Poisson-Nernst-Planck model

A Differential Geometry-Based Poisson-Nernst-Planck Model... 

Energy in Poisson-Boltzmann and Poisson-Nernst-Planck Models of Ion Channels. 

Corry, B., Kuyncak, S., and Chung, S. H. 2003. Dielectric self-energy in Poisson-Boltzmann and Poisson-Nernst-Planck models of ion chaimels. Bionhv.s. J.. 84(6), 3594—3606. 

Equations 12.39, 12.35, and 12.40 form a coupled system of equations describing the surface function S, charge concentrations Pa, and electrostatic potential. This coupled system differs from the original PNP equations through the coupling of the surface definition are to charge concentrations and electrostatics. We call this DG-based system the "Laplace-Beltrami Poisson-Nernst-Planck" (LB-PNP) model. 

Q. Zheng and G. W. Wei. Poisson-Boltzmann-Nernst-Planck model. ]. Chem. Phys., 134 194101, 2011. 

This section describes the numerical techniques used for solving the set of differential equations that model the electrodiffusion of ions in solution. The method has historically been called the Poisson-Nernst-Planck (PNP) method because it is based on the coupHng of the Poisson equation with the Nernst-Planck equation. The basic equations used in the PNP method include the Poisson equation (Eq. [18]), the charge continuity equation (Eq. [55]), and the current density of the Nemst-Planck equation (Eq. [54]). 

Theories as Models of Ion Channels. II. Poisson-Nernst-Planck Theory versus Brownian Dynamics. 

Comparison of Dynamic Lattice Monte Carlo Simulations and the Dielectric Self-Energy Poisson-Nernst-Planck Continuum Theory for Model Ion Channels. 

The distribution of proton concentration Ch+ and potential in solution is governed by the Poisson-Nernst-Planck (PNP) model, widely used in the theory of ion transport in biological membranes (Coalson and Kurnikova, 2007 Keener and Sneyd, 1998). Oxygen diffusion is determined by Pick s law. Inside the pore, the continuity and transport equations for protons and oxygen are... 

The model of water-filled nanopores, presented in the section ORR in Water-Filled Nanopores Electrostatic Effects in Chapter 3, was adopted to calculate the agglomerate effectiveness factor. As a reminder, this model establishes the relation between metal-phase potential and faradaic current density at pore walls using Poisson-Nernst-Planck theory. Pick s law of diffusion, and Butler-Volmer equation... 

Graf, P, Kurnikova, M. G., Coalson, R. D., and Nitzan, A. 2004. Comparison of dynamic lattice Monte Carlo simulations and the dielectric self-energy Poisson-Nernst-Planck continuum theory for model ion channels, 108(6), 2006-2015. 

Moving up the scale to the level of flooded nanoporous electrodes, Michael s group has developed the first theoretical model of ionomer-free ultrathin catalyst layers—a type of layer that promises drastic savings in catalyst loading. Based on the Poisson-Nernst-Planck theory, the model rationalized the impact of interfacial charging effects at pore walls and nanoporosity on electrochemical performance. In the end, this model links fundamental material properties, kinetic parameters, and transport properties with current generation in nanoporous electrodes. 

Corry, B., Kuyucak, S., and Chung, S.H., 2000. Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus Brownian d)niamics, Biophys. J., 78, 2364-2381. 

Simulation Results. A onc-dimensional simulation model based on the Nernst-Planck and Poisson equations [14, in which all the acid-base reactions occurring in the membrane are taken into account, has been used to give a qualitative description of the pH step titration process. In these simulations, a pH step is applied outside a 2 mm thick stagnant layer, which is assumed to be present in front of an 8 mm thick membrane. Diffusion coefficients in the membrane are assumed to be 4/10 of those in water (this value is based on experience with ion step experiments). Lysozyme, used as a model protein, is assumed to contain 11 carboxylic groups (pKa = 4.4), 2 imidazole groups (pKa = 6.0), and 9 amino groups (pKa = 10.4) per molecule. Concern... 

The evolution of the numerical approaches used for solving the PNP equations has paralleled the evolution of computing hardware. The numerical solution to the PNP equations evolved over the time period of a couple of decades beginning with the simulation of extremely simplified structures " ° to fully three-dimensional models, and with the implementation of sophisticated variants of the algorithmic schemes to increase robustness and performance. Even finite element tetrahedral discretization schemes have been employed successfully to selectively increase the resolution in regions inside the channels. An important aspect of the numerical procedures described is the need for full self-consistency between the force field and the charge distribution in space. It is obtained by coupling a Poisson solver to the Nernst-Planck solver within the iteration scheme described. 

Valent I, Neogrady P, Schreiber I, Marek M (2012) Numerical solutions of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion in a simple ion channel. J Comput Interdiscip Sci 3 65-76... 

Finite-element simulations are useful to understand the mechanism of NDR and its dependence on the composition in the internal and external solutions, pore geometry, and nanopore surface charge density. Similar to modeling flow effects on nanopore ICR described earlier, the Nernst-Planck equation governing the diffusional, migrational, and convective fluxes of ions (Equation 2.18), the Navier-Stokes equation for low-Reynolds number flow engendered by the external pressure and electroosmosis (Equation 2.20), and Poisson s equation relating the ion distributions to the local electric field (Equation 2.19) were simultaneously solved to obtain local values of the fluid... 

The Nernst-Planck-Poisson model relates the electric potential cf) to the space-charge density p, which is defined by the local concentration C of all ions i at the distance x. For monovalent ions (z +l or -1),... 

Makra, I., G. Jagerszki, I. Bitter, and R.E. Gyurcsanyi. 2012. Nernst-Planck/Poisson model for the potential response of permselective gold nanopoies. Electrochim. Acta Ti 10-11. 

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