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Towards single-species selectivity of membranes with subnanometre pores

Nature Nanotechnology volume 15, pages 426–436 (2020)Cite this article

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Abstract

Synthetic membranes with pores at the subnanometre scale are at the core of processes for separating solutes from water, such as water purification and desalination. While these membrane processes have achieved substantial industrial success, the capability of state-of-the-art membranes to selectively separate a single solute from a mixture of solutes is limited. Such high-precision separation would enable fit-for-purpose treatment, improving the sustainability of current water-treatment processes and opening doors for new applications of membrane technologies. Herein, we introduce the challenges of state-of-the-art membranes with subnanometre pores to achieve high selectivity between solutes. We then analyse experimental and theoretical literature to discuss the molecular-level mechanisms that contribute to energy barriers for solute transport through subnanometre pores. We conclude by providing principles and guidelines for designing next-generation single-species selective membranes that are inspired by ion-selective biological channels.

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Fig. 1: Membranes with subnanometre pores.
Fig. 2: Energy barriers for solute transport through membranes with subnanometre pores.
Fig. 3: Experimental and simulated energy barriers for water and solute transport through different subnanometre pores.
Fig. 4: Guidelines for designing single-species selective membranes.

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References

  1. Elimelech, M. & Phillip, W. A. The future of seawater desalination: energy, technology, and the environment. Science 333, 712–717 (2011).

    Article  CAS  Google Scholar 

  2. Werber, J. R., Osuji, C. O. & Elimelech, M. Materials for next-generation desalination and water purification membranes. Nat. Rev. Mater. 1, 1–15 (2016).

    Article  CAS  Google Scholar 

  3. Werber, J. R., Deshmukh, A. & Elimelech, M. The critical need for increased selectivity, not increased water permeability, for desalination membranes. Environ. Sci. Technol. Lett. 3, 112–120 (2016).

    Article  CAS  Google Scholar 

  4. Park, H. B., Kamcev, J., Robeson, L. M., Elimelech, M. & Freeman, B. D. Maximizing the right stuff: The trade-off between membrane permeability and selectivity. Science 356, 1138–1148 (2017).

    Article  CAS  Google Scholar 

  5. Werber, J. R. & Elimelech, M. Permselectivity limits of biomimetic desalination membranes. Sci. Adv. 4, eaar8266 (2018).

    Article  CAS  Google Scholar 

  6. Werber, J. R., Porter, C. J. & Elimelech, M. A path to ultraselectivity: Support layer properties to maximize performance of biomimetic desalination membranes. Environ. Sci. Technol. 52, 10737–10747 (2018).

    Article  CAS  Google Scholar 

  7. Ritt, C. L., Werber, J. R., Deshmukh, A. & Elimelech, M. Monte carlo simulations of framework defects in layered two-dimensional nanomaterial desalination membranes: implications for permeability and selectivity. Environ. Sci. Technol. 53, 6214–6224 (2019).

    Article  CAS  Google Scholar 

  8. Homaeigohar, S. & Elbahri, M. Graphene membranes for water desalination. NPG Asia Mater. 9, e427 (2017).

    Article  CAS  Google Scholar 

  9. Luo, T., Abdu, S. & Wessling, M. Selectivity of ion exchange membranes: A review. J. Memb. Sci. 555, 429–454 (2018).

    Article  CAS  Google Scholar 

  10. Zhang, H. et al. Ultrafast selective transport of alkali metal ions in metal organic frameworks with subnanometer pores. Sci. Adv. 4, eaaq0066 (2018).

    Article  CAS  Google Scholar 

  11. Li, X. et al. Fast and selective fluoride ion conduction in sub-1-nanometer metal-organic framework channels. Nat. Commun. 10, 2490 (2019).

    Article  CAS  Google Scholar 

  12. Alvarez, P. J. J., Chan, C. K., Elimelech, M., Halas, N. J. & Villagrán, D. Emerging opportunities for nanotechnology to enhance water security. Nat. Nanotechnol. 13, 634–641 (2018).

    Article  CAS  Google Scholar 

  13. Sadeghi, I., Kaner, P. & Asatekin, A. Controlling and expanding the selectivity of filtration membranes. Chem. Mater. 21, 7328–7354 (2018).

    Article  CAS  Google Scholar 

  14. Nghiem, L. D. et al. Extraction and transport of metal ions and small organic compounds using polymer inclusion membranes (PIMs). J. Memb. Sci. 281, 7–41 (2006).

    Article  CAS  Google Scholar 

  15. Thiruraman, J. P. et al. Angstrom-size defect creation and ionic transport through pores in single-layer MoS2. Nano Lett. 18, 1651–1659 (2018).

    Article  CAS  Google Scholar 

  16. Radha, B. et al. Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222–225 (2016).

    Article  CAS  Google Scholar 

  17. Jones, E., Qadir, M., van Vliet, M. T. H., Smakhtin, V. & Kang, S. The state of desalination and brine production: A global outlook. Sci. Total Environ. 657, 1343–1356 (2019).

    Article  CAS  Google Scholar 

  18. Campione, A. et al. Electrodialysis for water desalination: A critical assessment of recent developments on process fundamentals, models and applications. Desalination 434, 121–160 (2018).

    Article  CAS  Google Scholar 

  19. Faucher, S. et al. Critical knowledge gaps in mass transport through single-digit nanopores: A review and perspective. J. Phys. Chem. C. 123, 21309–21326 (2019).

    Article  CAS  Google Scholar 

  20. Wijmans, J. G. & Baker, R. W. The solution-diffusion model: a review. J. Memb. Sci. 107, 1–21 (1995).

    Article  CAS  Google Scholar 

  21. Mukherjee, P. & Sengupta, A. K. Ion exchange selectivity as a surrogate indicator of relative permeability of ions in reverse osmosis processes. Environ. Sci. Technol. 37, 1432–1440 (2003).

    Article  CAS  Google Scholar 

  22. Epsztein, R., Cheng, W., Shaulsky, E., Dizge, N. & Elimelech, M. Elucidating the mechanisms underlying the difference between chloride and nitrate rejection in nanofiltration. J. Memb. Sci. 548, 694–701 (2017).

    Article  CAS  Google Scholar 

  23. Sata, T. Studies on anion exchange membranes having permselectivity for specific anions in electrodialysis - Effect of hydrophilicity of anion exchange membranes on permselectivity of anions. J. Memb. Sci. 167, 1–31 (2000).

    Article  CAS  Google Scholar 

  24. Cheng, W. et al. Selective removal of divalent cations by polyelectrolyte multilayer nanofiltration membrane: Role of polyelectrolyte charge, ion size, and ionic strength. J. Memb. Sci. 559, 98–106 (2018).

    Article  CAS  Google Scholar 

  25. Collins, F. C. Activation energy of the Eyring theory of liquid viscosity and diffusion. J. Chem. Phys. 26, 398–400 (1957).

    Article  CAS  Google Scholar 

  26. Eyring, H. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283–291 (1936).

    Article  CAS  Google Scholar 

  27. Ewell, R. H. & Eyring, H. Theory of the viscosity of liquids as a function of temperature and pressure. J. Chem. Phys. 5, 726–736 (1937).

    Article  CAS  Google Scholar 

  28. Zwolinski, B. J., Eyring, H. & Reese, C. E. Diffusion and membrane permeability. J. Phys. Colloid Chem. 53, 1426–1453 (1949).

    Article  CAS  Google Scholar 

  29. Castillo, L. F. Del, Mason, E. A. & Viehland, L. A. Energy-barrier models for membrane transport. Biophys. Chem. 9, 111–120 (1979).

    Article  Google Scholar 

  30. Sogami, M. et al. Application of the transition state theory to water transport across cell membranes. Biochim. Biophys. Acta - Biomembr. 1511, 42–48 (2001).

    Article  CAS  Google Scholar 

  31. Babu, J. S. & Sathian, S. P. Combining molecular dynamics simulation and transition state theory to evaluate solid-liquid interfacial friction in carbon nanotube membranes. Phys. Rev. E 85, 051205 (2012).

    Article  CAS  Google Scholar 

  32. Epsztein, R., Qin, M., Shaulsky, E. & Elimelech, M. Activation behavior for ion permeation in ion-exchange membranes: Role of ion dehydration in selective transport. J. Memb. Sci. 580, 316–326 (2019).

    Article  CAS  Google Scholar 

  33. Latorre, R. & Miller, C. Conduction and selectivity in potassium channels. J. Membr. Biol. 71, 11–30 (1983).

    Article  CAS  Google Scholar 

  34. Wang, J. H., Robinson, C. V. & Edelman, I. S. Self-diffusion and structure of liquid water. III. Measurement of the self-diffusion of liquid water with H2, H3 and O18 as tracers. J. Am. Chem. Soc. 75, 466–470 (1953).

    Article  Google Scholar 

  35. Venkataraman, L., Klare, J. E., Nuckolls, C., Hybertsen, M. S. & Steigerwald, M. L. Dependence of single-molecule junction conductance on molecular conformation. Nature 442, 904–907 (2006).

    Article  CAS  Google Scholar 

  36. Pati, R. & Karna, S. P. Current switching by conformational change in a π-σ-π molecular wire. Phys. Rev. B - Condens. Matter Mater. Phys. 69, 155419 (2004).

    Article  CAS  Google Scholar 

  37. Weigelt, S. et al. Chiral switching by spontaneous conformational change in adsorbed organic molecules. Nat. Mater. 5, 112–117 (2006).

    Article  CAS  Google Scholar 

  38. Daasbjerg, K. et al. Evidence for large inner reorganization energies in the reduction of diaryl disulfides: Toward a mechanistic link between concerted and stepwise dissociative electron transfers? J. Am. Chem. Soc. 121, 1750–1751 (1999).

    Article  CAS  Google Scholar 

  39. Pophristic, V., Goodman, L. & Guchhait, N. Role of lone-pairs in internal rotation barriers. J. Phys. Chem. A 101, 4290–4297 (1997).

    Article  CAS  Google Scholar 

  40. Sharma, R. R., Agrawal, R. & Chellam, S. Temperature effects on sieving characteristics of thin-film composite nanofiltration membranes: Pore size distributions and transport parameters. J. Memb. Sci. 223, 69–87 (2003).

    Article  CAS  Google Scholar 

  41. Luo, J. & Wan, Y. Effects of pH and salt on nanofiltration-a critical review. J. Membr. Sci. 438, 18–28 (2013).

    Article  CAS  Google Scholar 

  42. Nghiem, L. D., Schäfer, A. I. & Elimelech, M. Role of electrostatic interactions in the retention of pharmaceutically active contaminants by a loose nanofiltration membrane. J. Memb. Sci. 286, 52–59 (2006).

    Article  CAS  Google Scholar 

  43. Epsztein, R., Shaulsky, E., Dizge, N., Warsinger, D. M. & Elimelech, M. Role of ionic charge density in Donnan exclusion of monovalent anions by nanofiltration. Environ. Sci. Technol. 52, 4108–4116 (2018).

    Article  CAS  Google Scholar 

  44. Richards, L. A., Schäfer, A. I., Richards, B. S. & Corry, B. The importance of dehydration in determining ion transport in narrow pores. Small 8, 1701–1709 (2012).

    Article  CAS  Google Scholar 

  45. Marcus, Y. Thermodynamics of solvation of ions. J. Chem. Soc. Faraday Trans. 87, 2995–2999 (1991).

    Article  CAS  Google Scholar 

  46. Ben-Amotz, D., Raineri, F. O. & Stell, G. Solvation thermodynamics: Theory and applications. J. Phys. Chem. B 109, 6866–6878 (2005).

    Article  CAS  Google Scholar 

  47. Sahu, S., Di Ventra, M. & Zwolak, M. Dehydration as a universal mechanism for ion selectivity in graphene and other atomically thin pores. Nano Lett. 17, 4719–4724 (2017).

    Article  CAS  Google Scholar 

  48. Richards, L. A., Schäfer, A. I., Richards, B. S. & Corry, B. Quantifying barriers to monovalent anion transport in narrow non-polar pores. Phys. Chem. Chem. Phys. 14, 11633–11638 (2012).

    Article  CAS  Google Scholar 

  49. Zwolak, M., Wilson, J. & Di Ventra, M. Dehydration and ionic conductance quantization in nanopores. J. Phys. Condens. Matter 22, 454126 (2010).

    Article  CAS  Google Scholar 

  50. Tansel, B. Significance of thermodynamic and physical characteristics on permeation of ions during membrane separation: Hydrated radius, hydration free energy and viscous effects. Sep. Purif. Technol. 86, 119–126 (2012).

    Article  CAS  Google Scholar 

  51. Sata, T., Yamaguchi, T. & Matsusaki, K. Effect of hydrophobicity of ion exchange groups of anion exchange membranes on permselectivity between two anions. J. Phys. Chem. 99, 12875–12882 (1995).

    Article  CAS  Google Scholar 

  52. Hannesschlaeger, C., Horner, A. & Pohl, P. Intrinsic membrane permeability to small molecules. Chem. Rev. 119, 5922–5953 (2019).

    Article  CAS  Google Scholar 

  53. De Gier, J., Mandersloot, J. G., Hupkes, J. V., McElhaney, R. N. & van Veek, W. P. On the mechanism of non-electrolyte permeation through lipid bilayers and through biomembranes. Biochim. Biophys. Acta 233, 610–618 (1971).

    Article  Google Scholar 

  54. Noy, A. Kinetic model of gas transport in carbon nanotube channels. J. Phys. Chem. C. 117, 7656–7660 (2013).

    Article  CAS  Google Scholar 

  55. Boo, C. et al. High performance nanofiltration membrane for effective removal of perfluoroalkyl substances at high water recovery. Environ. Sci. Technol. 52, 7279–7288 (2018).

    Article  CAS  Google Scholar 

  56. DuChanois, R. M., Epsztein, R., Trivedi, J. A. & Elimelech, M. Controlling pore structure of polyelectrolyte multilayer nanofiltration membranes by tuning polyelectrolyte-salt interactions. J. Memb. Sci. 581, 413–420 (2019).

    Article  CAS  Google Scholar 

  57. Farrokhzad, H., Darvishmanesh, S., Genduso, G., Van Gerven, T. & Van Der Bruggen, B. Development of bivalent cation selective ion exchange membranes by varying molecular weight of polyaniline. Electrochim. Acta 158, 64–72 (2015).

    Article  CAS  Google Scholar 

  58. Vaselbehagh, M., Karkhanechi, H., Takagi, R. & Matsuyama, H. Surface modification of an anion exchange membrane to improve the selectivity for monovalent anions in electrodialysis - experimental verification of theoretical predictions. J. Memb. Sci. 490, 301–310 (2015).

    Article  CAS  Google Scholar 

  59. Epsztein, R., Nir, O., Lahav, O. & Green, M. Selective nitrate removal from groundwater using a hybrid nanofiltration–reverse osmosis filtration scheme. Chem. Eng. J. 279, 372–378 (2015).

    Article  CAS  Google Scholar 

  60. Zhou, Y. & MacKinnon, R. The occupancy of ions in the K+ selectivity filter: Charge balance and coupling of ion binding to a protein conformational change underlie high conduction rates. J. Mol. Biol. 333, 965–975 (2003).

    Article  CAS  Google Scholar 

  61. Doyle, D. A. et al. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 280, 69–77 (1998).

    Article  CAS  Google Scholar 

  62. Morais-Cabral, Ä. H., Kaufman, A. & Mackinnon, R. Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 Å resolution. Nature 414, 43–48 (2001).

    Article  Google Scholar 

  63. Gouaux, E. & MacKinnon, R. Principles of selective ion transport in channels and pumps. Science 310, 1461–1465 (2005).

    Article  CAS  Google Scholar 

  64. Barboiu, M. Encapsulation versus self-aggregation toward highly selective artificial K+ channels. Acc. Chem. Res. 51, 2711–2718 (2018).

    Article  CAS  Google Scholar 

  65. Gilles, A. & Barboiu, M. Highly selective artificial K+ channels: An example of selectivity-induced transmembrane potential. J. Am. Chem. Soc. 138, 426–432 (2016).

    Article  CAS  Google Scholar 

  66. Glasstone, S., Laidler, K. J. & Eyring, H. The Theory of Rate Processes (McGraw-Hill Book Company, 1941).

  67. Eyring, H. The activated complex and the absolute rate of chemical reactions. Chem. Rev. 17, 65–77 (1935).

    Article  CAS  Google Scholar 

  68. Kopec, W. et al. Direct knock-on of desolvated ions governs strict ion selectivity in K+ channels. Nat. Chem. 10, 813–820 (2018).

    Article  CAS  Google Scholar 

  69. Schoch, R. B., Han, J. & Renaud, P. Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839–883 (2008).

    Article  CAS  Google Scholar 

  70. Abraham, J. et al. Tunable sieving of ions using graphene oxide membranes. Nat. Nanotechnol. 12, 546–550 (2017).

    Article  CAS  Google Scholar 

  71. Li, W., Wu, W. & Li, Z. Controlling interlayer spacing of graphene oxide membranes by external pressure regulation. ACS Nano 12, 9309–9317 (2018).

    Article  CAS  Google Scholar 

  72. Simon, G. P. et al. Ion transport in complex layered graphene-based membranes with tuneable interlayer spacing. Sci. Adv. 2, e1501272 (2016).

    Article  Google Scholar 

  73. Chen, L. et al. Ion sieving in graphene oxide membranes via cationic control of interlayer spacing. Nature 550, 1–4 (2017).

    Article  Google Scholar 

  74. Joshi, R. K. et al. Precise and ultrafast molecular sieving through graphene oxide membranes. Science 343, 752–754 (2014).

    Article  CAS  Google Scholar 

  75. Choi, W. et al. Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotubes. Nat. Commun. 4, 2397 (2013).

    Article  CAS  Google Scholar 

  76. Tunuguntla, R. H. et al. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357, 792–796 (2017).

    Article  CAS  Google Scholar 

  77. Ali, S., Rehman, S. A. U., Luan, H. Y., Farid, M. U. & Huang, H. Challenges and opportunities in functional carbon nanotubes for membrane-based water treatment and desalination. Sci. Total Environ. 646, 1126–1139 (2019).

    Article  CAS  Google Scholar 

  78. Li, F., Li, L., Liao, X. & Wang, Y. Precise pore size tuning and surface modifications of polymeric membranes using the atomic layer deposition technique. J. Memb. Sci. 385–386, 1–9 (2011).

    Article  CAS  Google Scholar 

  79. Chen, P. et al. Atomic layer deposition to fine-tune the surface properties and diameters of fabricated nanopores. Nano Lett. 4, 1333–1337 (2004).

    Article  CAS  Google Scholar 

  80. Spichiger-keller, U. E. Ionophores, ligands and reactands. Anal. Chim. Acta 400, 65–72 (1999).

    Article  CAS  Google Scholar 

  81. Ovchinnikov, Y. A. Physico‐chemical basis of ion transport through biological membranes: ionophores and ion channels. Eur. J. Biochem. 94, 321–336 (1979).

    Article  CAS  Google Scholar 

  82. Ammann, D. et al. Preparation of neutral ionophores for alkali and alkaline earth metal cations and their application in ion selective membrane electrodes. Helv. Chem. Acta 58, 1535–1548 (1975).

    Article  CAS  Google Scholar 

  83. Bowman-James, K. Alfred Werner revisited: The coordination chemistry of anions. Acc. Chem. Res. 38, 671–678 (2005).

    Article  CAS  Google Scholar 

  84. Kang, S. O., Begum, R. A. & Bowman-James, K. Amide-based ligands for anion coordination. Angew. Chem. Int. Ed. 45, 7882–7894 (2006).

    Article  CAS  Google Scholar 

  85. Prets, E., Badertscher, M., Welti, M., Morf, W. E. & Simon, W. Design features of ionophores for ion selective electrodes. Pure Appl. Chem. 60, 567–574 (1988).

    Article  Google Scholar 

  86. Almeida, M. I. G. S., Cattrall, R. W. & Kolev, S. D. Recent trends in extraction and transport of metal ions using polymer inclusion membranes (PIMs). J. Memb. Sci. 415–416, 9–23 (2012).

    Article  CAS  Google Scholar 

  87. Sheng, C., Wijeratne, S., Cheng, C., Baker, G. L. & Bruening, M. L. Facilitated ion transport through polyelectrolyte multilayer films containing metal-binding ligands. J. Memb. Sci. 459, 169–176 (2014).

    Article  CAS  Google Scholar 

  88. Toutianoush, A., El-Hashani, A., Schnepf, J. & Tieke, B. Multilayer membranes of p-sulfonato-calix[8]arene and polyvinylamine and their use for selective enrichment of rare earth metal ions. Appl. Surf. Sci. 246, 430–436 (2005).

    Article  CAS  Google Scholar 

  89. Acar, E. T., Buchsbaum, S. F., Combs, C., Fornasiero, F. & Siwy, Z. S. Biomimetic potassium-selective nanopores. Sci. Adv. 5, eaav2568 (2019).

    Article  CAS  Google Scholar 

  90. Fang, A., Kroenlein, K., Riccardi, D. & Smolyanitsky, A. Highly mechanosensitive ion channels from graphene-embedded crown ethers. Nat. Mater. 18, 76–81 (2019).

    Article  CAS  Google Scholar 

  91. Richards, L. A., Richards, B. S., Corry, B. & Schäfer, A. I. Experimental energy barriers to anions transporting through nanofiltration membranes. Environ. Sci. Technol. 47, 1968–1976 (2013).

    Article  CAS  Google Scholar 

  92. Sigurdardottir, S. B., DuChanois, R. M., Epsztein, R., Pinelo, M. & Elimelech, M. Energy barriers to anion transport in nanofiltration membranes: role of intra-pore diffusion. J. Memb. Sci. 603, 117921 (2020).

    Article  CAS  Google Scholar 

  93. Khavrutskii, I. V., Gorfe, A. A., Lu, B. & McCammon, J. A. Free energy for the permeation of Na+ and CI- ions and their Ion-pair through a zwitterionic dimyristoyl phosphatidylcholine lipid bilayer by umbrella integration with harmonic fourier beads. J. Am. Chem. Soc. 131, 1706–1716 (2009).

    Article  CAS  Google Scholar 

  94. Gao, P., Hunter, A., Summe, M. J. & Phillip, W. A. A method for the efficient fabrication of multifunctional mosaic membranes by inkjet printing. ACS Appl. Mater. Interfaces 8, 19772–19779 (2016).

    Article  CAS  Google Scholar 

  95. Rajesh, S., Yan, Y., Chang, H. C., Gao, H. & Phillip, W. A. Mixed mosaic membranes prepared by layer-by-layer assembly for ionic separations. ACS Nano 8, 12338–12345 (2014).

    Article  CAS  Google Scholar 

  96. Malmir, H. et al. Induced charge anisotropy: A hidden variable affecting ion transport through membranes. Matter 2, 735–750 (2019).

    Article  Google Scholar 

  97. Haji-Akbari, A. Forward-flux sampling with jumpy order parameters. J. Chem. Phys. 149, 072303 (2018).

    Article  CAS  Google Scholar 

  98. Tu, K. L., Nghiem, L. D. & Chivas, A. R. Coupling effects of feed solution pH and ionic strength on the rejection of boron by NF/RO membranes. Chem. Eng. J. 168, 700–706 (2011).

    Article  CAS  Google Scholar 

  99. Somrani, A., Hamzaoui, A. H. & Pontie, M. Study on lithium separation from salt lake brines by nanofiltration (NF) and low pressure reverse osmosis (LPRO). Desalination 317, 184–192 (2013).

    Article  CAS  Google Scholar 

  100. Saraf, A., Johnson, K. & Lind, M. L. Poly(vinyl) alcohol coating of the support layer of reverse osmosis membranes to enhance performance in forward osmosis. Desalination 333, 1–9 (2014).

    Article  CAS  Google Scholar 

  101. Nicolini, J. V., Borges, C. P. & Ferraz, H. C. Selective rejection of ions and correlation with surface properties of nanofiltration membranes. Sep. Purif. Technol. 171, 238–247 (2016).

    Article  CAS  Google Scholar 

  102. Qi, S. et al. Polymersomes-based high-performance reverse osmosis membrane for desalination. J. Memb. Sci. 555, 177–184 (2018).

    Article  CAS  Google Scholar 

  103. Richards, L. A., Vuachère, M. & Schäfer, A. I. Impact of pH on the removal of fluoride, nitrate and boron by nanofiltration/reverse osmosis. Desalination 261, 331–337 (2010).

    Article  CAS  Google Scholar 

  104. Jeong, B. H. et al. Interfacial polymerization of thin film nanocomposites: A new concept for reverse osmosis membranes. J. Memb. Sci. 294, 1–7 (2007).

    Article  CAS  Google Scholar 

  105. Hong, S. U., Malaisamy, R. & Bruening, M. L. Optimization of flux and selectivity in Cl-/SO42- separations with multilayer polyelectrolyte membranes. J. Membr. Sci. 283, 366–372 (2006).

    Article  CAS  Google Scholar 

  106. Mukherjee, D., Kulkarni, A. & Gill, W. N. Flux enhancement of reverse osmosis membranes by chemical surface modification. J. Memb. Sci. 97, 231–249 (1994).

    Article  CAS  Google Scholar 

  107. Harrison, C. J., Le Gouellec, Y. A., Cheng, R. C. & Childress, A. E. Bench-scale testing of nanofiltration for seawater desalination. J. Environ. Eng. 133, 1004–1014 (2007).

    Article  CAS  Google Scholar 

  108. Giagnorio, M. et al. Achieving low concentrations of chromium in drinking water by nanofiltration: membrane performance and selection. Environ. Sci. Pollut. Res. 25, 25294–25305 (2018).

    Article  CAS  Google Scholar 

  109. Redondo, J. A. & Frank, K. F. Sea water applications with FILMTEC reverse osmosis membranes from small to large plants in 10 years. Desalination 82, 31–49 (1991).

    Article  CAS  Google Scholar 

  110. Arena, J. T., McCloskey, B., Freeman, B. D. & McCutcheon, J. R. Surface modification of thin film composite membrane support layers with polydopamine: Enabling use of reverse osmosis membranes in pressure retarded osmosis. J. Memb. Sci. 375, 55–62 (2011).

    Article  CAS  Google Scholar 

  111. Al-Zoubi, H., Hilal, N., Darwish, N. A. & Mohammad, A. W. Rejection and modelling of sulphate and potassium salts by nanofiltration membranes: neural network and Spiegler-Kedem model. Desalination 206, 42–60 (2007).

    Article  CAS  Google Scholar 

  112. Widjaya, A., Hoang, T., Stevens, G. W. & Kentish, S. E. A comparison of commercial reverse osmosis membrane characteristics and performance under alginate fouling conditions. Sep. Purif. Technol. 89, 270–281 (2012).

    Article  CAS  Google Scholar 

  113. Malaisamy, R., Talla-Nwafo, A. & Jones, K. L. Polyelectrolyte modification of nanofiltration membrane for selective removal of monovalent anions. Sep. Purif. Technol. 77, 367–374 (2011).

    Article  CAS  Google Scholar 

  114. Wang, K. Y., Chung, T. S. & Qin, J. J. Polybenzimidazole (PBI) nanofiltration hollow fiber membranes applied in forward osmosis process. J. Memb. Sci. 300, 6–12 (2007).

    Article  CAS  Google Scholar 

  115. Freger, V., Arnot, T. C. & Howell, J. A. Separation of concentrated organic/inorganic salt mixtures by nanofiltration. J. Memb. Sci. 178, 185–193 (2000).

    Article  CAS  Google Scholar 

  116. Nilsson, M., Trägårdh, G. & Östergren, K. The influence of sodium chloride on mass transfer in a polyamide nanofiltration membrane at elevated temperatures. J. Memb. Sci. 280, 928–936 (2006).

    Article  CAS  Google Scholar 

  117. Tsuru, T., Izumi, S., Yoshioka, T. & Asaeda, M. Temperature effect on transport performance by inorganic nanofiltration membranes. AIChE J. 46, 565–574 (2000).

    Article  CAS  Google Scholar 

  118. Tsuru, T., Ogawa, K., Kanezashi, M. & Yoshioka, T. Permeation characteristics of electrolytes and neutral solutes through titania nanofiltration membranes at high temperatures. Langmuir 26, 10897–10905 (2010).

    Article  CAS  Google Scholar 

  119. Sharma, R. R. & Chellam, S. Temperature and concentration effects on electrolyte transport across porous thin-film composite nanofiltration membranes: Pore transport mechanisms and energetics of permeation. J. Colloid Interface Sci. 298, 327–340 (2006).

    Article  CAS  Google Scholar 

  120. Snow, M. J. H., de Winter, D., Buckingham, R., Campbell, J. & Wagner, J. New techniques for extreme conditions: high temperature reverse osmosis and nanofiltration. Desalination 105, 57–61 (1996).

    Article  CAS  Google Scholar 

  121. Saltonstall, C. W. Jr Practical aspects of sea water desalination by reverse osmosis. Desalination 18, 315–320 (1976).

    Article  CAS  Google Scholar 

  122. Li, L., Dong, J. & Nenoff, T. M. Transport of water and alkali metal ions through MFI zeolite membranes during reverse osmosis. Sep. Purif. Technol. 53, 42–48 (2007).

    Article  CAS  Google Scholar 

  123. Mehdizadeh, H., Dickson, J. M. & Eriksson, P. K. Temperature effects on the performance of thin-film composite, aromatic polyamide membranes. Ind. Eng. Chem. Res. 28, 814–824 (1989).

    Article  CAS  Google Scholar 

  124. Connell, P. J. & Dickson, J. M. Modeling reverse osmosis separations with strong solute‐membrane affinity at different temperatures using the finely porous model. J. Appl. Polym. Sci. 35, 1129–1148 (1988).

    Article  CAS  Google Scholar 

  125. Chen, J.-Y., Nomura, H. & Pusch, W. Temperature dependence of membrane transport parameters in hyperfiltration. Desalination 46, 437–446 (1983).

    Article  CAS  Google Scholar 

  126. Lonsdale, H. K., Merten, U. & Riley, R. L. Transport properties of cellulose acetate osmotic membranes. J. Appl. Polym. Sci. 9, 1341–1362 (1965).

    Article  CAS  Google Scholar 

  127. Reid, C. E. & Kuppers, J. R. Physical characteristics of osmotic membranes of organic polymers. J. Appl. Polym. Sci. 2, 264–272 (1959).

    Article  CAS  Google Scholar 

  128. Gary-Bobo, C. M. Effect of geometrical and chemical constraints on water flux across artificial membranes. J. Gen. Physiol. 57, 610–622 (2004).

    Article  Google Scholar 

  129. Gary-Bobo, C. M. Role of hydrogen-bonding in nonelectrolyte diffusion through dense artificial membranes. J. Gen. Physiol. 54, 369–382 (2004).

    Article  Google Scholar 

  130. Badessa, T. & Shaposhnik, V. The electrodialysis of electrolyte solutions of multi-charged cations. J. Memb. Sci. 498, 86–93 (2016).

    Article  CAS  Google Scholar 

  131. Freger, V. et al. Diffusion of water and ethanol in ion-exchange membranes: Limits of the geometric approach. J. Memb. Sci. 160, 213–224 (1999).

    Article  CAS  Google Scholar 

  132. Kumar, M., Grzelakowski, M., Zilles, J., Clark, M. & Meier, W. Highly permeable polymeric membranes based on the incorporation of the functional water channel protein Aquaporin Z. Proc. Natl Acad. Sci. USA 104, 20719–20724 (2007).

    Article  CAS  Google Scholar 

  133. Borgnia, M. J., Kozono, D., Calamita, G., Maloney, P. C. & Agre, P. Functional reconstitution and characterization of AqpZ, the E. coli water channel protein. J. Mol. Biol. 291, 1169–1179 (1999).

    Article  CAS  Google Scholar 

  134. Corry, B. Designing carbon nanotube membranes for efficient water desalination. J. Phys. Chem. B 112, 1427–1434 (2008).

    Article  CAS  Google Scholar 

  135. Song, C. & Corry, B. Intrinsic ion selectivity of narrow hydrophobic pores. J. Phys. Chem. B 113, 7642–7649 (2009).

    Article  CAS  Google Scholar 

  136. Williams, C. D. & Carbone, P. Selective removal of technetium from water using graphene oxide membranes. Environ. Sci. Technol. 50, 3875–3881 (2016).

    Article  CAS  Google Scholar 

  137. Sahu, S. & Zwolak, M. Ionic selectivity and filtration from fragmented dehydration in multilayer graphene nanopores. Nanoscale 9, 11424–11428 (2017).

    Article  CAS  Google Scholar 

  138. Konatham, D., Yu, J., Ho, T. A. & Striolo, A. Simulation insights for graphene-based water desalination membranes. Langmuir 29, 11884–11897 (2013).

    Article  CAS  Google Scholar 

  139. Zwolak, M., Lagerqvist, J. & Di Ventra, M. Quantized ionic conductance in nanopores. Phys. Rev. Lett. 103, 128102 (2009).

    Article  CAS  Google Scholar 

  140. Arrhenius, S. A. Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Z. Phys. Chem. 4, 226–248 (1889).

    Google Scholar 

  141. Eyring, H. The theory of absolute reaction rates. Trans. Faraday Soc. 34, 41–48 (1938).

    Article  CAS  Google Scholar 

  142. Kramers, H. A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940).

    Article  CAS  Google Scholar 

  143. Hanggi, P. 50 years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990).

    Article  Google Scholar 

  144. Wynne-Jones, W. F. K. & Eyring, H. The absolute rate of reactions in condensed phases. J. Chem. Phys. 3, 492–502 (1935).

    Article  CAS  Google Scholar 

  145. Garrett, B. C. Variational transition state theory. Ann. Rev. Phys. Chem. 35, 159–189 (1984).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Center for Enhanced Nanofluidic Transport (CENT), an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0019112.

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Authors and Affiliations

  1. Department of Chemical and Environmental Engineering, Yale University, New Haven, CT, USA

    Razi Epsztein, Ryan M. DuChanois, Cody L. Ritt & Menachem Elimelech

  2. Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa, Israel

    Razi Epsztein

  3. Materials Science Division, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA

    Aleksandr Noy

  4. School of Natural Sciences, University of California Merced, Merced, CA, USA

    Aleksandr Noy

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Epsztein, R., DuChanois, R.M., Ritt, C.L. et al. Towards single-species selectivity of membranes with subnanometre pores. Nat. Nanotechnol. 15, 426–436 (2020). https://doi.org/10.1038/s41565-020-0713-6

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