{"_buckets": {"deposit": "c62d3e66-5021-43bb-ab13-640520f1658e"}, "_deposit": {"id": "21715", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "21715"}, "status": "published"}, "_oai": {"id": "oai:soar-ir.repo.nii.ac.jp:00021715", "sets": ["1221:1222"]}, "item_6_biblio_info_6": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2016-11-24", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "12", "bibliographicPageStart": "124006", "bibliographicVolumeNumber": "85", "bibliographic_titles": [{"bibliographic_title": "JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN"}]}]}, "item_6_description_20": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "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. 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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. 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