Revisiting the Charged Shell Model: A Density Functional Theory for Electrolytes

Classical density functional theory (DFT) has proven to be a sophisticated and efficient approach for investigating charge systems. In DFT, the excess free energy functional for inhomogeneous charged hard-sphere fluids consists of hard-core interactions and charge-charge electrostatic interactions. The former component can be precisely described by well-established fundamental measure theory (FMT). The latter component is usually computed using the Poisson equation combined with the mean spherical approximation (MSA). In order to predict accurate density profiles of ions and satisfy some thermodynamics sum rules, Roth and Gillespie [J. Phys.: Condens. Matter 2016, 28, 244006] proposed a DFT combining a functional-based version of MSA and an approximated charged shell model. Here, we rebuild the DFT based on the exact charged shell model, and the analytic expressions for the shell interaction potential and the corresponding thermodynamic quantities are provided. The structural and thermodynamic properties of both bulk and inhomogeneous electrolyte systems are analyzed. Moreover, the software named Atif (an advanced theoretical tool for inhomogeneous fluids) is released to the public via this work.