The Size of AOT Reverse Micelles

Abstract

Reverse micelles (RMs) made from water and sodium bis(2-ethylhexyl) sulfosuccinate (AOT) are commonly studied experimentally as models of aqueous microenvironments. They are small enough for individual RMs to also be studied by molecular dynamics (MD) simulation, which yields detailed insight into their structure and properties. Although RM size is determined by the water loading ratio (i.e., the molar ratio of water to AOT), experimental measurements of RM size are imprecise and inconsistent, which is problematic when seeking to understand the relationship between water loading ratio and RM size, and when designing models for study by MD simulation. Therefore, a systematic study of RM size was performed by MD simulation with the aims of determining the size of an RM for a given water loading ratio, and of reconciling the results with experimental measurements. Results for a water loading ratio of 7.5 indicate that the interaction energy between AOT anions and other system components is at a minimum when there are 62 AOT anions in each RM. The minimum is due to a combination of attractive and repulsive electrostatic interactions that vary with RM size and the dielectric effect of available water. Overall, the results agree with a detailed analysis of previously published experimental data over a wide range of water loading ratios, and help reconcile seemingly discrepant experimental results. In addition, water loss and gain from an RM is observed and the mechanism of water exchange is outlined. This kind of RM model, which faithfully reproduces experimental results, is essential for reliable insights into the properties of RM-encapsulated materials.

Figure 1

Cross section of an RM model with W₀ = 7.5 and 62 AOT. Water molecules are rendered as CPK models, sodium cations as yellow van der Walls spheres with a radius of 0.6 Å, AOT anions as a blue surface, and isooctane as lines. A single AOT anion is rendered as a CPK model in the lower right corner.

Figure 2

Eccentricity vs time for the WD, RM₃₄, RM₆₄, and RM₁₀₆ systems. On either end of each graph, the initial and final structures are illustrated by representing water molecules as blue spheres, sodium cations as yellow spheres, and AOT anions as a surface. The starting structures were energy minimized before marking time “0” in the eccentricity graphs. Note that the final structure of the RM₁₀₆ system is highly distorted. This degree of distortion was not reflected in the eccentricity calculations, fission into smaller systems appeared imminent. There were no shape distortions suggesting imminent fission observed in any of the smaller systems.

Figure 3

The relative magnitudes of all pairwise non-bonded interaction energies for an RM₆₂ system, normalized by n_AOT .

Figure 4

RM system nonbonded interaction energies in kcal/mole normalized by n_AOT. (A) AOT anion – AOT anion interaction energies with an inverse second order fit. (B) Sodium cation – Sodium cation interaction energies with an inverse second order fit. (C) AOT anion – Sodium cation interaction energies with an inverse second order fit. (D) AOT anion – isoO interaction energies with an inverse second order fit. (E) The sum of water – AOT anion and water – Sodium cation interaction energies. There are two results for each system in panels A-E from the two independent 30 ns simulations, that sometimes superimpose. (F) AOT energy (defined in the text, i.e. the sum of the energies depicted in panels A-E) with a quadratic fit to all data except the RM₁₀₆ system (indicated in open circles). The value of n_AOT at the minimum is 60.9 (vertical red arrow). All energies are normalized by n_AOT. The two results for each system are from the two independent 30 ns simulations. (G) Histograms of the AOT energies combined into a contour graph. Autocorrelation times for the AOT energies were generally less than 100 ps. Therefore, energies were calculated at 100 ps intervals for the two 15 ps simulations for each system, divided into 1 kcal/mol bins, and color-coded according to bin counts as indicated.

Figure 5

The average number of sodium cations within 3Å of the SO₃⁻ groups. The two results for each value of n_AOT were derived from the two independent 30 ns simulations.

Figure 6

The average number of water molecules within 3Å (circles) and 5Å (triangles) of the SO₃⁻ groups. The two results for each value of n_AOT were derived from the two independent 30 ns simulations.

Figure 7

The average number of water molecules within 3Å of sodium cations. The two results for each value of n_AOT were derived from the two independent 30 ns simulations.

Figure 8

AOT energies over 100 ns for an RM₆₂ system.

Figure 9

Distribution of components in an RM₆₂ system. Lower panel: Nearest distance metrics analysis with distance to the nearest SO₃ group on the horizontal axis. The polar phase is comprised primarily of water (blue) and sodium cations (magenta). The apolar phase is comprised of AOT chains (black) and isoO (green). The AOT terminal methyl groups are indicated to enable the determination of r_AOT as described in the text. Upper panel: a radial electron density profile approximated by weighting an ordinary radial density profile by atomic numbers. The horizontal axis is roughly aligned with the distance scale of the lower panel. The vertical axis is arbitrary.

Figure 10

Radius of gyration vs n_AOT for simulated RM systems. The two results for each value of n_AOT were derived from the two independent 30 ns simulations. The average radius of gyration for the RM₆₂ system is 15.7 Å, and indicated with dotted lines.

Figure 11

Extrapolated results for various W₀ and comparison with experimental studies. Solid line – n_AOT values obtained from equation 7-f which include the $n_{\mathit{AOT}}^0$ “dry” term and a slightly larger value of a_AOT . Dotted line – n_AOT values obtained from equation 7-e. Red circles – the published experimental data of Eicke and Rehak. Blue diamonds – the published experimental results of Amararene et al.