Thermodynamics of Micellization of Multiheaded Single-Chain

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Thermodynamics of Micellization of Multiheaded Single-Chain Cationic Surfactants† Santanu Bhattacharya* and Jayanta Haldar Department of Organic Chemistry, Indian Institute of Science, Bangalore 560012, India Received February 21, 2004. In Final Form: May 24, 2004 The energetics of micelle formation of three single-chain cationic surfactants bearing single (h ) 1), double (h ) 2), and triple (h ) 3) trimethylammonium [+N(CH3)3] headgroups have been investigated by microcalorimetry. The results were compared with the microcalorimetric data obtained from well-known cationic surfactant, cetyl trimethylammonium bromide (CTAB), bearing a single chain and single headgroup. The critical micellar concentrations (cmc’s) and the degrees of counterion dissociation (R) of micelles of these surfactants were also determined by conductometry. The cmc and the R values increased with the increase in the number of headgroups of the surfactant. The relationship between the cmc of the surfactant in solution and its free energy of micellization (∆Gm) was derived for each surfactant. Exothermic enthalpies of micellization (∆Hm) and positive entropies of micellization (∆Sm) were observed for all the surfactants. Negative ∆Hm values increased from CTAB to h ) 1 to h ) 2 and decreased for h ) 3 whereas ∆Sm values decreased with increase in the number of headgroups. The ∆Gm values progressively became less negative with the increase in the number of headgroups. This implies that micelle formation becomes progressively less favorable as more headgroups are incorporated in the surfactant. From the steady-state fluorescence measurements using pyrene as a probe, the micropolarities sensed by the probe inside various micelles were determined. These studies suggest that the micelles are more hydrated with multiheaded surfactants and the micropolarity of micelles increases with the increase in the number of headgroups.

Introduction Molecular design of surfactants with widely varying architectures offers excellent opportunity for tailoring the surfactant aggregation behavior and the physical chemical properties of their solutions.1,2 The critical micelle concentration (cmc) is an important solution property of surfactant solutions. For each type of surfactant system, there is a need to precisely evaluate cmc to confirm the existence of micelles in solution and to investigate the thermodynamics of micellization. Recently, we have introduced a novel set of multiheaded cationic surfactants.3 These were developed to investigate how an increasing number of headgroups on one end of a hydrocarbon chain of a surfactant molecule influence their aggregation properties. Small-angle neutron scattering (SANS) and fluorescence studies show that with the increase in the number of headgroups, the cmc values and the degrees of micellar ionization (R) increase, while their aggregation numbers decrease progressively. The micelles also become smaller in size with increase in the number of headgroups in the surfactants.3 It is important to ascertain how progressive increases in the number of headgroups influence the thermodynamics of micelle formation and govern the stability and spontaneity of formation of the resulting aggregates. Toward this end, the calorimetric titration method has been employed for the determination of cmc and enthalpy of micellization (∆Hm) of a number of surfactants.4-7 However, no such investigation has been undertaken to examine the above-mentioned multiheaded surfactants. Herein, we report the results of our studies on the † This paper is dedicated to Professor C. N. R. Rao on the occasion of his 70th birthday. * Corresponding author. Tel: +91-80-2293-2664. Fax: +91-802360-0529.

(1) Schnur, J. M. Science 1993, 262, 1669-1676. (2) Menger, F. M.; Keiper, J. S. Angew. Chem., Int. Ed. 2000, 39, 1906-1920. (3) Haldar, J.; Aswal, V. K.; Goyal, P. S.; Bhattacharya, S. Angew. Chem., Int. Ed. 2001, 40, 1228-1232.

thermodynamics of aggregation of multiheaded surfactants bearing single, double, and triple trimethylammonium headgroups. We also include the comparison of these results with that of a single-headed surfactant, CTAB, by conductometric and microcalorimetric methods. The micropolarity of different micellar solutions as sensed by pyrene is also presented.

Experimental Section Materials. All the surfactants bearing headgroups h ) 1, 2, and 3 were synthesized and purified as described elsewhere.3 Spectroscopic characterizations involving 1H NMR, 13C NMR, FT-IR, electrospray ionization/mass spectrometry, and elemental analysis confirmed the high purities of these surfactants. The (4) Chatterjee, A.; Maiti, S.; Sanyal, S. K.; Moulik, S. P. Langmuir 2002, 18, 2998-3004. (5) Wettig, S. D.; Nowak, P.; Verrall, R. E. Langmuir 2002, 18, 53545359. (6) Willemen, H. M.; Marcelis A. T. M.; Sudho¨lter, E. J. R. Langmuir 2003, 19, 2588-2591. (7) Grosmaire, L.; Chorro, M.; Chorro, C.; Partyka S.; Zana R. Prog. Colloid Poym. Sci. 2000, 115, 31-35.

10.1021/la0495433 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/11/2004

Micellation of Multiheaded Single-Chain Surfactants surfactant CTAB (99% Fluka, USA) was used after recrystallization with a CHCl3/ethyl acetate mixture. Conductometry. Doubly distilled water (specific conductivity 2-4 µS cm-1 at 312.5 K) was used to prepare the solutions for all the studies. Solubilization of the newly synthesized surfactants in water depended on the number of headgroups that these surfactants possessed. Thus dissolving of the single-headed surfactant (h ) 1) in water required heating at 40 °C, and the resulting solution appeared slightly translucent. Surfactants with h ) 2 and h ) 3 were, however, highly soluble in water at ambient temperature. The facile solubilization of h ) 2 or 3 in water could be a consequence of increased hydrophilicity of these surfactants possessing a larger number of headgroups. However, to study each surfactant solution under comparable conditions, all the experiments were performed at 312.5 K. The critical micellar concentration (cmc) values for each surfactant solution in water were measured conductometrically by using a conductivity meter, Schott-Gerate model Konduktometer CG855, having an electrode with cell constant of 0.93 cm-1. Concentrated solutions of individual surfactants of known concentration were progressively diluted, and the specific conductivity values at 312.5 K were measured. The cmc values for each surfactant, h ) 1, 2, and 3, were determined at 312.5 K by plotting the values of the specific conductivites against the respective surfactant concentrations. Fluorometry. Pyrene, a micelle-soluble fluorescence probe, exhibits fine structure in its steady-state fluorescence emission spectra. The nature and the intensity of such fine-structured bands are quite dependent on the polarity of the environment.8,9 The first and third vibronic peaks, I1 and I3 show the greatest solvent dependency. When solubilized in surfactant micelles, the ratio of intensity of the pyrene fluorescence emission peaks, i.e., I3/I1, provides a measure of the micropolarity of the aggregate.8 Fluorescence measurements were performed using a Hitachi F-4500 spectrofluorometer equipped with a thermostated watercirculating Julabo model F10 bath. The measurements were carried out at 40 °C and at 10 mM surfactant concentration, i.e., above the cmc of all the surfactants. At the same temperature the emissions due to pyrene in water and n-hexane were also measured. The pyrene concentration was maintained at 2 µM in all the cases. Excitation wavelength was fixed at 337 nm and emission spectra of the region 360-460 nm were recorded keeping the bandwidths fixed at 2.5 and 10 nm respectively for the emission and the excitation. Microcalorimetry. Enthalpies were measured at 312.56 K using a Calorimetry Sciences Corp. model 4200 isothermal titration calorimeter (ITC). The sample and reference cells (1.3 mL) were filled with double-distilled water and thermally stabilized at 312.56 K. As already mentioned, the solubility of the single-headed surfactant (h ) 1) in water at room temperature is poor and hence all the experiments have been performed at 40 °C. Before each experiment, the concentrated surfactant solution of h ) 1 was made in water by heating the sample at 40 °C for 5 min. The resulting solution was stable although it appeared translucent. The other surfactants, CTAB, h ) 2 and h ) 3, were highly soluble in water at ambient temperature. However, to generate calorimetric information under identical conditions, the experiments involving the latter surfactant micelles were also carried out at 40 °C. Concentrated surfactant solution of known concentration was injected in 10 µL increments into the stirred sample cell using a 250 µL Hamilton syringe controlled by an autoinjection apparatus of the instrument. The intervals between consecutive injections were 400-600 s for surfactants CTAB, h ) 2 and h ) 3. But in the case of h ) 1, it was 1200 s. The addition of surfactant solution and the measurements of the heat exchanged were performed as programmed. The data were analyzed using Microcal Origin and “Titration bind work” programs provided by the manufacturers. The measurements with each surfactant solution were repeated at least three times to determine the reproducibility. (8) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039-2044. (9) Dong, D. C.; Winnik, M. A., Photochem. Photobiol. 1982, 35, 1721.

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Results and Discussion Conductivity Measurements. The cmc for each surfactant was first determined with the aid of electrical conductivity measurements at 312.5 K by plotting the specific conductivities (κ) of surfactant solutions as a function of its concentrations. For aqueous solution of each surfactant, reproducible breaks were observed in κ vs [surfactant] plots indicating the onset of aggregation (Figure 1). The cmc value (Figure 1A) obtained using the same method for CTAB (1.06 mM) has been found to be in good agreement with the cmc value reported for CTAB in the literature.10 In the case of surfactant with h ) 1, two breakpoints were observed. To ensure this observation, the conductivity measurements with h ) 1 were carefully repeated. When we measured the conductivity of the surfactant solution in the lower concentration range (up to 0.4 mM), only one break point was observed at the surfactant concentration of ∼0.26 mM (Figure 1B). However, we observed two breakpoints when we measured the conductivity up to the surfactant concentration of 2 mM. In addition to the break at ∼0.26 mM, a second break was seen at ∼0.8 mM (not shown). It is clear that for h ) 1, two different microheterogeneous phases exist in its aqueous solution at higher concentration. We consider that the first breakpoint is due to the micellization of surfactant h ) 1, and hence for h ) 1, the cmc is 0.26 mM. This is in agreement with the cmc value obtained for h ) 1 using ITC (see below). The break at ∼0.8 mM is due to the onset of secondary aggregation of the surfactant h ) 1. Such types of postmicellar aggregation are known in other instances.11,12 Indeed SANS studies with surfactant h ) 1 indicated the formation of larger micellar aggregates at higher concentration.3 This is also consistent with the fact that the resulting solution appeared quite translucent even at 40 °C. The cmc values obtained for surfactants h ) 2 and h ) 3 were 5.2 and 5.9 mM respectively (Figure 1C,D). It may be noted that the break point observed with h ) 2 was quite pronounced while the same for h ) 3 was rather mild. This is consistent with earlier SANS results with these two types of micelles. Analysis of SANS data suggests that with the increase in the number of headgroups the aggregation number of the resulting micelles decrease progressively and for h ) 3 it is particularly low.3 Since the micellar aggregation for h ) 3 is not highly cooperative, the onset of micellization is not drastic (see below). Plots in Figure 1 show that the slopes of the linear region above the breakpoint are less than that below this break. This may be a consequence of counterion binding at the interfaces of micellar aggregates, once they are formed. The cmc values were found to increase with each increase in the number of headgroups per surfactant molecule. This is likely due to greater headgroup repulsion in the molecules bearing multiple headgroups causing micelle formation to be less favorable. The conductivity data suggest that the cmc value is less in the case of h ) 1 compared to CTAB, which is also a single-headed surfactant. Furthermore for the surfactant h ) 1, a second break is observed at g0.8 mM, which is caused due to a postmicellar aggregation. This may be due to the presence of an ester linkage [-OC(O)-] between the headgroup and the hydrocarbon chain in h ) 1. Such (10) Jana P. K.; Moulik S. P. J. Phys. Chem. 1991, 95, 9525-9532 and references therein. (11) Ghosh, H. N.; Palit, D. K.; Sapre, A. V.; Ramarao, K. V. S.; Mittal, J. P. Chem. Phys. Lett. 1993, 203, 5-11. (12) Tanford, C.; Nozakk Y.; Rohde, M. F. J. Phys. Chem. 1977, 81, 1555-1560.

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Bhattacharya and Haldar

Figure 1. Specific conductance versus surfactant concentration at 312.5 K for surfactant solutions of (A) CTAB, (B) h ) 1, (C) h ) 2, and (D) h ) 3.

a linkage within the surfactant located at the micellar Stern layer region facilitates intermolecular association of the surfactants through dipole-induced dipolar interactions and therefore probably enhances its tendency to aggregate further. Indeed the existence of such intermolecular association in vesicular aggregates generated from cationic lipids possessing ester linkages at the hydrocarbon chain-headgroup connection has been demonstrated.13,14 Degree of Micellar Counterion Dissociation. The degree of micellar ionization, R can be estimated from the ratio of the slope of the lines above and below the breakpoints due to cmc in the conductivity vs concentration plots.15 With the increase in the number of headgroups, the R value increases from 0.36 for h ) 1 to 0.48 for h ) 2 and to 0.81 for h ) 3 (Table 1). When one considers the second break at ∼0.8 mM for h ) 1, the corresponding R value for this inflection is found to be 0.09, which is much lower than the R value obtained for the break at the cmc value of h ) 1 (0.36), CTAB (0.32), and h ) 2 (0.48). Such low R value also indicates that the second break in the conductivity plot for h ) 1 (not shown) is due to the formation of larger aggregates. Thus for micelles, the R value increases with the increase in the number of headgroups. This should be a consequence of greater hydration as the number of headgroups per surfactant is increased. Improved hydration at the headgroup level (13) Bhattacharya, S.; Haldar, S. Langmuir 1995, 11, 4748-4757. (14) Moss, R. A.; Ganguli, S.; Okumura, Y.; Fujita, T. J. Am. Chem. Soc. 1990, 112, 6391-6392 and references therein. (15) Evans, H. C. J. Chem. Soc. 1956, 579-586.

Table 1. Micellar Parameters and the I3/I1 Ratio for the Multiheaded Cationic Surfactants (10 mM) at 40 °C systems

I3/I1 (λex 337 nm)a

cmc (cond.) (mM)

R

water CTAB h)1 h)2 h)3 n-hexane

0.61 0.86 0.91 0.82 0.80 1.48

1.06 ( 0.1 0.26 ( 0.2 (0.8)b 5.2 ( 0.1 5.9 ( 0.4

0.32 ( 0.02 0.36 ( 0.01 (0.09)b 0.48 ( 0.01 0.81 ( 0.02

a This is based on the ratio of the λ max of the vibronic peaks em due to pyrene (2 µM) in 10 mM micellar solution. b As mentioned in the text, for h ) 1, two breakpoints have been observed in the conductivity vs [h ) 1] plots. The values shown in parentheses indicate the R value at the second breakpoint in this plot, which is observed due to postmicellar association.

facilitates greater ionization. The counterion condensation on micellar interfaces is also dependent on the size of micelles. It is known that a larger micelle has greater tendency to attract counterions than a smaller micelle.16 SANS studies suggest that micelles with single-headed surfactant (h ) 1) are larger in size than their double- and triple-headed counterparts.3 Therefore, the degree of micellar ionization (R) increases progressively with the increase in the number of headgroups due to improved headgroup hydration and progressive decreases in the micellar sizes. Micropolarity. The ratio of emission intensities due to the third and the first vibronic peaks (I3/I1) obtained (16) Tsao, H. K. J. Phys. Chem. B 1998, 102, 10243-10247.

Micellation of Multiheaded Single-Chain Surfactants

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from pyrene solubilized in a given solvent is considered to be a good measure of solvent polarity (Figure 2A).8,17 For instance, this ratio has been found to vary from ca.1.48 in n-hexane to 0.61 in water at 40 °C (Table 1). The I3/I1 ratio in micelles was found to be within the extreme values obtained in the nonpolar solvent, n-hexane, and polar solvent, water. With the increase in the number of headgroups per surfactant in micellar solutions, the I3/I1 ratio decreased from 0.91 (h ) 1) to 0.8 (h ) 3) (Figure 2B). These results indicate that the micelles prepared from surfactants with multiple headgroups are more hydrated than their counterparts with a single headgroup and thus pyrene experiences more polar environment in multiheaded surfactant micelles. Thermodynamics of Micellization. The relationship between the cmc of a surfactant in solution and its free energy of micellization (∆Gm) has been derived for various surfactants by Zana.18 We adopted an analogous approach for the calculation of the free energy of micellization for the new multiheaded surfactants upon making modifications wherever appropriate. It has been assumed that for dilute surfactant solutions the activities are equal to the concentration of the surfactants and, in this situation, the intermicellar interactions may be considered to be insignificant. Consider a surfactant ion, SjiZs, where j is the number of alkyl chains and i is the number of charge groups possessing valency Zs (total charge iZs). If Zc is the valency of the counterion, CZc, then according to the principle of electroneutrality, the number of counterions per surfactant molecule would be

(1)

Figure 2. (A) Fluorescence emission spectra of 2 µM pyrene (λex 337 nm) at 40 °C in various media. (B) Variation of the micropolarity (b) and critical micellar concentration (O) for multiheaded surfactants.

Now if we consider that the micelle is made up of N surfactant ions and P counterions, then the process of micellization may be written as

energy of micellization may be expressed as per mole of surfactant. From eqs 3 and 4, the free energy of micellization can be written as

nc )

i|Zs| |Zc|

Mj,NNiZs-PZc + PCZc f Mj,NNiZs-PZc

(2)

where Mj,NNiZs-PZc refers to a micelle of aggregation number N, that contains Nj alkyl chains, and it possesses an electrical charge of NiZs - PZc. Generally in the absence of added salt, the sign of the micelle charge is the same as the sign of the surfactant ion, i.e., NiZs > PZc. The law of mass action is applied to the above process. If the concentrations of species involving the surfactant are expressed in moles of alkyl chain dm-3, the equilibrium constant K for the above reaction becomes

K)

[Mj,NNiZs-PZc]/jN ([SjiZs]/j)N[CZc]p

RT ln K jN

{

}

[Mj,NNiZs-PZc]/jN RT ln jN ([SjiZs]/j)N[CZc]p

(5)

The term [Mj,NNiZs-PZc]/jN is the molar micellar concentration, and this term is negligible compared to the other terms at concentration slightly above the micellar concentration. Therefore eq 5 can be rewritten as

{

}

[SjiZs] RT N ln + P ln[CZc] ∆Gm ) jN j

(6)

(3)

where [Mj,NNiZs-PZc]/jN is the molar micellar concentration, [CZc] is the molar concentration of counterion, and [SjiZs]/j is the molar concentration of the surfactant. The free energy of micellization, expressed in per moles of alkyl chain provides a convenient means for the comparison of results for various types of surfactants. This is given by

∆Gm ) -

∆Gm ) -

(4)

At critical micellar concentration, the electroneutrality of the system imposes the concentration

(ij)|Z |[S s

] ) |Zc|[CZc]

iZs

j

(7)

In addition, the fraction of charges (β) of micellized surfactant ions neutralized by micelle-bound counterions becomes

If surfactant consists of a single alkyl chain, then the free

β ) P|Zc|/Ni|Zs|

(17) Fendler, J. H. Membrane Mimetic Chemistry; Wiley: New York, 1982. (18) Zana, R. Langmuir 1996, 12, 1208-1211.

[CZc] from eq 7 and P from eq 8 can be inserted into eq 6, and by taking into account that [SjiZs] ≈ cmc, the following

(8)

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equation results, i.e.

∆Gm )

{

RT

| |}

i Zs 1 +β j j Zc

{| | | |

ln cmc + RT

}

i Zs i Zs 1 β ln - ln j j Zc j Zc j (9)

In the case of a single-headed surfactant, j ) 1, i ) 1, |Zs| ) 1, and |Zc| ) 1. Therefore the free energy of micellization will be

∆Gm ) RT(1 + β) ln cmc

(10)

In the case of a double-headed surfactant, j ) 1, i ) 2, |Zs| ) 1, and |Zc| ) 1, the free energy of micellization will be

∆Gm ) RT(1 + 2β) ln cmc + 2RTβ ln 2

(11)

For the triple-headed surfactant, j ) 1, i ) 3, |Zs| ) 1, and |Zc| ) 1, the free energy of micellization will be

∆Gm ) RT(1 + 3β) ln cmc + 3RTβ ln 3

(12)

The degree of micellar ionization (R) can be determined above and below the critical micellar concentration from the ratio of the slope of the conductivity versus concentration lines. It is related with β as

β)1-R

(13)

The entropy of micellization (∆Sm) can be evaluated by the Gibbs equation

∆Sm )

(∆Hm - ∆Gm) T

(14)

Calorimetry. Isothermal titration calorimetry was used to gain experimental information on the thermodynamics of micellization of different surfactants. To the sample cell containing water, a concentrated solution of a given surfactant, well above the cmc, was successively injected in small steps. The typical titration plots of the output of the microcalorimeter with individual surfactant solution are shown in Figures 3A, 4A, 5A, and 6A. The endothermic heats of dilution were observed with all the surfactant solutions under these experimental conditions. When the final concentration of surfactant in the calorimetric vessel is in the pemicellar region, the added micelles dissociate into monomers, and the monomers are further diluted. At concentrations above the cmc, the added micelles are only diluted. The calorimetric curves of the variation of the observed enthalpies of dilution (∆Hobs) with concentration of the surfactants are shown in Figures 3B-6B. The inflection points in the enthalpy of dilution vs concentration of surfactant curves (Figures 3C-6C) correspond to the cmc, and the difference between the observed enthalpies of the two linear segments of the plots gives a measure of the enthalpy of micellization.19-21 Each enthalpogram in Figures 3B-6B can be subdivided into three distinct surfactant concentration regions. The first region shows large reaction enthalpy upon the initial injections of the concentrated surfactant solutions. In this region the final concentrations in the sample cell remain (19) Bai, G.; Wang, J.; Yan, H.; Li, Z. Thomas, R. K. J. Phys. Chem. B 2001, 105, 3105-3108. (20) Majhi P. R.; Moulik, S. P. Langmuir 1998, 14, 3986-3990. (21) del Rı´o, J. M.; Prieto, G.; Sarmiento, F.; Mosquera V. Langmuir 1995, 11, 1511-1514.

Figure 3. Isothermal titration of CTAB solution at 312.5 K: (A) heat flow vs time; (B) enthalpy change per mole of CTAB vs [CTAB] (dotted line is the sigmoidal fitting); (C) different enthalpy change with respect to concentration vs [CTAB].

below the cmc, where large enthalpic effects are observed due to the dilution of micelles, the demicellization process, and the dilution of the resultant monomers. The second region, records a sharp decrease in the reaction enthalpy in the curve over a concentration range, which indicates the onset and completion of the micellization process. Finally the third region is observed, above the cmc, where the reaction enthalpies are less and remain almost constant because the added micelles are only injected to the cell where preformed micelles already exist. The curves for the variation of the observed enthalpies of dilution (∆Hobs) as a function of concentration of the surfactants (Figures 3B-6B) were subjected to sigmoidal fitting to find out the range where the cmc is reached. The cmc corresponds to the concentration where the first derivative of the sigmoidal fitting curve displays a


Figure 4. Isothermal titration of h ) 1 solution at 312.5 K: (A) heat flow vs time; (B) enthalpy change per mole of h ) 1 vs [h ) 1] (dotted line is the sigmoidal fitting); (C) differential enthalpy change with respect to concentration vs [h ) 1].

minimum (Figures 3C-6C). In the case of CTAB and h ) 2, sharp transitions at the cmc were observed (Figures 3 and 5). For h ) 3 however, a significantly broader transition region was observed around the cmc (Figure 6). It may be noted that although the minimum observed in Figure 6C is taken as the cmc for h ) 3, this is only approximate. This indicates that the aggregation occurs over a wide concentration range for h ) 3 which also suggests that the micelle formation is significantly less cooperative in this case. This is consistent with the fact that micelles are formed with much smaller aggregation number with surfactant h ) 3.3 This is understandable as the presence of more charged headgroups in the surfactant contributes to larger headgroup area and increases the repulsion between the surfactant monomers inside the micelle.

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Figure 4 presents the calorimetric titration curve and the variation of the observed enthalpies of dilution ∆Hobs (kJ mol-1) with concentration of the single-headed surfactant (h ) 1) at 312.56 K. Clearly the data for h ) 1 are somewhat different from the data of the other surfactants. It may be noted that the solubility of the single-headed surfactant (h ) 1) in water at room temperature is quite poor. For this reason, the experiments were performed at 312.5 K although the resulting solution appeared a little turbid even at this temperature. In fact SANS data on micellar solutions of these surfactants suggest that surfactant of h ) 1 forms larger aggregates especially at higher concentration. It may be possible that a small extent of phase separation during the ITC titration experiments results in the appearance of the noisy data. For this reason, this experiment was repeated several times and the

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Bhattacharya and Haldar Table 2. Thermodynamic Parametersa for the Micellization of Multiheaded Cationic Surfactants at 312.5 K surfactants

cmc (itc) (mM)

∆Hm (kJ mol-1)

∆Sm (J K-1 mol-1)

∆Gm (kJ mol-1)

CTAB h)1 h)2 h)3

1.3 ( 0.04 0.2 ( 0.05 5.5 ( 0.08 8.0 ( 0.3

-14.1 -15.7 -19.9 -15.0

48.0 68.4 18.7 9.6

-29.1 -37.1 -25.7 -18.0

a The error limits are ∆G ) (3%, ∆H ) (3%, and ∆S ) m m m (5%.


observation was found to be highly reproducible. Chromatographic analyses with the solution sample of h ) 1 confirmed that the noise was not caused by the surfactant decomposition under the experimental conditions. Instances are known where noisy ITC titration curves are observed with other surfactant micelles.20 It may also be noted that larger time intervals (1200 s) are necessary for h ) 1 between consecutive injection points during the calorimetric titration. Surfactants h ) 2, h ) 3, and CTAB on the other hand are highly soluble in water at ambient temperature, and the intervals between consecutive injections remain within 400-600 s for these surfactants. This suggests that the kinetics of demicellization is considerably slower for h ) 1 than the kinetics for the other surfactants.

The relevant cmc data as obtained from the ITC experiments with each surfactant solutions are presented in Table 2. It may be instructive to compare these with the cmc values obtained from conductivity measurements. Clearly the cmc values obtained for CTAB and h ) 2 agree quite well involving two entirely different experimental techniques. The cmc value (0.2 mM) obtained for h ) 1 by ITC is also in agreement with the value obtained from the conductivity experiment if one considers the first break at 0.26 mM in the conductivity vs [h ) 1] plot. In the case of h ) 3, the conductivity data suggest a cmc of ∼5.9 mM whereas the ITC data indicate that micellization occurs within a broad range from 3 to 12 mM. Since both experiments indicate that the micellization is least cooperative in this case, the cmc values are approximate. Nevertheless the values remain within a similar order of concentration. Overall the cmc values were found to increase with each increase in the number of headgroups per surfactant molecule (Figure 2B). Although the cmc was measured by both conductivity and ITC experiments, cmc derived from ITC has been used to calculate the thermodynamic properties. This is because in the calorimetric method, both the cmc and the enthalpy are obtained from a single run and is, therefore, more appropriate for calculation. In recent years, the availability of a high sensitivity microcalorimeter has made the determination accurate and authentic. It has been reported23 that the enthalpy of micellization (∆Hm) obtained by direct method of calorimetry in most cases appreciably differs from that calculated from the temperature effect on cmc using the van’t Hoff equation. The changing aggregation number, shapes, and the counterion binding of micelles are believed to influence the ∆Hm of the process, which are usually not rigorously considered in the data treatment by the van’t Hoff analysis. In the direct determination of the ∆Hm by calorimetry, the consequence of the above effects is, on the other hand, included in the measurement. The heat of solvationdesolvation of the species, their ionization, molecular rearrangements, mixing, etc. may contribute their shares toward the overall enthalpy change in the calorimetric measurements. Such contributions are normally absent in the equilibrium mass action concept of micellization where the van’t Hoff enthalpy is calculated by measuring cmc’s at different temperatures. The enthalpy of micellization (∆Hm) was obtained by subtracting the observed initial average enthalpy of the nonmicellar region from the final average enthalpy of the micellar region.19-21 The free energy of micellization (∆Gm) has been calculated from the cmc (obtained from ITC) and the degree of counterion association, β (obtained from conductivity studies using eq 13). For the calculation of ∆Gm values, eq 10 was used for CTAB and single-headed surfactant (h ) 1). Similarly for the double-headed surfactant (h ) 2) and for the triple-headed surfactant (h ) 3), eqs 11 and 12, respectively, were used for obtaining ∆Gm values. The entropy of micellization (∆Sm) was


obtained from the values of ∆Hm and ∆Gm using eq 14. The relevant data are summarized in Table 2. In all the cases, the enthalpy of micellization was found to be negative while the entropy of micellization was found to be positive. Therefore, the micellization process has been driven by both the loss in enthalpy and the increase in entropy. But overall micelle formation became increasingly less spontaneous as the number of headgroups on the surfactants increased. The enthalpy of micellization (∆Hm) for h ) 1 was -15.7 kJ mol-1, which increased to -19.9 kJ mol-1 for h ) 2 but decreased to -15.0 kJ mol-1 again for h ) 3. Stabilizing forces such as van der Waals and hydrophobic interactions make micelle formation favorable. Therefore the negative enthalpy of micellization is expected to increase as the total number of carbon atoms in the surfactant molecule increases.22,23 However, the repulsions between the headgroup charges dominate as one goes from h ) 1 to h ) 3 decreasing the negative enthalpy of micellization. Combination of these opposing factors determines the overall magnitude of the enthalpy of micellization. In the case of CTAB, under our experimental conditions ∆Hm was found to be -14.1 kJ mol-1. This is comparable with the reported value in the literature.24,25 This value for CTAB is lower than that of the surfactant with h ) 1 although both are single-head/single-chain systems. The presence of an ester linkage [-OC(O)-] between the headgroup and the hydrocarbon chain in h ) 1 might be responsible for this, which the CTAB molecule does not possess. The presence of an ester linkage may facilitate intermonomer association between the surfactant molecules in aggregate through dipole-induce dipole and hydrogen bonding interactions with interfacial water.13,14 This also explains why there is an increase in the negative value of ∆Hm. In the case of surfactant with h ) 2, two such ester linkages are present between the headgroup and the hydrocarbon chain. Therefore, the enthalpy of micellization of h ) 2 is even more negative than that of h ) 1 although the charge repulsion near the headgroup is more in the case of h ) 2 than that in h ) 1. With the increase in the number of headgroups in h ) 3, the Coulombic repulsion between the headgroups increases even further, and this suppresses the weak, noncovalent interactions among the surfactant monomers making the enthalpy of micellization less negative. The headgroup hydration increases with the increase in the number of headgroups. Under these circumstances more water molecules associate with surfactant molecules at the (22) Bai, G.; Yan H.; Thomas, R. K. Langmuir 2001, 17, 4501-4504. (23) Chatterjee, A.; Moulik, S. P.; Sanyal, S. K.; Mishra, B. K. Puri, P. M. J. Phys. Chem. B 2001, 105, 12823-12831. (24) Parades, S.; Tribout, M.; Sepulveda, L. J. Phys. Chem. 1984, 88, 1871-1875. (25) Bashford, M. T.; Woolley, E. M. J. Phys. Chem. 1985, 89, 31733179.

Langmuir, Vol. 20, No. 19, 2004 7947

chain-headgroup linker region leading to enhanced hydration of the micelle. This explains why ∆Hm is less negative for h ) 3 compared to its counterparts bearing a smaller number of headgroups. In the present study we find that the entropies of micellization (∆Sm) are positive for all the surfactants. This is consistent with the notion that during monomer to micelle formation ordered water molecules are excluded from the micellar interior, leading to an increase in entropy. However, ∆Sm values progressively decrease with the increase in the number of headgroups (Table 2). ∆Sm is 68.4 J K-1 mol-1 in the case of surfactant with h ) 1 whereas it is 18.7 and 9.6 J K-1 mol-1 for the surfactant with h ) 2 and h ) 3, respectively. In the case of singleheaded surfactant (h ) 1), more water molecules are excluded from the micellar interior when monomers aggregate to form micelles. This is because these surfactants, compared to their multicharged counterparts, need a fewer number of water molecules for hydration. As the number of headgroups increase per hydrocarbon chain, the hydrophilicity of the surfactant molecules increases. This in turn leads to greater hydration of the corresponding micelle. Therefore the propensity of release of water molecules on micellization becomes progressively less on increasing the number of headgroups of surfactants with h ) 1 to h ) 3. Indeed the micropolarity also increases with the increase in the number of headgroups in the surfactant. With the increase in the number of headgroups, the free energy of micellization (∆Gm) becomes less negative. ∆Gm for the surfactant with h ) 1 was found to be -37.1 kJ mol-1 whereas the same for h ) 2 and h ) 3 were -25.7 and -18.0 kJ mol-1, respectively. Therefore, the micelle formation becomes less spontaneous with the increase in the number of headgroups of the surfactant. In summary, we report a study on the thermodynamics of micellization of the multiheaded surfactants. The critical micellar concentrations (cmc’s) and the degrees of micellar ionization increase with the increase in the number of headgroups. The enthalpy of micellization is negative and the entropy of micellization is positive for every surfactant. Although the micelle formation is both an enthalpically and entropically favorable process, the overall changes in the free energy of micellization become progressively less negative with the increase in the number of headgroups. Therefore, the micelle formation becomes increasingly less favorable as more headgroups are attached to the surfactant. This suggests that further increase of the number of headgroups in single-chain surfactant might impede micelle formation. Acknowledgment. This work was supported by a grant from the Department of Biotechnology. LA0495433

Thermodynamics of Micellization of Multiheaded Single-Chain

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