DOI: 10.5061/dryad.jwstqjqj5
title: Shape of AOT reverse micelles: the mesoscopic assembly is more than the sum of the parts

description: 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.
description: A series of five reverse micelles were simulated using different
 force fields. Reverse micelles are typically characterized by a parameter
 known as w<sub>0</sub> = [H2O]/[AOT]. All reverse micelles
 simulated here were set to w<sub>0</sub>=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
 w<sub>0</sub>=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
 <em>Multiwfn</em> 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<sup>+</sup> + 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.
description: # Shape of AOT reverse micelles: the mesoscopic assembly is more than the
 sum of the parts ## Provided Files We provide three groups of data in this
 archive: the raw simulation trajectories from our papers, CSV files of the
 shape data from the simulations, and equilibrated structures from pulled
 from our simulations. These are provided as a series of ZIP compressed
 folders. Due to the size, the raw trajectories are bundled as individual
 ZIP folders for each simulation while the other groups of data are
 provided in their own ZIP folders, labelled "Shape_Analysis" and
 "Equilibrated_Structures". ## Raw Trajectories These
 subdirectories provide the files necessary for loading our raw
 trajectories. We performed five simulations and have files for each. Each
 ZIP compressed folder contains five files from each simulation. A summary
 of the provided files is given in Table 1. Table 1: Naming conventions and
 description of simulation files | File Suffix | File Type | Function | |
 :------------------ | :-------- |
 :---------------------------------------------------------------------------------------------------------------------------------------------------------------- | | -.prod1.gro | GRO | Structure file containing coordinates of single frame | | -.cent\_prod.xtc | XTC | Trajectory file containing full 1 microsecond simulation, centered so reverse micelle stays within PBC box | | -.RotAuto\_cent.xtc | XTC | Trajectory file containing a 100 ns extension to -.cent\_prod.xtc, saved every 0.1 ps to provide resolution for computing the rotational autocorrelation of water | | -.prod1.tpr | TPR | GROMACS-style portable binary run input file, contains all info needed to read XTC into analysis program | | -.RotAuto.tpr | TPR | GROMACS-style portable binary run input file, contains all info needed to read XTC into analysis program | The prefix of each file specifies which simulation the file is referring to. Specifications of the file prefixes and a brief summary of all simulations is provided in Table 2. The ZIP compressed folders are named according to the second column of Table 2. We provide a more thorough description of the simulations at the end of this document and we refer readers to Ref. 3 for complete details on the simulations. Table 2: Table of simulation names and force fields | File Prefix | Name | AOT+Solvent Model | Water Model | Notes | | :------------------ | :-------- | :---------------- | :---------- | :-------------------------------------------------------------------------- | | P2\_MIC\_CH\_TIP3P- | CHARMM | CHARMM36 | TIP3P | | | P2\_MIC\_CH\_TIP4P- | CHARMM-4P | CHARMM36 | TIP4P/2005 | | | P2\_MIC\_OPLSST- | OPLS-Std | OPLS | TIP4P/2005 | Sulfonate values from literature, see below | | P2\_MIC\_OPLSC5- | OPLS-CM5 | OPLS- modified | TIP4P/2005 | Same as OPLS-Std, AOT partial charges modified using CM5 calculation scheme | | P2\_MIC\_OPLSRE- | OPLS-RESP | OPLS- modified | TIP4P/2005 | Same as OPLS-Std, AOT partial charges modified using RESP calclation scheme | The OPLS force field lacks native parameters for the sulfonate moiety, parameters for this group were taken from literature. Charges and intramolecular parameters (bond stretching, etc) were taken from Ref. 4, while Lennard-Jones parameters were taken from Ref. 5, both provided below. 1. Canongia Lopes, J.N.; Padua, A.A.H.; Shimizu, K. Molecular force field for ionic liquids IV: Trialkylimidazolium and alkoxycarbonyl-imidazolium cations; alkylsulfonate and alkylsulfate anions. *J. Phys. Chem. B* **20**, *112*, 5039-5046. 2. Rios-Lopez, M.; Mendez-Bermudez, J.G.; Dominguez, H. New Force field parameters for the sodium dodecyl sulfate and alpha olefin sulfonate anionic surfactants. *J. Phys. Chem. B* **2018**, *122*, 4558-4565. We also provide MDP files which are common to all simulations, which are provided in the archive as individual files outside of ZIP folders. The MDP file is the GROMACS file used to specify the options utilized in the simulation and therefore these serve as references of the exact options set for each simulation. Each simulation used the same MDP file so only two are provided. The MDP file information is provided in Table 3. Note that semicolons are the MDP files comment operator so any line starting with a semicolon has been commented out. Table 3: Description of the provided MDP files | File Name | Associated Simulations | General Description | | :---------- | :--------------------- | :------------------------------------------------------------------------------------------- | | prod.mdp | -.cent\_prod.xtc | Options file for the main production run, the full microsecond simulation | | RotAuto.mdp | -.RotAuto\_cent.xtc | Options file for the short extension used to compute the rotational autocorrelation of water | Simulations were performed using the 2019 version of GROMACS, which provides excellent documentation and so we refer readers to [their website](https://manual.gromacs.org/2019/reference-manual/file-formats.html) for details about each file type. There are several options for reading and analyzing GROMACS trajectories, including the Python package MDAnalysis and the free program VMD. The provided files should be more than sufficient to read in the trajectory via whatever interface the user prefers. Note that the inclusion of both the “-prod1.tpr” and “-RotAuto.tpr” files is redundant as either can be used to provide the necessary information to read the XTC trajectory files. We have included them mostly for completeness and out of an abundance of caution. When accessing the trajectories, it is often useful to know the residue names and/or the atom names. The residue names are given below with the common name of the molecule on the left and the residue name used by the simulations on the right. * water - SOL * AOT - AOT * isooctane - ISO Note that the sodium cation was considered a part of the AOT residue for the purposes of these simulations. It simplified packing the initial structures greatly and only impacts the residue name given to sodium. Users just need to be aware of that fact. Atom names are recorded most effectively in the PDB files found in the “Equilibrated_Structures”. All OPLS simulations used the same atom names for all residues as the only difference between these simulations were the partial charges on each atom. The OPLS atom names are generally different than the CHARMM atom names. The CHARMM atom names between the CHARMM and CHARMM-4P are identical except for the water atom names, where we switch between a 3-site and 4-site water model. ## "Equilibrated\_Structures" Directory We have created sets of 20 frames for each simulation taken from the production run of our simulation. The structures may be used as pre-equilibrated starting structures of a *w*<sub>0</sub> = 5 reverse micelle for each force field we utilized. These frames were generated using a k-means clustering, implemented via the Scikit-Learn Python package based on the CPE and convexity measured at the 5<sup>*th*</sup>, outermost surface (see Ref. 3 for more details about surfaces). This has the effect of generating a set of frames which are as different from each other as possible while also spanning the entire range of observed shapes. They therefore represent a highly diverse set of starting structures, which may or may not be important to someone interested in simulating AOT reverse micelles. We also note that these files serve as a reference for the atom naming conventions used in each simulation. Files are named with a prefix specifying the simulation, a middle portion indicating that the file is part of the equilibrated structures, and a suffix specifying the cluster and frame number, mostly for debugging and logging purposes. For example, consider a file named below. **CHARMM_EqStructures.k15_f96324.pdb** This indicates that the frame is from the CHARMM simulations, is an equilibrated structure, representing the 16th k-means cluster (they are numbered starting from 0), and is the 96,324<sup>*th*</sup> frame of the CHARMM simulation. The files have been extensively commented to indicate where they come from, give a short summary of the system, and detail the shape data at this particular frame. ## "Shape\_Analysis" Directory We provide the shape data for each simulation, analyzed at all frames, in a simple CSV files for convenience. Because the curvature data is relatively larger and, as we showed in Ref. 1, not usually necessary and especially not in the case of AOT reverse micelles, we have separated the data into 3 files for each simulation: CPE and convexity data in one CSV file, the mean curvature data in its own CSV file, and the Gaussian curvature data in its own CSV file. Each file is given a suffix as shown below: * CPE and Convexity data: -.CandC.csv * mean curvature: -.mean.csv * Gaussian curvature: -.gauss.csv For the CandC files, the columns are given by Table 4. Table 4: Data in each column for the convexity and CPE files (-.CandC.csv) | Column | Data | | :----- | :----------------------- | | 1 | time (in ps) | | 2 | CPE - *e*<sub>*ab*</sub> | | 3 | CPE - *e*<sub>*ac*</sub> | | 4 | Convexity | Data in each column for the CandC files We remind the user that the curvature is a distribution of values computed over each vertex of the Delauney triangulated surface which results from using the Willard-Chandler algorithm to compute the interface for a given group of atoms. The number of vertices is not constant over time but we generally found it to be somewhere around ~3,000 points. To conserve space, we reduced this to a distribution characterized by 9 percentile values. These values include the median and 25<sup>*th*</sup> and 75<sup>*th*</sup> percentile so that the median and interquartile range can be computed. Columns for the mean curvature files is given by 5. Table 5: Data in each column for mean curavture files (-.mean.csv) | Column | Data | | :----- | :------------------------------------------- | | 1 | time (in ps) | | 2 | Mean Curvature, 5<sup>*th*</sup> percentile | | 3 | Mean Curvature, 15<sup>*th*</sup> percentile | | 4 | Mean Curvature, 25<sup>*th*</sup> percentile | | 5 | Mean Curavture, 35<sup>*th*</sup> percentile | | 6 | Mean Curvature, 50<sup>*th*</sup> percentile | | 7 | Mean Curvature, 65<sup>*th*</sup> percentile | | 8 | Mean Curvature, 75<sup>*th*</sup> percentile | | 9 | Mean Curvature, 85<sup>*th*</sup> percentile | | 10 | Mean Curvature, 95<sup>*th*</sup> percentile | Columns for the Gaussian curvature files is given by Table 6. Table 6: Data in each column for Gaussian curvature files (-.gauss.csv) | Column | Data | | :----- | :----------------------------------------------- | | 1 | time (in ps) | | 2 | Gaussian Curvature, 5<sup>*th*</sup> percentile | | 3 | Gaussian Curvature, 15<sup>*th*</sup> percentile | | 4 | Gaussian Curvature, 25<sup>*th*</sup> percentile | | 5 | Gaussian Curavture, 35<sup>*th*</sup> percentile | | 6 | Gaussian Curvature, 50<sup>*th*</sup> percentile | | 7 | Gaussian Curvature, 65<sup>*th*</sup> percentile | | 8 | Gaussian Curvature, 75<sup>*th*</sup> percentile | | 9 | Gaussian Curvature, 85<sup>*th*</sup> percentile | | 10 | Gaussian Curvature, 95<sup>*th*</sup> percentile | # Simulation Details ## System Stoichiometry The stoichiometry of the reverse micelle is kept constant across all simulations, only changing the force field used to describe the system. The stoichiometry is provided in Table 7. Table 7: Molecular stoichiometry | Chemical | Number | | :-------- | :----- | | Water | 210 | | AOT | 42 | | Isooctane | 1500 | The more experimentally relevant or experimentally "preferred" values that this stoichiometry yields are provided on the right in Table 8. Table 8: Some key values of the reverse micelle | Metric | Value | | :----------------- | :----- | | *w*<sub>0</sub> | 5 | | Aggregation Number | 42 | | Conc. of AOT | 0.17 M | ## Simulations and Force Fields The simulations are varied by the force fields used. A full accounting of the details can be found in Ref 3. Non-standard parameters used in this work are provided in a program agnostic format in the supplementary information (SI) attached to Ref 3. The parameters for AOT in GROMACS-style parameter files are provided on the [Levinger GitHub page](https://github.com/Levinger-Group/How-to-think-about-Shape). A brief overview of simulations was provided in Table 2 above. The CM5 and RESP atomic charges were calculated using the *Multiwfn* program based on DFT calculations for a single geometry of AOT. As the names imply, the OPLS-CM5 force field uses the CM5 method of computing partial charges, while the OPLS-RESP method uses the restricted electrostatic potential mapping (RESP) method of computing partial charges. Please see Ref. 3 for further details and the appropriate citations. A reminder that the MDP files are provided as a more complete record of what options were used for the simulations, but a brief overview is provided here. The shape analyses we performed were based on a 1 μs simulation with frames saved every 8 ps. To accomodate calculating the rotational autocorrelation functions of water, a short extension was also performed. This was a 100 ns extension, with frames saved every 0.1 ps. Both simulations were held at a constant 1 bar and 298 K pressure and temperature using a Parrinello-Rahman barostat and velocity-rescale thermostat. Electrostatics were computed using the Particle Mesh Ewald scheme. ## Shape Analyses The shape analyses we used have been extensively documented in Refs 1-3. An example of the code needed to compute these values is provided on the Levinger GitHub page [Levinger GitHub page](https://github.com/Levinger-Group/How-to-think-about-Shape). # References The simulations presented here have been used in the following manuscripts: 1. Gale, C. D.; Derakhshani-Molayousefi, M.; Levinger, N. E. How To Characterize Amorphous Shapes: The Tale of a Reverse Micelle. *J. Phys. Chem. B* **2022**, *126* (4), 953-963. DOI: 10.1021/acs.jpcb.1c09439 2. Gale, C. D.; Levinger, N. E. Predicting the Geometry of Core-Shell Structures: How a Shape Changes with Constant Added Thickness. *J. Phys. Chem. B* **2024**, *128* (5), 1317-1324. DOI: 10.1021/acs.jpcb.3c07652 3. Gale, C. D.; Derakhshani-Molayousefi, M.; Levinger, N. E. Shape of AOT Reverse Micelles: The Mesoscopic Assembly is More Than the Sum of the Parts. Submitted to *J. Phys. Chem. B*, **2024**, *128* (26), 6410-6421. DOI: 10.1021/acs.jpcb.4c02569 Ref. 1 develops the shape-measuring methods which form the basis of this series of works. Ref. 2 develops a model for how the coordinate-pair eccentricity, one of my shape-measuring methods, is expected to change with size, e.g. as a shell is "grown" onto an arbitrary core, providing a reference for comparison. Ref. 3 uses the methods and ideas developed in the previous references to fully explore the shape of AOT reverse micelles. Ref. 1 used only the first 100 ns of the CHARMM simulation. Ref. 2 used the full 1 *μ*s of only the CHARMM simulation. Ref. 3 used the full time of all simulations.