In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolyte model. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge, electrolyte concentration, and pore radius). We present current data that characterize the nanopore’s behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics, and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns, that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore but are relatively transferable to different voltages and charge patterns with the same total charge.

An empirical extension, based on the Kirkwood–Fröhlich equation, of a molecular based second-order perturbation theory is proposed to calculate the relative permittivity of dipolar liquids and mixtures in terms of the molecular dipole moment, the refractive index, density and temperature. Using the resulting equation, and giving an estimation for the dipole moments of the pure components, good agreement is obtained between the theoretical and experimental results for the relative permittivity of mixtures of carbonyl compounds with aprotic liquids. We show that our extension of the Kirkwood–Fröhlich equation describes the dielectric properties of mixtures more accurately than the original equation.

A new theory for the electrostatic component of the chemical potential for homogeneous electrolytes modeled with the primitive model is developed. This Mean Countershell Approximation (MCSA) is an analytic theory derived by including the interactions between the ions’ screening clouds. At molar concentrations, these contribute substantially to the excess chemical potential but are absent in classical Debye–Hückel and Mean Spherical Approximation (MSA) theories. Simulations show that the MCSA is highly accurate, including at the low dielectric constants of ionic liquids. While sharing a mathematical framework with the MSA, the MCSA has simpler formulas and is qualitatively more accurate when there is ion size asymmetry.