Force Fields for High Concentration Aqueous KOH Solutions and Zincate Ions.

Motivated by increasing interest in electrochemical devices that include highly alkaline electrolytes, we investigated two force fields for potassium hydroxide (KOH) at high concentrations in water. The "FNB" model uses the SPC/E water model, while the "FHM" model uses the TIP4P/2005 water model. We also developed parameters to describe zincate ions in these solutions. The density and viscosity of KOH using the FHM model are in better agreement with experiment than the values from the FNB model. Comparing the properties of the zincate solutions to the available experimental data, we find that both force fields agree reasonably well, although the FHM parameters give a better prediction of the viscosity. The developed force field parameters can be used in future simulations of zincate/KOH solutions in combination with other species of interest.

Molecular dynamics simulations of the dielectric constants of salt-free and salt-doped polar solvents.

We develop a Stockmayer fluid model that accounts for the dielectric responses of polar solvents (water, MeOH, EtOH, acetone, 1-propanol, DMSO, and DMF) and NaCl solutions. These solvent molecules are represented by Lennard-Jones (LJ) spheres with permanent dipole moments and the ions by charged LJ spheres. The simulated dielectric constants of these liquids are comparable to experimental values, including the substantial decrease in the dielectric constant of water upon the addition of NaCl. Moreover, the simulations predict an increase in the dielectric constant when considering the influence of ion translations in addition to the orientation of permanent dipoles.

Accurate Calculation of Solvation Properties of Lithium Ions in Nonaqueous Solutions.

We perform all-atom molecular dynamics simulations of lithium triflate in 1,2-dimethoxyethane using six different literature force fields. This system is representative of many experimental studies of lithium salts in solvents and polymers. We show that multiple historically common force fields for lithium ions give qualitatively incorrect results when compared with those from experiments and quantum chemistry calculations. We illustrate the importance of correctly selecting force field parameters and give recommendations on the force field choice for lithium electrolyte applications.

Effect of surface properties and polymer chain length on polymer adsorption in solution.

In polymer nanoparticle composites (PNCs) with attractive interactions between nanoparticles (NPs) and polymers, a bound layer of the polymer forms on the NP surface, with significant effects on the macroscopic properties of the PNCs. The adsorption and wetting behaviors of polymer solutions in the presence of a solid surface are critical to the fabrication process of PNCs. In this study, we use both classical density functional theory (cDFT) and molecular dynamics (MD) simulations to study dilute and semi-dilute solutions of short polymer chains near a solid surface. Using cDFT, we calculate the equilibrium properties of polymer solutions near a flat surface while varying the solvent quality, surface-fluid interactions, and the polymer chain lengths to investigate their effects on the polymer adsorption and wetting transitions. Using MD simulations, we simulate polymer solutions near solid surfaces with three different curvatures (a flat surface and NPs with two radii) to study the static conformation of the polymer bound layer near the surface and the dynamic chain adsorption process. We find that the bulk polymer concentration at which the wetting transition in the poor solvent system occurs is not affected by the difference in surface-fluid interactions; however, a threshold value of surface-fluid interaction is needed to observe the wetting transition. We also find that with good solvent, increasing the chain length or the difference in the surface-polymer interaction relative to the surface-solvent interaction increases the surface coverage of polymer segments and independent chains for all surface curvatures. Finally, we demonstrate that the polymer segmental adsorption times are heavily influenced only by the surface-fluid interactions, although polymers desorb more quickly from highly curved surfaces.

Solvation Energy of Ions in a Stockmayer Fluid.

We calculate the solvation energy of monovalent and divalent ions in various liquids with coarse-grained molecular dynamics simulations. Our theory treats the solvent as a Stockmayer fluid, which accounts for the intrinsic dipole moment of molecules and the rotational dynamics of the dipoles. Despite the simplicity of the model, we obtain qualitative agreement between the simulations and experimental data for the free energy and enthalpy of ion solvation, which indicates that the primary contribution to the solvation energy arises mainly from the first and possibly second solvation shells near the ions. Our results suggest that a Stockmayer fluid can serve as a reference model that enables direct comparison between theory and experiment and may be invoked to scale up electrostatic interactions from the atomic to the molecular length scale.

Quantifying Single-Ion Transport in Percolated Ionic Aggregates of Polymer Melts.

Single-ion conducting polymers such as ionomers are promising battery electrolyte materials, but it is critical to understand how rates and mechanisms of free cation transport depend on the nanoscale aggregation of cations and polymer-bound anions. We perform coarse-grained molecular dynamics simulations of ionomer melts to understand cation mobility as a function of polymer architecture, background relative permittivity, and corresponding ionic aggregate morphology. In systems exhibiting percolated ionic aggregates, cations diffuse via stepping motions along the ionic aggregates. These diffusivities can be quantitatively predicted by calculating the lifetimes of continuous association between oppositely charged ions, which equal the time scales of the stepping (diffusive) motions. In contrast, predicting cation diffusivity for systems with isolated ionic aggregates requires another time scale. Our results suggest that to improve conductivity the Coulombic interaction strength should be strong enough to favor percolated aggregates but weak enough to facilitate ion dissociation.

Morphology and proton diffusion in a coarse-grained model of sulfonated poly(phenylenes).

A coarse-grained model previously used to simulate Nafion using dissipative particle dynamics (DPD) is modified to describe sulfonated Diels-Alder poly(phenylene) (SDAPP) polymers. The model includes a proton-hopping mechanism similar to the Grotthuss mechanism. The intramolecular parameters for SDAPP are derived from atomistic molecular dynamics (MD) simulation using the iterative Boltzmann inversion. The polymer radii of gyration, domain morphologies, and cluster distributions obtained from our DPD model are in good agreement with previous atomistic MD simulations. As found in the atomistic simulations, the DPD simulations predict that the SDAPP nanophase separates into hydrophobic polymer domains and hydrophilic domains that percolate through the system at sufficiently high sulfonation and hydration levels. Increasing sulfonation and/or hydration leads to larger proton and water diffusion constants, in agreement with experimental measurements in SDAPP. In the DPD simulations, the proton hopping (Grotthuss) mechanism becomes important as sulfonation and hydration increase, in qualitative agreement with experiment. The turning on of the hopping mechanism also roughly correlates with the point at which the DPD simulations exhibit clear percolated, hydrophilic domains, demonstrating the important effects of morphology on proton transport.

The evolution of acidic and ionic aggregates in ionomers during microsecond simulations.

We performed microsecond-long, atomistic molecular dynamics simulations on a series of precise poly(ethylene-co-acrylic acid) ionomers neutralized with lithium, with three different spacer lengths between acid groups on the ionomers and at two temperatures. Ionic aggregates form in these systems with a variety of shapes ranging from isolated aggregates to percolated aggregates. At the lower temperature of 423 K, the ionic aggregate morphologies do not reach a steady-state distribution over the course of the simulations. At the higher temperature of 600 K, the aggregates are sufficiently mobile that they rearrange and reach steady state after hundreds of nanoseconds. For systems that are 100% neutralized with lithium, the ions form percolated aggregates that span the simulation box in three directions, for all three spacer lengths (9, 15, and 21). In the partially neutralized systems, the morphology includes lithium ion aggregates that may also include some unneutralized acid groups, along with a coexisting population of acid group aggregates that form through hydrogen bonding. In the lithium ion aggregates, unneutralized acid groups tend to be found on the ends or sides of the aggregates.

Fluctuation Effects on the Brush Structure of Mixed Brush Nanoparticles in Solution.

A potentially attractive way to control nanoparticle assembly is to graft one or more polymers on the nanoparticle, to control the nanoparticle-nanoparticle interactions. When two immiscible polymers are grafted on the nanoparticle, they can microphase separate to form domains at the nanoparticle surface. Here, we computationally investigate the phase behavior of such binary mixed brush nanoparticles in solution, across a large and experimentally relevant parameter space. Specifically, we calculate the mean-field phase diagram, assuming uniform grafting of the two polymers, as a function of the nanoparticle size relative to the length of the grafted chains, the grafting density, the enthalpic repulsion between the grafted chains, and the solvent quality. We find a variety of phases including a Janus phase and phases with varying numbers of striped domains. Using a nonuniform, random distribution of grafting sites on the nanoparticle instead of the uniform distribution leads to the development of defects in the mixed brush structures. Introducing fluctuations as well leads to increasingly defective structures for the striped phases. However, we find that the simple Janus phase is preserved in all calculations, even with the introduction of nonuniform grafting and fluctuations. We conclude that the formation of the Janus phase is more realistic experimentally than is the formation of defect-free multivalent mixed brush nanoparticles.

Electrostatics of Nanoparticle-Wall Interactions within Nanochannels: Role of Double-Layer Structure and Ion-Ion Correlations.

We perform computational investigations of the electrolyte-mediated interactions of charged nanoparticles with the walls of nanochannels. We investigate the role of discrete ion effects, valence, and electrolyte strength on nanoparticle-wall interactions. We find for some of the multivalent charge regimes that the like-charged nanoparticles and walls can have attractive interactions. We study in detail these interactions and the free-energy profile for the nanoparticle-wall separation. We find there are energy barriers and energy minima giving preferred nanoparticle locations in the channel near the center and at a distance near to but separated from the channel walls. We characterize contributions from surface overcharging, condensed layers, and overlap of ion double layers. We perform our investigations using coarse-grained particle-level simulations with Brownian dynamics, classical density functional theory, and the mean-field Poisson-Boltzmann theory. We discuss the implications of our results for phenomena in nanoscale devices.

Nonequilibrium simulations of model ionomers in an oscillating electric field.

We perform molecular dynamics simulations of a coarse-grained model of ionomer melts in an applied oscillating electric field. The frequency-dependent conductivity and susceptibility are calculated directly from the current density and polarization density, respectively. At high frequencies, we find a peak in the real part of the conductivity due to plasma oscillations of the ions. At lower frequencies, the dynamic response of the ionomers depends on the ionic aggregate morphology in the system, which consists of either percolated or isolated aggregates. We show that the dynamic response of the model ionomers to the applied oscillating field can be understood by comparison with relevant time scales in the systems, obtained from independent calculations.

Charged Nanoparticle Attraction in Multivalent Salt Solution: A Classical-Fluids Density Functional Theory and Molecular Dynamics Study.

Negatively charged nanoparticles (NPs) in 1:1, 1:2, and 1:3 electrolyte solutions are studied in a primitive ion model using molecular dynamics (MD) simulations and classical density functional theory (DFT). We determine the conditions for attractive interactions between the like-charged NPs. Ion density profiles and NP-NP interaction free energies are compared between the two methods and are found to be in qualitative agreement. The NP interaction free energy is purely repulsive for monovalent counterions, but can be attractive for divalent and trivalent counterions. Using DFT, the NP interaction free energy for different NP diameters and charges is calculated. The depth and location of the minimum in the interaction depend strongly on the NPs' charge. For certain parameters, the depth of the attractive well can reach 8-10 kBT, indicating that kinetic arrest and aggregation of the NPs due to electrostatic interactions is possible. Rich behavior arises from the geometric constraints of counterion packing at the NP surface. Layering of counterions around the NPs is observed and, as secondary counterion layers form the minimum of the NP-NP interaction free energy shifts to larger separation, and the depth of the free energy minimum varies dramatically. We find that attractive interactions occur with and without NP overcharging.

Phase Behavior of Ternary Polymer Brushes.

Ternary polymer brushes consisting of polystyrene, poly(methyl methacrylate), and poly(4-vinylpyridine) have been synthesized. These brushes laterally phase separate into several distinct phases and can be tailored by altering the relative polymer composition. Self-consistent field theory has been used to predict the phase diagram and model both the horizontal and vertical phase behavior of the polymer brushes. All phase behaviors observed experimentally correlate well with the theoretical model.

Amphiphilic triblocks to control assembly of mixed or segregated bilayers and monolayers.

Triblock amphiphilic molecules composed of three distinct segments provide a large parameter space to obtain self-assembled structures beyond what is achievable with conventional amphiphiles. To obtain a molecular understanding of the thermodynamics of self-assembly, we develop a coarse-grained triblock polymer model and apply self-consistent field theory to investigate the packing mechanism into layer structures. By tuning the structural and interaction asymmetry, we are able to obtain bilayers and monolayers, where the latter may additionally be mixed (symmetric) or segregated (asymmetric). Of particular interest for a variety of applications are the asymmetric monolayers, where segregation of end blocks to opposite surfaces is expected to have important implications for the development of functional nanotubes and vesicles with distinct surface chemistries.

Electrical double layers and differential capacitance in molten salts from density functional theory.

Classical density functional theory (DFT) is used to calculate the structure of the electrical double layer and the differential capacitance of model molten salts. The DFT is shown to give good qualitative agreement with Monte Carlo simulations in the molten salt regime. The DFT is then applied to three common molten salts, KCl, LiCl, and LiKCl, modeled as charged hard spheres near a planar charged surface. The DFT predicts strong layering of the ions near the surface, with the oscillatory density profiles extending to larger distances for larger electrostatic interactions resulting from either lower temperature or lower dielectric constant. Overall the differential capacitance is found to be bell-shaped, in agreement with recent theories and simulations for ionic liquids and molten salts, but contrary to the results of the classical Gouy-Chapman theory.

Electrostatically tuned self-assembly of branched amphiphilic peptides.

Electrostatics plays an important role in the self-assembly of amphiphilic peptides. To develop a molecular understanding of the role of the electrostatic interactions, we develop a coarse-grained model peptide and apply self-consistent field theory to investigate the peptide assembly into a variety of aggregate nanostructures. We find that the presence and distribution of charged groups on the hydrophilic branches of the peptide can modify the molecular configuration from extended to collapsed. This change in molecular configuration influences the packing into spherical micelles, cylindrical micelles (nanofibers), or planar bilayers. The effects of charge distribution therefore have important implications for the design and utility of functional materials based on peptides.

Hydrogen-bonded aggregates in precise acid copolymers.

We perform atomistic molecular dynamics simulations of melts of four precise acid copolymers, two poly(ethylene-co-acrylic acid) (PEAA) copolymers, and two poly(ethylene-co-sulfonic acid) (PESA) copolymers. The acid groups are spaced by either 9 or 21 carbons along the polymer backbones. Hydrogen bonding causes the acid groups to form aggregates. These aggregates give rise to a low wavevector peak in the structure factors, in agreement with X-ray scattering data for the PEAA materials. The structure factors for the PESA copolymers are very similar to those for the PEAA copolymers, indicating a similar distance between aggregates which depends on the spacer length but not on the nature of the acid group. The PEAA copolymers are found to form more dimers and other small aggregates than do the PESA copolymers, while the PESA copolymers have both more free acid groups and more large aggregates.

Simulation of a small molecule analogue of a lithium ionomer in an external electric field.

We have investigated the ion dynamics in lithium-neutralized 2-pentylheptanoic acid, a small molecule analogue of a precise poly(ethylene-co-acrylic acid) lithium ionomer. Atomistic molecular dynamics simulations were performed in an external electric field. The electric field causes alignment of the ionic aggregates along the field direction. The energetic response of the system to an imposed oscillating electric field for a wide range of frequencies was tracked by monitoring the coulombic contribution to the energy. The susceptibility found in this manner is a component of the dielectric susceptibility typically measured experimentally. A dynamic transition is found and the frequency associated with this transition varies with temperature in an Arrhenius manner. The transition is observed to be associated with rearrangements of the ionic aggregates.

Atomistic Simulations Predict a Surprising Variety of Morphologies in Precise Ionomers.

The nature of ionic aggregates in ionomers remains an important open question, particularly considering its significance to their unique electrical and mechanical properties. We have carried out fully atomistic molecular dynamics simulations of melts of lithium-neutralized precise ionomers that reveal the structural features of ionic aggregates in unprecedented detail. In particular, we observe a rich variety of aggregate morphologies depending on neutralization level and ionic content, including string-like and percolated aggregates. The traditional assumption of spherical ionic aggregates with liquid-like ordering that is typically used to interpret experimental scattering data is too simplistic; a more rich and complex set of structures exist that also fit the scattering data.

Activated pathways for the directed insertion of patterned nanoparticles into polymer membranes.

We combine the string method with self-consistent field theory to compute the most probable transition pathway, i.e. the minimum free energy path, for the insertion of Janus and protein-like nanoparticles into a polymer membrane bilayer. The method makes no assumptions in the reaction coordinate and overcomes the long timescales challenge associated with simulating rare events. Our study suggests that one approach to building functional polymer­nanoparticle composite membranes with oriented nanoparticles is through electrostatic interactions. In particular, hydrophobic Janus nanoparticles with an asymmetric charge distribution can be made to directionally insert into charged membranes. This process is kinetically driven, and involves overcoming a thermally surmountable activation barrier, which requires favorable interactions between the nanoparticle and the hydrophilic block of the membrane. In contrast, the insertion of protein-like nanoparticles with alternating hydrophilic­hydrophobic­hydrophilic domains into polymer membranes does not occur as a thermally activated event.