52
A. S. Kazemi and M. A. Abdol
discuss the transport of water and ions and selectivity issues that were the center of
attention in the corresponding literature. Some of the materials in this section are
reproduced with permission from Ref. [98], Copyright © 2012, American Chemical
Society and Ref. [99] Copyright © 2016, American Chemical Society.
(a) Pristine and functionalized membranes
A graphene monolayer can be considered as the thinnest membrane, as its thickness is only one carbon atom. Because of the superior strength of graphene [100],
porous graphene is a potential membrane for molecular sieving or water filtration.
Nanopores of various diameters can be realized in graphene via mono vacancies or
multi vacancies [101]. One of the first attempts in functionalization of nanopores in
graphene monolayers showed that they could serve as ionic sieves of high selectivity
and transparency [44]. The chemically modified graphene nanopores were terminated by negatively charged nitrogen and fluorine, favoring the passage of cations.
These were compared with nanopores terminated by positively charged hydrogens,
favoring the passage of anions [44].
Transport of water through porous graphene membrane was studied by Suk and
Aluru [102] using molecular dynamics (MD) simulations where various diameters
of nanopores ranging from 0.75 to 2.75 nm were tested. Their simulation set-up with
graphene membrane constituted 6 nm water baths on each side of the membrane. The
pressure-driven flow was simulated by applying a 100 MPa pressure drop across the
pore and water flux was calculated by counting the net amount of water molecules
transported through the pore. For larger pores, the flow rate of water was higher
because of the reduced energy barrier at the entrance of the graphene sheet pore.
The dipole orientation of water molecules that formed the single file chain in the
membrane was also calculated. Dipole orientation is defined as the angle between
the water dipole vector and the tube axis and is averaged over all the water molecules
in the membrane [102]. They found that the dipole orientation flipped frequently in
the graphene membrane which indicated frequent breaking of the hydrogen-bonding.
They also investigated water transport through graphene by computing the energetics
of water permeation. The energy barrier at the entrance was estimated to be a relatively
low value of 0.32 k B T by computing the Potential of Mean Force (PMF) of water.
Since the energy barrier arises from reduced interaction energies, directly connected
water baths may have been the source of low energy barrier by creating a more
bulk-like environment.
Cohen-Tanugi and Grossman [98] found that both the size and chemical functionalization of graphene pores play an important role in blocking salt ions while
allowing water to flow through the graphene membranes. Their MD examination of
the structure of water in the pore vicinity revealed that the hydrophobic character of
hydrogenated pores reduces the water flow by imposing additional conformational
order on the system, even as the limited hydrogen bonding allows for greater salt
rejection relative to hydroxylated pores. Additionally, the water flux through pristine and OH-functionalized pores membranes was predicted to be 2–3 times faster
than that typical of the current state-of-the-art desalination technology at an equal
A. S. Kazemi and M. A. Abdol
discuss the transport of water and ions and selectivity issues that were the center of
attention in the corresponding literature. Some of the materials in this section are
reproduced with permission from Ref. [98], Copyright © 2012, American Chemical
Society and Ref. [99] Copyright © 2016, American Chemical Society.
(a) Pristine and functionalized membranes
A graphene monolayer can be considered as the thinnest membrane, as its thickness is only one carbon atom. Because of the superior strength of graphene [100],
porous graphene is a potential membrane for molecular sieving or water filtration.
Nanopores of various diameters can be realized in graphene via mono vacancies or
multi vacancies [101]. One of the first attempts in functionalization of nanopores in
graphene monolayers showed that they could serve as ionic sieves of high selectivity
and transparency [44]. The chemically modified graphene nanopores were terminated by negatively charged nitrogen and fluorine, favoring the passage of cations.
These were compared with nanopores terminated by positively charged hydrogens,
favoring the passage of anions [44].
Transport of water through porous graphene membrane was studied by Suk and
Aluru [102] using molecular dynamics (MD) simulations where various diameters
of nanopores ranging from 0.75 to 2.75 nm were tested. Their simulation set-up with
graphene membrane constituted 6 nm water baths on each side of the membrane. The
pressure-driven flow was simulated by applying a 100 MPa pressure drop across the
pore and water flux was calculated by counting the net amount of water molecules
transported through the pore. For larger pores, the flow rate of water was higher
because of the reduced energy barrier at the entrance of the graphene sheet pore.
The dipole orientation of water molecules that formed the single file chain in the
membrane was also calculated. Dipole orientation is defined as the angle between
the water dipole vector and the tube axis and is averaged over all the water molecules
in the membrane [102]. They found that the dipole orientation flipped frequently in
the graphene membrane which indicated frequent breaking of the hydrogen-bonding.
They also investigated water transport through graphene by computing the energetics
of water permeation. The energy barrier at the entrance was estimated to be a relatively
low value of 0.32 k B T by computing the Potential of Mean Force (PMF) of water.
Since the energy barrier arises from reduced interaction energies, directly connected
water baths may have been the source of low energy barrier by creating a more
bulk-like environment.
Cohen-Tanugi and Grossman [98] found that both the size and chemical functionalization of graphene pores play an important role in blocking salt ions while
allowing water to flow through the graphene membranes. Their MD examination of
the structure of water in the pore vicinity revealed that the hydrophobic character of
hydrogenated pores reduces the water flow by imposing additional conformational
order on the system, even as the limited hydrogen bonding allows for greater salt
rejection relative to hydroxylated pores. Additionally, the water flux through pristine and OH-functionalized pores membranes was predicted to be 2–3 times faster
than that typical of the current state-of-the-art desalination technology at an equal