Publications

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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.

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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.

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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.

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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.

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We detail the development of a flexible simulation program (NMR_DIFFSIM) that solves the nuclear magnetic resonance (NMR) spin diffusion equation for arbitrary polymer architectures. The program was used to explore the proton (1H) NMR spin diffusion behavior predicted for a range of geometrical models describing polymer exchange membranes. These results were also directly compared with the NMR spin diffusion behavior predicted for more complex domain structures obtained from molecular dynamics (MD) simulations. The numerical implementation and capabilities of NMR_DIFFSIM were demonstrated by evaluating the experimental NMR spin diffusion behavior for the hydrophilic domain structure in sulfonated Diels-Alder Poly(Phenylene) (SDAPP) polymer membranes. The impact of morphology variations as a function of sulfonation and hydration level on the resulting NMR spin diffusion behavior were determined. These simulations allowed us to critically address the ability of NMR spin diffusion to discriminate between different structural models, and to highlight the extremely high fidelity experimental data required to accomplish this. A direct comparison of experimental double-quantum-filtered 1H NMR spin diffusion in SDAPP membranes to the spin diffusion behavior predicted for MD-proposed morphologies revealed excellent agreement, providing experimental support for the MD structures at low to moderate hydration levels. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 62–78.

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.

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.

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