Poisson boltzmann equation using helmholtz pde model. In this paper, the analytical validation of poissonboltzmann pb equation computed with comsol multiphysics, in the case of a polarized surface in. Comsol software users who are onsubscription should submit. Poissonboltzmann equation an overview sciencedirect topics. Poisson boltzmann is not sufficient to determine surface charge density, you need. Dec 20, 2017 creating new physics interfaces that you can save and share, modifying the underlying equations of a model, and simulating a wider variety of devices and processes. The distribution of ions is described by the boltzmann distribution. Comsol software users who are onsubscription should submit their questions via the support center for a more comprehensive response from the technical support team. Analytical solution of the poissonboltzmann equation in. Apbs solves the equations of continuum electrostatics for large biomolecular assemblages. The comsol discussion forum covers a wide variety of simulation topics. Nov 17, 2009 dear all, anyone experienced in modelling a simple charge surface with poisson boltzmann equation. I want to simulate capacitor with comsol by using poissons equation in genaral and weak form. These are just a few ways you can benefit from the equationbased modeling capabilities of the comsol multiphysics software.
An exact analytical solution of the poisson boltzmann pb equation in cases of spherical, axial, and planar geometry has been obtained in the form of the logarithm of a power series. The poisson boltzmann equation i background i the pb equation. Two methods for modeling free surfaces in comsol multiphysics. Comsolbased modeling and simulation of sno 2 rgo gas sensor. How to define poisson boltzmann equation in cylindrical coordinates. May 15, 2018 in fact, the source term in the phase field equation includes fourthorder terms. Numerical simulation of the electrical double layer based on. To motivate the work, we provide a thorough discussion of the poisson boltzmann equation, including derivation from a few basic assumptions, discussions of special case solutions, as well as common analytical approximation techniques. Adding and customizing expressions in the physics interfaces allows for freely coupling them with each. Also, your interval is 1 m long, which makes no sense, i. An exact analytical solution of the poissonboltzmann pb equation in cases of spherical, axial, and planar geometry has been obtained in the form of the logarithm of a power series.
The poisson boltzmann pb equation is well known for its success in describing the debye layer that arises from the charge separation phenomenonat the silicawater interface. How to derive the twoterm approximation for the boltzmann. To account for the steric comsol multiphysics software application effects of the ion crowding at the. Poissonboltzmann model for proteinsurface electrostatic. How can i define poissons equation in general and weak form in. Now, with one species leaving, the concentration changes and therfore the space charge density, which over the poissonequation and and the defined space charge density should have influence on the migrationterm in the nernstplanck equation as far as i understand.
The schrodingerpoisson equation multiphysics interface, available as of comsol multiphysics version 5. An iterative method for finiteelement solutions of the. I am interested by the potential and the concentration profiles of the edl. Poissonboltzmann equation 4 2 0 1 f i i i h h \ f z c nernstplanck equation.
This software was designed from the ground up using modern design principles to ensure its ability to interface with other computational packages and evolve as methods and applications change over time. No external field or voltage is applied, my goal is to check whether these. Lattice boltzmann model for the volumeaveraged navierstokes equations. The poissonboltzmann equation is a useful equation in many settings, whether it be to understand physiological interfaces, polymer science, electron interactions in a semiconductor, or more. And you have not given the units of the global parameters. The limitations of the poissonboltzmann pb equation. Solving the finitedifference nonlinear poissonboltzmann. Creating new physics interfaces that you can save and share, modifying the underlying equations of a model, and simulating a wider variety of devices and processes. Warning your internet explorer is in compatibility mode and may not be displaying the website correctly. Whichever reaction takes place in the active layer, comsol software uses poissons equation given by equation, to construct the electrical parameters of the sensor, such as. Linearization of the exponential terms in the poissonboltzmann equation. In fact, the source term in the phase field equation includes fourthorder terms. The poissonboltzmann theory of continuum electrostatics with application to variational solvation of molecules bo li department of mathematics and center for.
To obtain the weak formulation of the general poisson equation, we multiply it with a. Moreover, some extensions called by picard, gaussseidel, and successive overrelaxation sor methods are also presented and analyzed for the fe solution. Hi, i want to define poisson boltzmann equation in cylindrical. Numerical simulation of electricallydriven flows using. A simple derivation of the boltzmann relation for the electrons can be obtained using the momentum fluid equation of the twofluid model of plasma physics in absence of a. Holst department of applied mathematics and crpc california institute of technology 21750 pasadena, ca usa 91125 faisal saied department of computer science 4 west spring eld avenue urbana, il usa 61801.
Dear all, anyone experienced in modelling a simple charge surface with poissonboltzmann equation. The poissonboltzmann theory of continuum electrostatics. Numerical simulation of the electrical double layer based on the poissonboltzmann models for ac electroosmosis flows pascale pham 1, matthieu howorth, anne planatchretien and sedat tardu2. The poisson boltzmann equation can be applied in a variety of fields mainly as a modeling tool to make approximations for applications such as charged biomolecular interactions, dynamics of electrons in semiconductors or plasma, etc. Comsolbased modeling and simulation of sno 2 rgo gas. Equationbased modeling for custom simulations in comsol. You cannot use nernstplanck equation because that assumes electroneutrality which contradicts with the poisson equation. A system of partial differential equations models this situation, with a poisson equation governing inside the protein and a linearized poissonboltzmann equation governing in the solvent region. The comsol multiphysics software offers this level of flexibility with its builtin equation interpreter that can interpret expressions, equations, and other mathematical descriptions on the fly before it generates the numerical model. We demonstrate the utility of our methods and software in chapter 7 by including a nonlinear pbe calculation of the. The easiest way to describe a point source in comsol multiphysics is by using an extra weak term. Finitedifference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of nonlinear terms. For simplicity we will assume that both coions and counterions have the same size a.
Pdf numerical simulation of the electrical double layer based on. However, by treating only the ionic chmobile arges in the liquid, the pb equation essentially only half of the electrical double layer, with the accounts for. The iterative method solves the nonlinear equations arising from the fe discretization procedure by a nodebynode calculation. Dear all, anyone experienced in modelling a simple charge surface with poisson boltzmann equation. The values of the electric potential drop near the electrodes surface are compared and it is shown their area of validity. Otherwise, conceptually, both models go through a similar process of solving the poissonboltzmann equation, assuming a constant dielectric, finding the resulting ion distributions, and. Now, with one species leaving, the concentration changes and therfore the space charge density, which over the poisson equation and and the defined space charge density should have influence on the migrationterm in the nernstplanck equation as far as i understand.
The poissonboltzmann equation is a nonlinear partial differential equation. The old version, which was available in 1d, is now retired. In an ideal situation, this is a sharp boundary located at z 0 which limits the ionic solution to the half space z0. We see that the primary difference between the two models is how the energy is defined. Solving poisson, nernstplanck and navierstokes for a nanopore in comsol. The poissonboltzmann theory of continuum electrostatics with. In what concerns available software packages, comsol multiphysics. A widely used electrostatics model in the biomolecular modeling community, the nonlinear poissonboltzmann equation, along with its. Nu multiion charge regulation equation 2 2 n a b s total a s b s k k h f k h k h v comsol multiphysics p02 p u \u e u 0 stokes equation continuity equation highly coupled equations nonlinear partial.
Whichever reaction takes place in the active layer, comsol software uses poissons equation given by equation, to construct the electrical parameters of the sensor, such as current, resistance. Numerical simulation of the electrical double layer based on the. Even the most advanced analytic solutions of the pb equation, however, use approximations that limit their applicability for many applications, such as when higher electric potentials or finite solution volumes as encountered in microfluidic cells are involved. I assumed that there is no chemical reaction at the interface, so it means that the current density is zero. Numerical solution of the nonlinear poissonboltzmann equation. Otherwise, conceptually, both models go through a similar process of solving the poisson boltzmann equation, assuming a constant dielectric, finding the resulting ion distributions, and determining the electron density profiles. Poissonboltzmann is not sufficient to determine surface charge density, you need. Can anyone suggest software to compute surface charge density. Browse the threads and share your ideas with the comsol community. Jan 22, 2016 poissonboltzmann equation the poissonboltzmann equation is a useful equation in many settings, whether it be to understand physiological interfaces, polymer science, electron interactions in. Solving poissons equation with comsol multiphysics inside of a sphere. The poisson boltzmann theory of continuum electrostatics with application to variational solvation of molecules bo li department of mathematics and center for theoretical biological physics uc san diego february 3, 2009.
This model solves the poisson equation on a unit disk with a point source in the origin. Numerical solution of the nonlinear poissonboltzmann. Some examples i existence, uniqueness, and uniform bound i freeenergy functional. Lattice gas formulation consider an aqueous solution of charged ions. I want to model the electric double layer using the nernstplanck equation, also coupled with poisson equation. Solving poisson, nernstplanck and navierstokes for a nanopore in.
You have a problem with the units both in the poisson boltzmann and nernstplanck equation. It aims to describe the distribution of the electric potential in solution in the direction normal to a charged surface. How can i define poissons equation in general and weak form. Numerical simulation of the electrical double layer based on the poissonboltzmann models for ac electroosmosis flows. Numerical analysis of electrokinetic flow through a cylindrical.
Can anyone suggest software to compute surface charge density of hydrated solute using poisson equation. Another freely available program is called apbsmem, and it is designed for carrying out the electrostatics calculations in the presence of a. Comsol multiphysics software understand, predict, and optimize. This solution describes an electrostatic potential distribution around a charged macroscopic particle wire, plane under conditions of thermal equilibrium at an arbitrary ratio of the density of charge borne by. If you want to use the poissonboltzmann analytical method developed by the teresa headgordon lab, when invoking cmake. One of the most popular software for electrostatics calculations is apbs, which is used for modeling biomolecular solvation through solution of the poissonboltzmann equation baker et al. The poissonboltzmann pb equation is well known for its success in describing the debye layer that arises from the charge separation phenomenonat the silicawater interface. The poisson boltzmann equation and the charge separation. Changed the functionality so that the boltzmann equation, twoterm approximation interface is now only available in 0d components. The poissonboltzmann equation i background i the pb equation. The electric potential from the electrostatics contributes to the potential energy term in the schrodinger equation. The update can be applied to comsol software version 5. On the other hand, the poisson boltzmann equation dictates the potential distribution near the channel wall and allows the solution of laplace equation to hold elsewhere.
Corrected the equation display for poisson s equation in the. This means that, for practical reasons, the equation is often broken up into two equations, where an auxiliary dependent variable is defined as a function of the second derivatives of this is also what is done in comsol multiphysics. How to derive the twoterm approximation for the boltzmann equation. However, by treating only the ionic chmobile arges in the liquid, the pb equation essentially. How to define poisson boltzmann equation in cylindrical. You will experience speedup by a factor of up to ten in software responsiveness, as well as new and improved features for solving, meshing, and the physicsbased addon modules. To motivate the work, we provide a thorough discussion of the poissonboltzmann equation, including derivation from a few basic assumptions, discussions of special case solutions, as well as common analytical approximation techniques. Numerical simulation of the electrical double layer based on the poisson boltzmann models for ac electroosmosis flows. Most applications of this equation are used as models to gain further insight on electrostatics. Poissonboltzmann equation the poissonboltzmann equation is a useful equation in many settings, whether it be to understand physiological interfaces.
1365 1480 464 1246 340 1114 81 73 783 14 1220 651 529 104 892 1049 1434 650 1136 1346 390 1175 155 628 934 947 1176 776 1065 738 1101 1013 1253 351 306 590 139 55 381 100 91 1175 1012 1169