scholarly journals Adsorption of large ions from an electrolyte solution: a modified Poisson–Boltzmann equation

2000 ◽  
Vol 46 (2-3) ◽  
pp. 221-229 ◽  
Author(s):  
I. Borukhov ◽  
D. Andelman ◽  
H. Orland
Keyword(s):  
Boltzmann Equation ◽  
Electrolyte Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Analytical resolution of the Poisson–Boltzmann equation for a cylindrical polyion immersed in an electrolyte solution: using the optimal linearization method

2019 ◽  
Vol 97 (6) ◽  
pp. 656-661
Author(s):  
Leila Djebbara ◽  
Mohammed Habchi ◽  
Abdalhak Boussaid
Keyword(s):  
Boltzmann Equation ◽  
Electrolyte Solution ◽  
Electrostatic Potential ◽  
Analytical Calculation ◽  
Linearization Method ◽  
General Potential ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Analytical Resolution ◽  
Potential Conditions

By using the optimal linearization method (OLM), the potential of the electrical double layer created by a highly charged cylindrical polyion immersed in an electrolyte reservoir, which is represented by the so-called Poisson–Boltzmann equation (PBE), has been solved analytically under general potential conditions. For this system, three regions must be considered. The first one is in the near-neighborhood of the polyion and it is deprived of coions because of the repulsion phenomenon between the polyion and the coions, as proposed by Fuoss et al. (Proc. Natl. Acad. Sci. 37, 579 (1951). doi: 10.1073/pnas.37.9.579 ). For the second region, where the potential is slightly lower, we propose an OLM for solving the PBE. In the last region, where the potential is sufficiently low, the approximation of Debye–Hückel is adopted. This method allowed us to overcome some shortcomings in the analytical calculation of the electrostatic potential created by a polyion in an electrolyte solution.

Numerical solution of a modified poisson-boltzmann equation in electrolyte solution theory

1971 ◽  
Vol 9 (2) ◽  
pp. 109-112 ◽  
Author(s):  
D.M. Burley ◽  
V.C.L. Hutson ◽  
C.W. Outhwaite
Keyword(s):  
Boltzmann Equation ◽  
Numerical Solution ◽  
Electrolyte Solution ◽  
Solution Theory ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

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

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 ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation
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