Breakdown of electroneutrality in nanopores

Levy, Amir; de Souza, J. Pedro; Bazant, Martin Z.

doi:10.1016/j.jcis.2020.05.109

Breakdown of electroneutrality in nanopores

Journal Article · Tue Jun 09 00:00:00 EDT 2020 · Journal of Colloid and Interface Science

DOI:https://doi.org/10.1016/j.jcis.2020.05.109· OSTI ID:1852823

Levy, Amir ^[1]; de Souza, J. Pedro ^[2]; Bazant, Martin Z. ^[3]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Chemical Engineering
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Chemical Engineering; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Mathematics

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. Additionally, we show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019112

OSTI ID:: 1852823

Alternate ID(s):: OSTI ID: 1775884

Journal Information:: Journal of Colloid and Interface Science, Journal Name: Journal of Colloid and Interface Science Journal Issue: C Vol. 579; ISSN 0021-9797

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (91)

159 Comparison of gene Expression Profiles Between Normal and Sclerosis Regions of Human Osteoarthritic Subchondral bone Chou, C. -H.; Pan, R. -Y.; Lu, L. -S. Osteoarthritis and Cartilage, Vol. 18 https://doi.org/10.1016/s1063-4584(10)60186-0	journal	October 2010
Response to Comment on “Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins” Tunuguntla, Ramya H.; Zhang, Yuliang; Henley, Robert Y. Science, Vol. 359, Issue 6383 https://doi.org/10.1126/science.aaq1241	journal	March 2018
Nonlinear dynamics of ion concentration polarization in porous media: The leaky membrane model Dydek, E. Victoria; Bazant, Martin Z. AIChE Journal, Vol. 59, Issue 9 https://doi.org/10.1002/aic.14200	journal	August 2013
La perméabilité des membranes I. Théorie de la perméabilité ionique Meyer, Kurt H.; Sievers, J. -F. Helvetica Chimica Acta, Vol. 19, Issue 1 https://doi.org/10.1002/hlca.19360190199	journal	January 1936
The gramicidin a channel: A review of its permeability characteristics with special reference to the single-file aspect of transport Finkelstein, Alan; Andersen, Olaf Sparre The Journal of Membrane Biology, Vol. 59, Issue 3 https://doi.org/10.1007/BF01875422	journal	October 1981
Power generation from concentration gradient by reverse electrodialysis in ion-selective nanochannels Kim, Dong-Kwon; Duan, Chuanhua; Chen, Yu-Feng Microfluidics and Nanofluidics, Vol. 9, Issue 6 https://doi.org/10.1007/s10404-010-0641-0	journal	June 2010
What makes a nano-channel? A limiting-current criterion Yaroshchuk, Andriy Microfluidics and Nanofluidics, Vol. 12, Issue 1-4 https://doi.org/10.1007/s10404-011-0902-6	journal	November 2011
Electrolyte osmosis through capillaries Sasidhar, Varanasi; Ruckenstein, Eli Journal of Colloid and Interface Science, Vol. 82, Issue 2 https://doi.org/10.1016/0021-9797(81)90386-6	journal	August 1981
Transport of electrolytes in charged pores: Analysis using the method of spatial averaging Hawkins Cwirko, E.; Carbonell, R. G. Journal of Colloid and Interface Science, Vol. 129, Issue 2 https://doi.org/10.1016/0021-9797(89)90466-9	journal	May 1989
Violation of the electroneutrality condition in confined unsymmetrical electrolytes Lozada-Cassou, Marcelo; Olivares, Wilmer; Sulbarán, Belky Physica A: Statistical Mechanics and its Applications, Vol. 231, Issue 1-3 https://doi.org/10.1016/0378-4371(95)00451-3	journal	September 1996
How electrolyte shielding influences the electrical potential in transmembrane ion channels Jordan, P. C.; Bacquet, R. J.; McCammon, J. A. Biophysical Journal, Vol. 55, Issue 6 https://doi.org/10.1016/S0006-3495(89)82903-0	journal	June 1989
Ion Permeation and Glutamate Residues Linked by Poisson-Nernst-Planck Theory in L-Type Calcium Channels Nonner, Wolfgang; Eisenberg, Bob Biophysical Journal, Vol. 75, Issue 3 https://doi.org/10.1016/S0006-3495(98)74048-2	journal	September 1998
Modelling the performance of membrane nanofiltration—critical assessment and model development Bowen, W. Richard; Welfoot, Julian S. Chemical Engineering Science, Vol. 57, Issue 7 https://doi.org/10.1016/S0009-2509(01)00413-4	journal	April 2002
Non-neutrality in a charged slit pore Lee, Ming; Chan, Kwong-Yu Chemical Physics Letters, Vol. 275, Issue 1-2 https://doi.org/10.1016/S0009-2614(97)00737-9	journal	August 1997
Deviation from electroneutrality in cylindrical pores Lee, Ming; Chan, Kwong-Yu; Nicholson, David Chemical Physics Letters, Vol. 307, Issue 1-2 https://doi.org/10.1016/S0009-2614(99)00502-3	journal	June 1999
Porous glass electroosmotic pumps: theory Yao, Shuhuai; Santiago, Juan G. Journal of Colloid and Interface Science, Vol. 268, Issue 1 https://doi.org/10.1016/S0021-9797(03)00731-8	journal	December 2003
Transport Processes and Electrical Phenomena in Ionic Membranes Teorell, Tarsten Progress in Biophysics and Biophysical Chemistry, Vol. 3 https://doi.org/10.1016/S0096-4174(18)30049-0	journal	January 1953
Streaming potential and streaming current measurements at planar solid/liquid interfaces for simultaneous determination of zeta potential and surface conductivity Werner, Carsten; Zimmermann, Ralf; Kratzmüller, Thomas Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 192, Issue 1-3 https://doi.org/10.1016/S0927-7757(01)00725-7	journal	November 2001
Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions Bazant, Martin Z.; Kilic, Mustafa Sabri; Storey, Brian D. Advances in Colloid and Interface Science, Vol. 152, Issue 1-2 https://doi.org/10.1016/j.cis.2009.10.001	journal	November 2009
Electrokinetic phenomena at grafted polyelectrolyte layers Dukhin, Stanislav S.; Zimmermann, Ralf; Werner, Carsten Journal of Colloid and Interface Science, Vol. 286, Issue 2 https://doi.org/10.1016/j.jcis.2005.01.088	journal	June 2005
Electrostatic potential and electroosmotic flow in a cylindrical capillary filled with symmetric electrolyte: Analytic solutions in thin double layer approximation Petsev, Dimiter N.; Lopez, Gabriel P. Journal of Colloid and Interface Science, Vol. 294, Issue 2 https://doi.org/10.1016/j.jcis.2005.07.037	journal	February 2006
Nernst-Planck transport theory for (reverse) electrodialysis: I. Effect of co-ion transport through the membranes Tedesco, M.; Hamelers, H. V. M.; Biesheuvel, P. M. Journal of Membrane Science, Vol. 510 https://doi.org/10.1016/j.memsci.2016.03.012	journal	July 2016
Transport in one-dimensional Coulomb gases: From ion channels to nanopores Kamenev, A.; Zhang, J.; Larkin, A. I. Physica A: Statistical Mechanics and its Applications, Vol. 359 https://doi.org/10.1016/j.physa.2005.05.097	journal	January 2006
Tough Electrodes: Carbon Nanotube Fibers as the Ultimate Current Collectors/Active Material for Energy Management Devices Vilatela, Juan J.; Marcilla, Rebeca Chemistry of Materials, Vol. 27, Issue 20 https://doi.org/10.1021/acs.chemmater.5b02783	journal	October 2015
Direct Observation of Charge Inversion in Divalent Nanofluidic Devices Li, Sylvia Xin; Guan, Weihua; Weiner, Benjamin Nano Letters, Vol. 15, Issue 8 https://doi.org/10.1021/acs.nanolett.5b01115	journal	June 2015
Interplay between Nanochannel and Microchannel Resistances Green, Yoav; Eshel, Ran; Park, Sinwook Nano Letters, Vol. 16, Issue 4 https://doi.org/10.1021/acs.nanolett.6b00429	journal	March 2016
Strong Electroosmotic Coupling Dominates Ion Conductance of 1.5 nm Diameter Carbon Nanotube Porins Yao, Yun-Chiao; Taqieddin, Amir; Alibakhshi, Mohammad A. ACS Nano, Vol. 13, Issue 11 https://doi.org/10.1021/acsnano.9b05118	journal	November 2019
Diffusion and Membrane Permeability. Zwolinski, Bruno J.; Eyring, Henry; Reese, Cecil E. The Journal of Physical and Colloid Chemistry, Vol. 53, Issue 9 https://doi.org/10.1021/j150474a012	journal	September 1949
Monte Carlo Simulations of the Mechanism for Channel Selectivity: The Competition between Volume Exclusion and Charge Neutrality Boda, Dezsö; Busath, David D.; Henderson, Douglas The Journal of Physical Chemistry B, Vol. 104, Issue 37 https://doi.org/10.1021/jp0019658	journal	September 2000
Double-Layer in Ionic Liquids: Paradigm Change? Kornyshev, Alexei A. The Journal of Physical Chemistry B, Vol. 111, Issue 20 https://doi.org/10.1021/jp067857o	journal	May 2007
Energy Conversion Efficiency of Nanofluidic Batteries: Hydrodynamic Slip and Access Resistance Yan, Yu; Sheng, Qian; Wang, Ceming The Journal of Physical Chemistry C, Vol. 117, Issue 16 https://doi.org/10.1021/jp400238v	journal	April 2013
Electrochemomechanical Energy Conversion in Nanofluidic Channels Daiguji, Hirofumi; Yang, Peidong; Szeri, Andrew J. Nano Letters, Vol. 4, Issue 12 https://doi.org/10.1021/nl0489945	journal	December 2004
Electrokinetic Energy Conversion Efficiency in Nanofluidic Channels van der Heyden, Frank H. J.; Bonthuis, Douwe Jan; Stein, Derek Nano Letters, Vol. 6, Issue 10 https://doi.org/10.1021/nl061524l	journal	October 2006
Enhanced Fluid Flow through Nanoscale Carbon Pipes Whitby, Max; Cagnon, Laurent; Thanou, Maya Nano Letters, Vol. 8, Issue 9 https://doi.org/10.1021/nl080705f	journal	September 2008
Electric Field Modulation of the Membrane Potential in Solid-State Ion Channels Guan, Weihua; Reed, Mark A. Nano Letters, Vol. 12, Issue 12 https://doi.org/10.1021/nl303820a	journal	February 2012
Ionic Selectivity of Single Nanochannels Vlassiouk, Ivan; Smirnov, Sergei; Siwy, Zuzanna Nano Letters, Vol. 8, Issue 7 https://doi.org/10.1021/nl800949k	journal	July 2008
Zwitterion Functionalized Carbon Nanotube/Polyamide Nanocomposite Membranes for Water Desalination Chan, Wai-Fong; Chen, Hang-yan; Surapathi, Anil ACS Nano, Vol. 7, Issue 6 https://doi.org/10.1021/nn4011494	journal	May 2013
Mechanism of ion permeation through calcium channels Hess, Peter; Tsien, Richard W. Nature, Vol. 309, Issue 5967 https://doi.org/10.1038/309453a0	journal	May 1984
Energetics of ion conduction through the K+ channel Bernèche, Simon; Roux, Benoît Nature, Vol. 414, Issue 6859 https://doi.org/10.1038/35102067	journal	November 2001
Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube Siria, Alessandro; Poncharal, Philippe; Biance, Anne-Laure Nature, Vol. 494, Issue 7438 https://doi.org/10.1038/nature11876	journal	February 2013
Electroneutrality breakdown and specific ion effects in nanoconfined aqueous electrolytes observed by NMR Luo, Zhi-Xiang; Xing, Yun-Zhao; Ling, Yan-Chun Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7358	journal	February 2015
Anomalous ion transport in 2-nm hydrophilic nanochannels Duan, Chuanhua; Majumdar, Arun Nature Nanotechnology, Vol. 5, Issue 12 https://doi.org/10.1038/nnano.2010.233	journal	November 2010
Direct seawater desalination by ion concentration polarization Kim, Sung Jae; Ko, Sung Hee; Kang, Kwan Hyoung Nature Nanotechnology, Vol. 5, Issue 4, p. 297-301 https://doi.org/10.1038/nnano.2010.34	journal	March 2010
Observation of extreme phase transition temperatures of water confined inside isolated carbon nanotubes Agrawal, Kumar Varoon; Shimizu, Steven; Drahushuk, Lee W. Nature Nanotechnology, Vol. 12, Issue 3 https://doi.org/10.1038/nnano.2016.254	journal	November 2016
Monte Carlo simulations of ion selectivity in a biological Na channel: Charge–space competition Boda, Dezső; Busath, David D.; Eisenberg, Bob Phys. Chem. Chem. Phys., Vol. 4, Issue 20 https://doi.org/10.1039/B203686J	journal	January 2002
Ionic selectivity and filtration from fragmented dehydration in multilayer graphene nanopores Sahu, Subin; Zwolak, Michael Nanoscale, Vol. 9, Issue 32 https://doi.org/10.1039/C7NR03838K	journal	January 2017
Role of Stefan–Maxwell fluxes in the dynamics of concentrated electrolytes Balu, Bhavya; Khair, Aditya S. Soft Matter, Vol. 14, Issue 41 https://doi.org/10.1039/C8SM01222A	journal	January 2018
Ion and potential distributions in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation. Comparison with generalized Debye–Hückel and Donnan theory Sørensen, Torben Smith; Sloth, Peter J. Chem. Soc., Faraday Trans., Vol. 88, Issue 4 https://doi.org/10.1039/FT9928800571	journal	January 1992
Nanofluidic concentration devices for biomolecules utilizing ion concentration polarization: theory, fabrication, and applications Kim, Sung Jae; Song, Yong-Ak; Han, Jongyoon Chemical Society Reviews, Vol. 39, Issue 3, p. 912-922 https://doi.org/10.1039/b822556g	journal	January 2010
Water and ion transport through functionalised carbon nanotubes: implications for desalination technology Corry, Ben Energy & Environmental Science, Vol. 4, Issue 3 https://doi.org/10.1039/c0ee00481b	journal	January 2011
General discussion Cowan, S. L.; Schulman, J. H.; Teorell, T. Transactions of the Faraday Society, Vol. 33 https://doi.org/10.1039/tf9373301051	journal	January 1937
Non-equilibrium thermodynamics of membrane processes Staverman, A. J. Transactions of the Faraday Society, Vol. 48 https://doi.org/10.1039/tf9524800176	journal	January 1952
Membrane Transport Characteristics of Ultrafine Capillaries Gross, R. J.; Osterle, J. F. The Journal of Chemical Physics, Vol. 49, Issue 1 https://doi.org/10.1063/1.1669814	journal	July 1968
Reverse Electrodialysis in Charged Capillary Membranes Fair, J. C.; Osterle, J. F. The Journal of Chemical Physics, Vol. 54, Issue 8 https://doi.org/10.1063/1.1675344	journal	April 1971
Exact Statistical Mechanics of a One‐Dimensional System with Coulomb Forces Lenard, A. Journal of Mathematical Physics, Vol. 2, Issue 5 https://doi.org/10.1063/1.1703757	journal	September 1961
Exact Statistical Mechanics of a One‐Dimensional System with Coulomb Forces. II. The Method of Functional Integration Edwards, S. F.; Lenard, A. Journal of Mathematical Physics, Vol. 3, Issue 4 https://doi.org/10.1063/1.1724281	journal	July 1962
Gaseous Diffusion in Porous Media at Uniform Pressure Evans, R. B.; Watson, G. M.; Mason, E. A. The Journal of Chemical Physics, Vol. 35, Issue 6 https://doi.org/10.1063/1.1732211	journal	December 1961
The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel Boda, Dezső; Valiskó, Mónika; Eisenberg, Bob The Journal of Chemical Physics, Vol. 125, Issue 3 https://doi.org/10.1063/1.2212423	journal	July 2006
Charge neutrality breakdown in confined aqueous electrolytes: Theory and simulation Colla, Thiago; Girotto, Matheus; dos Santos, Alexandre P. The Journal of Chemical Physics, Vol. 145, Issue 9 https://doi.org/10.1063/1.4962198	journal	September 2016
Optimizing water permeability through the hourglass shape of aquaporins Gravelle, S.; Joly, L.; Detcheverry, F. Proceedings of the National Academy of Sciences, Vol. 110, Issue 41 https://doi.org/10.1073/pnas.1306447110	journal	September 2013
Non-neutrality in a charged capillary Lo, Wai Yin; Chan, Kwong-Yu Molecular Physics, Vol. 86, Issue 4 https://doi.org/10.1080/00268979500102341	journal	November 1995
Grand Canonical Ensemble Monte Carlo Simulations of Donnan Potentials, Nonelectroneutrality, Activity Coefficients and Excess Energy in Spherical Charged or Uncharged Pores with Restricted Primitive Model Electrolytes Rivera, Sergio Roberto; S⊘srensen, Torben Smith Molecular Simulation, Vol. 13, Issue 2 https://doi.org/10.1080/08927029408021978	journal	May 1994
XXXIX. Structure and capacity of electrical double layer Bikerman, J. J. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 33, Issue 220 https://doi.org/10.1080/14786444208520813	journal	May 1942
Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena Yang, Jun; Lu, Fuzhi; Kostiuk, Larry W. Journal of Micromechanics and Microengineering, Vol. 13, Issue 6 https://doi.org/10.1088/0960-1317/13/6/320	journal	October 2003
Violation of the electroneutrality condition in confined charged fluids Lozada-Cassou, Marcelo; Olivares, Wilmer; Sulbarán, Belky Physical Review E, Vol. 53, Issue 1 https://doi.org/10.1103/PhysRevE.53.522	journal	January 1996
Deionization shocks in microstructures Mani, Ali; Bazant, Martin Z. Physical Review E, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevE.84.061504	journal	December 2011
Ion fluxes through nanopores and transmembrane channels Bordin, J. R.; Diehl, A.; Barbosa, M. C. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.031914	journal	March 2012
Analysis of electrolyte transport through charged nanopores Peters, P. B.; van Roij, R.; Bazant, M. Z. Physical Review E, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevE.93.053108	journal	May 2016
Analysis of ionic conductance of carbon nanotubes Biesheuvel, P. M.; Bazant, M. Z. Physical Review E, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevE.94.050601	journal	November 2016
Fluctuating hydrodynamics of electrolytes at electroneutral scales Donev, Aleksandar; Nonaka, Andrew J.; Kim, Changho Physical Review Fluids, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevFluids.4.043701	journal	April 2019
Scaling Behavior for Ionic Transport and its Fluctuations in Individual Carbon Nanotubes Secchi, Eleonora; Niguès, Antoine; Jubin, Laetitia Physical Review Letters, Vol. 116, Issue 15 https://doi.org/10.1103/PhysRevLett.116.154501	journal	April 2016
Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation Borukhov, Itamar; Andelman, David; Orland, Henri Physical Review Letters, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevLett.79.435	journal	July 1997
Surface-Charge-Governed Ion Transport in Nanofluidic Channels Stein, Derek; Kruithof, Maarten; Dekker, Cees Physical Review Letters, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevLett.93.035901	journal	July 2004
Combined Effect of Pore Radius and Protein Dielectric Coefficient on the Selectivity of a Calcium Channel Boda, Dezső; Valiskó, Mónika; Eisenberg, Bob Physical Review Letters, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevLett.98.168102	journal	April 2007
Non-selective conductance in calcium channels of frog muscle: calcium selectivity in a single-file pore. Almers, W.; McCleskey, E. W. The Journal of Physiology, Vol. 353, Issue 1 https://doi.org/10.1113/jphysiol.1984.sp015352	journal	August 1984
Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes Holt, J. K. Science, Vol. 312, Issue 5776 https://doi.org/10.1126/science.1126298	journal	May 2006
Coherence Resonance in a Single-Walled Carbon Nanotube Ion Channel Lee, Chang Young; Choi, Wonjoon; Han, Jae-Hee Science, Vol. 329, Issue 5997 https://doi.org/10.1126/science.1193383	journal	September 2010
The Structure of the Potassium Channel: Molecular Basis of K+ Conduction and Selectivity Doyle, D. A. Science, Vol. 280, Issue 5360 https://doi.org/10.1126/science.280.5360.69	journal	April 1998
Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins Tunuguntla, Ramya H.; Henley, Robert Y.; Yao, Yun-Chiao Science, Vol. 357, Issue 6353 https://doi.org/10.1126/science.aan2438	journal	August 2017
Size effect in ion transport through angstrom-scale slits Esfandiar, A.; Radha, B.; Wang, F. C. Science, Vol. 358, Issue 6362 https://doi.org/10.1126/science.aan5275	journal	October 2017
Anomalously low dielectric constant of confined water Fumagalli, L.; Esfandiar, A.; Fabregas, R. Science, Vol. 360, Issue 6395 https://doi.org/10.1126/science.aat4191	journal	June 2018
Ion Flow through Narrow Membrane Channels: Part I Barcilon, Victor SIAM Journal on Applied Mathematics, Vol. 52, Issue 5 https://doi.org/10.1137/0152080	journal	October 1992
Homogenization of the Poisson--Nernst--Planck equations for Ion Transport in Charged Porous Media Schmuck, Markus; Bazant, Martin Z. SIAM Journal on Applied Mathematics, Vol. 75, Issue 3 https://doi.org/10.1137/140968082	journal	January 2015
Permeation and Selectivity in Calcium Channels Sather, William A.; McCleskey, Edwin W. Annual Review of Physiology, Vol. 65, Issue 1 https://doi.org/10.1146/annurev.physiol.65.092101.142345	journal	March 2003
Ion and Solvent Transport in Ion-Exchange Membranes Verbrugge, Mark W. Journal of The Electrochemical Society, Vol. 137, Issue 3 https://doi.org/10.1149/1.2086573	journal	January 1990
Multicomponent Gas Diffusion in Porous Electrodes Fu, Yeqing; Jiang, Yi; Poizeau, Sophie Journal of The Electrochemical Society, Vol. 162, Issue 6 https://doi.org/10.1149/2.0911506jes	journal	January 2015
Overscreening in a 1D lattice Coulomb gas model of ionic liquids Démery, V.; Dean, D. S.; Hammant, T. C. EPL (Europhysics Letters), Vol. 97, Issue 2 https://doi.org/10.1209/0295-5075/97/28004	journal	January 2012
A Poisson/Nernst-Planck model for ionic transport through synthetic conical nanopores Cervera, J.; Schiedt, B.; Ramírez, P. Europhysics Letters (EPL), Vol. 71, Issue 1 https://doi.org/10.1209/epl/i2005-10054-x	journal	July 2005
Electrostatics of ions inside the nanopores and trans-membrane channels Levin, Y. Europhysics Letters (EPL), Vol. 76, Issue 1 https://doi.org/10.1209/epl/i2006-10240-4	journal	October 2006
Zur Theorie der anomalen Osmose. Schlögl, R. Zeitschrift für Physikalische Chemie, Vol. 3, Issue 1_2 https://doi.org/10.1524/zpch.1955.3.1_2.073	journal	January 1955
Steric Selectivity in Na Channels Arising from Protein Polarization and Mobile Side Chains Boda, Dezső; Nonner, Wolfgang; Valiskó, Mónika Biophysical Journal, Vol. 93, Issue 6 https://doi.org/10.1529/biophysj.107.105478	journal	September 2007

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
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Nanopores
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Breakdown of electroneutrality in nanopores

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