We develop a Stockmayer fluid model for molecular dynamics simulations of ionic liquids that captures molecular polarization, ionic conductivity, viscosity, and glass transition temperature, using ethylammonium nitrate (EAN) as an example. The ions in EAN are treated as spheres interacting via the Lennard-Jones potential with an embedded point charge and a permanent dipole moment. We show that our simulation results for EAN are consistent with experimental data and then explore the effects of the molecular parameters on the viscosity of ionic liquids. Our results indicate that viscosity monotonically increases with ionic charge and dipole moment but non-monotonically changes with ionic diameter (or molar volume). This non-monotonic trend arises from the competition among the electrostatic interactions, molecular packing, and size asymmetry between the cation and anion. Our model also shows that long-lived ion pairs result in higher viscosities.
The binding of the sulfate ligand group to monovalent cations in the presence of water is important for many systems. To understand the structure and energetics of sulfate complexes, we use density functional theory to study ethyl sulfate binding to the monovalent cations Li+, Na+, and K+, and to water. The free energies of binding and optimal structures are calculated for a range of the number of ethyl sulfates and waters. Without water, the most optimal structure for all the cations is bidentate binding by two ethyl sulfates, yielding a 4-fold coordination. With water, the lowest free energy structures also have two ethyl sulfates, but the coordination varies with cations. For complexes with water, the four oxygen atoms in the sulfate group enable multiple binding geometries for the cations and for hydrogen bonding with water. Many of these geometries differ in free energy by only a small amount (1–2 kcal/mol), meaning there will be multiple binding configurations in bulk solution. In comparison to the optimal structures for binding to the carboxylate group, there is more variation for binding to the sulfate group as a function of cation type and the number of waters. Further, the polarization of the atoms is significant and varies among the sulfate oxygen atoms. The water oxygen charge is often larger than that of sulfate oxygen, which plays a role in the preference for monodentate ligand binding to cations in the presence of water.
The rapid transport of specific ions through matter is critical to energy storage, membrane separations, and health. However, commercial materials resist ion transport, lack specificity, or both, making ion transport costly and ineffective. Inspiration for new material designs can be taken from biology, where membrane transport proteins exert exquisite control over the specificity and rate of ion transport. The challenge in understanding and designing transport pathways is that ions often exchange their hydrating waters for direct contacts with atoms in the transport pathway. Despite intense study over decades, no theory exists to explain local ion binding and transport mechanisms and experiments cannot differentiate reliably between ions and water in binding sites. Here, we developed a new approach, based on quantum methods and extension of the quasi-chemical free energy theory, to understand and design pathways through materials for rapid transport of specific ions. Understanding ion transport mechanisms will significantly advance our nation’s ability to develop cost-effective materials for energy sustainability and therapeutics for health.
In this study, we demonstrate that a multiblock lithium-ion-conducting polymer can be swollen with ethylene carbonate solvent to increase the conductivity relative to the dry polymer material by nearly 4 orders of magnitude. This increase is due to the partial solvation of lithium ions by ethylene carbonate, which leads to Li+ diffusion along the solvent–polymer interface. This differs from the vehicular transport mechanism for lithium ions in pure solvent. We use a combination of broadband dielectric spectroscopy, X-ray scattering, and all-atom molecular dynamics simulations to probe the effect of the solvent on the polymer morphology and to elucidate the mechanism of lithium ion transport.
Cation conducting channelrhodopsins (ChRs) are a popular tool used in optogenetics to control the activity of excitable cells and tissues using light. ChRs with altered ion selectivity are in high demand for use in different cell types and for other specialized applications. However, a detailed mechanism of ion permeation in ChRs is not fully resolved. Here, we use complementary experimental and computational methods to uncover the mechanisms of cation transport and valence selectivity through the channelrhodopsin chimera, C1C2, in the high- and low-conducting open states. Electrophysiology measurements identified a single-residue substitution within the central gate, N297D, that increased Ca2+ permeability vs. Na+ by nearly two-fold at peak current, but less so at stationary current. We then developed molecular models of dimeric wild-type C1C2 and N297D mutant channels in both open states and calculated the PMF profiles for Na+ and Ca2+ permeation through each protein using well-tempered/multiple-walker metadynamics. Results of these studies agree well with experimental measurements and demonstrate that the pore entrance on the extracellular side differs from original predictions and is actually located in a gap between helices I and II. Cation transport occurs via a relay mechanism where cations are passed between flexible carboxylate sidechains lining the full length of the pore by sidechain swinging, like a monkey swinging on vines. In the mutant channel, residue D297 enhances Ca2+ permeability by mediating the handoff between the central and cytosolic binding sites via direct coordination and sidechain swinging. We also found that altered cation binding affinities at both the extracellular entrance and central binding sites underly the distinct transport properties of the low-conducting open state. This work significantly advances our understanding of ion selectivity and permeation in cation channelrhodopsins and provides the insights needed for successful development of new ion-selective optogenetic tools.
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. Here, 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.
Conceptually, single-ion polymer electrolytes (SIPE) with the anion bound to the polymer could solve major issues in Li-ion batteries, but their conductivity is too low. Experimentally, weakly interacting anionic groups have the best conductivity. To provide a theoretical basis for this result, density functional theory calculations of the optimized geometries and energies are performed for charged ligands used in SIPE. Comparison is made to neutral ligands found in dual-ion conductors, which demonstrate higher conductivity. Further, the free energy differences between adding and subtracting a ligand are small enough for the neutral ligands to have the conductivity seen experimentally. However, charged ligands have large barriers, implying that lithium transport will coincide with the slow polymer diffusion, as observed in experiments. Overall, SIPE will require additional solvent to achieve a sufficiently high conductivity. Additionally, the binding of mono- and bidentate geometries varies, providing a simple and clear reason that polarizable force fields are required for detailed interactions.
The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. Here, in order to gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.
Here, 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.
Strongly charged polyelectrolytes (PEs) demonstrate complex solution behavior as a function of chain length, concentrations, and ionic strength. The viscosity behavior is important to understand and is a core quantity for many applications, but aspects remain a challenge. Molecular dynamics simulations using implicit solvent coarse-grained (CG) models successfully reproduce structure, but are often inappropriate for calculating viscosities. To address the need for CG models which reproduce viscoelastic properties of one of the most studied PEs, sodium polystyrene sulfonate (NaPSS), we report our recent efforts in using Bayesian optimization to develop CG models of NaPSS which capture both polymer structure and dynamics in aqueous solutions with explicit solvent. We demonstrate that our explicit solvent CG NaPSS model with the ML-BOP water model [Chan et al. Nat Commun 10, 379 (2019)] quantitatively reproduces NaPSS chain statistics and solution structure. The new explicit solvent CG model is benchmarked against diffusivities from atomistic simulations and experimental specific viscosities for short chains. We also show that our Bayesian-optimized CG model is transferable to larger chain lengths across a range of concentrations. Overall, this work provides a machine-learned model to probe the structural, dynamic, and rheological properties of polyelectrolytes such as NaPSS and aids in the design of novel, strongly charged polymers with tunable structural and viscoelastic properties
Here, 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.
Almost all studies of specific ion binding by carboxylates (-COO−) have considered only a single cation, but clustering of ions and ligands is a common phenomenon. We apply density functional theory to investigate how variations in the number of acetate ligands in binding to two monovalent cations affects ion binding preferences. We study a series of monovalent (Li+, Na+, K+, Cs+) ions relevant to experimental work on many topics, including ion channels, battery storage, water purification and solar cells. We find that the preferred optimal structure has 3 acetates except for Cs+, which has 2 acetates. The optimal coordination of the cation by the carboxylate O atoms is 4 for both Na+ and K+, and 3 for Li+ and Cs+. There is a 4-fold coordination minimum just a few kcal mol−1 higher than the optimal 3-fold structure for Li+. For two cations, multiple minima occur in the vicinity of the lowest free energy state. We find that, for Li, Na and K, the preferred optimal structure with two cations is favored over a mixture of single cation complexes, providing a basis for understanding ionic cluster formation that is relevant for engineering proteins and other materials for rapid, selective ion transport.
The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager-Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the "ground-truth" molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ38from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.
For strongly charged polyelectrolytes in salt-free solutions, we use molecular dynamics simulations of a coarse-grained bead-spring model to calculate overlap concentrations c∗ and chain structure for polymers containing N = 10 to 1600 monomers. Over much of this range, we find that the end-to-end distance R∗ at c∗ increases faster than linearly with increasing N, as chains at the overlap concentration approach strongly extended conformations. This trend results in the overlap concentration c∗ decreasing as a stronger function of N than the classical prediction c∗ ∼N-2. This stronger dependence can be fit either by a logarithmic correction to scaling or by an apparent scaling c∗ ∼N-m, with m > 2.
This report summarizes molecular and continuum simulation studies focused on developing physics - based predictive models for the evolution of polymer molecular order during the nonlinear processing flows of additive manufacturing. Our molecular simulations of polymer elongation flows identified novel mechanisms of fluid dissipation for various polymer architectures that might be harnessed to enhance material processability. In order to predict the complex thermal and flow history of polymer realistic additive manufacturing processes, we have developed and deployed a high - performance mesh - free hydrodynamics module in Sandia's LAMMPS software. This module called RHEO – short for Reproducing Hydrodynamics and Elastic Objects – hybridizes an updated - Lagrange reproducing - kernel method for complex fluids with a bonded particle method (BPM) to capture solidification and solid objects in multiphase flows. In combination, our two methods allow rapid, multiscale characterization of the hydrodynamics and molecular evolution of polymers in realistic processing geometries.
Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials.
Designing polymers with controlled nanoscale morphologies and scalable synthesis is of great interest in the development of fluorine-free materials for proton-exchange membranes in fuel cells. This study focuses on a precision polyethylene with phenylsulfonic acid branches at every fifth carbon, p5PhSA, with a high ion-exchange capacity (4.2 mmol/g). The polymers self-assemble into hydrophilic and hydrophobic co-continuous nanoscale domains. In the hydrated state, the hydrophilic domain, composed of polar sulfonic acid moieties and water, serves as a pathway for efficient mesoscopic proton conductivity. The morphology and proton transport of p5PhSA are evaluated under hydrated conditions using in situ X-ray scattering and electrochemical impedance spectroscopy techniques. At 40 °C and 95% relative humidity, the proton conductivity of p5PhSA is 0.28 S/cm, which is four times greater than Nafion 117 under the same conditions. Atomistic molecular dynamics (MD) simulations are also used to elucidate the interplay between the structure and the water dynamics. The MD simulations show strong nanophase separation between the percolated hydrophilic and hydrophobic domains over a wide range of water contents. The percolated hydrophilic nanoscale domain facilitates the rapid proton transport in p5PhSA and demonstrates the potential of precise hydrocarbon-based polymers as processible and effective proton-exchange membranes.
Polymerization induced phase separation (PIPS) in a three component thermoset is studied using molecular dynamics simulations of a new coarse-grained thermoset model. The system includes two crosslinker molecules, which differ in their glass transition temperatures (Tg) and chain length and thus have the potential for phase separation. One crosslinker has a high Tg corresponding to a rubbery behavior, and simulations were performed for a short length (4 beads) and a long length (33 beads). The resin and other crosslinker have low Tg. A coarse-grained model is developed with these features and with interaction parameters determined so that for either rubbery crosslinker length, the system is in the liquid state at the cure temperature. For sufficiently slow reaction rates, the long rubbery molecule exhibits PIPS into a bicontinuous array of nanoscale domains, but the short one does not, reproducing recent experimental results. The simulations demonstrate that the reaction rates must be slow enough to allow diffusion to yield phase separation. Particularly, the reaction rate corresponding to the secondary amine must be very slow, else the structure of crosslinked clusters and the substantially increased diffusion time will prevent PIPS.
Umbrella sampling, coupled with a weighted histogram analysis method (US-WHAM), can be used to construct potentials of mean force (PMFs) for studying the complex ion permeation pathways of membrane transport proteins. Despite the widespread use of US-WHAM, obtaining a physically meaningful PMF can be challenging. Here, we provide a protocol to resolve that issue. Then, we apply that protocol to compute a meaningful PMF for sodium ion permeation through channelrhodopsin chimera, C1C2, for illustration.
Dynamic instability of microtubules is characterized by stochastically alternating phases of growth and shrinkage and is hypothesized to be controlled by the conformation and nucleotide state of tubulin dimers within the microtubule lattice. Specifically, conformation changes (compression) in the tubulin dimer following the hydrolysis of GTP have been suggested to generate stress and drive depolymerization. In the present study, molecular dynamics simulations were used in tandem with in vitro experiments to investigate changes in depolymerization based on the presence of islands of uncompressed (GMPCPP) dimers in the microtubule lattice. Both methods revealed an exponential decay in the kinetic rate of depolymerization corresponding to the relative level of uncompressed (GMPCPP) dimers, beginning at approximately 20% incorporation. This slowdown was accompanied by a distinct morphological change from unpeeling “ram’s horns” to blunt-ended dissociation at the microtubule end. Collectively these data demonstrated that islands of uncompressed dimers can alter the mechanism and kinetics of depolymerization in a manner consistent with promoting rescue events.
