DOI: 10.1021/la9027173 2491Langmuir 2010, 26(4), 2491–2496 Published on Web 09/10/2009

pubs.acs.org/Langmuir

© 2009 American Chemical Society

A Study of the Interactions of Ternary Surfactant Systems at the

Water-Air Interface

Katarzyna Szymczyk and Bronisleaw Ja�nczuk*

Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Skleodowska University,Maria Curie-Skleodowska Sq. 3, 20-031 Lublin, Poland

Received July 25, 2009. Revised Manuscript Received August 21, 2009

Surface tension measurements were carried out for the systems containing ternary mixtures of cetyltrimethylammo-nium bromide (CTAB) and p-(1,1,3,3-tetramethylbutyl)phenoxypoly(ethylene glycols), Triton X-100 (TX100) andTriton X-165 (TX165). The aqueous solution of ternary surfactant mixtures were prepared by adding the thirdsurfactant to the binary mixture of the surfactants where the synergetic effect in the reduction of the surface tension ofwater were determined to compare the influence of the third surfactants on the adsorption of this binary mixture at thewater-air interface. The obtained results and calculations indicate that the synergetic effect in the reduction of thesurface tension of water was deepened after adding the third surfactant to the binarymixture at the composition at whichthis effect was observed. The best synergetic effect in the γLV reduction was determined on the basis of the values of themolecular interaction parameter for aqueous solutions of ternary mixtures of CTABþTX165 (R CTAB=0.2) (γLV=50 mN/m, C=4.3 � 10-5 M) þTX100 (C=108-10-2 M).

1. Introduction

Surfactants are usually prepared commercially as mixtures

rather than pure forms because it is simply much more efficient

and more economically viable to synthesize mixtures. This saves

on separation costs as the product is generally not required in

a singular pure form for purposes of cleaning and detergency

work.1,2 So, it is important to compare and contrast the behavior

of the mixtures with the pure forms to analyze the effects of head

groups and chain length mixing. Often the mixed systems are

more efficient in an environment, which is called synergism.3-5

This synergism can be attributed to nonideal mixing effects in the

aggregates, and it results in critical micelle concentrations

(CMCs) and interfacial tensions that are substantially lower than

would be expected on the basis of the properties of the unmixed

surfactants alone. The fundamentals of the synergism in binary

systems have been well understood on the basis of nonideal

theories, for example, the regular solution approximation,6-9

especially by means of β parameters. In our earlier studies, we

proved that there was synergism in the surface tension reduction

and the mixed micelle formation in the binary mixtures of two

nonionic and nonionic-cationic surfactants.10,11 In the mixtures

of two nonionics we also proved the synergetic effect in reduction

of the contact angle ofwater on a polytetrafluoroethylene (PTFE)

surface.12

However, while most experimental and theoretical work onmixtures of surfactants has focused on binary mixtures, inpractice, ternary and other complex multicomponent surfactantmixtures are also encountered. Liquid detergents, for example,commonly include synthetic anionic surfactants, nonionic surfac-tants, and natural soaps.13 Compared to binary surfactantsystems, ternaries are less studied, and quantification of resultsin terms of mutual interaction of components and ideality/nonideality states has been only limitedly done. Moreover, thesestudies especially deal with the prediction of the CMCs ofdifferent ternary surfactant mixtures.14,15 For example, it hasbeen observed that the proportion of the nonionic surfactantcomponents and their activity coefficients in the ternary mixedmicelles is higher than that of the ionic components.16 To ourknowledge, rare studies on mixed adsorption and surface tensionreduction of ternary surfactant mixtures, taking properties of abinary mixtures into consideration, can be found in the litera-ture.17 Thus, the purpose of our studies was to determine theinfluence of the concentration of a aqueous solution of a thirdsurfactants on the values of the surface tension of the diffe-rent binary mixtures of the aqueous solutions composed of twononionic surfactants, p-(1,1,3,3-tetramethylbutyl) phenoxy-poly(ethyleneglycols), Triton X-100 (TX100) and Triton X-165(TX165), and a cationic surfactant, cetyltrimethylammoniumbromide (CTAB), in which the synergism was confirmed on thebasis of the values of the molecular interaction parameters.Ternary mixtures were prepared by adding the third surfac-tant to the binary mixture of TX100þTX165 (R TX100 =0.2), CTABþTX100 (R CTAB=0.2), and CTABþTX165

*To whom correspondence should be addressed. Phone: (48-81) 537-5649.Fax: (48-81) 533-3348. E-mail: bronislaw.janczuk@poczta.umcs.lublin.pl.(1) Hill, R. M. InMixed Surfactant Systems; Ogino, K., Abe, M., Eds; Surfactant

Science Series 46; Marcel Dekker: New York, 1993; Chapter 11.(2) Murphy, A.; Taggard, G Colloids Surf., A 2002, 205, 237.(3) Lucassen-Reynders, E. H.; Lucassen, J.; Giles, D. J. Colloid Interface Sci.

1981, 82, 150.(4) Rosen J. M. Surfactants and Interfacial Phenomena; Wiley-Interscience:

New York, 2004.(5) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1980, 90, 212.(6) Cui, Z. G.; Canselier, j. P.; Zhou, X. Q. Colloid Polym. Sci. 2005, 283, 539.(7) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5567.(8) Schiloach, A..; Blankschtein, D. Langmuir 1998, 14, 1618.(9) Schiloach, A..; Blankschtein, D. Langmuir 1998, 14, 4105.(10) Szymczyk, K.; Ja�nczuk, B. Langmuir 2007, 23, 4972.(11) Szymczyk, K.; Ja�nczuk, B. Colloids Surf., A 2007, 293, 39.(12) Szymczyk, K.; Ja�nczuk, B. Langmuir 2007, 23, 8740.

(13) Smulders, E.; Krings, P. Chemistry Ind. 1990, March 19, 174.(14) Gosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357.(15) Ghoulam, M. B.; Moatadid, N.; Graciaa, A.; Lachaise, j.; Marion, G.;

Schechter, R. S. J. Colloid Interface Sci. 1998, 200, 74.(16) Chakraborty, S.; Ghosh, S.; Moulik, S. P. J. Phys. Chem. 2005, 109, 14813.(17) Das Burman, A.; Dey, T.; Mukherjee, B; Das, A. R. Langmuir 2000, 16,

10020.

2492 DOI: 10.1021/la9027173 Langmuir 2010, 26(4), 2491–2496

Article Szymczyk and Ja�nczuk

(R CTAB= 0.2). The interactions between surfactants in thesurface layers were also investigated.

2. Experimental Section

Materials. p-(1,1,3,3-Tetramethylbutyl) phenoxypoly(ethyl-eneglycols), Triton X-100 (TX100) (C14H21 (CH2CH2O)x OH,x=10) (Sigma) and Triton X-165 (C14H21 (CH2CH2O)xOH, x=16) (TX165) (Fluka), and cationic surfactant, CTAB (C19H42-NBr) (Sigma) were used for preparation of aqueous solutions.

Aqueous solutions of the individual surfactants (TX100,TX165, CTAB), their binary mixtures (TX100þTX165, CTABþTX100, CTABþTX165), and different ternary mixtures (TX100,CTABþTX165;CTAB,TX100þTX165;TX165,CTABþTX100)at different monomer mole fractions, R, were prepared usingdoubly distilled and deionized water received from a DestamatBi18Edistiller.The surface tensionofwaterwas always controlledbefore solution preparation.

Liquid Surface Tension Measurements. Surface tensionmeasurements were made at 293 K with a Kr€uss K9 tensiometerunder atmospheric pressure by the ring method. The platinumring was thoroughly cleaned, and flame-dried before each mea-surement. The measurements were done in such a way that thevertically hung ring was dipped into the liquid to measure itssurface tension.

It was then pulled out. The maximum force needed to pull thering through the interface was then expressed as the surfacetension, γLV (mN/m). Measurements of the surface tension ofpure water at 293 K were performed to calibrate the tensiometerand to check the cleanliness of the glassware. In all cases, morethan 10 measurements were carried out, and the standard devia-tion did not exceed(0.2 mN/m. The temperature was controlledwithin (0.1 K.

3. Results and Discussion

The Surface Tension Isotherms of Individual Surfactants

and Their Binary Mixtures. From the comparison of the sur-face tension isotherms of aqueous solution of individual surfac-tants (Figure 1), it results that the influence of the individualsurfactant on the reduction of the surface tension of waterdepends on their concentration range. It is observed that, at aconcentration corresponding to an unsaturated monolayer at thewater-air interface, the best reduction of the water surfacetension shows nonionic TX165, while, at a concentration corre-sponding to a saturated monolayer, it shows TX100. The max-imal reduction of water surface tension is also observed forTX100; however, it is minimal for TX165. So, it results that theusefulness of an aqueous solution of a given surfactant dependsnot only on the kind of the surfactant but also on the range of itsconcentration. Therefore, to show the properties of the surfactant,which are taking into account, in practice, the values of the CMC,negative logarithms of the concentration of surfactants in the bulkphase required to produce a 20 mN/m reduction in the surfacetension of the solvent, pC20, were determined, and surface excessconcentration at the surface saturation, Γm, with minimal area(Am) per molecule at the interface was calculated by using theGibbs equation of adsorption4 and is presented in Table 1.10,11

From this table it results that the highest efficiency of the adsorp-tion, which is related to pC20, has nonionic TX100, but cationicsurfactant CTAB shows the highest effectiveness at the water-airinterface because it has the biggest value of Γm. These propertiesof aqueous solutions of individual surfactants are reflectedin the properties of their binary mixtures (Figure 2).10,11 Inthese mixtures, there is not a linear dependence between thevalues of their surface tension and the composition of the mix-ture, and, moreover, in the binary mixtures of TX100þTX165,

CTABþTX100, and CTABþTX165, at the monomer molefraction of TX100 in TX100þTX16510 and CTAB in CTABþTX100,11CTABþTX165 equals 0.2, and there is even aminimumat the relation between γLV and R, which may suggest a synerge-tic effect in the reduction of the surface tension of water.The deviation from the linear dependence and existence ofthese minima influences the values of the CMC, pC20, Γm,

Figure 1. Dependence of the surface tension of aqueous solutions,γLV, of TX100 (curve 1), TX165 (curve 2), and CTAB (curve 3) onlog C (C represents the concentration of TX100, TX165, andCTAB).10,11

Table 1. Values of the CMC, the Negative Logarithm of the

Concentration of Surfactants in theBulkPhaseRequired toProduce a

20 mN/m Reduction in the Surface Tension of the Solvent, pC20,

Maximal Excess of Surfactant Concentration at the Water-Air

Interface, Γm, and the Minimal Area Per Molecule, Am, for TX100,

TX165, and CTAB10,11

CMC (mol/dm3) pC20 Γm (mol/m2) Am (nm2)

TX100 2.90 � 10-4 4.725 2.83 � 10-6 0.587TX165 5.41 � 10-4 4.496 2.22 � 10-6 0.748CTAB 9.15 � 10-4 3.470 3.10 � 10-6 0.536

Figure 2. Dependence of the surface tension of aqueous solutionsof binarymixtures of surfactants TX100þTX165 (RTX100=0.2)(curve 1), CTABþTX100 (R CTAB = 0.2) (curve 2), andCTABþTX165 (R CTAB= 0.2) (curve 3) on log C (C representsthe concentration of the binary mixture at a given R).10,11

DOI: 10.1021/la9027173 2493Langmuir 2010, 26(4), 2491–2496

Szymczyk and Ja�nczuk Article

andAm (Table 2).10,11 FromTable 2, it results that the mixture ofcationic and nonionic surfactant, CTABþTX100 at the molefraction of TX100, R, equals 0.2, shows the higher efficiency andeffectiveness in the reduction of the surface tension of water. If wecompare the values from Tables 1 and 2, it is seen that the valuesof pC20 and Γm arrange in the following orders:

pC20 : CTAB < TX165 < CTABþTX165 < TX100< TX100þTX165 < CTABþTX100

Γm : CTABþTX165 < TX165 < TX100þTX165< CTABþTX100 < TX100 < CTAB

that is, the highest efficiency at the water-air interface has amixture of CTAB and TX100 at R CTAB=0.2.

The synergetic effect in the reduction of the surface tension ofwater by these binarymixtures was confirmed by the values of themolecular interaction parameter calculated using the equationderived by Rubingh and Rosen:4,18,19

βσ ¼ lnðRC12=X1C01Þ

ð1-X1Þ2ð1Þ

where R is the mole fraction of surfactant 1 in the mixture of twosurfactants, X1 is the mole fraction of surfactant 1 in the mixedmonolayer,C1

0 andC12 are themolar concentrations in the bulk ofsurfactant 1 and of the mixture of surfactant 1 and 2, respectively,required toproduce a given surface tension value. The values ofβσ

for the mixtures are presented in Table 3 together with the valuesof X1 obtained from the equation

ðX1Þ2 lnðRC12=X1C01Þ

ð1-X1Þ2 ln½ð1-RÞC12=ð1-X1ÞC02 �

¼ 1 ð2Þ

whereC20 is themolecular concentration of surfactant 2 in the bulk

required to produce a given surface tension and values of theactivity coefficient of the surfactants in the mixtures calculatedfrom the equations

ln f1 ¼ βσð1-X1Þ2 ð3Þ

ln f2 ¼ βσðX1Þ2 ð4Þ

From Table 3 it results that the best synergism exists in themixture of CTAB and TX100 at γLV=60mN/m (βσ=-7.284), inwhich the monomer mole fraction of CTAB in the mixedmonolayer is higher than in the bulk phase. The smallest valueof βσ shows the mixture of two nonionic surfactants, TX100 andTX165, at γLV=50 mN/m (βσ=-1.879), but, at this value of thesurface tension, the monomer mole fraction of TX100 in themixed monolayer is almost 2 times higher than in the bulk phase.

From calculation of the activity coefficients, it appears that alltheir values are smaller than 1, which, according to the Villeneuveet al. model,20 indicates that interactions between differentsurfactant molecules in the mixture are stronger than betweenthe single surfactants; however in mixtures of cationic andnonionic surfactants, the activity coefficients of CTAB are verysmall. The biggest activity coefficient shows the nonionic sur-factant TX165 in the mixture with CTAB at γLV =60 mN/m(f2=0.972).Surface Tension Isotherms of Ternary Mixtures of Sur-

factants. It was interesting whether the addition of a thirdsurfactant to presented binary mixtures deepened the reductionof the surface tension of water. So we examined the followingternary systems of surfactants:

1 TX100þTX165 (RTX100=0.2) (γLV=60mN/m,C=4 � 10-6 M) þ CTAB (C=10-8-10-2 M), m1,

2 TX100þTX165 (RTX100=0.2) (γLV=50mN/m,C=4 � 10-5 M) þ CTAB (C=10-8-10-2 M), m2

3 CTABþTX100 (RCTAB=0.2) (γLV=60 mN/m,C=4 � 10-6 M) þTX165 (C=10-8-10-2 M), m3

4 CTABþTX100 (RCTAB=0.2) (γLV=50 mN/m,C=2.4 � 10-5 M) þTX165 (C = 10-8-10-2 M), m4

5 CTABþTX165 (RCTAB=0.2) (γLV=60 mN/m,C=5 � 10-6 M) þTX100 (C=10-8-10-2 M), m5

6 CTABþTX165 (RCTAB=0.2) (γLV=50 mN/m,C=4.3 � 10-5 M) þTX100 (C=10-8-10-2 M), m6.

Presented binary mixtures of surfactants were chosen to pre-pare the ternary systems because they show a synergetic effect inthe surface tension reduction, especially at values of γLV equal to50 and 60 mN/m (Table 3).

The analysis of the results of the surface tension measurementsfor aqueous solutions of ternary mixtures of surfactants(Figures 3-8) clearly indicates that, in the reduction of the surfacetension of the presented binarymixture of surfactants by additionof the third surfactant, we can obtain better results if we useaqueous solutions of the binary mixtures at smaller concentra-tions, that is, at bigger values of surface tension (mixture m1, m3,and m5). The differences between values of ΔγLV at the sameconcentration (Figures 4,6, and 8), that is, the distinction betweenthe value of the surface tension of the ternary surfactant mixtureand the values of γLV of the binary surfactant mixture, alsoindicate that there is a different efficiency and effectiveness of thereduction of the surface tension of an aqueous solution of astudied binarymixture of surfactants by the third surfactant and adifferent mechanism of their adsorption at the water-air inter-face. From Table 4, where, apart from the values of the CMCwehave also the values of Γm calculated from the Gibbs equation,4 itresults that the highest adsorption effectiveness shows formixturem1, and the smallest shows for mixture m3. For all studiedaqueous solutions of ternary mixtures of surfactants, we cannotdetermined the values of pC20 to show the best efficiency ofadsorption, but we can compare the values of surface tension ofternary mixtures of surfactants not only to the binary mixturesbut also to the value of the surface tension of water at 293K. If wetake into account the values of the surface tension of the ternarymixtures at a concentration equal to 10-4 M (Table 5), they arearranged in the following order:

m6 < m5 < m4 < m3 < m2 < m1

Table 2. Values of CMC, pC20, Γm, and Am for TX100þTX165

(r TX100 = 0.2), CTABþTX100 (r CTAB = 0.2), andCTABþTX165 (r CTAB = 0.2) Mixtures

10,11

CMC (mol/dm3) pC20 Γm(mol/m2) Am (nm2)

TX100þTX165 4.35 � 10-4 4.729 2.53 � 10-6 0.656CTABþTX100 2.66 � 10-4 4.821 2.73 � 10-6 0.608CTABþTX165 3.39 � 10-4 4.611 2.18 � 10-6 0.762

(18) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1982, 87, 469.(19) Rubingh D. N. In Solution Chemistry of Surfactants; Mittal, K., Ed.; Plenum

Press: New York, 1979; p 337.(20) Villeneuve, M.; Sakamoto, H.; Minamizawa, H.; Aratono, M. J. Colloid

Interface Sci. 1997, 194, 301.

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Article Szymczyk and Ja�nczuk

that is, at this concentration, the best efficiency in the reduction ofthe surface tension of water (γLV=37.0 mN/m) is shown by theternary mixture of surfactants m6 [(CTABþTX165, R CTAB=0.2,γLV=50mN/m,C=4.3� 10-5M)þTX100], and theworst isshown by the mixturem1 [(TX100þTX165, R TX100=0.2, γLV=60 mN/m, C=4 � 10-6 M) þ CTAB] (γLV=54.7 mN/m).

From the analysis of the smallest values of the surface tensionof the ternary mixture of surfactants, γLV, that is, for the highest

values of the concentration of the third surfactant (Table 6), itresults that themixturem6 [(CTABþTX165,RCTAB=0.2,γLV=50 mN/m, C=4.3 � 10-5 M) þTX100] has not only the bestefficiency but also the best effectiveness in the reduction of thesurface tension of water. From this point of view, it was interest-ing whether this ternary mixture of surfactants shows the bestsynergetic effect in the reduction of surface tension of wateramong these six studiedmixtures and has a better synergetic effect

Figure 3. Dependence of the surface tension of aqueous solutionsof ternarymixtures of surfactants TX100þTX165 (RTX100=0.2)(γLV=60mN/m,C=4� 10-6M)þCTAB (C=10-8-10-2M),m1

(curve 1) andTX100þTX165 (RTX100=0.2) (γLV=50mN/m,C=4 � 10-5 M) þ CTAB (C=10-8-10-2 M), m2, on log C CTAB.

Table 3. Values of theMonomerMole Fraction of Surfactants,X1, Molecular Interaction Parameters, βσ, and Activity Coefficient, f1 and f2, in theMixedMonolayer Formed byMixtures of TX100þTX165 (r TX100= 0.2), CTABþTX100 (rCTAB= 0.2), and CTABþTX165 (rCTAB=

0.2) at γLV = 60 and 50 mN/m10,11

X1 βσ f1 f2

TX100þTX165 (R TX100 =0.2) γLV =60 mN/m (1-TX100) 0.286 -1.974 0.366 0.851TX100þTX165 (R TX100 =0.2) γLV =50 mN/m (1-TX100) 0,420 -1.879 0.504 0.719CTABþTX100 (R CTAB =0.2) γLV =60 mN/m (1-CTAB) 0.243 -7.284 0.015 0.650CTABþTX100 (R CTAB =0.2) γLV =50 mN/m (1-CTAB) 0.207 -4.684 0.053 0.818CTABþTX165 (R CTAB =0.2) γLV =60 mN/m (1-CTAB) 0.090 -3.523 0.054 0.972CTABþTX165 (R CTAB =0.2) γLV =50 mN/m (1-CTAB) 0.254 -4.499 0.082 0.748

Figure 4. The values of ΔγLV for mixtures of TX100þTX165 (RTX100=0.2) atγLV=60mN/m (m1) and γLV=50mN/m (m2) withthe addition of CTAB at concentrations of CTAB equal to 10-5,5 � 10-5, 10-4, and 5 � 10-4 M.

Figure 5. Dependence of the surface tension of aqueous solutionsof ternary mixtures of surfactants CTABþTX100 (RCTAB=0.2)(γLV=60mN/m,C=4� 10-6M)þTX165 (C=10-8-10-2M),m3

(curve 1) andCTABþTX100 (RCTAB=0.2) (γLV=50mN/m,C=2.4� 10-5M)þ TX165 (C=10-8-10-2M),m4, on logC TX165.

Figure 6. The values of ΔγLV for mixtures of CTABþTX100 (RCTAB=0.2) at γLV=60mN/m (m3) and γLV=50mN/m (m4) withthe addition of TX165 at concentrations of TX165 equal to 10-5,5 � 10-5, 10-4, and 5 � 10-4 M.

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Szymczyk and Ja�nczuk Article

than the binarymixture of CTABþTX165 (RCTAB=0.2) (γLV=50 mN/m, C=4.3 � 10-5 M). However, Rosen’s equations usedfor calculations of the monomer mole fraction and the molecularinteraction parameters in a mixed binary monolayer can not beapplied directly for ternary mixtures. It is possible to determineof molecular interaction parameter from eq 1 if we assumethe binary system as a one-surface active agent. Taking theseinto account, the following interaction parameters were cal-culated: (TX100, TX165)-CTAB, β(12)-3; (CTAB, TX100)-TX165 β(13)-2; (CTAB, TX165)-TX100, β(23)-1, but not at thesame value of the surface tension for all ternary mixtures becauseof the limitation of Rosen’s equation for values of R between0.2 and 0.8. From Table 7, it results that, for ternary mixturesm1

and m2, that is, when we added the cationic surfactant CTAB tothe binary mixture of two nonionic surfactants, the monomermole fraction of CTAB in the mixed monolayer is smaller than inthe bulk phase, also the activity coefficient of CTAB is very small.Only in mixture m2 at γLV = 48.8 mN/m does this activitycoefficient have a value equal to 0.452. At these two ternarymixtures (m1 and m2), at different values of the surface tension,the nonionic surfactant TX165 shows the biggest value of theactivity coefficient in the mixed monolayer, but molecular inter-action parameter β(13)-2, which describe the interaction of TX165with the binary mixture of TX100þCTAB, has the highestnegative values, which means that the interaction betweenTX165 andTX100þCTAB is theweakest. In the ternarymixturesm3 and m4 [(CTABþTX100) þ TX165], the monomer molefraction of cationic surfactant in the mixed monolayer is muchhigher than in the bulk phase, but the activity coefficient of thiscationic surfactant in these mixtures has a very little value, whichmay result from the structure of TX100, TX165, and CTABmolecules and hydration of the hydrophobic and hydrophilicparts of themolecule. It is know that the oxyethylene group can beassociated with two molecules of water; it means that the hydro-philic group of TX100 is associated with 20 molecules of water,and TX165 is associatedwith 32molecules. The association of thewater molecules to CTAB is considerably smaller.

The values of the molecular interaction parameter β(12)-3 arenegative,whichdecreasewith thedecreaseof the surface tension, andthey, together with the second condition of existing synergism, con-firm this effect. The smallest value of β(12)-3 in these two mixtures(m3 and m4) shows the mixture m3 at γLV=52.0 mN/m (-22.965).

Whenwe add nonionic surfactant TX100 to binarymixtures ofCTABþTX165 in these ternary mixtures (m5 and m6), TX100shows the biggest values of activity coefficients. The smallestvalue of molecular interaction parameter exists for mixturem5 atγLV=48.0mN/m,whereβ(12)-3=-25.599. This value ofβ(12)-3 isnot only the smallest for mixtures m5 and m6, but for all studiedsystems, which indicate that, for mixture m5, at a value of γLV=48.0 mN/m, the best synergism exists.

If we compare the smallest values of surface tension(mN/m) obtained for individual surfactants studied, theirbinary and ternary mixtures (Figures 1, 2, 3, 5, and 7) they arearranged in the following order: m6 (33.0)<m5 (33.3)<TX100(33.7)<CTABþTX100 (35.2)<TX100þTX165 (36.8)<CTAB

Figure 8. The values of ΔγLV for mixtures of CTABþTX165 (RCTAB=0.2) at γLV=60mN/m (m5) and γLV=50mN/m (m6) withthe addition of TX100 at concentrations of TX100 equal to 10-5,5 � 10-5, 10-4, and 5 � 10-4 M.

Figure 7. Dependence of the surface tension of aqueous solutionsof ternary mixtures of surfactants CTABþTX165 (RCTAB=0.2)(γLV=60mN/m,C=5� 10-6M)þTX100 (C=10-8-10-2M),m5

(curve 1) andCTABþTX165 (RCTAB=0.2) (γLV=50mN/m,C=4.3� 10-5M)þ TX100 (C=10-8-10-2M),m6, on logC TX100.

Table 4. Values of the CMC and Γm for Ternary Mixtures of Surfactants

m1 m2 m3 m4 m5 m6

CMC (mol/dm3) 1.28 � 10-3 1.40 � 10-3 3.22 � 10-4 3.42 � 10-4 3.53 � 10-4 2.63 � 10-4

Γm (mol/m2) 4.14 � 10-6 1.67 � 10-6 1.56 � 10-6 1.60 � 10-6 2.03 � 10-6 2.66 � 10-6

Table 5. Values of the Surface Tension of Aqueous Solutions of

Ternary Mixtures of Surfactants at Concentrations of an Added

Third Surfactant Equal to 10-5, 5 � 10-5, 10-4, and 5 � 10-4 M

m1 m2 m3 m4 m5 m6

10-5 58.6 49.5 51.7 47.7 48.4 46.85 � 10-5 56.5 48.8 46.1 44.6 42.6 40.810-4 54.7 48.2 43.0 42.0 39.5 37.05 � 10-4 46.0 42.6 39.6 39.1 33.4 33.2

Table 6. Values of the Surface Tension of a Ternary Mixture of

Surfactants at a Concentration of the Third Surfactant Equal to

8 � 10-3

M

m1 m2 m3 m4 m5 m6

γLV 38.3 38.5 39.4 39.0 33.3 33.0

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Article Szymczyk and Ja�nczuk

(37.8) < m1 (38.3)< m2 (38.5)< m4 (39.0)< CTABþTX165(39.2)<m3 (39.4)< TX165 (39.5), which means that, amongthese systems, ternary mixtures of surfactantsm5 andm6 have thebest synergetic effect in the reduction of the surface tension ofwater.

Conclusions

From the measurement of the surface tension of aqueoussolutions of singular surfactants and their binary and ternarymixtures and from literature data of their analysis, it resultsthat there is no linear dependence between the surface tensionand the monomer mole fraction of the surfactants in binarymixtures of TX100þTX165 (R TX100= 0.2), CTABþTX100

(R CTAB=0.2), and CTABþTX165 (R CTAB=0.2). The addi-tion of a third surfactant to these binary mixtures deepens thenegative deviation between values of γLV and R. It means that thesynergism in the reduction of surface tension of water by aqueoussolutions of ternary surfactant mixtures is expected. This syner-getic effect was confirmed for all studied ternary mixtures ofsurfactants by the values of molecular interaction parameterscalculated from Rosen’s equation on the assumption that thebinary system is a one-surface active agent.

Acknowledgment. The financial support from the PolishMinistry of Science and Higher Education, Project No. N N204130635 is gratefully acknowledged.

Table 7. Values of the Mole Fractions of Surfactants in the Bulk Phase (r), Monomer Mole Fractions in the Mixed Monolayer (X), ActivityCoefficients (f ), and Molecular Interaction Parameters ( β) for Aqueous Solutions of Ternary Surfactant Mixtures Composed of TX100, TX165,

and CTAB at Different Values of γLV (TX100-1, TX165-2, CTAB-3)

mixture γLV R1/R2/ R3 X1 /X2 /X3 f1 /f2 /f3 β(12-3) /β(13-2) /β(23-1)

m1 59.4 0.090/0.354/ 0.556 0.340/0.417/ 0.243 0.185/0.918/ 0.053 -5.112/-0.253/ -3.86858.9 0.601/0.241/ 0.699 0.482/0.314/ 0.204 0.151/1.098/ 0.141 -3.093/-0.200/ -7.043

m2 49.0 0.104/0.416/ 0.480 0.311/0.389/ 0.300 0.357/0.552/ 0.129 -4.186/-1.592/ -2.17048.4 0.065/0.261/ 0.674 0.432/0.309/ 0.258 0.328/0.882/ 0.452 -1.442/-0.263/ -3.464

m3 54.0 0.361/0.549/ 0.090 0.304/0.317/ 0.379 0.361/0.300/ 0.004 -14.642/-2.562/ -2.18552.0 0.249/0.689/ 0.062 0.246/0.258/ 0.496 0.424/0.542/ 0.003 -22.965/-1.114/ -1.507

m4 46.0 0.356/0.556/ 0.090 0.348/0.322/ 0.331 0.570/0.322/ 0.021 -9.438/-1.933/ -1.32544.0 0.225/0.718/ 0.056 0.258/0.238/ 0.504 0.765/0.546/ 0.011 -18.364/-1.043/ -0.486

m5 50.0 0.542/0.367/ 0.092 0.317/0.275/ 0.408 0.342/0.275/ 0.003 -9.931/-3.874/ -2.29948.0 0.693/0.245/ 0.061 0.272/0.210/ 0.518 0.714/0.156/ 0.003 -25.599/-2.972/ -0.637

m6 44.0 0.327/0.538/ 0.135 0.397/0.350/ 0.252 0.245/0.094/ 0.018 -7.202/-5.591/ -3.87343.5 0.360/0.512/ 0.128 0.345/0.353/ 0.253 0.295/0.138/ 0.017 -7.849/-4.721/ -3.333