Shape of AOT reverse micelles: the mesoscopic assembly is more than the sum of the parts

AOT reverse micelles are a common and convenient model system for studying the effects of nanoconfinement on aqueous solutions. The reverse micelle shape is important to understanding how the constituent components come together to form the coherent whole and the unique properties observed there. The shape of reverse micelles impacts the amount of interface present and distance of the solute from the interface and is therefore vital to understanding interfacial properties and the behavior of solutes in the polar core. In this work, we use previously introduced measures of shape, the coordinate-pair eccentricity and convexity, and apply them to a series of simulations of AOT reverse micelles. We simulate the most commonly used force field for AOT reverse micelles, the CHARMM force field, but we also adapt the OPLS force field for use with AOT, the first work to do so, in addition to using both 3- and 4-site water models. Altogether, these simulations are designed to examine the impact of the force field on the shape of the reverse micelles in detail. We also study the time autocorrelation of shape, the water rotational anisotropy decay, and how the coordinate-pair eccentricity changes between the water pool and AOT tail groups. We find that although the force field changes the shape noticeably, AOT reverse micelles are always amorphous particles. The shape of the micelles changes on the order of 10 ns. The water rotational dynamics observed match experiment and demonstrate slower dynamics relative to bulk water, and suggest a two population model that fits a core/shell hypothesis. Taken together, our results indicate that it is likely not possible to create a perfect force field that can reproduce every aspect of the AOT reverse micelle accurately. However, the magnitude of the differences between simulations appears relatively small, suggesting that any reasonably derived force field should provide an acceptable model for most work on AOT reverse micelles.

Methods
A series of five reverse micelles were simulated using different force fields. Reverse micelles are typically characterized by a parameter known as w0 = [H2O]/[AOT]. All reverse micelles simulated here were set to w0=5, which has been shown to exhibit the effects of nanoconfinement clearly. The aggregation number, that is, the number of AOT surfactant molecules per reverse micelle, used in this work was 42. This mimics the numbers provided by the Abel lab, that fit well with the current best experimental estimates for w0=5 reverse micelles. The reverse micelle was dissolved in 1500 isooctane molecules. Using the average box dimensions of the simulations, the concentration of AOT in isooctane was ~0.17 M. All starting configurations were packed using PACKMOL. The simulations were performed using the 2019 edition of GROMACS. Generally, the system was minimized by steepest descent to remove overlapping contacts. The system was then equilibrated for a total of 10 ns in the NPT ensemble using a series of heavy-atom position restraints as described in our previous work and provided in SI. This system was designed to heavily bias the system toward spherical geometries to prove that non-spherical geometries are not an artifact of the initial configuration, but must reflect equilibrium behavior for the system. Equilibration used the velocity-rescale thermostat and Berendsen barostat with a 2 fs step size. Following this, a production run of 1 μs was performed using the velocity-rescale thermostat and Parrinello-Rahman barostat with a 2 fs step size, saving the coordinates every 8 ps. To study water dynamics, we created a short, 100 ps extension to the production run, saving the coordinates every 100 fs, with all other parameters kept the same. Both the equilibration and production runs were held at 1 bar and 298 K. All simulations used the Particle Mesh Ewald scheme for computing electrostatic interactions.

Each simulation differed in the force field used to model the system. One simulation used the CHARMM36 force field for AOT and isooctane and the TIP3P water model, the most commonly used parameters for all-atom MD simulations of AOT reverse micelles at present. We created a minor modification to this simulation by using the same force field for AOT and isooctane but using the TIP4P/2005 water model, to understand how the water model impacts the shape and behavior of the reverse micelle. This simulation is expected to be quite different because CHARMM was specifically parameterized for use with the TIP3P water model. We introduce the OPLS force field to explore how the AOT model impacts the reverse micelle. Currently, no major force field family other than CHARMM models a sulfonate-bearing surfactant without modification. We chose the OPLS force field because the majority of the reverse micelle simulation comprises organic molecules. We used literature values to properly simulate the sulfonate group. The literature values were parameterized for a sulfonate-bearing ionic liquid and linear alkyl sulfonate surfactant so none of the parameters are specific to the AOT molecule.

Without performing an expensive, full parameterization of AOT in the OPLS force field, we instead created two additional simulations that modify the partial charges on all atoms of AOT. Although this does not guarantee the parameters are accurate, with enough variation, it should at least ensure that the force fields straddle a minimum (with respect to any particular metric), with the additional benefit that these scheme will demonstrate specific parameters' impact on the reverse micelle's behavior, especially the shape. To alter the partial charges, we obtained the molecular orbitals for the AOT anion using a density functional theory calculation. Geometry was optimized at the M06/pc-1 level with a level-shift algorithm to help converge the wavefunction to a solution using GAMESS. At the optimized geometry, a single-point calculation using M06/pc-2 was performed to produce a final set of orbitals. These orbitals were used to compute the partial charges on every atom of AOT using the Multiwfn program. We used both the Hirshfeld-based, CM5 method, as well as the electrostatic potential mapping method, RESP. All simulations employing OPLS-based force fields used the TIP4P/2005 water model. Details about the OPLS force fields, including inter- and intramolecular parameters and partial charges are provided in SI of the manuscript. 

For each simulation, the micelle was divided into five sufaces to study how the shape changes between the inner water pool and the oil/surfactant interface. Surfaces are numbered starting from the interior, so that surface 1 corresponds to the shape of the water pool and surface 5 corresponds to the shape of water + Na+ + AOT. Each surface is created by defining a subset of the atoms in the micelle arranged as nested sets, so that surface 1 is defined as all water molecules, surface 2 is defined as all water plus the sodium plus the sulfonate-group atoms, etc. To compute CPE, the atoms contained in each surface's subset are used to calculate the moments of inertia, directly. To compute convexity, the atoms contained in each surface are used to generate a Willard-Chandler surface that is then used for the analysis. Custom Python code was used for all analyses, with key packages including the MDAnalysis package for manipulating the simulation trajectory, the PyTim package for computing the Willard-Chandler surface, and the PyVista package for manipulating the mesh surfaces.