@article{oai:soar-ir.repo.nii.ac.jp:00021715,
 author = {Sugioka, Hideyuki},
 issue = {12},
 journal = {JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN},
 month = {Nov},
 note = {The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids., Article, JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN.85(12):124006(2016)},
 title = {Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte},
 volume = {85},
 year = {2016}
}