Langmuir 1994,10, 2202-2205
2202
Thermodynamics of Micelle Formation for Zwitterionic (N-(12,12,12~Trifluorododecy1) -Nfl-dimethylammonio)alkanoate Surfactants Norbert Muller* H. C. Brown Laboratory of Chemistry, Purdue University, West Lafayette, Indiana 47907 Received January 18,1994. I n Final Form: April 25, 1994@ Four members of the series of fluorine-labeled zwitterionic surfactants CF~(CH~)~~N(CH~)Z(CHZ)~COZ, with n = 1 , 4 , 5, and 7, were prepared and their critical micelle concentrations (cmc) determined over a 60” temperature range from the concentration dependences of the chemical shifts of their 19Fnuclear magnetic resonance signals. For each compound the cmc exhibits a minimum at a temperature between 37 and 49 “C. Analysis of the temperature dependence of the cmc values with an equation analogous to one recently proposed for ionic surfactants providedvaluesfor changesin thermodynamicvariables associated with micellization, i.e. AG’ , AH:, AS:, and AC,. The results confirm earlier findings, showing that replacing a terminal methyflgroup by trifluoromethyl does not dramatically change micelle stability. The favorable Gibbs energies of micellization are considerably smaller for zwittfrionic surfactants than for similar ionic ones, mainly because of much larger positive values of AHm. The dependence of the thermodynamic parameters on n suggests that hydrophobic hydration effects associated with methylene groups in the intercharge arm are appreciably smaller than those for groups in the alkyl “tail”.
chains from an aqueous to a primarily nonpolar medium, Introduction is analogous to the transfer of an alkane from water to it The thermodynamics of micellization of ionic surfactants a hydrocarbon solvent. Therefore, large negative values has been extensively studied, often by measuring their of AC, are to be expected: and they are invariably found critical micelle concentrations (cmc) over a range of for ionic surfactants.2 temperatures, perhaps 40” to 70” wide.l In spite of the fact that micellar aggregation numbers and degrees of A further interesting feature of zwitterionic surfactants ionization, and heat capacities of micellization, are is that it is possible to change the length or flexibility of expected to be somewhat temperature dependent, treating the “intercharge arm”, e.g. the value of n for members of the process of micellization as an ordinary chemical The dependence the series CH~(CHZXN(CH~)Z(CH~)~COZ. equilibrium and applying the Gibbs-Helmholtz equation on n of the Gibbs energy of micellization, AG: ,has been yields Gibbs energies and enthalpies of micellization that studied for several such but the accompanying agree rather well with calorimetric Recently, values of A H : and A S : are still not known. it was shown2 that when the cmc passes through a Previous work in this laboratory showed that replacing minimum (cmc*) at a temperature P ,values of cmc at other temperatures obey a rather simple equation in which the terminal methyl group of the alkyl chain of an ionic the only additional parameters are the heat capacity of or nonionic surfactant by a trifluoromethyl group has only micellization, AC,, and the fractional degree of counterion a modest effect on the thermodynamic variables of binding, a. Excellentfits were obtainedfor20 setsofdata,in micelli~ation.~,~ The cmc of such a fluorine-labeled sureach case taking AC, and a to be independent of the factant can be determined by 19F nuclear magnetic temperature. resonance (NMR) spectroscopy, with an accuracy similar The possibility of applying this treatment to zwitterionic to that obtainable from conductimetry, at various temsurfactants is attractive because the need to evaluate the peratures. Since a supply of 12,12,12-trifluorododecanoic parameter a, and to consider how it may be affected by acid was available, it was decided to prepare several temperature changes, is eliminated. Not many measurecompounds of the series CF~(CH~)~~N(CH~)~(CHZ)~C ments of cmc at other than ambient temperature have determine their cmc’s in the range 10 5 T 5 70 “C and been reported for zwitterionics, probably because conevaluate the thermodynamic variables of micellization ductimetry, a very reliable method for obtaining such data, using the procedure of ref 2. Results are presented here is not applicable. The few available results are somewhat anomalous. For some N-alkyl betaines, CH~CHZ),N(CI~~Z-for materials with n = 1, 4, 5, and 7. CHzC02, plots of cmc against T show3 the expected minimum when x = 9 or 10, indicative of a large, negaExperimental Procedures and Results tive AC,, but for x = 11 it would seem that the enthalpy Materials. 12,12,12-Trifluorododecyldimethylamine, needed AH: is temperature independent, which requires AC, = 0. Again, for C-alkyl betaines, CH~(CHZXCH[N(CH~)~I-for the synthesis of the desired surfactants, was prepared as follows: 12,12,12-!l’rifluorododecanoic acidlo was treated with COz, with x = 7 , 9 , or 11, it appears that AC, = 0 in each thionyl chloride, and the resulting crude acid chloride was added case.4 Since micellization involvestransfer ofhydrocarbon
* Present
address: 744 Blue Spruce St., Woodland Park, CO
80866. @
Abstract published in Advance ACS Abstracts, June 1, 1994.
(1)Kresheck, G.C. In Water: A Comprehensive Treatise;Franks, F., Ed.; Plenum Press: New York, 1975;Vol. 4,p 95. (2)Muller, N. Langmuir 1993,9, 96. (3) Swarbrick, J.;Daruwala, J. J. Phys. Chem. 1969,73,2627. (4)Tori, K.;Nakagawa, T. Kolloid-2 2. Polym. 1963,189, 50.
( 5 ) Muller, N. ACC. Chem. Res. 1990,23,23.
(6)Chevalier, Y.; Germanaud, L.; Le Perchec, P. Colloid Polym. Sci. 1988,266,441. (7)Chevalier, Y.;Storet, Y.; Pourchet, S.; Le Perchec, P. Langmuir 1991,7,848. (8)Muller, N.; Birkhahn, R. H. J. Phys. Chem. 1968, 72, 583. (9)Muller, N.; Platko, F. E. J.Phys. Chem. 1971,75,547. (10)Muller, N. J. Og.Chem. 1984,49, 2826.
0743-7463/94/2410-22Q2$04.50/0 0 1994 American Chemical Society
Langmuir, Vol. 10, No. 7,1994 2203
Micellization Thermodynamics
Table 1. Melting Points and Analytical Data for Trifluorododecyl Betaines, CFS(CHp)llN(C~)e(CHz)nCO~HzO compound %C %H n X mp, "C calcd found calcd found 1 0 137.5-138.5 59.05 59.35 9.29 9.67 4 0.5 180.5-181.8 60.61 60.30 9.91 10.27 5 0.5 176.5-178.5 61.48 10.07 61.51 10.15 7 1.2 83-170 61.24 61.28 10.38 10.86 Table 2. Observed and Calculated Values of cmc (mollkg HpO) for CF~(CHZ)~~N(CH~)~(CH~)~CO~ Surfactants at Various Temperatures n=l n=4 n=5 n=7 cmc x io3 cmc x io3 cmc x 103 cmc x 103 T (K) obsd calcd T(K) obsd calcd T(K) obsd calcd T(K) obsd calcd 283.2 284.5 6.75 6.70 283.3 15.54 15.37 288.1 18.6 18.3 6.56 6.56 12.30 292.1 289.1 6.27 6.22 292.8 14.6 14.7 12.17 297.7 5.31 5.37 296.4 11.17 294.0 5.85 5.84 14.5 14.5 11.37 305.0 292.8 4.77 4.86 302.4 297.6 5.69 5.64 300.2 10.48 12.2 12.4 10.71 314.5 4.56 4.54 9.57 308.7 300.6 5.54 5.51 11.6 11.6 9.67 324.0 4.50 4.51 309.7 9.22 314.5 9.29 333.6 309.1 5.21 5.34 11.2 11.2 4.82 4.74 319.2 324.0 314.9 5.39 5.36 324.0 9.46 9.30 343.2 11.2 11.0 5.20 5.24 333.6 324.4 5.55 5.60 333.6 9.75 9.69 11.6 11.5 343.2" 10.06 343.2 333.6 6.16 6.10 12.2 12.4 10.60 343.2 10.45 10.60 343.2 6.83 6.94 1.4% rms dev 1.2% 1.2% 1.1% a This unaccountability deviant da 2 point was not used in selecting the parameters report d in Table 3 or in dculating the ~IK I deviation.
to excess dimethylamine dissolved in benzene11 or, preferably, in water.12 N,N-Dimethyl-12,12,12-trifluorododecanamide was obtained after recrystallization from hexane in yields of about 80%. The colorless needles, melting at 59.5-62 "C,were satisfactory as starting material for the next step. The amide was reducedll in ether with lithium aluminum hydride, molar ratio 1:1,to produce the (Muorododecy1)dimethylamine in yields better than 90% as a colorless oil, bp 82-83 "C/0.5Torr. Anal. Calcd for C14H28F3N C, 62.89;H, 10.55. Found: C, 63.05;H, 10.88. To prepare theN-(12,12,12-trifluorododecyl)betaines, 0.05mol of the above amine and 0.05 mol of an ethyl bromoalkanoate, BI(CH~)~CO~C~HS, were dissolved in 25 mL of methanol and refluxed7J3for periods ranging from 15 h for n = 2 to about a week for n = 7. The reaction wasjudged to be essentially complete if pumping off the methanol left a very viscous residue with no odor of the bromo ester. This residue, impure CF3(CH2)11N(CH&(CHz),,CO2C2&Br, was dissolved in water and the solution washed with ether or petroleum ether. It was then passed through an ion exchange column (Amberlite IRA-400)to replace the bromide with hydroxide and then slowly evaporated to dryness. During the evaporation, hydrolysis occurs and the resulting ethanol also evaporates,7J3 leaving the crude alkyl betaine CF3(CH2)11N(CH3)2(CH2)"CO2.On recrystallization from acetonehexane and drying in vacuum at room temperature, the product with n = 1 gave anhydrous crystals. Similar treatment of the other compounds gave white solids, which were shown, by elemental analysis and by examination of their lH NMR spectra (in acetone& containing a little deuterium oxide) to contain no detectable impurities other than water. The products with n = 4 or 5 were hemihydrates, while the one with n = 7 contained 1.2mol of water per mole of product. Their melting points and analytical data are given in Table 1. Since all I9Fshifts were to be determined for aqueous solutions, it was decided to allow for the residual water when calculating solution concentrations rather than to attempt to remove it. Stock solutions were prepared by weighing out appropriate amounts of solute and water from the laboratory deionized water supply. More dilute solutions were then also prepared gravimetrically. NMR Measurements. 19Fchemical shifts were determined with a Varian XL-200 variable-temperature spectrometer operating at 188.9 MHz. Temperature readings displayed on the spectrometer console were converted to "true" temperatures according to directions given in the operating manual, by means of a calibration curve based on the known temperature dependence of the separation between the methylene and hydroxyl signals from a standard ethylene glycol sample. The resulting
values should be reliable to about fO.1"C.Since cmc evaluations depend on relative shifts for samples of differing concentrations, shifts were measured relative to an arbitrary zero point. When they are plotted against the reciprocal concentration, the dilute solution points lie on a line of zero slope and the points for concentrated solutions determine a line which intersects the other at l/c = l/cmc.889 Because ofthe finite size of the micelles, points for concentrations close to the cmc do not fall on either line and should be disregarded. Each sample was equilibrated in the variable-temperature probe for at least 15 min prior to measurement. Since a 1" change in temperature may change the peak position by up t o 0.017 ppm,Bvgthe largest source of error is probably a slight temperature uncerthty, perhaps from not quite complete thermal equilibration. The resulting scatter did not usually prevent the cmc values from being reproducible to within 1 or 2%. Similar error limits were reported for cmc values of ionic surfactants based on conductimetric measurements.14 Results for each of the four surfactants at seven or more temperatures are presented in Table 2.
Discussion According to the development presented in ref 2, the cmc of a zwitterionic surfactant at temperature T should be given by cmc = cmc*exp[(ACdR)F(T,r*)l where F ( T , P ) = ln(T*/T)
+ 1- P I T .
(2)
With a trial value of F ,the function F(T,T*) is evaluated at each experimental temperature, and ln(cmc)is plotted against F. Using the best value of P,i.e. that which gives the most nearly linear plot, ln(cmc*)is given by the intercept at F = 0 and ACJR by the slope. Parameters thus derived appear in Table 3 and were used with eq 1 to find the calculated cmc values listed with the observed (11)Cope, A.C.; Engelbert,C. OrgunicSyntheses;Wiley: New York, 1963;Collect. Vol. IY,p 339. (12)Baumgarten, H.E.;Bower, F. A.; Okamoto, T. T. J.Ant. Chem. Soc. 1967,79,3145. (13)Laughlin, R. G.U.S.Patent 4 287 174,1981. (14)Adderson, J. E.;Taylor, H. J . Colloid Sci. 1964,19, 495.
2204 Langmuir, Vol. 10, No. 7, 1994
Muller
Table 3. Derived Thermodynamic Parameters and Chemical Shift Differences for Micellization of Several CFs(CHz)iiN(CHs)z(CHz),COa Surfactants
(r"- 273.2) ("C) cmc* x lo3 (mol/kg) AC,, [J/(mol K)] cmc298 x 103 (moVkg) AG; (kJ/mol) AGp (kJ/mol)" Mom (kJ/mol) AS, [J/mol Kl lAd129s (ppmIb
n=l 37.8 5.33 -474 5.61 -22.8 -25.4 6.1 97 0.93
n=4 48.6 11.02 -494 13.15 -20.7 -24.1 11.7 109 0.76
n=5 48 9.28 -510 11.04 -21.1 -24.7 11.7 110 0.74
n=7 47 4.49 -545 5.24 -23.0 -26.1 12.0 117 0.82
a Data for CH3(CH2)11N(CH3)2(CHz)nC02ref 7. Chemical shift difference between the 19FNMR signals of the monomeric and the micellized surfactants; the micelle signal occurs at higher field strength.
ones in Table 2. The rms (room mean squared)deviations (Table 2) are similar to those found with data for ionic surfactants2 and they cannot be significantly improved by allowing AC, to vary linearly with the temperature. As found previously,2 it is often possible to change r" by 1 or 2" with compensating changes in ACp, without making the rms deviation dramatically worse. Consequently the values of AC, are uncertain by about f 2 5 J/(mol K). However, other thermodynamic parameters for micellization at 298 K can be evaluated which are subject to much smaller errors. The enthalpy change is given2 by
AH: = AC,(r" - 298.2)
(3)
and it is found that acceptable pairs of values of !P and AC, then yield values of AH: that differ from the best-fit value by no more than 0.3 kJ/mol. The Gibbs energy change depends only on the cmc at 298 K, that is (when cmc
