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Langmuir 1998, 14, 3986-3990
Articles Energetics of Micellization: Reassessment by a High-Sensitivity Titration Microcalorimeter Pinaki Ranjan Majhi and Satya Priya Moulik* Centre for Surface Science, Department of Chemistry, Jadavpur University, Calcutta 700 032, India Received July 3, 1997. In Final Form: February 25, 1998 The critical micellar concentration (cmc) and energetics of surfactant self-organization have been reassessed at 303 K with the help of a high-sensitivity microcalorimeter. The calorimeter can operate in a stepwise addition mode, providing an excellent method of determination of cmc and enthalpy of demicellization (and hence micellization). It can as well distinguish between aggregating and nonaggregating amphiphiles (solutes) in solution. The reinvestigated surfactants are hexa- (cetyl-), tetra-, and dodecyltrimethylammonium bromide, cetylpyridinium chloride, sodium dodecyl sulfate, sodium bis(2-ethylhexyl)sulfosuccinate, sodium cholate, and polyoxyethylene tert-octyl ether.
Introduction The self-organization (micelle formation) of surfactants in solution is an important and amply studied thermodynamically favorable physicochemical phenomenon.1-5 The determination of critical micellar concentration (cmc) and energetics of the micellization process is normally done by tensiometric, conductometric, spectrophotometric, NMR, calorimetric, and other methods. Among all these methods, calorimetry has a distinction for it can estimate both cmc and enthalpy of micellization from a single run, which is not possible by any other method. The thermometric titration method for the determination of cmc and enthalpy of micellization (∆Hm) was elaborately introduced by Kresheck and Hergraves6 and pursued in our laboratory7-10 and by others.11-23 Very recently, Paula et al.24 have demonstrated how a high(1) Clint, J. H. Surfactant Aggregation; J. Blackie: London, Published in USA by Chapman and Hall: New York, 1991. (2) Moulik, S. P. Curr. Sci. 1996, 71, 368. (3) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 3320. (4) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980. (5) Moroi, A. Micelles: Theoretical and Applied Aspects; Plenum Press: New York, 1992. (6) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (7) Mukherjee, K.; Mukherjee, D. C.; Moulik, S. P. J. Phys. Chem. 1994, 98, 4713. (8) Jana, P. K.; Moulik, S. P. J. Phys. Chem. 1991, 95, 9523. (9) Haque, Md. E.; Das, A. R.; Moulik, S. P. J. Phys. Chem. 1995, 99, 14032. (10) Moulik, S. P.; Haque, Md. E.; Das A. R. J. Phys. Chem. 1996, 100, 701. (11) Bergstrom, S.; Olofsson, G. Thermochim. Acta 1986, 109, 155. (12) Gu, G.; Yan, H.; Chen, W.; Wang, W. J. Colloid Interface Sci. 1996, 178, 614. (13) Singh, P. K.; Ahluwalia, J. C. J. Surf. Sci. Technol. 1986, 2, 51. (14) Mazer, N. A.; Olofsson, G. J. Phys. Chem. 1982, 86, 4584. (15) Sharma, V. K.; Bhat, R.; Ahluwalia, J. C. J. Colloid Interface Sci. 1986, 112, 195. (16) Jha, R.; Ahluwalia, J. C. J. Phys. Chem. 1991, 95, 7782. (17) Anderson, B.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4087. (18) Nusselder, J. J. H.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1992, 148, 353. (19) Paredes, S.; Tribout, M.; Ferreira, J.; Leonis, J. J. Colloid Polym. Sci. 1976, 254, 637. (20) Birdi, K. S. Colloid Polym. Sci. 1983, 261, 45.
sensitivity titration microcalorimeter having a provision for multistage addition and working in demicellization mode can help determine the cmc and enthalpy of demicellization (∆Hdm) and hence the enthalpy of micellization (∆Hm) by selecting four surfactants, sodium dodecyl sulfate, octyl glucoside, sodium cholate, and sodium deoxycholate. The method is sensitive, precise, and versatile. Similar microcalorimetric procedures for the study of self-aggregating and interacting systems have been demonstrated recently by Johnson et al.25 and Blandamer et al.26 It is, therefore, worthwhile to reassess the basics of micellization with the help of this unique microcalorimetric method. We herein report the results obtained for a number of surfactants including the two members studied by Paula et al.24 It will be seen that the method can clearly demonstrate identification of both aggregating and nonaggregating systems in solution. The surfactants studied are sodium dodecyl sulfate (SDS), sodium bis(2-ethylhexyl)sulfosuccinate (AOT), sodium cholate (NaC), hexadecyl- or cetyltrimethylammonium bromide (CTAB), tetradecyltrimethylammonium bromide (TTAB), dodecyltrimethylammonium bromide (DTAB), cetylpyridinium chloride (CPC), and polyoxyethylene tertoctyl ether (Triton X-100). For the calorimetric identification of nonaggregating systems on a comparative basis, measurements on sodium dehydrocholate (NaDHC), phenyltrimethylammonium iodide (PTMAI) and NaCl were also undertaken. The evaluated cmc and ∆Hm values of the studied surfactants have been compared with authentic recent and past literature data. Our results together with those of Paula et al.24 clearly demonstrate the high potential of (21) Von Os, N. M.; Daane, G. J.; Haandrikman, G. J. Colloid Interface Sci. 1988, 266, 374. (22) Moroi, Y.; Matura, R.; Kuwamura, T.; Inokuma, S. J. Colloid Polym. Sci. 1988, 266, 374. (23) Blume, A.; Tuchtenhagen, J.; Paula, S. Prog. Colloid Polym. Sci. 1993, 93, 118. (24) Paula, S.; Siis, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (25) Johnson, I.; Olofsson, G.; Jonsson, B. J. Chem. Soc., Faraday Trans 1 1987, 83, 3331. (26) Blandamer, M. J.; Cullis, P. M.; Engberts, J. B. F. N. Pure Appl. Chem. 1996, 68, 1577.
S0743-7463(97)00743-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/30/1998
Energetics of Micellization
Figure 1. Titration of 120 µL aliquots of TTAB micelles (79.40 mM) into 1.325 mL of water in 30 steps at 30 °C. (A) Calorimetric traces (heat flow against time). (B) Process enthalpy versus [CTAB] in the cell. The ∆Hm is represented by the length of the arrow. (C) First derivative of curve B calculated from the interpolated values.
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Figure 2. Titration of 320 µL of aliquots of AOT micelles (30.23 mM) into 1.325 mL of water in 13 steps at 30 °C. (A) Calorimetric traces (heat flow against time). (B) Process enthalpy versus [AOT] in the cell. The ∆Hm is represented by the length of the arrow. The encircled point represents the location of the cmc (it is a chosen point on the basis of the trend not an experimental point). (C) First derivative of curve B calculated from the interpolated values. The encircled maximum point refers to the cmc, as explained in curve B.
Results and Discussion
differential plots are presented in Figures 1-3 as well as in Figure 4. The cmc points are indicated by arrowheads in the figures. When compared with the thermograms and the associated enthalpies per mole of injectant for NaDHC (Figure 5), NaCl, and PTAI (Figure 6A and B), a clear distinction between the nonaggregating and aggregating (micelle-forming) systems is evident. The enthalpy courses of the former (Figures 5 and 6A and B) are monotonic, but those of the latter (Figures 1-4) have modulations. This is critically justified in the case of the bile salt NaDHC, which according to reports8,27 normally does not micellize. Thus, first-hand knowledge on the micellization/nonmicellization properties of amphiphiles can be obtained by the use of the microcalorimetric method herein used. In addition to the inflection point in the enthalpy of dilution versus [surf] curve (plot B in the Figures 1-4), which corresponds to the cmc, the difference between the initial and the final levels (i.e., enthalpy levels between nonmicellar and micellar regions) gives a measure of the enthalpy of demicellization or micellization.24 The heat change at the initial stage of addition of micellar solution in water essentially stands for micellar dilution, demi-
Several thermograms with the corresponding enthalpies of dilution per mole of injectant at different stages of addition of surfactants together with the associated
(27) Small, D. M. In The Bile Acids: Chemistry, Physiology and Metabolism; Nair, P. P., Kritchevsky, D., Eds.; Plenum Press: New York, 1971; Vol. 1, Chapter 8.
the OMEGA ITC microcalorimeter in studying the selforganization of surfactants. It has a good potential for the identification of aggregating and nonaggregating amphiphiles (solutes). Experimental Section Materials. SDS, AOT, NaC, CTAB, TTAB, DTAB, CPC, and TX-100 were pure products of either Sigma, USA, or E. Merck, Germany, and the samples used in previous studies.7-10 The NaCl and PTMAI used were Excellar grade BDH products. The water used was doubly distilled (specific conductivity 2-4 µS cm-1 at 25 °C). Methods. An OMEGA, ITC, microcalorimeter of Microcal, Northampton, MA, was used for thermometric measurements. A concentrated solution of a surfactant was taken in a microsyringe of capacity 250 or 100 µL and was added in multiple stages to water in the calorimeter cell of capacity 1.325 mL under constant stirring conditions, and the stepwise thermograms of the heats of dilution of the surfactant solution were recorded. Each run was duplicated to check reproducibility. Enthalpy calculations were performed with the help of ITC software. All measurements were taken at 30 ( 0.01 °C.
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Figure 3. Titration of 120 µL aliquots of TX-100 micelles (7.61 mM) into 1.325 mL of water in 12 steps at 30 °C. Description and explanation as in Figure 1
cellization, and dilution of monomer existing with the micelles and those produced by the process of demicellization. At a concentration close to the cmc, the dilution of the monomer is minor; the enthalpy difference between the top and bottom bends (that is between the i and f levels in Figures 1-4 and 6 in line with the procedure followed by Paula et al.24 and Johnson et al.25) essentially quantifies the enthalpy of demicellization (∆Hdm).24 In this paper, we have expressed and discussed our results in terms of the process of micellization. The enthalpy of micellization (∆Hm) has been obtained by subtracting the initial enthalpy from the final enthalpy indicated by the vertical arrow in each figure. The estimation of the enthalpy of micellization (∆Hm) here is sharp and accurate. It may be mentioned that the nature of the enthalpy change per mole of injectant in the course of titration gives an overall understanding of the various physicochemical processes (viz., demicellization, dilution, solvent structure alteration, surfactant solvent interaction, etc.) occurring during a run keeping scope for quantitative analysis (this has been partially attempted by Paula et al.24 on the bile salt NaDC). In Table 1, the cmc and the ∆Hm values at 30 °C for the studied surfactants are presented and compared with authentic literature reports. Of the systems cited, CTAB, SDS, and TX-100 are more studied than the rest. It is found that although the cmc values obtained in this work are on the whole comparable with the earlier findings by calorimetry, the ∆Hm values differ in magnitude but not
Majhi and Moulik
Figure 4. Process enthalpy versus surfactant concentration in the cell during the titration of aliquots of CTAB, CPC, and DTAB into water in steps at 30 °C. (A) 84 µL aliquots of CTAB solution (30.94) into 1.325 mL of water in 14 steps. (B) 104 µL aliquots of CPC solution (31.29 mM) into 1.325 mL of water in 13 steps. (C) 100 µL aliquots of DTAB solution (447.87 mM) into 1.325 mL of water in 25 steps.
in sign except for that for NaC; it is endothermic by the present study but was found to be exothermic in a previous study8 using a less sensitive titration calorimeter. For obvious reasons, the presently obtained results are considered more accurate than those of most of the earlier reports. The surfactant AOT has exhibited two inflection points: one endothermic and fairly sharp (∆Hm ) 1.22 kJ mol-1) and the other exothermic but less sharp (∆Hm ) - 0.81 kJ mol-1). They correspond to two cmc points at 2.60 and 4.10 mM, respectively. In a previous work,7 by using a less sensitive titration calorimeter, a cmc value of 2.31 mM and ∆Hm ) 2.97 kJ mol-1, respectively, were reported. The second or the higher cmc is comparable with the value of 5 mM reported by Haffner et al.28 The thermometric behavior of AOT among the surfactants appears to be unique and needs further attention. The energetic parameters ∆Gm and ∆Sm (free energy and entropy of micellization, respectively) are also presented in Table 1. In the calculation of ∆Gm, 96% and 88% counterion binding to CTAB and SDS micelles were considered according to previous reports by the electrochemical method.29,30 The extents for TTAB, DTAB, and (28) Haffner, F. D.; Piccione, G. A.; Rosenblum, C. J. Phys. Chem. 1942, 46, 662.
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Figure 5. Titration of 126 µL aliquots of NaDHC solution (207.62 mM) into 1.325 mL of water in 14 steps at 30 °C. A) Calorimetric traces (heat flow versus time). (B) Process enthalpy versus [NaDHC] in the cell.
CPC were taken to be 73, 77, and 58%, respectively.10 10% counterion binding was considered for AOT;7 the NaC micelle was considered not to bind counterions.29 The fractions of the counterions bound for CTAB, TTAB, DTAB, CPC, SDS, AOT, and NaC micelles are thus 0.96, 0.73, 0.77, 0.58, 0.88, 0.10, and 0, respectively. The ∆Gm was calculated by the following relation
∆Gm ) (1 + f )RT ln cmc
(1)
where f stands for the fraction of counterions bound to a micelle. ∆Sm was evaluated by the Gibbs equation
∆Sm ) (∆Hm - ∆Gm)/T
(2)
As usual the ∆Sm values are all positive; the value of TX100 tops the list. As T∆Sm > ∆Hm, the micellization process turns to be entropy-governed. The cmc and ∆Hm for SDS at 30 °C reported by Paula et al.24 differ from our findings. Their cmc value (8.6 mM) is higher than ours (7.78 mM) by 10.5%, whereas the enthalpy difference is 1.0 unit. The enthalpy change per mole of injectant (SDS) versus [SDS] plot of the present study is illustrated in Figure 6C; the cmc and ∆Hm values are distinctly documented on it. The second surfactant studied for comparison has been NaC; for it the cmc and ∆Hm at 30 °C have been obtained from Paula et al.’s data (29) Bandopadhyay, A.; Moulik, S. P.; Das Gupta, P. K. Colloid Polym. Sci. 1989, 267, 1. (30) Evans, H. C. J. Chem. Soc. 1956, 579.
Figure 6. (A) Process enthalpy versus [PTMAI] in the cell during the titration of 300 µL aliquots of PTMAI solution (200.14 mM) into 1.325 mL of water in 20 steps at 30 °C (first 10 steps, 10 µL installments; the other 10, in 20 µL installments). (B) Process enthalpy versus [NaCl] in the cell during the titration of 320 µL aliquots of NaCl solution (208.55 mM) into 1.325 mL of water in 22 steps at 30 °C (first 12 steps, 10 µL installments; the remaining 10 steps, 20 µL installments, respectively). (C) Process enthalpy versus [SDS] in the cell during the titration of 112 µL aliquots of SDS solution (212.14 mM) into 1.325 mL of water in 28 steps at 30 °C.
by the method of interpolation (cf, note b in Table 1). The cmc value is 6.7% higher than ours, and the enthalpy difference is 0.53 unit. On the basis of the uncertainties allowed in surfactant aggregation studies, the above-noted disagreements are within the accepted limits. It is observed from Table 1 that among the cationic surfactants CTAB, TTAB, and DTAB, while cmc increases with decreasing length of the nonpolar tail, the magnitude of -∆Hm declines. The ∆Hm follows a curvilinear correlation with cmc whereas the ∆Hm versus log cmc course is fairly linear; CPC seriously deviates from it (illustration not shown). The T∆Sm values are fairly larger than ∆Hm; the entropy is a controlling factor of micellization. The increased ∆Sm in going from DTAB to CTAB (i.e. with increasing nonpolar tail length) is in conformity with increased disruption of water structure formed by the hydrophobic effect4) during micellization. In Figure 7, a profile of the energetic parameters ∆Gm, ∆Hm, and ∆Sm in three dimensions is presented. It has a look like a spatula, the cationic surfactants shaping the blade, NaC the waist, and the rest the handle. The points on the base plane with full circles represent the ∆Hm-
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Majhi and Moulik
Table 1. Critical Micellar Concentration and Energetic Parameters for the Micellization of Surfactants at 30 °C cmc/mM this work
system
lit.
CTAB TTAB DTAB CPC SDSa
0.9510 3.3110 17.8510 1.0610 6.67,12 8.20,8 3.8,6 8.6024 7.22,8 14.8024 2.317
NaCb AOT TX-100
0.279
f
1.03 3.98 15.98 1.12 7.78
0.9629 0.7310 0.7710 0.5810 0.8829
13.87 2.60(1) 4.10(2) 0.23
0.029 0.17
∆Hm/kJ mol-1 lit. this work -13.6,11 13.4,12 -8.5610 -7.3510 -1.7710 - 5.6010 -2.49,8 -4.02,6 -3.23,12 -1.8,11 -2.6,14 -2.524 -1.85,8 024 +2.977 10.96,15 4.80,12 4.4016
-13.90 -8.51 -5.10 -9.30 -3.50 +0.53 1.22(1) -0.81(2) 6.35
∆Gm/kJ mol-1 this work
∆Sm/J K-1 mol-1 this work
T∆Sm/kJ mol-1 this work
34.0 24.1 18.4 27.1 23.0
66.3 51.5 43.9 58.7 64.4
20.1 15.6 13.3 17.8 19.5
10.8 16.5(1) 15.2(2) 21.1
37.4 58.5(1) 47.5(2) 90.6
11.3 17.7 14.4 27.5
a For SDS Paula et al.24 obtained ∆H values of -2.50 kJ mol-1 at 303 K. Our value of -3.50 kJ mol-1 at 303 K is higher but in fair m agreement with those of Kresheck and Hargraves6 and Gu et al.12 b The ∆Hm and cmc values for NaC obtained by interpolation of the 24 -1 results of Paula et al. are 0 kJ mol and 14.8 mM, respectively.
Figure 7. Three-dimensional profile for the energetic parameters ∆Gm, ∆Hm, and ∆Sm for the micellization of the surfactant systems studied at 30 °C. 1-9 represent CTAB, CPC, TTAB, DTAB, SDS, AOT(2), NaC, AOT(1), and TX-100, respectively.
∆Sm correlation, which is nonlinear except for CTAB, TTAB, and DTAB (their linear correlation is shown on the base plane by the thin broken line). These two energetic parameters do not broadly compensate like various equilibrium and kinetic processes.31-34 The strong dependence of ∆Hm and ∆Sm on surfactant type is apparent. Conclusions (1) The OMEGA, ITC titration microcalorimeter is unique in determining the cmc and ∆Hm. It can differentiate between aggregating and nonagreegating solutes in solution. (2) AOT offers two cmc values with well-separated ∆Hm values.
(3) The T∆Sm values are fairly higher than the ∆Hm values; there is no visible correlation between ∆Hm and ∆Sm except for CTAB, TTAB, and DTAB. Acknowledgment. The work was done under a DSTsponsored project program. P.R.M. thanks UGC, Government of India, for financial support. LA9707437 (31) Maulik, S.; Moulik, S. P.; Chattoraj, D. K. J. Biomol. Struct. Dyn. 1996, 13, 771. (32) Ray, S.; Bisal, S. R.; Moulik, S. P. J. Chem. Soc., Faraday Trans. 1993, 89, 3277. (33) Lumry, R.; Rajender, S. Biopolymers 1970, 9, 1125. (34) Lee, B. Biophys. Chem. 1994, 51, 279.
