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.