Analytical Solutions to the Poisson-Boltzmann Equation

Equations [3] and either [4] or [5] are solved subject to appropriate boundary conditions to obtain the ion distributions through the system. Two boundary conditions (BCs) are required and most often these are chosen 

Fixed charge density (or electric field) on a surface (this includes the electroneutrality condition) (Neumann condition) 

A mixed condition coupling the charge density and potential on a surface (Cauchy condition) 

Finiteness of the potential or field within a specific region or at infinity (one of conditions BC1-BC3 applied at one surface with the other 

In addition to these conditions, the continuity of the potential throughout the system requires that further relationships involving the potential and/or electric field at botmdaries between regions need to be applied. 

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Analytical Solutions to the Poisson-Boltzmann Equation 221 to the potential of Eq. [196] leads to the coupled equations... 

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