Extended Ensemble Approach to Transferable Potentials for Low-Resolution Coarse-Grained Models of Ionomers.

We develop an extended ensemble method for constructing transferable, low-resolution coarse-grained (CG) models of polyethylene-oxide (PEO)-based ionomer chains with varying composition at multiple temperatures. In particular, we consider ionomer chains consisting of 4 isophthalate groups, which may be neutral or sulfonated, that are linked by 13 PEO repeat units. The CG models represent each isophthalate group with a single CG site and also explicitly represent the diffusing sodium counterions but do not explicitly represent the PEO backbone. We define the extended ensemble as a collection of equilibrium ensembles that are obtained from united atom (UA) simulations at 2 different temperatures for 7 chemically distinct ionomers with varying degrees of sulfonation. We employ a global force-matching method to determine the set of interaction potentials that, when appropriately combined, provide an optimal approximation to the many-body potential of mean force for each system in the extended ensemble. This optimized xn force field employs long-ranged Coulomb potentials with system-specific dielectric constants that systematically decrease with increasing sulfonation and temperature. An empirical exponential model reasonably describes the sensitivity of the dielectric to sulfonation, but we find it more challenging to model the temperature-dependence of the dielectrics. Nevertheless, given appropriate dielectric constants, the transferable xn force field reasonably describes the ion pairing that is observed in the UA simulations as a function of sulfonation and temperature. Remarkably, despite eliminating any explicit description of the PEO backbone, the CG model predicts string-like ion aggregates that appear qualitatively consistent with the ionomer peak observed in X-ray scattering experiments and, moreover, with the temperature dependence of this peak.

Depletion attraction of sheet-like ion aggregates in low-dielectric ionomer melts.

Ionomers are polymers in which an ionic group is covalently bonded to the polymer backbone. Ion aggregates in ionomers have morphologies that allow for the packing of the attached polymer backbone. Using ion-only coarse-grained molecular dynamics, we observe that string-like ion aggregates become flat and sheet-like at lower dielectric constants. A consequence of the changing morphology is that the sheet-like aggregates self-assemble to form ordered, lamellar structures. We use a simple thermodynamic model to demonstrate that depletion attraction mediated by small aggregates can explain the observed order. Our results suggest that depletion attraction can drive ions to form structures that have the size scale suggested by direct visualization, produce the commonly observed experimental correlation peak from X-ray and neutron scattering, and satisfy chain-packing constraints that have been demonstrated to be important in simulations.

Ion-mediated charge transport in ionomeric electrolytes.

Ionomers, or single-ion conductors, serve as a model system to study ion transport in polymeric systems. Conductivity is a system property that depends on the net charge transport in the system. The mechanism through which ions are transported can dramatically change the contribution of an ion's self-motion (i.e. diffusion coefficient) to the conductivity of the system. For example, positive and negative ions diffusing as a pair have no net contribution to conductivity. In a coarse-grained molecular dynamics simulation of sodium-neutralized poly(PEO-co-sulfoisophthalate), we show that ion transport is mediated through consecutive coordination with ion pairs and higher order clusters due to the high density of ions. This transport mechanism is highly efficient and shows evidence of cation relaying. We show that larger ion aggregates can serve as ion-conducting paths for positive charges, and demonstrate how a highly ordered ion aggregate network can improve conductivity by enhancing correlated ion transport.

Structural dynamics as a contributor to error-prone replication by an RNA-dependent RNA polymerase.

RNA viruses encoding high- or low-fidelity RNA-dependent RNA polymerases (RdRp) are attenuated. The ability to predict residues of the RdRp required for faithful incorporation of nucleotides represents an essential step in any pipeline intended to exploit perturbed fidelity as the basis for rational design of vaccine candidates. We used x-ray crystallography, molecular dynamics simulations, NMR spectroscopy, and pre-steady-state kinetics to compare a mutator (H273R) RdRp from poliovirus to the wild-type (WT) enzyme. We show that the nucleotide-binding site toggles between the nucleotide binding-occluded and nucleotide binding-competent states. The conformational dynamics between these states were enhanced by binding to primed template RNA. For the WT, the occluded conformation was favored; for H273R, the competent conformation was favored. The resonance for Met-187 in our NMR spectra reported on the ability of the enzyme to check the correctness of the bound nucleotide. Kinetic experiments were consistent with the conformational dynamics contributing to the established pre-incorporation conformational change and fidelity checkpoint. For H273R, residues comprising the active site spent more time in the catalytically competent conformation and were more positively correlated than the WT. We propose that by linking the equilibrium between the binding-occluded and binding-competent conformations of the nucleotide-binding pocket and other active-site dynamics to the correctness of the bound nucleotide, faithful nucleotide incorporation is achieved. These studies underscore the need to apply multiple biophysical and biochemical approaches to the elucidation of the physical basis for polymerase fidelity.

Scaling behavior and local structure of ion aggregates in single-ion conductors.

Single-ion conductors are attractive electrolyte materials because of their inherent safety and ease of processing. Most ions in a sodium-neutralized PEO sulfonated-isophthalate ionomer electrolyte exist as one dimensional chains, restricted in dimensionality by the steric hindrance of the attached polymer. Because the ions are slow to reconfigure, atomistic MD simulations of this material are unable to adequately sample equilibrium ion structures. We apply a novel coarse-graining scheme using a generalized-YBG procedure in which the polymer backbone is completely removed and implicitly represented by the effective potentials of the remaining ions. The ion-only coarse-grained simulation allows for substantial sampling of equilibrium aggregate configurations. We extend the wormlike micelle theory to model ion chain equilibrium. Our aggregates are random walks which become more positively charged with increasing size. Defects occur on the string-like structure in the form of "dust" and "knots," which form due to cation coordination with open sites along the string. The presence of these defects suggest that cation hopping along open third-coordination sites could be an important mechanism of charge transport using ion aggregates.

Superionic behavior in polyethylene-oxide-based single-ion conductors.

We demonstrate superionic ion conduction in simulations of a poly(ethylene oxide)-based polymer electrolyte. The superionic conduction uses cation hopping via chain-like ion aggregates, enabling long-range charge transfer while ions only move locally. The Na single-ion conductor achieves two essential features of superionic metal ion conductors: one-dimensional ion structure and immobile anions. The superionic conduction depends on the number and length of conduction pathways, the conduction pathway lifetime, and the rate at which end ions join and leave the pathway.

Does decreasing ion-ion association improve cation mobility in single ion conductors?

We report on poly(ethylene oxide) based single ion conductors for solid polymer electrolytes. The widely agreed upon vehicle for cation movement in PEO-based solid polymer electrolytes is the single cation, in which the cation is solvated by PEO ether oxygens. Here we report a different vehicle that becomes active with strong anion-cation interactions. In the common perspective, increasing ion-ion interactions would increase ion association, decrease cation solvation, and disable cation movement. Decreasing these interactions would have the opposite effect. We vary cation-anion interaction strength, using anion charge delocalization in molecular dynamics simulations. This creates a series of systems with levels of ion aggregation from single cations (weak interaction) to mostly ion aggregates (strong interaction). Although in the weak model single cations are faster than those in ion pairs and aggregates, with stronger interactions a different mechanism emerges. Paired cations move the fastest by visiting different anion partners in succession. The importance of this observation lies in the possibility of decoupling cation movement from polymer motion, which is required to prevent dendrite formation in both Li and Na ion batteries.

Adsorption of homopolypeptides on gold investigated using atomistic molecular dynamics.

We investigate the role of dynamics on adsorption of peptides to gold surfaces using all-atom molecular dynamics simulations in explicit solvent. We choose six homopolypeptides [Ala(10), Ser(10), Thr(10), Arg(10), Lys(10), and Gln(10)], for which experimental surface coverages are not correlated with amino acid level affinities for gold, with the idea that dynamic properties may also play a role. To assess dynamics we determine both conformational movement and flexibility of the peptide within a given conformation. Low conformational movement indicates stability of a given conformation and leads to less adsorption than homopolypeptides with faster conformational movement. Likewise, low flexibility within a given conformation also leads to less adsorption. Neither amino acid affinities nor dynamic considerations alone predict surface coverage; rather both quantities must be considered in peptide adsorption to gold surfaces.

Why are coarse-grained force fields too fast? A look at dynamics of four coarse-grained polymers.

Coarse-grained models decrease the number of force sites and thus reduce computational requirements for molecular simulation. While these models are successful in describing structural properties, dynamic evolution is faster than the corresponding atomistic simulations or experiments. We consider coarse-grained models for four polymers and one polymer mixture, where accurate dynamics are obtained by scaling to match the mean-squared displacements of the corresponding atomistic descriptions. We show that the required scaling is dictated by local friction and that this scaling is only valid after the onset of continuous motion.

A molecular picture of motion in polyolefins.

We examined three united atom models in light of their description of polyolefin dynamics and investigated the relative influence of various potentials on the resulting dynamics. Results were compared with a collection of experimental data on polyethylene, poly(ethylene-alt-propylene), polypropylene, and head-to-head polypropylene, including quasielastic neutron scattering measurements that we report for two of these materials. For materials with branching, differences between force fields are apparent at low temperature, with the NERD force field most accurate. Differences between NERD and the others are the strength of nonbonded interactions and the height of torsional barriers. We artificially raised each, both of which leads to a slow down in dynamics similar to that observed when lowering temperature. Increasing nonbonded interaction strength slows dynamics with the Vogel dependence of the alpha-relaxation, while raising torsional barriers, slows dynamics with the Arrhenius dependence of the beta-relaxation.

Investigating the specificity of peptide adsorption on gold using molecular dynamics simulations.

We report all-atom molecular dynamics simulations following adsorption of gold-binding and non-gold-binding peptides on gold surfaces modeled with dispersive interactions. We examine the dependence of adsorption on both identity of the amino acids and mobility of the peptides. Within the limitations of the approach, results indicate that when the peptides are solvated, adsorption requires both configurational changes and local flexibility of individual amino acids. This is achieved when peptides consist mostly of random coils or when their secondary structural motifs (helices, sheets) are short and connected by flexible hinges. In the absence of solvent, only affinity for the surface is required: mobility is not important. In combination, these results suggest the barrier to adsorption presented by displacement of water molecules requires conformational sampling enabled through mobility.

Comparison of explicit atom, united atom, and coarse-grained simulations of poly(methyl methacrylate).

We evaluate explicit atom, united atom, and coarse-grained force fields for molecular dynamics simulation of poly(methyl methacrylate) (PMMA) by comparison to structural and dynamic neutron scattering data. The coarse-grained force field is assigned based on output of the united atom simulation, for which we use an existing force field. The atomic structure of PMMA requires the use of two types of coarse-grained beads, one representing the backbone part of the repeat unit and the other representing the side group. The explicit atom description more closely resembles dynamic experimental data than the united atom description, although the latter provides a reasonable approximation. The coarse-grained description provides structural and dynamic properties in agreement with the united atom description on which it is based, while allowing extension of the time trajectory of the simulation.

Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts.

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.

The single chain limit of structural relaxation in a polyolefin blend.

The influence of composition on component dynamics and relevant static properties in a miscible polymer blend is investigated using molecular dynamics simulation. Emphasis is placed on dynamics in the single chain dilution limit, as this limit isolates the role of inherent component mobility in the polymer's dynamic behavior when placed in a blend. For our systems, a biased local concentration affecting dynamics must arise primarily from chain connectivity, which is quantified by the self-concentration, because concentration fluctuations are minimized due to restraints on chain lengths arising from simulation considerations. The polyolefins simulated [poly(ethylene-propylene) (PEP) and poly(ethylene-butene) (PEB)] have similar structures and glass transition temperatures, and all interactions are dispersive in nature. We find that the dependence of dynamics upon composition differs between the two materials. Specifically, PEB (slower component) is more influenced by the environment than PEP. This is linked to a smaller self-concentration for PEB than PEP. We examine the accuracy of the Lodge-McLeish model (which is based on chain connectivity acting over the Kuhn segment length) in predicting simulation results for effective concentration. The model predicts the simulation results with high accuracy when the model's single parameter, the self-concentration, is calculated from simulation data. However, when utilizing the theoretical prediction of the self-concentration the model is not quantitatively accurate. The ability of the model to link the simulated self-concentration with biased local compositions at the Kuhn segment length provides strong support for the claim that chain connectivity is the leading cause of distinct mobility in polymer blends. Additionally, the direct link between the willingness of a polymer to be influenced by the environment and the value of the self-concentration emphasizes the importance of the chain connectivity. Furthermore, these findings are evidence that the Kuhn segment length is the relevant length scale controlling segmental dynamics.

A comparison of united atom, explicit atom, and coarse-grained simulation models for poly(ethylene oxide).

We compare static and dynamic properties obtained from three levels of modeling for molecular dynamics simulation of poly(ethylene oxide) (PEO). Neutron scattering data are used as a test of each model's accuracy. The three simulation models are an explicit atom (EA) model (all the hydrogens are taken into account explicitly), a united atom (UA) model (CH(2) and CH(3) groups are considered as a single unit), and a coarse-grained (CG) model (six united atoms are taken as one bead). All three models accurately describe the PEO static structure factor as measured by neutron diffraction. Dynamics are assessed by comparison to neutron time of flight data, which follow self-motion of protons. Hydrogen atom motion from the EA model and carbon/oxygen atom motion from the UA model closely follow the experimental hydrogen motion, while hydrogen atoms reinserted in the UA model are too fast. The EA and UA models provide a good description of the orientation properties of C-H vectors measured by nuclear magnetic resonance experiments. Although dynamic observables in the CG model are in excellent agreement with their united atom counterparts, they cannot be compared to neutron data because the time after which the CG model is valid is greater than the neutron decay times.

Collective motion in poly(ethylene oxide)/poly(methylmethacrylate) blends.

We present neutron spin echo and structural measurements on a perdeuterated miscible polymer blend: poly(ethylene oxide)[PEO]/poly(methyl methacrylate)[PMMA], characterized by a large difference in component glass transition temperatures and minimal interactions. The measurements cover the q range 0.35 to 1.66 A(-1) and the temperature range Tg -75 to Tg +89 K, where Tg is the blend glass transition. The spectra, obtained directly in the time domain, are very broad with stretching parameters beta approximately 0.30. The relaxation times vary considerably over the spatial range considered however at none of the q values do we see two distinct relaxation times. At small spatial scales relaxations are still detectable at temperatures far below Tg. The temperature dependence of these relaxation times strongly resembles the beta-relaxation process observed in pure PMMA.

Speed up of dynamic observables in coarse-grained molecular-dynamics simulations of unentangled polymers.

Coarse-grained models that preserve atomistic detail display faster dynamics than atomistic systems alone. We show that this " indirect speed up" is robust: coarse-grained dynamic observables computed with time scaled by a constant factor are in excellent agreement with their underlying atomistic counterparts. Borrowing from accelerated dynamics methods used in the field of rare events, we predict the scaling factor within 7%, based on reduced intermolecular attraction yielding faster neighbor cage escapes.

A molecular dynamics study of the structural dependence of boron oxide nanoparticles on shape.

Molecular dynamics simulation is employed to study the effect of varying nanoparticle shape on the structure of boron oxide nanoparticles. Two nanoshapes are investigated and compared: a sphere of diameter 16 A and a cube of dimension 16 x 16 x 16 A. A many-body polarization model is employed within the simulation, accounting for dipole moments induced by local electric fields. The resulting network is described by a short-range structure consisting of planar BO(3) units, while the intermediate-range structure is described by six-membered planar boroxol rings. Both the fraction of boroxol rings and their locations differ between the two nanoshapes. All planar boroxol rings within the spherical simulation are located on the interior, while planar rings within the cubic simulation aggregate to the cube walls. In addition, structural differences appear between the two shapes at longer ranges, including the formation of "layers" aligned parallel to the walls of the cube, reminiscent of both the low-density crystalline phase and the high-density amorphous form of boron oxide.

A molecular interpretation of vitreous boron oxide dynamics.

The mobility of vitreous boron oxide is studied by molecular dynamics simulation. A polarization model that incorporates induced dipoles arising both from charges and from other induced dipoles on atoms with nonzero polarizability is used to simulate boron oxide glass at various temperatures above the glass transition temperature. Particle mobility is investigated through the calculation of the self-intermediate scattering function and the mean-squared displacement. The calculations clearly reveal a two-step relaxation with a plateau at intermediate times for all investigated temperatures. With respect to atomic species, boron atoms are less mobile than oxygen atoms at all temperatures within the plateau region. Through analyzing particle trajectories, it is revealed that BO(3) groups move as one unit and follow each other in a stringlike manner. Three connected BO(3) groups comprise a six-membered boroxol ring, which is shown to move in a collective manner, requiring the simultaneous movement of all ring atoms. The boroxol ring is observed to be confined, or caged, during the plateau region, and jumps to a new location at longer times. This observation is linked to the concept of strong versus fragile glass formers and the potential energy landscape. In addition to the caging feature, an overshoot or dip occurs in the plateau regions of the mean-squared displacement and self-intermediate scattering functions respectively. These features are followed by a ringing pattern, previously associated with finite size effects in other strong glass formers, which persist for the duration of the plateau region. Both features are shown to be consistent with the bending of atomic "cages" from the plane of the boroxol ring, and arise due to the displacement of atoms from local minimum energy configurations.

Spatial regimes in the dynamics of polyolefins: self-motion.

Molecular dynamics simulations are used to investigate the spatial dependence of dynamics in a series of polyolefins. The dynamic indicator used is the self-intermediate scattering function, which parallels the observable in an incoherent quasielastic neutron scattering experiment such as time of flight or backscattering. As with neutron time of flight experiments, two processes are evident. The fast process is a single exponential, and has relaxation times that scale as q(-2), where q is the momentum transfer. The slow process is the stretched exponential decay usually associated with the motion underlying the glass transition. The stretching exponent is a function of spatial scale, with the minimum values occurring near the spatial scale of interchain packing. Relaxation times for the slow process scale as q(-2/beta) for all materials investigated. The relative contribution of the two processes is a function of spatial scale, with the crossover from fast to slow dynamics at the location of closest possible interchain contacts, which is approximately three times the cage size. These observations apply equally well to the four materials considered. We consider the relative ordering of relaxation times of the series in light of their local chain architecture. This ordering varies depending on the observable calculated..