The solution procedure of the linearized Poisson-Boltzmann equation used above is not suited to include hard core effects of the ions, the most we can do is to give a size to the central ion, but that makes the pair distribution function asymmetric. To include the hard core effects in a symmetric way, we have to change the formalism. We notice, first, that Poisson s equation (1.8) relates the potential (r) to the charge distribution We can formally integrate this equation to yield [Pg.115]

Analytical results for the Green function are obtained for a planar geometry only. For a planar surface, the linearized Poisson-Boltzmann equation yields the screened potential [Pg.8]

In Figure 6a, the force per unit area between surfaces with grafted polyelectrolyte brushes, plotted as a function of their separation distance 2d, calculated in the linear approximation, is compared with the numerical solution of the nonlinear Poisson—Boltzmann equations, for a system with IV = 1000, a = 1 A, ce = 0.01 M, s2 = 1000 [Pg.647]

The cell model from Katchalsky, Onsager and Manning, which was originally only applicable to linear PEs [26], was extended by Deshkovski in 2001 to a more general two zone model based on the mean field approximation of the nonlinear Poisson Boltzmann equation [84]. In this two zone model, the counter ions around a cylindrical rod (PE) form the area close to the PE, and a spherical volume which extends up to the distances between the PE is the area far away from the PE [84]. This model is able to explain the mean distance of the counterions from the PE chain as a function of the counterion concentration. [Pg.43]

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