We apply explicit solvent, coarse-grained molecular dynamics simulations to the shear flow of sodium polystyrene sulfonate chains in dilute and semi-dilute, salt-free solutions. Simulations show that polyelectrolyte chains are first extended and aligned with the shear axis, and then a folding process occurs where a sharp bend folds the chain and the chain ends repeatedly switch front and rear positions. Folding only occurs for sufficiently long chains, i.e., not for 32 bead chains, but for 64 bead chains. This minimum chain length to observe chain folding is qualitatively consistent with extension occurring above a Weissenberg number of 1, assuming Zimm dynamics. The extension was shown by the appearance of a peak in the probability distributions of end-to-end distances of the polyelectrolyte chain P(Ree) at high Ree, and the folding in half appeared as a shoulder at low Ree. Folding times in the flow direction exhibited a power law scaling exponent of -2/3 in quantitative agreement with previously reported exponents. Folding times were also independent of polyelectrolyte concentration in the semi-dilute regime. Our simulations did not show evidence of counterion release under shear, in contrast to recent reports.

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.

We employ molecular dynamics simulations using the Stockmayer fluid (SF) model, in which ionic groups are treated as charged dipolar spheres, to study the dielectric constants of ionic liquids (ILs) and polymerized ionic liquids (PILs). The simulations model ethylammonium nitrate and poly(N-vinyl ethylimidazolium bromide) by implementing both a freely rotating dipolar PIL model and one with restricted dipolar motion for the side chains. We compare their dielectric constants and analyze their dipole orientational order and correlations. We find that there is a relationship between degrees of rotational freedom and the dielectric constants of PILs, and this relationship defines the change in the dielectric constant of PILs compared to their monomeric IL counterparts.

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.

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. 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.

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.

In potassium channels that conduct K+ selectively over Na+, which sites are occupied by K+ or water and the mechanism of selectivity are unresolved questions. The combination of the energetics and the constraints imposed by the protein structure yield the selective permeation and occupancy. To gain insight into the combination of structure and energetics, we performed density functional theory (DFT) calculations of multiple N-methyl acetamide (NMA) ligands binding to K+ and Na+, relative to hydrated K+ and Na+. NMA is an analogue of the amino acid backbone and provides the carbonyl binding to the ions that occurs in most binding sites of the K+ channel. Unconstrained optimal structures are obtained through geometry optimization calculations of the NMA ligand binding. The complexes formed by 8 NMA binding to the cations have the O atoms positioned in nearly identical locations as the O atoms in the selectivity filter. The transfer free energies between bulk water and K+ or Na+ bound to 8 NMA are almost identical, implying there is no selectivity by a single site. For water optimized with 8 NMA, binding is weak and O atoms are not positioned as in the K+ channel selectivity filter, suggesting that the ions are much more favored than water. Optimal structures of 8 NMA binding with two cations (K+ or Na+) are stable and have lower binding free energy than the optimal structures with just one cation. However, in the Na+ case, the optimal structure deforms and does not match the K+ channel; that is, two bound Na+ are destabilizing. In contrast, the two K+ structure is stabilized and the selectivity free energy favors K+. Overall, this study shows that binding site occupancy and the mechanism for K+ selectivity involves multiple K+ binding in multiple neighboring layers or sites of the K+ channel selectivity filter.

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.

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. 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. 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.

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.

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.

Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current challenge is to understand the connection between microscopic physical properties of misfitting "building blocks" and emergent assembly behavior at the mesoscale. We present and analyze a particle-based description of what is arguably the best studied example for frustrated soft matter assembly, negative-curvature ribbon assembly, observed in both assemblies of chiral surfactants and shape-frustrated nanoparticles. Based on our particle model, known as saddle wedge monomers, we numerically test the connection between microscopic shape and interactions of the misfitting subunits and the emergent behavior at the supra-particle scale, specifically focussing on the propagation and relaxation of inter-particle strains, the emergent role of extrinsic shape on frustrated ribbons and the equilibrium regime of finite width selection. Beyond the intuitive role of shape misfit, we show that self-limitation is critically dependent on the finite range of cohesive interactions, with larger size finite assemblies requiring increasing short-range interparticle forces. Additionally, we demonstrate that non-linearities arising from discrete particle interactions alter self-limiting behavior due to both strain-softening in shape-flattened assembly and partial yielding of highly strained bonds, which in turn may give rise to states of hierarchical, multidomain assembly. Tracing the regimes of frustration-limited assembly to the specific microscopic features of misfitting particle shapes and interactions provides necessary guidance for translating the theory of size-programmable assembly into design of intentionally-frustrated colloidal particles.

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.