2020/04/20 by Jinn‐Liang Liu, Jinn-Liang Liu, Bob Eisenberg · 69 citations
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Electrostatics and Colloid Interactions #Field (mathematics) #Ion #Ionic bonding #Mathematical physics #Mathematics #Mean field theory #Molecular Junctions and Nanostructures #Nernst equation #Physics #Planck #Poisson distribution #Pure mathematics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #cond-mat.soft
paper · pdf · doi:10.3390/e22050550
published in Entropy 22(5), 550 (Multidisciplinary Digital Publishing Institute) · 18 figures
arxiv created 2020/04/20 · openalex publication_date 2020/05/14 · arxiv updated 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We have developed a molecular mean-field theory-fourth-order Poisson-Nernst-Planck-Bikerman theory-for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.