Analysis of Generalized Debye-Hückel Equation from Poisson-Fermi Theory
arXiv:1808.02757
Abstract
The Debye-Hückel equation is a fundamental physical model in chemical thermodynamics that describes the free energy (chemical potential, activity) of an ion in electrolyte solutions at variable salt concentration, temperature, and pressure. It is based on the linear Poisson-Boltzmann equation that ignores the steric (finite size), correlation, and polarization effects of ions and water (or solvent molecules). The Poisson-Fermi theory developed in recent years takes these effects into account. A generalized Debye-Hückel equation is derived from the Poisson-Fermi theory and is shown to consistently reduce to the classical equation when these effects vanish in limiting cases. As a result, a linear fourth-order Poisson-Fermi equation is presented for which unique solutions are shown to exist for spherically symmetric systems. Moreover, a generalized Debye length is proposed to include the size effects of ions and water.
arXiv comment22 pages, 1 figures. arXiv admin note: text overlap with arXiv:1801.03470
References in corpus (5)
- Double layer in ionic liquids: Overscreening vs. crowding
- Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory
- Computing Counterion Densities at Intermediate Coupling
- Interacting Ions in Biophysics: Real is not Ideal
- Poisson-Fermi Modeling of Ion Activities in Aqueous Single and Mixed Electrolyte Solutions at Variable Temperature