Nano-Porous Graphene as Free-Standing Membranes
63
‘pore resistance’. When the pore radius is below 1–2 nm, the ‘pore resistance’ plays
the dominant role. The resistance for ions to transfer from one end of the pore to
the other is defined as the ‘pore resistance’. On the contrary, the resistance for ions
to converge from the bulk electrolyte away from the membrane to the mouth of the
pore is the ‘access resistance’ and occurs on both sides of the membrane. While
both resistances influence ion transport, pores in 2D membranes, balance these two
contributions differently than other membranes [137].
As earlier mentioned, pore functionalization can drastically change ionic transport, especially if the pore is smaller than the size of the hydrated ion [20]. Charged
or partially charged functional groups can reduce the energy barrier for ions of opposite charge and increase the barrier for ions of like charge [104] along the pore edge.
This will lead to cation/anion selectivity [109]. Astonishingly, the flexibility of the
membrane can also impact the ‘pore resistance’. In contrast to solid-state pores,
graphene pores are more flexible, and their dynamic area can be larger than the static
area [138].
In a less sophisticated view to ion transport, Thomas et al. [139] proposed six
main mechanisms for salt rejection by nano-porous (sub-nanometer) monolayer
graphene membranes: size exclusion, dehydration effects (steric exclusion of the
hydration shell), charge repulsion, interactions with the pore, interactions of solutes
with specific chemical structures of the pore and entropic differences. The strong
electric field around dissolved ions forces the nearby water molecules to orient into
hydration layers. The first hydration layer is strongly bound to the ion with an energy
range from ~1 eV in monovalent ions to ~10 eV in bivalent ions. This hydration layer
tends to move along with the ion. The second layer is only partially oriented, and
the third hydration layer is diffuse and only weakly defined [140]. As the diameters
of the first hydration shell for Na
+ , K
+ , Ca
2+ , Mg
2+ and Cl
− are 0.72 nm, 0.66 nm,
0.82 nm, 0.86 nm and 0.66 nm, respectively; which are larger than the effective size of
a water molecule (0.26 nm), attributing the size exclusion and dehydration effects are
the most important salt rejection mechanisms [17, 20, 141]. Neutrally charged pores
smaller than the ion hydration size, therefore, present a blockade to ion transport.
The transport of water is influenced by hydrogen bonding and structuring of water
molecules when the pore size is below ~2 nm [20]. Again, ‘pore resistance issues
should be carefully taken into account. The smallest pores in graphene that allow
water to pass through, can accommodate only a single water molecule in their crosssection and therefore exhibit single-file movement of water molecules [104]. In pores
with the diameter <1.5 nm, water molecules adopt certain preferential configurations
as they pass through the pores [104, 142].
While much effort is focused on the molecular understanding of microscopic
mechanisms driving water and ion transport through nano-porous graphene, only
few works [130, 143] have connected interfacial properties, such as surface tension
and friction to water and ion transport through graphitic monolayers. The experimental determination of the contact angle depends on the impurities and defects
on the surface, which may lead to the scattering of contact angle values. Because
the material surface is critical for compatibility with the surrounding environment,
several molecular simulations have been performed to describe the interfacial region
63
‘pore resistance’. When the pore radius is below 1–2 nm, the ‘pore resistance’ plays
the dominant role. The resistance for ions to transfer from one end of the pore to
the other is defined as the ‘pore resistance’. On the contrary, the resistance for ions
to converge from the bulk electrolyte away from the membrane to the mouth of the
pore is the ‘access resistance’ and occurs on both sides of the membrane. While
both resistances influence ion transport, pores in 2D membranes, balance these two
contributions differently than other membranes [137].
As earlier mentioned, pore functionalization can drastically change ionic transport, especially if the pore is smaller than the size of the hydrated ion [20]. Charged
or partially charged functional groups can reduce the energy barrier for ions of opposite charge and increase the barrier for ions of like charge [104] along the pore edge.
This will lead to cation/anion selectivity [109]. Astonishingly, the flexibility of the
membrane can also impact the ‘pore resistance’. In contrast to solid-state pores,
graphene pores are more flexible, and their dynamic area can be larger than the static
area [138].
In a less sophisticated view to ion transport, Thomas et al. [139] proposed six
main mechanisms for salt rejection by nano-porous (sub-nanometer) monolayer
graphene membranes: size exclusion, dehydration effects (steric exclusion of the
hydration shell), charge repulsion, interactions with the pore, interactions of solutes
with specific chemical structures of the pore and entropic differences. The strong
electric field around dissolved ions forces the nearby water molecules to orient into
hydration layers. The first hydration layer is strongly bound to the ion with an energy
range from ~1 eV in monovalent ions to ~10 eV in bivalent ions. This hydration layer
tends to move along with the ion. The second layer is only partially oriented, and
the third hydration layer is diffuse and only weakly defined [140]. As the diameters
of the first hydration shell for Na
+ , K
+ , Ca
2+ , Mg
2+ and Cl
− are 0.72 nm, 0.66 nm,
0.82 nm, 0.86 nm and 0.66 nm, respectively; which are larger than the effective size of
a water molecule (0.26 nm), attributing the size exclusion and dehydration effects are
the most important salt rejection mechanisms [17, 20, 141]. Neutrally charged pores
smaller than the ion hydration size, therefore, present a blockade to ion transport.
The transport of water is influenced by hydrogen bonding and structuring of water
molecules when the pore size is below ~2 nm [20]. Again, ‘pore resistance issues
should be carefully taken into account. The smallest pores in graphene that allow
water to pass through, can accommodate only a single water molecule in their crosssection and therefore exhibit single-file movement of water molecules [104]. In pores
with the diameter <1.5 nm, water molecules adopt certain preferential configurations
as they pass through the pores [104, 142].
While much effort is focused on the molecular understanding of microscopic
mechanisms driving water and ion transport through nano-porous graphene, only
few works [130, 143] have connected interfacial properties, such as surface tension
and friction to water and ion transport through graphitic monolayers. The experimental determination of the contact angle depends on the impurities and defects
on the surface, which may lead to the scattering of contact angle values. Because
the material surface is critical for compatibility with the surrounding environment,
several molecular simulations have been performed to describe the interfacial region