Nemst-Planck theory

The EMD studies are performed without any external electric field. The applicability of the EMD results to useful situations is based on the validity of the Nemst-Planck equation, Eq. (10). From Eq. (10), the current can be computed from the diffusion coefficient obtained from EMD simulations. It is well known that Eq. (10) is valid only for a dilute concentration of ions, in the absence of significant ion-ion interactions, and a macroscopic theory can apply. Intuitively, the Nemst-Planck theory can be expected to fail when there is a significant confinement effect or ion-wall interaction and at high electric... 

Another alternative that would help to raise catalyst utilization would be to make CLs of extremely thin two-phase composites. Electroactive Pt (eventually deposited on a substrate) should form the electronically conductive phase. The remaining volume should be filled with liquid water. Since the layer is only a two-phase composite, not impregnated with ionomer, the problem of the protonic contact resistance at the PEM CL interface could be mitigated, making the CCL insensitive to the type of PEM. Using Pois-son-Nemst-Planck theory, it could be shown that close to 100% of the catalyst would be utilized, since transport of oxygen and protons would be unproblematic for such thicknesses ( 100 nm) [129],... 

Theories of mass transport in electrolytes or elec-trolyttic solutions take into account that motion of dissolved species / can be driven by gradients in electric potential O (migration), as well as by gradients in molar concentration c, (diffusion) and by motion of material at the bulk velocity v (convection). The most commonly deployed model for electrolyte transport is the Nemst-Planck theory [1], developed in detail by Levich [2]. Within this theory, one constituent of the solution - typically a neutral species in relative excess - is identified as a solvent . The total molar flux of any remaining solute species i, Ni, is then expressed relative to a stationary coordinate frame as... 

The Nemst-Planck equation is often employed by practitioners because of its similarity to Pick s law and its convenient separation of diffusion and migratiOTi terms. It should be borne in mind, however, that the theory is inconsistent with the basic requirements of irreversible thermodynamics [6, 7]. Nemst-Planck theory uses n + k properties to characterize transport in an isothermal, isobaric n-species system containing... 

The Nemst-Planck theory (under the Nemst-Einstein Eq. 4) can be derived from the extended Stefan-Maxwell equation by taking O to be a quasi-electrostatic potential referred to one ion m and taking the limit of extreme dilution. Thus it can be seen formally that Nernst-Planck theory neglects solute-solute interactions, and applies strictly only in the limit of infinite dilution. In an n-component electrolytic phase, transport can be quantified using n(n — 1) independent species mobilities, which quantify the binary interactions between each pair of species. 

Alfredo AE, Cardenas RD, Kumikova MG. Three-dimensional Poisson-Nemst-Planck theory studies influence of membrane electrostatics on Gramicidin A channel conductance. Biophys J 2000 79(l) 80-93. 

Dimensional Poisson-Nemst-Planck Theory Studies Influence of Membrane Electrostatics on Gramicidin A Channel Conductance. 

A Lattice Relaxation Algorithm for 3D Poisson—Nemst—Planck Theory with Application to Ion Transport through the Gramicidin A Chaimel. (Meeting abstract). 

Chen, D., Lear, J., and Eisenberg, R.S., 1997. Permeation through an open channel Poisson-Nemst-Planck theory of a synthetic ion channel, Biophys. J., 72, 97-116. 

Previous to giving a quantitative elaboration of the Nemst-Planck equations for the different membrane processes, at first a qualitative treatment of membrane phenomena will be given here on the basis of M.S.T. theory and Donnan equilibrium. 

An outline of Butler s theory for the terms of the low surface state (transport-controlled) case is given in Section 10.3.5. Uosaki s 1977 theory of kinetics in the high surface state case was developed in greater detail by Khan (1984). Here, the beginning equation for the steady state (dnx/dt = 0) in the space charge region has a flux independent of distance, so that from the Nemst-Planck equation (4.226) and with dJIdx = 0, one obtains ... 

Kinetics of ion exchange is usually considered to be controlled by mass transfer in ion exchange particles or in the immediately surrounding liquid phase. The theory used to describe mass transfer in the particle is based on the Nemst-Planck equations developed by Helffericht which accounted for the effect of the electric field generated by ionic diffusion, but excluded convection. 

Another structure/function transport model, often referred to as the capillary or electroki-netic model, predefines the microlevel structure of an ion-exchange membrane as an array of pores of known dimensions with a specified distribution of ion-exchange sites on the pore walls. Equations describing solute and solvent transport and theories for molecularlevel ion/solvent and ion-membrane interactions are then generated, based on this pore structure [151], The fundamental transport equation for the molar flux of ionic species is the Nemst-Planck equation... 

There are three basic concepts that explain membrane phenomena the Nemst-Planck flux equation, the theory of absolute reaction rate processes, and the principle of irreversible thermodynamics. Explanations based on the theory of absolute reaction rate processes provide similar equations to those of the Nemst-Planck flux equation. The Nemst-Planck flux equation is based on the hypothesis that cations and anions independently migrate in the solution and membrane matrix. However, interaction among different ions and solvent is considered in irreversible thermodynamics. Consequently, an explanation of membrane phenomena based on irreversible thermodynamics is thought to be more reasonable. Nonequilibrium thermodynamics in membrane systems is covered in excellent books1 and reviews,2 to which the reader is referred. The present book aims to explain not theory but practical aspects, such as preparation, modification and application, of ion exchange membranes. In this chapter, a theoretical explanation of only the basic properties of ion exchange membranes is given.3,4... 

Seawater is a complicated mixture of many components. Hence, it is difficult to predict the manhrane performance under different operating conditions based on transport theories. Most of the theories treating the separation of multicomponent electrolytic systans are based on the Debye-Hiickel theory, Donnan effect, and Nemst-Planck eqnation [52,53]. Although they are applicable to the mixture of any number of ions involved in the feed, there are only few works in which... 

If two ionic solutions are brought into contact via a permeable membrane, difference in concentration or type of ion will give rise to a liquid junction potential. This concept differs from the earlier ones in that it involves the Nemst-Planck equation which embraces a theory of the influence of both electrical and concentration gradients on the ionic distribution. ... 

Reverse osmosis can be used for the separation of ions om an aqueous solution. Neutral membranes are mainly used for such processes and the transport of ions is determined by their solubility and diffusivity in the membrane (as expressed by the solute permeability coefficient, see eq V 162). The driving force for ion transport is the concentration difference, but if charged membranes or ion-exchange membranes are used instead of neutral membranes ion transport is also affected by the presence of the fixed charge. Teoreil [45] and Meyer and Sievers [46] have used a fixed charge theory to describe ionic transport through these type of systems. This theory is based on two principles the Nemst-Planck equation and Dorman equilibrium. 

An alternative to the Nemst Planck models of charge diffusion is the rate theory model, which views ion permeation through a channel or pump from a statistical thermodynamics perspective. In this approach, one or more energy barriers are assumed to exist at fixed points in the channel and ions permeate... 

A more in-depth elucidation of the mechanism of permselective membranes can be done by using the Nemst-Planck/Poisson equations. As a model system, the gold nanoporous membranes introduced by Martin et al. were used however, the surface charge was established by their chemical modification with self-assembled monolayers (SAMs) of chemisorbed electrically charged thiol derivatives. The average pore diameters of such membranes can be very precisely determined with gas permeation experiments based on the kinetic theory of gases ... 

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