Abstract
The electrostatic attraction between ions and water is the primary reason for the change in ion bare diameter, which plays a crucial role in saltwater transportation. This study utilizes molecular dynamics (MD) to analyze saltwater transport through a nanoporous graphene membrane by pressure-driven flow. In this work, we describe the impact of pore diameter atomic boundary position on single-ion transportation and signify the steric effect of ions on the water mass flow rate and velocity profile. Due to hydration layer formation, ions hinder the water molecules from their regular velocity, which also decreases the flow rate of water molecules. Interestingly, a significant deviation for different atomic boundary positions is observed for ion rejection for pore diameters less than 1 nm. However, for larger pore diameters, the ion rejection closely matches the atomic boundary position specified by a 2 % water density drop inside the nanopore.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- f i :
-
Fraction of the hydration layer inside the pore area
- ΔU :
-
Energy barrier for single ion transport
- E i :
-
Input energy for chlorine
- L :
-
Pore diameter
- a :
-
Pore radius
- L h :
-
Hydration diameter of ion
- R i :
-
Hydration layer radius
- V :
-
Interaction potential function
- V z, r :
-
Velocity inside pore
- q :
-
Volumetric flow rate of fluid
- σ :
-
Diameter of molecules (zero potential distance)
- μ :
-
Viscosity of fluid
References
P.H.W. Gleick, Water in Crisis, Oxford University Press (1993).
WWAP and UNESCO, The United Nations World Water Development Report 2019: Leaving No One Behind, United Nations Educational, Scientific and Cultural Organization (2019).
E. Jones, The state of desalination and brine production: A global outlook, Sci. Total Environ., 657 (2019) 1343–1356.
M. A. Shannon, P. W. Bohn, M. Elimelech, J. G. Georgiadis, B. J. Marinas and A. M. Mayes, Science and technology for water purification in the coming decades, Nanoscience and Technol. (2009) 337–346.
S. Zhao, Recent developments in forward osmosis: Opportunities and challenges, J. Memb. Sci., 396 (2012) 1–21.
M. Qasim, Reverse osmosis desalination: a state-of-the-art review, Desalination, 459 (2019) 59–104.
B. Corry, Mechanisms of selective ion transport and salt rejection in carbon nanostructures, MRS Bull., 42 (4) (2017) 306–310.
F. Fornasiero, Ion exclusion by sub-2-nm carbon nanotube pores, Proc. Natl. Acad. Sci., 105 (45) (2008) 17250–17255.
Y. Wang et al., Nanopore sequencing technology, bioinformatics and applications, Nat. Biotechnol., 39 (11) (2021) 1348–1365.
M. Heiranian, A. B. Farimani and N. R. Aluru, Water desalination with a single-layer MoS2 nanopore, Nat. Commun., 6 (1) (2015) 8616.
P. R. Kidambi et al., Assessment and control of the impermeability of graphene for atomically thin membranes and barriers, Nanoscale, 9 (24) (2017) 8496–8507.
C. T. Nguyen and A. Beskok, Saltwater transport through pristine and positively charged graphene membranes, J. Chem. Phys., 149 (2) (2018) 024704.
A. K. Geim and K. S. Novoselov, The rise of graphene, Nanoscience and Technology, UK (2009) 11–19.
K. Cao et al., Elastic straining of free-standing monolayer graphene, Nat. Commun., 11 (1) (2020) 284.
D. He, Engineered graphene materials: synthesis and applications for polymer electrolyte membrane fuel cells, Adv. Mater, 29 (20) (2017) 1601741.
M. Liu, R. Zhang and W. Chen, Graphene-supported nanoelectrocatalysts for fuel cells: synthesis, properties, and applications, Chem. Rev., 114 (10) (2014) 5117–5160.
D. Cohen-Tanugi and J. C. Grossman, Mechanical strength of nanoporous graphene as a desalination membrane, Nano Lett., 14 (11) (2014) 6171–6178.
A. Nicolaï, B. G. Sumpter and V. Meunier, Tunable water desalination across graphene oxide framework membranes, Phys. Chem. Chem. Phys., 16 (18) (2014) 8646.
J. Goldsmith and C. C. Martens, Pressure-induced water flow through model nanopores, Phys. Chem. Chem. Phys., 11 (3) (2009) 528–533.
D. Cohen-Tanugi and J. C. Grossman, Water desalination across nanoporous graphene, Nano Lett., 12 (7) (2012) 3602–3608.
D. Konatham, Simulation insights for graphene-based water desalination membranes, Langmuir, 29 (38) (2013) 11884–11897.
M. E. Suk and N. R. Aluru, Molecular and continuum hydrodynamics in graphene nanopores, RSC Adv., 3 (24) (2013) 9365.
M. Zwolak, J. Wilson and M. Di Ventra, Dehydration and ionic conductance quantization in nanopores, J. Phys. Condens. Matter, 22 (45) (2010) 454126.
M. Zwolak, J. Lagerqvist and M. Di Ventra, Quantized ionic conductance in nanopores, Phys. Rev. Lett., 103 (12) (2009) 128102.
F. Risplendi, Fundamental insights on hydration environment of boric acid and its role in separation from saline water, J. Phys. Chem. C, 124 (2) (2020) 1438–1445.
M. E. Suk and N. R. Aluru, Ion transport in sub-5-nm graphene nanopores, J. Chem. Phys., 140 (8) (2014) 084707.
J. P. K. Abal, J. R. Bordin and M. C. Barbosa, Salt parameterization can drastically affect the results from classical atomistic simulations of water desalination by MoS2 nanopores, Phys. Chem. Chem. Phys., 22 (19) (2020) 11053–11061.
O. Beckstein and M. S. P. Sansom, The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores, Phys. Biol., 1 (1) (2004) 42–52.
J. R. Bordin, Ion fluxes through nanopores and transmembrane channels, Phys. Rev. E, 85 (3) (2012) 031914.
B. Pinter, On the origin of the steric effect, Phys. Chem. Chem. Phys., 14 (28) (2012) 9846.
B. Tansel, Significance of hydrated radius and hydration shells on ionic permeability during nanofiltration in dead end and cross flow modes, Sep. Purif. Technol., 51 (1) (2006) 40–47.
L. A. Richards, The importance of dehydration in determining ion transport in narrow pores, Small, 8 (11) (2012) 1701–1709.
A. Tongraar and B. Michael Rode, Dynamical properties of water molecules in the hydration shells of Na+ and K+: ab initio QM/MM molecular dynamics simulations, Chem. Phys. Lett., 385 (5–6) (2004) 378–383.
K. Coutinho, Electronic polarization of liquid water: converged Monte Carlo-quantum mechanics results for the multipole moments, Chem. Phys. Lett., 369 (3–4) (2003) 345–353.
S. W. Rick and B. J. Berne, The aqueous solvation of water: a comparison of continuum methods with molecular dynamics, J. Am. Chem. Soc., 116 (1993) 3949–3954.
J. Aqvist and T. Hansson, On the validity of electrostatic linear response in polar solvents, J. Phys. Chem., 100 (22) (1996) 9512–9521.
S. Sahu, M. Di Ventra and M. Zwolak, Dehydration as a universal mechanism for ion selectivity in graphene and other atomically thin pores, Nano Lett., 17 (8) (2017) 4719–4724.
C. T. Nguyen, M. Barisik and B. Kim, Wetting of chemically heterogeneous striped surfaces: Molecular dynamics simulations, AIP Adv., 8 (6) (2018).
M. Barisik and A. Beskok, Equilibrium molecular dynamics studies on nanoscale-confined fluids, Microfluid. Nanofluidics, 11 (3) (2011) 269–282.
M. R. Hasan and B. Kim, Molecular transportation phenomena of simple liquids through a nanoporous graphene membrane, Phys. Rev. E, 102 (3) (2020) 033110.
Vishnu Prasad K., S. K. Kannam, R. Hartkamp and S. P. Sathian, Water desalination using rapheme nanopores: influence of the water models used in simulations, Phys. Chem. Chem. Phys., 20 (23) (2018) 16005–16011.
Grigera and T. P. Straatsma, The missing termi n effective pair potentials, The Journal Phys. Chem., 91 (24) (1987) 6269–6271.
J. P. Ryckaert, G. Ciccotti and H. J. C. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes, J. Comput. Phys., 23 (3) (1977) 327–341.
S. J. Stuart, A. B. Tutein and J. A. Harrison, A reactive potential for hydrocarbons with intermolecular interactions, J. Chem. Phys., 112 (14) (2000) 6472–6486.
M. Patra and M. Karttunen, Systematic comparison of force fields for microscopic simulations of NaCl in aqueous solutions: Diffusion, free energy of hydration, and structural properties, J. Comput. Chem., 25 (5) (2004) 678–689.
D. J. Allen, P. Michael and Tildesley, Computer Simulation of Liquids, Oxford University Press (2007).
S. Kim, Issues on the choice of a proper time step in molecular dynamics, Phys. Procedia, 53 (2014) 60–62.
S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117 (1) (1995) 1–19.
M. Masuduzzaman and B. Kim, Unraveling the molecular interface and boundary problems in an electrical double layer and electroosmotic flow, Langmuir, 38 (23) (2022) 7244–7255.
C. T. Nguyen and A. Beskok, Water desalination performance of h-BN and optimized charged graphene membranes, Microfluid. Nanofluidics, 24 (5) (2020).
C. T. Nguyen and B. Kim, Stress and surface tension analyses of water on graphene-coated copper surfaces, Int. J. Precis. Eng. Manuf., 17 (4) (2016) 503–510.
M. Masuduzzaman and B. Kim, Scale effects in nanoscale heat transfer for fourier’s law in a dissimilar molecular interface, ACS Omega, 5 (41) (2020) 26527–26536.
T. Q. Vo and B. Kim, Interface thermal resistance between liquid water and various metallic surfaces, Int. J. Precis. Eng. Manuf., 16 (7) (2015) 1341–1346.
B. H. Kim, A. Beskok and T. Cagin, Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solidliquid interfaces, Microfluid. Nanofluidics, 5 (4) (2008) 551–559.
L. Xue, P. Keblinski, S. R. Phillpot, S. U.-S. Choi and J. A. Eastman, Effect of liquid layering at the liquid-solid interface on thermal transport, Int. J. Heat Mass Transf., 47 (19–20) (2004) 4277–4284.
M. Masuduzzaman and B. H. Kim, Effects of dissimilar molecular interface and ion-concentration on wetting characteristics of nanodroplets, Microfluid. Nanofluidics, 25 (6) (2021) 1–14.
J. H. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes IV. The equations of hydrodynamics, J. Chem. Phys., 18 (1950) 817.
B. D. Todd, D. J. Evans and P. J. Daivis, Pressure tensor for inhomogeneous fluids, Phys. Rev. E, 52 (1995) 1627.
R. A. Sampson, XII. On Stokes’s current function, Philos. Trans. R. Soc. London., 182 (1891) 449–518.
C. T. Nguyen and A. Beskok, Saltwater transport through pristine and positively charged graphene membranes, J. Chem. Phys., 149 (2) (2018).
M. Heiranian, A. Taqieddin and N. R. Aluru, Revisiting sampson’s theory for hydrodynamic transport in ultrathin nanopores, Phys. Rev. Res., 2 (4) (2020) 43153.
J. Al Hossain and B. H. Kim, Scale effect on simple liquid transport through a nanoporous graphene membrane, Langmuir, 37 (21) (2021) 6498–6509.
I. S. Joung and T. E. Cheatham, Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters, J. Phys. Chem. B, 113 (40) (2009) 13279–13290.
L. Bocquet and E. Charlaix, Nanofluidics, from bulk to interfaces, Chem. Soc. Rev., 39 (3) (2010) 1073–1095.
A. Bondi, van der Waals volumes and radii, J. Chem. Phys., 68 (3) (1964) 441–451.
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (NRF-2019R1A2C1004661).
Author information
Authors and Affiliations
Corresponding author
Additional information
Morshed Mahmud is a Master of science candidate in Mechanical Engineering, University of Ulsan, Korea. His research interests are Molecular Dynamics simulation, micro-/nano-fluidics, ion transportation, desalination.
BoHung Kim is an Associate Professor in School of Mechanical Engineering, University of Ulsan, Korea. He received his Ph.D. degree from Department of Mechanical Engineering, Texas A&M University, United States. His research interests are molecular neuroscience, Molecular Dynamics and nanoscale gas/liquid flow, and numerical methods.
Rights and permissions
About this article
Cite this article
Mahmud, M., Kim, B. Atomic boundary position and steric effects on ion transport and separation through nanoporous graphene membrane. J Mech Sci Technol 37, 875–886 (2023). https://doi.org/10.1007/s12206-023-0129-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-023-0129-y