5322
J . Phys. Chem. 1985,89, 5322-5324 an interaction parameter Cl2 such that RT A7 = - T121[xIx2/(~1)2(~2)11 vlZi3 v22/3)1/2(12)
TABLE V Mean Values of Cn (Eq 12) for Various Systems'
vnl
methanol
water
acetone water acetonitrile water
278.15 298.15 298.15 298.15
1.82 1.78 2.37 2.24
2.24 2.14 2.17 2.10
6.3 3.8 -1.7 0.32
For acetone-water the shear viscosities were those of Dizechi and Mar~chell'~ and molar volumes were obtained from Fort and Moore;'* for acetonitrile-water the shear viscosities were from Cunningham and co-~orkers'~ and Mato and Hernandez20 and molar volumes from Easteal and Woolf.2' (I
(eq 10) give a good approximation, usually within experimental error, for the shear viscosity of mixtures where association between the components is not significant; the approach is usually much less successful when association such as hydrogen bonding is important. Thus eq 10 provides a poor prediction of 11 for methanol-water at 298.15 K as shown in Figure 5. However, it is interesting to examine the deviations from eq 10 by defining (21) Easteal, A. J.; Woolf, L. A. J . Chem. Thermodyn. 1982, 14, 755.
with A? = q12 - q (eq 10). The mean value of lI2 over the composition range 0 < x < 1 is given in Table V for several systems; the value for acetonitrile-water is included as an indication of the small magnitude of TI2 for a system which follows eq 10 within about 1-2%. The values of TI2 seem to correlate well with the earlier observations in this paper for methanol-water that the 1-2 interactions are promoted by lower temperatures. The negative value for acetonewater may indicate that the interactions in this system are of a different type to those in methanol-water as is indicated for example by the D*(i) values examined earlier. Further investigation of this approach through the Albright equation will require extensive intradiffusion data for a number of systems representative of particular interactions.
Acknowledgment. We are indebted to Professor R. H. Stokes for his provision of data for the enthalpy of mixing of methanol and water. Registry No. CH30H, 67-56-1; H20, 7732-18-5.
Ionization Degrees and Crltical Micelle Concentrations of Hexadecyltrimethylammonium and TetradecyCtrimethylammonlum Micelles wlth Different Counterlons Luis Sepirlveda* and Juan Cortes Department of Chemistry, Faculty of Sciences, University of Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile (Received: April 1 1 , 1985; In Final Form: August 2, 1985,)
Ionization degrees (a)of micelles of hexadecyltrimethylammonium(CTAX) and tetradecyltrimethylammonium (TTAX) (X = OH-, Br-, C1-, NO3-,SO4", and eo?-) were measured by a modified free electrophoresismethod and by Evan's method. Cmc values for the CTAX and TTAX surfactants were also measured. Whenever possible the a and cmc values thus obtained were compared with those reported in the literature.
Introduction
The ionization degree (a)of cationic micelles is quite important for the quantitative treatment of micellar catalysis and inhibition,'-, ionic exchange models in micellar systems,e6 and micellar effects on the ionization degree of weaks acids and bases' and on the shape and size of micelles.' a values for some counterions are not reliable and confirmation of their existing values by a direct method is of interest. Romsted8 has made a cofnprehensive review of a values and from his collected data it is clear that, in general, a is highly dependent on the method used to determine it.
The above considerations led us to measure a values in micelles of hexadecyltrimethylammonium X- (CTAX) and tetradecyltrimethylammonium X- (TTAX), (X = OH-, Br-, C1-, NO3-, SO4*-,C032-)by a modified free electrophoresis method and by the Evans m e t h ~ d . ~ Critical micelle concentrations (cmc) for the same systems were also measured. We must note that cmc and a values for (CTA)2SO4, (CTA)N03, and TTANO, are first reported on here. Finally the a and cmc values, whenever possible, are compared with existing literature values. Experimental Section
(1) Bunton, C. A.; Romsted, L. S.; Sepiilvea, L. J . Phys. Chem. 1980,84, 261 1. (2) Romsted, L. S. In 'Micellization, Solubilization and Microemulsions"; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 1 . (3) Chaimovich, H.; Aleixo, R. M. V.; Cumvia, J. M.;Zanette, D.; Quina, F. H. In "Symposium on Solution Behavior of Surfactants"; Mittal, K. L., Fendler, H. Eds.; Plenum Press: New York, 1982; Vol. 1. (4) Bartet, D.; Gamboa, C.; Sepiilveda, L. J . Phys. Chem. 19%0,84, 272. ( 5 ) Gamboa, C.; Sepiilveda, L.;Soto, R. J . Phys. Chem. 1981,85, 1429. (6) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979, 83, 1844. (7) Dorshow, R.; Briggs, J.; Bunton, C. A,; Nicoli, D. F. J . Phys. Chem. 1982, 86, 2388. (8) Romsted, L. S . Ph.D. Thesis, Indiana University, Bloomington, IN, 1975.
0022-3654/85/2089-5322$01.50/0
CTAOH was prepared by mixing a CTAB solution with a Ag2S04solution followed by filtration and further precipitation of the sulfate by addition of Ba(OH)2. Manipulation of the solutions was done under N2in order to avoid contamination with ambient C 0 2 . The concentration of CTAOH was controlled by titration with HC1. The other compounds were separated by neutralizing CTAOH with the corresponding HX acid. TTAOH was a 0.5 M solution labeled by Baker Chem. Co. as a 0.5 M CTAOH solution. However, in spite of the label, a micro Hoffman elimination analysis kindly done by Dr. F. Quina (Institute of (9) Evans, H.
C. J . Chem. SOC.1956, part
0 1985 American Chemical Society
1, 579
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5323
Ionization Degree of Cationic Micelles Chemistry, University of Sao Paulo, Brasil) showed that the compound in the 0.5 M solution was more than 99% TTAOH. The ionization degrees for the different CTAX and TTAX micelles were obtained by using two different methods. One was a free electrophoresis method used by Hoyer et all0 which consists in measuring the micellar mobilities U, and the specific conductivities (A) of the same micellar solutions. The U, values were obtained by tagging the micelles with Orange OT which has an extinction coefficient of 17 300 that allows its experimental determination at extremely low concentrations which would not affect the micellar properties. One important contribution of this work consists in the modification of the free electrophoresis method proposed by Hoyer et al. The sealed electrode compartments were replaced by a simple agar agar salt bridge which seals the electrode compartments and completes the circuit. The entire cell was immersed in a thermostated bath at 25 f 0.01 OC. The modified cell is shown in Figure 1. Diffusion problems were diminished by doing the experiment in no more than 2 h. Specific conductivities were measured in a Tinsley bridge Type 4896 with an oscilloscope as detector and coupled to an YSI conductivity cell of constant 1.O. According to Hoyer et al., U, is given by
TABLE I: Final and Initial Absorbances ( A and A ,) of the Tagged Variations of Surfactant Solutions, Micellar Mobilities ( U,,,), Conductivities with Surfactant Concentration (dA/dC), and Ionization Degrees (a)Obtained by the Free Electrophoretic Method for Several Cationic Surfactants a Ai U, X lo4 dX/dC surfactant AE
CTAB CTAOH CTACl CTANOj (CTA)?SO,
TTAB TTAOH
0.522 0.647 0.392 0.508 0.370 0.364 0.419 0.282 0.483 0.660 0.508 0.498 0.610 0.532
0.650 0.770 0.625 0.712 0.780 0.698 0.722 0.500 0.620 0.925 0.755 0.807 0.685 0.885
2.375 2.100 8.45 7.80 11.60 5.53 4.89 5.37 3.24 4.60 5.74 3.99 1.85 9.98
0.0245 0.136 0.068 0.045 0.042
0.027 0.138
0.240 0.248 0.480 0.490 0.360 0.360 0.376 0.360 0.370 0.340 0.310 0.350 0.270 0.470
QdX/dCstands for the slope of X vs. surfactant concentration plots above the cmc and equal to S7 (Table 11). TABLE II: Slopes of the Specific Conductivity-Concentration Plots and above (S,) the Cmc and Micellar Ionization Degrees below (SI) ( a ) Obtained by the Evans Method
surfactant CTAB CTAOH CTACl (CTA)zS04 CTANOj (CTA)2CO3 (CTA)ZHPO, TTAOH TTAB
where Ai and Af are the absorbances at 495 nm of the tagged solution contained in the capillary section of the cell (Figure 1) before and after the electrophoresis. respectively, t is the time in seconds during which a current of i A measured in a Keithley 172A multimeter passed through the cell, and Vis the volume of solution contained in the capillary between stopcocks 1 and 2 (Figure 1); a is then obtained from the relationlO.ll
where F is the Faraday, Uxthe mobility of the counterion, and C the concentration of the surfactant. Ux-was obtained from the equivalent conductivity of the given counterion at infinite dilution.’* The values so calculated were essentially independent of C. The other method was the one proposed by Evans9 in which a is given by a = (n - m)/n
(3)
where n is the micellar aggregation number and m the number of micellar bound counterions. According to Evans, n and m are related through the equation (n - m)*
1OOOS2 = n4/3 (1OOOS1 - Ax-)
+
(n - m
y ) A x -
(4)
where SIand S2 are the slopes of the specific conductivity-concentration curves below and above the cmc, respectively, and are listed in Table 11. An arbitrary value must be given to n in order to calculate a. The value of a is, fortunately, very insensitive to n. For example, for CTAB, n values of 40, 60, and 80 gave a values of 0.22, 0.2 1, and 0.20, respectively. Therefore an n value of 60 was chosen in this work. The conductivities were measured in a Schott Gerate conductivity meter at 25.00 O C and the cmc’s were obtained from the intersection of the specific concentration straight lines below and above the cmc. The cmc of CTAOH was also measured by (10) Hoyer, M.; Mysels, K.J.; Sitgter, D. J . Phys. Chem. 1954, 58, 385. (1 1) Keh, E.;Gavach, C.; Guastalla, J. C.R. Acod. Sci., Paris 1966, 263, 1488. (12) Harned, H. S.; Owen, B. B. “The Physical Chemistry of Electrolytic Solutions”, 3rd ed.; Reinhold: New York, 1958.
SI
S,
0.091 0.2105 0.100 0.1057 0.0944 0.166 0.177 0.200 0.1057
0.0245 0.136 0.068 0.042 0.045 0.115 0.116 0.138 0.027
a 0.22 0.52 0.37 0.26 0.30 0.29 0.648 0.20
surface tension with a Dunouy tensiometer fitted with a platinum ring. For both U, and dX/dC measurements, concentrations of surfactants were varied from 0 to 0.01 M.
Results and Discussion In Table I are presented the values of the parameters used in eq 2 for obtaining a from the free electrophoresis method. It is seen in Table I that there is no significant difference between the values of a obtained from different experiments and the error is, therefore, insignificant. In Table I1 are shown the parameters used to calculate a from the Evans method (eq 3 and 4). Finally, in Table 111 are presented the average a and cmc values for the different micellar systems (CTAX and TTAX) together with reported values and transfer free energies of X- counterions from water to CTA micelles. It is seen in Table 111 that our a values for CTAB, CTANO,, and TTAB agree well with reported values. However, large differences are detected for CTAOH, CTAC1, and TTAOH. These differences reflect the high a dependence of the measurement method which has been already discussed by RomstedS8We believe that the electrophoresis method is one of the most reliable because it is based on direct measurements and does not include adjustable parameters or extra assumptions. In this context it is interesting to note that the Evans method which includes several extra assumptions gives a values not too far from those obtained by the free electrophoresis method. Surprisingly, the sequence in the magnitude of a for the anions studied is different from the lyotropic series found for the same anions and obtained from ionic exchange constant^.^.^ and from enthalpies and free energies of transfer from water to micelle^.^,^^'^ (13) 1871. (14) (15) Savelli,
Paredes, S.; Tribout, M.; Sepiilveda, L. J . Phys. Chem. 1984, 88, Lianos, P.; Zana, R. J . Phys. Chem. 1983, 87, 1289. Bunton, C. A,; Leong-Huat Gan, Moffatt, J . K.; Romsted, L. S.; G. J . Phys. Chem. 1981, 85, 4118.
5324 The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
Sepdlveda and CortBs
TABLE III: Ionization Degrees (a),Transfer Free Energies of Counterions from Water to Micelles (Apt), and Cmc Values for Different CTAX and TTAX Micellar Solutions a' cmc X lo3 M surfactant I 2 3 -Ab:: kcal/mol 4 5 CTAOH 0.49 0.52 0.70" 2.34 2.3-3.4' 1.8," 0.86c CTABr 0.24 0.22 0.25," 0.22' 4.14 0.8 0.9: 0.9g CTANO, 0.36 0.30 0.35d 4.10 0.9 0.811 CTACI 0.36 0.37 0.5d 3.17 1.4 1.3; 1.38 (CTA)2S04 0.35 0.26 0.6 (CTA)zC03 0.29 2.72 0.8 TTAOH 0.47 0.65 0.66," 0.69" 4.5 7.2," 3.7f TTABr 0.27 0.20 0.21' 3.5 3.5h TTANO, 0.18 2.7 ~~~~
" From ref 14. "his work, by surface tension. 'From ref 15. dFrom ref 1. 'From ref 8. 'From ref 13. 8 From ref 16. *From ref 17. 1, This work, free electrophoresis method; 2, this work, Evans method; 3, reported values. 4, this work, specific conductivity method unless specified; 5, reported values. 'References 4 and 5.
la
IR
NmC'I
-
+
fl
c:
c--
2
1
Figure 1. Free liquid tracer electrophoresis cell: ( G ) galvanometer, (P) power supply, (C) capillary tube containing a volume of 3.96 mL of tagged solution, (u) untagged solution of detergent, (Ag) silver electrodes immersed in NaCl solution, (1, 2) triple three-way stopcocks, (3, 4) one-way stopcocks, (5) agar agar salt bridge with 1 M NH4N03.
These values reflect directly the relative strength of the binding of the counterions to the cationic micelles and follow the series NO3- > B; > C1- >> OH-. It may have been expected that the same sequence would be followed by a. However, Table I11 shows that the sequence in terms of the association degree (1 - a) is Br> C1- N NO3- = Sodz-> OH- from the free electrophoresis method, Br- > NO; > Cl- >> OH- from reported values, and Br> NO3- > C1- >> OH- from the Evans method. The a values for OH- in CTA and TTA micelles are larger than the values for the other counterions in accordance with its low (16) Mukerjee, P.; Mysels, K. Natl. Stand. Ref. Data Ser. (US.Natl. Bur. Stand.) 1971, NSKDS-NBS 36. (17) Venable, R. L.; Nauman, R. V. J . Phys. Chem. 1964, 68, 3498.
free energy of transference from water to CTA micelles. However, NO3- counterions present a large a value in spite of its large negative free energy of transfer (Table 111). It may seem that binding energies of counterions are not decisive in determining the micellar ionization degree but other factors such as micellar size and shape are also contributing to it. This suggestion is in line with that proposed by Romsted* in the sense that "only the variables that directly or indirectly alter the hydrophobic attraction-electrostatic repulsion balance will change the degree of ionization of the micelle". It is interesting to note that OHand Br- counterions have practically the same values in both CTA and TTA micelles. Another aspect to be noted in Table 111 is that dianions like Sod2-and C03*-have a values similar to those of Br- and NO3counterions indicating that the charge of the counterion is not fundamental for determining the micellar ionization degree. The transfer free energies from water to CTA micelles (Table 111) of C03*- counterions point out to the same conclusion. The cmc values shown in Table I11 agree fairly well with reported values and follow the expected trend in the sense that micelles having the more strongly bound counterions present the lowest cmc and also that TTAX micelles have higher cmc values than the corresponding CTAX micelles.
Acknowledgment. Support of this work by the Departamento de InvestigaciBn y Bibliotecas de la Universidad de Chile and by the Fondo Nacional de Desarrollo Cientifico y Tecnolbgico is gratefully acknowledged. Registry NO. CTAOH, 505-86-2; CTAB, 57-09-0; CTACI, 112-02-7; CTAN03, 371 14-85-5; (CTA)zSOd, 67355-36-6; TTAB, 11 19-97-7; TTAOH, 84927-25-3; (CTA)zCOI, 98652-62-1; (CTA)ZHPO,, 9865263-2; TTANO1, 30862-45-4.
