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Notes Ion Exchange Effects on the Electrical Conductivity of Acidified (HCl) Sodium Dodecyl Sulfate Solutions Roma´n Pazo-Llorente,† Carlos Bravo-Dı´az,*,† and Elisa Gonza´lez-Romero‡ Universidad de Vigo, Facultad de Ciencias, Departamento de Quı´mica Fı´sica and Departamento de Quı´mica Ana´ litica y Alimentaria, 36200 Vigo, Spain Received September 25, 2003. In Final Form: December 19, 2003
Introduction Prediction of solution conductivities based on the concentration of surfactant ions, counterions, and micelles requires realistic models for micellization. The mass-action model is quite reasonable to discuss micellar formation and to interpret thermodynamic data provided that the micellar aggregation number is relatively small, in the order of a few hundreds, and dispersion of micellar sizes is not significant.1-5 Conductivity data are then analyzed in terms of the Debye-Hu¨ckel-Onsager theory by treating the aqueous monomers and micelles as a solution of mixed electrolytes according to Kohlrausch’s law.1,6-10 Electric conductivity data are typically obtained by employing common electrodes and/or ion selective electrodes, and they are most commonly used to verify the presence of aggregates and to determine the critical micellar concentration, cmc, the degree of ionization of micelles R (or the fraction of bounded counterions, β ) 1 - R),4,5,11,12 and a variety of thermodynamic data.11 New approaches to determine micellization parameters such as micellization constants, aggregation numbers, numbers of counterions per micelle, and critical aggregation concentrations of mixed ionic-nonionic surfactants have been recently reported.4,12-15 Conductivity data have also * To whom correspondence should be addressed. E-mail: cbravo@ uvigo.es. † Dpto. Quı´mica Fı´sica. ‡ Dpto. Quı´mica Ana ´ litica y Alimentaria. (1) Evans, H. C. J. Chem. Soc. 1956, 579. (2) Shanks, P. C.; Franses, E. I. J. Phys. Chem. 1992, 96, 1794. (3) Moroi, Y. Micelles: Theoretical and Applied Aspects; Plenumm Press: New York, 1992. (4) Moroi, Y.; Yoshida, N. Langmuir 1997, 13, 3909. (5) Patist, A. Determining Critical Micelle Concentration. In Handbook of Applied Surface and Colloid Chemistry; J. Wiley & Sons: Chichester, U.K., 2002; Vol. 2. (6) Zana, R. J. Colloid Interface Sci. 1974, 46, 372. (7) Saito, M.; Moroi, Y.; Matuura, R. J. Colloid Interface Sci. 1982, 88, 578. (8) Saito, M.; Moroi, Y.; Matuura, R. Dissolution and Micellization Parameters of Long-Chain Alkylsulfonic Acids and Their Sodium Salts in Water. In Surfactants in Solution; Mittal, K. L., Lindman, J., Eds.; Plenum Press: New York, 1984. (9) Lianos, P.; Lang, J. J. Colloid Interface Sci. 1983, 96, 222. (10) Zana, R. Surfactant Solutions: New Methods for Investigation; Marcel Dekker: New York, 1985. (11) Gonza´lez-Pe´rez, A.; Del Castillo, J. L.; Czapliewicz, J.; Rodriguez, J. R. J. Phys. Chem. B 2001, 105, 1720. (12) Carpena, P.; Aguiar, J.; Bernaola-Galva´n, P.; Carnero-Ruiz, C. Langmuir 2002, 18, 6054. (13) Dev, S.; Gunaseelan, K.; Ismail, K. Langmuir 2000, 16, 6110.
been employed to interpret changes in the structure of mixed micelles, to explain micellar effects on chemical reactivity, and to evidence formation of ion pairs between ions of interest.16-20 Much less attention has been given to analyzing the conductivity of micellar systems containing two or more different electrolytes. When Mxn+Xym- ions (Mxn+ * Na+) are added to anionic surfactants such as sodium dodecyl sulfate, SDS, the counterions Mxn+ compete for the ionic headgroup of the micelles with the surfactant counterions that already exist in solution and displacement of ions can occur depending on the relative affinities of counterions for the headgroups and on their relative concentrations.21,22 For instance, binding of H+ ions to SDS micelles was first pointed out by Bunton et al.,23 concluding that there is little difference in the binding of hydrogen and sodium ions to the anionic micelle and that approximately 80% of the micelle headgroups are neutralized by counterions. Further investigations showed that ion exchange effects have considerable impact in systems containing charged aggregates playing a fundamental role in interpreting micellar catalysis or inhibition.21,22,24 Ion exchange effects are currently rationalized in terms of the pseudophase ion exchange, PIE, model, that treats micelles as selective ion exchangers saturated with counterions.25 In this work, we have explored the effects of ion exchange on the conductivity of SDS micellar solutions by employing different amounts of HCl and an equation, applicable to any acidified anionic surfactant solutions bearing monovalent, divalent, or trivalent counterions, is derived allowing one to estimate κ values by computer simulation procedures.26 In the absence of added electrolytes, that is, [HCl] ) 0 M, the electrical conductance of the system increases continuously, the gradient of the increase below (14) Gunaseelan, K.; Ismail, K. J. Colloid Interface Sci. 2003, 258, 110. (15) Gunaseelan, K.; Umlong, I. M.; Mukhim, T.; Ismail, K. Langmuir 2003, 19, 7276. (16) Bravo, C.; Leis, J. R.; Pen˜a, M. E. J. Phys. Chem. 1992, 96, 1957. (17) Freire, L.; Iglesias, E.; Bravo, C.; Leis, J. R.; Pena, M. E. J. Chem. Soc., Perkin Trans. 2 1994, 1887. (18) Iglesias, E.; Montenegro, L. Phys. Chem. Chem. Phys. 1999, 1, 4865. (19) Bravo-Diaz, C.; Soengas-Fernandez, M.; Rodriguez-Sarabia, M. J.; Gonzalez-Romero, E. Langmuir 1998, 14, 5098. (20) Bravo-Dı´az, C.; Romero-Nieto, M. E.; Gonzalez-Romero, E. Langmuir 2000, 16, 42. (21) Bunton, C. A.; Nome, F.; Quina, F. H.; Romsted, L. S. Acc. Chem. Res. 1991, 24, 357. (22) Savelli, G.; Germani, R.; Brinchi, L. Reactivity control by Aqueous self-Assembling Systems. In Reactions and Synthesis in Surfactant Systems; Texter, J., Ed.; Marcel Dekker: New York, 2001. (23) Bunton, C. A.; Ohmenzetter, K.; Sepulveda, L. J. Phys. Chem. 1977, 81, 2000. (24) Bunton, C.; Yao, J.; Romsted, L. S. Curr. Opin. Colloid Interface Sci. 1997, 2, 622. (25) Romsted, L. S. Micellar Effects on Reaction Rates and Equilibria. In Surfactants in Solution; Mittal, K. L., Lindman, J., Eds.; Plenum Press: New York, 1984. (26) In the course of the reviewing process, a paper by Dominguez et al. (J. Chem. Educ. 1997, 74, 1227) came to our attention. This paper was apparently designed to familiarize students with micellar solutions through the determination of the cmc of some surfactants by different techniques and contained a piece of work similar to the one described in the present paper but performed at a single [HCl] and where no simulation procedures are indicated.
10.1021/la035793s CCC: $27.50 © 2004 American Chemical Society Published on Web 02/11/2004
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tions below the cmc, that is, in the absence of micelles, can be determined as the sum of the corresponding molar equivalent conductivities of the Na+ (λNa+) and DS(λDS- , DS- ) C12H25SO4-) ions according to eq 1,
κ ) λNa+[Na+] + λDS-[DS-]
(1)
Given that surfactants behave as strong electrolytes at very low concentrations, it is reasonable to assume a perfect dissociation of the SDS monomers,4 that is, [Na+] ) [DS-] ) [SDS]T, and the electrical conductance of the solution is then given by eq 2, which predicts a linear increase in κ with [SDS] with a slope given by eq 2a.
Figure 1. Variation of the electrical conductivity of a pure SDS aqueous solution at T ) 25 °C. All data shown are experimental.
κ ) (λNa+ + λDS-)[SDS]T
(2)
S1 ) κ/[SDS]T ) λNa+ + λDS-
(2a)
the cmc being positive and higher than that obtained above the cmc, which is also positive, reflecting the formation of micelles in agreement with previous reports.10,27 However, in acidified aqueous solutions of SDS ([HCl] ) 10-2 M), the electrical conductivity of the solution increases upon increasing [SDS] up to the cmc but decreases once micelles are formed up to a minimum after which a positive increase is again observed. The κ value at the minimum is much lower than that of an aqueous acid solution of the same pH, leading to apparently anomalous experimental results that can be perfectly rationalized once the data are interpreted in terms of the PIE model.
The breakpoint observed in Figure 1 is indicative of formation of micelles, which have a different degree of ionization from that of the monomer because of the partial incorporation of counterions.2,27 The concentration of free counterions, [Na+]F, above the critical micellar concentration, C0, can be obtained by considering the electroneutrality condition, that is, [Na+]F ) C0 + RDn, where Dn represents the concentration of micellized surfactant, Dn ) [SDS]T - C0, and R is the degree of ionization of the SDS micelles. At concentrations above C0, the specific conductivity of the aqueous micellar solution is given by eq 3, where λM and [M] stand for the molar conductivity of micelles and the concentration of micelles, respectively.
Experimental Section
κ ) (λNa+ + λDS-)C0 + λNa+RDn + λM[M]
Materials. Reagents were of maximum purity available and were used without further purification. Sodium chloride, NaCl, hydrochloric acid, HCl, and SDS (99.9%) were purchased from Aldrich. All solutions were prepared by using Milli-Q grade water (κ ) 1.2 µS cm-1). Instrumentation. Specific conductivities were obtained by employing a Metrohm model 712 conductometer provided with a four-pole measuring cell (the measured cell-factor was equal to 0.82 cm-1) and a Pt-100 temperature sensor attached to a computer for data storage. Solutions were thermostated in the conductivity cell, equipped with a magnetic stirring device, at T ) 25 ( 0.1 °C. pH was measured by employing a previously calibrated Metrohm model 744 pH-meter equipped with a temperature sensor. Methods. κ values were obtained by following an addition method. For the purpose, a stock HCl solution was prepared and its concentration was determined by potentiometric measurements. A known volume of this solution was introduced in the conductivity cell and thermostated at T ) 25 ( 0.1 °C with continuous stirring. The other portion was employed to prepare a highly concentrated stock SDS solution ([SDS] ) 1.5 M) by dissolving the appropriate amount of SDS. Diluted SDS solutions were prepared by adding aliquots of the concentrated SDS stock solution to the required volumes of the HCl solution. Aliquots (20-100 µL) of the less concentrated SDS solutions were added to the HCl solution in the conductivity cell to get the desired SDS concentration.
Results and Discussion Figure 1 shows the typical variation of the electrical conductivity of a pure aqueous SDS solution upon increasing [SDS] at T ) 25 °C.3,10,12 Assuming that the aqueous surfactant solution obeys Kohlrausch’s law, the specific conductivity, κ, of the system at SDS concentra(27) Fendler, J. H.; Fendler, E. F. Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975.
(3)
Assuming that the contribution of the micelle is given by λM ) NRλDS-, where N denotes the aggregation number, [M] ) ([SDS]T - C0)/N, and bearing in mind eq 2, eq 3 can be rearranged to eq 4,
κ ) (1 - R)(λNa+ + λDS-)C0 + (λNa+ + λDS-)R[SDS]T ) S1(1 - R)C0 + S1R[SDS]T (4) which again predicts a linear increase in κ upon increasing [SDS] with a slope S2 ) S1R from which the degree of ionization of the micelles is given by the ratio of the slopes above and below the cmc, that is, R ) S2/S1. The cmc value can be obtained from the cross point of the two straight lines defined by eqs 2 and 4. From the data in Figure 1, values of R ) 0.25 and C0 ) 7.6 × 10-3 M can be estimated, in agreement with published data.5,10,27 The electric conductivity variation of an aqueous surfactant solution containing intentionally added NaCl ([NaCl] ) 10 mM) is very similar to that shown in Figure 1 (data not shown), owing to the increase in κ compared to that in the absence of NaCl due to the extra contributions of the Na+ and Cl- ions, hence consistent with the predictions of eqs 2 and 4. However, a lower C0 value is obtained, consistent with published electrolyte effects on the cmc.27 Figure 2 shows the Z-shaped profile obtained when a 10 mM HCl aqueous SDS solution is employed. Addition of SDS makes κ increase up to a maximum after which a significant decrease is observed upon increasing SDS up to a minimum at about [SDS] ) 2.5 × 10-2 M. Further addition of SDS causes κ to increase again. Note that the κ value at the minimum is much lower than that of a 10 mM HCl solution without SDS. When higher concentra-
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Notes
higher than ∼0.15 M (data not shown for clarity). It is apparent that the observed behavior in Figures 2 and 3 is completely different from that shown in Figure 1 and hence it is not consistent with the predictions of eq 4. As noted before, surfactants behave as strong electrolytes at surfactant concentrations below the cmc, and thus when HCl is present in the system, eq 2 becomes eq 5, which predicts that κ should increase upon increasing [HCl] and [SDS], owing to the independent contributions of the Na+, DS-, H+, and Cl- ions. The maximum in Figures 2 and 3 is attained at the concentration where micelles are formed, that is, the critical micellar concentration C0, which is lower than that in the absence of HCl, in agreement with literature reports.27,28 Figure 2. Variation of the electrical conductivity of an acidified ([HCl] ) 10 mM) aqueous SDS solution at T ) 25 °C. (O) Experimental points. (b) Simulated points obtained by emH+ ploying eqs 7 and 8 and by employing β ) 0.8 and KNa + ) 0.7.
κ ) (λNa+ + λDS-)[SDS]T + (λH+ + λCl-)[HCl]T ) S1[SDS]T + κHCl (5) The variation of κ shown in Figures 2 and 3 can be rationalized by bearing in mind that micelles behave as selective ion exchangers. In the first advance in the quantitative treatment of ion exchange effects, Romsted21,24 expressed the amount of bound counterions in + the micellar Stern layer, mH s , as the mole ratio of + micellar bound ions, [HM ], to micellized surfactant, Dn, and assumed that the micelle is saturated with counterions + + regarding their nature or concentration, that is, mNa s + mH ) β ) 1 R ) constant. Advantages and limitations s of this formalism are discussed elsewhere.25,29-31 Assuming that above the cmc H+ and Na+ ions compete for the micellar surface, the exchange of ions can be expressed through an ion exchange constant,22,25,31 eq 6, H+ KNa +
)
H [Na+ W]ms Na [H+ W]ms
+
+
)
+ [Na+ W][HM]
(6)
+ [Na+ M][HW]
where the subscripts W and M refer to the aqueous and micellar pseudophases, respectively. Combination of eq 6 with the corresponding mass balance leads to eq 7, which + + allows one to obtain mH s and hence [HM]. + 2 (mH s )
+
+ (mH s )
[
]
+
H + [H+]T + KNa +[Na ]T +
H (KNa + - 1)Dn
-β β[H+]T +
H (KNa + - 1)Dn
) 0 (7)
The specific conductivity of the solution above the critical micelle concentration C0 is then given by eq 8, where [H+ M] represents the concentration of bound H+ ions.
Figure 3. Electrical conductivity behavior of an acidified aqueous SDS solution at T ) 25 °C. (A) [HCl] ) 18 mM. (B) [HCl] ) 70 mM. (O) Experimental points. (b) Simulated points obtained by employing eqs 7 and 8 and by employing β ) 0.8 H+ H+ and KNa + ) 0.8 (panel A) and β ) 0.7 and KNa+ ) 0.6 (panel
B).
tions of HCl are used, Figure 3, the minimum becomes broader and takes place at increasingly higher SDS concentrations. For [HCl] > 70 mM, a continuous decrease in the electrical conductivity can be observed in the concentration range where [SDS] > cmc (Figure 3B) in agreement with previous reports;23 an increase in the electrical conductivity is, however, detected at [SDS]
κ ) κ0 + κ1 + κ2 + κ3 + κ4 ) (1 - R)(λNa+ + λDS-)C′0 + (λH+ + λCl-)[HCl]T + (λNa+ + λDS-)R[SDS]T + (λNa+ - λH+)[H+ M] ) βC′0S1 + κHCl + S1R[SDS]T + (λNa+ - λH+)[H+ M] (8) Equation 8 allows one to rationalize qualitatively and quantitatively the observed variation in the κ values upon increasing [SDS], Figures 2 and 3. Qualitatively, the observed behavior can be rationalized by considering the (28) Sowada, R. Tenside, Surfactants, Deterg. 1994, 31, 195. (29) Romsted, L. S. J. Phys. Chem. 1985, 89, 5113. (30) Romsted, L. S. J. Phys. Chem. 1985, 89, 5107. (31) Romsted, L. S.; Zanette, D. J. Phys. Chem. 1988, 92, 4690.
Notes
relative weight of the terms included in eq 8. Above the critical micelle concentration C′0, the first (κ0 ) βC′0S1) and second (κ1 ) κHCl) terms are constant; meanwhile the third (κ3 ) S1R[SDS]T) and fourth (κ4 ) (λNa+ - λH+)[H+ M]) ones depend on [SDS]T and [H+ ], respectively. The fourth M term turns out to be negative because λNa+ ) 50.1 Ω-1 cm2 -1 -1 mol and λH+ ) 349.7 Ω cm2 mol-1 32 and thus may predominate over the third term depending on the particular [H+ M] and [SDS]T values, making a negative contribution to κ, that is, decreasing the value of κ, Figure 2. Upon increasing [SDS]T, [H+ M] decreases because of the increasing amount of Na+ counterions in the system, and hence the fourth term may become negligible compared to the third one, leading to an increase in κ, as observed at high [SDS] in Figure 2. By solving eq 7, [H+ M] values at any [SDS] can be obtained, hence allowing one to estimate κ values by means of eq 8. Interpretation of the kinetic behavior of a given reaction where ion exchange effects play an important role is typically attained by computer simulation procedures, allowing one to obtain the “best” KNa+H+ values that fit the experimental data by considering Dn and β ()1 R ≈ 0.8) as known values.21,22,29 The procedure leads to a H+ relatively narrow range of KNa + values that fit the (32) CRC Handbook of Chemistry and Physics, 78th ed.; CRC Press: Boca Raton, FL, 1997.
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experimental data. Another computer simulation posH+ sibility is to consider KNa + as a known constant and estimate β values that best fit the experimental data. In H+ this work, we have obtained the best KNa + by increasing H+ β values between 0.6 and 0.9 in 0.5 unit steps. KNa + values ranging from 0.7 to 0.9 were obtained, in agreement with those reported in the literature.22 The solid points in Figures 2 and 3 show the theoretically calculated κ values obtained by employing eqs 7 and 8. In conclusion, we have shown that to interpret conductivity data in acidified (HCl) aqueous SDS systems, it is necessary to take into account ion exchange effects. Furthermore, given that the λH+ value is much higher than those of other mono-, di-, and trivalent cations32 typically employed in micellar systems, the behavior shown in Figures 2 and 3 is representative for the expected variation in the conductivity of any acidified anionic surfactant solution. Acknowledgment. Financial support from the following institutions is acknowledged: MCYT of Spain (BQU2000-0239-C02), Xunta de Galicia (XUGA 38301A92 and XUGA 38305A94), and Universidad de Vigo. R. P.-Ll. thanks Xunta de Galicia for a graduate research training grant. LA035793S
