Poisson—Boltzmann theory

Vlachy V 1999 Ionic effects beyond Poisson-Boltzmann theory Ann. Rev. Phys. Chem. 50 145... 

To describe the simple phenomena mentioned above, we would hke to have only transparent approximations as in the Poisson-Boltzmann theory for ionic systems or in the van der Waals theory for non-coulombic systems [14]. Certainly there are many ways to reach this goal. Here we show that a field-theoretic approach is well suited for that. Its advantage is to focus on some aspects of charged interfaces traditionally paid little attention for instance, the role of symmetry in the effective interaction between ions and the analysis of the profiles in terms of a transformation group, as is done in quantum field theory. 

The ideal conductor model does not account for diffuseness of the ionic distribution in the electrolyte and the corresponding spreading of the electric field with a potential drop outside the membrane. To account approximately for these effects we apply Poisson-Boltzmann theory. The results for the modes energies can be summarized as follows [89] ... 

At low electric fields [0(lV/cm)] the speed (U) of the particles is directly proportional to the applied field ( ) and hence we can define a parameter called the electromobility ( x) of the particles, given by U/E. Using the Poisson-Boltzmann theory of the diffuse electrical layer next to a charged surface, a simple relationship between p and V /o can be... 

Poisson-Boltzmann theory of the diffuse double layer... 

Despite these strong assumptions, the Poisson-Boltzmann theory describes electric double layers surprisingly well. The reason is that errors lead to opposite effects and compensate each other. Including non-coulombic interactions leads to an increase of the ion concentration at the surface and a reduced surface potential. On the other hand, taking the finite size of the ions into account leads to a lower ion concentration at the surface and thus an increased surface potential. A reduction of the dielectric permittivity due to the electric field increases its range but at the same time reduces the surface potential because less ions dissociate or adsorb. 

The interaction between two charged surfaces in liquid depends on the surface charge. Here, we only consider the linear case and assume that the surface potentials are low. If we had to use the nonlinear Poisson-Boltzmann theory, the calculations would become substantially more complex. In addition, only monovalent salts are considered. An extension to other salts can easily be made. 

Using Poisson-Boltzmann theory we can derive a simple expression for the disjoining pressure. For the linear case (low potentials) and for a monovalent salt, the one-dimensional Poisson-Boltzmann equation (Eq. 4.9) is... 

Misra, V. K., and Draper, D. E. (1999). The interpretation ofMg2"1" binding isotherms for nucleic acids using Poisson-Boltzmann theory. /. Mol. Biol. 294, 1135—1147. 

Grochowski, P., and Trylska, J. (2008). Continuum molecular electrostatics, salt effects and counterion binding. A review of the Poisson-Boltzmann theory and its modifications. Biopolymers 89, 93—113. 

Keywords Rod-like polyelectrolytes Poisson-Boltzmann theory Osmotic coefficient Electric birefringence SAXS... 

Poisson-Boltzmann Theory for the Cylindrical Cell Model. 5... 

First of all, the comparison of the PB-theory and experiment shown in Fig. 8 proceeds virtually without adjustable parameters. The osmotic coefficient (j) is solely determined by the charge parameter polyelectrolyte concentration. The latter parameter determines the cell radius R0 (see the discussion in Sect. 2.1) Figure 8 summarizes the results. It shows the osmotic coefficient of an aqueous PPP-1 solution as a function of counterion concentration as predicted by Poisson-Boltzmann theory, the DHHC correlation-corrected treatment from Sect. 2.2, Molecular Dynamics simulations [29, 59] and experiment [58]. 

The fact that Poisson-Boltzmann theory overestimates the osmotic coefficient is well-known in literature. Careful studies of typical flexible polyelectrolytes in solution ([2, 23] and further references given there) indicated that agreement of the Poisson-Boltzmann cell model and experimental data could only be achieved if the charge parameter was renormalized to a higher value. To justify this procedure it was assumed that the flexible polyelectrolytes adopt a locally helical or wiggly main chain in solution. Hence,... 

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