Importance of varying permittivity on the conductivity of polyelectrolyte solutions.

Dissolved ions can alter the local permittivity of water; nevertheless most theories and simulations ignore this fact. We present a novel algorithm for treating spatial and temporal variations in the permittivity and use it to measure the equivalent conductivity of a salt-free polyelectrolyte solution. Our new approach quantitatively reproduces experimental results unlike simulations with a constant permittivity that even qualitatively fail to describe the data. We can relate this success to a change in the ion distribution close to the polymer due to the buildup of a permittivity gradient.

The influence of charged-induced variations in the local permittivity on the static and dynamic properties of polyelectrolyte solutions.

There is a large body of literature investigating the static and dynamic properties of polyelectrolytes due both to their widespread application in industrial processes and their ubiquitous presence in biology. Because of their highly charged nature, polyelectrolytes tend to alter the local dielectric permittivity of the solution within a few nanometers of their backbone. This effect has, however, been almost entirely ignored in both simulations and theoretical work. In this article, we apply our recently developed electrostatic solver based on Maxwell's equations to examine the effects of the permittivity reduction in the vicinity of the polyelectrolyte. We first verify our new approach by calculating and comparing ion distributions around a linear fixed polyelectrolyte and find both quantitative and qualitative changes in the ion distribution. Further simulations with an applied electric field show that the reduction in the local dielectric constant increases the mobility of the chains by approximately ten percent. More importantly, variations in the local dielectric constant lead to qualitatively different behavior of the conductivity.

Simulation of electric double layers around charged colloids in aqueous solution of variable permittivity.

The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system, let alone in the surrounding solvent. In this article, we introduce two relatively new methods that can solve the Poisson equation for systems with varying permittivity. The harmonic interpolation method approximately solves the Green's function in terms of a spherical harmonics series, and thus provides analytical ion-ion potentials for the Hamiltonian of charged systems. The Maxwell equations molecular dynamics algorithm features a local approach to electrostatics, allowing for arbitrary local changes of the dielectric constant. We show that the results of both methods are in very good agreement. We also found that the renormalized charge of the colloid, and with it the effective far field interaction, significantly changes if the dielectric properties within the vicinity of the colloid are changed.

Comparison of scalable fast methods for long-range interactions.

Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability.