Nano-Porous Graphene as Free-Standing Membranes
53
pressure drop [98]. Note that these studies with the aim of reducing computational
time employed pressures that are several orders of magnitude higher (1000–2000
bars) than those in real RO systems (10–100 bars). Moreover, they have kept the
atoms in the nano-porous graphene membrane frozen to decouple the desalination
performance from mechanical effects. However, graphene membranes synthesized
experimentally are flexible and the functional groups at the edge of each nanopore are
susceptible to deformation under the influence of water molecules and salt ions. This
in turn may affect the permeability and salt rejection of the membrane [103]. This
was addressed in [103] where the permeability of nano-porous graphene remained
approximately constant down to very low pressures. it was demonstrated by MD
simulations that nano-porous graphene maintained its desalination performance even
when the flexibility of the membrane atoms was considered [103].
MD simulations were employed by Konatham et al. [104] to comprehensively
study the transport of water and ions through pores created on the basal plane of one
graphene sheet. They quantified the effect of functionalizing pores with carboxyl
anion COO
− , amine cation NH3
+ , and hydroxyl OH
− groups on the pores’ ability to
reject NaCl. The pores that were considered had diameters of 14.5, 10.5, and 7.5 Å.
The ease of Na
+ and Cl
− ions and water translocation across the pores was monitored
by calculating the PMF along the direction perpendicular to the graphene sheet pore.
The results indicated that effective ion exclusion can be achieved only using pristine
pores of diameter ~7.5 Å, whereas the ions can easily penetrate pristine pores of
diameters ~10.5 and 14.5 Å. It was shown that not only the ion size (the diameters of
Na
+ and Cl
− are 2.58 and 4.40 Å, respectively) but also the ion hydration structure
might affect the free-energy profile. It was demonstrated that carboxyl functional
groups enhance ion exclusion for all pores considered, but the effect becomes less
pronounced as both the ion concentration and the pore diameter increase. The results
in [104] suggest that narrow graphene pores functionalized with hydroxyl groups
remain effective at excluding Cl
− ions even at moderate solution ionic strength.
In another study [105], graphene nanopores with diameters of 3.8–8.2 Å, with
different geometries were terminated by hydrogen and hydroxyl functional groups
and studied with MD under 10–200 MPa pressures. Their results demonstrated that
water flux permeating the membranes scaled linearly with external pressure and pore
diameter. Both Na
+ and Cl
− ions permeated through the membrane with the largest
pore, and the selectivity of the permeated ions exhibited a significant correlation
with the functional group [105]. Water desalination across Si-passivated nanopores
graphene was investigated for systems with fixed and unfixed membranes [106]. The
results indicated that membrane curvature reduces water flux as well as salt passage
through the pore rim. In contrast with fixed membranes, salt rejection for systems
with unfixed membranes increases with increasing the applied pressure. It was shown
that the symmetrical shape of the density surface at low pressure increases the salt
rejection [106].
Methyl, ethyl and a combination of fluorine and hydrogen molecules were
distributed around the graphene nanopores [107]. The different number of functional molecules was employed to find an optimum distribution of the groups at
hand. The results showed that an appropriate distribution of alkyl groups properly
53
pressure drop [98]. Note that these studies with the aim of reducing computational
time employed pressures that are several orders of magnitude higher (1000–2000
bars) than those in real RO systems (10–100 bars). Moreover, they have kept the
atoms in the nano-porous graphene membrane frozen to decouple the desalination
performance from mechanical effects. However, graphene membranes synthesized
experimentally are flexible and the functional groups at the edge of each nanopore are
susceptible to deformation under the influence of water molecules and salt ions. This
in turn may affect the permeability and salt rejection of the membrane [103]. This
was addressed in [103] where the permeability of nano-porous graphene remained
approximately constant down to very low pressures. it was demonstrated by MD
simulations that nano-porous graphene maintained its desalination performance even
when the flexibility of the membrane atoms was considered [103].
MD simulations were employed by Konatham et al. [104] to comprehensively
study the transport of water and ions through pores created on the basal plane of one
graphene sheet. They quantified the effect of functionalizing pores with carboxyl
anion COO
− , amine cation NH3
+ , and hydroxyl OH
− groups on the pores’ ability to
reject NaCl. The pores that were considered had diameters of 14.5, 10.5, and 7.5 Å.
The ease of Na
+ and Cl
− ions and water translocation across the pores was monitored
by calculating the PMF along the direction perpendicular to the graphene sheet pore.
The results indicated that effective ion exclusion can be achieved only using pristine
pores of diameter ~7.5 Å, whereas the ions can easily penetrate pristine pores of
diameters ~10.5 and 14.5 Å. It was shown that not only the ion size (the diameters of
Na
+ and Cl
− are 2.58 and 4.40 Å, respectively) but also the ion hydration structure
might affect the free-energy profile. It was demonstrated that carboxyl functional
groups enhance ion exclusion for all pores considered, but the effect becomes less
pronounced as both the ion concentration and the pore diameter increase. The results
in [104] suggest that narrow graphene pores functionalized with hydroxyl groups
remain effective at excluding Cl
− ions even at moderate solution ionic strength.
In another study [105], graphene nanopores with diameters of 3.8–8.2 Å, with
different geometries were terminated by hydrogen and hydroxyl functional groups
and studied with MD under 10–200 MPa pressures. Their results demonstrated that
water flux permeating the membranes scaled linearly with external pressure and pore
diameter. Both Na
+ and Cl
− ions permeated through the membrane with the largest
pore, and the selectivity of the permeated ions exhibited a significant correlation
with the functional group [105]. Water desalination across Si-passivated nanopores
graphene was investigated for systems with fixed and unfixed membranes [106]. The
results indicated that membrane curvature reduces water flux as well as salt passage
through the pore rim. In contrast with fixed membranes, salt rejection for systems
with unfixed membranes increases with increasing the applied pressure. It was shown
that the symmetrical shape of the density surface at low pressure increases the salt
rejection [106].
Methyl, ethyl and a combination of fluorine and hydrogen molecules were
distributed around the graphene nanopores [107]. The different number of functional molecules was employed to find an optimum distribution of the groups at
hand. The results showed that an appropriate distribution of alkyl groups properly