Poisson-Nemst- Planck

As long as the length scale is larger than 5 nm, continuum dynamics provides an adequate description for the transport phenomena. In continuum dynamics, the steady flow is governed by using Poisson-Nemst-Planck equations as follows ... 

Xu Z, MaM, Liu P Self-energy-modified Poisson-Nemst-Planck equations WKB approximation and finite-difference approaches, Phys Rev E 90(1) 013307, 2014. 

The alternative is to fabricate CCLs as ultrathin two-phase composites 100 mn -200 mn), in which electroactive Pt could form the electronically conducting phase, or Pt nanoparticles could be supported on a conductive substrate. The remaining volume should be filled with liquid water, as the sole medium for proton and reactant transport. The ultra-thin two-phase catalyst layer was explored by using the Poisson-Nemst-Planck (PNP) equations as employed for water-filled spherical agglomerates [69, 118]. The equations in Section 8.5.2 can be rewritten for the ID planar situation... 

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. 

Corry B, Kuyucak S, -Chun SHg. Dielectric self-energy in Poisson-Boltzmann and Poisson-Nemst-Planck models of ion channels. Biophys J 2003 84(6) 3594—606. 

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). 

Zhou YC, Lu B, Huber GA, Holst MJ, McCammon JA. Continuum simulations of acetylcholine consumption by acetylcholinesterase a Poisson-Nemst-Planck approach. J Phys Chem B 2008 112 270-5. 

Schmuck, M. and Bazant, M. Z. 2012. Homogenization of the Poisson-Nemst-Planck equations for ion transport in charged porous media. arXiv, 32, 168—174. 

These basic equations form the so-called Poisson-Nemst-Planck (PNP) model for IPMCs and describe the fundamental physics wifliin the polymer membrane. A number of aufliors have developed electromechanical (actuator) and mechanoe-lectrical (sensor) models based on the PNP model as well as modified PNP models (Nemat-Nasser 2002 Nemat-Nasser and Zamani 2006 Wallmersperger et al. 2007 Zhang and Yang 2007 Porfiri 2008 Chen and Tan 2008 Aureli et al. 2009). This model will be described further in subsequent chapters of this book. 

Equations 1 and 2 make up what is commonly called the Poisson-Nemst-Planck (PNP) model for IPMCs and describes the fundamental physics within the polymer membrane. 

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. 

The overlap between CDL and EDL and its effects on the voltanunetric responses of nanoscale electrodes were first theoretically treated by White and coworkers in the early 1990s using the Poisson-Nemst-Planck equations. The possible failure of the electroneutrality condition at the nanoscale electrode interface has also been studied by Oldham and Bond, Dickinson and Compton, and other researchers. Most of these studies, however, may have overestimated the EDL effect due to the inappropriate treatment of the compact part of the EDL, especially the dielectric screening of solvent in EDL (will be discussed later on). To rationally treat the EDL effect at... 

Cervera, J. Schiedt, B. Ramirez, R A Poisson/Nemst-Planck Model for ionic transport through synthetic... 

Constantin, D. Siwy, Z. S. Poisson-Nemst-Planck model of ion current rectification through a nanofluidic diode. Phys Rev E 2007, 76, 041202. 

---