Approximate analytical solutions to the Poisson–Boltzmann equation

The Journal of Chemical Physics ◽

10.1063/1.431469 ◽

1975 ◽

Vol 63 (4) ◽

pp. 1699-1700 ◽

Author(s):

J.‐Y. Parlange

Keyword(s):

Boltzmann Equation ◽

Analytical Solutions ◽

Approximate Analytical Solutions ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solutions of the Poisson-Boltzmann equation within an interstitial electrical double layer in various geometries

Chemical Physics ◽

10.1016/j.chemphys.2019.01.026 ◽

2019 ◽

Vol 522 ◽

pp. 147-162 ◽

Author(s):

Hadi Saboorian-Jooybari ◽

Zhangxin Chen

Keyword(s):

Boltzmann Equation ◽

Double Layer ◽

Analytical Solutions ◽

Electrical Double Layer ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solutions of the nonlinear Poisson–Boltzmann equation in mixture of electrolytes

Surface Science ◽

10.1016/j.susc.2012.09.008 ◽

2013 ◽

Vol 607 ◽

pp. 197-202 ◽

Author(s):

Xinmin Liu ◽

Hang Li ◽

Rui Li ◽

Rui Tian

Keyword(s):

Boltzmann Equation ◽

Analytical Solutions ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solutions to the linearized poisson—boltzmann equation in cylindrical coordinates for different ionic—strength distributions

Journal of Colloid and Interface Science ◽

10.1016/0021-9797(85)90359-5 ◽

1985 ◽

Vol 105 (1) ◽

pp. 172-182 ◽

Author(s):

Richard E Rice ◽

Frederick H Horne

Keyword(s):

Boltzmann Equation ◽

Ionic Strength ◽

Analytical Solutions ◽

Cylindrical Coordinates ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Strength Distributions

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Approximative Analytical Solutions of the Poisson-Boltzmann Equation for Charged Rods in the Presence of Salt: An Analysis of the Cylindrical Cell Model

Journal of Colloid and Interface Science ◽

10.1006/jcis.1995.1081 ◽

1995 ◽

Vol 170 (1) ◽

pp. 134-145 ◽

Author(s):

H. van Keulen ◽

J.A.M. Smit

Keyword(s):

Boltzmann Equation ◽

Analytical Solutions ◽

Cylindrical Cell ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique

Colloid & Polymer Science ◽

10.1007/s00396-012-2622-1 ◽

2012 ◽

Vol 290 (12) ◽

pp. 1165-1180 ◽

Author(s):

S. Zhou ◽

H. Wu

Keyword(s):

Boltzmann Equation ◽

Electrolyte Solution ◽

Analytical Solutions ◽

Colloidal Particles ◽

Perturbation Technique ◽

Homotopy Perturbation ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Homotopy Perturbation Technique

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Fast multipole method for 3-D Poisson-Boltzmann equation in layered electrolyte-dielectric media

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110379 ◽

2021 ◽

pp. 110379

Author(s):

Bo Wang ◽

Wenzhong Zhang ◽

Wei Cai

Keyword(s):

Boltzmann Equation ◽

Fast Multipole Method ◽

Fast Multipole ◽

Dielectric Media ◽

Multipole Method ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

ESAIM Proceedings and Surveys ◽

10.1051/proc/201448020 ◽

2015 ◽

Vol 48 ◽

pp. 420-446 ◽

Author(s):

Mireille Bossy ◽

Nicolas Champagnat ◽

Hélène Leman ◽

Sylvain Maire ◽

Laurent Violeau ◽

...

Keyword(s):

Monte Carlo ◽

Boltzmann Equation ◽

Monte Carlo Methods ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Designing scalable ultrafiltration/diafiltration process of monoclonal antibodies via mathematical modeling by coupling mass balances and Poisson–Boltzmann equation

Biotechnology and Bioengineering ◽

10.1002/bit.27598 ◽

2020 ◽

Author(s):

Rok Ambrožič ◽

Dejan Arzenšek ◽

Aleš Podgornik

Keyword(s):

Mathematical Modeling ◽

Monoclonal Antibodies ◽

Boltzmann Equation ◽

Mass Balances ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Solvation free energies of non-polar and polar solutes reproduced by a combination of extended scaled particle theory and the Poisson-Boltzmann equation

Molecular Physics ◽

10.1080/00268979500101791 ◽

1995 ◽

Vol 85 (6) ◽

pp. 1227-1238 ◽

Author(s):

Masayuki Irisa ◽

Takuya Takahashi ◽

Kuniaki Nagayama ◽

Fumio Hirata

Keyword(s):

Boltzmann Equation ◽

Scaled Particle Theory ◽

Free Energies ◽

Particle Theory ◽

Polar Solutes ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Solvation Free Energies

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Modified Poisson-Boltzmann equation and free energy of electrical double layers in hydrophobic colloids

Discussions of the Faraday Society ◽

10.1039/df9664200069 ◽

1966 ◽

Vol 42 ◽

pp. 69 ◽

Author(s):

S. Levine ◽

G. M. Bell

Keyword(s):

Free Energy ◽

Boltzmann Equation ◽

Double Layers ◽

Electrical Double Layers ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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