Computational Study of the Structure and Behavior of Aqueous Mixed

17600

J. Phys. Chem. B 2006, 110, 17600-17606

Computational Study of the Structure and Behavior of Aqueous Mixed System Sodium Unsaturated Carboxylate-dodecyltrimethylammonium Bromide M. L. Ferreira,†,‡ M. B. Sierra,† M. A. Morini,† and P. C. Schulz*,† Departamento de Quı´mica, UniVersidad Nacional del Sur, Bahı´a Blanca, Argentina, and Planta Piloto de Ingenierı´a Quı´mica, UniVersidad Nacional del Sur, Bahı´a Blanca, Argentina ReceiVed: April 27, 2006; In Final Form: July 6, 2006

The mixed surfactant system sodium 10-undecenoate (SUD)-dodecyltrimethylammonium bromide (DTAB) was studied by computational simulation to determine the composition and structure of the mixed microstructures. Results were contrasted with experimental data obtained from literature and our own laboratory. The modelization predicts spherical or cylindrical micelles with a preferential composition of SUD-DTAB of about 1:2, while the system predicts a lamellar structure with a proportion of 1:1 when SUD is replaced by the saturated soap sodium undecanoate. The model also predicts the deep inclusion of bromide ions in the micelle Stern layer. All predictions were in agreement with previous experimental results.

Introduction Surfactant mixtures have numerous technical applications. When mixing surfactants, new properties are found, and in general, surfactant mixtures are not well-understood at the theoretical and fundamental level. Understanding the interplay of forces that govern the phase behavior is crucial to improve the surfactant mixtures and to develop new and more efficient ones in view of their uses. The main literature work has been devoted to the electrostatic interactions, but steric and hydrophobic/hydrophilic interactions are far away of being understood or described properly. Previous work in our laboratory indicated that the presence of a double bond in the alkyl chain of one component in a surfactant mixture gives rise to properties that were not contemplated in the current theories on mixed surfactant systems.1-4 Also, the presence of the double bond in the alkyl chain and its interaction with water explains the polymerization behavior in the different microstructures (micelles, lamellar or hexagonal mesophases) of polymerizable surfactants.5,6 The molecular mechanism that produces hydrophobicity is one of the most important that determines the thermodynamic stability of globular proteins, micelles, and biological membranes. Hydrophobicity is usually measured by the Gibbs energy change upon transferring a nonpolar solute molecule from a nonaqueous solvent to water.7 The hydration Gibbs energy change is large and positive for aliphatic hydrocarbons but negative for aromatic ones. In the case of the hydration of aliphatic hydrocarbons, the enthalpy and entropy of solvent reorganization largely compensate each other so that the free energy change due to solvent reorganization is small.7,8 When the solute molecule is polar and can form hydrogen bonds with the water molecules in the hydration shell, these hydration water molecules form less hydrogen bonds with bulk water molecules. Therefore, the solvent-solvent interaction energy increases substantially even when the binding energy * To whom correspondence should be addressed. E-mail: pschulz@ criba.edu.ar. † Departamento de Quı´mica, Universidad Nacional del Sur. ‡ Planta Piloto de Ingenierı´a Quı´mica, Universidad Nacional del Sur.

of each solvent molecule remains largely unchanged. The entropy of solvent reorganization is comparable in magnitude to the change in the total binding energy of the solvent molecules and not to the change in the solvent-solvent interaction energy alone. There are relatively few theoretical studies on the interaction of water with aromatic compounds, unsaturated compounds, and fatty acids or their salts in surfactant microstructures. Even for benzene, there is actually controversy about the nature of these interactions with water. The Lee group has performed several studies on this topic.7,8 These authors studied the nature of the π-H interaction in the ethene-H2O, benzene-H2O, and benzene-(H2O)2 complexes using large basis sets (ranging from 6-31 + G* to TZ2P++) and high levels of theory. The minimum geometries and the vibrational frequencies of all the complexes have been obtained at the second-order MollerPlesset MP2 level of theory. The analysis demonstrated that the repulsive exchange energies play a crucial role in governing the energies and geometric preferences of these complexes. Dispersion energies have an important role in describing the π-H bond. Mixing of σ-H and π-H bonds has been found in the theoretical study of the benzene dimer. Therefore, the task of modeling these interactions is not easy because of the lack of an adequate potential surface.8 Studies using molecular dynamics of the benzene hydration have shown that water molecules bind strongly in a hydrogen-bonding orientation at the planar faces of the benzene ring. The high-resolution map of the water structure surrounding benzene and cyclohexane revealed details of the positional preferences of water not resolved by other methods. The faces of benzene are very different due to the localized negative charge; each face acts as a hydrogen-bonding acceptor for a water molecule, greatly enhancing the benzene solubility in water.9 Other work on the interaction of a water dimer with π-systems established two different properties: the stretching and bending frequencies of the π-system are quite accurate indicators of the nature of interaction prevailing between water dimers ((H2O)2) and the π-system. The intermolecular van der Waals mode proved to be quite useful in mimicking the binding energies of the dimer with the π-system.10

10.1021/jp062599g CCC: $33.50 © 2006 American Chemical Society Published on Web 08/11/2006

Carboxylate-dodecyltrimethylammonium Bromide Molecular dynamics simulations on micelles have been performed on ionic surfactant systems, but the systems have not been large enough nor have they been studied in very long time scales. Investigations on the behavior of the larger ionic surfactant sodium dodecyl sulfate (SDS) have been performed.11,12 Studies in the course of a 5 ns molecular dynamics simulation have determined that a micelle composed of 60 SDS monomers and 7579 molecules of water is stable. The micelle is not completely spherical but has ellipsoidal components. The surfactant monomers are not all perfectly arranged around the center of the micelle. The liquid state of the interior of the micelle allows torsional motion to assist the tails in orientating themselves in a variety of directions toward and away from the hydrocarbon core while they remain generally associated with the other tails. The average radius of the micelle was 2.2 nm.13 Hydrophobic hydration is being studied more and more.14 In the same sense, carboxylic acid salts as part of surfactant systems are being analyzed more and more.15 The authors evaluated the adequacy of two methodological approaches to study complex liquids by means of computer simulations. They conclude that there are many other features that also should be evaluated to validate the simulation protocols. Structural and dynamical information derived from reliable simulation models are complementary to the experimental data since they provide a detailed description at time and distance intervals that cannot be experimentally reached. They also included ab initio results from interaction with the sodium-water and sodium-propanoate dimers. However, the only parameters that they calculated were the energy minimum and the profile/shape of the potential energy of interactions at the dimer level. Therefore, this situation is expected to be different than the study of systems formed by several molecules. The present paper focused on van der Waals and nonbonding interactions, and in this sense, ab initio results are not considered because quantitative results are not expected to be obtained. To obtain a better knowledge of our experimental findings, we performed computational modeling of the structure of mixed micelles having one component with a double bond in the alkyl chain. Since much of our experimental information was obtained on the aqueous catanionic mixture sodium 10-undecenoate (SUD)-dodecyltrimethylammonium bromide (DTAB), we have modeled this system using molecular mechanics (MM2) and a semiempirical method (PM3). To determine the effect of the presence of water on the structure of aggregates, the mixtures were modeled both with and without water. The effect of the double bond in the DTAB-SUD system is compared with the interactions in the DTAB-sodium undecanoate (SUDECA) system. To analyze the kind of interactions that take place here (mainly van der Waals and noncovalent interactions), high-level methods such as DFT were not adequate. They are especially suitable to reactions, where new bonds are formed, but they do not adequately represent the nonbonding interactions, especially when a high number of atoms is consideredsor must besto analyze certain properties, such as in this case. For DFT to become the method of choice for applications such as are proposed here, improvements in both scaling behavior and precision are required, so that they will stay competitive as compared to wave function methods.

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17601 electrostatic and van der Waals terms with the fifth order polynomial switching function, automatic π-system calculations when necessary, and torsional and nonbonded constraints. PM3 is the other method used in this work. This method provides the standard enthalpy of formation ∆Hf° based on a semiempirical approach to the solution of the Hamiltonian. Although it is true that a micellar system is very complex, the study of the interaction at the micelle-water interface can be separated in several parts. Local interactions are always important to understand the nature of the bonding, and these can be studied by MM2 semiempirical and ab initio theory levels with different degrees of complexity and application, depending on the consideration or not of the solvent. Global interactions must be considered in analyzing the effect of thousands of water molecules. However, all the interactions are conditioned by the addition of the pairwise interactions at short and long ranges. Results are commonly affected by initial structures of the modeling. Therefore, a local interaction must first be understood to give a coherent initial structure for the modeling of very large structures. These situations applied to different levels of complexity are reported in refs 16-18. By studying small models, different trends at local interactions can be obtained. By increasing the size of the modelswith a higher number of moleculessthe effect of the size can be also addressed. But, the local interactions are very useful to plan a strategy to introduce a first guess for the simulation and to understand general trends found at certain conditions. With this aim, the theoretical method was first applied to different systems. First, only terminal olefins were considered: ethylene, propylene, and 1-butene interacting with one to three water dimers. Then, 2-butene (cis and trans) was analyzed. Long alkenes and selected unsaturated carboxylic acids were also analyzed for their interaction with water. The comparisons presented in this work include the full structures of sodium undecenoate (SUD)-dodecyltrimethylammonium bromide (DTAB), far away from each other or in different conformations of interactions, resembling the possible structures that can be found in micelles and other microstructures in diluted aqueous solutions. The configurations were analyzed by being dry or in contact with water. We also made comparisons between the role and the energy of hydrogen bonding in the interaction of unsaturated hydrocarbons with water and fatty acids/surfactants including counterions with water. PM3 mainly takes into account the electronic effects instead of steric effects, whereas in the MM2, the steric interactions were considered. Using the same atom number and under certain constraints (that are the more important topic of the calculation in terms of limitations), the method is sensitive enough to give values that can be compared qualitatively with experimental ones. Some possible conformations that fit with experimental work (ours and from other authors) in which we based the models were evaluated, and results are in agreement with them. Consequently, the models used here are not the unique possible ones, but they were selected taking into account the available experimental evidence. Different geometries of the micelle (rectangular or spherical) were chosen to analyze, considering the proportion of both components needed to obtain different local structures and interactions. The amount of available experimental results is enough to design a complete modeling study.

Theoretical Methods The program Chem 3D (from Cambridge Soft, version 5.0) uses a modified version of the Allinger MM2 force field. The principal addition to Allinger’s MM2 force field is a chargedipole interaction term, a quartic stretching term, cutoffs for

Experimental Procedures The system SUD-DTAB was extensively studied in our laboratory, and the following information was obtained. The system did not precipitate, even at the 1:1 proportion, but

17602 J. Phys. Chem. B, Vol. 110, No. 35, 2006 showed the formation of a coacervate in a range of surfactant mixture compositions. Micelles have a preferential composition of a 0.35 mol fraction of SUD. Structural computations demonstrate that the mentioned proportion produces the total coverage of the hydrocarbon/water interface of the mixed micelles by the terminal double bonds of the undecenoate tails.3 The formation of the coacervate was also studied and explained on the basis of the packing parameter computed by that of DTAB and that of a SUD molecule folded to expose the vinyl group to water, which gives a curvature that impedes the formation of planar structures even when the ζ-potential at the surface of aggregates approaches zero.19 The presence of the double bond in the SUD molecule produces an unusual nonideality in the partial molar volume behavior of the mixed SUD-DTAB micelles, and the phenomenon was explained on the basis of the energy of interaction between the π-electrons of the double bond and water.4 The difference in polymerization yields of SUD mesophases when initiated by water soluble initiators (34.5% in hexagonal mesophase, 19% in lamellar liquid crystal20) and by γ-irradiation (83% in hexagonal and 60 in lamellar21) was explained on the basis of the vinyl groups exposed to the initiator: the water soluble initiator can only promote the polymerization of the double bonds exposed to water, while the γ-radiation can also initiate the polymerization of the double bonds inside the liquid crystal structure.21 Unpublished results on SUD-sodium dodecanoate (SDD) mixed micelles indicate that there is a preferential proportion of about 0.36-0.4 mol fraction of SUD in micelles, and the interaction is strongly attractive, with an interaction parameter of βM ) -4.22 kBT, while the value must be zero if the interactions were ideal. The mixed micelles were also more ionized than the pure component micelles. In the paper now in redaction, these facts are also explained by the water-vinyl interaction. Also, the aggregation of sodium oleate (SOL)-hexadecyltrimethylammonium bromide (CTAB) was studied.1 The system did not precipitate, even at the 1:1 proportion. Spherical micelles formed at the CMC, having a preferential proportion SOLCTAB 1:3. Using a mixed micelle model, this proportion was explained on the basis of replacing the saturated hydrocarbonwater contact at the micelle/water interface by the oleate double bond-water contact. The mixed system SOL-sodium dehydrocholate (SDHC)2 also showed behavior that can be explained by the tendency of the double bond at the middle of the oleate chain to remain in contact with water. Micelles showed a strong attraction between the two surfactants and a preferential composition of 1:1, while the two components repelled each other at the air-water surface. Results and Discussion Interaction Between Unsaturated Hydrocarbon-Water. Table 1 presents the results of calculations performed on the interaction between water and unsaturated hydrocarbons of different lengths and also fatty acids. The length of the hydrocarbon and the location of the double bond (internal or terminal) influence the results. When comparing ethylene with propylene and 1-butene, it is evident that the length of the chain and the number of hydrocarbons interacting with water are important. The cis-2-butene/water dimer interaction presents a far lower formation enthalpy than in the case of 1-butene and trans-2-butene. It is clear that the interactions are more important in terms of electronic interaction because they are stronger when the minimization is done using procedure 2 (MM2 minimization

Ferreira et al. TABLE 1: Enthalpy of Formation (kJ/mol) of Interactions of Water-Hydrocarbon Using Different Proceduresa configuration

(1) MM2 + (PM3)

(2) PM3

water dimer Ethylene water dimer-ethylene water dimer-2-ethylene water dimer-3-ethylene Propylene water dimer-propylene water dimer-2-propylene water dimer-3-propylene 1-butene water dimer-1-butene water dimer-2,1-butene water dimer-3,1-butene cis-2-butene water dimer-1-cis-2-butene water dimer-2-cis-2-butene water dimer-3-cis-2-butene trans-2-butene water dimer-1-trans-2-butene water dimer-2-trans-2-butene water dimer-3-trans-2-butene

-443.1 70.7 -367.7 (+4.6) -1230.5 (+12.1) -223.8 (-0.4) 28.1 -409.6 (+5.4) -382.2 (+4.01) -352.3 (+6.44) 8.78 -429.3 (+5.0) -425.5 (-0.42) -418.4 (-2.1) -8.8 -444.3 (+7.5) -462.3 (-1.7) -444.9 (24.6) -13.6 -452.3 (+2.3) -461.5 (+8.8) -475.3 (+8.58)

-473.2 69.5 -401.2 (+2.9) -346.9 (-15.1) -280.7 (-3.3) 26.8 -444.8 (+1.7) -429.3 (-9.6) -420.2 (-27.3) 5.9 -465.3 (+2.1) -482.0 (-20.5) -450.0 (-44.4) -15.1 -480.7 (+7.5) -515.9 (-12.5) -544.3 (-25.9) -16.0 -486.6 (+0.92) -528.4 (-25.5) -566.7 (-45.6)

a (1) MM2 minimization and PM3 at the obtained minimum. (2) MM2 minimization and PM3 minimization in sequence. Notation: water dimer-n organic molecule means that one water dimer interacts with n organic molecules. The difference between the enthalpy of formation and the sum of the formation enthalpies of the separate components is shown between parentheses.

Figure 1. Configuration 1, dry 1:1 SUD-DTAB complex.

and PM3 minimization in sequence). Moreover, the net effect would be a steric repulsion, but increasing the amount of water there is a decrease of this repulsion and a more efficient H-bonding with the double bond. The lowest value obtained for the interaction is near -46 kJ/mol, which is very close to the values commonly obtained for H-bonding. Interactions of SUD-DTAB With and Without Water. When the SUD-DTAB systems were analyzed, different configurations were studied. To clarify the discussion, the sodium undecanoate (SUDECA)-DATB system was analyzed at selected configurations. Configuration 1. In this configuration, the soap molecule is folded to include the double bond at the polar layer (see Figure 1). This configuration was analyzed both in dry form and in contact with water. (a) Without Water. Figure 1 shows the configuration of the mixed system 1:1 SUD-DTAB without water, considering that

Carboxylate-dodecyltrimethylammonium Bromide

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17603 TABLE 2: Results of MM2 Computation of Steric Energy (SE) and PM3 Calculation of Enthalpy of Formation (∆Hf) for Dry System SUD-DTABa complex

SE (MM2)

∆Hf (PM3)

sodium 10-undecenoate (SUD) dodecyltrimethylammonium (DTAB) 1:1 SUD-DTAB

-405.0 -147.9 -639.36 (-86.46) -814.2 (-113.4) -1490.6 (-236.9) -1648.7 (-247.1)

-774.9 -186.2 -1087.2 (-126.4) -1238.6 (-91.2) -2424.6 (-316.3) -2590.7 (-296.2)

1:2 SUD-DTAB Figure 2. Configuration 1, dry 1:2 SUD-DTAB complex.

2:3 SUD-DTAB 2:4 SUD-DTAB

a Results are in kJ/mol. The difference between SUD and DTAB separated molecules and joined in configuration 1 is shown in parenthesis.

Figure 3. Configuration 1, dry 2:4 SUD-DTAB complex, showing the deep inclusion of bromide ions in the polar layer.

the double bond of SUD is included in the polar layer, and therefore, the SUD molecule occupies more polar surface than only the carboxylate head. The contribution of the DTAB to stabilize this terminal olefinic double bond is considered, being then two different DTAB molecules per one SUD. Figure 2 shows the position of a second DTAB near the double bond of the SUD, and Figure 3 shows the position of a 4:2 DTABSUD complex. From the last two figures, it is clear how the counterion has changed the position as a simple counter balance to interact with the chains of the surfactant (see the arrow and compare the position of bromide in Figures 2 and 3). The presence of the second surfactant molecule makes the position of the bromide arising from the first DTAB molecule more favorable between chains, balancing positive charges, whereas the second bromide ion and the sodium one from SUD interact with the co-coordination of the negative charge on the carboxylate (see the circle in Figure 3). This arrangement provides an additional stabilization and probably generates a different distribution of the charge with a simple one to one counterion interaction. In a recent work,19 we have found that the measured ζ-potential of the SUD-DTAB mixtures is systematically more negative than the expected on the basis of the micelle composition, which was explained on the supposition that bromide ions are captured by micelles, even if they have an excess of SUD. This finding is in agreement with the computational results in this work. Table 2 summarizes the results for the formation enthalpy of the different arrangements without water. As can be seen from the ∆Hf (PM3) values, the more stable combination is the dry conformation SUD-DTAB 2:4. Much of the prior work on micelles has been focused on simulations that are less than 200 ps and without water.22,23 In addition, these studies have considered only few monomers and molecules, and only limited studies were performed.24-27 Our work is focused to equilibrium systems having several molecules.

Figure 4. (a) Configuration 1-1:1 SUD-DTAB complex with a water monolayer in contact with the polar layer and (b) configuration 1 of the 1:2 SUD-DTAB complex in contact with a water monolayer.

(b) With Water. To determine the effect of water on the stability of the SUD-DTAB mixtures, a monolayer of water molecules was added to the original configuration 1:1 and 1:2 SUD-DTAB. Figure 4a,b shows the distribution of these water molecules. Table 3 shows the results of MM2 and PM3 calculations applied to these combinations of SUD-DTAB. It is clear that the 1:2 conformation is the most stable, although the difference with the proportion 1:1 is small. When the conformation 1:2 of the wet SUDECA-DTAB system is analyzed in the presence of 11 water molecules, the difference in formation enthalpy is near 126 kJ/mol favoring SUD (∆Hf ) -293 kJ/mol for SUDECA vs -463.6 kJ/mol for SUD). The unique difference is the lack of the terminal double bond in SUDECA. Figure 5 shows the possible organization of SUD and DTAB molecules in a model of a spherical micelle that by rotation on an axis generates the total micelle (note that the structure is

17604 J. Phys. Chem. B, Vol. 110, No. 35, 2006

Ferreira et al.

TABLE 3: Results of MM2 (Steric Energy SE) and PM3 Calculation (Enthalpy of Formation ∆Hf) for the System SUD-DTAB With Watera complex

SE

∆Hf (PM3)

sodium undecenoate-SUD dodecyltrimethylammonium DTAB conformation 1:1 SUD-DTAB with eight water molecules conformation 1:2 SUD-DTAB with 11 water molecules conformation 2:4 SUD-DTAB with 11 water molecules

-405.0 -147.9 -975.54 (-422.64 ) -1272.8 (-572.0) -2649.8 (-1248.2 )

-774.9 -186.2 -3138.0 (-399.6) -4054.7 (-463.6) -2694.1 (-399.5)

a Difference between SUD-DTAB molecules separated and in configuration 1 with water molecules is shown in parentheses. All results are in kJ/mol.

Figure 6. Lamellar micelle model having SUD-DTAB 1:2 proportion in configuration 1 and in contact with water. See the deep inclusion of bromide ions in the Stern layer.

Figure 5. Spherical micelle model having SUD-DTAB of 1:2 proportion in configuration 1 and in contact with water. Total molecular SUD-DTAB relation for the view was 12:24.

also compatible with a cylindrical micelle). The diameter of this micelle resulted between 5 and 4.4 nm, which is very close to the 4.4 nm reported in a previous work3. In that paper, we have found that the SUD-DTAB mixed micelles have a composition ranging from XSUD ) 0.33 to 0.5 (XSUD being the mol fraction of SUD in the SUD-DTAB mixed micelle, without considering water). We also found that the interaction parameter βM in the mixed micelle has a minimum at the composition XSUD ) 0.37 with βM ) -6.15kBT (where kB is the Boltzmann constant and T the absolute temperature). The βM value was -5.61kBT for XSUD ) 0.33 (i.e., the difference is not very high). In the same paper, we obtained a preferential composition XSUD ) 0.39 from geometrical considerations using a micelle model similar to that of Figure 5. Taking into account the approximations made in the geometrical and in the present computations, it may be concluded that the three methods give essentially the same result. Figure 6 shows a wet lamellar structure with a configuration 1 and a 1:2 proportion. The spherical and lamellar models show different energies. The dry spherical structure has ∆Hf ) -4748 kJ/mol, whereas the dry lamellar structure has ∆Hf ) -5167 kJ/mol (i.e., the lamellar structure is more stable in the absence of water). When water is added to the model, the enthalpies are -8036.6 and -6962 kJ/mol, respectively (i.e., water makes the spherical structure more stable than the lamellar one). The

Figure 7. System 1:2 SUD-DTAB with configuration 2 in contact with a water monolayer.

wet spherical structure has a diameter between 4.4 and 5 nm, while in the lamellar arrangement, the width is near 7 nm. The deep inclusion of some bromide ions into the microstructure Stern layer can also be seen. In a recent work,19 transmission electronic microphotographies of the aggregates formed in the aqueous SUD-DTAB system by the negative staining method with uranyl acetate have shown spherical, globular, and cylindrical forms, but not lamellar microstructures, in agreement with the previous conclusions. Configuration 2. This configuration shows the polar headgroups at the polar surface, but the SUD double bond is inside the hydrocarbon core of the microstructure, as in the systems that do not have secondary hydrophilic groups (Figure 7). (a) Systems Without Water. It is clear from the MM2 calculation on the 1:1 SUD-DTAB system that the polar COOgroup interacts with the N(CH3)3+. To test the difference between different conformations, we included the interactions of SUDECA with DTAB in this configuration. Results are shown in Table 4. It is well evident that in this case, there is not a preferential composition of aggregates that stabilizes the

Carboxylate-dodecyltrimethylammonium Bromide

J. Phys. Chem. B, Vol. 110, No. 35, 2006 17605

TABLE 4: MM2 and PM3 Results of Calculation for Configuration 2 Without Watera complex

∆Hf (PM3)

SE

sodium undecenoate (SUD) -405.0 sodium undecanoate (SUDECA) dodecyltrimethylammonium bromide (DTAB) -147.9 SUD-DTAB 1:1 -622.7 (-365.6) SUDECA-DTAB 1:1 -904.5 (-206.7) -1366.5 (-260.7)

SUD-DTAB 1:2 SUD-DTAB 2:2 SUDECA-DTAB 2:2

-2097.0 (-438.3) -2825.5 (-613.9)

SUD-DTAB 3:3 SUD-DTAB 4:4

-774.9 -897.0 -186.2 -997.7 (-36.7) -1224.2 (-141.8) -1363.1 (-215.9) -2135.5 (-213) -2476.1 (-309) -3263.9 (-381)

SE ) steric energy and ∆Hf ) enthalpy of formation (PM3). Difference between SUD and DTAB molecules separated and in configuration 2 is shown. All results in kJ/mol.

complex

Watera

SE

TABLE 6: Configurations 1 and 2 With and Without Watera Connolly accessible area (Å2)

Connolly molecular area (Å2)

Connolly solvent excluded volume (Å3)

1:2 (XSUD ) 0.33) with water

7655.9

5750.3

1:2 (XSUD ) 0.33) without water 1:1 (XSUD ) 0.5) without water

6706.4

4883.4

6795 (260.6 cm3 mol-1 ) 432.7 Å3) 5759.6

6801.7

5016.2

structure

a

TABLE 5: Interaction of Configuration 2 With

Figure 8. Dry spherical and lamellar structures of configuration 2, 1:1 SUD-DTAB complex.

∆Hf (PM3)

sodium undecenoate (SUD) -405.0 dodecyltrimethylammonium bromide (DTAB) -147.9 SUD-DTAB 1:1 with six water molecules -885.8 (-625.9) SUDECA-DTAB 1:1 with six water molecules

-774.9 -186.2 -2384.5 (-90.4) -2612.5 (-203.8) SUD-DTAB 1:2 with eight water molecules -1209.6 -3227.5 (-508.8) (-302.9) SUD-DTAB 2:2 with 12 water molecules -1897.3 -4877.7 (-791.5) (-389.5) SUDECA-DTAB 2:2 with 12 water molecules -5245.9 (-428.4)

a SE ) steric energy and ∆Hf ) enthalpy of formation (PM3). Difference between SUD-DTAB molecules separated and in configuration 1 with water molecules is shown between parentheses. All results are in kJ/mol.

microstructure. The enthalpy of formation increases monotonically when the aggregate size increases in the proportion 1:1. This reflects the formation of a mixed crystal in both SUDDTAB and SUDECA-DTAB systems. (b) Systems With Water. Table 5 shows the computation results in systems showing configuration 2 and the polar headgroup layer in contact with water. Computational results show that the behavior of the SUD-DTAB and SUDECA-DTAB systems with configuration 2, in contact with water, does not show substantial differences. In the absence of a waterπ-electron interaction, both soap-cationic surfactant systems favor the formation of a 1:1 mixture whose formation enthalpy increases monotonically with the size of aggregates (i.e, the formation of a lamellar liquid crystal or a crystalline precipitate is favored at this proportion). Figure 8 shows the spherical and lamellar dry models of microstructures with configuration 2 and proportion 1:1. The width of the lamellar form is near 3.5 nm, whereas the diameter of the sphere is between 4.4 and 5 nm. The lamellar structure is more stable than the sphere (∆Hf ) -7545 kJ/mol for the

a

5899.97 (241.7 cm3 mol-1 ) 401.3 Å3)

Partial molar volume from ref 4 is shown in parentheses.

lamellar vs -7102 kJ/mol for the spherical structure). The central void in the representation of the spherical micelles is an artifact of the representation procedure. Using dodecyl sulfate, the micelles’ size is similar to that reported here.28,29 The surface area of the micelle is nearly 2 times that of a sphere due to its surface roughness. An additional contribution to surface area is also due to the fact that the micelle is not completely spherical but ellipsoidal. The nonspherical nature of the micelle contributes to the increased surface area. Area of Molecules and Water Excluded Volumes. Table 6 shows the computed Connolly areas and solvent excluded volumes of the dry and wet 1:1 proportion in configuration 1 and the dry 1:1 proportion in configuration 2. The value of the experimental partial molar volumes obtained from ref 4 is also shown between parentheses. It can be seen that there is a certain correlation between the experimental partial molar volumes and the water excluded volumes. Since the partial molar volume is not the true volume of the solute molecules, it is not expected that both properties be equal (except for ideal mixtures, which is not the case in the studied system4), but the general trends must be the same. Conclusion The calculation results from MM2 and PM3 demonstrate that the role of water is crucial to understand the composition and structure of the mixed micelles with one component having π-electrons. In the case of configuration 1, when no water is included, the SUD-DTAB 1:1 complex (XSUD ) 0.5) is the more stable in the case of configuration 1, but when water is included, the SUD-DTAB 1:2 complex (XSUD ) 0.33-0.4) is the more stable proportion, which coincides with the experimental findings in previous work. In the case of configuration 2, the 1:1 proportion is the more stable both in dry and in wet systems. This favors the formation of lamellar mesophases or crystals.

17606 J. Phys. Chem. B, Vol. 110, No. 35, 2006 The presence of water in configuration 1 clearly stabilizes the SUD-DTAB 1:2 complex, in about 126-146 kJ/mol (compare Tables 2 and 4). Previous work3 has shown that there is a preferential composition of about XSUD ≈ 0.37 (from the intramicellar energy of interaction) or 0.39 (from geometrical considerations). Taking into account the different approximations made, it may be concluded that the three methods essentially give the same result.19 The molar relation can be explained by the molecular model discussed here. The modeling also has shown that some bromide ions are deeply included in the micelle Stern layer, which is coherent with experimental ζ-potential results reported by our group. Finally, the computed solvent excluded volumes are coherent with the partial molar volumes reported in a previous work. Acknowledgment. This work was financed by a grant from the Universidad Nacional del Sur. M.A.M. and M.L.F. are adjunct researchers of the Concejo Nacional de Investigaciones Cientı´ficas y Te´cnicas de la Repu´blica Argentina (CONICET). M.B.S. has a fellowship of the Comisio´n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires (CIC). References and Notes (1) El-Kadi, N.; Martins, F.; Clausse, D.; Schulz, P. C. Colloid Polym. Sci. 2003, 281, 353-362. (2) Messina, P.; Morini, M. A.; Schulz, P. C. Colloid Polym. Sci. 2003, 281 (11), 1082-1091. (3) Sierra, M. B.; Morini, M. A.; Schulz, P. C. Colloid Polym. Sci. 2003, 282 (6), 633-641. (4) Sierra, M. B.; Morini, M. A.; Schulz, P. C.; Ferreira, M. L. Colloid Polym. Sci. 2005, 283, 1016-1024. (5) Rodrı´guez, J. L.; Schulz, P. C.; Pieroni, O.; Vuano, B. Colloid Polym. Sci. 2004, 282 (7), 734-739. (6) Rodrı´guez, J. L.; Soltero, J. F. A.; Puig, J. E.; Schulz, P. C.; Espinoza-Martı´nez, M. L.; Pieroni, O. Colloid Polym. Sci. 1999, 277, 12151219.

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