Extended Nernst–Planck Equation Incorporating Partial Dehydration Effect
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Abstract
Novel ionic transporting phenomena emerge as nanostructures approach the molecular scale. At the sub-2 nm scale, widely used continuum equations, such as the Nernst–Planck equation, break down. Here, we extend the Nernst–Planck equation by adding a partial dehydration effect. Our model agrees with the reported ion fluxes through graphene oxide laminates with sub-2 nm interlayer spacing, outperforming previous models. We also predict that the selectivity sequences of alkali metal ions depend on the geometries of the nanostructures. Our model opens a new avenue for the investigation of the underlying mechanisms in nanofluidics at the sub-2 nm scale. -
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References
[1] Kratochvil H T, Carr J K, Matulef K et al.. 2016 Science 353 1040 doi: 10.1126/science.aag1447[2] Liu S and Gonen T 2018 Commun. Biol. 1 38 doi: 10.1038/s42003-018-0040-8[3] Nair R R, Wu H A, Jayaram P et al.. 2012 Science 335 442 doi: 10.1126/science.1211694[4] Joshi R K, Carbone P, Wang F C et al.. 2014 Science 343 752 doi: 10.1126/science.1245711[5] Jain T, Rasera B C, Guerrero R J S et al.. 2015 Nat. Nanotechnol. 10 1053 doi: 10.1038/nnano.2015.222[6] Radha B, Esfandiar A, Wang F C et al.. 2016 Nature 538 222 doi: 10.1038/nature19363[7] Wen Q, Yan D X, Liu F et al.. 2016 Adv. Funct. Mater. 26 5796 doi: 10.1002/adfm.201601689[8] Abraham J, Vasu K S, Williams C D et al.. 2017 Nat. Nanotechnol. 12 546 doi: 10.1038/nnano.2017.21[9] Esfandiar A, Radha B, Wang F C et al.. 2017 Science 358 511 doi: 10.1126/science.aan5275[10] Wang P F, Wang M, Liu F et al.. 2018 Nat. Commun. 9 569 doi: 10.1038/s41467-018-02941-6[11] Zhang H C, Hou J, Hu Y X et al.. 2018 Sci. Adv. 4 eaaq0066 doi: 10.1126/sciadv.aaq0066[12] Wang P F, Wang X, Ling Y et al.. 2018 Radiat. Meas. 119 80 doi: 10.1016/j.radmeas.2018.09.007[13] Feng Y X, Zhang Y C, Ying C F et al.. 2015 Genomics Proteomics & Bioinf. 13 4 doi: 10.1016/j.gpb.2015.01.009[14] Wang L D, Boutilier M S H, Kidambi P R et al.. 2017 Nat. Nanotechnol. 12 509 doi: 10.1038/nnano.2017.72[15] Wei N, Peng X S and Xu Z P 2014 ACS Appl. Mater. & Interfaces 6 5877 doi: 10.1021/am500777b[16] Sahu S, Di Ventra M and Zwolak M 2017 Nano Lett. 17 4719 doi: 10.1021/acs.nanolett.7b01399[17] Wang M, Shen W H, Ding S Y et al.. 2018 Nanoscale 10 18821 doi: 10.1039/C8NR04962A[18] Moy G, Corry B, Kuyucak S et al.. 2000 Biophys. J. 78 2349 doi: 10.1016/S0006-34950076780-4[19] Corry B, Kuyucak S and Chung S H 2000 Biophys. J. 78 2364 doi: 10.1016/S0006-34950076781-6[20] Song C and Corry B 2011 PLOS ONE 6 e21204 doi: 10.1371/journal.pone.0021204[21] Chen P R, Xu Z C, Gu Y et al.. 2016 Chin. Phys. B 25 086601 doi: 10.1088/1674-1056/25/8/086601[22] Gao Y, Huang J, Liu Y W et al.. 2019 Curr. Opin. Electrochem. 13 107 doi: 10.1016/j.coelec.2018.11.007[23] Suk M E and Aluru N R 2014 J. Chem. Phys. 140 084707 doi: 10.1063/1.4866643[24] Mouterde T, Keerthi A, Poggioli A R et al.. 2019 Nature 567 87 doi: 10.1038/s41586-019-0961-5[25] Qiao Y and Lu B Z 2016 Chin. Phys. B 25 018705 doi: 10.1088/1674-1056/25/1/018705[26] Gillespie D, Xu L and Meissner G 2014 Biophys. J. 107 2263 doi: 10.1016/j.bpj.2014.09.031[27] Laio A and Torre V 1999 Biophys. J. 76 129 doi: 10.1016/S0006-34959977184-5[28] Zwolak M, Lagerqvist J and Di Ventra M 2009 Phys. Rev. Lett. 103 128102 doi: 10.1103/PhysRevLett.103.128102[29] Zwolak M, Wilson J and Di Ventra M 2010 J. Phys.: Condens. Matter 22 454126 doi: 10.1088/0953-8984/22/45/454126[30] Schlaich A, Knapp E W and Netz R R 2016 Phys. Rev. Lett. 117 048001 doi: 10.1103/PhysRevLett.117.048001[31] Fumagalli L, Esfandiar A, Fabregas R et al.. 2018 Science 360 1339 doi: 10.1126/science.aat4191[32] Amiri H, Shepard K L, Nuckolls C et al.. 2017 Nano Lett. 17 1204 doi: 10.1021/acs.nanolett.6b04967[33] Baimpos T, Shrestha B R, Raman S et al.. 2014 Langmuir 30 4322 doi: 10.1021/la500288w[34] Eisenman G 1962 Biophys. J. 2 259 doi: 10.1016/S0006-34956286959-8[35] Krauss D, Eisenberg B and Gillespie D 2011 Eur. Biophys. J. 40 775 doi: 10.1007/s00249-011-0691-6[36] Wu J 1991 Biophys. J. 60 238 doi: 10.1016/S0006-34959182046-X[37] Luchinsky D G, Tindjong R, Kaufman I et al.. 2009 Phys. Rev. E 80 021925 doi: 10.1103/PhysRevE.80.021925[38] Ohtaki H and Radnai T 1993 Chem. Rev. 93 1157 doi: 10.1021/cr00019a014[39] Marcus Y 1991 J. Chem. Soc., Faraday Trans. 87 2995 doi: 10.1039/FT9918702995[40] Saxena A and García A E 2015 J. Phys. Chem. B 119 219 doi: 10.1021/jp507008x[41] Yoo J, Wilson J and Aksimentiev A 2016 Biopolymers 105 752 doi: 10.1002/bip.22868[42] Hong S, Constans C, Surmani Martins M V et al.. 2017 Nano Lett. 17 728 doi: 10.1021/acs.nanolett.6b03837[43] Zhang Z K, Shen W H, Lin L X et al.. 2020 Adv. Sci. 7 2000286 doi: 10.1002/advs.202000286[44] Xu W L, Fang C, Zhou F L et al.. 2017 Nano Lett. 17 2928 doi: 10.1021/acs.nanolett.7b00148[45] Ren C E, Hatzell K B, Alhabeb M et al.. 2015 J. Phys. Chem. Lett. 6 4026 doi: 10.1021/acs.jpclett.5b01895[46] Feng J D, Liu K, Graf M et al.. 2016 Nat. Mater. 15 850 doi: 10.1038/nmat4607[47] Guo Y, Ying Y L, Mao Y Y et al.. 2016 Ngewandte Chem.-Int. Ed. 55 15120 doi: 10.1002/anie.201607329[48] Surwade S P, Smirnov S N, Vlassiouk I V et al.. 2015 Nat. Nanotechnol. 10 459 doi: 10.1038/nnano.2015.37 -
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