Atomic-Level Molecular Modeling of AOT Reverse Micelles. 1. The AOT Molecule in Water and Carbon Tetrachloride

Atomic-Level Molecular Modeling of AOT Reverse Micelles.1. The AOT Molecule in Water and Carbon Tetrachloride

Bela Derecskei,† Agnes Derecskei-Kovacs,‡ and Z. A. Schelly*,†

Center for Colloidal and Interfacial Dynamics, Department of Chemistry and Biochemistry,University of Texas at Arlington, Arlington, Texas 76019-0065, and the Laboratory of

Molecular Simulation, Department of Chemistry, Texas A&M University,College Station, Texas 77843-3255

Received April 10, 1998. In Final Form: August 21, 1998

The anionic surfactant bis(2-ethylhexyl) sodium sulfosuccinate (Aerosol OT or AOT) is studied by atomic-level molecular modeling, using the second-generation ESFF (extensible systematic force field). Thegeometries of seven representative conformers are analyzed. The energies of these conformers correspondto those of the most probable ones based on random-sampling statistics and differ by, at most, 10 kcal/mol.Thus, these conformers should be available for the system under typical ambient conditions. Interactionswith water and carbon tetrachloride modify the geometries only to a modest extent. The solvation by wateris found to be exoergic, and the analysis of individual AOT-water interactions identified four stronglybound water molecules (with >10 kcal/mol of interaction energy), in accordance with experimental results.A CCl4 box was generated for the investigation of the effects of carbon tetrachloride as a solvent. A truncated-cone-geometry model of the AOT molecule yields 14.5 as the estimated aggregation number N of AOTreverse micelles in CCl4, in good agreement with the experimental value of the mean aggregation, ⟨n⟩ )15-17, of the solution. The predicted diameter of the dry reverse micelles d ) 2.8 nm is comparable withthe experimental apparent hydrodynamic diameter, ⟨Dh⟩ ) 3.2 nm (at wo ) 0.8).

IntroductionOrganized assemblies have generated considerable

interest not only within the boundaries of traditionalcolloid chemistry but in analytical, synthetic, and me-dicinal chemistry as well. Compartmentalized and guest-host systems such as aqueous and reverse micelles,microemulsions, cyclodextrins, vesicles, and liposomeshave improved the performance of numerous analyticaland separation methods and have opened entirely novelstrategies for synthetic methods and drug-delivery sys-tems. Major questions related to such applications concernthe structure, size (mainly of the interior compartment),and surfactant-aggregation number of the particularvehicle. At the present stage of computational methods,molecular modeling may complement and augment theexperimental efforts aimed at selecting the suitableamphiphile and estimating the relevant parameters of itsaggregates. To examine this capacity, we chose thecommonly used anionic surfactant, bis(2-ethylhexyl) so-dium sulfosuccinate (Aerosol OT or AOT) as a test system.The advantages of AOT are that it forms normal as wellas reverse micelles and that its typical aggregation numberis conveniently low from a computational point of view(10-60, depending on the solvent and possible othercomponents present). The choice of carbon tetrachlorideas the solvent was prompted by its symmetry, by ourprevious experience of its favorable optical properties inthermal lens1 and laserE-jumpstudiesof reversemicelles,2and by the small number of atoms in the molecule. Therelatively moderate size of the aggregates and solventmolecules allows atomic-level modeling instead of the useof lower level approximations for the description of thesurfactant molecule.3-6 The results of a series of suchtheoretical calculations are presented, and estimates for

the aggregation number and diameter of AOT/CCl4 reversemicelles are compared with experimental findings.

Commercially available program packages permit thegeneration and analysis of molecular information such asgeometry and energetics, as well as electronic, spectro-scopic, and bulk properties. They also provide 3-dimen-sional representation and visualization of the chemicalsystem studied. A wide variety of methods have beendeveloped and implemented. Ab initio methods have beensuccessfully utilized in the study of small- and middle-size systems (most often 20-30 atoms), yielding resultsat the level of experimental accuracy. In the study of largersystems (100-200 atoms), approximate methods (e.g.,semiempirical techniques) have been proven to be useful.However, chemical systems in the range of severalhundreds or thousands of atomsswhich is the case whendealing with drugs, biomolecules, polymers, aggregates,etc.srequire treatments involving further approximationsin the computation. One such treatment is molecularmechanics, which relies on the laws of classical physicsand on parameters derived from experimental data orresults of more accurate theoretical methods. Thesemethods utilize quantum mechanics only implicitly (forthe calculation of geometrical parameters, partial charges,etc.) in the development of methodology and not at all inthe direct applications. The calculations are computa-tionally very efficient. Even systems containing severalthousand atoms can be examined theoretically, but theresults for new systems must be validated since thecalculations rely on approximations.

Presently, we apply molecular modeling to the descrip-tion of AOT reverse micelles in carbon tetrachloride. The

† University of Texas at Arlington.‡ Texas A&M University.(1) Chen, H. M.; Schelly, Z. A. Chem. Phys. Lett. 1994, 224, 61.(2) Chen, H. M.; Schelly, Z. A. Langmuir 1995, 11, 758.

(3) Smit, B.; Hilbers, P. A. J.; Esselink, K. Int. J. Mod. Phys. C. 1993,4, 393.

(4) Esselink, K.; Hilbers, P. A. J.; van Os, N. M.; Smit, B.; Karaborni,S. Colloids Surf., A 1994, 91, 155.

(5) Karaborni, S.; Smit, B. Curr. Opin. Colloid Interface Sci. 1996,1, 411.

(6) Palmer, B. J.; Liu, J. Langmuir 1996, 12, 746.

1981Langmuir 1999, 15, 1981-1992

10.1021/la980419r CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 02/25/1999

dynamic process of micelle formation occurs on a timescale that is nowadays still prohibitive for theoreticalapproaches, unless one uses less than atomic-level de-scription of surfactant molecules.3-6 Therefore, we restrictourselves to molecular mechanics and conformationsearch. Although this approach does not yield certainthermodynamic data about the system (e.g., free energyor enthalpy), it does provide useful qualitative andquantitative information. At every possible step of themodeling process, results are compared to experimentaldata available. The present paper deals with one AOTmolecule and its interactions separately with water andwith carbon tetrachloride. Future studies will be directedtoward the description of the interaction of AOT moleculeswith each other in a vacuum, in water, in carbontetrachloride, and in reverse micelles with variable watercontent.

Experimental SectionThe surfactant bis(2-ethylhexyl) sodium sulfosuccinate (AOT)

was obtained in purum grade (>98%) from Fluka and furtherpurified by precipitation, titration, and drying as describedelsewhere.7-9 Reverse micellar solutions were prepared bydissolving the appropriate amount of AOT in CCl4 and solubilizingthe desired amount of water. The CCl4 was HPLC grade (watercontent <100 ppm, by Karl Fischer titration). The resultingtransparent, homogeneous solutions were characterized by theirsurfactant concentration and wo value (≡water/AOT molar ratio).The water was deionized and distilled. The apparent hydro-dynamic diameter Dh of the reverse micelles was determined bydynamic-light-scattering measurements using a Brookhaven BI-3010 AT instrument.

Hardware and Software. All calculations were performedby using the ESFF (extensible systematic force field) and UFF(universal force fields) developed by Molecular Simulations, Inc.10

The universal force field was applied in the conformer search,and ESFF was used for geometry optimizations and energyevaluation. The MSI Insight 95.0 and Cerius2 Version 3.0 softwarepackages were run on an SGI O2 workstation.

Results and Discussion

1. Atomic-Level Modeling of One AOT Moleculein Vacuum. The 3-dimensional shape and size of sur-factant molecules play a crucial role in their packing inthe aggregate and indirectly determine the aggregationnumber and diameter of the reverse micelle formed. Thelatter can be compared with the apparent hydrodynamicdiameter Dh obtained through dynamic-light-scattering

measurements. To establish the structure of likely con-formers of AOT, conformer search by random samplingwas performed on the molecule in a vacuum using theUFF of MSI within the Cerius2 environment. Details ofthe search are discussed in the Appendix. Seven repre-sentatives of the most probable conformers were chosenfor detailed analysis. The comparison of energies andgeometries was carried out in the Insight II environmentbecause of its ability to simulate solvent boxes. The sevenrepresentative structures were reoptimized using theESFF force field since UFF is not available in Insight.The reoptimization resulted only in modest changes ingeometries and relative energies (see Appendix).

A generic depiction of the molecule (Figure 1) illustratesthe definitions of the linear distances li between selectedatoms calculated, which we use for the geometricaldescription of individual conformers. These distanceparameters together with some other characteristic geo-metrical data are summarized in Table 1 for seven of themost probable conformers.

Figure 2 shows the optimal geometries for the sevenrepresentative conformers. The first four conformers canclearly be characterized as “closed-tail” and the last threecan be characterized as “open-tail”, on the basis of themagnitude of parameter l4. At first glance, the two classesseem to deviate significantly from each other; however,the only difference is the interchange in position of themain tails’ terminal groups (propyl) and the side groups(ethyl). No obvious correlation has been found between

(7) Martin, C. A.; Magid, L. J. Phys. Chem. 1981, 85, 3938.(8) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1979, 70, 577.(9) Menger, F. M.; Saito, G. J. Am. Chem. Soc. 1978, 100, 4376.(10) Force Field Based Simulations, Molecular Simulations Inc., San

Diego, CA, April 1997.

Table 1. Energy and Geometrical Parameters for the Seven Representatives of the Most Probable Conformers of theAOT Molecule Depicted in Figure 2 (Energy in kcal/mol, Distances in nm, and Volume in nm3)

parameter conf. 1 conf. 2 conf. 3 conf. 4 conf. 5 conf. 6 conf. 7

energy -122.11 -123.96 -124.60 -122.95 -125.68 -120.72 -131.04max xa 0.69 0.61 0.56 0.67 0.60 0.82 0.68max y 1.38 1.31 1.32 1.35 1.17 0.92 0.98max z 1.17 1.02 0.98 0.88 1.83 1.70 1.26volume 1.11 0.815 0.724 0.796 1.28 1.28 0.839l1

b 0.248 0.248 0.248 0.248 0.240 0.249 0.250l2 0.412 0.392 0.419 0.464 0.379 0.433 0.428l3 1.230 1.059 1.020 0.970 1.376 1.364 0.652l4 0.637 0.630 0.671 0.588 1.904 1.574 1.257l5 1.077 1.088 1.023 1.038 1.074 0.978 1.084l6 0.925 0.993 0.939 0.901 0.869 0.893 0.844

a The max x, -y, and -z values are the maximum extents |qmax - qmin| of the AOT molecule along the corresponding coordinate axes. Theirproduct for a particular conformer is the volume () max x × max y × max z) of the enclosing right-rectangular prism. b The linear distancesli between selected atoms are defined in Figure 1.

Figure 1. Schematic representation of the AOT molecule anddefinitions of the characteristic linear distances li betweenselected atoms.

1982 Langmuir, Vol. 15, No. 6, 1999 Derecskei et al.

the stability of a conformer and the corresponding li values.At room temperature, probably all of these conformationsare available to the molecule. This energetic flexibility ofthe AOT monomer probably allows the outside surface ofits reverse micelle to be able to undergo significantgeometrical change with only minor penalty in energy.

All the above conformers show the expected charac-teristics of a surfactant molecule: clearly distinguishablehydrophobic tails and a hydrophilic domain. The latter isnot contiguous because it involves the SO3Na group aswell as the nearby COO ester groups (referred to as the“elbow” regions hence on) at the origins of the tails. As isknown from experiments, the elbows play an importantrole in the interaction with water molecules,11,12 and ourcalculations will be shown to be in accord with thosefindings. The size of the hydrophilic head (characterizedby l1 and l2) varies by no more than 22% among thedifferent conformers. The length of the tail chains (l5 andl6) is fairly consistent from conformer to conformer as well(Table 1). The most significant differences appear to bein the relative positions of the terminal tail branches andthe side chains.

Figure 3 depicts the Connolly surface of conformer 1(i.e., the boundary surface around the molecule that isavailable for interaction with solvent) from two differentperspectives. High partial charges (see color code) areconcentrated around the hydrophilic groups while the twotail branches are almost neutral. The picture also il-lustrates that the molecule is not shaped like a circularcone13 but rather as a cone having a base which can beapproximated by an ellipse. This observation may be

invoked for estimating the aggregation number of AOTreverse micelles.

2. Atomic Level Modeling of One AOT Molecule inWater. To investigate the atomic-level interaction be-tween an AOT molecule and the surrounding bulk waterin aqueous solutions, we “soaked” the AOT molecule. A0.5-nm-thick solvent layer around the AOT molecule wasgenerated by using a solvent box that contained H2Omolecules at distances reproducing the room-temperaturedensity of water and had all solvent molecules positionedin randomized orientations. The layer contained 80-100water molecules depending on the conformation of AOT.Our parallel-model studies on the ethyl alcohol moleculerevealed that this thickness provides a reasonable balancebetween computational accuracy and CPU time. Table 2illustrates that even a modest increase in the thicknessof the hydrate layer around CH3CH2OH results in adramatic increase in the number of necessary watermolecules and, hence, in computational time. At the sametime, if the thickness is increased beyond 0.5 nm, thereis only a moderate improvement in the accuracy ofmodeling the solvation process. Upon increasing thethickness of the hydrate layer from 0.5 to 0.75 nm, thenumber of required water molecules doubled, while thenumber of hydrogen bonds remained unchanged and themagnitude of the interaction energy ∆Eint increased onlyby 2.4 kcal/mol.

Allowing the AOT-water system to relax allows all themolecules to move in order to minimize energy. Naturally,the final geometry reached is, again, only one of a largernumber of possible conformations, and very likely, it does

(11) Tamura, K.; Schelly, Z. A. J. Am. Chem. Soc. 1981, 103, 1018.(12) Goto, A.; Harada, S.; Fujita, T. Langmuir 1993, 9, 86.

(13) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.;Academic Press: San Diego, California, 1995.

Figure 2. Optimal geometries of seven representatives of the most probable conformers of the AOT molecule in a vacuum ascalculated with the ESFF force field. The corresponding energies are listed in Table 1. (The atomic coordinates and partial chargesfor each conformer are available as Supporting Information.)

The AOT Molecule in Water and Carbon Tetrachloride Langmuir, Vol. 15, No. 6, 1999 1983

not necessarily represent the absolute minimum on thepotential-energy surface. Nevertheless, the resultingstructure is probably a representative example of theinteracting AOT-water system since optimizations wereperformed starting from several different initial AOTgeometries. By performing analogous calculations for allthe conformers described above, and analyzing theirhydration, one can obtain a representative picture of theinteraction between an AOT molecule and the surroundingwater. Figure 4 depicts the effect of water on the optimalgeometries of the seven representative conformers, andTable 3 summarizes their geometrical data in the presenceof water.

Compared with the geometries found in a vacuum (Table1), there are only minor changes in the geometry of AOTupon solvation in water. The only relevant general trendobserved is a slight decrease in the distance (l4) betweenthe main chains. This and other minor changes result ina decrease of the average volume (averaged over the sevenconformers) of the enclosing right rectangular prism from0.977 nm3 in a vacuum to 0.842 nm3 in water. During theoptimization process, the migration of water moleculestoward binding sites can be observed, and ultimately thestate of having the maximum number of water molecules

bound is reached. This number is largely independent ofthe initial position of the water molecules. The numberof water molecules in the primary hydrate layer and theirlocations for the seven conformers are presented in Table4.

Figure 3. The solvent-available Connolly surface for Conformer 1 of the AOT molecule.

Table 2. Dependence of the Number of Hydrogen BondsFormed (Nbond) and the Interaction Energy on the

Thickness of the Hydrate Layer for an Ethyl AlcoholMolecule in a Water Box

thickness ofhydrate layer (nm) Ntot

a Nbond

∆Eint(kcal/mol)

CPUtime (s)

0.25 3 2 -12.0 130.50 25 3 -19.7 470.75 51 3 -22.1 751.00 86 3 -23.7 2961.50 195 3 -23.7 1376

a Total number of water molecules in the solvent box.

Table 3. Geometrical Parameters for the SevenRepresentatives of the Most Probable Conformers of the

AOT Molecule in the Presence of Water (Distances innm, Volume in nm3)


max xa 0.63 0.74 0.65 0.68 0.52 0.79 0.65max y 1.28 1.25 1.44 1.35 1.11 0.97 0.97max z 1.12 0.85 0.99 0.96 1.80 1.59 1.06volume 0.903 0.786 0.927 0.881 0.581 1.218 0.668l1

b 0.253 0.253 0.249 0.253 0.249 0.251 0.250l2 0.364 0.401 0.437 0.454 0.430 0.399 0.450l3 1.223 0.845 0.970 0.998 1.09 1.26 0.619l4 0.621 0.662 0.616 0.585 1.784 1.500 1.027l5 1.062 1.033 0.981 1.009 1.068 0.972 1.038l6 0.886 1.040 0.970 0.913 0.971 0.820 0.761

a The max x, -y, and -z values are the maximum extents |qmax -qmin| of the AOT molecule along the corresponding coordinate axes.Their product for a particular conformer is the volume() max x × max y × max z) of the enclosing right-rectangularprism. b The linear distances li between selected atoms are definedin Figure 1.

Table 4. Number of Water Molecules Bound to the AOTMolecule in the Different Conformations and the

Number and Location of the Bonds

n conf. 1 conf. 2 conf. 3 conf. 4 conf. 5 conf. 6 conf. 7

n(H2O)a 11 9 12 11 11 10 11n(Helbow)b 3 3 3 6 3 4 3n(Hhead)c 12 13 15 10 11 10 10

a Total number of water molecules in the primary hydrate layer.b Number of hydrogen bonds between water molecules and theoxygen atoms in the elbow region. c Number of bonds between watermolecules and the constituents of the SO3Na head group.


As can be seen from Table 4, the number of watermolecules that are directly bound to AOT is consistentlybetween 9 and 12, varying only slightly with the geometryof the conformer. In all conformers, there are watermolecules (most often 3) bound to the elbow regions by3-6 hydrogen bonds. The remaining water molecules arebound to the sodium ion and to the oxygen atoms of theSO3 group. There are water molecules bound by more thanone bond, linking the SO3 group to the sodium. As a typicalrepresentative, conformer 1 was chosen for a detailedanalysis of the AOT-water interaction. With 86 watermolecules in the water box, the AOT molecule and itsprimary hydrate layer (11 water molecules) are shown inFigure 5.

To assess the strength of the interaction between thewater molecules and AOT, the interaction energy wasevaluated by calculating the following energy difference:

For a system with 86 water molecules in the box, wefind the hydration of AOT to be strongly exoergic (∆Eint) -172.1 kcal/mol). When considering only the primaryhydrate layer with just 11 water molecules involved, ∆Eintis calculated as -119.6 kcal/mol. The magnitude of thedifference (52.5 kcal/mol) is due to the energy associatedwith the omission of 75 water molecules and to the inherentlimitations of force field methods related to bond-break-ing/-forming processes. Thus, the primary hydrate layeris responsible for at least 70% of the total energy ofinteraction. The relative strength of interaction for theindividual water molecules within the primary hydratelayer can also be estimated by freezing the system and,subsequently, omitting all but a particular bound watermolecule from the box. Table 5 summarizes the results.

The sum of the individual interaction energies in Table5 (-96.7 kcal/mol) is less than the ∆Eint ) -119.6 kcal/mol for the primary hydrate layer. The reasons for the

difference are analogous to those described in the preced-ing paragraph. The apparent interactions between AOTand water molecules nos. 3 and 4 are slightly repulsive(Table 5), although calculations of hydrogen bond interac-tions for the same water molecules at the specific sitesand distances, of course, yield attractive interactions.Apparently, the omission of bulk water from the box leaveswater molecules nos. 3 and 4 frozen in unfavorableorientations. For the other water molecules, the interac-tions can be classified as weak (3-6 kcal/mol) and strong(17-23 kcal/mol). In this particular system, there are fiveweak and four strong interactions. All the strong interac-tions belong to the headgroup (SO3 and Na). This finding

Figure 4. Comparison of the optimal geometries of the seven representative conformers of the AOT molecule in a vacuum (darkbonds and sodium) and in water (green bonds, pink sodium).

∆Eint ) E(AOT + water) - E(AOT) - E(water)

Figure 5. Conformer 1 and the 11 water molecules constitutingthe primary hydrate layer.


is in agreement with results of ESR spin-labeling experi-ments14 which revealed four strongly bound water mol-ecules in the AOT-water system. Similar results wereobtained in analogous computational analysis of theinteraction between the open-tail conformer 5 and water(4 strong and 5 weak interactions; Table 6).

3. Atomic Level Modeling of One AOT Molecule inCarbon Tetrachloride. As the MSI Insight modelingsoftware package lacks a prebuilt solvent box for CCl4, ithad to be generated for the purpose of the present studies.The construction of the solvent box can be accomplishedby generating a 3-dimensional lattice of CCl4 moleculesplaced into positions that simulate the room-temperaturedensity of the solvent. The system is then randomized bya high-temperature molecular-dynamics calculation whichis followed by a cooling of the system back to roomtemperature. Due to the fact that only well-equilibratedsolvent boxes are expected to function properly, the

dynamic simulation must be long enough to ensuresufficient randomization. Not surprisingly, it is a ratherCPU time demanding procedure.

With the CCl4 solvent box at hand, the seven repre-sentative conformers of AOT were soaked with a 1.5-nm-thick solvent layer. The chosen thickness is greater thanthat in the case of water as the solvent, owing to the largersize of the CCl4 molecule, itself. Following the proceduredescribed above, the AOT-CCl4 system was then relaxedand the energy optimized. Table 7 summarizes therelevant geometrical data, and Figure 6 shows thedifference between the geometries of the AOT conformersin a vacuum and those in carbon tetrachloride.

The effects of solvation in CCl4 on the geometry of AOTare even more modest than those of solvation in water.Again, although in some cases the AOT molecule opensup, on the average over the seven conformers it becomesmore compact. Upon solvation, the volume of the enclosingright-rectangular prism is reduced from 0.977 nm3 in avacuum to 0.945 nm3 in carbon tetrachloride. Clearly, CCl4,as a medium, resembles a vacuum more than water does.

(14) Hauser, H.; Haering, G.; Pande, A.; Luisi, P. L. J. Phys. Chem.1989, 93, 7869.

Figure 6. Comparison of the optimal geometries of the seven representative conformers of the AOT molecule in a vacuum (darkbonds and sodium) and in CCl4 (green bonds, pink sodium).

Table 5. The Energy of Interaction Between theIndividual Water Molecules and Conformer 1

(closed-tail) of the AOT Molecule

no. of watermolecule site of bond

bonddistance (Å)

∆Eint(kcal/mol)

1 2 O’s in elbow 2.23, 1.97 -3.52 elbow O 2.06 -3.43 elbow O 2.11 +0.54 O in SO3 1.93 +0.25 O in SO3, Na 2.96, 2.15 -18.06 O in SO3 1.89 -4.37 O in SO3, Na 2.90, 2.24 -17.68 O in SO3, Na 2.99, 2.25 -22.49 O in SO3 1.82 -4.7

10 Na 2.44 -5.211 Na 2.23 -18.3

Table 6. Energy of Interaction between the IndividualWater Molecules and Conformer 5 (open-tail) of the AOT

Molecule

no. of watermolecule site of bond

bonddistance (Å)

∆Eint(kcal/mol)

1 Na 2.28 -11.82 Na 2.20 -10.63 O in SO3, Na 2.94, 2.21 -11.64 O in SO3, Na 2.84, 2.26 -13.25 2 O’s in SO3 2.09, 2.06 -0.26 O in SO3 1.91 -0.37 O in SO3 1.81 +6.48 elbow O 2.27 +3.99 elbow O 1.89 -4.1

10 elbow O 2.20 -2.111 elbow O 1.83 -3.3


On the basis of geometric considerations and assumingclose packing of the surfactant molecules in sphericalaggregates, the calculated size and shape of the AOTmolecule allow comparison with experimental resultsobtained on its reverse micelles. The apparent hydro-dynamic diameter, Dh, of AOT/CCl4 reverse micellesdepends on the water content wo (≡ molar ratio of waterto surfactant) of the solution.15 Since the solubility of waterin CCl4 is only 0.010% w/w (at 24 °C),16 essentially all thewater present in a ternary AOT/CCl4/H2O solution issolubilized in the reverse micelles, provided the amountof water is less than that in which phase separation occurs(wo ≈ 16, at [AOT] ) 0.50 M and 25 °C).15 Hence, at wo< 16, the wo of the solution approximately equals the H2O/AOT molar ratio in the aggregates. For an AOT/CCl4solution with no water added, wo equals 0.8 because of thesmallamountofwateroriginallypresent in thehygroscopicsurfactant. For such a system, we found Dh ) 3.2 ( 0.3nm from light-scattering measurements. wo ) 0.8 corre-sponds to less than a single water molecule bound to AOTat the SO3Na headgroup (see Table 5). As mentionedbefore, the shape of the AOT molecule can be modeled asa truncated right elliptical cone (Figure 1), the height ofwhich is the largest extent of the molecule (max y in thetables). The height h of the truncated cone can be estimatedby averaging the max y values of the conformers obtainedin the CCl4 box (Table 7), which results in h ) 1.21 nm.By correcting for the van der Waals radius of hydrogen(0.10 nm) and that of the sodium ion (0.11 nm), theexpected radius r and diameter d of the reverse micelleare r ) (1.21 + 0.10 + 0.11) nm ) 1.42 nm and d ) 2.84nm. Although the calculated d is smaller by 12% than the⟨Dh⟩ ) 3.2 nm measured, the agreement is reasonable.Improvements in the agreement can be expected fromfuture studies of larger systems where the simultaneouseffects of water and other AOT molecules in a CCl4 boxwill be included for the estimation of h.

Geometric considerations also permit the estimation ofthe aggregation numberN through calculating the numberof cones of which the elliptical bases would cover thesurface area of the spherical reverse micelle, Am ) 4π-(⟨Dh⟩/2)2 ) 32.17 nm2. The major axis a of the base ellipsecan be approximated by the conformer average of thegreatest distances between the two tails (l3 for conformers1-4 and l4 for conformers 5-7, Table 7) corrected by the

van der Waals radii of the two terminal hydrogen atoms:a ) (1.270 + 2 × 0.11) nm ) 1.49 nm. For the minor axisb of the ellipse one can take the conformer average“thickness” of the tails, i.e., the smallest dimension of the

(15) Derecskei, B.; Schelly, Z. A., manuscript in preparation.(16) Riddick, J. A.; Bunger, W. B. Organic Solvents; Wiley-Inter-

science: New York, 1970; p 353.

Table 7. Geometrical Parameters for the SevenRepresentatives of the Most Probable Conformers of theAOT Molecule in the Presence of Carbon Tetrachloride

(Distances in nm, Volume in nm3)


max xa 0.72 0.54 0.46 0.71 0.61 0.80 0.69max y 1.33 1.32 1.30 1.40 1.17 0.97 0.97max z 1.05 0.95 1.16 0.93 1.73 1.63 1.20volume 1.005 0.677 0.694 0.924 1.235 1.265 0.854l1

b 0.246 0.248 0.248 0.249 0.249 0.247 0.258l2 0.457 0.459 0.440 0.506 0.420 0.418 0.442l3 1.102 0.951 1.241 0.982 1.248 1.416 0.669l4 0.596 0.655 0.655 0.710 1.839 1.600 1.177l5 1.037 1.030 1.002 1.041 1.077 0.987 1.054l6 0.957 0.979 0.946 0.831 0.884 0.882 0.891

a The max x, -y, and -z values are the maximum extents |qmax -qmin| of the AOT molecule along the corresponding coordinate axes.Their product for a particular conformer is the volume() max x × max y × max z) of the enclosing right-rectangularprism. b The linear distances li between selected atoms are definedin Figure 1.

Figure 7. Numbering scheme of atoms (generated in thesequence of assembling the AOT molecule) used in the defini-tions of torsions for the conformer search.

Figure 8. Overlay of 20 geometry-optimized conformersgenerated via random sampling of torsion angles of one of thehydrophobic tails of AOT.


right rectangular prism enclosing the molecule (max x,Table 7) corrected by the van der Waals radii: b ) (0.647+ 2 × 0.11) nm ) 0.867 nm. With these mean lengths ofthe axes, the area of the ellipse is Ael ) abπ/4 ) 1.01 nm2

and the upper limit to the aggregation number is N )Am/Ael ) 31.8. This, of course, is a vast overestimation ofN since it also includes the excluded area (between thecurved perimeters of adjoining ellipses) as being covered.To correct for the excluded area, one can use the area ofthe rectangle enclosing the ellipse, Ara ) ab, instead of Ael.This yields N ) Am/Ara ) 24.9, which still would onlyrepresent the aggregation number of a frozen system withperfect, seamless tiling of the micellar surface by therectangles. A more realistic model can be developed byallowing free rotation of the tails around the height h ofthe cone as the axis. This transforms the time averagebase of the cone to a circle, with a as its diameter. Withthese assumptions, and accounting for the excluded area,the estimated aggregation number is calculated as N )Am/a2 ) 14.5. This number is comparable with the meanaggregation number ⟨n⟩ ) 15-17 of the solution obtainedthrough vapor-pressure osmometric measurements.17

Summary

Atomic-level molecular modeling using second-genera-tion force fields was applied for the description of theinteraction between the anionic surfactant AOT and waterand AOT and carbon tetrachloride. For the computationsin the latter medium, a CCl4 box was generated. Hundredsof minima were found on the potential-energy surfacewithin a narrow range of energy. All the correspondingconformers of AOT are most likely accessible to themonomer at room temperature in solution. As AOT isknown to form both reverse and normal micelles, it wasnot unexpected to find that, compared with a vacuum, thepresence of either solvent caused only minor and, gener-ally, similar distortions in the geometry of the surfactant.

Depending on the conformation of AOT, the hydrophilichead and the ester elbow regions form 9-12 bonds withthe surrounding water molecules. On the basis of thecalculated interaction energies, four of these bonds canbe classified as strong, in excellent agreement withexperimental results. On the basis of the computed shapeand dimensions of the AOT molecule, the estimatedaggregation number N and geometric diameter d for theAOT/CCl4 reverse micelle are comparable with the ex-perimentally established mean aggregation number ⟨n⟩and apparent hydrodynamic diameter Dh of the sphericalaggregates found in carbon tetrachloride solution of lowwater content (wo ) 0.8).

Acknowledgment. This work was supported in partby the National Science Foundation, the Welch Founda-tion, the donors of Petroleum Research Fund administeredby the American Chemical Society, and the Texas Ad-(17) Ueno, M.; Kishimoto, H. Bull. Chem. Soc. Jpn. 1977, 50, 1631.

Figure 9. Population distribution vs energy for the 20conformers depicted in Figure 8.

Figure 10. Population distribution vs torsion angle for the 20conformers shown in Figure 8: (a) rotation around the bond46-49; (b) rotation around the bond 43-46.


vanced Research Program. A.D.K. also thanks ChristopherC. Landry at the University of Vermont and Eric Vorpagelat MSI for many useful discussions.

Appendix

Computational Details of the Conformer Search.Initial geometry for the conformer search was generatedby minimization of an AOT molecule constructed fromsimple hydrocarbon and other organic and inorganicfragments. The Cartesian coordinates and partial chargesof this initial structure are available as SupportingInformation. The numbering of the atoms (which reflectsonly the order in which the molecule was assembled fromfragments) used for the definition of individual torsionangles is shown in Figure 7.

The relevant torsional degrees of freedom were identi-fied on the basis of the following rules: (i) torsions aroundsingle bonds were allowed; (ii) torsions which involvedterminal hydrogen atoms were excluded; (iii) torsionswhich involved double bonds were excluded. Even withthese initial simplifications, the number of degrees offreedom is still too large for performing a systematicsearch. To further reduce the number of torsions to besampled, we examined, separately, the effect of distortionsrestricted to the terminal butyl segment of one of thehydrophobic tails. With random sampling of two torsionalangles (43-46-49-52 (end of the tail) and 41-43-46-49 (middle of the tail)) between -180 and +180°, thetwenty structures generated in this search are shown asan overlay in Figure 8.

Evidently, changes in the butyl segment of the tailhardly affect the other parts of the molecule. Thedistribution of energy of the same 20 conformers (Figure9) is very narrow: all the conformers have energiesbetween -52.78 and -49.53 kcal/mol, although thetorsional angles themselves have optima over wide ranges(Figure 10a, b).

This conformer search revealed that torsions involvingthe terminal segment of a main hydrocarbon chain yieldvery similar energies and that the other parts of the AOTmolecule undergo only very modest changes. On the basisof these findings, torsions involving the terminal butylsegments of the main hydrocarbon chains were excluded,but torsions of the ethyl side chains were retained. As aresult, the number of degrees of freedom was reduced to12.

We performed a random sampling of the remaining 12torsional angles: 29-15-18-2, 28-27-29-15, 36-30-33-27, 38-35-36-30, 35-38-41-43, 18-15-29-27,

Figure 11. Overlay of 995 unique, geometry-optimized conformers generated via random sampling of 12 torsion angles in the AOTmolecule.

Figure 12. Population distribution vs energy for the 995conformers depicted in Figure 11.



Figure 13. Population distribution vs torsion angle for the 995 conformers shown in Figure 11. Rotation around the followingbonds: (a) 15-18, (b) 27-29, (c) 30-33, (d) 35-36, (e) 38-41, (f) 15-29, (g) 18-24, (h) 27-33, (i) 30-36, (j) 33-63, (k) 35-38,and (l) 41-60.


2-18-24-20, 28-27-33-30, 33-30-36-35, 27-33-63-64, 36-35-38-41, and 38-41-60-56. The 995unique (of 1000) conformers generated in the search areshown as overlay in Figure 11.

As can be determined from the composite structure,members of the ensemble are very similar and representintermediate states between the closed-tail and open-tailconformations. The most apparent change is in the locationof the sodium ion that occasionally appears between thetails (in conformations with the highest energy localminima). The relative-energy distribution for the ensembleis shown in Figure 12.

A more detailed analysis of the distribution reveals thatall the lowest energy conformers (with energy -20 to -10kcal/mol relative to that of the initial structure) containthe sodium ion coordinated to two oxygen atoms of theSO3 group and to the oxygen of one of the carbonyl groups.In contrast, the highest energy conformers (+10 to +30kcal/mol) may contain the sodium atom not even coor-dinated to the SO3 group but linked to the ester oxygens.The majority of the conformers (78%) have energies in arelatively narrow energy range, -10 to +10 kcal/molrelative to that of the initial structure. The distributionof the torsional angles is also very informative (see Figure13a-l). Surprisingly, several of the torsional angles havea dominant population around a single angle measure,and only a few of the torsion angles have a significantnumber of conformers at more than three preferred values.

The seven representative conformers discussed in the

paper belong to the populations of maximum probabilityfound through random sampling as described above. Weonly considered conformers with the sodium ion coordi-nated to the SO3 group, since that is the most likelysituation in the presence of an aqueous pool in the coreof reverse micelles (except, perhaps, under the influenceof a strong external electric field). Since the water boxwhich could model the water-AOT interaction wasavailable only in the Insight II software package, the sevenrepresentative conformers were reoptimized using theESFF force field. The final coordinates of the optimizationalong with the partial charges are available as SupportingInformation. It is important to emphasize that althoughthe absolute energies are, of course, very different withthe two force fields, the relative energies are quite similar.For example, the energy difference between the highestand lowest energy conformers discussed in the paper(conformers 6 and 7, calculated with both force fields) is11.82 kcal/mol with the UFF and 10.32 kcal/mol calculatedwith the ESFF force field.

Supporting Information Available: Initial coordi-nates and partial charges of the AOT molecule for the randomsampling conformer search with the UFF force field and finalcoordinates and partial charges of Conformers 1 to 7 aftergeometry optimization with the ESFF force field. This materialis available free of charge via the Internet at http://pubs.acs.org.

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Documents

Atomic-Level Molecular Modeling of AOT Reverse Micelles. 1. The AOT Molecule in Water and Carbon Tetrachloride