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Langmuir 1994,10,2578-2582

Thermodynamics of Micelle Formation by 1-Methyl-4-alkylpyridiniumHalides Koos Bijma and Jan B. F. N. Engberts* Department of Organic and Molecular Inorganic Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Gert Haandrikman and Nico M. van Os Koninklijke JShell-Laboratorium, Shell Research B.V., P.O. Box 3800, 1030 BN Amsterdam, The Netherlands

Michael J. Blandamer, Michael D. Butt, and Paul M. Cullis Department of Chemistry, University of Leicester, Leicester LE1 7RH, U.K. Received February 2, 1994. I n Final Form: April 15, 1994@ This paper reports enthalpies ofmicellizationfor a series of 1-methyl-4-alkylpyridinium halide surfactants at 303.2 K with different lengths and degrees of branching of the 4-alkyl chain and different sizes of counterions using two microcalorimeters (LKB 2277 and Omega Microcal). The standard enthalpy of micellization (AH",) becomes more exothermic with increasing chain length and with increasing size of the halide counterion. No trend could be observed with respect to the degree of branching of the alkyl chain. Critical micelle concentrations (cmc) were determined as a function of temperature using conductometry. These cmc values were used to calculatethe standard Gibbs energy of micellization(AGO,) accordingto the phase separation model. From this we calculated the standard enthalpy of micellization (AH",), which was compared with the microcalorimetric enthalpies of micellization.

Introduction Surfactant molecules aggregate in aqueous solution. Depending on the molecular structure of the surfactant, the concentration, and the temperature, a variety of aggregates can be formed. Single-chained surfactants usually form micelles, either spherical or wormlike. Micellization is primarily driven by the tendency of the hydrophobic moieties to reduce the hydrocarbon-water contact. This effect is counteracted by headgroup repulsion. The hydrocarbon chain, headgroup, and counterions all play their part in this delicate balance of molecular interactions, which determines the size and shape of the aggregates. 1-Methyl-4-n-dodecylpyridinium iodide forms mol spherical micelles at concentrations above 2.4x dm-3 a t 303 K. Above 45 x mol dm-3, these micelles change to form wormlike structures.' This change in morphology is often accompanied by the onset of viscoelasticity. Enthalpies of micellization are among the characteristic parameters yielding information on micelle formation. Microcalorimetry has been used widely to study the thermodynamic behavior of cationic,2-8 anionic,+14 and nonionic15surfactants in aqueous solution. Thermodynamic models have been developed to calculate thermodynamic properties of micelle formation. A Abstract published in Advance ACS Abstracts, July 1, 1994. (1)Nusselder, J. J. H.; Engberts, J. B. F. N. J . Org. Chem. 1991,56, @

5522. (2)Nusselder, J. J. H.; Engberts, J. B. F. N. J . Colloid Interface Sci. 1992,148,353. (3)Nguyen, D.; Bertrand, G. L. J . Colloid Interface Sci. 1992,150, 143. (4)Koshy, L.; Pegaidou-Koemtjopoulou, D.; Rakshit, A. K. J . Colloid Interface Sci. 1991,59, 1. ( 5 ) Mehrian, T.; de Keizer, A.; Korteweg, A. J.; Lyklema, J. Colloids Surf. A: Physicochem. Eng. Aspects 1993,71,255. (6)Stenius, P.;Backlund, S.; Ekwall, P. In Thermodynamics and Transport Properties of Organic Salts; Franzosina, P., Sanesi, M., Eds.; Pergamon: Oxford, 1980. (7)Kresheck, P.; Hargraves, W. A. J. J . Colloid Interface Sci. 1974, 48,481. (8)Bashford, M.T.; Woolley, E. M. J . Phys. Chem. 1986,89,3173.

comparison of the calculated with the experimental values provides information on the reliability of these models. One objective is to predict thermodynamic properties a t elevated temperatures, which cannot be reached experimen tall^.^ In this study we report the use of microcalorimetry to obtain W ,values for three different series of compounds: (1)1-methyl-4-n-alkylpyridinium iodides with different alkyl chain lengths, (2) 1-methyl-4-alkylpyridinium iodides with different alkyl chain branching, halides with and (3) 1-methyl-4-n-dodecylpyridinium different sizes ofthe counterions. For six surfactants the calorimetric results are compared with calculated values using the phase separation model. We have applied the phase separation model to the micellization of 1-methyl-4-alkylpyridinium halides, in order to calculate the standard Gibbs energies (AGO,) and entropies (AS",) of micellization. For these calculations we need the critical micelle concentration (cmc) as a function of temperature. These data were determined using conductometry.

Experimental Section Materials. The surfactants used in this study (Figure 1)all form micelles above their cmc values. The synthesis of these (9)Van Os,N. M.; Daane, G. J.;Haandrikman, G. J . Colloid Interface Sci. 1991,141,199. (10)Skold, R. 0.; Tunius, M. A. R. J. J . Colloid Interface Sci. 1993, 155,43. (11)Sivakumar, A.;Somasundaran, P.; Thach, S. Colloids Surf. A: Physicochem. Eng. Aspects 1993,70, 69. (12)Maa, Y. F.;Chen, S. H. J . Colloid Interface Sci. 1987,115,437. (13)Mazer, N. A.;Olofsson, G. J . Phys. Chem. 1982,86,4584. (14)Sharma, V. K.;Bhat, R.; Ahluwalia, J. C. J. Colloid Interface Sci. 1987,115,396. (15)Olofsson, G. J.Phys. Chem. 1986,89,1473. (16)(a)Tanford,C. TheHydrophobicEfect; Wiley: New York, 1979. (b) Nagarajan, R. Adv. Colloid Interface Sci. 1986,26,205. (17)Van Os, N. M.; Daane, G. J.; Bolsman, T. A. B. M. J . Colloid Znterfme Sci. 1987,115,402. (18)Barry, B. W.; Russel, G. F. J. J . Colloid Interface Sci. 1972,40, 174.

0743-746319412410-2578$04.50/00 1994 American Chemical Society

Thermodynamics of Micelle Formation

Langmuir, Vol.10,No. 8,1994 2579 1

0

3

2 !

'

5

4 I

'

I

6

'

!

7

'

l

4004 -

4000

1

z

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AHO,,,

2000

2ooo-

......__.. 1

Figure 1. Structures of the 1-methyl-4-alkylpyridinium halides.

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.

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.

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.

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.

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.

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.

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Figure 3. Enthalpy of dilution of 1-methyl-4-n-dodecylpyridinium iodide a t 303 K.

0

I(

20

40

80

80

Timelmin

Figure 2. Calorimetric signals corresponding to dilution of a concentrated solution of 1-methyl-4-n-dodecylpyridiniumiodide in water at 303 K. surfactants has been described e1~ewhere.l~Critical micelle concentrations and critical rod concentrations (crc) have also been reported peviously.1~2J9Water was purified10 by pumping demineralized water through a Milli-Q reagent-grade water system (type 1)and removing any remaining COz by nitrogen stripping. Calorimetry. Experiments were performed a t 303,323,343, and 368 K i n a stirred LKB perfusion cellz0installed in an LKB 2277 microcalorimeter.z1 A 10-pL sample of aqueous surfactant solution (concentration >> cmc, but < crc) was injected with either a Hamilton Microlab M syringe or a Gilson Dilutor 401 syringe into the perfusion cell, which contained 1-2 mL of pure water a t the start ofthe experiment. The heat absorbed or evolvedwas recorded, and after thermal equilibrium was reached, the next injection of 1OpLwas added. This procedure was repeated until the desired concentration range was covered. The solution was stirred to ensure complete mixing. Enthalpies of micelle formation were also determined using an Omega titration calorimeterz2(Microcal,Northampton, MA). For the Omega titration calorimeter a similar procedure was followed, although the injectionswere automated under computer control. Figure 2 is a typical recorder plot (using an Omega titration calorimeter) of the dilution of 1-methyl-4-n-dodecylpyridinium iodide a t 303 K. Integration of peaks, as shown in Figure 3, yields the enthalpy of dilution in kilojoules per mole, which is plotted against the surfactant concentration. The difference in enthalpy between the two horizontal parts of the s-shaped curve of the enthalpogram is equal to AH", (Figure 31.26 (19) Nusselder, J. J. H.; Engberts, J. B. F. N. Langmuir 1991, 7, 2089. Laynez,J.; Schoen,A.; Suurkuusk,J.;Wadsoe, (20) Nordmark,M. G.; I. Biochem. Biophys. Methods 1984, 10, 187. (21) Wadsoe, I. Thermochim. Acta 1985,85,245. (22) Blandamer, M. J.;Butt, M. D.; Cullis, P. M. Thermochim.Acta 1992,211,49. (23) Nusselder,J.J.H. Ph.D. Thesis, University of Groningen, 1990. (24) Stenius, P.; Backlund, S.;Ekwall, P. IUPAC Chem. Data Ser. 1980,84,1044. (25) Marcus, Y. Ion Sohation; Wiley: New York, 1985. (26) (a) Desnoyer, J. E.; De Lisi, R.; Perron, G. Pure Appl. Chem. 1980,52,433. (b) Lindheimer, M.;Partyka, S.; Rouviere, J.; Cygankievicz, N.; Brun, B. Calorim. A d . Therm. 1983,14,274.

Conductivity Measurements. Conductivities were measured using a Wayne-Kerr autobalance Universal Bridge B642 fittedwith a Philips electrode,PW9512101,havinga cellconstant of 0.71 cm-'. The solutions were thermostated in the cell for at least 30 min. The conductivitycell was equipped with a magnetic stirrer device. Surfactant concentrations were varied by the addition (microsyringe) of 30-50-pL portions of a concentrated stock solution of surfactant to the conductivity medium. Concentrations were corrected for volume changes. cmc values were taken from the intersection of the tangents drawn before and after the break in the conductivity vs concentration plot. The degree of counterion binding @) was determined from the ratio of slopes of the conductivity vs concentration curve above and below the cmc.

Results and Discussion Phase Separation Model. The simplest model for micelle formation, which assumes 100%counterion binding, is the phase separation model. The agreement between calculated and experimental enthalpies of micellization is usually poor when ionic surfactants are ~ t u d i e d .As ~ expected better agreement is obtained when nonionic surfactants are being s t ~ d i e d . ~From ' Table 1 it can be seen that the surfactants studied in this paper all possess relatively high degrees of counterion binding. Therefore, it seemed worthwhile to test the accuracy of the enthalpies of micellization calculated by means of the phase separation model. Although micelles can be polydisperse,16this model assumes a monodisperse micellar solution. According to this model,17J8the standard Gibbs energy of micelle formation of a monovalent ionic surfactant per mole of monomer in the absence of added electrolyte is given by AGm = 2,RT ln(cmc)

(1)

where R is the gas constant and T the absolute temperature. The cmc is expressed in mole fraction units. cmc values of the surfactants used in this study are listed in Table 1. The standard enthalpy of micelle formation per mole of monomer is calculated using the Gibbs-Helmholtz equation:

The dependence of AGO, on temperature was fitted to a second-order polynomial: (27) Moroi, Y. Micelles; Plenum Press: New York, 1992.

Bijma et al.

2580 Langmuir, Vol. 10, No. 8, 1994 Table 1. Critical Micelle Concentration and Degree of Counterion Binding as a Function of Temperature, Measured by Conductometry surfactant T (K) B (%) cmc (mM) 1 303.2 78 42.7" 10.65a 2 303.2 79 11.5 313.3 80 12.6 78 323.6 14.8 75 334.5 2.45a 3 298.2 83 2.5P 83 303.2 2.900 81 313.2 79 3.31" 323.2 3.96" 77 333.2 4.43" 74 343.2 3.66" 84 4 298.2 3.93" 83 303.2 4.64a 82 313.6 5.27a 80 323.0 6.090 77 333.3 7.4P 73 343.2 4.65a 79 5 298.2 4.17" 6 298.2 80 4.75a 313.2 77 5.590 76 323.8 6.28" 333.2 76 7.28" 341.8 75 5.0 71 7 299.0 4.95" 71 303.2 5.5 313.7 68 6.0 324.3 67 5.5 63 8 303.4 6.0 61 313.7 6.6 323.9 59 7.3 56 333.2 a

Table 2. Second-OrderPolynomial Coefficientsa A B C surfactant (kJ mol-') (kJ mol-' K-l) (kJ mol-' K-2) 2 105.93 -0.86 1.2 10-3 9.8 10-4 7 81.86 -0.72 8 34.61 -0.42 5.0 10-4 Similar data for 3, 4, and 6 are given in ref 2.

Table 3. Enthalpies of Micellization of Structurally Related Compounds

T

Table 4. AH surfactant 1 2

According to ref 2.

AGO, = A

+ BT + cla

AITm = AGO, - ( B

+ 2CT)T

3

(3)

whered, B, and Care fitting coefficients (Table 2). Higherorder polynomials did not yield statistically better fits. Combination of eqs 2 and 3 yields (4)

The standard entropy of micellization can then be calculated from

mom = (AH",- AG",)/T The results for 2 in Figure 3 show that dilution of a concentrated solution in the premicellar region (concentration in the vessel < cmc) is accompanied by relatively large endothermic heat effects, which can be ascribed to the breaking up of micelles into monomers. In the micellar region (concentration in the vessel > cmc) the titration curve approaches the baseline. Here the pattern is determined by the dilution enthalpy of micelles. Linear least-squares lines were drawn through the points belonging to either the monomeric or the micellar region, and the distance separating them a t the cmc was taken as the standard enthalpy of micelle formation (AH",). Enthalpies of micellization for the surfactants studied in this paper are all exothermic (Tables 4-6). Table 3 provides enthalpies of micellization for structurally related compounds; it is clear that our data are rather similar to these enthalpies of micellization (e.g., compare the value for 3 with the value for l-n-dodecylpyridinium iodide6). From these data and the experiments reported in this paper, the enthalpy of micellization seems to be exothermic for cationic surfactants with halide counterions having sizes comparable to or larger than chloride a t temperatures above 303 K.

AH",

(K) (kJmol-l) ref 303 -14.5 6 1-n-dodecylpyridinium iodide 6 303 -5.48 1-n-dodecylpyridinium bromide 303 7 -5.56 1-n-dodecylpyridinium bromide 7 303 -1.55 1-n-dodecylpyridinium chloride 279 5 12.2 1-n-dodecylpyridinium chloride 303 5 -0.2 5 -7.4 308 279 5 13.0 1-n-decylpyridinium chloride 5 -2.0 308 5 279 13.9 1-n-tetradecylpyridinium chloride 308 -13.2 5 8 -2.3 298 n-dodecyltrimethslammonium bromide n-tetradecyltrimethylammonium bromide 298 -4.9 8 n-hexadecyltrimethylammonium bromide 298 - 12.0 31 298 -9.8 8 surfactant

(I

Om

as a Function of Alkyl Chain Length T (K) AH Om (kJ mol-') 303 -7.7 f 1.0 323 -15.4 f 3.5 343 -11.4 f 7.0 303 -12.9 f 1.0, -11.8 f 0.5" 323 -16.8 f 3.6, -16.7 f 1.7= 303 -17.9 f 4.3, -15.3 f 0.1" 323 -19.9 i 4.3 343 -25.2 f 5.0 368 -27.0 f 2.0

Measured using an Omega titration calorimeter.

Table 4 shows that the enthalpies of micellization strongly depend on the chain length of the hydrophobic moiety. AH",becomes more exothermic when the alkyl chain length is increased. The increment amounts to -2.6 f 0.2 k J mol-l per CH2 group a t 303 K. This observation is in accordance with data published by Bashford and Woollep for n-alkyltrimethylammonium bromide surfactants. From their data a n increment in AH", of -1.9 k J mol-' a t 298 K can be calculated. However, the increment is temperature dependent. The same dependence of AHO, on chain length holds for anionic surfactants. Van Os et ale9studied the effect of chain length on AH", for a number of alkylbenzenesulfonates and reported an increment in AH", of -1.5 f 1 k J mol-l per CH2 group a t 303 K. This increment increases with increasing t e m p e r a t ~ r e .We ~ conclude that the increment in the enthalpy of micellization appears t o depend on the type of surfactant used and presumably reflects the efficiency of the hydrophobic interactions between the alkyl chains in the core of the micelle. The data in Table 5 show that the influence ofbranching of the alkyl chain is modest. The same conclusion holds for a series of sodium alkylbenzenesulfonates.9 At 303 K AH", decreases with increasing degree of branching, although the differences are small. At higher temperatures this effect is not found. Chain branching leads to a reduction of the hydrophobic molecular surface area of the surfactant monomer exposed to water. This reduction can be quite significant, amounting up to 30%.23Unexpectedly, this reduction of the hydrophobic surface area and leads to a change in AHO, of about 0.6 k J

Langmuir, Vol. 10, No. 8, 1994 2581

Thermodynamics of Micelle Formation

Table 6. Influence of the Counterion on AH surfactant T (K) AH O m (kJ mol-')

Table 5. Influence of Alkyl Chain Branching on AH O m surfactant T (K) AH O m (kJ mol-') 3 303 -17.9 f 0.8,-15.3 f 0.1' 323 -19.9 f 4.3 343 -25.2 f 5.0 368 -27.0 f 2.0 4 303 -13.3 f 0.5 -23.3 f 3.8,-22.9 f 0.1' 323 368 -26.0 f 2.0 6 303 -11.7 f 2.3 323 -20.1 f 3.8 343 -22.7 f 2.4 6 303 -12.6 k 0.1' 313 -17.2 f 0.2" 323 -21.6 f 0.4' 333 -25.2 f 0.2' a

7

8

Q

Measured using an Omega titration microcalorimeter.

Table 7. Thermodynamic Parameters for Micellization According to the Phase Separation Model at 303 K

Measured using an Omega titration calorimeter. ~~

-12

-17.9 f 0.5.-15.3 f 0.5" -19.9 f 4.3' -25.2 f 5.0 -27.0 f 2.0 -7.6 f 0.3,-7.5 f 0.1" -16.9 f 0.6 -22.7 f 3.0 -39.0 f 6.6 -6.2 f 1.3 -13.9 f 1.0 -21.9 f 3.6

303 323 343 368 303 323 343 368 303 323 368

3

Om

~~~~

I

AG Oma

A s "mQ

surfactant (kJ mol-*) (J mol-l K-l) 1 -36.1 2 -43.1 121 133b 3 -50.44b 4 -48.16b 123b 6 -47.64b 128b 7 -47.0 128 8 -46.5 116

AH Om' (kJ mol-l) -6.4

-lob -llb

-96 -8.0 -11.2

AH Om' (kJ mol-') -7.7 f 1.0 -12.9 f 1.0 -17.9 f 4.3 -13.3 f 0.5 -12.6 f 0.1 -7.6 f 0.3 -6.2 f 1.3

According to the phase separation model. See ref 2. Calorimetric values.

taking the error limits into account, these differences are too small to be measured. This point is further illustrated by the effective chain length, estimated using the cmc (Figure 4). Using surfactants 1-3 as a standard, a n effective chain length of 11.4 is found for 4 and 11.2 for 6 a t 303 K. Literature values of AHfi, calculated assuming 100% counterion binding are in good agreement with experimental values for n-alkylpyridinium halide^^^,^^ and for alkyltrimethylammonium halides'* a t ambient temperatures. Maa and Chen12concluded from this observation that counterions are unimportant for the thermodynamics of micellization. However, the data in Table 6 illustrate that the enthalpy of micellization is strongly dependent on the size of the halide counterion. Enthalpies of micellization are less exothermic for cationic surfactants with smaller counterions. This indicates that the influence of the counterion is significant, a n observation which is often ignored. This pattern can be rationalized by taking into account that the smaller counterions are more strongly hydrated and possess a more endothermic enthalpy of dehydration.26 Upon aggregation the counterions will be partially dehydrated; hence, the enthalpy of micellization will be less exothermic on going from iodide to bromide to chloride as a counterion. We note, however, that the change of the aggregation number with counterion should

also be taken into account; unfortunately the aggregation numbers are not known for our surfactants. Despite the availability of sensitive microcalorimeters, discrepancies in reported enthalpies of micellization are encountered in the literature (Table 3). Therefore, we studied the reliability of our data by independent measurements, using two different microcalorimeters. Most of the calorimetric experiments have been performed using a n LKB 2277 microcalorimeter with a cell volume of 1or 2 cm3, depending on the compound to be measured. For compounds 2 and 3, enthalpies of micellization have also been measured using a n Omega titration calorimeter with a cell volume of ca. 1.3cm3. As can be seen from the data in Tables 4-6, the different calorimeters yield identical enthalpies of micellization, despite different calorimeter designs and experimental protocols. To our knowledge this is the first time that a comparison of enthalpies of micellization, obtained using two different calorimeters, has been reported. Table 7 reported thermodynamic parameters of micellization according to the phase separation model. The data show that AGO, decreases with increasing chain length of the hydrophobic moiety. This increase amounts to -3.7 k J mol-l per CH2 group at 303.2 K (which agrees well with expected hydrophobic Gibbs energies of transfer16). The enthalpies of micellization for 2-4 and 6 calculated according to the phase separation model are generally lower than the experimental ones. The trend is predicted correctly when different chain lengths are compared (2 vs 3). Experimental critical micelle concentrations as a function of temperature are interpreted in terms of the van't Hoff relation t o provide the enthalpy of micellization. Holtzer et aLZ9pointed out that this is principally incorrect. Less exothermic enthalpies of micellization will be obtained when the aggregation number is temperature dependent (e.g., diVldTis not zero, as is assumed in the monodisperse phase separation model). According to van Os,30 this effect can be quite

(28)Jones, M. N.; Agg, G.;Plicher, G . J. J . Chem. Thermodyn. 1971, 3, 801. (29) Holtzer, A.; Holtzer, M. F. J.Phys. Chem. 1974,78,1442.

(30)van Os,N. M. Personal communication. (31)Bergstrom, S.; Olofsson, G.Thermochim.Acta 1980,109,155.

7

8

9

10

11

12

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Effectivechain length

Figure 4. ln(cmc)as a function of the effective chain length of 1-4 and 6 at 303 K.

2582 Langmuir, Vol. 10,No.8,1994

significant and can lead to a n enthalpy of micellization which is about 2-3 k J mol-' less exothermic. With different degrees of branching, no trend can be observed in the calculated enthalpies of micellization (3, 4, and 6). This could be due to the similar effective chain length in this series (Figure 4). The phase separation model assumes that micelle formation is akin to the precipitation of a separate phase. The counterion binding is assumed to be 100%;the system is thus described in terms ofuncharged components. It is, therefore, hardly surprising that agreement between calculated and experimental enthalpies of micellization is usually poor for ionic surfactants, whereas better agreement is obtained for nonionic surfactant^.^^ Because specific counterion effects (e.g., counterion binding and aggregation number) are not taken into account in the monodisperse phase separation model, no accurate calculation of the enthalpy of micellization as a function of the counterion size seems possible. The model even fails to predict the trend in A I P m i c as a function of counterion size. The degree of counterion binding increases when the size of the counterion increases (Table 1);however, the phase separation model does not give better results when the counterion binding of the surfactants is higher (compare 3,7, and 8). This implies that the degree of counterion binding is not the most important factor when calculated and experimental enthalpies of micellization are compared. We suggest that the aggregation number may vary considerably with counterion size. Presumably this effect has a marked influence on the calculated enthalpy of micellization. Therefore, a comparison between calculated enthalpies of micellization and experimental ones as a function of counterion size cannot be made using this model.

Bzjma et al.

Conclusions A good accordance was found in enthalpies of micellization for four alkylpyridinium surfactants measured using an LKB 2277 microcalorimeter and an Omega titration calorimeter. The enthalpy of micellization was found to be dependent on the chain length of the hydrophobic moiety and on the size of the counterion of the 1-methyl-4-alkylpyridinium halide surfactant. The enthalpy of micellization becomes more exothermic with increasing chain length of the 4-alkyl chain and with increasing size of the halide counterion. No trend could be observed with variation of the degree of branching in the 4-alkyl chain. The latter can be explained in terms of the effective chain length, which varies only moderately upon branching. For the surfactants with iodide as the counterion and different alkyl chain lengths and degrees of branching, and enthalpies of micellization calculated according to the phase separation model are less exothermic than the calorimetric values. Upon increasing the alkyl chain length, the enthalpy of micellization was found to increase -3.7 k J mol-l per CH2 group a t 303 K. No trend could be observed in the calculated values when the degree of branching was varied.

Acknowledgment. The work described in this paper was performed in part a t the KoninklijkdShell-Laboratorium, Amsterdam, and at the University of Leicester. The investigations were supported by the Netherlands Foundation of Chemical Research (SON) with financial aid from the Netherlands Foundation for Scientific Research (NWO)and by the SERC under the Molecular Recognition Initiative.