Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study

Barcilon, Victor; Chen, D.-P.; Eisenberg, Robert S.; Jerome, Joseph W.

doi:10.1137/s0036139995312149

Cited by 132 publications

(30 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[22,32]). As goes to zero, the asymptotic behavior of solutions φ of (1.11)-(1.12) in the domain (−1, 1) can be clearly classified into two situations α = β (global charge neutrality) and α = β (charge non-neutrality): 1] |φ | is uniformly bounded for all > 0 (cf. Theorem 2.1(i) of [23] and Theorem 3.1 of [21]); • When α = β, for each x ∈ (−1, 1), φ (x) asymptotically blows up as ↓ 0 (cf.…”

Section: )mentioning

confidence: 99%

Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

Lee¹

2015

DCDS-A

View full text Add to dashboard Cite

Concerning the influence of the dielectric constant on the electrostatic potential in the bulk of electrolyte solutions, we investigate a charge conserving Poisson-Boltzmann (CCPB) equation [31,32] with a variable dielectric coefficient and a small parameter (related to the Debye screening length) in a bounded connected domain with smooth boundary. Under the Robin boundary condition with a given applied potential, the limiting behavior (as ↓ 0) of the solution (the electrostatic potential) has been rigorously studied. In particular, under the charge neutrality constraint, our result exactly shows the effects of the dielectric coefficient and the applied potential on the limiting value of the solution in the interior domain. The main approach is the Pohozaev's identity of this model. On the other hand, under the charge non-neutrality constraint, we show that the maximum difference between the boundary and interior values of the solution has a lower bound log 1 as goes to zero. Such an asymptotic blow-up behavior describes an unstable phenomenon which is totally different from the behavior of the solution under the charge neutrality constraint. 2010 Mathematics Subject Classification. Primary: 35J25, 35J60, 35C20; Secondary: 35Q92, 45K05. Key words and phrases. Charge conserving Poisson-Boltzmann, effect of variable dielectrics, small Debye length, Pohozaev's identity, asymptotic blow-up behavior. 1 When N = 1, Ω becomes a bounded open interval.

show abstract

Section: )mentioning

confidence: 99%

Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

Lee¹

2015

DCDS-A

View full text Add to dashboard Cite

show abstract

“…For classical PNP models with the electroneutrality assumption (1.3) and that D k = 1, it is known (e.g., [4,48] for n = 2 and [42] for general n) that, if Q = 0, then V 0 and I have the same sign (independent of the boundary concentrations l k 's and r k 's). Furthermore, as an immediate consequence of (1.6), one has the simple property below.…”

Section: Pnp Models For Ionic Flowsmentioning

confidence: 99%

Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models

Eisenberg

Liu

2014

Nonlinearity

View full text Add to dashboard Cite

In this work, we are interested in effects of a simple profile of permanent charges on ionic flows. We determine when a permanent charge produces current reversal. We adopt the classical Poisson-Nernst-Planck (PNP) models of ionic flows for this study. The starting point of our analysis is the recently developed geometric singular perturbation approach for PNP models. Under the setting in the paper for case studies, we are able to identify a single governing equation for the existence and the value of the permanent charge for a current reversal. A number of interesting features are established. The related topic on reversal potential can be viewed as a dual problem and is briefly examined in this work too.We will briefly discuss a particular aspect of ionic flows from the model which leads to our question in terms of specific quantities in the model.Dividing h(x)D k c k through the Nernst-Planck equation for the ion flux J k in (1.1) and integrating from x = 0 to x = 1, one has J k 1 0

show abstract

“…Note, however, that in [34][35][36] it is assumed that the concentrations of both species (cation and anion) are non-zero in each reservoir. In the case of OLEDs, the appropriate boundary conditions set the concentration of electrons (holes) to zero at the anode (cathode).…”

Section: Mathematical Modelmentioning

confidence: 99%

Asymptotic analysis of double-carrier, space-charge-limited transport in organic light-emitting diodes

2013

View full text Add to dashboard Cite

We analyse electron and hole transport in organic light-emitting diodes (OLEDs) via the drift-diffusion equations. We focus on space-charge-limited transport, in which rapid variations in charge carrier density occur near the injecting electrodes, and in which the electric field is highly non-uniform. This motivates our application of singular asymptotic analysis to the drift-diffusion equations. In the absence of electronhole recombination, our analysis reveals three regions within the OLED: (i) 'space-charge layers' near each electrode whose widthλ s is much smaller than the device widthL, wherein carrier densities decay rapidly and the electric field is intense; (ii) a 'bulk' region whose width is on the scale ofL, where carrier densities are small; and (iii) intermediate regions bridging (i) and (ii). Our analysis shows that the currentĴ scales asĴ ∝εμV 2 /L 2λ s , whereV is the applied voltage,ε is the permittivity andμ is the electric mobility, in contrast to the familiar diffusionfree scalingĴ ∝εμV 2 /L 3 . Thus, diffusion is seen to lead to a large O(L/λ s ) increase in current. Finally, we derive an asymptotic recombination-voltage relation for a kinetically limited OLED, in which charge recombination occurs on a much longer time scale than diffusion and drift.

show abstract

Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study

Cited by 132 publications

References 8 publications

Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models

Asymptotic analysis of double-carrier, space-charge-limited transport in organic light-emitting diodes

Contact Info

Product

Resources

About