Search results for "Poisson–Boltzmann equation"
showing 7 items of 7 documents
A fast solver for nonlocal electrostatic theory in biomolecular science and engineering
2011
Biological molecules perform their functions surrounded by water and mobile ions, which strongly influence molecular structure and behavior. The electrostatic interactions between a molecule and solvent are particularly difficult to model theoretically, due to the forces' long range and the collective response of many thousands of solvent molecules. The dominant modeling approaches represent the two extremes of the trade-off between molecular realism and computational efficiency: all-atom molecular dynamics in explicit solvent, and macroscopic continuum theory (the Poisson or Poisson--Boltzmann equation). We present the first fast-solver implementation of an advanced nonlocal continuum theo…
Pore entrance effects on the electrical potential distribution in charged porous membranes and ion channels
2007
Abstract Models for the electrical potential distribution in the interfacial region between a fixed charge membrane and an electrolyte solution have traditionally employed the Donnan equilibrium formalism that assumes discontinuous changes in concentrations and electric potential. In the case of the charged capillary membrane model, we propose to check rigorously the validity of this approach by solving the linearized Poisson–Boltzmann equation for the diffuse electrical double layer at the membrane|solution interface. The comparison of the resulting axial distribution for the electric potential with the Donnan potential drop shows that the discontinuous approach is only valid for membrane …
Charged particles at fluid interfaces as a probe into structural details of a double layer
2011
Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trappe…
Enhanced ion transfer rate due to the presence of zwitterionic phospholipid monolayers at the ITIES
2000
Abstract The transfer of cations across phospholipid monolayers at ITIES is studied both experimentally and theoretically. Further evidence of the enhanced rate for cation transfer due to the presence of the monolayer is presented, and a theoretical model that can explain these observations is worked out. The system considered experimentally is Li + ion transfer across a hemispherical water ∣ 1,2-dichloroethane interface covered by distearoyl phosphatidylcholine. The theoretical description is based on the electrical double layer correction to the Butler–Volmer equation, coupled with a solution of the Poisson–Boltzmann equation across the interfacial region. The phospholipid monolayer is mo…
On the existence of kinetic equations
1974
The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.
Distribution potential in electrified microemulsions with potential determining salts
2018
Abstract The electrical polarization of lamellar and water-in-oil microemulsions composed of the aqueous solution of a potential determining salt (PDS), an organic solvent and a nonionic surfactant has been studied. The distribution of the PDS ions across the interface between two immiscible electrolyte solutions (ITIES) generates an electrical potential difference which can be used to control charge transfer processes. In macroscopic ITIES, this distribution potential is independent of the PDS concentration and can be determined from the electroneutrality condition far from the interface. In microemulsions, on the contrary, the distribution potential is smaller in magnitude and depends on …
Qualitative characterisation of effective interactions of charged spheres on different levels of organisation using Alexander’s renormalised charge a…
2005
Abstract Effective interactions are conveniently determined from experimental or numerical data by fitting a Debye–Huckel potential with an effective charge Z ∗ and an effective electrolyte concentration c ∗ as free parameters. In this contribution we numerically solved the Poisson–Boltzmann equation to obtain the so-called renormalised charge Z PBC ∗ . For sufficiently large bare charge Z one finds a saturation of Z ∗ which scales as Z ∗ = A a / λ B , where a is the particle radius, λ B the Bjerrum length and A a proportionality factor of order (8–10). The saturation value increases with increased total micro-ion concentration and shows a shallow minimum as a function of packing fraction. …