Quantitative treatment of indicator equilibria in micellar solutions of

Aug 1, 1988 - U. Costas-Costas, Carlos Bravo-Diaz, and Elisa Gonzalez-Romero .... Zanette, Sandro José Froehner, Edson Minatti, and Ângelo Adolfo Ruzz...
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J . Phys. Chem. 1988, 92, 4690-4698

4690

of the sample were substantially higher. IV. Possible Incidence of Support Restructuration on SMSI Behauior. The question then arises of the possible relationship between these phenomena and SMSI-type effects. Evidently, the structural changes at the support revealed by ESR, and the electronic effects correlated with them which give rise to the Rh BE shift, are not by themselves alone the origin of SMSI, since they remain after oxidation at 673 K and subsequent mild rereduction while the H2adsorption capacity of the metal is recovered, as shown by N M R . Indeed, SMSI behavior can be monitored quite directly with N M R spectroscopy, which shows that, in agreement with the well-known behavior of this type of catalysts in volumetric chemisorption experiments, the ability for hydrogen chemisorption (directly measurable in our experiments through the shifted line B) decreases drastically upon reduction in dynamic conditions (vanishing for reductions at 773 K), is not recovered to significant amounts through high-temperature outgassing after this treatment, and reappears after oxidation at 673 K followed by low-temperature reduction. On the contrary, in our first studies using static reductions we had found that the partial suppression of hydrogen chemisorption induced at 773 K could be reversed partially upon outgassing at the same temp e r a t ~ r e . ~Thus, . ~ ~ our results show that, under the reduction conditions which lead to the mentioned structural changes, a SMSI effect appears which, in comparison to that generated in static reductions, is much more effective and shows a different behavior against high-temperature outgassing. One should therefore consider the possibility that a stronger bonding between rhodium and the underlying titania surface, occurring in samples subjected to dynamic reduction thanks to the generation of higher concentrations of anion vacancies as described above, could be a cause of enhancement of the SMSI effects and affect their detailed behavior. The influence of this ( 2 5 ) Conesa, J. C.; et al. Proc. Inf. Congr. Catal., 8th 1984,d (Discussions volume), 285.

bonding on SMSI could be related to a flattening of the metal particle on the support (induced by the strength of those Rh-Ti bonds), resulting in a “pillbox” shape for the particle, similar to that observed previously for Pt/Ti02 systems, or to any other effect affecting the Rh-Rh bonding. These changes might directly influence the adsorption properties of the metal in the strongly reduced state of the catalyst; or, accepting the widespread decoration model for SMSI, they might affect the characteristics and properties of the decorating TiO, species (or HTiO,, as proposed by us9J2)or the way in which the electronic effect of the latter suppresses the chemisorptive properties of the more or less closely located metal atoms. A more thorough discussion of these factors, via detailed analysis of the behavior of NMR line B in the different reduction conditions, will be the subject of a subsequent paper. Conclusions

From the present results, we deduce that (a) in the Rh/Ti02 catalysts, upon strong reduction in flowing hydrogen a restructuration at the support surface occurs, favored by the presence of the metal; (b) this change is not reversed by oxidation at 673 K, in contrast with the behavior of nonloaded Ti02, a fact which indicates that the metal is involved in stabilizing this modification; (c) the electronic characteristics of the metal particles in this state are appreciably modified, due probably to the formation of the direct Rh-Ti bonds, a phenomenon which would contribute to the SMSI effect without being necessarily a sufficient condition for it; (d) NMR can be used to monitor directly the influence of the SMSI state on the adsorption of hydrogen, which is observed to behave in agreement with the results of hydrogen chemisorption reported in the literature. Acknowledgment. We give thanks to Prof. G. L. Haller for kindly giving us a specimen of IEX-type catalyst. We also thank the Spain-US. Joint Committee, the CAICyT, and the Fundacidn Ramdn Areces for financial support. Registry No. Rh, 7440-16-6; TiO,, 13463-67-7; H,, 1333-74-0.

Quantitative Treatment of Indicator Equilibria in Micellar Solutions of Sodium Decyl Phosphate and Sodium Lauryl Sulfate Laurence S. Romsted* Department of Chemistry, Wright-Rieman Laboratories, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903

and Dino Zanette* Departamento de Quimica. Universidade Federal de Santa Catarina, Florianopolis, 88.000, Santa Catarina, Brasil (Received: August 13, 1987; In Final Form: February 8, 1988) The pseudophase ion-exchange (PIE) model provides both a qualitative and quantitative interpretation of micellar effects on reaction rates and equilibria for a number of reactions between organic molecules and ions in aqueous solution in the presence and absence of buffer. Our results show that this model is also applicable to micellar solutions of sodium decyl phosphate monoanion, NaDP. We measured the ratio of the acid and base forms of the indicator, pyridine-2-azo-p-dimethylaniline (PADA), in the pH range of 4-6, succinate buffer, at a variety of surfactant and counterion concentrations. Measurements were carried out at 50 “Cto ensure that NaDP remained in solution at the lower end of the pH range. Parallel experiments were run in sodium lauryl sulfate, NaLS, to check for special effects of the head groups of micellized NaDP in the indicator equilibria. None were found. NaDP micelles behave “normally”, and the assumptions of the model are well-obeyed provided (a) measured values of the pH are used instead of assuming that the buffer maintains the pH of the aqueous phase constant at all salt concentrations and (b) the concentrations of sodium ions in the aqueous phase are converted to activities by using the mean ion activity coefficient of NaC1. Limitations of the approach and sources of error are discussed. Introduction

Five decades ago Hartley developed a simple set of rules for correlating the direction of the apparent pK, shift of visual indicators in surfactant solutions with the charge on the surfactant head group.’,* Since then a wide variety of spectrophotometric 0022-3654/88/2092-4690$01.50/0

indicators have been used to probe the interfacial properties of the Panoply of aqueous interfaces, including ~-~~ono(1) Hartley, G. s. Trans. Faraday SOC.1934, 30, 44. (2) Hartley, G. S . ; Roe, J. W. Trans. Faraday SOC.1940, 36, 101.

0 1988 American Chemical Society

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layer^,^ microemulsions,6 vesicle^,^ and biological membranes.* In principle, the typical 1-2 unit shift in apparent pK, produced on binding of the indicator to the micellar pseudophase can be related to interfacial potential and interfacial P H . ~However, even in "simple" interfacial systems like micelles, the apparent pKa depends not only on head group charge, surfactant, and counterion concentration but also on counterion type.9 Nor can one assume that the intrinsic acidities of all indicators are shifted to the same extent by micelles. The apparent pKa's of some carbon acids are shifted by more than 4 pK, units.I0 A number of quantitative treatments were developed over the past 20 years for interpreting micellar effects on indicator e q ~ i l i b r i a . ~ ~ These " - ~ ~ treatments usually work equally on micellar effects on the rates of thermal reactions, which show a similar dependence upon the same experimental variables. One of the most successful treatments is the pseudophase ion-exchange (PIE) model, and its strengths and weaknesses have been reviewed repeatedly.9-2*25 The crucial assumptions of this model for completely micellar bound indicators are as follows: (a) Micelles act as a separate phase uniformly distributed throughout the solution, the pseudophase assumption, and the medium properties of this phase are independent of solution composition. Thus, ionization of the bound indicator is described by an intrinsic acidity constant whose value reflects the medium properties of the micelle. (b) The total concentration of counterions at the micelle surface is constant and independent of surfactant concentration and counterion concentration and type. (c) The distribution of the two counterions between micelles and water is described by an empirical ion-exchange constant whose value reflects the difference in specific interactions of the two counterions with the micelle surface. The validity of these assumptions has been tested r e p ~ t e d l y ; ~ J ~ and the model breaks down severely under two extreme conditions: when the concentration of very hydrophilic counterions is in large excess and at surfactant concentrations near the cmc where specific interactions between indicators or substrates and small numbers of surfactant monomers may be important. Neither condition is approached in this study. Recently, Bunton and and Moffatt (3) Mukerjee, P.; Banerjee, K. J. Phys. Chem. 1964, 68, 3567. (4) Garcia-Soto, J.; Fernandez, M. S. Biochem. Biophys. Acta 1983, 731, 275. ( 5 ) Goddard, E. D. Adu. Colloid Interface Sci. 1974, 4 , 45. (6) Mackay, R. A. Adv. Colloid Interface Sci. 1981, 15, 131. (7) Fernandez, M. S. Biochim. Biophys. Acta 1981, 646, 23. (8) Waggoner, A. S. Annu. Rev. Biophys. Bioeng. 1979, 8,47. (9) Romsted, L. S. J. Phys. Chem. 1985, 89, 5107, 5113. (10) Minch, M. J.; Shah, S. S. J . Org. Chem. 1979, 44, 3252. (11) Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755. (12) Berezin, I. V.; Martinek, K.; Yatsimirski, A. K. Russ. Chem. Rev. (Engl. Transl.) 1973, 42, 487. (13) Martinek, K.; Yatsimirski, A. K.; Levashov, A. V.; Berezin, I. V. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum: New York, 1977; Vol. 2, p 489. (14) Romsted, L. S. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum: New York, 1977; Vol. 2, p 509. (15) Gaboriaud, R.; Charbit, G.; Dorion, F. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1191. (16) Charbit, G.; Dorion, F.; Gaboriaud, R. J. Chim. Phys. Phys.-Chim. Biol. 1984, 81, 187. (17) Lelievre, J.; Gaboriaud, R. J . Chem. SOC.,Faraday Trans. I 1985, 81, 335. (18) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979, 83, 1844. (19) Bunton, C. A,; Moffatt, J. R. In Colloids and Surfactants: Fundamentals and Applications; Barni, E., Pelizzetti, E., Eds.; reprinted from Ann. Chim. (Rome) 1987, 77, 117, and references therein. (20) Bunton, C. A.; Romsted, L. S. In The Chemistry of the Functional Groups. Supplement B: The Chemistry of Acid Derivatiues; Patai, S., Ed.; Wiley-Interscience: London, 1979; Part 2, p 945. (21) Sudholter, E. J. R.; Van de Langkruis, G . B.; Engberts, J. B. F. N. Recl. Trau. Chim. Pays-Bas 1980, 99, 73. (22) Fendler, J. H. Membrane Mimetic Chemistry; Wiley-Interscience: New York, 1982. (23) Chaimovich, H.; Aleixo, R. M. V.; Cuccovia, I. M.; Zanette, D.; Quina, F. M. In Solution Behavior of Surfactants: Theoretical and Applied Aspects; Mittal, K. L., Fendler, E. J., Eds.; Plenum: New York, 1982; Vol. 2, p 949. (24) Romsted, L. S. In Surfactants in Solution;Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015. (25) Bunton, C. A,; Savelli, G. Adu. Phys. Org. Chem. 1986, 22, 213.

demonstrated that reactions in micelles with hydrophilic counterions, in the presence or absence of nonreactive uni- or bivalent ions, can be treated quantitatively by calculating Coulombic effects using the Poisson-Boltzmann equation solved in spherical symmetry combined with an absorption isotherm for describing specific ion effects.I9 The motivation for this work originates in a long-range project designed to mimic the complex interfacial properties of biological membranes with micelles, which are thermodynamically more stable and structurally simpler. The head groups of the surfactants are to contain one or more of the functional groups found on common membrane phospholipids. We decided to begin with simple monofunctional alkyl phosphate monoanion as a model of phosphatidic acid. A substantial amount of basic information is already published on some alkyl phosphate micelles, including critical micelle concentrations (cmc), Krafft points of alkyl phosphate and the sodium and potassium salts of the alkyl phosphate mono- and dianions, and degrees of ionization of monoand dianions with several different counter ion^.^^^^^ However, nothing is known about the surface acidity of these systems or if the interfacial properties respond to added counterions like other anionic surfactants, such as NaLS, which, unlike the alkyl phosphate monoanion, cannot possibly form intermolecular hydrogen bonds. We selected the spectrophotometric indicator pyridine-2-azop-dimethylaniline, PADA, to probe the interfacial properties of micelles of sodium decyl phosphate monoanion, NaDP, at several pH and surfactant concentrations over a large NaCl concentration range. The pKa of PADA in water is about 4.5,2* which is within the pH range needed to monitor the interfacial properties of the micellized monoanion of NaDP, the dominant alkyl phosphate form between pH -4 and 6.27 We decided to work with the decyl phosphate surfactant at 50 OC because, unlike the dodecyl derivative, it remains in solution over a wide range of pH, surfactant, and counterion concentration, yet its cmc is low enough to permit working at surfactant concentrations well above the cmc. To check our experimental methodology and to reveal any potential special effects caused by the proton on the phosphate head group, we also measured the effect of added NaCl on the apparent pK, of PADA in sodium lauryl sulfate, NaLS, over the same range of pH and added NaC1. Just as micelles alter the apparent pKa of an indicator in solution, so they influence the solution pH of buffers which associate with micelles.29 Conversely, Funasaki demonstrated that the rate of alkaline ester hydrolysis in cationic micelles depends strongly on the buffer used,30showing that buffers influence micelle surface pH. Quina and co-workers demonstrated that the alkaline hydrolysis of alkyl cyanopyridinium ions in cationic micelles in the presence of borate buffer could be interpreted quantitatively using the PIE model, using an empirical ion-exchange constant to describe the distribution of borate anion between the aqueous and micellar p~eudophases.~'In our experiments the pH had to be maintained between pH -4 and 6, so careful selection of the buffer was crucial to minimizing the complexity of the interpretation. No information is currently available on the association of cationic buffers with anionic surfactants, and to minimize complications we chose an anionic buffer, succinic acid. The completely protonated form of succinic acid is quite soluble in water but insoluble in nonpolar solvents. In the pH range of interest, the buffer is primarily in either its mono- or dianion form and both should be excluded from the interfaces of our anionic micelles. Thus, succinic acid should only buffer the pH of the aqueous phase. (26) 1201. (27) (28) 7 4 , 10. (29)

Tahara, T.; Satake, I.; Matuura, R. Bull. Chem. SOC.Jpn. 1969, 42, Arakawa, J.; Pethica, B. A. J. Colloid Interface Sci. 1980, 75, 441. James, A. D.; Robinson, B. H. J. Chem. Soc., Faraday Trans. I 1978, Bunton, C. A,; Minch, M. J. J. Phys. Chem. 1974, 78, 1490.

(30) Funasaki, N. J . Phys. Chem. 1979, 83, 237.

(31) Quina, F. H.; Politi, M. J.; Cuccovia, I. M.; Baumgarten, E.; Martins-Franchetti, s.;Chaimovich, H. J. Phys. Chem. 1980, 84, 361.

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Using succinate buffer, or virtually any buffer, creates another complication; solution acidity will depend upon the amount of added salt. We found that the measured solution pH dropped by about 0.3 pH unit between 0 and 0.4 M added NaCI, much too large a pH change to permit assuming that the solution pH was constant. Consequently, we measured the solution pH potentiometrically over the identical range of conditions used in the indicator experiments and established an empirical relation between pH and NaCl concentration. To simplify the quantitative treatment, we worked at sufficiently high surfactant concentration to ensure complete binding of both forms of PADA to the micelles. We checked this assumption by measuring the binding constant of PADA to NaLS and assumed the same binding constant to NaDP and carried out several additional control experiments to show that added NaCl does not displace PADA from NaLS and, by inference, NaDP micelles. The extinction coefficients of the fully protonated and deprotonated forms of PADA were easy to measure in NaLS but proved difficult to obtain in NaDP. Special methods were developed to compensate for the fact that NaDP begins to precipitate about pH 53.6 and begins deprotonating aroud pH 27. Finally, to obtain an accurate estimate of the micelle concentration, which depends upon the quantity of added salt because added salt depresses the cmc, we measured the cmc's of both surfactants at 50 OC across a wide range of NaCl concentrations and pH. Here, too, we obtained an empirical relation which is commonly observed between the cmc and added salt (see Results). Once all these controls were instituted, we found that all our results could be interpreted quantitatively using the PIE model with almost identical values for the intrinsic pK, of PADA in micellar solutions of NaLS and NaDP, provided we expressed the quantity of protons and sodium ions in the aqueous phase as activities. In addition, the interfacial properties of NaDP proved to be virtually identical with those of NaLS and probably those of other anionic surfactants. Experimental Section A . Materials. Sodium Lauryl Sulfate. NaLS (BDH, specially purified) was recrystallized from water, vacuum-dried, washed with anhydrous ether, and vacuum-dried again. This procedure was repeated five times until the surface tension-surfactant concentration profile was without a minimum ( f 0 . 1 dyn/cm). M at ambient The critical micelle concentration, cmc = 6.5 X temperature, was slightly below the preferred literature value of M.32 However, the cmc obtained from a plot of specific 8X conductivity versus [NaLS] at ambient temperature showed a M. sharp break at 8.5 X Monosodium Decyl Phosphate. Monodecyl phosphate was prepared from 1-decanol (Aldrich, 99%) and POC13 (Aldrich, 99%).33 The product was recrystallized extensively from hexane, giving a white crystalline solid: mp 48 OC (lit.2748 "C). A 3'P N M R spectrum of the decyl phosphate showed a single peak at 3.13 ppm in benzene, indicating the absence of didecyl phosphate. The external reference was 85% H3P04,and the spectrum was taken at ambient temperature on a Varian CF-20 spectrophotometer. NaDP was prepared by neutralization of a weighed amount of decyl phosphate dissolved in warm ethanol with 1 equiv of standardized 1 M NaOH. The product was crystallized out on standing overnight in the refrigerator. It was isolated and dried under vacuum. NaDP has a Krafft point of 33 O C , but even at 40 OC a precipitate appears just below pH 4, which is probably the quarter salt of decyl phosphate and decyl phosphate mon ~ a n i o n At . ~ ~50 O C NaDP remains in solution at all pH's used in the experiments. The surface tension-log NaDP profiles in aqueous succinate buffer at the same concentration used in the indicator experiments and in the presence and absence of NaCl were without minima (fO.l dyn/cm). The cmc values are listed in Table 11. The 31PN M R spectrum of NaDP also showed a (32) Mukerjee, P.; Mysels, K. J. Natl. Stand. Ref, Data Ser. (US.Natl. Bur. Stand.) 1971, No. 36. ( 3 3 ) Imokavoa, G.; Tsutsumi, H. J . Am. Oil Chem. SOC.1978, 55, 839.

TABLE I: Wavelength Maxima of Acid and Base Forms of PADA in Water, NaLS, and NaDP and Their Molar Absorptivities at bx of the Acid Form 6 at , ,X of AH' , , ,X nm

H20 NaLS NaDP

AH'

A

AH'

A

554" 552' 5454

465' 450' 448'

52000 51 000 42 000

1200 1200 3000

"In 0.01 M HCI. 'In 0.02 M borate buffer, pH 9.030, [NaLS] = succinate buffer, pH 3.700, [NaLS] = 0.08 M. sufficient acetic acid to ensure complete protonation. CIn 0.4 M NaDP, plus sufficient NaOH to ensure complete deprotonation.

0.04 M. C I n 0.02 M

single peak in water at 50 OC with a chemical shift of 1.36 ppm relative to 85% H3P04as an external standard. Pyridine-2-azo-p-dimethylanilinewas supplied by Sigma. TLC's of PADA in hexane and hexane/Et20 mixtures up to 20% E t 2 0 showed only one spot under UV light, and the indicator was used without further purification. Sodium chloride, succinic acid, and sodium hydroxide (Fisher standardized concentrate) were reagent grade and used without further purification. All solutions were prepared from water which was distilled, passed over activated carbon, demineralized, redistilled, and then boiled and cooled under nitrogen, just prior to use, to remove distilled carbon dioxide. B. Methods. Absorbance Measurements. All absorbance measurements were made with a Perkin-Elmer 559A UV/vis dual-beam spectrophotometer electronically thermostated at 50 OC with a precision of fO.l OC. Each absorbance measurement was made in matched 1-cm quartz cuvettes with a reference solution of identical composition, less PADA. The effect of added NaCl on the absorbance of PADA in aqueous solution and in micellar solutions of NaLS and NaDP was determined by successive additions of small aliquots of a 5 M NaCl solution to a 2.0-mL solution of a weighed amount of surfactant dissolved in succinate buffer, which was prepared from buffer stock solutions of the desired initial pH. Buffer stock solutions were prepared by careful manual titration of succinic acid stock solutions with small aliquots of about 1 M NaOH to the desired pH. A typical salt effect run was carried out as follows. A known volume of between 4 and 6 pL of 0.01 M PADA in CH,CN (spectrophotometric grade) was added to 2.0 mL of a buffered NaLS or NaDP solution via an independently calibrated Hamilton syringe. Successive aliquots of 5 M NaCl were then added, again via a calibrated microliter syringe. The aliquot volumes were always 10, 15, 25, 25, 25, 25, and 50 ML,giving final molarities of added NaCl of 0.0249, 0.0617, 0.122, 0.181, 0.238,0.294, and 0.402 M, respectively. The absorbance spectrum was recorded after each addition, and the absorbance at the wavelength maximum for PADA in aqueous, NaLS, and NaDP solutions (Table I) was recorded from the digital readout. The M, and final concentration of PADA never exceeded 3 X each absorbance reading was corrected for dilution. The maximum correction for the increase in solution volume was 8%. p H Measurements. All pH measurements were carried out using a Corning pH meter, Model 130, using a Ross semimicro combination pH electrode, Model 81-03. The pH meter was calibrated at pH 4.00 and 7.00 with standard buffers prior to use. The solution pH was determined at all the same NaCl concentrations used in the absorbance measurements in the presence and absence of NaLS and NaDP. The initial solution volume was larger, 5 mL, to cover the electrode effectively, and the aliquot sizes were increased proportionately. Determination of Critical Micelle Concentrations (cmc). All cmc's of NaLS and NaDP were determined under the experimental conditions identical with those used for the spectrophotometric determination of the apparent pK, of PADA. Separate cmc's were determined at selected NaCl concentrations and pH's (0.02 M succinate buffer) in a glass vessel thermostated at 50.0 "C with a Fisher DuNouy tensiometer. Each surface tension-log surfactant concentration profile was obtained by dissolving a weighed amount of surfactant in a stock solution of succinate

NaDP and NaLS Micellar Solutions

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TABLE II: Critical Micelle Concentrations of NaLS and NaDP in 0.02 M Succinate Buffer at 50 OC

surfactant NaLS

cmc, M

[ N ~ T ]M,

PH'

0.0033 0.0026 0.0022

0.0167 0.0260 0.0406

4.400 4.400 4.400

NaDP

0.0177 0.0193 0.0153 0.01 26 0.0100 0.0221 0.021 6 0.0178 0.01 57 0.0125 0.0209 0.0216

0.0086 0.0327 0.0547 0.0760 0.1230 0.0183 0.0446 0.0659 0.0887 0.1355 0.0270 0.0320

4.030 4.400 4.400 4.400 4.400 4.830 5.200 5.200 5.200 5.200 5.509 5.873

"This is the pH of the surfactant and buffer solution before addition of NaCI. buffer and NaCl, giving a surfactant concentration about 2 times greater than the cmc. The surfactant solution was then diluted with successive aliquots of the same stock solution of buffer and NaCl to surfactant concentrations of about 2 times smaller than the cmc. Table I1 lists the cmc's obtained from the intersection point of the lines described by the data above and below the C ~ C All the surface tension-log surfactant concentration profiles were without minima (fO.l dyn/cm). The single conductivity experiment to check the cmc of NaLS was run on a YSI, Model 32, conductivity meter using a closed type conductivity cell at ambient temperature.

Results Determination of the Absorbance Ratio [ A H + ] / [ A ] .The concentration ratios of the acid and neutral forms of the indicator, [AH']/ [A], were calculated from measured absorbance, A , values via eq 1, where A,,, is the absorbance of the fully protonated species and A- is the absorbance of the fully deprotonated species at the wavelength used. Square brackets indicate concentration in molarity here and throughout the text. We determined the absorbance at the A, of the protonated form of PADA in the presence and absence of surfactant (Table I). At this wavelength the molar absorptivity, t, of the neutral form is much smaller than that of the protonated form. [AH'] A - Amin -=[AI Amax - A The determination of A , and A- in the presence and absence of surfactant proved to be nontrivial. We carefully determined t for AH' and A in aqueous NaLS and NaDP to ensure that the values used for A , and A- contained minimal or no contribution from other species. First, we established that the absorption spectrum of the protonated form was free of contributions from the diprotonated species under our experimental conditions and that in micellar solutions the protonated form was completely micellar bound (see below). Second, we did control experiments to ensure that the spectrum of the deprotonated form in NaLS and NaDP was that of the micellar bound species. The results are summarized in Table I. In aqueous solution, t was determined from wavelength scans at a pH required to ensure complete protonation. In 0.01 M HCl, PADA is completely monoprotonated and we saw no indication of the formation of the diprotonated species clearly observable in NaLS (see below). We note that the Beer's law plot for AH+ and 3 X M is linear at X = 554 nm between 0.5 X PADA. In NaLS, we established from inspection of wavelength scans as a function of pH that, at pH 3.7, PADA is completely monoprotonated and that diprotonation is insignificant. We also M) in 0.02 measured the apparent pK,' for PADA (2.5 X M NaLS spectrophotometrically (A, = 456 nm for AH2z+)and obtained a value of 1.72 at 50 OC. This result supports our

. ~

assumption that the amount of diprotonated species is insignificant at pH 3.7. As noted above, determination of the molar absorptivity in NaDP is considerably more difficult because of the precipitate formation below pH 3.6. However, careful titration of PADA in NaDP with 40-7O-kL aliquots of 1 M acetic acid rapidly produces spectra which are independent of acetic acid concentration after a small correction for dilution. N o increase in absorbance was observed at X = 456 nm, indicating formation of the diprotonated species. Also, the maximum absorbance is independent of NaDP concentration for all NaDP concentrations used in the salt effect studies. The molar absorptivities of PADA in NaDP and NaLS listed in Table I are an average of four runs at each pH with a mean deviation of less than f l % . Determination of the molar absorptivities of the neutral form of PADA in aqueous and NaLS was straightforward. Absorbances were obtained in 0.02 M borate buffer, pH 9.030. Again Beer's law is obeyed in water,, ,X = 465 nm, between 0.5 X and 3 X M PADA, showing that the indicator does not aggregate over this concentration range. Addition of NaLS blue shifts A, about 15 nm, but the molar absorptivity in 0.04 M NaLS is about the same as in water. We note that, at this NaLS concentration, PADA is at least 98% bound, based on our estimate of the binding constant, K, (see binding experiments below). Obtaining the molar absorptivity of PADA in NaDP was more difficult. In basic solution, NaDP deprotonates to form the alkyl phosphate dianion which has a much higher cmc than the mo~ noanion in water, 0.15 M,34so that even in the presence of 0.4 M NaCl a substantial fraction of neutral PADA may be in the aqueous phase. In addition, the increase in head group charge may alter the absorption spectrum of neutral PADA. To obtain its spectrum, we titrated a very high concentration of NaDP, 0.4 M, with small aliquots of about 1 M NaOH, until the absorbance was constant after a small correction for dilution. Only 0.25 equiv of NaOH was added, which means that 125% of the dianion is present. Gratifyingly, the absorbance at X = 545 nm is close to the one obtained during the measurement of the apparent pK, as a function of added salt (see below). The actual values of A , and A- used in eq 1 were determined each time we measured the effect of added salt on the absorbance ratio. Stock solutions of the appropriate pH and surfactant concentration were prepared according to the conditions summarized in Table I, and the absorbances were measured after injection of a volume of PADA stock solution identical with the one used in the salt effect studies. In general, the mean deviation in A,,, and Aminwas f l % . In NaDP, Aminwas determined by adding an aliquot of 1 M NaOH, large enough to make the surfactant solution strongly basic, after adding the last aliquot of NaC1. The absorbance at X = 545 nm was almost identical with the absorbance obtained at this wavelength when we measured the molar absorptivity of neutral PADA in NaDP after a small correction for dilution. The mean deviation in A ~ innthis case is somewhat poorer, about f13%. This uncertainty may be responsible for some of the deviation in our simulations in our experiments at higher pH (for example, curves 22 and 25, Figure 5). Binding of PADA to NaLS and NaDP. We carried out several control experiments to ensure that both the acid and neutral forms of PADA were completely micellar bound under our experimental conditions. 1. Acid Form of PADA, AH'. Added counterions are known to displace organic counterions from micelles.9~24~z5~35~36 To check for displacement of AH' by Na+ in NaLS, aliquots of 5 M NaCl were added to solutions containing 1.82 X M PADA in 0.02, 0.05, and 0.08 M NaLS with 0.02 M succinate buffer (pH 3.70, 50 "C), using the same dilution schedule described above. We (34) The cmc of the disodium salt of alkyl phosphate dianion was estimated by extrapolating line 6 of Figure 9, a log cmc versus carbon number plot in ref 3. (35) Lissi, E.; Abuin, E.; Ribot, G . ; Valenzulea, E.; Chaimovich, H.; Araujo, P.; Aleixo, R. M. V.; Cuccovia, I. M. J . Colloid Interface Sci. 1985, 103, 139. (36) Bartet, D.; Gamboa, C.; Sepulveda, L. J . Phys. Chem.1980,84,272.

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found that the measured absorbance was constant within experimental error, f l % . Had a significant fraction of AH+ been displaced, e.g., lo%, the absorbance would have decreased around 3%. At pH 3.7, PADA is about 73%protonated in H20. Separate experiments under the same conrJtions, but in the absence of added NaC1, showed that the absorbance of AH+ is also independent of NaLS concentration from 0.01 to 0.1 M and of NaDP concentration between 0.04 and 0.1 M. 2. Neutral Form, A . The wavelength maximum of PADA in basic solution is red-shifted about 15 nm in NaLS compared to water (see Table I). Using a standard method for determining the binding constant from spectral shift data,37we measured the effect of added NaLS on the absorbance in 0.02 M borate buffer (pH 9.030) containing 3.5 X M PADA. A plot of the ratio of micellar bound to free PADA versus total NaLS (not shown) gave K, N 1400 M. A cmc of 0.006 M was obtained by extrapolation to zero binding. Under these conditions PADA is at least 95%bound at 0.02 M NaLS. We did not attempt to measure the binding constant of PADA to NaDP, in part because of the formation of the alkyl phosphate dianion in the pH region required to do the experiment but also because the micellar concentration of NaDP was equal to or greater than that of NaLS, where the extent of binding to the micellar pseudophase is at least 95%. For completeness, we also tested for a possible salt effect on the binding of the neutral form by NaLS. Aliquots of 5 M NaCl solution were added to a 0.0230 M solution of NaLS containing 0.02 M borate buffer (pH 9.030) and 3.5 X M PADA. The absorbance at 450 nm remained unchanged within *l% up to 0.35 M NaCl after correction for dilution. Apparent p K , of PADA in Water. The pKa of PADA in aqueous solution in the absence of surfactant was estimated from the intercepts of plots of log [AH+]/[A] versus the measured pH of succinate buffer solutions (0.02 M) in aqueous solution at 35 and 50 "C via eq 2. The ionic strength varied somewhat because (2) pKa = pH + log [AH'] / [A] it was determined only by the amounts of buffer and added NaOH. The calculated pKa values are 4.35 at 35 OC (slope = -0.88, correlation coefficient = 0.999) and 4.13 at 50 OC (slope = -0.87, correlation coefficient = 0.999), which are close to the literature value of 4.5 at 25 O C 2 * We have also calculated the pKa in aqueous solution as a function of added NaCl from pH and log [AH+]/[A] data at 50 OC (Figures 1 and 4). The pKa increases linearly from 4.13 to 4.19 up to 0.23 M NaCl and then drops to 4.04 at 0.382 M NaC1. Thus, our estimates of the pKa in the absence of NaCl are only modestly affected by ionic strength. Effect of Added NaCl on the cmc. The logarithm of the cmc often has a linear dependence on the log of the counterion con~ e n t r a t i o n and , ~ ~ we found such a relation for both NaLS and NaDP (Table 11) log cmc = -B log ([Naad] [Nab] cmc) A (3)

Romsted and Zanette monopotassium octyl phosphate at 25 0C.27 Estimation of Sodium Ion Activity. Because single ion activity coefficients cannot be measured, we used the mean ion activity coefficient for NaCl, y*, at 50 OC in water, to convert aqueous sodium ion concentrations to activities aNa = [Nawly* (4) where [Na,] is the total sodium ion in the aqueous phase [Na,] = [Nab] + [Naad] + cmc + (1 - p)([&] - cmc) (5)

and [Nab], [Naad],cmc, and (1 - p)( [&I - cmc) are the amounts of aqueous sodium ion contributed by the buffer, added NaC1, surfactant monomer, and micellized surfactant, respectively. The first three terms on the right-hand side of eq 5 were defined above; (1 - p ) is the degree of ionization of the micellar pseudophase, and ( [DT] - cmc) is the total amount of micellized surfactant: [D,] = [ DT] - cmc (6) To estimate y* above 0.1 M NaC1, we used an empirical equation employed by Robinson and Harned,40 eq 7. The values

log ?* = I - A / T - B log T

(7)

of constants I , A , and B are listed in Table (12-4-1), p 377, of ref 40, at T = 323 K. To estimate y* below 0.1 M, we used the data in Table (12-1-1) of ref 40, p 360, at 25 OC. We note that changing the temperature from 25 to 50 OC reduces the y* of NaCl by about 1%, substantially less than the average deviation in our estimate of the intrinsic acidity constant of PADA (Table 111). Salt and Surfactant Effects on Solution p H . Over the concentration range of added NaCl used in our experiments the ionization of weak acids in aqueous solution is primarily dependent upon the ionic strength of the solution and secondarily upon the specific ions which are ~ r e s e n t . ~ To , , ~ensure ~ that we knew the activity of the proton at all surfactant and NaCl concentrations, we measured the effect of added NaCl on the pH of succinate buffer in aqueous solution, in the presence and absence of added surfactant, at 50 "C over the identical range of [NaCl] and pH used in the surfactant studies. We found that the salt effect on pH obeyed a simple empirical relation pH = - k , log [Na,] k2 (8)

+

where [Naad], [Nab], cmc, A , and B are respectively the concentrations of sodium ion in the aqueous phase from added NaC1, buffer, and surfactant monomer and two empirical constants. The amount of sodium ion from the buffer was estimated from the ionization constants of the first and second ionizations of succinic and 2.09 X M, respectively, taken acid at 50 OC, 6.52 X 3 was solved by iterative fit using from the l i t e r a t ~ r e . Equation ~~ a computer and used to fit all measured cmc's as a function of added NaC1, and a least-squares fit gave correlation coefficients better than 0.999 for both surfactants. The slope, B, is sometimes equated to the degree of counterion binding, p, to the micelle.38 Typical results for the absolute value of p at 50 "C are as follows: NaLS, 0.45 at pH 4.4; NaDP, 0.49 at pH 5.2 and 0.50 at pH 4.4. N o other estimates of p for NaDP appear to be published, but Arakawa and Pethica obtained a similar value of (3 = 0.54 for

where [Na,] is defined by eq 5 and kl and k2 are constants whose values are slightly different for each initial pH. The results are summarized in Table 111, including correlation coefficients for each line. When we measured the effect of added NaCl on solution pH in the presence of 0.02 M NaLS, we found that measured pH values were virtually unaffected by the surfactant at all initial pH's. Figure 1 illustrates this close correspondence for the effect of added NaCl on the measured pH in the presence and absence of added 0.02 M NaLS when the initial pH is 5.185. This is an important result because it supports our assumption that added NaLS does not interact with our electrode or significantly affect the pH of the aqueous phase. We also measured the effect of changing buffer concentration on the [AH]/[A] ratio from 0 to 0.4 M NaCI. In 0.02 M NaLS, pH 5.185, with 0.02,0.03,0.04, and 0.05 M succinate buffer the log [AH]/[A] versus aNaplots are superimposable on curve 3 of Figure 4, within experimental error (data not shown). Taken together, these results provide strong support for our assumptions that NaLS does not significantly affect the ionization of the buffer and that the neutral and anionic components of the buffer are not associated with anionic NaLS micelles. Figure 1 also illustrates the effect of added NaCl on the solution pH of selected NaDP solutions in the presence and absence of

(37) Sepulveda, L. J . Colloid Interface Sci. 1974, 46, 372. (38) Mukerjee, P.; Mysels, K. J.; Kapauan, P. J . Phys. Chem. 1967, 71, 4166. (39) Kortum, G.; Vogel, W.; Andrussow, K. Pure Appl. Chem. 1960, 1 , 190.

(40) Harned, H. S.;Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 2nd ed.; Reinhold: New York, 1950. (41) Bates, R. G. Determination o f p H Theory and Practice; Wiley: New York, 1954; p 108. (42) Harned, S . H.; Hickey, F. C. J . Am. Chem. SOC.1937, 59, 1284.

+

+

+

The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4695

NaDP and NaLS Micellar Solutions

TABLE III: Parameters Used To Fit the Effect of Added NaCl on pH in Water, NaLS, and NaDP and Calculated Values of the Intrinsic Acidity Constant, KAm,with Error Estimates, in NaLS and NaDP at 50 "C run no. concn, M PH' -kl k2 1 0 5 ~ error, %

H2O

1

NaLS

2 3 4 5

0.020 0.020 0.020 0.020

5.430

0.274

5.007

4.820 5.185 5.496 5.876

0.235 0.274 0.290 0.305

4.439 4.760 5.067 5.448

av NaDP

0.040 0.060 0.080 0.100 0.150 0.200 0.300 0.040 0.045 0.050 0.060 0.070 0.080 0.090 0.100 0.150 0.200 0.060 0.060 0.060

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

4.651 4.756 4.836 4.894 4.995 5.050 5.108 5.217 5.229 5.241 5.246 5.244 5.301 5.318 5.322 5.393 5.431 5.010 5.483 5.779

0.239 0.278 0.305 0.308 0.9321 0.319 0.352 0.285 0.291 0.296 0.293 0.316 0.3 18 0.322 0.316 0.330 0.349 0.284 0.292 0.304

4.320 4.390 4.452 4.524 4.640 4.722 4.789 4.847 4.855 4.864 4.881 4.901 4.920 4.939 4.956 5.040 5.083 4.638 5.122 5.414

'Initial solution pH, in the absence of added salt. bAssuming@ = 0.75 in NaLS and pH

5.8 5.6

1

pH 5 . 2

3.20 3.06 3.20 2.92 3.10 f 0.10

av

3.52 3.45 3.63 2.89 4.08 3.26 3.03 3.92 3.75 3.89 3.88 3.42 3.47 3.59 3.39 3.07 2.88 3.19 3.30 3.70 av 3.47 f 0.28

a = 0.70 in NaDP.

2.82 4.32 6.32 8.37 5.46 f 1.89

8.89 3.13 2.73 0.82 6.12 7.47 3.02 9.89 10.04 7.80 7.50 8.55 6.55 7.06 7.73 8.02 6.11 4.47 10.01 7.34 av 6.66 f 2.04

cPercent standard deviation.

i

5.04.8

-

4.6 -

4'8

4.4

t

I

I -16

-14

-12

-IO

-08

-06

-04

-02

5

IO

added succinate buffer. In the absence of buffer, solution pH depends on both the [NaDP] (0.06 and 0.1 M) and the amount of added NaCl. However, unlike the results with added NaLS, the addition of 0.06 M NaDP to 0.02 M succinate buffer (initial pH 5.430) increases the measured pH about 0.06 pH units at all [NaCI], but the dependence on log [NaCl] added is now linear. Linear correlations were obtained at all [NaDP] and initial pH's, with correlation coefficients 0.998 or better. Figure 2 shows the effect of increasing [NaDP] in the presence and absence of added NaCl in 0.02 M succinate buffer with an initial pH of 4.400. The increase in pH with added NaDP is almost certainly caused by the competitive buffering action of NaDP monomer and micelles overwhelming the buffering capacity of the succinate buffer. The decrease in pH with added salt is probably caused by displacement of protons from the micellar surface. In our analysis of the data we assumed that, like NaLS, NaDP does not significantly affect the response of pH electrode

20

25

30

IO2 [NoDP]M

LOG [No] M

Figure 1. Effect of added NaCl on the pH of 0.02 M succinate buffer in the presence and absence of added NaLS and NaDP. Solid lines fit eq 5 (see text). The initial solution pH, prior to NaCl addition, is indicated below: buffer alone, pH 5.185 (A);0.02 M NaLS, pH 5.185 (0); buffer alone, pH 5.430 (A);0.06 M NaDP, pH 5.430 ( 0 ) ;0.06 M NaDP, no added buffer (0); 0.1 M NaDP, no added buffer (0).

15

Figure 2. Effect of added NaDP on the measured pH in 0.02 M succinate buffer. Initial pH is always 4.400 (0.0 M NaDP) at several [NaCI]: 0.000 M (0);0.181 M (0); 0.402 M (A). Lines are drawn only to aid the eye.

or interact with the components of the buffer. The excellent fit of the model to the data supports this assumption. Theoretical Treatment of Acidity in Micelles: The Pseudophase Zon-Exchange Model. The assumptions of the PIE model and the derivation of the relevant equations have been published numerous times.9,'8,20,23-2s,43 We will only summarize here the derivation for indicator equilibria in anionic surfactants in the presence of buffer, using the formalism originally developed by Bunton and Romsted for micellar effects on reaction rate^.^^^^ Ionization of the indicator is assumed to occur in the micellar pseudophase, and deprotonation within the micellar pseudophase is defined by an intrinsic acidity constant: (9)

where mHs = [H,]/([D,]

- cmc), the superscript S indicates

(43) Romsted, L. S. Ph.D. Thesis, Indiana University, 1975.

4696

The Journal of Physical Chemistry, Vol. 92, No. 16, 1988

Romsted and Zanette / /

I

O

C

O

I

I

I

/ I

0

0

1

2

A

B O

A

I

A

I

O

A

l O A

A

A

A

0

* A

*

A

4

5

0

I

2

A II

C A

A

A * * *

3

6 3 0

A

7

8

4 I

5 2

o

9 6 3

I I I ',',,

IO

I!

7

8

I2 9

4

5

6 "

'/',, 10

7

A, 8 ,

20 17

39

27

c

Figure 3. Plot of all data for PADA in 0.02 M NaLS, 0.02 M succinate buffer at four different initial solution pH's: curve A, following eq 14 (see text); curve B, no Y ~ correction; ~ + curve C, no yNa+correction and setting [Hb+] = constant = antilog (-pH) of initial solution pH. Initial pH: 5.876 (0); 5.496(A);5.185( 0 ) ;4.820 (0). Solutions with 0.4 M added NaCl prepared by a separate method (0); see text. Vertical dashed line marks change of scale on x axes.

location in the micelle Stern layer, and the subscript m indicates unspecified location within the micellar pseudophase. We define the concentration of counterions as mole ratios instead of ordinary concentration units to avoid having to specify the exact reaction volume within the micellar pseudophase. The intrinsic acidity constant, KAm,is a unitless number, but it can be converted to conventional units by defining a reaction volume for the counterions in the micellar pseudophase (see Discussion). We assume that, under our experimental conditions, both forms of PADA are completely micellar bound so that the stoichiometric amount of indicator, [AT],is given by [AT] = [A,] + [AH',]. Finally, the surfactant concentration in our experiments is approximately 1000 times greater than the PADA concentration. Assuming an aggregation of 100, the micelle concentration is about 10 times the PADA concentration, and indicator perturbation of the micellar phase should be minimal. Under these conditions, micellar bound PADA is a good probe of surface pH. In the PIE model, the proton concentration at the micelle surface is governed by ion exchange with sodium counterions Naw + H, Na, H,

+

+

where subscript w indicates location in the aqueous pseudophase. The selectivity of anionic micelles toward these two ions is defined by an empirical ion-exchange constant

where m N 2 = [Na,]/([DT] - cmc). The fraction of the micelle surface covered by the two counterions is given by mHs + mN2 = p (11) As in earlier treatments, we assume that p is constant and independent of surfactant and counterion concentration and Under the experimental conditions used in this study, the sodium ion concentration ranges from approximately 0.04 to 0.44 M, whereas the pH is between 4 and 6. Because the stoichiometric sodium ion concentration is always several orders of magnitude greater the proton concentration, we assume that m N 2 >> mHs and that eq 1 1 reduces to mN2 = P

(12)

Equations 10 and 12 are combined and rearranged to give eq 13, which defines the proton concentration in the micellar pseudophase.

Combining eq 13, with concentration units converted to activities, and eq 9 gives a simple expression for the ratio of the two forms of the indicator.

- [AI [AH+]

- KAmKHNaaNa [AH+,]

paH

(14)

Equation 14 was used to estimate K A m for PADA in NaLS and NaDP. The indicator ratio on the left-hand side was calculated from absorbance data via eq 1, aH was calculated from aH = antilog - pH, and aNawas calculated via eq 4 and 5. We set KHNa = 1@ and p = 0.75 for NaLS38*43 and assumed that /3 = 0.70 for NaDP (see Discussion). Equation 14 predicts a simple linear relation with an intercept of zero between [A]/[AH+] and aNa/aH.The plot in Figure 3 contains all our data for PADA in NaLS, at all [NaCl] and pH's. Except for the data above activity ratios of 6 X lo4 (curve A), all the points fall on a good straight line (correlation coefficient = 0.996, intercept = 0.032) with a slope of 3.95 X One possible source of error in the absorbance ratio is cumulative error produced by the serial addition of aliquots of NaCl. To check for this possibility, we prepared a set of separate solutions which were 0.02 M NaLS, 0.02 M succinate buffer, and 2 X M PADA at 0.4 M NaCl at four different pH's between 4.4 and 5.9 following a method developed earlier? The data (hexagons) are coincident with the other results on curve A of Figure 3. Had serial dilution error been serious, the discrepancy between the methods should have been greatest at 0.4 M NaCI. For comparison, we have also plotted [A]/[AH+] versus [Na,]/aH, and [Na,] / [Hb] is calculated from the pH of the buffer stock solutions. The substantial scatter in the data and the strong curvature in the plot of the data set at each pH demonstrate the importance (44) Bunton, C.A.; Ohmenzetter, K.;Sepulveda, L.J. Phys. Chem. 1977, 81, 2000.

The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4697

NaDP and NaLS Micellar Solutions

I .o

I 'ah

0.00.6

-

0.4 -

0.2 0-

0.2

0

0.4 -

0.6

4

0

12

16

IO2

20

24

20

32

aNa

Figure 4. Effect of increasing U N ~ +on the [AH]/[A] ratio for PADA in 0.02 M succinate buffer and 0.02 M NaLS at four different initial solution pH's. Curve numbers correspond to run numbers in Table 111. Solid points ( 0 )were determined in 0.02 M succinate buffer (pH 4.4) in the absence of NaLS. Solid lines are theoretical. Error bars indicate effect of changing the measured absorbance &5%.

of converting [Na,] to U N and ~ [Hb] to U H from measured pH values. Using the values for 6 and KHNagiven above, we estimated the intrinsic acidity constant for PADA in NaLS from the slope to be KAm = 2.96 X Figures 4 and 5 show the effect of increasing sodium ion activity on log [AH]/[A] in aqueous solutions of NaLS and NaDP. Not all the results for NaDP listed in Table I11 are shown in Figure 5, because several of the curves are, coincidentally, virtually superimposable, even though [NaDP] and initial pH are different. Equation 14 was also used to generate the theoretical curves of ~ lines in Figures 4 and 5); however, log [AH]/[A] versus U N (solid the approach was somewhat different from that used to generate the curve in Figure 3. Experiments at different initial pH's were handled as separate data sets. At each pH, average values of KA"' were computed from the individual KA"' values calculated for each set of log [AH]/[A], U N values ~ obtained from eq 14, and the assumed values of /3 and KHNalisted above. The average values of KAmfor sets of eight data at each pH in NaLS and NaDP are listed in Table 111. The average KAmvalue at each pH was used to generate the solid curve through the data at that pH in Figure 4 for the experiments in NaLS and Figure 5 in NaDP. The standard deviations of the log [AH]/[A] values from the theoretical curves at each pH are also listed in Table 111. The greatest deviation is about lo%, and the overall mean deviation is about 5.5% in NaLS and 6.7% in NaDP.

Discussion The excellent fit of the data in Figures 3-5 shows that the PIE model provides a complete description of the effect of added NaCl on the apparent pKa of PADA in both NaLS and NaDP. Assuming that both p and KHNaare constant, almost identical values of KAmcan be used to fit the data in NaLS and NaDP (average values, Table 111). However, fitting micellar effects on rate or equilibrium data by use of the PIE model does not permit estimating a unique value for KAm.9*45 A wide combination of values (45) Bunton, C. A.; Hong, Y.-S.; Romsted, L. S. In Solution Behavior of Surfactants: Theoretical and Applied Aspects; Mittal, K.L., Fendler, E. J., Eds.; Plenum: New York, 1982; Vol. 2, p 1137.

4

8

12 IO2

16

20

24

20

32

aNa

Figure 5. Effect of increasing aNat on the [AH]/[A] ratio for PADA at several [NaDP] and initial solution pH's. Curve numbers correspond to run numbers in Table 111. Solid lines are theoretical.

for 6, KHNa,and KAmwill fit the product term in eq 14. Generally, 6 values determined from cmc data are smaller than those obtained by other methods,43and we selected the p values which gave the best overall fit of our data. Although is simply part of a product term in eq 14, /i' also appears in eq 5, and the overall quality of the fit at low added NaCl will depend to some extent upon the value of /i' selected. Although a substantial body of data is available on the ion-exchange constants for a wide variety of counteranions to cationic surfactant^,^^"^^^ only a little information is available on the selectivity of anionic surfactants toward different cations and it was obtained by using a different m0de1.l~ Bunton and co-workers estimated KHNa= 0.82 from potentiometric data," and for simplicity, we set K"* = 1, for both NaLS and NaDP. The apparent pKA of PADA at 50 OC in 0.02 M NaLS (pH 5.185) and 0.06 M NaDP (pH 4.76) is 5.95 and 5.76, respectively, about 1.8 and 1.6 PKA units greater than the value of 4.13 in water at 50 OC. This pKa difference is within the typically observed micellar induced 1-2 unit shift in apparent pKa of acid-base indicator^,^-',^^,^^,^^ In terms of the PIE model, this shift is caused primarily by the transfer of the indicator and the hydronium ion out of the large volume of the aqueous phase into the much smaller volume of the micellar pseudophase. Assuming that the whole micellar volume is available to the indicator, the potential concentration increase is approximately 290-fold (2.46 log units) in 0.02 M NaLS (cmc = 0.008, micelle density = 1 g/mL). At surfactant concentrations sufficient to bind both forms of the indicator, only the interfacial concentration of the proton is affected by increasing the surfactant or salt concentration (eq 14). Note that as [NaDP] increases, log [AH]/[A] vs aNacurves are progressively lower (Table 111, Figure 5 , curves 6 , 7, 8, 11, and 12), caused by dilution of the hydronium ions at the micelle surface with increasing micelle c o n c e n t r a t i ~ n . ~ ~ ~ ~ The addition of added NaCl produces a sharp drop in apparent pKA (Figures 4 and 5 ) , and at 0.4 M added NaC1, the highest concentration reached, the apparent pKA decreases about 1 PKA unit in both surfactants. This decrease is much larger than the small changes in apparent PKA observed with added NaCl in water (see Results). Large salt effects are always observed in micellar effects on indicator equilibria and the rates of bimolecular reactions

4698

The Journal of Physical Chemistry, Vol. 92, No. 16, 1988

when both the substrate or indicator and the reactive counterion (usually the hydronium ion in anionic surfactants and the hydroxide ion in cationic surfactants) associate with the micellar p s e u d ~ p h a s e . ~In~the ~ ~PIE J ~model, ~ ~ ~ the ~ ~sharp decrease in apparent pK, is attributed to ion exchange, Le., in NaLS and NaDP the displacement of hydronium ions from the micelle surface by added sodium ions. We note that about 0.3 unit of the decrease in apparent PKA is caused by the salt effect on solution pH (Table 111). The intrinsic acidity constant, KAm,is a unitless number, but it can be converted to a micellar acidity constant, KAv,expressed in more conventional units by assuming the reaction occurs only in the Stern layer of the micellar pseudophase and dividing by the molar volume of the Stern layer:20,24,25 KAv = KAm/0.14

(15)

By use of the average KAm values for PADA in Table 111, KAv M is 2.21 X lo-“ M (pKAv = 3.66) in NaLS and 2.48 X (pKAv = 3.61) in NaDP at 50 “C. These results suggest that PADA is a somewhat stronger acid in anionic surfactants than in water (PKA = 4.13 at 50 “C). N o other examples of intrinsic acidity constants are published; however, several intrinsic basicity constants have been estimated in basic solution in cationic surf a c t a n t ~ . ~As , ~ with ~ , ~ the ~ rate constants of most bimolecular reactions in micelle^,^^^^^ intrinsic basicity constants in micelles are somewhat smaller than in water. Thus, like PADA, they are slightly stronger acids in micelles than water. The small difference in PKA between micelles and water is consistent with the assumption that the indicator is located at the micelle surface and the high polarity typically estimated for aqueous interfaces of surfactant aggregates.22 Several sources of experimental error reduce the quality of the fit of the PIE model to the data. The primary limit is one that affects all indicator experiments; Le., accurate results cannot be obtained at a pH 2 units either side of the pK, of the indicator because the measured absorbance approaches that of the fully protonated or deprotonated form and small errors in the absorbance will have a large effect on the calculated absorbance ratio (eq l).46 This limitation probably contributes to some of the discrepancy between theory and experiment at the high and low indicator ratios in Figures 4 and 5. To illustrate the potential contribution of this type of error, Figure 4 shows error bars calculated by assuming a f5% error in the absorbance and recalculating the log [AH]/[A] values at low and high added NaCl (curve 5). Note that the three points which are off the line in curve A of Figure 3 are also the last three points on curve 5 in Figure 4. In NaDP, the relatively large uncertainty in Amin(see Results) probably contributes to the observed discrepancies in curves 22 and 25, Figure 5. Another minor source of experimental error arises from our estimates of the sodium ion contributed by buffer, surfactant monomer, and micelle ionization to the total sodium ion concentration in the aqueous phase (eq 5). Of these, the uncertainty in fl is probably greatest contributor. Precise estimates of 0are difficult to ~ b t a i n ,and ~ ~ the , ~ ~meaning of 0 cannot be defined unambiguously. Nevertheless, in 0.02 M NaLS, only about 0.003 M sodium ions are contributed by the micelles to the aqueous phase (cmc = 0.008 M, 0 = 0.75),and this contribution will be virtually negligible, even in the absence of added NaC1, because of the larger contributions of sodium ions by buffer and surfactant monomer. Finally, the quality of the fit will also depend upon the known limits of the PIE model and upon our assumption that the activity coefficient of the sodium ion is equivalent to the mean ion activity coefficient of NaC1. Our experimental conditions are also well (46) Albert, A.; Serjeant, E. P. The Determination of Ionization Comtants: A Laboratory Manual, 3rd ed.; Chapman and Hall: London, 1984; Chapter

4.

Romsted and Zanette within the normal limits of the PIE model; the surfactant concentration is well above the cmc, and the concentration of sodium ion is in large excess over the proton concentration. We cannot assess the significance of the latter assumption numerically, although the quality of our results indicates that it is quite good. The reliability of our numbers might be improved by measuring the activity of the sodium ion directly with a sodium ion electrode, provided it is not affected by added surfactant.

Conclusions Chaimovich and Quina demonstrated that the PIE model works in micellar solutions containing buffers in the absence of added ~ a l t . ’ We ~ ? ~have ~ shown here, for the first time, that the model also works well in micellar solutions containing buffers even in the presence of a large quantity of added counterion, provided that the amounts of exchangeable counterions in the aqueous pseudophase are expressed as activities and that the buffer is hydrophilic, of like charge to the micelle surface, and, therefore, located only in the aqueous phase. In most studies of micellar effects on indicator equilibria, indicators were chosen which function at very high or low acidities, buffers were not required to control solution pH, and the concentrations of the counterions in the aqueous phase are related through empirical ion-exchange constants and mass balance equations to their stoichiometric concentrations.9~24~25 In the absence of buffer, changes in the ionic strength were implicitly assumed to affect the activity coefficients of both counterions equally, in both the micellar and aqueous pseudophases, and the ratio of their activity coefficients remains constant and approximately one (eq 10 and 14). In principle, this simplification cannot be used for exchange between mono- and divalent c o ~ n t e r i o n salthough ,~~ it worked well in one set of experiments in which the quantity of added counterions remained relatively Micelles of NaDP behave “normally”, that is, like NaLS, with no apparent special contribution to surface acidity produced by the proton on the phosphate head group over the pH range studied (pH -4-6). This implies that the micellized NaDP head groups are primarily in their monoanion forms in this pH region as indicated in the literat~re.~’However, we do not know at this time if our indicator would be sensitive to changes in head groups charge, Le., if a fraction of the head groups are completely protonated (ROP0,H2) near pH 4 or completely deprotonated (ROP032-) near pH 6. We plan to determine the protonation state of the head groups using phosphorus N M R and FTIR soon. Also, despite the fact that added NaDP overwhelms the buffering capacity of the succinate buffer (Figure 3), we obtained an excellent fit of all our data in NaDP when we used the measured value of the solution pH (Figure 5). In the pH range of our experiments, NaDP is certainly self-buffering and our additional buffer was probably unnecessary precaution in terms of protecting against changes in solution pH caused by small amounts of impurities or dissolved COz. However, this does not mean that the solution pH will be unaffected by NaDP or salt concentration because the contribution of the NaDP micelles and monomer to solution pH will be changing continuously with added NaDP. Acknowledgment. We are grateful to Dr. Dorothy Denney for obtaining all the 31PN M R spectra. We acknowledge financial support from the Research Council and Biological Sciences Research Fund of Rutgers University and the National Institutes of Health, GM32972. Registry No. NaDP, 115245-02-8;PADA, 13103-75-8; NaLS, 15121-3. (47) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1980, 84, 3114. (48) Lissi, E.; Abuin, E.; Sepulveda, L.; Quina, F. H. J . Phys. Chem. 1984, 88, 81. (49) Nascimento, M. G.; Miranda, S. A. F.; Nome, F. J . Phys. Chem. 1986, 90, 3366.