  We present a nonlocal electrostatic formulation of nonuniform ions and water
molecules with interstitial voids that uses a Fermi-like distribution to
account for steric and correlation effects in electrolyte solutions. The
formulation is based on the volume exclusion of hard spheres leading to a
steric potential and Maxwell's displacement field with Yukawa-type interactions
resulting in a nonlocal electric potential. The classical Poisson-Boltzmann
model fails to describe steric and correlation effects important in a variety
of chemical and biological systems, especially in high field or large
concentration conditions found in and near binding sites, ion channels, and
electrodes. Steric effects and correlations are apparent when we compare
nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric
double layer and to experimental measurements on the selectivity of potassium
channels for K+ over Na+. The present theory links atomic scale descriptions of
the crystallized KcsA channel with macroscopic bulk conditions. Atomic
structures and macroscopic conditions determine complex functions of great
importance in biology, nanotechnology, and electrochemistry.
