Next Article in Journal
E-Bayesian Estimation of Chen Distribution Based on Type-I Censoring Scheme
Previous Article in Journal
Intermittent Information-Driven Multi-Agent Area-Restricted Search
Previous Article in Special Issue
Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model
Open AccessArticle

Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan
Entropy 2020, 22(6), 632; https://doi.org/10.3390/e22060632
Received: 11 May 2020 / Revised: 3 June 2020 / Accepted: 4 June 2020 / Published: 8 June 2020
The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model. View Full-Text
Keywords: steric effect; Poisson-Boltzmann model; Bikerman model; entropy; specific ion size steric effect; Poisson-Boltzmann model; Bikerman model; entropy; specific ion size
Show Figures

Figure 1

MDPI and ACS Style

Horng, T.-L. Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation. Entropy 2020, 22, 632.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop