Approximate analytic solution of the Poisson–Boltzmann equation for a spherical colloidal particle

Journal of the Chemical Society Faraday Transactions 2 Molecular and Chemical Physics ◽

10.1039/f29777300577 ◽

1977 ◽

Vol 73 (5) ◽

pp. 577-596 ◽

Author(s):

Lee R. White

Keyword(s):

Boltzmann Equation ◽

Colloidal Particle ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Spherical Colloidal Particle

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Approximate analytic solution of the nonlinear Poisson–Boltzmann equation for spherical colloidal particles immersed in a general electrolyte solution

Colloid & Polymer Science ◽

10.1007/s00396-012-2683-1 ◽

2012 ◽

Vol 290 (15) ◽

pp. 1511-1526 ◽

Author(s):

S. Zhou ◽

G. Zhang

Keyword(s):

Boltzmann Equation ◽

Electrolyte Solution ◽

Colloidal Particles ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Poisson-Boltzmann equation and electrokinetics for a spherical colloidal particle in a salt-free medium

Interface Science and Technology - Theory of Colloid and Interfacial Electric Phenomena ◽

10.1016/s1573-4285(06)80035-9 ◽

2006 ◽

pp. 283-300

Keyword(s):

Boltzmann Equation ◽

Colloidal Particle ◽

Free Medium ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Spherical Colloidal Particle

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An approximate analytic solution to the modified Poisson-Boltzmann equation: effects of ionic size

Colloid & Polymer Science ◽

10.1007/s00396-016-3973-9 ◽

2016 ◽

Vol 294 (12) ◽

pp. 2121-2125 ◽

Author(s):

Hiroyuki Ohshima

Keyword(s):

Boltzmann Equation ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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A simple algorithm for the calculation of an approximate electrophoretic mobility of a spherical colloidal particle based on the modified Poisson-Boltzmann equation

Colloid & Polymer Science ◽

10.1007/s00396-017-4038-4 ◽

2017 ◽

Vol 295 (4) ◽

pp. 543-548 ◽

Author(s):

Hiroyuki Ohshima

Keyword(s):

Boltzmann Equation ◽

Electrophoretic Mobility ◽

Colloidal Particle ◽

Simple Algorithm ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Spherical Colloidal Particle

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An approximate analytic solution of the three-dimensional Poisson–Boltzmann equation

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/40/39/019 ◽

2007 ◽

Vol 40 (39) ◽

pp. 12001-12006 ◽

Author(s):

José Luis G Pestaña ◽

Donald H Eckhardt

Keyword(s):

Boltzmann Equation ◽

Analytic Solution ◽

Three Dimensional ◽

Approximate Analytic Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Variational solution of the Poisson-Boltzmann Equation for a spherical colloidal particle

The Journal of Physical Chemistry ◽

10.1021/j100639a001 ◽

1973 ◽

Vol 77 (20) ◽

pp. 2367-2370 ◽

Author(s):

Stephen L. Brenner ◽

Robert E. Roberts

Keyword(s):

Boltzmann Equation ◽

Colloidal Particle ◽

Variational Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Spherical Colloidal Particle

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Solution to the Poisson-Boltzmann equation for the potential distribution in the double layer of a single spherical colloidal particle

Transactions of the Faraday Society ◽

10.1039/tf9534901471 ◽

1953 ◽

Vol 49 ◽

pp. 1471 ◽

Author(s):

N. E. Hoskin

Keyword(s):

Boltzmann Equation ◽

Double Layer ◽

Potential Distribution ◽

Colloidal Particle ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Spherical Colloidal Particle

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Approximate expressions for the surface charge density/surface potential relationship and double-layer potential distribution for a spherical or cylindrical colloidal particle based on the modified Poisson-Boltzmann equation

Colloid & Polymer Science ◽

10.1007/s00396-018-4286-y ◽

2018 ◽

Vol 296 (4) ◽

pp. 647-652 ◽

Author(s):

Hiroyuki Ohshima

Keyword(s):

Boltzmann Equation ◽

Surface Charge Density ◽

Potential Distribution ◽

Colloidal Particle ◽

Double Layer Potential ◽

Layer Potential ◽

Poisson Boltzmann ◽

Density Surface ◽

Poisson Boltzmann Equation ◽

Approximate Expressions

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Parallel Newton–Krylov–Schwarz algorithms for the three-dimensional Poisson–Boltzmann equation in numerical simulation of colloidal particle interactions

Computer Physics Communications ◽

10.1016/j.cpc.2010.05.003 ◽

2010 ◽

Vol 181 (9) ◽

pp. 1529-1537

Author(s):

Feng-Nan Hwang ◽

Shang-Rong Cai ◽

Yun-Long Shao ◽

Jong-Shinn Wu

Keyword(s):

Numerical Simulation ◽

Boltzmann Equation ◽

Colloidal Particle ◽

Three Dimensional ◽

Particle Interactions ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Schwarz Algorithms

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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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