4234
Langmuir 1996,11, 4234-4240
Aqueous Solutions of Zwitterionic Surfactants with Varying Carbon Number of the Intercharge Group. 2. Ion Binding by the Micelles N. Kamenka" Laboratoire des Procidis et Matiriaux Membranaires, UMR9987, CNRS, Universitk de Montpellier 11, Place Eugkne Bataillon, 34095 Montpellier Cedex 5, France
M. Chorro Laboratoire des Agrigats Molkculaires et des Matiriaux Inorganiques, URA 79, CNRS, Universitk de Montpellier 11, Place Eugkne Bataillon, 34095 Montpellier Cedex 5, France
Y . Chevalier Laboratoire des Matiriaux Organiques a Propriitts Spkcifiques, CNRS, BP 24, 69390 Vernaison, France
H. Levy and R. Zana Institut Charles Sadron (CRM-EAHP), CNRS-ULP, 6 rue Boussingault, 67083 Strasbourg Cedex, France Received May 11, 1995. In Final Form: July 28, 1995@ Electrical conductivity, spectrofluorometry, and self-diffusionmeasurements have been used to provide evidence for, and study of, the binding of ions (Na+,C1-) to the micelles of a series of zwitterionic surfactants type with the intercharge alkanediyl group of the alkanediyl-a-(dodecyldimethylammonio)-~-carboxylate being CH2, C3H6, CsHlo, and C10H20 (referred to as C12NlC02, C12N3C02, C12N5C02, and C12NlOC02, respectively). These surfactants permitted us to assess the effect of the carbon number of the intercharge group on the binding of Na+ and C1- to the zwitterionic micelles. The propanediyl-1-(dodecyldimethylammonio)-3-sulfonate (C12N3S03)has also been investigated to check the effect of the headgroup. In most experiments,the molar concentration ratio [surfactant]/[salt]was kept constant and equal to 1. The degrees of ion bindinghave been obtained for both Na+ and C1- as a function of the surfactant concentration, from self-diffusion measurements. The degree of binding is always larger for the anion and follows the sequence C12NlC02 < C12N3S03 < C12N3C02 C12N5C02 FZ C12NlOC02, both for Na+and C1-. The results show that, contrary to what is observed for micellar solutions of ionic surfactants, the binding of ions by zwitterionic micelles starts only well above the cmc and increases rapidly with concentration. A mass action model has been developed and provides a quantitative account of the results.
Introduction In part 1 of this series, we have investigated the aggregation behavior of zwitterionic surfactants of the alkanediyl-a-(dodecyldimethy1ammonio)-w -carboxylate type, with the intercharge alkanediyl group being CH2, C3H6, C5H10, and C10H20 (referred to as C12NlC02, C12N3C02, C12N5C02, and C12NlOC02, respectively), and of the propanediyl-l-(dodecyldimethylammonio)-3sulfonate type (C12N3S03).l The results showed that the micelle aggregation numbers of these surfactants are quite insensitive to salt (NaC1) and amphiphile concentrations and to temperature. The aggregation numbers in particular do not depend on the presence of NaCl and are consistent with a spherical or near-spherical shape of the mice1les.l Since zwitterionic surfactant micelles carry a net charge equal to zero, one may think that the insensitivity of the aggregation number to the presence of salt indicates that these aggregates do not bind cations or anions. However, several studies2-8have shown that the micelles of various zwitterionic surfactants can bind anions. In two s t u d i e ~ ,binding ~,~ of cations was also
* To whom correspondence should be addressed. Abstract published inAdvance ACSAbstracts, October 1,1995. (1)Kamenka, N.; Chevalier, Y.; Zana, R. Langmuir 1996,11,3351. (2) Kamenka, N.;Partyka, S.; Amin-Alami, A,; Chorro, M.; Faucompr6, B.; Zana, R. In preparation. @
evidenced. The reported results suggest that the binding of anions to zwitterionic micelles increases in the sequence F- < C1- < Br- 4-8 and that the binding of anions is stronger than for ~ a t i o n s . ~Similarly, s it has been shown that betaine surfactants interact more strongly with anionic surfactants than with cationic ones.g The literature reports no study of the effect of the intercharge carbon number and the nature of the headgroup on the ion binding by zwitterionic micelles. This situation led us to investigate the binding of anions and cations to the micelles of the five zwitterionic surfactants listed above and for which the aggregation numbers are reported in part 1in this series. This study has been performed using electrical conductivity and spectrofluorometry for the qualitative aspects of the binding and measurements of ion and micelle (3)Amin-Alami. A.Thesis, University of MontDellier, Montuellier, France, 1989. (4)Pillensdorf, A.; Katzenhendler, J. Isr. J. Chem. 1979,18,330. ( 5 ) Bunton. C.A.: Mhala. M. M.: Moffatt. J. R. J.Phvs. Chem. 1989, 93,854. (6) Hodge, D. J.; Laughlin, R. G.; Ottewill, R. H.; Rennie, A. R. Langmuir 1991,7,878. (7)Brochsztain, S.;Filho, P. B.; Berci, P. F.; Toscano, V. G.; Chaimovich, H.; Politi, M. J. J. Phys. Chem. 1990,94, 6781. (8)Baptista, M. S.;Politi, M. J. J.Phys. Chem. 1991,95,5936. (9)Rosen, M. J. Langmuir 1991,7,885.
O743-7463/95/2411-4234$O9.OOIO 0 1995 American Chemical Society
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Aqueous Solutions of Zwitterionic Surfactants self-diffision coefficients for the quantitative aspects of the binding. Recall that self-diffision is the only method that permits a simultaneous determination of the degrees of binding of anions and cations to a given micelle. This method has been largely used in our previous studies of aqueous solutions of ionic surfactant s o l ~ t i o n s , ~and ~-'~ from the variation of the counterion self-diffusion coefficient with the surfactant concentration, the degree of counterion binding has been obtained in a large concentration range. Degrees of ion binding to mixed micelles,16 nonionic surfactant micelles,17 and to polymer-bound micelles18J9 have also been recently obtained from selfdiffusion studies. The work presented below constitutes the first quantitative study of the binding ofions to zwitterionic micelles. The results clearly show that the zwitterionic micelles used bind anions more strongly than cations and that the degree of ion binding increases a lot with the surfactant concentration. This increase has been accounted for by a model based on the mass action law. In this respect, the interaction between ions and zwitterionic surfactant micelles qualitatively differs from that with ionic surfactant micelles where the interaction is similar to that in polyelectrolyte solutions and involves a condensation of the counterions on the m i c e l l e ~ ' ~ -(or ~ ~the J ~polyions).zO
Experimental Section Materials. The samples of C12NlC02, C12N3C02, C12N5C02, C12NlOC02, and C12N3S03 were the same as in part 1.
The radioactively-labeled compounds used in self-diffusion measurements were the following: 22Na-labeledsodiumchloride with a specific activity of 500 mCi mg-l, 36C1-labeledsodium chloride with a specific activity of 7 pCi mg-l, and 14C-labeled decanolwith a specific activity of 10mCi mmol-l fromAmersham, Radiochemical Center, Buckinghamshire, England. The sample of pyrene used as the fluorescent probe was the same as in part 1. Methods. The electrical conductivity was measured using an autobalanced Wayne-Kerr bridge (Model 6425) operated at 1kHz and a conductivitycellwith platinized electrodesembedded in glass (Tacussel, Type TE100). The cell was thermostated at 25 i~0.01 "C. The conductivity measurements were performed on aqueous solutions of the surfactant, in the presence of NaC1, keeping the molar concentration ratio [surfactantl/[NaCll constant and very close to 1throughout the surfactant concentration run. For the sake ofcomparison,the conductivitiesofthe aqueous solutionsofNaClwere measured in the same concentrationrange. The fluorescence measurements concerned the fluorescence intensity ofmicelle-solubilizedpyrene upon addition ofincreasing amounts of NaBr or TlzS04. Indeed, Na+ and C1-, which were the ions most often used in the present study (see below),do not quench the pyrene fluorescence, whereas T1+ and Br- do. The experimentswere performed addingthe dry saltsto the surfactant solution containing solubilized pyrene at a concentration of about (10)Lindman, B.; Puyal, M. C.; Kamenka, N.; Rymden, R.; Stilbs, P. J.Phys. Chem. 1984,88,5048. (11)Lindman, B.; Puyal, M. C.; Kamenka, N.; Brun, B.; Gunnarson, G. J.Phys. Chem. 1982,86,1702. (12)Lindstrom, B.; Khan, A.;Soderman, 0.;Kamenka, N.; Lindman, B. J . Phys. Chem. 1985,89,5313. (13)Almgren, M.; Stilbs, P.; Alsius, J.; Linse, P.; Kamenka, N. J. Phys. Chem. 1986,89,2666. (14)Lindman, B.; Kamenka, N.; Puyal, M. C.; Brun, B.; Jonsson, B. J . Phys. Chem. 1984,88,53. (15)Kamenka, N.; Chorro, M.; Talmon, Y.; Zana, R. Colloids Surf. 1992,67,213. (16)Alami, E.;Kamenka, N.; Raharimihamina, A.;Zana,R. J.Colloid Interface Sci. 1993,158,342. (17)Zana, R.: Binana-Limb616, W.; Kamenka, N.; Lindman, B. J. Phys. Chem. 1992,96,5461. (18)Kamenka,N.;Burgaud,I.:Zana,R.;Lindman,B.J.Phys. Chem. 1994,98,6785. (19)Lindman, B.; Wennerstrom, H. Top. Cum. Chem. 1980,87,1. (20) Manning, G. S. Q.Rev. Biophys. 1978,11, 179.
I
'
I
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I
I
I
B
, bJV
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I
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20
30
40
50
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Figure 1. Variation of the electrical conductivity of solutions of NaCl(0 and 0 correspond t o two independent runs) and of mixtures of NaCl zwitterionic surfactants at a molar concentration ratio [surfactantl/[NaCll = 1,with the NaCl concentration. (v)C12NlC02; (+) C12N3S03; (A) C12N5C02. 6x M. The small decrease of fluorescenceintensity arising from the dilution of the solution upon addition of solid salt was corrected for, assuming a linear change of the fluorescence intensity with the concentration for the small changes involved in the experiments. The fluorescenceintensities were measured using a Hitachi F 4010 spectrofluorometer, at an excitation wavelength of 335 nm and an emission wavelength of 374 nm. The open-ended capillary tube method using radioactive labeling was employed to measure the self-diffusion coefficients.10-18Small amounts of the radioactive labels were added to the solutions to determine the self-diffusioncoefficients of the species of interest: 22NaC1for Na+, Na3%1for C1-, and labeled decanol for the micelles (decanolis completelysolubilized in the micellesand.diffises at the same rate). The diffision experiments were performed keeping the ratio [surfactantl/[NaCll zz 1 throughout the measurements. The fluorescence and self-diffision measurements were performed at 25 "C. The solutions were prepared using ion-exchanged Milliporefiltered water (MilliporeMilli-Ro3-Plus). The pH ofthe solutions was not controlled.
Results and Discussion Electrical Conductivity. Figure 1 shows the variations of the electrical conductivity of solutions of C12NlC02, C12N5C02, and C12N3S03 in the presence of a near equimolar amount of NaC1, and of aqueous solutions of NaC1, with the NaCl concentration, C N ~ CThe ~ . plot for NaCl is nearly linear in the concentration range investigated, whereas the plots for the surfactant-containing systems are slightly curved. At low C N ~ all C ~the , plots are coincident. Then, above 20-30 mM, the plots for the surfactant-containing systems depart from that for NaCl and remain below this plot, the difference increasing with CNaC,. A n obstruction effect of the micellesz1 cannot account for the difference between the conductivities of the NaCl solutions in the absence and in the presence of surfactant. Indeed, at the highest surfactant concentration used in these experiments, the surfactant volume fraction is of about 1.5% and the obstruction effect of ,the spherical or nearly spherical micelles present in the
Kamenka et al.
4236 Langmuir, Vol. 11, No. 11, 1995 1.05
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c (M) Figure 2. Variation ofthe relative intensity of the fluorescence emission of micelle-solubilized pyrene at 374 nm, with the surfactant concentration in mixtures of KBr and zwitterionic surfactants at a molar concentration ratio [surfactantl/[KBrl = 1: (v) C12NlC02 and (A) C12N5C02. The symbols v correspondto C12NlC02 in the absence ofKBr. The intensities have been normalized with respect to the intensity value at about 0.04 M for the three systems. system1would result in a decrease of conductivity of less than 1%.Besides, the obstruction effect should show a weak dependence on the nature ofthe surfactant, contrary to the experimental observation (see Figure 1 and the comments below). A more likely explanation for the results in Figure 1is that part of the Na+ and C1- ions are bound by the zwitterionic micelles, resulting in a decreased conductivity of the solution with respect to that in the absence of surfactant. The relative positions of the plots in Figure 1 suggest that the ion binding to C12N5C02 micelles is stronger than to the micelles of C12NlC02 and C12N3S03. The plot for C12N3C02 has also been determined and found to fall between those for C12N5C02 and C12NlC02. Fluorescence Quenching. These experiments were performed with KBr and TlzS04 replacing NaCl because neither Na+ nor C1- is a quencher of the pyrene fluorescence, whereas Br- and T1+ strongly quench this fluorescence. The binding of Br- ions to zwitterionic micelles has been monitored by measuring the decrease of the pyrene fluorescence intensity due to the quenching by Br- as a function ofthe surfactant and salt concentrations, keeping the molar concentration ratio [surfactantl/[KBrl % 1, as in electrical conductivity measurements. The results are shown in Figure 2 for C12NlC02 and C12N5C02. For the sake of comparison, measurements have also been performed on solutions of C12NlC02 in the absence of KBr. For C12NlC02 in the absence of KBr, the relative intensity is independent of the surfactant concentration, within experimental error. A decrease of intensity is observed for the systems in the presence of KBr, which can be attributed to the quenching of the pyrene fluorescence associated to the binding of Br- to the zwitterionic micelles. This decrease is larger for C12N5C02 than for C12NlC02, indicating a stronger binding by the C12N5C02 micelles, in agreement with the conductivity results in Figure 1. Note that the addition of Br- ions to a micellar solution containing solubilized pyrene changes the fluorescence intensity only when the Br- ions bind to the micelles. Thus, addition ofNaBr to micellar solutions
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,
,
,
I
,
I
,
1 0.6
1
0.3
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i
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Figure 4. Variation of the relative intensity ofthe fluorescence emission of micelle-solubilized pyrene at 374 nm, with the concentration of added TlzS04. (VI C12NlC02 (0.513M); (0) C12N3C02 (0.535 M); (A) C12N5C02 (0.525 M); and (+) C12N3S03 (0.515 M). The intensities have been normalized with respect to the value in the absence of KBr.
of sodium dodecyl sulfate had no effect on the fluorescence intensity of micelle-solubilized pyrene, because the Brions were repelled by the negatively charged micelle surface, whereas such additions to a micellar solution of dodecyltrimethylammonium chloride resulted in a decrease of fluorescence intensity, as Br- ions bind to the positively charged micelles more strongly than C1- ions and quench the pyrene emission. The second series of experiments involved the addition of increasing amounts of KBr and TlzS04 to solutions of the investigated surfactants a t a constant and high surfactant concentration (between 0.43 and 0.53 MI and a constant pyrene concentration. The results represented in Figures 3 and 4 show that, in all instances, the addition of salt results in a decrease of the fluorescence intensity, which reflects the quenching of the micelle-solubilized pyrene upon binding of Br- and Tlf to the micelles. At low concentrations of added salt, the values of the intensity depend on the nature of the surfactant and define the following sequences: C12NlC02 x C12N3S03 < C12N3C02 < C12NlOC02 < C12N5C02 for Br- and C12N3S03 < C12N5C02 < C12N3C02 < C12NlC02 for T1+. Self-Diffusion. Figures 5 and 6 show the variations of the self-diffision coefficients of Na+ and C1- with the surfactant concentration, C , for C12N3C02 and C12N10-
Aqueous Solutions of Zwitterionic Surfactants
Langmuir, Vol. 11, No. 11, 1995 4237
16
i v K
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.
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above cmc and then decreases to reach a constant value as the ionic surfactant concentration is increased.lOJi The distribution ofNa+and C1- between the zwitterionic micelles and the intermicellar solution can be obtained in the same manner as in our previous work on ionic surfactant solutions, using a two-state model where the measured ion diffusion coefficient is taken as a populationweighted average of the ion diffusion coefficients in the free state and in the micelle-bound state.1° In this model, the self-diffusion coefficient, Dx, of ion X, is given by
- 4
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6
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' 0 0.6
0.8
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C (mollkg)
Figure 6. Variation of the self-diffusioncoefficients of (0)Na+ and (0)C1- (left scale)and of (a)micelles (rightscale)in micellar solutions of C12NlOC02. with the surfactant concentration. C02, respectively. Similar plots, not shown, have been obtained for C12NlC02, C12N3S03, and C12N5C02. All of the surfactants studied show the same behavior, that is, a decrease of the ion (Na+ and C1-) self-diffusion coefficient which becomes detectable only at a surfactant concentration well above the cmc, typically a t C > 30 mM. Recall that the cmc's ofthe surfactants investigated range from 0.13 mM for C12NlOC02 to 4.3 mM for C12N3C02.21 These decreases of ion self-diffusion coefficients are much larger than those expected on the basis of the micelle obstruction effect,22although this effect is significant a t the highest surfactant concentrations used and has been taken into account in the quantitative analysis of the results (see below). Thus, the results suggest that both Na' and C1- become increasingly bound to the zwitterionic micelles at C > 30 mM, in agreement with the conductivity data. Such a behavior is quite different from that for solutions of ionic surfactants, where a drastic decrease of ion diffusion coefficient is observed right above the cmc. For both anionic or cationic surfactants, it has been shown that the degree of counterion binding is the largest right (21) Chevalier, Y.; Storet, Y.; Pourchet, S.; Le Perchec, P. Langmuir 1991, 7, 848. (22) Jonsson, B.: Wennerstrom. H.: Nilsson. P. G.: Linse. P. Colloid Polym. Sci. 1986,77, 264.
where the subscripts f and m refer to the free and micellebound states of ion X pi and Di are the fraction and selfdiffusion coefficient of Xin state i. The bound ions diffuse with the diffusion coefficient, D,, of the micelles, whereas the free ions diffuse in the intermicellar media with their diffusion coefficients, DF. As seen p r e v i o ~ s l y , lD ~ ,- ~can ~ be obtained from measurements with labeled decanol and variations with the surfactant concentration, C, are illustrated in Figures 5 and 6 for C12N3C02 and C12NlOC02 (similar variations of D,, not shown, have been obtained for the other three surfactants investigated, and the values of D , are used in part 3 in this series to obtain information on micelle size and hydration and intermicellar interactions). To obtain the value of D f , one must take into account the obstruction effect of the micelles on the diffusion of Na+ and C1-. The obstruction effect of the spherical or nearly spherical micelles present in the system1 reduces DF according to the equation21
DF = D&(1
+ 0.5@)-1
(2)
where @ is the micelle volume fraction which must be calculated for each value of C and Dto is the self-diffusion coefficient of Na+ or C1- in aqueous NaCl or in a dilute solution of NaCl in the presence of surfactant a t C < cmc. Interionic interactions were taken in account by means of a n iterative procedure," as the variations of DNa+and Dc'- with the NaCl concentration in aqueous solution were also measured as part of this work. Within the two-state model, the concentration of bound ions is
where C: is the total molal concentration of ion X (equal to the molal concentration of added salt (NaC1) plus the concentration ofthe labeled NaC1) and# the ion diffusion coefficient measured a t the surfactant concentration C (and volume fraction @I. The value of 0; in eq 3 is obtained from eq 2. The degree of ion binding, PX,is equal to Cz/C,, where C, = C - cmc is the molal concentration of micellized surfactant. The values of3! , have been calculated for Na+ and C1-, and the results are plotted in Figures 7 and 8. As expected from the conductivity and ion self-diffusion results, P is very small for surfactant concentrations up to 30 mM, and the calculated values are just indicative of the low degree of binding of the two ions. PNa+and Pcl- increase with the surfactant concentration. For the five surfactants, the binding degree is larger for C1- (anion)than for Na+ (cation). Also, the ion binding is seen to increase with the length of the spacer in the sequence C12NlC02 < C12N3C02 < C12N5C02 x C12NlOC02. C12N3S03
Kamenka et al.
4238 Langmuir, Vol. 11, No. 11, 1995
An identical equation is obtained by directly applying the mass action law to reaction 4. Inserting the equations
and
into eq 7 yields
c (MI Figure 7. Variation of the degree of Na+binding to zwitterionic micelles with the surfactant concentration. (v)C12NlC02; (0) C12N3C02; (A) C12N5C02; (0) C12BlOC02; and (+) C12N3S03. The solid lines going through the experimental points have been calculated as indicated in the text.
gt il 0.4
0.3
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P
(1- pcl-)c,(c,- pcl-c,)
(10)
For C > 50 mM, C, x C, because of the low value of the cmc. Notice that C and C, are not exactly equal because ofthe labeled NaCl added to the solution. This correction to C, is, however, small and becomes negligible a t C > 100 mM. Equation 10 can be solved for , P I - , which is written as
pcl- = [C, + c, + l/Kcl- -
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Figure 8. Variation of the degree of C1- binding to zwitterionic micelles with the surfactant concentration. (v)C12NlC02; (0) C12N3C02; (A) C12N5C02; (0) C12BlOC02; and (+) C12N3S03. The solid lines going through the experimental points have been calculated as indicated in the text.
appears to bind ions slightly less than C12N3C02 but clearly more than C12NlC02. A simple model, based on a Langmuir-type adsorption of ions on sites a t the micelle surface and which reduces to apply the mass action law to the ion binding equilibrium by the micelles, can be used to explain the variation of j? with the concentration of the surfactant and/or added salt. Considering, for example, the binding of C1- ions by the quaternary ammonium headgroups, referred to as N+, the adsorption equilibrium is written as
N+
+ C1-
-
NC1
(4)
If Kc1- is the adsorption equilibrium constant, then
where r N C 1 and r N + are the surface excess of bound ions and binding sites, expressed in moles per unit surface. Since the micelle size does not depend on the concentrations of surfactant and salt,' the following approximation holds:
where C y is the concentration of free binding sites in the micelles. Equation 5 becomes
A similar equation holds for Na+. In Figures 7 and 8, the solid lines going through the experimental points have been calculated using eq 11and the appropriate values of the concentrations C, and C, and taking Kx as a n adjustable parameter. The values o f p a ' andGl-providing the best fit ofeq 11to the results are listed in Table 1. The agreement between the experimental and calculated values of j?" is good; the differences between calculated curves and experimental results are indeed well within the experimental error. Note that the model used is the most simple one and involves only one parameter, the binding constant Kx. The agreement is good enough for excluding the need to use more complex models with additional parameters. The mass action law model developed above is a phenomenologicalapproach which provides a quantitative tool for comparing various surfactants or different added salts but does not explain the origin of ion binding to zwitterionic micelles. These micelles being electrically neutral, they cannot attract ions at long distances and the question which arises concerns the driving force for ion binding. Specific binding, as, for instance, of H+ions to carboxylate groups, cannot be involved, as very different types of ions were shown to bind to the zwitterionic micelles. More likely, the binding is ofelectrostatic origin. For all of the surfactants investigated, the density of the N+(CH& positively charged groups is larger than that of the COz- negatively charged groups because the former are located closer to the micelle center. This should result in a stronger binding of anions than of cations, as experimentally observed, if ion binding is given a purely electrostatic origin. To test this hypothesis, a rough model of zwitterionic micelle shown Figure 9 can be used to evaluate the electrostatic potential, q, in the absence of salt. Each micelle is modeled as a hydrophobic sphere of radius R1,where ions cannot enter and on the surface of which are located N (micelle aggregation number) positive charges. The N negative charges are located on a concentric spherical surface of radius Rz. The origin of the potentials is chosen a t a n infinite distance from the micelle center (q(-)= 0). The electrostatic potential q ( r )
Aqueous Solutions of Zwitterionic Surfactants
Langmuir, Vol. 11, No. 11, 1995 4239
Table 1. Average Values of pa+ and KC'-, in M-l, at 25 "C, for the Surfactants Investigated
surfactant C12N1c02
pa+ 0.29 Kc'0.49
C12N3c02
C12N5c02
C12N10c02
C12N3SO3
0.55 0.86
0.67 1.35
0.76
0.43 0.56
1.14
Figure 9. Model of the zwitterionic micelle used in the
calculations (see text).
at a distance r from the micelle center, in the spherical shell of radii R1 and Rz, is then given by
Ne R 2-r v(r) = for R, 4n6,~ R,r
Ir IR,
(12)
whereas
v ( r )= 0
for r
IR,
(13)
In eq 12, E is the dielectric constant in the spherical shell. The above expressions neglect the contribution of image charges for the order ofmagnitude calculations which are attempted at this stage. Equation 12 indicates that a positive electrostatic potential exists between R1 and Rz which accounts qualitatively for anion binding. The interaction energy of a n anion located a t r = R1 is E = -eq(Rl). Taking the case of C12NlC02 micelles (N = 75, R1= 1.85 nm, RP R1 = 0.3 nm), the surface potential v(R1) is found to be close to 100 mV and the interaction energy E is about -4 kT, when taking for the value of the dielectric constant E that of pure water. Interaction energies between -3 and -4 kT were similarly calculated for the other surfactants investigated, when using the values of the reported aggregation numbers' and Rz - R1 w 0.3 nm. This magnitude (E > IZT) makes the electrostatic mechanism a good rationale for the binding of anions to zwitterionic micelles. Since anions can bind to micelles, a charge compensation phenomenon necessarily occurs by cation binding. This charge compensation is described by the ratio of the degrees of binding pNa+lpC1which always falls between 0.7 and 0.85. This compensation results in approximately constant surface charge densities, lying between 1and 2 pClcm2,slightly lower but of the same order of magnitude as those of ionic surfactants where this charge regulation phenomenon has been extensively s t ~ d i e d . ~ ~ - ~ ~ These approximate calculations show that the ion binding to zwitterionic micelles can be of purely electrostatic origin. The electrostatic effects here are of very (23)Chevalier, Y.; Belloni, L.; Hayter, J.B.; Zemb, T. J.Phys. 1986, 46,749. (24)Drifford, M.;Belloni, L.; Dalbiez, J.-P.;Chattopadhyay, A. K. J. Colloid Interface Sci. 1985,105, 587. (25)Bendedouch, D.;Chen, S. H.; Koehler, W. C. J. Phys. Chem. 1983,87,2621. (26)Chevalier, Y.; Zemb, T. Rep. Prog. Phys. 1990,53,279.
short range, as they take place in the spherical shell of radii R1 and RP,in the dipolar region of the interface. As a consequence, ion binding depends strongly on the interfacial structure at a molecular level. It is indeed observed that the effective length of the intercharge group of the surfactant strongly influences ion binding. Because of the short-range character of such phenomena, a more accurate calculation of the electrostatic ion binding should account for the effects of the dielectric constant discontinuity a t r =R1, of the dielectric properties of the spherical shell, of the surface roughness, of the excluded volume of the molecules, and of the hydration. Notice that the potential calculated above shows a strong dependence on the thickness of the interfacial region (R2 - RI), that is, on the intercharge group length and orientation. The increase of the degree of binding with the carbon number s of the intercharge group is clearly reflected in the values of the binding constants for the C12NsC02 surfactants. An explanation for this behavior has to be looked for in the thin interfacial region of radii R1 and Rz for which there exist no precise experimental structural data. A possible explanation may lie in the following electrostatically driven reorganization of this region. Adsorption of C1- ions close to the quaternary ammonium headgroups results in a decrease of the positive surface charge density of the sphere of radius R1. The carboxylate groups are then less attracted by this surface, and the intercharge group is expected to extend, a t least for large values of s, and R2 - R1 is expected to increase. This accounts for the increase of pa- with s, as v(R1) is an increasing function of Rz - R1 in the above electrostatic model. Of course, this electrostatic increase of the interfacial thickness is opposed by the hydrophobic character of the intercharge group and by entropic effects. Thus, the increase of binding of C1- with s is expected to level off for large values ofs, as is experimentally observed. Also, the interfacial region is of lower polarity because it contains (CHZ).groups. Recall that the degree ofcation binding to micelles of surfactants with carboxylate headgroups is smaller than that of halide ions to micelles with quaternary ammonium h e a d g r o u p ~ ,while ~ ~ Ja~simple ~~~~~~ electrostatic model would predict identical values of p for anions and cations. As a n alternative explanation, the increase of C1- binding with s may reflect the tendency of the less hydrated halide ion to adsorb a t hydrophobic cationic interfaces. The results also show that C12N3C02 binds ions more than C12N3S03, indicating some effect of the nature of the surfactant headgroup. Recall that the values of the degree of binding of Naf to micelles of sodium octanoate and of sodium octyl sulfonate are respectively 0.50 and 0.3514J0 and thus show the same behavior as the zwitterionic surfactants. These differences are related to the subtleties involved in ion-ion interactions. Recall also that the carboxylate group is more hydrophilic than the sulfonate A weak protonation of the C02- groups under the experimental conditions used may be responsible for the difference of behavior between C12N3C02 and C12N3S03. Changes in the surfactant sequence of binding are also suggested by the results in Figures 3 and 4 when going from Na' to T1+ and also, but to a lesser extent, in going from C1- to Br-. Both the size of the ion and its detailed electronic structure may be responsible for these changes. ~
~~
~~
~
(27)Fabre, H.; Kamenka, N.; Khan, A,; Lindblom, G.; Lindman, B.; Tiddy, G. J.Phys. Chem. 1980,84,3428. (28)Zana, R. J. Colloid Interface Sa.1980,78, 330. (29)Laughlin, R. G.Advances in Liquid Crystals; Brown, G. H., Ed.; Academic: New York, 1978;p 41.
4240 Langmuir, Vol. 11, No. 11, 1995
Conclusion We have shown that the micelles of a series of zwitterionic surfactants of increasing intercharge carbon number, s, can bind both anions and cations. Anions are more bound than cations, whatever the value of s. Nevertheless, the net negative charge taken by the micelle remains low. This explains the insensitivity of the micelle aggregation number to the addition of NaCl and the little influence of added salts on the phase diagram of zwitterionic surfactant^.^^ The binding appears to be of essentially electrostatic nature. The variation of the (30)Kamenka, N.;Haouche, G.; Brun, B.; Lindman, B. Colloids Surf. 1987,25,2a7.
Kamenka et al. degree of counterion binding with the concentration of the surfactant and added salt has been accounted for using a simple mass action law model for the binding. The increase of the degree of ion bindingwith the spacer carbon number appears to be related to the conformation and orientation of the intercharge group.
Acknowledgment. N. K., Y. C., and R. Z. also belong to the GDR No. 1082“SystemesColloidaux Mixtes” of the CNRS, directed by Dr. T. Zemb (CEA, Saclay, Gif sur Yvette, France), and acknowledge the financial support received from this group. LA950370E
