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.