1918
Langmuir 1997, 13, 1918-1924
Aqueous Hexadecyltrimethylammonium Acetate Solutions: pH and Critical Micelle Concentration Evidence for Dependence of the Degree of Micelle Ionic Dissociation on Acetate Ion Concentration Jean Toullec* and Sabine Couderc Laboratoire SIRCOB (CNRS, EP 102), Universite´ de Versailles, 45 Avenue des Etats-Unis, 78035 Versailles Cedex, France Received April 15, 1996. In Final Form: January 2, 1997X The counterion binding parameters (β) of aqueous hexadecyltrimethylammonium acetate (C16TAOAc) are estimated from pH data at various C16TAOAc-AcOH concentrations with or without added sodium acetate buffer. In contrast to what is usually reported for ionic amphiphiles associated with less hydrophilic counterions, β varies from ca. 0.4 to ca. 0.7 and depends upon the acetate ion concentration in the aqueous phase. The critical micelle concentrations (cmc) for C16TAOAc, C16TAOAc-NaOAc, C16TAOAc-AcOH, and C16TAOAc-NaOAc-AcOH solutions, measured from extinction data for fluorescence of acridine, are also examined in terms of AcO- concentration dependence. The plot of the logarithm of the amphiphile activity at cmc vs the logarithm of acetate ion activity is markedly curved, as expected for significant variations in β.
Introduction It is well-known that many physicochemical properties of ionic surfactants and their ability to promote micelle catalysis are strongly influenced by counterions,1 and in recent years, interest has shifted from inorganic ions to organic ions.2-11 The parameter that is commonly considered is the degree of counterion binding, β, usually determined by conductometry, emf, pH and ion-selective electrode measurements, cyclic voltammetry, electrophoresis, light and neutron diffraction, ultrafiltration, selfdiffusion, and fluorescence experiments, as well as from the dependence of critical micelle concentration (cmc) on common-ion salt concentration. (For reviews of the methods and of the data obtained in the case of the cationic surfactants, see refs 12 and 13.) This parameter is defined as β ) m/n, where n and m are the mean numbers of the amphiphile monomers in the micelles and of the associated counterions, respectively. There is a great deal of theoretical and experimental work7,12-19 suggesting that β does not usually depend very X Abstract published in Advance ACS Abstracts, February 15, 1997.
(1) Romsted, L. S. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 509. (2) Broxton, T. J. Aust. J. Chem. 1981, 34, 2313. (3) Anacker, E. W.; Underwood, A. L. J. Phys. Chem. 1981, 85, 2463. (4) Underwood, A. L.; Anacker, E. W. J. Colloid Interface Sci. 1984, 100, 128. (5) Underwood, A. L.; Anacker, E. W. J. Phys. Chem. 1984, 88, 2390. (6) Jansson, M.; Stilbs, P. J. Phys. Chem. 1987, 91, 113. (7) Jansson, M.; Jo¨nsson, B. J. Phys. Chem. 1989, 93, 1451. (8) Underwood, A. L.; Anacker, E. W. J. Colloid Interface Sci. 1987, 117, 242. (9) Sugihara, G.; Arakawa, Y.; Tanaka, K.; Lee, S.; Moroi, Y. J. Colloid Interface Sci. 1995, 170, 399. (10) Furuya, H.; Moroi, Y.; Sugihara, G. Langmuir 1995, 11, 774. (11) Sugihara, G.; Nagao, F. O.; Tanaka, T.; Lee, S. J. Colloid Interface Sci. 1995, 171, 246. (12) Bunton, C. A. In Cationic Surfactants, Physical Chemistry; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; p 323. (13) Zana, R. In Cationic Surfactants, Physical Chemistry; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; p 41. (14) Hall, D. G.; Price, T. J. J. Chem. Soc., Faraday Trans. 1 1984, 80, 1193. (15) Charbit, G.; Dorion, F.; Gaboriaud, R. J. Colloid Interface Sci. 1985, 106, 265. (16) Hall, D. G. J. Chem. Soc., Faraday Trans. 1 1981, 77, 1121.
S0743-7463(96)00363-0 CCC: $14.00
muchseven though some variations are predicted based on thermodynamics or on the Poisson-Boltzmann equation7,16,17seither on the surfactant concentration or on that of electrolytes with a common anion. This parameter takes a value between 0.5 and unity which depends mainly on counterion hydrophobicity. The lower the hydrophobicity, the smaller it is.3-8 However, most of the data indicating that β is concentration-independent within the accuracy of the experimental method concern significantly hydrophobic counterions (e.g., Br- in C16TAB). On the other hand, in the case of hexadecyltrimethylammonium hydroxide (C16TAOH) and fluoride (C16TAF) it was shown20 by conductometry that β is much smaller than for other hexadecyltrimethylammonium salts, C16TAX, and depends on the surfactant concentration. Significant variations of β are also in keeping with the rate-concentration profiles observed for HO-- and F--promoted organic reactions in C16TAOH or C16TAF occurring at the micelle interface.12,21-26 This behavior is considered to be typical of ionic surfactants when the counterions are very hydrophilic. However, since the observation of significant β variations is limited to a few cases and since these variations provide information on the factors involved in the micellization process, we decided to examine the behavior of other C16TAX, with various hydrophilic counterions. For this purpose, we first selected (17) Hall, D. G. In Aggregation Processes in Solution; Wyn-Jones, E., Gormally, J., Eds.; Elsevier: Amsterdam, 1983; p 7. (18) Delville, A.; Herwats, L.; Laszlo, P. Nouv. J. Chim. 1984, 8, 557. (19) Berr, S.; Jones, R. R. M.; Johnson, J. S. J. Phys. Chem. 1992, 96, 5611. (20) Neves, M. de F. S.; Quina, F.; Moretti, M. T.; Nome, F. J. Phys. Chem. 1989, 93, 1502. (21) Bunton, C. A.; Romsted, L. S. In Solution Behavior of Surfactants; Mittal, K. L., Fendler, E. J., Eds.; Plenum Press: New York, 1982; Vol. 2, p 975. (22) Bunton, C. A.; Nome, F.; Quina, F. H.; Romsted, L. S. Acc. Chem. Res. 1991, 24, 357. (23) Bunton, C. A.; Frankson, J.; Romsted, L. S. J. Phys. Chem. 1980, 84, 2605. (24) Bunton, C. A.; Romsted, L. S.; Savelli, G. J. Am. Chem. Soc. 1979, 101, 1253. (25) Bunton, C. A.; Gan, L.-H.; Moffatt, J. R.; Romsted, L. S.; Savelli, G. J. Phys. Chem. 1981, 85, 4118. (26) Stadler, E.; Zanette, D.; Rezende, M. C.; Nome, F. J. Phys. Chem. 1984, 88, 1892.
© 1997 American Chemical Society
Aqueous C16TAOAc Solutions
acetate, which is close to HO- and F- in the lyotropic series and has been shown to bind only weakly to decyltrimethylammonium micelles.3,6 Moreover, even though it seems that only Zana and Lianos used this method in the case of CnTAOH,27 it was expected that pH data would provide the concentrations of AcO- in the aqueous phase when the surfactant solution also contains acetic acid. This paper reports the determination of β from pH data for mixtures of hexadecyltrimethylammonium acetate (C16TAOAc) and AcOH, with or without added sodium acetate buffer, as well as cmc values measured from the concentration dependence of the fluorescence decay of acridine. Since it is well-known that the amplitude of common-ion salt effects on cmc depends on β, we expected that deviations from normal behavior would indicate β variations. Experimental Section Materials. Hexadecyltrimethylammonium acetate was prepared by three different procedures. According to method A, hexadecyltrimethylammonium ethyl xanthate was prepared as described by Sepu´lveda et al.28 and mixed in 75:25 methanol/ water with equimolar amounts of acetic acid. The mixture was allowed to react for 1 week at room temperature. The solvent was then removed by evaporation after successive additions of methanol. The solid residue was dissolved in 10 mL of methanol, and a crop of crystals was obtained at 5 °C after addition of a minimum amount of diethyl ether. These were recrystallized twice from ether/methanol (ca. 20:1, v:v) and dried under vacuum. The C16TA+ ions were titrated by the dichromate method,28 which consists in mixing potassium dichromate and C16TAOAc solutions, eliminating the insoluble dichromate salt by centrifugation and measuring the excess of dichromate ion concentration by UV-vis absorbance spectrophotometry after addition of H2SO4. The acetate ions were titrated pH-metrically in 90:10 (v:v) ethanol/water. Purity was ca. 98%. By pH measurements in 90:10 ethanol/water and comparison with pH data for sodium acetate at the same concentrations, the C16TAOAc samples were checked to ensure that they did not contain any significant amounts of free acetic acid. According to method B, (a) hexadecyltrimethylammonium hydrogenosulfate (C16TAHSO4) was prepared and titrated by the same procedure as for C16TAOAc and (b) hexadecyltrimethylammonium hydroxide solutions were obtained by mixing equimolar amounts of C16TAHSO4 and Ba(OH)2, followed by elimination of the BaSO4 precipitate by centrifugation. The hydroxide and CTA+ ion concentrations in the supernatant were measured pH-metrically by titration with HCl and (after neutralization) by the dichromate method, respectively. By addition of sodium sulfate and barium chloride to aliquots of C16TAOH solutions it was checked that these did not contain any significant amounts of barium or sulfate ions. The solutions of C16TAOAc or the C16TAOAc/AcOH buffers were obtained by mixing appropriate volumes of C16TAOH and AcOH solutions. The properties of the C16TAOAc solutions and of the C16TAOAc/AcOH buffers (cmc and pH) were shown to be identical to those observed when commercial C16TAOH (Aldrich) (method C) was used. Other materials were AR grade and used as received. Distilled water was treated in a Millipore Milli-Q fourstage cartridge system and deaerated by continuous nitrogen bubbling. pH Determination. pH data were obtained at 25 ( 0.1 °C by using a Methrom pH-meter (Model 632) equipped with a Methrom glass electrode (ref 6.0219.100) with a sleeve diaphragm and a double-junction to the Ag/AgCl ([KCl] ) 3 M) inner reference. This electrode is well adapted to pH measurements in surfactant solutions because clogging of the diaphragm is prevented. The sleeve diaphragm allows a freshly formed continuous-mixture type junction between the outer KCl electrolyte and the solution. pH data were corrected for liquidjunction potentials by means of the classical Henderson equa(27) Lianos, P.; Zana, R. J. Phys. Chem. 1983, 87, 1289. (28) Sepu´lveda, L.; Cabrera, W.; Gamboa, C.; Meyer, M. J. Colloid Interface Sci. 1987, 117, 460.
Langmuir, Vol. 13, No. 7, 1997 1919 tion.29 The molar ionic conductivities at infinite dilution were from ref 30. λ°+ for the unmicellized CTA+ ions, (λ°+)CTA, was taken as 20 S cm2 mol-1,31 an average value from conductivity data for various C16TAX surfactant solutions. For the contribution of the micelles to the liquid-junction potential, it was assumed that the micelles move with a molar conductivity at infinite dilution given by eq 1.31-33 The aggregation number, n, was
λ°m ) n2/3(1 - β)2(λ°+)CTA
(1)
estimated as 20/(1 - β) (with β derived from the pH data) since small-angle neutron diffraction data19 indicate that n(1 - β) (ca. 20), corresponding to the charge of the micelles, is approximately concentration-independent. The liquid-juntion potential for the potassium hydrogenophthalate buffer was calculated to be 2.75 mV with λ° taken as 32 S cm2 mol-1 for the hydrogenophthalate ion. The glass electrode was standardized by using a pH 7 buffer (Sigma) and a home-made 0.05 M potassium hydrogenophthalate buffer (pH ) 4.005). As shown in Table 1, the dependence of pH on concentration for sodium acetate buffers is as expected when the AcOH and AcO- concentrations are corrected for [H3O+] and when the liquid-junction correction is made. Cmc Measurements. Although the use of luminescent probes for the measurement of critical micellar concentrations has been criticized by many authors34 (the incorporation of the dye into the micelles can change the cmc values), we used Wolff’s method35 based on the fluorescence of acridine. Our choice is motivated by the high sensitivity and accuracy of the method. The quantum yield of acridine is very high, and measurements of the IF/IF° ratios, i.e., the ratios of fluorescence intensities in the presence and in the absence of surfactant, are accurate even for acridine concentrations below 10-6 M. This means that [P]/c, expressing the ratio between the concentrations of the probe, [P], and the surfactant, c, is e10-3 at the cmc. Moreover, it was observed that the IF values are in agreement with eq 2 (which states that
I°F/(I°F - IF) ) 1 + [(Pacr/55.5) (c - cmc)]-1
(2)
the I°F - IF is proportional to the amount of acridine dissolved in the micelle pseudophase) if the acridine mole fraction-basis partition coefficient between micelles and water on the mole fraction basis, Pacr, is taken as ca. 5 × 104. The relatively low value of Pacr means that only a small fraction of acridine is dissolved in micelles for c close to cmc. For instance, for cmc ) 10-3 M and c exceeding cmc by 10%, this fraction is equal to 0.10. Only 10% of the micelles contain one molecule of the probe. It is therefore highly unlikely that the presence of such low concentrations of the probe can introduce significant errors. Nevertheless, in order to check the validity of the method, we also varied the acridine concentration from 2 × 10-7 to 10-6 M. No changes in cmc were observed. Fluorescence measurements were carried out by means of a Perkin-Elmer LS50 luminescence spectrophotometer, the excitation and emission wavelengths being set to 356 nm (slit width ) 5 nm) and to 430 nm (slit width ) 4 nm), respectively. In contrast to Wolff,35 who plotted IF/IF° vs log c, we observed that better straight lines are obtained before and after cmc by plotting log(IF/IF°) vs log c for a series of C16TAOAc-NaOAc solutions for various [C16TAOAc]/[NaOAc] ratios. Figure 1 shows a typical cmc determination. The cmc is defined by the intersection of the two lines. Similar cmc determinations were performed in C16TAOAcAcOH and C16TAOAc-NaOAc-AcOH buffer solutions in order to examine the effect of acetic acid concentration. Since under these conditions acridine is partly in its protonated form (pKa (29) Bates, R. G. Determination of pH, Theory and Practice; Wiley: New York, 1973; p 36. (30) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1955; p 452. (31) Sepu´lveda, L.; Corte´s, J. J. Phys. Chem. 1985, 89, 5322. (32) Evans, H. C. J. Chem. Soc. 1956, 579. (33) Shanks, P. C.; Franses, E. I. J. Phys. Chem. 1992, 96, 1794. (34) Mukerjee, P.; Mysels, K. J. Natl. Stand. Ref. Data Ser. (U.S. Natl. Bur. Stand.) 1971, NSKDS-NBS 36. (35) Wolff, T. J. Colloid Interface Sci. 1981, 83, 658.
1920 Langmuir, Vol. 13, No. 7, 1997
Toullec and Couderc
Table 1. pH Data for the NaOAc-HOAc and C16TAOAc-HOAc Buffer Solutions, and Derived β Counterion Binding Parameters (25 °C) [AcO-]st/[AcOH]st ) 2.0 C16TAOAc-AcOH
NaOAc-AcOH
c (mM)a pHmeasb pHcorrc pHthd pHmeasb pHcorrc 0.3 0.5 0.75 1.0 1.5 2.0 3.0 4.0 5.0 6.0 8.0 10.0
5.13 5.10 5.09 5.08
5.10 5.07 5.064 5.056
5.082 5.067 5.056 5.052
5.06 5.04
5.042 5.031
5.041 5.034
5.03
5.022
5.025
5.02 5.01
5.011 5.009
5.017 5.012
∆pHe
5.11
5.077
-0.007
5.07 5.04 4.98 4.89 4.83 4.78 4.75 4.70 4.67
5.047 5.016 4.965 4.875 4.806 4.762 4.727 4.684 4.655
0.005 0.032 0.077 0.156 0.221 0.260 0.290 0.327 0.354
β
0.62 0.47 0.54 0.58 0.60 0.62 0.63 0.64
[AcO-]st/[AcOH]st ) 1.0 C16TAOAc-AcOH
NaOAc-AcOH c
(mM)a 0.3 0.5 0.75 1.0 1.5 1.8 2.0 2.5 3.0 4.0 5.0 6.0 7.0 7.5 8.0 10.0
b
c
pHmeas
pHcorr
4.83 4.81 4.78 4.77
4.80 4.770 4.764 4.755
d
pHth
4.793 4.773 4.761 4.755
4.75
4.738
4.741
4.74
4.728
4.734
4.73
4.717
4.725
4.71
4.706
4.717
4.71
4.705
4.711
pHmeasb pHcorrc
∆pHe
Figure 1. Example of cmc determination for C16TAOAcNaOAc solutions containing equal concentrations of C16TAOAc and NaOAc at 25.0 ( 0.1 °C.
β
4.81
4.773
-0.003
4.77 4.75 4.71 4.68 4.63 4.59 4.52 4.48 4.44 4.42
4.750 4.726 4.686 4.660 4.609 4.567 4.503 4.460 4.420 4.400
0.005 0.020 0.055 0.078 0.122 0.161 0.218 0.257 0.292 0.309
4.39 4.36
4.379 4.350
0.327 0.64 0.355 0.65
0.44 0.47 0.50 0.53 0.56 0.59 0.61 0.62 0.63
[AcO-]st/[AcOH]st ) 0.5 C16TAOAc-AcOH
NaOAc-AcOH
c (mM)a pHmeasb pHcorrc pHthd pHmeasb pHcorrc 0.3 0.5 0.70 0.75 1.0 1.5 1.8 2.0 3.0 4.0 5.0 7.0 8.0 10.0
4.56 4.52
4.53 4.485
4.509 4.485
4.49 4.48
4.469 4.456
4.470 4.461
4.46 4.45
4.439 4.430
4.444 4.436
4.43
4.420
4.425
4.42 4.41
4.441 4.411
4.418 4.411
∆pHe
4.52 4.50
4.485 4.475
0.000 -0.005
4.49 4.44 4.40 4.38 4.29 4.22 4.19 4.12
4.465 4.417 4.384 4.359 4.270 4.203 4.160 4.103
-0.009 0.029 0.058 0.080 0.160 0.220 0.260 0.312
4.07
4.055
β
0.75 0.52 0.54 0.57 0.60 0.62 0.63
0.346 0.65
a
CTAOAc or NaOAc concentration. b Experimental pH. c pH corrected for liquid-junction potential and for deviations from the smoothed pH-concentration curves. d pH calculated as pKa + log(aAcO/[AcOH]t) with aAcO ) yAcO[AcO-]t and pKa ) 4.754. e pH difference between the NaOAc and C16TAOAc buffers for the same concentrations.
5.5836) and since the emission spectrum shows maximum intensity at 470-480 nm, the excitation and emission wavelengths were set to 356 nm (slit width ) 5 nm) and to 470 nm (slit width ) 4 nm), respectively.
Results and Discussion Cmc Dependence on Counterion Concentration. Figure 2 shows the dependence of cmc on NaOAc (or (36) CRC Handbook of Chemistry and Physics, 61st ed.; Weast, R. C., Astle, M. J., Eds.; CRC: Boca Raton, FL, 1981.
Figure 2. Dependence of cmc for C16TAOAc-NaOAc solutions on the acetate ion concentration in absence or presence of acetic acid ([AcO-]st/[AcOH]st ) 1) (25.0 ( 0.1 °C).
NaOAc-AcOH buffer) concentration (cs) for aqueous C16TAOAc solutions in the absence of acetic acid and for the C16TAOAc-AcOH buffers. The two series of points fall on the same line. The presence of acetic acid does not cause any detectable variation in cmc. Since it is wellknown that the changes in cmc due to the presence of neutral solutes are closely related to their incorporation into the micelles,37,38 this is a first indication that AcOH is located only in the aqueous phase. The values measured for C16TAOAc from different sources (methods A, B, and C; see Experimental Section) were compared. They did not exhibit significant differences. It has been common practice to derive β values from the dependence of cmc on counterion concentration as the slopes of the so-called Corrin-Harkins plots,9-11,39,40 the plots of log(aM)cmc [or log(cM)cmc], the logarithms of the activities (or concentrations) of amphiphile at cmc vs log(aA)cmc [or log(cA)cmc], the logarithms of the activities (or concentrations) of counterions. This approach was initially based on the earliest mass-law approach to the thermodynamics of micellization and is supported by a (37) Mukerjee, P. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 153. (38) Treiner, C. J. Colloid Interface Sci. 1982, 90, 444. (39) Corrin, M. L.; Harkins, W. D. J. Am. Chem. Soc. 1947, 69, 679. Corrin, M. L. J. Colloid Sci. 1948, 3, 333. (40) Mukerjee, P.; Mysels, K. J.; Kapauan, P. J. Phys. Chem. 1967, 71, 4166.
Aqueous C16TAOAc Solutions
Langmuir, Vol. 13, No. 7, 1997 1921
Figure 3. Plot of log aM against log aAcO for C16TAOAc-NaOAc solutions.
detailed analysis by Hall.16,17 This author provided a theoretical justification of the procedure by deriving eq 3,
-d ln aM ) β d ln aA - [d ln(c - cw)]/n
(3)
where c and cw are the overall and water-phase amphiphile concentrations, which should be valid at c = cmc or at c > cmc, whatever the origin of the variations in counterion concentrations, changes either in surfactant concentration or the addition of common-ion salts. Equation 3 can be integrated to give eq 4, provided that β is constant and
log aM ) -β log aA + constant
(4)
that the second term on the right-hand side can be neglected. Although ln(c - cw) varies very rapidly with c in the cmc region, it is considered to be legitimatesif n is sufficiently largesto assume that d ln(c - cw) is close to zero when c ) cmc, since minute adjustments in c would make this assumption more rigorously true. Figure 3 shows the plot of log(aM)cmc vs log(aA)cmc, the activity coefficients of the unmicellized amphiphile cations, yM, and of the free acetate ions, yAcO, being calculated by the Debye-Hu¨ckel equation (eq 5)29 with a˚ taken as 8 Å
log yi ) -AI1/2 ˚ Ic1/2) c /(1 + Ba
(5)
(by analogy with the tetrapropylammonium ion41) and 4.5 Å29 for the CTA+ and AcO- ions, respectively. Even when the uncertainty limits of the cmc (ca. 2%) are considered, it is obvious that the relationship observed is not linear, but markedly curved, with the tangent to the line varying from ca. 0.30 to ca. 0.70. On the other hand, the plot of log cmc vs log[AcO-]w is more linear with a slope β ) 0.48. Many β determinations by the Corrin-Harkins method have been based on the amphiphile and counterion activities, the activity coefficients being calculated by the Debye-Hu¨ckel or equivalent equations. For instance, Wyn-Jones et al.42,43 found a good relationship for dodecylpyridinium and tetradecylpyridinium bromides, giving β values in agreement with other determinations. However, in most studies, the activity coefficients of M+ and A- were taken as unity, giving rise to better straight lines than when the activity coefficients are allowed. This point (41) Kielland, J. Am. Chem. Soc. 1937, 59, 1675. (42) Palepu, R.; Hall, D. G.; Wyn-Jones, E. J. Chem. Soc., Faraday Trans. 1990, 86, 1535. (43) Wan-Badhi, W. A.; Palepu, R.; Bloor, D. M.; Hall, D. G.; WynJones, E. J. Phys. Chem. 1991, 95, 6642.
has been addressed by Mukerjee et al.40 who suggested the occurrence of compensating effects. However, in the case of C16TAOAc and in view of the pH data described below, we believe that the marked curvature of the log(a)M vs log aAcO plot is typical for significant variations of β with acetate ion concentration, perhaps in addition to other effects. This means that the cmc variations can be accounted for by the differential eq 3 and not by eq 4. The β values correspond to the slopes of the tangents to the curve for each AcO- concentration. Derivation of β from pH Data. Table 1 gives the pH values (measured and corrected for liquid-junction potential) in terms of C16TAOAc concentration dependence for three buffer ratios ([AcO-]st/[AcOH]st ) 0.5, 1.0, and 2.0, where [AcO-]st and [AcOH]st are the stoichiometric concentrations of acetate ion and acetic acid, respectively), as well as the pH values observed and corrected for the sodium acetate buffers at the same concentrations. As expected, the pH decreases when c increases, this being attributed to incorporation of acetate ion into the micelle pseudophase. Shifts in pH when cationic surfactants are added to buffers are classically interpreted on the basis of the pseudophase model in terms of variations in the concentrations of the acid and/or base forms in the aqueous phase.44 This means that the pH for the C16TAOAc-AcOH solutions can be expressed by eq 6, where aAcO and [AcOH]w
pH ) pKa + log{aAcO/[AcOH]w}
(6)
are the activity of AcO- and the concentration of AcOH in the intermicellar pseudophase, respectively. (The activity coefficient of acetic acid is taken as unity.) The acetate and acetic acid concentrations in the aqueous phase depend primarily on the partition equilibria between water and the micelle pseudophase, but some dissociation of acetic acid should also be considered. Equations 7 and 8 account for electric neutrality and for
[AcO-]t ) [AcO-]w + [AcO-]m ) c + [H3O+]
(7)
[AcOH]t ) [AcOH]w + [AcOH]m ) [AcOH]st + c - [AcO-]t (8) mass balance, respectively. In these equations, the subscripts “m” and “w” refer to the concentrations in the micelles and in water (but relative to the whole volume of the solution), respectively. It follows that [AcO-]w is given by eq 9, where the third right-hand term accounts
[AcO-]w ) c + [H3O+] - β(c - cw)
(9)
for the acetate ions associated with the micelles. On the other hand, [AcOH]w can be expressed by eq 10, where PAcOH is the mole fraction basis partition coefficient of AcOH between the micelles and water.
[AcOH]w ) [AcOH]t[(1 + (PAcOH/55.5)(c - cw)]-1 (10) The pH dependence on [AcOH]st for C16TAOAc-AcOH solutions has been examined for [C16TAOAc] ) 0.01 M. Figure 4 shows that pH depends linearly on log{[AcO-]t/ [AcOH]t} with a slope strictly equal to unity. Since under the conditions of these experiments (corresponding to low concentrations of H3O+ relative to c) [AcO-]w/[AcO-]t should be fairly constant, the unit slope of the straight (44) Chaimovich, H.; Aleixo, R. M. V.; Cuccovia, I. M.; Zanette, D.; Quina, F. H. In Solution Behavior of Surfactants, Mittal, K. L., Fendler, E. J., Eds.; Plenum Press: New York, 1982; Vol. 2, p 949.
1922 Langmuir, Vol. 13, No. 7, 1997
Figure 4. Dependence of the pH of C16TAOAc-AcOH buffers on log([AcO-]t/[AcOH]t) for [C16TAOAc] ) 10-2 M (25.0 ( 0.1 °C). The slope of the line is 1.00.
line observed suggests that the term (PAcOH/55.5)(c - cw) in eq 10, i.e., the fraction of AcOH incorporated into the micelles, is very small. This conclusion is in agreement with what was observed for solutes of comparable hydrophilicity. For instance, the partition coefficient P of ethanol between water and trimethyldodecylammonium bromide micelles was found to be 10 from cmc variations.45 A similar value can be assumed for AcOH between water and C16TAOAc micelles because a linear relationship has been observed between the logarithms of the partition coefficients of polar molecules between water and micelles (log P) and water and octanol (log Poct)46 and because the log Poct values are about the same for ethanol and AcOH. It follows that the fraction of incorporated AcOH can be calculated to be e0.2% for c ) 10-2 M. This estimate of the fraction of AcOH incorporated into the micelles is in agreement with Zana’s data47 on the effects of carboxylic acids on the cmc of tetradecyltrimethylammonium bromide. In contrast to higher homologues, AcOH does not cause any variations of cmc. In Figure 5 are plotted the differences between the pH data (from Table 2) for the C16TAOAc-AcOH and NaOAcAcOH solutions at the same concentrations vs log c. The three series of points fall on the same line, this confirming that acetate ion association with the micelles does not depend on [AcOH]st. Figure 5 also shows that log cmc for C16TAOAc-AcOH can be derived from these plots by extrapolation to ∆pH ) 0. The value obtained, (1.36 ( 0.02) × 10-3 M, agrees nicely with that measured by fluorescence spectroscopy in either the presence or the absence of AcOH (1.38 ( 0.02) × 10-3 M. Derivation of β values from the pH data also requires calculation of cw, the concentration of unmicellized CTA+. Although in many studies dealing with ionic surfactants it was assumed that cw is constant and equal to cmc whatever c, it was shown by several authors using amphiphile-selective electrode potentiometry that cw decreases significantly with increasing c.41,42,47,48 It was emphasized above that eq 3 is valid whatever the origin of the aAcO variations and regardless of changes in (45) Treiner, C. J. Colloid Interface Sci. 1983, 93, 33. (46) Treiner, C.; Mannebach, M.-H. J. Colloid Interface Sci. 1987, 118, 243. (47) Zana, R.; Djavanbakht, A. Tenside, Surfactants, Deterg. 1989, 26, 227. (48) Koshinuma, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1975, 48, 2755. (49) Yamauchi, A.; Kunisaki, T.; Minematsu, T.; Tomokiyo, Y.; Yamaguchi, T.; Kimizuka, H. Bull. Chem. Soc. Jpn. 1978, 51, 2791.
Toullec and Couderc
Figure 5. Dependence of the difference in pH between the C16TAOAc-AcOH and NaOAc-AcOH buffer solutions on the logarithm of buffer concentration. [AcO-]st/[AcOH]st ) 0.5 (4), 1.0 (O), and 2.0 (b).
surfactant concentration or of the addition of commonion salts. Provided that the second right-hand term of this equation can be neglected, and sincesas shown belowsβ depends only on aAcO, this means that starting from (a)°cmc ) yMcmc0 (where cmc0 is the cmc value in the absence of NaOAc-AcOH buffer), the variations of aM ) yMcw with surfactant and/or salt concentrations can be accounted for by eq 11. The integration limits are the
∫ β d(log aAcO) + log(aM)°cmc
log aM ) -
(11)
values of log aAcO for c ) cmc0 and cs ) 0 on the one hand and that of log aAcO for a given situation (c > cmc0 and cs ) 0 or c ) cmc and cs > 0) on the other. It follows that aM depends only on aAcO and that the variations of aM with surfactant concentration, and then those of cw, can be estimated from the data of common-salt effects on cmc (Figure 2). The activity aM for given surfactant and NaOAc concentrations can be considered to be equal to aM at cmc for the same aAcO value. This assumption is in line with the cmc and free cation concentration data obtained for tetradecylpyridinium bromide.42 In this case, the slope of the linear plot of log aM vs log aBr at various surfactant concentrations is almost identical with that of the plot of log(aM)cmc vs log aBr for various concentrations of added NaBr. In order to apply the pH-data procedure to the determination of β, the activity coefficients need to be calculated. When specific interactions between ions (cation dimer formation and ion-pairing) are neglected, i.e., when the Debye-Hu¨ckel equation (eq 5) is used, an important issue that arises is that of the ionic strength (Ic when expressed on the basis of molarities) in micellar solutions. This problem has been addressed by various authors in order to account for the potential terms associated with the charged micelles.33,42,43,50,51 It was concluded33 that the highly charged micelles do not contribute much to the ionic strength, much less than the smaller unaggregated ions do. Ic can be calculated by considering only the presence of the free ions. In the case of C16TAOAc, this means that Ic can be calculated by eq 12.
Ic ) [2cw + (c - cw)(1- β)]/2
(12)
(50) Burchfield, T. E.; Woolley, E. M. J. Phys. Chem. 1984, 88, 2149. (51) Pashley, R. M.; Ninham, B. W. J. Phys. Chem. 1987, 91, 2902.
Aqueous C16TAOAc Solutions
Langmuir, Vol. 13, No. 7, 1997 1923
Table 2. Dependence of pH and Counterion Binding Parameter (β) on the Concentration of Added Sodium Acetate for [C16TAOAc] ) r[AcOH] ) 3 × 10-3 M (25 °C) r ) 0.50a
r ) 1.00a
r ) 2.00a
[buffer] (mM)
pHmeasb
pHcorrc
β
pHmeasb
pHcorrc
β
pHmeasb
pHcorrc
β
cwd (mM)
0 0.5 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0
4.29
4.276
0.56
4.31 4.32 4.33
4.291 4.305 4.315
0.60 0.62 0.63
4.342
4.333
0.66
4.35 4.36
4.344 4.348
0.69 0.70
4.59 4.60 4.61 4.62 4.63 4.64 4.65 4.65 4.65 4.66
4.568 4.581 4.590 4.605 4.618 4.628 4.638 4.640 4.647 4.650
0.56 0.57 0.59 0.62 0.62 0.63 0.63 0.65 0.66 0.68
4.89 4.90 4.90 4.92 4.93 4.93 4.94 4.94 4.95 4.95
4.870 4.880 4.887 4.902 4.915 4.924 4.931 4.937 4.944 4.948
0.55 0.57 0.60 0.63 0.63 0.65 0.67 0.67 0.69 0.71
1.23 1.12 1.07 0.95 0.83 0.80 0.75 0.70 0.62 0.57
a [NaOAc] /[AcOH] . b Experimental pH. c pH corrected for liquid-junction potential and for deviations from the smoothed pH-[buffer] st st curves. d Estimated concentration of unmicellized hexadecyltrimethylammonium ions (see text).
The concentration of AcO- in the bulk, [AcO-]w, is related to pH by eq 13. It follows that β, i.e., [AcO-]m/(c
[AcO-]w ) [AcOH]t × 10(pH-pKa)/yAcO
(13)
- cw), can be expressed by eq 14 when eq 7 is taken into
β)1-
{[AcOH]t × 10(pH-pKa)/yAcO} - cw - [H3O+] c - cw (14)
account, and that this parameter can be calculated from the pH data (Ka ) 1.76 × 10-5)36 for the various concentrations used. However, since yAcO (calculated by eq 5 with Ic estimated by eq 12) and cw (aM/yM with aM and yM calculated by eqs 11 and 5, respectively) both depend on [AcO-]w, and therefore on β, we used an iterative method starting with an initial β value. In these calculations, [H3O+] was calculated as 10-pH/yH, the activity coefficient of H3O+, yH, being estimated by eq 5 with a˚ ) 9 Å. The β values are listed in Table 1. It is obvious that β depends on the surfactant concentration (from ca. 0.4 for c ) 1.8 × 10-3 M to ca. 0.65 for c ) 10-2 M). The determination of the β values from the pH data requires reliable pH data. In view of the excellent linear dependence of pH on the AcOH concentration (Figure 4) it can be reasonably assumed that random errors on pH determination do not exceed 0.01 pH unit. However, in order to evaluate the incidence of pH (or pKa) errors on the conclusion that β changes markedly with c, we recalculated β after adding or subtracting 0.01 to or from the experimental figures. For c changing from 2 × 10-3 to 10-2 M, we observed that β increases with c from 0.44 to 0.64 when 0.01 is added to pH and from 0.56 to 0.66 when 0.01 is subtracted, instead of from 0.50 to 0.65 as shown in Table 1. It follows that systematic errors in pH determination can cause significant differences in the total range of the β variations, but that the conclusion that β is not constant remains valid. As described above and in line with recent literature conclusions,33,51,52 we calculated Ic by assuming that eq 12 is valid, i.e., by neglecting the contribution of the charged micelles. Such a hypothesis is, however, in disagreement with Burchfield and Woolley’s conclusions50 that Ic should be calculated by adding the δ(c - cw)n(1 - β)2 term (δ ca. 0.5) to the right-hand side of eq 12, the empirical coefficient δ accounting for the fact that micelles contribute to Ic, but less than monovalent ions. Since the pH-derived β values depend on the way that Ic is estimated, we recalculated Ic by adding this term and derived new β values. When c was changed from 2 × 10-3 to 10-2 M, β was observed (52) Marra, J.; Hair, M. L. J. Colloid Interface Sci. 1989, 128, 511.
Figure 6. Dependence of the counterion binding parameter for C16TAOAc on the activity of acetate ion in the intermicellar aqueous phase. Closed symbols correspond to β variations due to changes in surfactant concentration; open symbols correspond to β variations due to sodium acetate addition for [C16TAOAc] ) 3 × 10-3 M. [AcO-]st/[AcOH]st ) 0.5 (2 and 4), 1.0 (b and O), and 2.0 (9 and 0).
to vary from 0.46 to 0.61. These values are uniformly 0.04 unit lower than those listed in Table 1. We conclude that other estimates of Ic and of the activity coefficients can provide slightly different [AcO-]w values but that in any case β increases with c. Table 2 lists the pH values observed when sodium acetate buffer is added to CTAOAc-AcOH solutions at c ) 3 × 10-3 M for constant buffer ratios [AcO-]st/[AcOH]st ) 0.5, 1, and 2. As expected, the pH increases with buffer concentration and reaches values close to those observed in the absence of surfactant. In a way similar to that described above when dealing with pH data in the absence of added buffer, [AcO-]w was derived by eq 13 from the corrected pH data, and β was calculated by eq 15. This
β)1{[AcOH]t × 10(pH-pKa)/yAcO} - cw - cS - [H3O+] (15) c - cw latter equation, which is analogous to eq 14, was derived from the electric neutrality and mass balance equations when the concentration in Na+, cs, was taken into account.
1924 Langmuir, Vol. 13, No. 7, 1997
Toullec and Couderc
obtained as the tangent values from the curve of Figure 3. Such differences may be indicative of a problem associated with neglecting the second right-hand term when eq 3 is integrated. Many authors reported that the aggregation number is not independent of the concentration in surfactant (or salt) and increases sharply around the cmc.19,53-57 Since the acetate ions are very hydrophilic, a value of n as low as 30-40 at cmc is expected for the salt-free C16TAOAc solutions. It may therefore not be valid to neglect the d[ln(c - cw)]/n term when deriving β from the cmc data. On the other hand, since the calculations of β from pH do not require any assumption about the mean values and variations of the aggregation number, the β variations shown in Figure 6 seem more reliable, despite the large incidence of experimental errors. Conclusion Figure 7. Plot of log[(aM)cmc/(aM)cmc°] vs the integral term of eq 11, calculated from the pH-derived dependence of β on aAcO.
Since any calculation of β requires the β-dependent yAcO and cw values to be known, the same iterative method as above was used. The values of β are listed in Table 2 and plotted in Figure 6 against aAcO, together with those derived for cs ) 0. It is remarkable that the points corresponding to the lowest cs values are on the same line as those for various c and cs ) 0. Although the values of β are somewhat scattered for the lowest and the highest AcO- concentrationsssmall errors in pH result in large variations of βsit appears that β increases significantly with aAcO until β ) ca. 0.7 for aAcO ) 10-2. The whole curve is analogous to adsorption isotherms and to those recently observed in the case of betain micelles which bind positively or negatively charged ions.53 When the pH-derived β values are taken into account, it is possible to use the cmc data to test the validity of eq 11. (In this case, aM is the activity of the amphiphiles at cmc for the different NaOAc concentrations.) The integrals were calculated numerically from the β-log aAcO plot, the integration limits corresponding to log aAcO in the absence (c ) cmc0, cs ) 0) and presence of NaOAc (c ) cmc, cs). Figure 7 shows that log aM depends linearly on the integral term, but with a slope of 0.76, significantly different from unity. This reflects the fact that the β values derived from the pH data are slightly higher than those (53) Kamenka, N.; Chorro, M.; Chevalier, Y.; Levy, H.; Zana, R. Langmuir 1995, 11, 4234.
This report shows that both pH and cmc data for C16TAOAc or C16TAOAc-AcOH buffer solutions can be accounted for by assuming that the relative number of counterions bound to the micelles varies significantly. In agreement with theoretical approaches (purely thermodynamic16,17 or based on the Poisson-Boltzmann equation7) and with previous reports dealing with C16TAOH and C16TAF,12,21-26 this key parameter varies with the concentrations of both surfactant and added sodium acetate and depends only on the activity of the free acetate ions. It is noteworthy that, in contrast to the study of the common-ion salt concentration on cmc, which may provide ambiguous conclusions because of the changes in aggregation number, pH determination of the β values does not require any assumption concerning this latter parameter. Acknowledgment. Support of this work by the Direction des Recherches et Etudes Techniques, Ministe`re de la De´fense, is gratefully acknowledged. LA9603636 (54) Croonen, Y.; Gelade´, E.; Van der Zegel, M.; Van der Auweraer, M.; Vandendriessche, H.; De Schryver, F. C.; Almgren, M. J. Phys. Chem. 1983, 87, 1426. (55) Baumgardt, K.; Klar, G.; Strey, R. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 912. (56) Bezzobotnov, V. Y.; Borbe´ly, S.; Cser, L.; Farago´, B.; Gladkih, I. A.; Ostanevich, Y. M.; Vass, S. J. Phys. Chem. 1988, 92, 5738. (57) Wikander, G.; Johansson, L. B. Langmuir 1989, 5, 728. (58) Quina, F. H.; Nassar, P. M.; Bonilha, J. B. S.; Bales, B. L. J. Phys. Chem. 1995, 99, 17028.
