Nernst Planck System Research Articles

Simulation of electronic/ionic mixed conduction in solid ionic memory devices

The electronic/ionic mixed conduction is examined in solid ionic memory devices by numerically solving the Poisson–Nernst–Planck equations using the computational platform PROPHET. The boundary conditions for the Poisson–Nernst–Planck system are determined based on the theoretical treatments as a Dirichlet type. The chemical composition of the mixed conductor under the reference electrode and the magnitude of applied biases are considered as important parameters in the simulation. The results show that the deviation of carrier distribution increases from the analytical solutions with the increase of applied biases and the decrease of the partial pressure of the non-metallic component near the reference electrode in solid ionic memory devices.

Competitive permeation of calcium ions through the calcium release channel (Ryanodine receptor) of cardiac muscle: An application of the coupled Poisson–Nernst–Planck system of equations

The coupled set of Poisson–Nernst–Planck (PNP) equations is extended to include the local chemical interaction of mobile charged ions with the ion channel—a porous protein facilitating electrical signal transduction in biology. This set of coupled equations is then solved numerically to calculate the ion fluxes. The numerical result is then compared directly with single-channel current–voltage ( IV) relations measured from the calcium release channel of cardiac sarcoplasmic reticulum (RyR2) in 21 mixed solutions of 250 mM alkali metal ions ( Na + , K + , and Cs + ) with sarcoplasmic reticulum lumenal Ca 2 + ranging from 5 to 50 mM, and Mg 2 + from 1 to 50 mM. The measured IV relations were analyzed by the extended PNP formulation to reveal the competitive permeating of Ca 2 + and other cations, in particular Mg 2 + . The results indicate that applying PNP theory, two adjustable parameters (diffusion coefficient ( D) and “excess” chemical potentials ( μ ¯ )) suffice to predict the flow of Ca 2 + from the sarcoplasmic reticulum in cardiac muscle. The data are used to predict the calcium ion activity profiles in the RyR2 pore, the calcium ion fluxes in solutions of physiological interest, and the competitive permeation of Ca 2 + and Mg 2 + . The coupling of ion permeation is through purely electrostatic interaction, promoted by the local chemical interaction of ion-specific interaction with the pore of ion channel proteins. The analogy to the charge coupling phenomena found in the semiconductor devices is discussed.

Numerical simulation of pH-stimuli responsive hydrogel in buffer solutions

In this paper, the chemo-electro-mechanical behavior of the responsive hydrogel actuated by pH-stimuli is addressed. A chemo-electro-mechanical model, describing the hydrogel behavior with multi-field effects, is developed to simulate the swelling of the captivating biomaterials, and it is termed the multi-effect-coupling pH-stimulus (MECpH) model. This model delineates the effects of electric potential and mechanical deformations of the hydrogel as well as the transports of ionic fluxes within both the hydrogel and bath solution. The main contribution of this model laid on the incorporation of the relationship between the concentrations of the ionized fix-charge groups and the diffusive hydrogen ion, which follows a Langmuir isotherm theory, into the Poisson–Nernst–Planck system. In order to validate the MECpH model, one-dimensional steady-state simulations are conducted under varying pH conditions generated by buffer solution. The mathematical models are solved via a meshless Hermite–Cloud method and the numerical results are compared well with available experimental data. In conclusion, the presently developed MECpH model is able to predict the swelling behavior of the hydrogel precisely. This study provides a better understanding of the behavior of the pH-sensitive hydrogels.

Ionic diffusion through confined geometries: from Langevin equations to partial differentialequations

Ionic diffusion through and near small domains is of considerable importance inmolecular biophysics in applications such as permeation through protein channelsand diffusion near the charged active sites of macromolecules. The motion of theions in these settings depends on the specific nanoscale geometry and chargedistribution in and near the domain, so standard continuum type approaches haveobvious limitations. The standard machinery of equilibrium statistical mechanicsincludes microscopic details, but is also not applicable, because these systems areusually not in equilibrium due to concentration gradients and to the presence of anexternal applied potential, which drive a non-vanishing stationary current throughthe system. We present a stochastic molecular model for the diffusive motion ofinteracting particles in an external field of force and a derivation of effective partialdifferential equations and their boundary conditions that describe the stationarynon-equilibrium system. The interactions can include electrostatic, Lennard-Jones andother pairwise forces. The analysis yields a new type of Poisson–Nernst–Planck equations,that involves conditional and unconditional charge densities and potentials. Theconditional charge densities are the non-equilibrium analogues of the well studied paircorrelation functions of equilibrium statistical physics. Our proposed theory isan extension of equilibrium statistical mechanics of simple fluids to stationarynon-equilibrium problems. The proposed system of equations differs from thestandard Poisson–Nernst–Planck system in two important aspects. First, the forceterm depends on conditional densities and thus on the finite size of ions, andsecond, it contains the dielectric boundary force on a discrete ion near dielectricinterfaces. Recently, various authors have shown that both of these terms areimportant for diffusion through confined geometries in the context of ion channels.

ANALYTICAL APPROACHES TO CHARGE TRANSPORT IN A MOVING MEDIUM

ABSTRACT We consider electrodiffusion in an incompressible electrolyte medium which is in motion. The Cauchy problem is governed by a coupled Navier-Stokes/Poisson–Nernst–Planck system. We prove the existence of a unique smooth local solution for smooth initial data, with nonnegativity preserved for the ion concentrations. We make use of semigroup ideas, originally introduced by T. Kato in the 1970s for quasi-linear hyperbolic systems. The time interval is invariant under the inviscid limit to the Euler/Poisson–Nernst–Planck system.

Numerical simulation of multi-species diffusion

A numerical model has been developed to simulate the transport of several ionic species across a saturated concrete or mortar sample. The chloride binding as well as the electrical coupling between the different ionic fluxes are included in the model by using the Nernst-Planck system of equations. This model highlights which parameters affect substantially chloride penetration into reinforced concrete structures and then shows that the use of Fick’s first law in a predictive model for chloride penetration is strongly challenged. The simulations are in good agreement with diffusion-cell experiments and membrane potential measurements.

Modelling ion diffusion mechanisms in porous media

The main features of a numerical model aiming at predicting the drift of ions in electrolytic solutions are presented. The mechanisms of ionic diffusion are described by solving the Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Two algorithms using the finite element method for spatial discretization are compared for simple test cases. One is based on the Picard iteration method while the other is based on the Newton–Raphson scheme. Test results clearly indicate that the range of application is broader for the algorithm based on the Newton–Raphson method. Selected examples of the application of the algorithm to more complex 1-D and 2-D cases are given. Copyright © 1999 John Wiley & Sons, Ltd.

Modelling ion diffusion mechanisms in porous media

The main features of a numerical model aiming at predicting the drift of ions in electrolytic solutions are presented. The mechanisms of ionic diffusion are described by solving the Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Two algorithms using the finite element method for spatial discretization are compared for simple test cases. One is based on the Picard iteration method while the other is based on the Newton–Raphson scheme. Test results clearly indicate that the range of application is broader for the algorithm based on the Newton–Raphson method. Selected examples of the application of the algorithm to more complex 1-D and 2-D cases are given. Copyright © 1999 John Wiley & Sons, Ltd.

Numerical Solution of the Extended Nernst–Planck Model

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst–Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Numerical solution of the Nernst-Planck and poisson equation system with applications to membrane electrochemistry and solid state physics

An efficient finite difference simulation procedure for the steady state and transient solution of the Nernst-Planck and Poisson equation system is presented. The procedure is general and extremely efficient, containing refinements in time and distance scaling. The implicitly-formulated non-linear equations are solved with an iterative Newton-Raphson technique. The derivation is presented in sufficient detail for the reader to directly formulate similar computer codes. Steady state solutions, transient responses, and impedance-frequency responses are presented for a number of examples from the fields of membrane electrochemistry and solid state physics.