Numerical Solution Of Poisson-Boltzmann Equation Research Articles

Nano-colloid electrophoretic transport: Fully explicit modelling via dissipative particle dynamics

Abstract In present study, a novel fully explicit approach using dissipative particle dynamics (DPD) method is introduced for modelling electrophoretic transport of nano-colloids in an electrolyte solution. Slater type charge smearing function included in 3D Ewald summation method is employed to treat electrostatic interaction. Moreover, capability of different thermostats are challenged to control the system temperature and study the dynamic response of colloidal electrophoretic mobility under practical ranges of external electric field in nano scale application ( 0.072 E 0.361 v / n m ) covering non-linear response regime, and ionic salt concentration (0.049 S C 0.69 [M]) covering weak to strong Debye screening of the colloid. The effect of different colloidal repulsions are then studied on temperature, reduced mobility and zeta potential which is computed based on charge distribution within the spherical colloidal EDL. System temperature and electrophoretic mobility both show a direct and inverse relationship respectively with electric field and colloidal repulsion. Mobility declining with colloidal repulsion reaches a plateau which is a relatively constant value at each electrolyte salinity for A i i > 600 in DPD units regardless of electric field intensity. Nose–Hoover–Lowe–Andersen and Lowe-Andersen thermostats are found to function more effectively under high electric fields ( E > 0.145 [ v / n m ] ) while thermal equilibrium is maintained. Reasonable agreements are achieved by benchmarking the radial distribution function with available electrolyte structure modellings, as well as comparing reduced mobility against conventional Smoluchowski and Huckel theories, and numerical solution of Poisson-Boltzmann equation.

Ion trapping on silica nanoparticles: Effect on the ζ-potential

We propose a model to interpret the concentration dependence of the ζ-potential of a suspension of silica nanoparticles of spherical shape in an electrolytic solution. The model is based on the numerical solution of Poisson-Boltzmann equation, in spherical geometry, taking into account the ionic adsorption from the nanoparticles. The kinetic equation used for the description is a generalization of the Langmuir's isotherm, modified to take into account the saturation of the adsorption phenomenon. A good agreement between the theoretical model and the experimental data is found. The model allows the determination of adsorption/desorption parameters of the nanoparticles.

Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, finding an efficient method to simulate the numerical solution of PB equation is very useful. In this paper, we establish a probabilistic interpretation of the nonlinear PB equation with Backward Stochastic Differential Equations (BSDEs). This interpretation requires an adaptation of existing results on BSDEs.

Poisson-Boltzmann calculations for nucleic acids and nucleic acids complexes

Abstract Numerical solution of Poisson-Boltzmann equation with the finite difference DelPhi program is applied to calculations of the electrostatic energy of nucleic acids and their complexes with ligands. It is shown that this approach improves on the results obtained with a simple distance dielectric function. In the case of DNA-drug complexation, the correct preference for binding mode is observed and complexation energies are brought much closer to the experimental results. The procedure is nevertheless sensitive to the number of parameters and determining correct sequence preferences will probably require geometry optimisation within the PB framework.

Selective Counterion Binding to Linear Polyelectrolytes in Aqueous Solutions

The selective counterion condensation induced by a charged cylindrical polyelectrolyte in aqueous solution containing different mono- and di-valent ions was investigated by means of the numerical solutions of the non linearized cylindrical Poisson-Boltzmann equation. The critical charge fraction fc, above which the condensation predicted by the Manning theory occurs, has been evaluated in some selected cases of relevance in biopolyelectrolyte systems and a selective binding of counterions has been shown to occur. To take into account the effects of different types of mono- and di-valent salts, an extension of the Manning theory recently proposed by Paoletti et al. and based on Gibbs free energy minimization, was considered. Discrepancies between the charge distribution of bound ions calculated by means of numerical solutions of Poisson-Boltzmann equation and those predicted by the extended Manning theory, were found.