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Modelling and MD simulations on ultra-filtration using graphene sheet

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Abstract

In this paper, we investigate the ion rejection of salt water using graphene sheet as a semi-permeable membrane. Both the mathematical modeling and MD simulations will be performed to determine the acceptance conditions for a water molecule or a sodium ion permeating into the membrane. Chloride ion is always blocked by the graphene due to the fact that the ionic size of the chloride ion is larger than the pore size of the graphene leaving the sieve of water and sodium ions which depends on the strength of the external forces. In particular, certain ranges of the external forces will be theoretically deduced for the complete desalination, which turn out to depend intimately on the size of the permeate container and the hydraulic force acting among salt water. In this paper, we reduce the multi-body system into several two-body systems and reduce the 3D problem into degenerated 1D problems using the continuous approximation, where the molecular interactions between the water molecule or the sodium ion and the graphene could be determined in terms of surface integrals. Given the force fields between the intruder and the membrane, MD simulations could be used to investigate the time evolution of the system and compare with the theoretical results deduced by the present mathematical model. We confirm the computational results given by Tanugi and Grossman (Nano Lett 12:3602–3608, 2012). Moreover, our approach is computationally rapid and generates inductive results for more engineering applications.

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Acknowledgments

We gratefully acknowledge the financial support from small research Grant (UNNC), and Ningbo Natural Science Foundation (2014A610025) and (2014A610172), and Qianjiang Talent Scheme (QJD1402009).

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  1. School of Mathematical Sciences, Faculty of Science and Engineering, The University of Nottingham, 199 Taikang East Road, Ningbo, 315100, China

    Y. Chan

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Correspondence to Y. Chan.

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Chan, Y. Modelling and MD simulations on ultra-filtration using graphene sheet. J Math Chem 54, 1041–1056 (2016). https://doi.org/10.1007/s10910-016-0606-y

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  • DOI: https://doi.org/10.1007/s10910-016-0606-y

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