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.
Here, using atomistic molecular dynamics simulations, we investigate the morphology and transport properties of a new family of fluorine-free terpolymers designed as proton-exchange membranes. Simulated random terpolymers consist of three monomers with a 5-carbon backbone with a phenylsulfonate, phenyl, or no pendant group and have ion exchange capacities (IECs) ranging from 1.06–4.14 mmol/g. At a hydration level of 9, cluster analysis reveals macrophase separation between water and terpolymers with IEC < 2.1 mmol/g and continuous, percolated hydrophilic and hydrophobic nanoscale domains at higher IECs. Channel width distribution analysis of the percolated morphologies revealed that more hydrophobic units produce less uniform channels. Decreasing the surface area per sulfonate group and increasing the fractal dimension of the hydrophilic domains correlate with increased water diffusivity, due to a more acidic interface and more isotropic water channels. Relative to the previously studied phenylsulfonate homopolymer, these terpolymers with lower IECs have only modestly lower water diffusion, and we anticipate other advantages related to processability.
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.
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.
This work explores the influence of blend composition, network architecture, and hydrogen bonding on the material properties of crosslinked epoxy networks, focusing on the glass transition temperature (Tg) and Young’s modulus (Y). We used coarse-grained molecular dynamics simulations to simulate varying compositions of stiff and flexible components in epoxy monomer blends with varying excess of curative. We find that, without hydrogen bonding, networks of any composition show a monotonically increasing Tg with decreasing excess curative, consistent with theory. In contrast, we find that when hydrogen bonding is introduced, the binary blend networks show significant enhancement in Tg for lightly crosslinked systems. This result contributes to an explanation of the anomalous Tg behavior observed experimentally in these systems. We further find that Y is generally enhanced by hydrogen bonds, especially below Tg, demonstrating that hydrogen bonding has a significant influence on mechanical properties and can allow access to other desirable dynamic behavior, especially self-healing.
Recent studies on off-stoichiometric thermosets reveal unique viscoelastic behavior derived from increased free volume and physical interactions between chain ends. To understand structural characteristics arising from cure and its effect on properties, we developed a Monte Carlo model based on step-growth polymerization. Our model accurately predicted structure-property trends for a two-component system of EPON 828 (EPON) and ethylenediamine. A second epoxy monomer, D.E.R. 732 (DER), was investigated to modulate Tg. Binary mixtures of EPON and DER in off-stoichiometric, amine-rich formulations resulted in nonlinear evolution of thermomechanical properties with respect to initial formulation stoichiometry. Modifying our model with kinetic parameters allowing for differential epoxide/amine reaction kinetics only partially accounted for trends in Tg, suggesting that spatiotemporal contributions─not captured by our model─were significant determinants of material properties compared to polymer architecture for three-component systems. These findings underpin the importance of spatial awareness in modeling to inform the development of dynamic thermosets.
Elastomeric rubbers serve a vital role as sealing materials in the hydrogen storage and transport infrastructure. With applications including O-rings and hose-liners, these components are exposed to pressurized hydrogen at a range of temperatures, cycling rates, and pressure extremes. Cyclic (de)pressurization is known to degrade these materials through the process of cavitation. This readily visible failure mode occurs as a fracture or rupture of the material and is due to the oversaturated gas localizing to form gas bubbles. Computational modeling in the Hydrogen Materials Compatibility Program (H-Mat), co-led by Sandia National Laboratories and Pacific Northwest National Laboratory, employs multi-scale simulation efforts to build a predictive understanding of hydrogen-induced damage in materials. Modeling efforts within the project aim to provide insight into how to formulate materials that are less sensitive to high-pressure hydrogen-induced failure. In this document, we summarize results from atomistic molecular dynamics simulations, which make predictive assessments of the effects of compositional variations in the commonly used elastomer, ethylene propylene diene monomer (EPDM).
Elastomeric rubber materials serve a vital role as sealing materials in the hydrogen storage and transport infrastructure. With applications including O-rings and hose liners, these components are exposed to pressurized hydrogen at a range of temperatures, cycling rates, and pressure extremes. High-pressure exposure and subsequent rapid decompression often lead to cavitation and stress-induced damage of the elastomer due to localization of the hydrogen gas. Here, we use all-atom classical molecular dynamics simulations to assess the impact of compositional variations on gas diffusion within the commonly used elastomer ethylene−propylene−diene monomer (EPDM). With the aim to build a predictive understanding of precursors to cavitation and to motivate material formulations that are less sensitive to hydrogen-induced failure, we perform systematic simulations of gas dynamics in EPDM as a function of temperature, gas concentration, and cross-link density. Our simulations reveal anomalous, subdiffusive hydrogen motion at pressure and intermediate times. We identify two groups of gas with different mobilities: one group exhibiting high mobility and one group exhibiting low mobility due to their motion being impeded by the polymer. With decreasing temperatures, the low-mobility group shows increased gas localization, the necessary precursor for cavitation damage in these materials. At lower temperatures, increasing cross-link density led to greater hydrogen gas mobility and a lower fraction of caged hydrogen, indicating that increasing cross-link density may reduce precursors to cavitation. Finally, we use a two-state kinetic model to determine the energetics associated with transitions between these two mobility states.
High-pressure storage and cyclic (de)pressurization of hydrogen gas is known to result in degradation and failure of gas canisters, hoses, linings, and O-rings as the relatively small hydrogen molecule can readily permeate most materials. Hence, identifying material compositions that are less susceptible to hydrogen-induced damage is of significant importance to the hydrogen energy infrastructure. Here, we use classical atomistic molecular dynamics simulations to study hydrogen exposed ethylene-propylene-diene monomer (EPDM) rubber, an elastomer typically used in O-rings. We make chemical modifications to the model by adjusting the crosslink density and report on gas solubility, diffusivity, and molecular restructuring in response to rapid decompression. Our simulations indicate that increases in crosslink density can reduce volumetric expansion during decompression and result in smaller free volume pore sizes. However, these favorable properties for sealing materials come with a tradeoff. At pressure, crosslinks introduce extra free volume, providing potential sites for gas localization, the precursor to cavitation-induced failure.
In alkaline zinc–manganese dioxide batteries, there is a need for selective polymeric separators that have good hydroxide ion conductivity but that prevent the transport of zincate (Zn(OH)4)2-. Here we investigate the nanoscale structure and hydroxide transport in two cationic polysulfones that are promising for these separators. We present the synthesis and characterization for a tetraethylammonium-functionalized polysulfone (TEA-PSU) and compare it to our previous work on an N-butylimidazolium-functionalized polysulfone (NBI-PSU). We perform atomistic molecular dynamics (MD) simulations of both polymers at experimentally relevant water contents. The MD simulations show that both polymers develop well phase separated nanoscale water domains that percolate through the polymer. Calculation of the total scattering intensity from the MD simulations reveal weak or nonexistent ionomer peaks at low wave vectors. The lack of an ionomer peak is due to a loss of contrast in the scattering. The small water domains in both polymers, with median diameters on the order of 0.5–0.7 nm, lead to hydroxide and water diffusion constants that are 1–2 orders of magnitude smaller than their values in bulk water. This confinement lowers the conductivity but also may explain the strong exclusion of zincate from the PSU membranes seen experimentally.
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.
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.
Recent experimental and simulation studies have shown that polymer-nanoparticle (NP) composites (PNCs) with ultra-high NP loading (>50%) exhibit remarkable mechanical properties and dramatic increases in polymer glass-transition temperature, viscosity, and thermal stability compared to the bulk polymer. These deviations in macroscopic properties suggest a slowdown in both segmental and chain-scale polymer dynamics due to confinement. In this work, we examine the polymer conformations and dynamics in these PNCs using molecular dynamics simulations of both unentangled and entangled coarse-grained polymers in random-close-packed NP packings with varying polymer fill fractions. We find that the changes in the polymer dynamics depend on the number of NPs in contact with a polymer segment. Using the number of polymer-NP contacts and different polymer chain conformations as criteria for categorization, we further examine the polymer dynamics at multiple length scales to show the high level of dynamic heterogeneity in PNCs with ultra-high NP loading.
The self-Assembly of binary polymer-grafted nanoparticles (NPs) in a selective solvent is investigated using coarse-grained simulations. Simulations are performed using theoretically informed Langevin dynamics (TILD), a particle-based method that employs a particle-To-mesh scheme to efficiently calculate the nonbonded interactions. The particles are densely grafted with two immiscible polymers, A and B, that are permanently bound to the NP either at random grafting sites (random-grafted) or with all the A chains on one hemisphere of the NP and all the B chains on the other hemisphere (Janus-grafted). For NPs with random grafting, the polymers phase-separate on the surface of the NP to form Janus-Type structures in dilute solution, even though some of the chains have to stretch around the particle to form the Janus structure. When the solvent quality is sufficiently poor for the solvophobic chains, the binary grafted NPs assemble into various structures, including double-walled vesicles. In particular, vesicles are formed when the solvophilic volume fraction is between 0.2 and 0.3, in a similar range to that required for vesicle formation in diblock copolymers in a selective solvent. For mixed-grafted NPs, there is considerable variation in the structure of each individual NP, but nevertheless, these NPs form ordered vesicles, similar to those formed by Janus-grafted NPs.
We describe a set of precise single-ion conducting polymers that form self-assembled percolated ionic aggregates in glassy polymer matrices and have decoupled transport of metal cations. These precise single-ion conductors (SICs), synthesized by a scalable ring-opening metathesis polymerization, consist of a polyethylene backbone with a sulfonated phenyl group pendant on every fifth carbon and are fully neutralized by a counterion X+ (Li+, Na+, or Cs+). Experimental X-ray scattering measurements and fully atomistic molecular dynamics (MD) simulations are in good agreement. The MD simulations show that the ionic groups nanophase separate from the polymer backbone to form percolating ionic aggregates. Using graph theory, we find that within the Li+- and Na+-neutralized polymers the percolated aggregates exhibit planar and ribbon-like configurations at intermediate length scales, while the percolated aggregates within the Cs+-neutralized polymers are more isotropic. Electrical impedance spectroscopy measurements show that the ionic conductivities exhibit Arrhenius behavior, with conductivities of 10-7 to 10-6 S/cm at 180 °C. In the MD simulations, the cations move between sulfonate groups in the percolated aggregates, larger ions travel further, and overall cations travel further than the polymer backbones, indicating a decoupled ion-transport mechanism. Thus, the percolated ionic aggregates in these polymers can serve as pathways to facilitate decoupled ion motion through a glassy polymer matrix.
Macromolecules is an exceptional resource in the field of polymer science and now publishes more than 1000 original articles a year that set the standard for scientific rigor and creative insights. Over the years, these individual contributions have combined to build the foundation of polymer science, broadly and inclusively defined. In addition to the individual articles, many of which are being celebrated in this series of editorials, Macromolecules has published invaluable reviews and perspectives. These scholarly contributions integrate the insights and results from numerous sources into a unified whole and often recommend future directions for the field. Novices and experts alike benefit from these works that capture topics from emerging discoveries to long-pondered topics and everything in between. To explore the importance of Macromolecules’ reviews and perspectives, we considered their influence on the field and found the 1994 review by Fetters et al. entitled “Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties”1 to be a singularity. This review expertly curates and compiles a trove of data to build robust correlations between molecular characteristics and macroscopic viscoelastic properties of polymer melts, in the context of the tube model of entanglements.
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.
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.
Polymer nanoparticle composites (PNCs) with ultrahigh loading of nanoparticles (NPs) (>50%) have been shown to exhibit markedly improved strength, stiffness, and toughness simultaneously compared to the neat systems of their components. Recent experimental studies on the effect of polymer fill fraction in these highly loaded PNCs reveal that even at low polymer fill fractions, hardness and modulus increase significantly. In this work, we aim to understand the origin of these performance enhancements by examining the dynamics of both polymer and NPs under tensile deformation. We perform molecular dynamics simulations of coarse-grained, glassy polymer in random-close-packed NP packings with a varying polymer fill fraction. We characterize the mechanical properties of the PNC systems, compare the NP rearrangement behavior, and study the polymer segmental and chain-level dynamics during deformation below the polymer glass transition. Finally, our simulation results confirm the experimentally observed increase in modulus at low polymer fill fractions, and we provide evidence that the source of mechanical enhancement is the polymer bridging effect.
We analyze the dynamics from microsecond-long, atomistic molecular dynamics (MD) simulations of 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. At short times, the intermediate structure factor calculated from the MD simulations is in reasonable agreement with quasi-elastic neutron scattering data for partially neutralized ionomers. For ionomers that are 100% neutralized with lithium, the simulations reveal three dynamic processes in the chain dynamics. The fast process corresponds to hydration librations, the medium-time process corresponds to local conformational motions of the portions of the chains between ionic aggregates, and the long-time process corresponds to relaxation of the ionic aggregates. At 600 K, the dynamics are sufficiently fast to observe the early stages of lithium-ion motion and ionic aggregate rearrangements. In the partially neutralized ionomers with isolated ionic aggregates, the Li-ion-containing aggregates rearrange by a process of merging and breaking up, similar to what has been observed in coarse-grained (CG) simulations. In the 100% neutralized ionomers that contain percolated ionic aggregates, the chains remain pinned by the percolated aggregate at long times, but the lithium ions are able to move along the percolated aggregate. Here, the ion dynamics are also qualitatively similar to those seen in previous CG simulations.
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.
Koski, Jason P.; Krook, Nadia M.; Ford, Jamie; Yahata, Yoshikazu; Ohno, Kohji; Murray, Christopher B.; Frischknecht, Amalie L.; Composto, Russell J.; Riggleman, Robert A.
There are limited theoretically predicted phase diagrams for polymer nanocomposites (PNCs) because conventional modeling techniques are largely unable to predict the macroscale phase behavior of PNCs. Here, we show that recent field-based methods, including PNC field theory (PNC-FT) and theoretically informed Langevin dynamics, can be used to calculate phase diagrams for polymer-grafted nanoparticles (gNPs) incorporated into a polymer matrix. We calculate binodals for the transition from the miscible, dispersed phase to the macrophase separated state as functions of important experimental parameters, including the ratio of the matrix chain degree of polymerization (P) to the grafted chain degree of polymerization (N), the enthalpic repulsion between the matrix and grafted chains, the grafting density (σ), the size of the NPs, and the NP volume fraction. We demonstrate that thermal and polymer conformational fluctuations enhance the degree of phase separation in gNP-PNCs, a result of depletion interaction effects. We support this conclusion by experimentally investigating the phase separation of poly(methyl methacrylate)-grafted silica NPs in a polystyrene matrix as a function of P/N. The simulations only agree with experiments when fluctuations are included because fluctuations are needed to properly capture the depletion interactions between the gNPs. We clarify the role of conformational entropy in driving depletion interactions in PNCs and suggest that inconsistencies in the literature may be due to polymer chain length effects since conformational entropy increases with increasing chain length.
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.
Multiple computational and experimental techniques are used to understand the nanoscale morphology and water/proton transport properties in a series of sulfonated Diels-Alder poly(phenylene) (SDAPP) membranes over a wide range of temperature, hydration, and sulfonation conditions. New synthetic methods allow us to sulfonate the SDAPP membranes to much higher ion exchange capacity levels than has been previously possible. Nanoscale phase separation between the hydrophobic polymer backbone and the hydrophilic water/sulfonic acid groups was observed for all membranes studied. We find good agreement between structure factors calculated from atomistic molecular dynamics (MD) simulations and those measured by X-ray scattering. With increasing hydration, the scattering ionomer peak in SDAPP is found to decrease in intensity. This intensity decrease is shown to be due to a reduction of scattering contrast between the water and polymer and is not indicative of any loss of nanoscale phase separation. Both MD simulations and density functional theory (DFT) calculations show that as hydration levels are increased, the nanostructure morphology in SDAPP evolves from isolated ionic domains to fully percolated water networks containing progressively weaker hydrogen bond strengths. The conductivity of the membranes is measured by electrical impedance spectroscopy and the equivalent proton conductivity calculated from pulsed-field-gradient (PFG) NMR diffusometry measurements of the hydration waters. Comparison of the measured and calculated conductivity reveals that in SDAPP the proton conduction mechanism evolves from being dominated by vehicular transport at low hydration and sulfonation levels to including a significant contribution from the Grötthuss mechanism (also known as structural diffusion) at higher hydration and sulfonation levels. The observed increase in conductivity reflects the impact that changing hydration and sulfonation have on the morphology and hydrogen bond network and ultimately on the membrane performance.
Cheap and efficient ion conducting separators are needed to improve efficiency and lifetime in fuel cells, batteries, and electrolyzers. Current state-of-the-art polymeric separators are made from Nafion, which is too expensive to be competitive with other technologies. Sandia has developed unique polymer separators that have lower cost and equivalent or superior ion transport compared to Nafion. These membranes consist of sulfonated Diels-Alder poly(phenylene) (SDAPP), a completely hydrocarbon polymer that conducts protons when hydrated. SDAPP membranes are thermally and chemically robust, with conductivities rivaling those of Nafion at high sulfonation levels. However, rational design of new separators requires molecular-level knowledge, currently unknown, of how polymer morphology affects transport. Here we describe the use of multiple computational and experimental techniques to understand the nanoscale morphology and water/proton transport properties in a series of sulfonated SDAPP membranes over a wide range of temperature, hydration, and sulfonation conditions.
In this work we present a computational capability featuring a hierarchy of models with different fidelities for the solution of electrokinetics problems at the micro-/nano-scale. A multifidelity approach allows the selection of the most appropriate model, in terms of accuracy and computational cost, for the particular application at hand. We demonstrate the proposed multifidelity approach by studying the mobility of a colloid in a micro-channel as a function of the colloid charge and of the size of the ions dissolved in the fluid.
We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.
We performed atomistic simulations on a series of sulfonated polyphenylenes systematically varying the degree of sulfonation and water content to determine their effect on the nanoscale structure, particularly for the hydrophilic domains formed by the ionic groups and water molecules. We found that the local structure around the ionic groups depended on the sulfonation and hydration levels, with the sulfonate groups and hydronium ions less strongly coupled at higher water contents. In addition, we characterized the morphology of the ionic domains employing two complementary clustering algorithms. At low sulfonation and hydration levels, clusters were more elongated in shape and poorly connected throughout the system. As the degree of sulfonation and water content were increased, the clusters became more spherical, and a fully percolated ionic domain was formed. These structural details have important implications for ion transport.
Melt state dynamics for a series of strictly linear polyethylenes with precisely spaced associating functional groups were investigated. The periodic pendant acrylic acid groups form hydrogen-bonded acid aggregates within the polyethylene (PE) matrix. The dynamics of these nanoscale heterogeneous morphologies were investigated from picosecond to nanosecond timescales by both quasi-elastic neutron scattering (QENS) measurements and fully atomistic molecular dynamics (MD) simulations. Two dynamic processes were observed. The faster dynamic processes which occur at the picosecond timescales are compositionally insensitive and indicative of spatially restricted local motions. The slower dynamic processes are highly composition dependent and indicate the structural relaxation of the polymer backbone. Higher acid contents, or shorter PE spacers between pendant acid groups, slow the structural relaxation timescale and increase the stretching parameter (β) of the structural relaxation. Additionally, the dynamics of specific hydrogen atom positions along the backbone correlate structural heterogeneity imposed by the associating acid groups with a mobility gradient along the polymer backbone. At time intervals (<2 ns), the mean-squared displacements for the four methylene groups closest to the acid groups are up to 10 times smaller than those of methylene groups further from the acid groups. At longer timescales acid aggregates rearrange and the chain dynamics of the slow, near-aggregate regions and the faster bridge regions converge, implying a characteristic timescale for the passage of chains between aggregates. The characterization of the nanoscale chain dynamics in these associating polymer systems both provides validation of simulation force fields and provides understanding of heterogeneous chain dynamics in associating polymers.
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.
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.
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.
Controllable end-to-end alignment of nanorods in polymer films would enable new applications, especially for metallic nanorods, where coupling of surface plasmon resonances can lead to enhanced electric fields (hot spots) between nanorod ends. To achieve end-to-end alignment, we investigate the dispersion and aggregation behavior of polymer brush-coated nanorods in a chemically identical homopolymer matrix using self-consistent field theory (SCFT). We find good agreement with previous DFT calculations and experiments for side-by-side alignment. However, we also find that thermodynamic aggregation of uniformly grafted nanorods in a polymer matrix will preferentially occur side-by-side rather than end-to-end. To achieve preferential end-to-end linking, we propose using different grafting molecular weights (relative to the length of the matrix chains) on the sides and the ends of the nanorods. We demonstrate this idea with an example system in which the side brush length is chosen so that the side-by-side interaction energy is purely repulsive, while the end grafted polymer chains are shorter so that the end-to-end interaction energy has a strong attractive well due to autophobic dewetting effects. We thus show that using chemically similar brushes with different molecular weights on the sides and ends of the nanorods can lead to entropically driven end-linked nanorods in an organic matrix. The gap between the nanorod ends is tunable by changing the end brush molecular weight, and therefore the plasmon enhancement would also be tunable.
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.
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.
Designing acid- and ion-containing polymers for optimal proton, ion, or water transport would benefit profoundly from predictive models or theories that relate polymer structures with ionomer morphologies. Recently, atomistic molecular dynamics (MD) simulations were performed to study the morphologies of precise poly(ethylene-co-acrylic acid) copolymer and ionomer melts. Here, we present the first direct comparisons between scattering profiles, I(q), calculated from these atomistic MD simulations and experimental X-ray data for 11 materials. This set of precise polymers has spacers of exactly 9, 15, or 21 carbons between acid groups and has been partially neutralized with Li, Na, Cs, or Zn. In these polymers, the simulations at 120 °C reveal ionic aggregates with a range of morphologies, from compact, isolated aggregates (type 1) to branched, stringy aggregates (type 2) to branched, stringy aggregates that percolate through the simulation box (type 3). Excellent agreement is found between the simulated and experimental scattering peak positions across all polymer types and aggregate morphologies. The shape of the amorphous halo in the simulated I(q) profile is in excellent agreement with experimental I(q). The modified hard-sphere scattering model fits both the simulation and experimental I(q) data for type 1 aggregate morphologies, and the aggregate sizes and separations are in agreement. Given the stringy structure in types 2 and 3, we develop a scattering model based on cylindrical aggregates. Both the spherical and cylindrical scattering models fit I(q) data from the polymers with type 2 and 3 aggregates equally well, and the extracted aggregate radii and inter- and intra-aggregate spacings are in agreement between simulation and experiment. Furthermore, these dimensions are consistent with real-space analyses of the atomistic MD simulations. By combining simulations and experiments, the ionomer scattering peak can be associated with the average distance between branches of type 2 or 3 aggregates. This direct comparison of X-ray scattering data to the atomistic MD simulations is a substantive step toward providing a comprehensive, predictive model for ionomer morphology, gives substantial support for this atomistic MD model, and provides new credibility to the presence of stringy, branched, and percolated ionic aggregates in precise ionomer melts.
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. In conclusion, 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.
There is national interest in the development of sophisticated materials that can automatically detect and respond to chemical and biological threats without the need for human intervention. In living systems, cell membranes perform such functions on a routine basis, detecting threats, communicating with the cell, and triggering automatic responses such as the opening and closing of ion channels. The purpose of this project was to learn how to replicate simple threat detection and response functions within artificial membrane systems. The original goals toward developing 'smart skin' assemblies included: (1) synthesizing functionalized nanoparticles to produce electrochemically responsive systems within a lipid bilayer host matrices, (2) calculating the energetics of nanoparticle-lipid interactions and pore formation, and (3) determining the mechanism of insertion of nanoparticles in lipid bilayers via imaging and electrochemistry. There are a few reports of the use of programmable materials to open and close pores in rigid hosts such as mesoporous materials using either heat or light activation. However, none of these materials can regulate themselves in response to the detection of threats. The strategies we investigated in this project involve learning how to use programmable nanomaterials to automatically eliminate open channels within a lipid bilayer host when 'threats' are detected. We generated and characterized functionalized nanoparticles that can be used to create synthetic pores through the membrane and investigated methods of eliminating the pores either through electrochemistry, change in pH, etc. We also focused on characterizing the behavior of functionalized gold NPs in different lipid membranes and lipid vesicles and coupled these results to modeling efforts designed to gain an understanding of the interaction of nanoparticles within lipid assemblies.
Ionomers--polymers containing a small fraction of covalently bound ionic groups--have potential application as solid electrolytes in batteries. Understanding ion transport in ionomers is essential for such applications. Due to strong electrostatic interactions in these materials, the ions form aggregates, tending to slow counterion diffusion. A key question is how ionomer properties affect ionic aggregation and counterion dynamics on a molecular level. Recent experimental advances have allowed synthesis and extensive characterization of ionomers with a precise, constant spacing of charged groups, making them ideal for controlled measurement and more direct comparison with molecular simulation. We have used coarse-grained molecular dynamics to simulate such ionomers with regularly spaced charged beads. The charged beads are placed either in the polymer backbone or as pendants on the backbone. The polymers, along with the counterions, are simulated at melt densities. The ionic aggregate structure was determined as a function of the dielectric constant, spacing of the charged beads on the polymer, and the sizes of the charged beads and counterions. The pendant ion architecture can yield qualitatively different aggregate structures from those of the linear polymers. For small pendant ions, roughly spherical aggregates have been found above the glass transition temperature. The implications of these aggregates for ion diffusion will be discussed.
We use the modified iSAFT density functional theory (DFT) to calculate interactions among nanoparticles immersed in a polymer melt. Because a polymer can simultaneously interact with more than two nanoparticles, three-body interactions are important in this system. We treat the nanoparticles as spherical surfaces, and solve for the polymer densities around the nanoparticles in three dimensions. The polymer is modeled as a freely-jointed chain of spherical sites, and all interactions are repulsive. The potential of mean force (PMF) between two nanoparticles displays a minimum at contact due to the depletion effect. The PMF calculated from the DFT agrees nearly quantitatively with that calculated from self-consistent PRISM theory. From the DFT we find that the three-body free energy is significantly different in magnitude than the effective three-body free energy derived from the two-particle PMF.
The objective of the experimental effort is to provide a model particle system that will enable modeling of the macroscopic rheology from the interfacial and environmental structure of the particles and solvent or melt as functions of applied shear and volume fraction of the solid particles. This chapter describes the choice of the model particle system, methods for synthesis and characterization, and results from characterization of colloidal dispersion, particle film formation, and the shear and oscillatory rheology in the system. Surface characterization of the grafted PDMS interface, dispersion characterization of the colloids, and rheological characterization of the dispersions as a function of volume fraction were conducted.
Nanoparticle interactions and their impact on particle dispersion and rheology are well known to be functions of the interfacial structure between the particle and the fluid phase. The dispersion and flow properties of a titania nanopowder were evaluated in polydimethylsiloxane fluid using ''grafted to'' surface modification of the titania with short molecular weight PDMS polymers. The interaction energy between particles was modeled using analytical expressions as well as dynamic functional theory for polymer surface chains. Particle dynamics as a function of volume fraction were characterized using light scattering, acoustic spectroscopy, and shear and oscillatory measurements. Autophobic dewetting is a novel short range interaction in this system that may be impacting the maximum packing fraction of particles in a suspension.
Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. Here I use a classical density functional theory to study the polymer-mediated interactions between two nanorods. The rods are immersed in an athermal, melt polymer blend consisting of: (1) a small fraction of chains of length N=20 with 'sticky' ends that are attracted to the rods with energy e/kT so that they form a polymer brush on the rods; and (2) a matrix of chains of length P which have no interactions with the rods. The structure of the brushes depends on the nanorod diameter, P, and e/kT. There is an attractive well in the force between the rods near contact, followed by a strong repulsion as the brushes are compressed. The depth of the well increases with increasing P. I will discuss the implications for experimental systems.
A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to generate trial bond lengths, angles and dihedrals is described and shown to provide similar acceptance rates with substantially less computational effort. Several different trial distributions are studied and a linear combination of the ideal distribution plus Gaussian distributions automatically fit to the energetic and ideal terms is found to give the best results. The use of these arbitrary trial distributions enables a new formulation of coupled-decoupled configurational bias Monte Carlo that has significantly higher acceptance rates for cyclic molecules. The chemical potential measured via a modified Widom insertion is found to be ill-defined in the case of a molecule that has flexible bond lengths due to the unbounded probability distribution that describes the distance between any two atoms. We propose a simple standard state that allows the computation of consistent chemical potentials for molecules with flexible bonds. We show that the chemical potential via Widom insertion is not computed properly for molecules with Coulombic interactions when the number of trials for any of the nonbonded selection steps is greater than one. Finally, we demonstrate the power of the new algorithms by sampling the side-chain conformations of a polypeptide.
Carbon nanotubes (CNT) are unique nanoscale building blocks for a variety of materials and applications, from nanocomposites, sensors and molecular electronics to drug and vaccine delivery. An important step towards realizing these applications is the ability to controllably self-assemble the nanotubes into larger structures. Recently, amphiphilic peptide helices have been shown to bind to carbon nanotubes and thus solubilize them in water. Furthermore, the peptides then facilitate the assembly of the peptide-wrapped nanotubes into supramolecular, well-aligned fibers. We investigate the role that molecular modeling can play in elucidating the interactions between the peptides and the carbon nanotubes in aqueous solution. Using ab initio methods, we have studied the interactions between water and CNTs. Classical simulations can be used on larger length scales. However, it is difficult to sample in atomistic detail large biomolecules such as the amphiphilic peptide of interest here. Thus, we have explored both new sampling methods using configurational-bias Monte Carlo simulations, and also coarse-grained models for peptides described in the literature. An improved capability to model these inorganichiopolymer interfaces could be used to generate improved understanding of peptide-nanotube self-assembly, eventually leading to the engineering of new peptides for specific self-assembly goals.
Understanding the properties and behavior of biomembranes is fundamental to many biological processes and technologies. Microdomains in biomembranes or ''lipid rafts'' are now known to be an integral part of cell signaling, vesicle formation, fusion processes, protein trafficking, and viral and toxin infection processes. Understanding how microdomains form, how they depend on membrane constituents, and how they act not only has biological implications, but also will impact Sandia's effort in development of membranes that structurally adapt to their environment in a controlled manner. To provide such understanding, we created physically-based models of biomembranes. Molecular dynamics (MD) simulations and classical density functional theory (DFT) calculations using these models were applied to phenomena such as microdomain formation, membrane fusion, pattern formation, and protein insertion. Because lipid dynamics and self-organization in membranes occur on length and time scales beyond atomistic MD, we used coarse-grained models of double tail lipid molecules that spontaneously self-assemble into bilayers. DFT provided equilibrium information on membrane structure. Experimental work was performed to further help elucidate the fundamental membrane organization principles.
Classical density functional theory (DFT) is applied to study properties of fully detailed, realistic models of poly(dimethylsiloxane) liquids near silica surfaces and compared to results from molecular dynamics simulations. In solving the DFT equations, the direct correlation functions are obtained from the polymer reference interaction site model (PRISM) theory for the repulsive parts of the interatomic interactions, and the attractions are treated via the random-phase approximation (RPA). Good agreement between density profiles calculated from DFT and from the simulations is obtained with empirical scaling of the direct correlation functions. Separate scaling factors are required for the PRISM and RPA parts of the direct correlation functions. Theoretical predictions of stress profiles, normal pressure, and surface tensions are also in reasonable agreement with simulation results.