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Thermodynamic Characterization of Temperature-Induced Micellization and Demicellization of Detergents Studied by Differential Scanning Calorimetry Pinaki R. Majhi and Alfred Blume* Martin-Luther-Universita¨ t Halle-Wittenberg, Institute of Physical Chemistry, Muehlpforte 1, D-06108 Halle/Saale, Germany Received November 29, 2000. In Final Form: April 10, 2001 The micellization and demicellization of surfactants can be induced not only by changes in concentration but also by changes in temperature, because the critical micellar concentration (cmc) exhibits a characteristic temperature dependence with a minimum at temperatures between 20 and 50 °C, depending on the nature of the surfactant. We obtained differential scanning calorimetry (DSC) curves of the three nonionic surfactants octylglucoside, nonylglucoside (NG), and decylmaltoside and the anionic surfactant sodium dodecyl sulfate at surfactant concentrations just below and above the minimal cmc. The DSC curves exhibit characteristic maxima at temperatures (critical micellization temperatures (cmt)) where the micellization or demicellization process occurs and a minimum at the same temperature where the cmc minimum is observed by isothermal titration calorimetry (ITC) measurements. The DSC curves were calculated using a mass-action model with fixed aggregation number and thermodynamic parameters for the demicellization process as obtained by simulations of the titration curves obtained from ITC measurements of the same surfactants. The results show that it is possible to obtain cmt or cmc values of surfactants directly from DSC experiments provided that the minimal cmc of the surfactant is not below 2 mM. The DSC curves of NG show a more complicated temperature-induced aggregation behavior than expected from the ITC measurements.
Introduction The self-assembly of surfactants in water into micelles is a widely studied phenomenon and many techniques have been used to explore this process.1-14 Among them isothermal titration calorimetry (ITC) has increasingly been employed,15-22 because of its capability for the direct determination of the cmc (in the range of 50 µM to 500 * To whom correspondence may be addressed. Tel: +49-34555-25850. Fax: +49-345-55-27157. E-mail:
[email protected]. (1) Clint, J. H. Surfactant Aggregation; J. Blackie: London, Published in USA by Chapman and Hall: New York, 1991. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980. (3) Moroi, A. Micelles: Theoretical and applied Aspects; Plenum Press: New York, 1992. (4) Moulik, S. P. Curr. Sci. 1996, 71, 368. (5) Nusselder, J. J. H.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1992, 148, 353. (6) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 3320. (7) Roda, A.; Hofman, A. F.; Mysels, K. J. J. Biol. Chem. 1983, 258, 6362. (8) Paredes, S.; Tribout, M.; Ferreira, J.; Leonis, J. Colloid Polym. Sci. 1976, 254, 637. (9) Shanks, P. C.; Franses, E. I. J. Phys. Chem. 1992, 96, 1794. (10) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986. (11) Shinoda, K.; Yamaguchi, T.; Hori, R. Bull. Chem. Soc. Jpn. 1961, 34, 237. (12) Kameyama, K.; Toshio, T. J. Colloid Interface Sci. 1990, 137, 1. (13) Miguel, M. G.; Eidelman, O.; Ollivon, M.; Walter, A. Biochemistry 1989, 28, 8921. (14) Blokzijl, W.; Engberts, J. B. F. N. Angew. Chem. 1993, 105, 1610. (15) Paula, S.; Su¨s, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (16) Garidel, P.; Hildebrand A.; Neubert, R.; Blume, A. Langmuir 2000, 16, 5267. (17) Johnson, I.; Olofsson, G.; Jonsson, B. J. Chem. Soc., Faraday Trans. 1 1987, 83, 3331. (18) Blandamer, M. J.; Cullis, P. M.; Engberts, J. B. F. N. Pure Appl. Chem. 1996, 68, 1577. (19) Majhi, P. R.; Moulik, S. P. Langmuir 1998, 14, 3986. (20) Blume, A.; Tuchtenhagen, J.; Paula, S. Prog. Colloid Polym. Sci. 1993, 93, 118.
mM) and the heat of demicellization (∆Hdemic) (or the micellization) in one experiment within a short time (approximately 2 h). The process is followed by diluting a micellar surfactant solution into water at a fixed temperature. The experimentally accessible temperature range is between 2 and 80 °C. From this calorimetric titration curve, the critical micelle concentration (cmc) and ∆Hdemic can be directly obtained from the extreme value of the first derivative of the titration curve and from the enthalpy difference of the two levels, respectively, as reported before. The other thermodynamic parameters ∆Gdemic and ∆Sdemic associated with the demicellization process can be calculated using the pseudophase separation or a mass-action model.15,16 The simulation of the titration curves using a mass action model yields the values of the thermodynamic parameters along with the aggregation number.15,16 From the temperature dependence of ∆Hdemic, the change in heat capacity (∆Cp(demic)) for the demicellization process is obtained. This quantity contains information on the change in hydration of apolar surfaces during the demicellization. The cmc is temperature dependent and shows a characteristic minimum between 20 and 50 °C because of the strong temperature dependence of the enthalpy of micellization, i.e., the transfer enthalpy of surfactant from water to a micelle. As a consequence, the concentration of surfactant in monomeric and micellar form changes with temperature. All these previous findings from ITC and the temperature dependence of the cmc and ∆Hdemic encouraged us to explore the micellization and demicellization process of surfactants using a high sensitivity differential scanning calorimeter. Differential scanning calorimetry (DSC) has already been used for the temperature-dependent micellization process (21) Keller, M.; Kerth, A.; Blume, A. Biochim. Biophys. Acta 1997, 1326, 178. (22) Majhi, P. R.; Mukhrjee, K.; Moulik, S. P.; Sen, S.; Sahu, N. P. Langmuir 1999, 15, 6624.
10.1021/la001660k CCC: $20.00 © 2001 American Chemical Society Published on Web 06/02/2001
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of block copolymers23-25 and gangliosides26 but has not been used for the micellization and demicellization of surfactants in solution, because this requires a sensitivity which is only recently available due to the development of the VP-DSC instrument by MicroCal.27 Because the transfer enthalpy of a surfactant from water to a micelle is positive at low temperature and negative at high temperature, DSC curves with two endothermic peaks should be observed when a micellar solution is heated under certain conditions, i.e., the total concentration is slightly higher than the cmc value at the minimum. A temperature scan should first lead to a micellization and then to a demicellization process at higher temperature. DSC has not been used before for the micellization process of a surfactant in such a way. The recent publication by Kresheck is the only one that has addressed this problem.28 However, the experimental DSC curves shown in that article covered only a temperature and concentration range where the micelles already existed, only their concentration changed with temperature. The actual micellization and demicellization processes were not observed. Another recent publication reported results from temperature-induced demicellization of chlorpromazine hydrochloride. However, this aggregation process seems to be significantly different from the micellar aggregation of surfactants with alkyl chains.29 To obtain a reliable data set for the interpretation of the DSC curves of surfactants, we have first performed ITC experiments with the nonionic surfactants octylglucoside (OG), nonylglucoside (NG), and decylmaltoside (DeM) and the anionic surfactant sodium dodecyl sulfate (SDS). From the simulation of the calorimetric titration curves using the mass-action model, we obtained all thermodynamic data and the aggregation numbers of the surfactants. We will show that based on this data set, the experimental DSC curves with their heat capacity maxima due to the micellization and demicellization process can be understood and calculated. The values for the critical micellization temperatures (cmt) agree in most cases with the cmc values obtained by ITC. Experimental Section Materials. Octylglucoside (OG), nonylglucoside (NG), decylmaltoside (DeM), and sodium dodecyl sulfate (SDS) were pure products purchased from Sigma, Bachem, or Aldrich, Germany. The products were used without further purification. Surfactant solutions of a definite concentration were freshly prepared by weighing a certain amount of surfactant and dissolving it in deionized water. Methods. ITC experiments were performed with a Micocal MCS isothermal titration calorimeter (Microcal Inc., Northampton, MA). The removable integrated injection-stirrer syringe (250 µL) was filled with a concentrated solution of a surfactant which was added in multiple steps (5-10 µL) to the pure water in the calorimeter cell (1.335 mL capacity) under constant stirring (∼400 rpm) conditions. The thermograms of the heats of dilution of the surfactant were recorded and analyzed using the supplied ORIGIN 5.0 software. DSC measurement were performed using a Microcal VP-DSC differential scanning calorimeter (Microcal). A heating rate of 1 (23) Paterson, I.; Armstrong, J.; Chowdhry, B.; Leharne, S. Langmuir 1997, 13, 2219. (24) Alexandridis, P.; Holzwarth, J. F. Langmuir 1997, 13, 6074. (25) Armstrong, J. K.; Chowdhry, B. Z.; Snowden, M. J.; Leharne, S. A. Langmuir 1998, 14, 2004. (26) Cantu, L.; Corti, M.; Favero, E. D.; Muller, E. Raudino, A.; Sonnino S. Langmuir 1999, 15, 4975. (27) Plotnikov, V. V.; Brandts, J. M.; Lin, L. N.; Brandts, J. F. Anal. Biochem. 1997, 250, 237. (28) Kresheck, G. C. Langmuir 2000, 16, 3067. (29) Saito, Y. D.; Tehrani, S.; Okamoto, M. M.; Chang, H. H.; Dea, P. Langmuir 2000, 16, 6391.
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Figure 1. Titration of a total volume of 205 µL of an NG solution with a concentration of 122 mM into 1.335 mL of water in 40 steps with different titration volumes (T ) 30 °C): (A) calorimetric traces (heat flow against time); (B) reaction enthalpy versus concentration of NG in the cell; (C) first derivative of curve B calculated from the interpolated values. °C/min was used, and the measurements were performed in the temperature interval from 2 to 90 °C. For a check of the reproducibility, three consecutive scans of each sample were recorded. The experimental data were again evaluated using the ORIGIN 5.0 software. For the simulation of ITC titration curves and the calculation of the experimental DSC curves, the software SCIENTIST version 2.02 (Micromath Inc., Salt Lake City, UT) was used. The methods underlying the simulation and fitting have been published16 and are described below in abbreviated form. In essence, the mathematical equations describing the concentration of monomers and micelles were transferred into the programming language of SCIENTIST, and the changes in these concentrations were then numerically calculated. SCIENTIST enables a nonlinear least-squares fitting of experimental data using a modified Powell algorithm until user-specified convergence is reached.
Results and Discussion Isothermal Titration Calorimetry Studies. As an example for the ITC measurements for the determination of the cmc and demicellization enthalpies, we present a typical experimental titration curve obtained from a dilution of a micellar NG solution into water at 10 °C together with the corresponding enthalpies of dilutions per mole of injectant and the differentiated curve to determine the cmc (Figure 1). The cmc corresponds to the concentration where the enthalpy of dilution vs total surfactant concentration curve shows an inflection (Figure 1B) or, more accurately, where the first derivative of this curve in Figure 1B displays an extremum (Figure 1C). Figure 2 shows demicellization curves at different temperatures for the demicellization process of NG in water. As observed before with octylglucoside,15 the demicellization enthalpy is positive at higher temperature, decreases upon lowering the temperature, and, passing through zero, becomes negative at low temperature. From
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Figure 2. Reaction enthalpy Q versus total NG concentration in the cell for the titration of NG (122 mM, 5 µL steps) into 1.335 mL of water at different temperatures.
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Figure 4. Calculated titration curves for the demicellization curves of OG at 13 °C with different values of the aggregation number n, but constant enthalpy ∆Hodemic and Gibbs free energy of demicellization ∆Godemic.
stepwise change of the observed heat of reaction exactly at the cmc. In a second approach, we have simulated the titration curves according to a mass-action model with the assumption of a single micellar aggregation number using our earlier simulation procedures.15,16 In this model, the formation of a micelle (Mn) with n monomers of S is described by the equilibrium
nS- + βnB+ h Mn-(1-β)n
(1)
with β being the degree of counterion binding (β ) 0 and B+ ) 0 in the case of nonionic surfactants) The equilibrium constant K is then defined as
K ) [Mn-(1-β)n]/([S-]n[B+]βn)
(2)
From the values of the equilibrium constant K obtained from the simulation of the ITC curves using the mass action model, the ∆Gdemic values for the transfer of one surfactant molecule from the micelle to water are calculated using the relation
K ) exp(n∆Godemic/RT)
(3)
The concentration of surfactant in monomeric form [S] and in micellar form n[Mn] ([Mn] is the concentration of the micelles) is related to the total surfactant concentration Ctotal by Figure 3. Values for the cmc and cmt, respectively for DeM, OG, NG, and SDS, as determined by ITC (cmc, full circles) and DSC (cmt, open squares).
the derivative plot we obtain the cmc and its variation with temperature. Similar titration experiments were also performed with the other nonionic surfactant DeM and the anionic surfactant SDS. The results of the titration experiments with OG were taken from our previous publication.15,21 The cmc values obtained from ITC and DSC experiments (see below) at different temperatures are presented in Figure 3. The cmc of the surfactants shows a characteristic temperature dependence with a minimum between 35 and 45 °C for the nonionic surfactants; for the anionic surfactant SDS, this minimum is shifted to 25 °C. The titration curves obtained from ITC can be simulated in two ways. The first one uses the pseudophase separation model where the micelles are regarded as a separate phase. This is the simple standard model for evaluation of the thermodynamic parameters ∆G, ∆H, and T∆S for the demicellization process. The simulation would give a
Ctotal ) [S-] + n[Mn-(1-β)n] ) [B+] + βn[Mn-(1-β)n] (4) The observed heats in the calorimetric experiments are always related to the change in concentration of micelles multiplied with the heat of demicellization. This model was successfully applied before to determine average aggregation numbers for sodium cholate and sodium deoxycholate aggregates.16 These numbers are relatively small compared to aggregation numbers usually found for surfactants with alkyl chains. The question therefore arises, whether this procedure is useful to obtain reliable aggregation numbers also for these surfactants. Figure 4 shows calculated curves for the demicellization of OG at 13 °C using the massaction model with a fixed value for ∆Godemic, the value for the transfer of one monomer from the micelle to water, and varying the aggregation number n. The simulations show that with increasing n the slopes of the curves become steeper but that at large values of n, the sensitivity to an increase in n decreases. If values of n are to be determined
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Figure 5. Experimental and calculated titration curves for the demicellization of NG in water at low and high temperature. The simulation was performed using the mass action model as described in the text with an aggregation number n ) 58 and thermodynamic parameters as shown in Table 1.
from experimental curves, it is clear that the precision in the determination of n decreases rapidly with larger aggregation numbers. However, not only is the slope of the curves sensitive to n but also the midpoint and the curvature at higher total concentration. Whereas the midpoint can be arbitrarily shifted by changing ∆Godemic, the curvature contains additional information of n. Overall, the calculations show that aggregation numbers n below 30 can be determined with a precision of approximately (10%, depending on the quality of the experimental data, whereas for systems with higher aggregation numbers, the precision rapidly decreases. Representative experimental titration curves along with the simulated curve using the mass-action model for the demicellization of NG in water at 12 and 70 °C are presented in Figure 5. The simulation of the NG demicellization curves using a nonlinear least-squares procedure gave an aggregation number n ) 58. Figure 6 shows the temperature variation of the thermodynamic parameters ∆Hodemic, ∆Godemic, and T∆Sodemic obtained from the simulation of the titration curves using a mass-action model for the demicellization of NG in water. These curves show the usual trend as observed in the temperaturedependent demicellization phenomena. The experimental ∆Godemic and ∆Hodemic values obtained by ITC (see Table 1) are temperature dependent and were fitted by polynomials
∆Godemic ) a + bT + cT2 + dT3 + . . .
(5)
∆Hodemic ) a′ + b′T + c′T2 + d′T3 + . . .
(6)
where a, a′, b, b′, c, and c′ are the polynomial coefficients. The ∆Gdemic and ∆Hdemic curves were fitted with polynomials which were used later for the simulation of DSC curves (see below). The thermodynamic parameters ∆Hodemic, ∆Godemic, and T∆Sodemic obtained from the simulation of the titration curves for NG and all other studied surfactants are presented in Table 1. From Table 1 it is seen that the ∆Godemic values obtained from the pseudophase separation model and from the mass-action model agree surprisingly well. For the anionic surfactant SDS we also determined the thermodynamic parameters without including counterion binding (not shown). The ∆Godemic values are then
Figure 6. Thermodynamic parameters for the demicellization of NG in water using the mass-action model as a function of temperature.
smaller and agree with those determined before.15 These were later used for the simulation of the DSC curves where only the temperature dependence of ∆Godemic and ∆Hodemic is important (see below). From the simulation of the ITC curves, values for the aggregation number n can be obtained.16 However, when the demicellization curves become very steep, i.e., the aggregation numbers are large, this is not very precise as discussed above. We obtained aggregation numbers of 45 for OG, 58 for NG, 35-45 for DeM (increasing with temperature), and 50 for SDS (with β ) 0.82). These numbers have errors of (10% and are comparable to other reported values using different methods.30-33 Particularly for SDS, a wealth of data exists for the aggregation number n as a function of concentration and temperature.34-37 In general, the aggregation number for SDS and other ionic surfactants decreases with temperature and increases with concentration. For instance, for SDS n decreases from 75 at 20 °C to 49 at 51 °C for a 0.1 M SDS solution.34 The concentration dependence at 25 °C was measured by Bales and Almgren.36 The aggregation number increased from 57 at 20 mM to 89 at 200 mM SDS. For nonionic surfactants, published values are much scarcer. For Triton X-100 Malliaris et al.34 found an increase in n with temperature. However, for a 60 mM OG solution with n ) 92 hardly any temperature dependence of n was found,38 and also for alkyl 2-amino-2-deoxy-β-D-glucopyranosides the temper(30) Roxby, R. W.; Mill, B. P. J. Phys. Chem. 1990, 94, 456. (31) Kratohvil, J. J. Colloid Interface Sci. 1980, 75, 271. (32) Phillips, N. M. Trans. Faraday Soc. 1955, 51, 561. (33) Turo, N. J.; Yekta, A. J. Am. Chem. Soc. 1978, 100, 5951. (34) Malliaris, A.; Moigne, J. L.; Sturm, J.; Zana, R. J. Phys. Chem. 1985, 89, 2709. (35) Gehlen, M. H.; De Schryver, F. C. J. Phys. Chem. 1993, 97, 11242. (36) Bales, B. L.; Almgren, N. J. J. Phys. Chem. 1995, 99, 15153. (37) Quina, F. H.; Nassar, P. M.; Bonilha, J. B. S.; Bales, B. L. J. Phys. Chem. 1995, 99, 17028.
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Table 1. Thermodynamic Parameters of Demicellization of OG, NG, DeM, and SDS in Water as a Function of Temperature Calculated from Microcalorimetric Titration Measurements Using the Pseudophase Separation and the Mass Action Model, Respectively pseudophase separation model compound OG
NG
DeM
SDSa
a
T (K)
cmc (mM)
∆H°demic (kJ/mol)
286 300 313 323 343 285 293 303 313 323 333 343 283 293 303 313 323 333 283 293 303 313 323 333
27.90 22.60 20.80 22.60 23.70 8.85 8.00 7.70 7.44 7.59 8.00 8.85 2.54 2.29 2.12 2.11 2.28 2.51 9.02 8.73 9.06 9.26 10.10 10.83
-13.99 -7.01 -1.92 1.05 8.23 -12.00 -8.19 -2.98 0.025 3.99 7.58 9.83 -10.55 -6.24 -1.99 2.31 6.45 9.97 -5.88 -1.55 3.42 7.96 11.32 14.77
mass-action model
∆G°demic (kJ/mol)
T∆S°demic (kJ/mol)
∆H°demic (kJ/mol)
∆G°demic (kJ/mol)
T∆S°demic (kJ/mol)
18.07 19.30 20.49 20.95 22.13 20.72 21.55 22.38 23.21 23.89 24.47 24.93 23.51 24.59 25.62 26.48 27.12 27.70 37.40 38.83 39.98 41.20 42.09 43.04
-32.06 -26.31 -22.41 -19.90 -13.90 -32.72 -29.74 -25.36 -23.18 -19.90 -16.90 -15.11 -34.06 -30.83 -27.61 -24.17 -20.67 -17.73 -43.82 -40.38 -36.56 -33.24 -30.77 -28.27
-16.90 -9.00 -2.25 1.35 8.58 -13.53 -9.00 -3.50 0.07 4.30 8.25 11.08 -12.68 -7.71 -2.27 2.77 7.73 11.79 -5.74 -1.29 3.53 7.92 11.78 15.46
17.14 18.35 19.42 20.05 20.95 20.03 20.78 21.60 22.37 23.05 23.62 24.02 22.32 23.35 24.35 25.31 25.96 26.61 36.18 37.64 38.64 39.80 40.76 41.63
-34.04 -27.35 -21.67 -18.70 -12.37 -33.56 -29.78 -25.10 -22.30 -18.75 -15.37 -12.94 -35.00 -31.06 -26.62 -22.54 -18.23 -14.82 -41.92 -38.93 -35.11 -31.88 -28.98 -26.17
The SDS values were obtained from calculations considering the degree of counterion binding β (β ) 0.823).
ature dependence was negligible.39 Our data for OG and NG also indicate no clear-cut temperature dependence of n, but for DeM an increase in n with temperature was observed as reported for Triton X-100. The aggregation numbers determined by ITC are generally lower than those reported because they are determined at a particular concentration, namely, the cmc, whereas with other methods such as light scattering, small angle neutron scattering, or fluorescence quenching methods the micellar aggregation number is usually determined at concentrations well above the cmc. Therefore, it is not surprising that the aggregation numbers n determined by ITC are on the lower limit, because the aggregation number increases with concentration. Differential Scanning Calorimetry Studies. Because of the temperature dependence of the cmc, the micellization and demicellization process can also be followed by high-sensitivity differential scanning calorimetry. We have performed DSC experiments of OG, NG, DeM, and SDS of different concentrations and could indeed observe heat capacity maxima due to micellization and demicellization processes. Our experimental protocol is graphically shown in Figure 7. As can be seen from the scheme, a temperature-induced micellization and demicellization process should be observed at lower and higher temperature, respectively. The critical micellization temperatures (cmt) depend on the total surfactant concentration; i.e., with an increase in surfactant concentration the lower cmt shifts to lower temperature and the upper cmt to higher temperature and the temperature difference between these two cmt values therefore increases with higher surfactant concentration. From the ITC experiments we know that at low temperature, below the temperature of the cmc minimum, the micellization process is endothermic and that the demicellization process at temperatures above that of the cmc minimum (38) Frindi, M.; Michels, B.; Zana, R. J. Phys. Chem. 1992, 96, 8137. (39) Boullanger, P.; Chevalier, Y. Langmuir 1996, 12, 1771.
Figure 7. Scheme of the variation of the cmc of OG with temperature as observed by ITC. The horizontal lines indicate the way in which the DSC experiments proceed with a fixed concentration of OG and with increasing temperature. When the cmc curve is crossed at low temperature, micellization occurs, and at high temperature, demicellization takes place. In ITC experiments, the concentration is changed at a fixed temperature. This would correspond to vertical lines crossing the cmc curve.
is also endothermic. According to the scheme in Figure 7, we would therefore expect two endothermic peaks, the lower representing the endothermic micellization process, and the one at higher temperature the demicellization process. To illustrate the changes in concentration of the surfactants in monomeric and micellar form with temperature, we calculated curves for different total concentrations of the surfactant OG as a function of temperature using the mass-action model and the pseudophase separation model as described below (see Figure 8). As can be seen from the calculated concentration curves, the mass-
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for SDS (see above). A constant value for n was therefore used for the calculations. In the experimental DSC curves the heat capacity (Cp) of the sample is plotted as a function of temperature. The total heat capacity is the sum of the heat capacity of water in the surfactant solution, the heat capacity of the surfactant monomers, Cp(monomer), the heat capacity of the surfactant in micellar form, Cp(micellar), and the excess heat capacity, Cp(excess), arising from the transfer of monomers to a micelle or vice versa. The total heat capacity Cp(s) arising only from the surfactant is calculated from the following sum containing the molar heat capacities Cp(monomer) and Cp(micellar) ) Cp(monomer) - ∆Cp(demic)
Cp(s) ) {Cp(excess) + [S]Cp(monomer) + n[Mn-(1-β)n](Cp(monomer) - ∆Cp(demic))}vcell (7) Figure 8. Calculated curves using the mass-action model and the pseudophase separation model, respectively, for the variation of monomer and micellar concentration of OG.
action model leads to a gradual onset of micellization, whereas the pseudophase separation model shows the sudden appearance of micelles at a certain temperature. The concentration of surfactant in micellar form increases with temperature and shows a maximum at the temperature where the cmc has a minimum. In addition the onset of micellization and demicellization changes with total surfactant concentration as expected from the scheme in Figure 7. Calculation of Experimental DSC Curves. The shape of the heat capacity curves observed in DSC experiments can be calculated using either the pseudophase separation model or the mass action model with the ∆Gdemic and ∆Hdemic values obtained from the simulation of the ITC titration curves with a fixed aggregation number and the change in heat capacity for the surfactant transfer from water to the micelle, which was taken from the temperature dependence of the transfer enthalpy ∆Hdemic. The principle of the calculation of the heat capacity curves was already outlined by Kresheck using the pseudophase separation model.28 However, Kresheck used experimental data of surfactant solutions showing no peaks because of surfactant concentrations which were 5-10 times higher than the cmc. In this case, the peaks due to temperature-induced micellization and demicellization are shifted outside the accessible temperature range of the DSC. Kresheck therefore simulated the curvature of the DSC curves using the simpler pseudophase separation model as a basis. The pseudophase separation model cannot describe the shape of the endothermic peaks as observed in the experiment. The pseudophase separation model would give maxima at the cmt with a sudden steplike jump of the curves and not peaks with a certain half-width. This can be seen from Figure 8, because the heat capacity curves are related to the differentiated curves of Figure 8 (see calculations below). This is similar to the stepwise jump in the ITC curves calculated for the pseudophase separation model. We therefore used the mass-action model for the calculation and are going in the opposite way, namely, calculating the experimental DSC curves from parameters determined by ITC without fitting the DSC curves to obtain thermodynamic parameters. The difficulty in fitting the DSC curves lies in the fact that the mass action model contains an additional parameter the aggregation number n, which is not easy to extract from the fitting of the DSC curves and which can be temperature dependent as shown
The excess molar heat capacity Cp(excess) arising from the transfer of monomers to a micelle or vice versa, is the product of the molar transfer enthalpy ∆Hodemic and the change in concentration with temperature of surfactant in monomeric form, ∆[S], or the change in concentration of surfactant in micellar form -∆(n[Mn-(1-β)n]), i.e.
Cp(excess) ) (∆[S]/∆T) ∆Hodemic
(8)
The concentrations [S] and n[Mn-(1-β)n] in eq 7 and their changes with temperature are calculated using eqs 2-4. The experimental ∆Hodemic values obtained from the ITC experiments are temperature dependent, and the temperature dependence was described using a polynomial (see above) and inserted into eq 8. The heat capacity of the surfactant in micellar form Cp(micellar) ) Cp(monomer) ∆Cp(demic), with ∆Cp(demic) calculated from the differentiation of the polynomial for the experimental ∆Hodemic values, i.e.
∆Cp(demic) ) b′ + 2c′T + 3d′T2 + . . .
(9)
Cp(monomer) is calculated from the experimental Cp curve obtained by DSC with the lowest surfactant concentration using the following relation
(
Cp(monomer) ) cp,W
)
VS ∆ M VW mS S
(10)
with cp,W the specific heat of water, VW and VS the specific volumes of water and surfactant, respectively, mS the mass of surfactant in the sample cell, MS the molar weight of the surfactant, and ∆ being the displacement of the experimental curve relative to a water/water baseline40,41 (see Figures 9-12). To calculate the Cp(monomer) values, the specific volume of water and of the surfactant have to be known or estimated. The specific volume and heat capacity of water can be taken from standard tables; for the specific volume of the surfactant OG, a value of 0.8 cm3 g-1 was estimated. It turns out that the specific volume of the surfactant has not to be precisely known. Any error in this quantity cancels in the calculations, because only the shifts in the DSC curves of solutions with concentrations above the cmc minimum relative to that below the cmc minimum are important. To compare the heat capacity Cp(s) with the experimental DSC plots, the cell volume, the total concentration of (40) Privalov, P.; Khechinashvili, N. N. J. Mol. Biol. 1974, 86, 665. (41) Blume, A. Biochemistry 1983, 22, 5436.
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Figure 9. (left) Experimental DSC curves for OG solutions with different concentrations. The water-water baseline is also included for comparison. The OG solution with the lowest concentration contains only monomers. (right) Calculated DSC curves using the mass-action model with parameters obtained from the ITC experiments (see text for further explanations). Arrows indicate the cmt.
Figure 11. (left) Experimental DSC curves for DeM solutions with different concentrations. The water-water baseline is also included for comparison. The DeM solution with the lowest concentration contains only monomers. (right) Calculated DSC curves using the mass-action model with parameters obtained from the ITC experiments (see text for further explanations). Arrows indicate the cmt.
Figure 10. (left) Experimental DSC curves for NG solutions with different concentrations. The water-water baseline is also included for comparison. The NG solution with the lowest concentration contains only monomers. (right) Calculated DSC curves using the mass-action model with parameters obtained from the ITC experiments (see text for further explanations). Arrows indicate the cmt.
Figure 12. (left) Experimental DSC curves for SDS solutions in water with different concentrations. The water-water baseline is also included for comparison. The SDS solution with the lowest concentration contains only monomers. (right) Calculated DSC curves using the mass-action model with parameters obtained from the ITC experiments (see text for further explanations). Arrows indicate the cmt.
surfactant, and the temperature variation of Cp,W of water in the cell have to be considered. In the calculation of the DSC curves for SDS we have used the mass-action model without counterion condensation for simplicity. This gives no error, because we are interested only in a comparison of the shape of the DSC curves. The ITC curves for SDS can be just as well fitted without considering counterion binding, but different absolute values for K and for ∆Godemic are then obtained. However, for the calculation of the DSC curves only the temperature dependence of these values is of interest, and this is not affected by the model. The experimental and theoretical DSC curves of surfactant solutions with concentration just below and above the cmc minima are presented in Figures 9-12. For the nonionic surfactants, two endothermic peaks at low and high temperature are observed as expected. The position of the first peak is shifted toward the lower temperature region with an increase in total surfactant concentration in the cell as expected from the scheme in Figure 7. The reverse case is true for the second peak. From Figure 3 and Figures 9-12 we can also see that the minimum of the cmc and the minimum of the DSC curves for a
particular surfactant occur at the same temperatures, i.e., at 47, 40, 37, and 23 °C for OG, NG, DeM, and SDS, respectively. Two cmt values are obtained from the maxima of the DSC curves for the three nonionic surfactants. These cmt values are plotted in Figure 3 along with the cmc values obtained from experimental ITC curves. The cmt and cmc values obtained from DSC and ITC measurements agree well except for NG, where at lower concentrations the DSC peaks show a shoulder indicating that the temperature-induced micellization and demicellization process seems to be more complicated. The temperatures taken from the maxima do no fit on the cmc curve (see Figure 3), because they stay almost constant with concentration. The DSC curves for NG show that the micellization process seems to proceed in two steps at concentrations close to the minimal cmc (see Figure 10). In the case of SDS, where the cmc minimum is at 23 °C, only the second cmt peak due the demicellization is observable, because the DSC instrument is limited in its temperature range at low temperatures (see Figure 12). The shift of the DSC curves and their form are influenced
Temperature-Induced Micellization
by changes in apparent molar heat capacity of the surfactants and the processes connected with the micellization and demicellization. As expected, no peak was observed when the total concentration of the surfactant was below the value of the cmc minimum. This is because of the presence of monomer only in the entire temperature scan region. With the exception of NG, the calculated DSC curves presented in Figures 9-12 show good agreement with the experimental curves. This shows that the use of ITC data obtained from simulation of the titration curves at different constant temperature using the mass-action model are in general adequate to describe also the temperaturedependent behavior of surfactant solutions and the temperature-induced micellization and demicellization as observed by DSC. However, due to differences in experimental protocols in ITC and DSC experiments, the parameters used for the calculations must necessarily be different. In ITC experiments, the aggregation number is determined over a concentration range in the vicinity of the cmc. The DSC curves, however, are recorded at constant total concentration. At the cmt the aggregation number n should be similar to the one determined by ITC at this particular temperature. In the DSC experiment, however, the concentration of surfactant in micellar form changes with temperature, because the difference between the cmc and the total concentration changes, and therefore the aggregation number n besides its normal temperature dependence can have an additional dependence due to the change in micellar concentration. These effects complicate the fitting of the DSC curves with the aggregation number n as a variable parameter. In our calculations we therefore used a temperature-independent aggregation number n, which in some cases had to be varied with total concentration of the surfactant. Only then could reasonable agreement between experimental and calculated curves be obtained. The aggregation numbers used for the calculation of the DSC curves were in general smaller than those obtained from the ITC curves. For NG, for instance, they varied between 25 at the lowest concentration just above the cmc to 37 for the 10 mM solution. Likewise, for SDS they varied between 28 and 65 for the SDS solution with the highest concentration. In principle, all thermodynamic parameters for a temperature-induced micellization and demicellization of a surfactant could be extracted from a fitting procedure of the experimental DSC curves using the mass-action model. However, because of the large number of adjustable parameters, this would not be sensible. Therefore, a combined approach where the demicellization parameters as a function of temperature are determined by ITC is more appropriate.
Langmuir, Vol. 17, No. 13, 2001 3851
Summary and Conclusions DSC curves of nonionic surfactant solutions with concentrations slightly above the minimal cmc show two endothermic peaks at low and high temperature. The lowtemperature peak corresponds to a micellization process, which is endothermic at temperatures below the cmc minimum. The high-temperature peak is caused by a demicellization, which is endothermic at high temperature. The DSC curves yield two cmt values from one curve. The temperature difference between these values decreases with decreasing surfactant concentration. For surfactants where the cmc minimum is at lower temperature, such as the anionic surfactant SDS, only the hightemperature peak is seen. In the case of more complicated temperature-induced aggregation processes, the DSC curves can give additional hints on the nature of the process, as is the case for NG, where the DSC curves show that the micellization process seems to proceed in two steps at concentrations close to the minimal cmc. The DSC curves can be calculated using a mass-action model with fixed aggregation number n and Gibbs free energies and transfer enthalpies of micellization obtained from the simulation of ITC curves using the same massaction model. The change in heat capacities for the transfer was taken from the temperature dependence of the transfer enthalpy. The heat capacity of the monomeric surfactant is determined from the DSC curves once its specific volume is known. In principle, the DSC curves contain all the relevant information on the temperature dependence of the cmc, the heat of transfer, the aggregation number n, and the specific volumes of the surfactant in monomeric and micellar form. However, a meaningful simulation or fitting can only be performed on the basis of known parameters obtained from ITC experiments. The only quantities which can be obtained directly and without model assumptions are cmt values, which in the case of simple micellization processes are identical to the cmc values obtained by other methods, and the temperature where the cmc has its minimal value. The limitation in determining cmt or cmc values of surfactants by DSC is the sensitivity of DSC instruments. In the case of the VP-DSC by MicroCal used in this study, the limiting lowest cmc value of surfactants where DSC curves of significance can be obtained is around 1-2 mM. Acknowledgment. This work was supported by the Max-Planck-Gesellschaft and the Fonds der Chemischen Industrie. LA001660K
