J. Colloid Surf., 23, (1987), 119. 3. Schwuger M. J., Smolka H. G., Mixed adsorption of ionic and nonionic surfactants on active carbon, Colloid Polym. Sci., 255, (1977), 589. 4. Rosen M. J., Zhu Z. H., Synergism in binary mixtures of surfactants. 7. Synergism in foaming and its relation to other types of synergism, J Am. Oil. Chem. Soc., 65, (1988), 663. 5. von Rybinski W., Schwuger M. J., Adsorption of Surfactant mixtures in froth flotation, Langmiur, 2, (1986), 639. 6. Treiner C., Vaution C., Miralles E., Puisieux F., Influence of sodium dodedecylsulphate and of inorganic electrolytes on the micellar solubilization of butobarbitone in aqueous polyoxyethylene lauryl ether solutions at 293.15 K, Colloid Surf., 14, (1985), 285. 7. Aronson M. P., Gum M. L., Goddard E. D., Behavior of surfactant mixtures in model oily-soil detergency studies, J. Am. Oil Chem. Soc. 60, (1983), 1333. 8. Schwuger M. J., Effects of adsorption on detergency phenomena: II, J. Am. Chem. Soc., 59, (1982), 265. 9. Rosen M. J., Tracy D. J.: Gemini Surfactants. J. Surfactants and Detergents, 4, (1998), 547. 10. Zana R., Xia J., GEMINI SURFACTANTS Synthesis, Interfacial and Solution-Phase Behavior, and Applications, Marcel Dekker inc.New York Bassel, (2005). 11. R. Zana, H. Lévy, K. Kwetkat, Mixed Micellization of dimeric (gemini) Surfactants and conventional Surfactants I. Mixtures of an Anionic Dimeric Surfactant and the Nonionic Surfactants C12E5 and C12E8, Journal of Colloid and Interface Science, 197, (1998), 370-376. 12. J. x. Zhao, X. F. Yang, R. Jiang, Y. H. Ma, J. J. Cao, Adsorption layer structure at the air/water interface in aqueous mixtures of an anionic carboxylate gemini and a cationic surfactant, Colloids and Surfaces A: Physicochem. Eng. Aspects, 275, (2006), 142-147. 13. R. G. Alargova, I. I. Kochijashky, M. L. Sierra, K. Kwetkat, R. Zana, Mixed Micellization of Dimeric (Gemini) Surfactants and Conventional Surfactants II. CMC and Micelle Aggregation Numbers for Various Mixtures, Journal of Colloid and Interface Science, 235, (2001), 119-129.

14. T. Chakraborty, S. Ghosh, Mixed micellization of an anionic gemini surfactant (GA) with conventional polyethoxylated nonionic surfactants in brine solution at pH 5 and 298 K, Colloid Polym Sci 285, (2007) 1665-1673. 15. Tsubone K., The interaction of an anionic gemini surfactant with conventional anionic surfactants, J. Colloid Interface Sci., 261, (2003), 524 16. Kabir-ud-Din, M. S. Sheikih, A. A. Dar, Interaction of a cationic gemini surfactant with conventional surfactants in the mixed micelle monolayer formation in aqueous medium, Journal of Colloid and Interface Science, 333 (2009), 605-612. 17. Wang Y., Marques E. F., Non-ideal behavior of mixed micelles of cationic gemini surfactants with varying spacer length and anionic surfactants: A conductometric study, Journal of Molecular Liquids, 142, (2008), 136-142. 18. M. S. Bakshi, J. Singh, K. Singh, G. Kaur, Mixed micelles of cationic 12-2-12 gemini with conventional surfactants: the head group and counterion effects, Colloids and Surfaces A: Physicochem. Eng. Aspects 237 (2004) 61-71. 19. M. S. Bakshi, J. Singh, K. Singh, G. Kaur, Mixed micelles of cationic gemini with tetraalkyl ammonium and phosphonium surfactants: the head group and hydrophobic tail contributions, Colloids and Surfaces A: Physicochem. Eng. Aspects 234 (2004) 77-84. 20. M. S. Bakshi, K. Singh, Synergistic interactions in the mixed micelles of cationic gemini with zwitterionic surfactants: Fluorescence and Krafft temperature studies, Journal of Colloid and Interface Science, 287, (2005), 288-297. 21. K. Esumi, M. Miyazaki, T. Arai, Y. Koide, Mixed micellar properties of a cationic gemini surfaktant and a nonionic surfaktant, Colloids and Surfaces A: Physicochem. Eng. Aspects, 135, (1998), 117-122. 22. N. Azum, A. Z. Naqvi, M. Akram, Kabir-ud-Din, Studies of Mixed micelle formation between cationic gemini and cationic conventional surfactants, Journal of Colloid and Interface Science, 328, (2008), 429-435. 23. L. Liu and M. J. Rosen, the interaction of some Novel Diquarternary Gemini Surfactants with Anionic Surfactants, Journal of Colloid and Interface Science, 179, (1996), 454-459. 24. K. S. Sharma, P. A. Hassan, A. K. Rakshit, Self aggregation of binary mixtures of a cationic dimeric (gemini) surfactant with nonionic surfactants in aqueous medium, Colloids and Surfaces A: Physicochem. Eng. Aspects, 289, (2006), 17-24. 25. K. Singh, D. G. Marangoni, Synergistic interactions in the mixed micelles of cationic gemini with zwitterionic surfactants: the pH and spacer effect, Journal of Colloid and Interface Science, 315, (2007), 620-626. 26. K. S. Sharma, C. Rodgers, R. M. Palepu, A. K. Rakshit, Studies of mixed surfactant solutions of cationic dimeric (gemini) surfactant with nonionic surfactant C12E6 in aqueous medium Journal of Colloid and Interface Science, 268, (2003), 482-488. 27. Din K., Shafi M., Bhat P. A., Dar A. A., Solubilization capabilities of mixtures of cationic emini surfactant with conventional cationic, nonionic and anionic surfactants towards polycyclic aromatic hydrocarbons, J. Hazardous Materials, 167, (2009), 575. 28. Din K., Sheikh M. S., Dar A. A., Interaction of a cationic gemini surfactant with conventional surfactants in the mixed micelle and monolayer formation in aqueous medium, J. Colloid Interface Sci., 333, (2009), 605. 29. Alami E., Holmberg K., Heterogemini Surfactants Based on Fatty Acid Synthesis and Interfacial Properties, J. Colloid Interface Sci., 239, (2001), 230.

30. Castro M. J. L., Kovensky J., Fernández Cirelli A., New Family of Nonionic Gemini Surfactants. Determination and Analysis of Interfacial Properties, Langmuir, 18, (2002), 2477. 31. FitzGerald P.A., Carr M. W., Davey T. W., Serelis A. K., Such Ch. H., Warr G. G., Preparation and dilute solution properties of model gemini nonionic surfactants, J. Colloid Interface Sci., 275, (2004), 649. 32. FitzGerald P. A., Davey T. W., Warr G. G., Micellar Structure in Gemini Nonionic Surfactants from Small-Angle Neutron Scattering, Langmuir, 21, (2005), 7121. 33. Paddon-Jones G., Regismond S., Kwetkat K., Zana R., Micellization of Nonionic Surfactant Dimers and of the Corresponding Surfactant Monomers in Aqueous Solution, J. Colloid Interface Sci., 243, (2001), 496. 34. Zhou T., Yang H., Xu X., Wang X., Wang J., Dong G.; Synthesis, surface and aggregation properties of nonionic poly(ethylene oxide) gemini surfactants, Colloids and Surfaces A; Physicochem. Eng. Asp., 317, (2008), 339. 35. Sato S., Kishimoto H., Entalpic Studies on the Formation and Interaction of Micelles of a Nonionic Surfynol 465, J. Colloid Interface Sci., 123, (1988), 216. 36. Sato S., Micellar Behavior of a Nonionic Surfactant, Surfynol 465, from 13C NMR Resonance Frequencies in D2O, J. Phys. Chem., 93, (1989), 4829. 37. Nieh M.-P., Kumar S. K., Fernando R. H., Colby R. H., Katsaras J., Effect of the Hydrophilic Size on the Structural Phases of Aqueous Nonionic Gemini Surfactant Solutions, Langmuir, 20, (2004), 9061. 38. Rubingh D. N., Mixed Micelle Solutions in K. L. Mittal (Ed) Solution Chemistry of Surfactants, Plenum Press, New York, Vol. 1, (1979) p.337. 39. Zhou Q., Rosen M. J., Molecular Interactions of Surfactants in Mixed Monolayers at the Air/Aqueous Solution Interface and in Mixed Micelles in Aqueous Media: The regular solution Approach, Langmuir, 19, (2003), 4555. 40. Hua X. Y., Rosen M. J., Conditions for synergism in surface tension reduction effectiveness in binary mixtures of surfactants, J. Colloid Interface Sci., 125, (1988), 730. 41. Rosen M. J., Zhou Q., Surfactant−Surfactant Interactions in Mixed Monolayer and Mixed Micelle Formation, Langmuir, 17, (2001), 3532 42. Clint J.H., Micellization of mixed nonionic surface active agents, J. Chem. Soc., Faraday Trans., 71 (1975), 1327. 43. Maeda H., A simple Thermodynamic Analysis of the Stability of Ionic/Nonionic Mixed Micelles, J. Colloid Interface Sci., 172, (1995), 98. 44. Cuniberti C., Ferrando R., Electron microscope investigation of poly(ethylene oxide) supermolecular particles in solution Polymer, 13, (1972), 379.

CH3

CH3

CH3CHCH2CC

CH3 CH3 CCCH2CHCH3

O

O

R'

R"

Fig.1. Molecular structure of nonionic gemini surfactant S-10 ( α, α'-[2,4,7,9-tetrametyl-5-decyne4,7-diyl]bis[ω-hydroxy -polioxyetylene]) where: R’ = (CH2CH2O)m – H; R” = (CH2CH2O)n – H; m + n = 10; [37]

b) 80

80

70

70

60

60

g [mN/m]

g [mN/m]

a)

50 S-10

40

S-10 + DeTAB (0,1)

DeTAB

-5

S-10 + DTAB (0,1)

30

S-10 + DeTAB (0,9)

20

S-10

40

S-10 + DTAB (0,5)

S-10 + DeTAB (0,5)

30

50

S-10 + DTAB (0,9) DTAB

20 -4

-3

-2

log C

-1

-5.5

80

80

70

70

60

60

50 S-10

40

-3.5

-2.5

-1.5

S-10

40

S-10 + CTAB (0,1)

30

S-10 + CTAB (0,9)

S-10 + TTAB (0,9)

CTAB

TTAB

-5.5

-1.5

S-10 + CTAB (0,5)

S-10 + TTAB (0,5)

20

-2.5

log C

50

S-10 + TTAB (0,1)

30

-3.5

d)

g [mN/m]

g [mN/m]

c)

-4.5

20 -4.5

-3.5

log C

-2.5

-1.5

-5.5

-4.5

log C

Fig.2. Plots of surface tension () wersus concentration (logC scale) in solutions of pure surfactants (gemini S-10 and cationic DeTAB, DTAB, TTAB, CTAB) and their mixtures of different composition. Values in brackets (α1) denotes RTAB molar fraction in the mixture.

1 S-10 : DeTAB

S-10 : DTAB

S-10 : TTAB

S-10 : CTAB

XsRTAB

0.8

0.6

0.4

0.2

0 0

0.2

0.4

0.6

0.8

1

aRTAB

Fig.3. Plots of mole fraction of RTAB (X RTAB ) in the mixed film, versus their bulk fraction (αRTAB ) in S-10 + RTAB mixtures. The solid lines are guides for the eyes. The dotted line represents similar composition in both, bulk and mixed film (X = α).

1 S-10 : DeTAB

S-10 : DTAB

S-10 : TTAB

S-10 : CTAB

XMRTAB

0.8

0.6

0.4

0.2

0 0

0.2

0.4

0.6

0.8

1

aRTAB

Fig. 4. Plots of micellar mole fraction of RTAB (XM RTAB ), versus their bulk fraction (α RTAB) in S-10 + RTAB mixtures. The solid lines are guides for the eyes. The dotted line represents similar composition in both, bulk and mixed miceles (XM = α);

38 36

g cmc [mN/m]

34 32 30 28 26 24 22

S-10+DeTAB

S-10+DTAB

S-10+TTAB

S-10+CTAB

20 0

0.2

0.4

aRTAB

0.6

0.8

1

Fig. 5. Dependence of surface tension at the cmc (cmc) versus mole fraction of RTAB in surfactants mixtures. The solid lines are guides for the eyes.

a)

b)

0.07

0.016 0.014

0.05

cmc [mol/dm3]

cmc [mol/dm3]

0.018

cmcid (ideal) cmcex (experimental)

0.06

0.04 0.03 0.02

0.012 0.01 0.008 0.006 0.004

0.01

0.002 0

0 0

0.2

0.4

aDeTAB

0.6

0.8

1

0.2

0.4

0.6

0.8

1

aDTAB

b)

d)

0.012

0.012

0.01

0.01

cmc [mol/dm3]

cmc [mol/dm3]

0

0.008 0.006 0.004 0.002

0.008 0.006 0.004 0.002

0

0 0

0.2

0.4

aTTAB

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

aCTAB

Fig. 6. Plots of cmc vs αRTMABr in the S-10 + RTAB mixtures. Experimental cmc - points and solid lines which are guides for the eyes; cmcid predicted from Clint model - dashed lines.

6

S-10 + DTAB S-10 + TTAB S-10 + CTAB

5

d [nm]

4

3

2

1

0 0

0.2

0.4

aRTAB

0.6

0.8

1

Fig.7. The mean diameter of micelles in the micellar solutions of S-10 and RTAB mixtures

S-10 + DeTAB

-6

S-10 + DTAB S-10 + TTAB

-8

S-10 + CTAB

DG0Ma [kJ/mol]

-10 -12 -14 -16 -18 -20 0

0.2

0.4

0.6

0.8

1

aRTAB

Fig.8. Free energy of mixed micelle formation in air/water systems, versus RTAB

Table 1. Adsorption parametrs in mixed systems of S-10 + RTAB cmcex [mmol/dm3]

cmcid [mmol/dm3]

gcmc [mN/m]

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

11.0 5.8 5.0 4.6 6.0 7.0 13.5 33.8 60.0

11.0 11.5 12.0 14.6 18.6 25.7 41.5 49.1 60.0

27.17 26.68 27.15 28.64 29.30 29.13 28.70 31.92 35.43

4.10 4.16 4.22 4.18 4.05 3.76 3.49 3.22 1.87 S-10 + DTAB

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

11.0 4.6 4.5 4.5 4.4 4.4 6.9 7.2 15.4

11.0 11.2 11.3 12.0 12.8 13.8 14.8 15.1 15.4

27.17 27.35 27.79 28.64 29.33 30.53 32.35 33.99 34.61

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

11.0 3.0 2.8 2.5 2.2 2.7 3.0 3.0 3.8

11.0 10.0 9.2 7.0 5.6 4.7 4.1 3.9 3.8

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

11.0 1.5 1.2 1.1 0.8 0.6 0.68 0.7 0.794

11.0 6.7 4.8 2.3 1.5 1.1 0.88 0.83 0.794

a1

max pC20 [mol/m2]10-6 S-10 + DeTAB

A [Å2] Aex

Aid

cmc/C20

2.80 2.73 2.14 2.21 2.43 2.78 2.76 2.55 2.95

59.31 60.83 77.60 75.14 68.34 59.73 60.17 65.12 56.29

59.31 58.98 58.77 58.74 58.71 58.59 58.37 58.16 56.29

174.3 83.8 83.0 69.6 67.3 40.3 41.7 56.1 4.4

4.10 4.12 4.16 4.16 4.14 3.99 3.44 3.38 2.40 S-10 + TTAB

2.80 2.48 2.70 2.76 2.05 2.12 2.72 2.92 3.51

59.31 66.96 61.50 60.17 81.00 78.33 61.05 56.87 47.31

59.31 59.00 58.23 56.67 55.95 55.11 53.67 52.47 47.31

174.3 60.6 65.0 65.0 60.7 43.0 19.0 17.3 3.9

27.17 29.60 29.66 29.82 31.69 31.52 33.31 33.51 34.52

4.10 4.35 4.34 4.23 4.20 4.01 3.62 3.46 3.12 S-10 + CTAB

2.80 2.21 2.15 2.32 3.04 3.50 4.00 4.14 3.65

59.31 75.14 77.24 71.58 54.62 47.45 41.51 40.11 45.50

59.31 56.82 56.82 55.58 53.79 52.41 48.68 48.12 45.50

174.3 67.2 61.3 42.5 34.9 27.6 12.5 8.7 5.0

27.17 30.56 31.47 33.68 34.19 34.04 34.34 35.15 35.72

4.10 4.48 4.40 4.23 4.19 4.17 4.16 4.00 3.75

2.80 2.72 2.78 2.96 3.24 3.84 3.09 3.34 3.25

59.31 61.05 59.73 56.10 51.25 43.24 53.74 49.72 51.06

59.31 57.00 56.67 55.85 54.86 54.11 53.37 52.79 51.06

174.3 45.3 30.1 18.7 12.4 8.9 9.8 7.0 4.6

Table 2. Parameters of mixed films in systems: S-10 + RTAB

a1 0.05 0.1 0.3 0.5 0.7 0.9 0.95 0.05 0.1 0.3 0.5 0.7 0.9 0.95 0.05 0.1 0.3 0.5 0.7 0.9 0.95 0.05 0.1 0.3 0.5 0.7 0.9 0.95

X1s

βs

f1 s S+10 + DeTAB 0.11 - 6.08 0.01 0.18 - 7.28 0.01 0.19 - 5.30 0.03 0.20 - 4.18 0.07 0.24 - 3.42 0.13 0.31 - 2.61 0.29 0.38 - 2.04 0.46 S-10 + DTAB 0.026 - 3.85 0.17 0.09 - 2.94 0.09 0.22 - 3.59 0.11 0.28 - 2.06 0.29 0.35 - 3.04 0.27 0.47 - 1.24 0.70 0.57 - 1.72 0.73 S-10 + TTAB 0.18 - 3.65 0.09 0.18 - 2.49 0.19 0.27 - 1.54 0.44 0.40 - 2.08 0.47 0.50 - 1.69 0.65 0.77 - 1.21 0.90 0.81 - 0.97 0.97 S-10 + CTAB 0.28 - 3.88 0.14 0.32 - 2.96 0.25 0.42 - 1.83 0.54 0.54 - 1.95 0.67 0.63 - 2.47 0.72 0.72 - 3.50 0.77 0.79 - 3.40 0.86 * calculated for  = 40mN/m

f2 s

βs - βM

|ln(C1s/C2s)|*

0.93 0.78 0.83 0.85 0.83 0.78 0.74

+ 0.79 + 0.62 + 1.22 + 1.25 + 2.03 + 1.97 + 2.78

3.90

0.99 0.97 0.84 0.90 0.69 0.76 0.57

+ 2.36 + 2.52 + 0.82 + 2.30 + 1.62 + 2.74 + 2.94

2.42

0.88 0.92 0.89 0.72 0.66 0.89 0.53

+ 2.30 + 2.69 + 2.59 + 1.97 + 1.45 + 1.87 + 2.61

0.85

0.73 0.74 0.80 0.56 0.37 0.16 0.12

+ 2.00 + 2.65 + 1.92 + 2.17 + 2.55 + 0.85 + 1.09

0.37

Table 3. Parameters of mixed micellization in systems: S-10 + RTAB

a1

X1

M

X1Mid

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

0 0.240 0.280 0.350 0.390 0.440 0.540 0.660 1

0 0.010 0.020 0.073 0.155 0.300 0.623 0.777 1

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

0 0.303 0.332 0.408 0.474 0.538 0.653 0.693 1

0 0.036 0.074 0.234 0.417 0.625 0.865 0.931 1

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

0.382 0.421 0.518 0.588 0.683 0.802 0.834 1

0.132 0.243 0.554 0.743 0.871 0.963 0.982 1

0 0.05 0.1 0.3 0.5 0.7 0.9 0.95 1

0 0.480 0.528 0.653 0.711 0.741 0.850 0.887 1

0 0.422 0.606 0.856 0.933 0.970 0.992 0.996 1

β

M

- 6.87 - 6.90 - 6.52 - 5.43 - 5.45 - 4.58 - 4.82

- 6.21 - 5.46 - 4.41 - 4.36 - 4.66 - 3.98 - 4.66

- 5.95 - 5.18 - 4.13 - 4.05 - 3.14 - 3.08 - 3.58

- 5.88 - 5.61 - 3.75 - 4.12 - 5.02 - 4.35 - 4.49

M

f1 f2 S-10 + DeTAB

M

0 1 0.02 0.66 0.03 0.57 0.06 0.45 0.13 0.44 0.18 0.34 0.38 0.27 0.81 0.45 1 0 S-10 + DTAB 0 1 0.049 0.565 0.087 0.548 0.213 0.480 0.299 0.375 0.369 0.259 0.619 0.183 0.644 0.107 1 0 S-10+TTAB 0 1 0.103 0.419 0.176 0.399 0.383 0.331 0.502 0.247 0.729 0.232 0.886 0.138 0.906 0.083 1 0 S-10+CTAB 0 1 0.197 0.250 0.286 0.209 0.636 0.202 0.709 0.124 0.714 0.063 0.907 0.043 0.944 0.029 1 0

DG0Ma [kJ/mol]

DG ex [kJ/mol]

1.70

- 11.18 - 13.30 - 13.46 - 13.38 - 12.75 - 12.62 - 11.77 - 9.41 - 6.97

- 2.38 - 2.49 - 2.39 - 1.96 - 1.84 - 1.32 - 0.34

0.34

- 11.18 - 14.18 - 13.90 - 13.48 - 13.48 - 13.61 - 12.87 - 13.06 - 10.34

- 3.25 - 3.00 - 2.64 - 2.70 - 2.88 - 2.24 - 2.46

1.06

- 11.18 - 15.67 - 15.42 - 15.10 - 15.16 - 14.66 - 14.51 - 14.61 - 13.81

- 3.48 - 3.13 - 2.55 - 2.43 - 1.69 - 1.21 - 1.23

2.63

- 11.18 - 18.02 - 18.08 - 17.53 - 17.90 - 18.39 - 18.08 - 18.07 - 17.69

- 4.69 - 4.40 - 2.17 - 2.11 - 2.57 - 0.93 - 0.61

M

M

|ln(C1 /C2 )|