ParallelO(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

Modeling electrokinetic flows with the discrete ion stochastic continuum overdamped solvent algorithm

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a "dry diffusion" approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

Structure and proton conduction in sulfonated poly(ether ether ketone) semi-permeable membranes: a multi-scale computational approach

The design of polymeric membranes for proton or ionic exchange highly depends on the fundamental understanding of the physical and molecular mechanisms that control the formation of the conduction channels. There is an inherent relation between the dynamical structure of the polymeric membrane and the electrostatic forces that drive membrane segregation and proton transport. Here, we used a multi-scale computational approach to analyze the morphology of sulfonated poly(ether ether ketone) membranes at the mesoscale. A self-consistent description of the electrostatic phenomenon was adopted, where discrete polymer chains and a continuum proton field were embedded in a continuum fluid. Brownian dynamics was used for the evolution of the suspended polymer molecules, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the proton concentration field. We varied the polymer concentration, the degree of sulfonation and the level of confinement to find relationships between membrane structure and proton conduction. Our results indicate that the reduced mobility of polymer chains, at concentrations above overlap, and a moderate degree of sulfonation - i.e., 30% - are essential elements for membrane segregation and proton domain connectivity. These conditions also ensure that the membrane structure is not affected by size or by potential gradients. Importantly, our analysis shows that membrane conductivity and current are linearly dependent on polymer concentration and quadratically dependent on the degree of sulfonation. We found that the optimal polymeric membrane design requires a polymer concentration above overlap and a degree of sulfonation around 50%. These conditions promote a dynamical membrane morphology with a constant density of proton channels. Our results and measurements agree with previous experimental works, thereby validating our model and observations.

Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles

Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.