Nernst‐Planck‐Poisson Model for the Description of Behaviour of Solid‐Contact Ion‐Selective Electrodes at Low Analyte Concentration

Jasielec, Jerzy J.; Lisak, Grzegorz; Wagner, Markus Robert; Sokalski, Tomasz; Lewenstam, Andrzej

doi:10.1002/elan.201200353

Cited by 19 publications

(12 citation statements)

References 36 publications

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“…Based on assumptions (3,4) in the bulk region, the two fluxes are almost the same as the two fluxes of original PNP system…”

Section: B Flux Boundary Conditionmentioning

confidence: 95%

“…For example in biological applications, there is certain relation between flux and ion concentration across cell membrane or ion channel, such as Hodgkin-Huxley model [25] or GHK flux model [29]. And, in electrolyte there is the Chang-Jaffle boundary condition [30,31] or modified Chang-Jaffle condition [4]. Suppose the boundary condition is in the form J p,0 = f (p 0 ), where f is some given function, then we need to supplement the two conditions at x = 0 with…”

Section: Dirichlet Boundary Condition Revisitedmentioning

confidence: 99%

“…Such a system and its variants have found extensive and successful applications in biological systems, in particular in the description of ion transport through cells and ion channels [1,2]. It has also been applied to many industrial fields, such as the semiconductor devices [3] and the detection of poisonous lead by ion-selective electrode [4].…”

Section: Introductionmentioning

confidence: 99%

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Electroneutral models for dynamic Poisson-Nernst-Planck systems

2018

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The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this paper, we derive simplified electro-neutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First of all, it is much cheaper to solve them numerically. Secondly, EN models are easier to deal with compared with the original PNP, therefore it is also easier to derive macroscopic models for cellular structures using EN models.Even though the approach is applicable to higher dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher order contributions into effective boundary conditions. For Dirichlet boundary conditions, the higher order terms can be neglected and classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, however, neglecting higher contribution leads to physically incorrect solutions since they account for accumulation of ions in boundary layer. The validity of our EN model is verified by several examples and numerical computation. In particular, our EN model is much more efficient than the original PNP model when applied to the computation of membrane potential. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time step sizes.

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“…Based on assumptions (3,4) in the bulk region, the two fluxes are almost the same as the two fluxes of original PNP system…”

Section: B Flux Boundary Conditionmentioning

confidence: 95%

Section: Dirichlet Boundary Condition Revisitedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electroneutral models for dynamic Poisson-Nernst-Planck systems

2018

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“…The NPP model has been successfully used for the description of a large variety of electrochemical sensors used in potentiometry [31][32][33][34][35][36][37]47] and impedance spectroscopy [13,48,49]. That includes the NPP description of neutral carrier electrodes [50], solid-contact electrodes [51], coated-wire electrodes [52], and ion-selective field effect transistors [52]. Application of NPP in sensors leads to a deeper understanding of sensing mechanisms and underlying electrochemical processes, together with the miniaturization that can lead to the development of more robust and precise electrochemical sensors for in vivo measurements.…”

Section: The Nernst-planck-poisson Modelmentioning

confidence: 99%

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Jasielec

2021

Electrochem

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This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

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“…However, the application of the NPP model was mainly in the context of traditional ISEs containing an inner filling solution and a suspended membrane. There is earlier work in which the model was applied to a CWE [23], but it was applied to the specific context where a conductive polymer was used as an inter-layer [22] and ion-ionophore complexation was not considered [22].…”

Section: Introductionmentioning

confidence: 99%