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

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

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.

scholarly journals Modification of Bikerman model with specific ion sizes

2017 ◽  
Vol 5 (1) ◽  
pp. 142-149 ◽  
Author(s):  
Tzyy-Leng Horng ◽  
Ping-Hsuan Tsai ◽  
Tai-Chia Lin
Keyword(s):  
Steric Effect ◽  
Particle Distribution ◽  
Finite Size ◽  
Finite Size Effect ◽  
Ion Concentrations ◽  
Entropy Term ◽  
Direct Extension ◽  
Poisson Boltzmann ◽  
Ion Size ◽  
Forward Extension

Abstract Classical Poisson-Boltzman and Poisson-Nernst-Planck models can only work when ion concentrations are very dilute, which often mismatches experiments. Researchers have been working on the modification to include finite-size effect of ions, which is non-negelible when ion concentrations are not dilute. One of modified models with steric effect is Bikerman model, which is rather popular nowadays. It is based on the consideration of ion size by putting additional entropy term for solvent in free energy. However, ion size is non-specific in original Bikerman model, which did not consider specific ion sizes. Many researchers have worked on the extension of Bikerman model to have specific ion sizes. A direct extension of original Bikerman model by simply replacing the non-specific ion size to specific ones seems natural and has been acceptable to many researchers in this field.Herewe prove this straight forward extension, in some limiting situations, fails to uphold the basic requirement that ion occupation sites must be identical. This requirement is necessary when computing entropy via particle distribution on occupation sites.We derived a new modified Bikerman model for using specific ion sizes by fixing this problem, and obtained its modified Poisson-Boltzmann and Poisson-Nernst-Planck equations.

scholarly journals Finite electric boundary-layer solutions of a generalized Poisson–Boltzmann equation

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150024
Author(s):  
Bon M. N. Clarke ◽  
Peter J. Stiles
Keyword(s):  
Boundary Layer ◽  
Surface Charge ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Uniform Density ◽  
Nonlinear Phenomenon ◽  
Parallel Plates ◽  
Generalized Poisson ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

We solve the nonlinear Poisson–Boltzmann (P–B) equation of statistical thermodynamics for the external electrostatic potential of a uniformly charged flat plate immersed in an unbounded strong aqueous electrolyte. Our rather general variational formulation yields new solutions for the external potential derived from both the classical Boltzmann distribution and its heuristic Eigen–Wicke modification for concentrated symmetric electrolytes. Electrostatic potentials of these mean-field solutions satisfy a homogeneous condition at a free boundary plane parallel to the electrically conducting plate. The preferred position of this plane, characterizing the outer limit of the charged electrolyte, is determined by minimizing electrostatic free energy of the electrolyte. For a given uniform density of surface charge exceeding a well-defined and experimentally accessible threshold, we show that the generalized nonlinear P–B equation predicts a unique sharp interface separating a charged boundary layer or double layer from electroneutral bulk electrolyte. Sharp electric boundary layers are shown to be an essentially nonlinear phenomenon. In the super-threshold regime, the diffuse Gouy–Chapman solution is inapplicable and thus the Derjaguin–Landau–Verwey–Overbeek analysis, predicting electrostatic repulsion between two sufficiently separated and identically charged parallel plates must be rejected. Similar limitations restrict the applicability of the Grahame equation relating surface charge density to surface potential.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

2020 ◽  
pp. 2042006
Author(s):  
Jiahui Chen ◽  
Jingzhen Hu ◽  
Yongjia Xu ◽  
Robert Krasny ◽  
Weihua Geng
Keyword(s):  
Boltzmann Distribution ◽  
Dielectric Medium ◽  
Boundary Integral ◽  
Acid Dissociation ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
Computing Procedure ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Electrostatic Calculations

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

Groundwater remediation by anionic surfactant micelles - an innovative double layer model applied to Na+ and Mg2+ association with dodecylsulfate micelles

1998 ◽  
Vol 38 (7) ◽  
pp. 99-106 ◽  
Author(s):  
Ching Yuan ◽  
Chung-Hsuang Hung ◽  
Chad T. Jafvert
Keyword(s):  
Anionic Surfactant ◽  
Groundwater Remediation ◽  
Electrical Potential ◽  
Binding Constants ◽  
High Concentration ◽  
Experimental Conditions ◽  
Counterion Binding ◽  
Double Layer Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

The association reactions involving counterions, Na+ and Mg2+, and micelles composed of the anionic surfactant, dodecylsulfate (DS−), were investigated in ultrafiltration experiments. To access the data, an innovative model was developed that considered specific counterion binding within a Stern layer, with binding constant dependent upon the electrical potential as derived by the Poisson-Boltzmann equation and with calculation of the cmc as a function of counterion binding (or association). The experimental and model results both show that magnitude of counterion binding is greater for divalent species, Mg2+, than that for the monovalent species, Na2+. However, high concentration of Na+ compete for surface area diminishing the ability of the DS− to bind either divalent species. At experimental conditions from 0 to 100 mM NaCl addition, the binding ratio (BR) varied only from 0.58 to 0.63. The optimum binding constants, KMg and KNa, were determined to be 0.4 and 1.0 L mol−1, respectively, for the model. The experimental data and model calculated results were generally in good agreement.

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