Functionalized Carbon Honeycomb Membranes for Reverse Osmosis Water Desalination

Reverse osmosis desalination is a common technique to obtain fresh water from saltwater. Conventional membranes suffer from a trade‐off between salt rejection and water permeability, raising a need for developing new classes of membranes. C‐based membranes with porous graphene and carbon nanotubes offer high salt rejection, water permeability, and fouling resistance. However, controlling the pore size of these membranes is challenging. Therefore, a carbon honeycomb membrane is studied using classical molecular dynamics simulations. It is reported that functionalization with −COO– groups provides 100% salt rejection with around 1000 times higher water permeability than conventional polyamide membranes. Atomic‐level understanding of the effect of the functional groups' location on salt rejection and water permeability is developed.


Introduction
Fresh water is an essential resource for human, but due to the rapid growth of the world's population it is becoming increasingly scarce and polluted.Saltwater accounts for 97% of the Earth's total water reserve, and two thirds of the remaining 3% is unavailable for use. [1]Desalination techniques based on membranes, such as reverse osmosis [2] and forward osmosis, [3] are widely applied nowadays and provide 1% of the drinking water supply.Since their invention, mostly polyamide membranes [4] are in use in reverse osmosis systems. [5]7][8] DOI: 10.1002/admi.202300250Nanomaterials are promising candidates for membrane technology, possessing preferable adsorptive and antifouling properties. [9]For example, C-based nanomaterials, such as nanoporous graphene, [10] graphene oxide, [11] and carbon nanotubes, [12] provide high surface area and remarkable mechanical strength and stiffness.Since it was shown that water can flow through a narrow carbon nanotube with a diameter of 8.1 Å, [13] numerous studies investigated the desalination performance and water permeability of carbon nanotube membranes, which can be tuned by varying the pore size and by functionalization.[16][17] Both experimental [18][19][20] and numerical [21][22][23] studies put forward a diversity of carbon nanotube membranes with a water flux of 10 and more times that of polyamide membranes.Nanoporous graphene [24] can be regarded as a membrane thinner and more chemically resistant than the polyamide active layers. [6]32][33] The carbon honeycomb (CHC) allotrope was first obtained by deposition of vacuum-sublimated graphite. [34]It consists mainly of sp 2 -bonded C atoms and can be regarded as 3D graphene.It can store liquids and gases, [34] and shows high electrical [35] and thermal [36] conductivities.Due to its strong anisotropic Poisson effect, it is a candidate for applications ranging from biomedical engineering to energy and environment. [37,38]A recent molecular dynamics study of the reverse osmosis process using a CHC membrane showed excellent performance. [39]While nanoporous graphene and carbon nanotubes are widely studied, studies of CHC membranes for water desalination purposes are rare.CHC membranes can provide high water permeability due to their intrinsic pores with high density as compared to the extrinsic pores in other C-based membranes. [6]A pore diameter of 0.6-0.8nm is optimal for water desalination, [40] as a larger diameter will allow salt ions to pass, requiring control of the pore size.
We study the water desalination performance of -COO −functionalized CHC membranes by classical molecular dynamics simulations.Our results show that this functionalization is able to combine 100% salt rejection with around 1000 times higher water permeability than conventional polyamide membranes.As the location of the functional groups turns out to be critical, we develop atomic-level understanding of this behavior by analyzing the dynamics and mass density profiles.

Computational Methods
A CHC membrane with 48 pores of 1.4 nm diameter (average between the diameter of the inscribed and circumscribed circles of the hexagonal pore) and a thickness of 1.2 nm is shown in Figure 1a.In addition to this pristine membrane, we study a surface-functionalized membrane, where −COO − groups are located at the entrance of the pores (Figure 1b) and a wallfunctionalized membrane, where -COO − groups are located inside the membrane at the walls of the pores (Figure 1c).The functionalization density is 96 −COO − groups per 4896 C atoms in both cases and the simulation cell (Figure 1d) initially consists of the functionalized CHC membrane, two 91 Å × 79 Å graphene sheets acting as rigid pistons, 13 091 water molecules, 293 Na + and 293 Cl − ions in the feed zone, and 4363 water molecules in the permeate zone.The negative charge of the -COO − groups is neutralized by adding further 96 Na + counterions. [16,21]In the case of the surface-functionalized membrane, the functional groups face the feed zone.To reduce statistical effects by enhancing the probability of ions passing through the membrane, a salinity of more than twice that of seawater is used in the feed zone.A vacuum layer of 120 Å thickness is placed between the graphene pistons to prevent artificial interaction.Periodic boundary conditions are applied in all directions.Three of the membrane's C atoms are kept at fixed positions (marked pink in Figure 1a) to avoid an overall translation of the membrane.We also study a 2.4 nm thick membrane (pristine and with both functionalizations with unchanged amount of −COO − groups) and a 6.0 nm thick pristine membrane (with two additional water layers, i.e., 8726 molecules in the permeate zone).
The molecular dynamics simulations are carried out using the large-scale atomic/molecular massively parallel simulator package, [41] a canonical ensemble, a Nose-Hoover thermostat, [42] and a timestep of 1 fs.The simulation cell is equilibrated for 100 ps at 300 K, followed by reverse osmosis simulation at pressures of 1000 and 1500 bar in the feed zone and a pressure of 1 atm in the permeate zone.OVITO [43] is used for visualization.We perform simulations with a large number of atoms (63 028, 68 308, and 108 790 in the cases of the 1.2, 2.4, and 6.0 nm thick pristine membranes) to achieve better statistics of the ions and water molecules passing through the membrane.Therefore, we apply higher pressure than commonly used in water desalination (60 to 100 bar) to manage the required computational resources.The adaptive intermolecular reactive bond order potential [44] is utilized to describe the interaction between the C atoms of the membrane.Water is described by the four-site interaction potential TIP4P. [45]The other interactions are described by Lennard-Jones 6-12 potentials V (r) = 4[(/r) 12 − (/r) 6 ] [46] (where r is the distance,  is the depth of the potential, and  is the distance at which the particle-particle potential energy V is zero) and electrostatic Coulombic potentials, using a cutoff of 12 Å.Long-range Coulombic interactions are modeled via the particle-particle particle-mesh method.The adopted Lennard-Jones parameters and charges are summarized in Table 1.For interactions between different types of atoms i and j, the Lorentz-Berthelot mixing rules are utilized, where  = ( i +  j )/2 and  = √  i  j .The SHAKE [47] algorithm is used to constrain the water molecules with a tolerance of 10 -4 .
The salt rejection rate is R = (1 − (N I ∕N 0 I )∕(N w ∕N 0 w )), where N I and N w are the numbers of salt ions and water molecules that passed through the membrane at time t h when half of the water molecules reached the permeate zone, respectively, and N 0 I and N 0 w are the initial numbers of salt ions and water molecules in the feed zone.The water permeability is given by P = (N w /N A ) (M w /)/(At h p), where N A is the Avogadro number, M w is the molar mass of water,  is the mass density of water, A is the cross-sectional area of the membrane, and p is the applied pressure.Other C-based membranes Nanoporous graphene [51] 1000 to 2220 100 1625 to 2750 Graphdiyne [53] 4000 99 565 Carbon nanotube [54] 50 95 21.7 Conventional membranes Polyamide via polyepiamine: PA-300 [55] >69

and
The number of water molecules that passed through the membrane as a function of the simulation time is presented in Figure 2a, and the corresponding salt rejection rate and water permeability are given in Table 2. Video S1 in the Supporting Information shows the desalination process with the wallfunctionalized membrane.Figure 2a shows that the water flux through the membrane is linear in each case and it is higher through the pristine membrane than that through the functionalized membranes.According to Table 2, the functionalization enhances the salt rejection rate drastically.For example, at p = 1500 bar, it increases from 44% for the pristine membrane to 84% for the surface-functionalized membrane.The location of the functional groups is critical, as demonstrated by the fact that the wall-functionalized membrane achieves 100% salt rejection.As expected, the performance is better at lower pressure, e.g., at p = 1000 bar the salt rejection rates are 56%, 90%, and 100% for the pristine, surface-functionalized, and wall-functionalized membranes, respectively.Therefore, in the commonly used pressure range of 60 to 100 bar, the membranes are expected to provide better performance than predicted here.
According to Table 2, the water permeability ranges from exceptionally high 19 260 to 20 770 l m −2 h −1 bar −1 for the pristine membrane with low (44% to 56%) salt rejection rate to 2420 to 2580 l m −2 h −1 bar −1 for the wall-functionalized membrane with 100% salt rejection.Table 2 also gives a comparison to other membranes.Note that in the study of nanoporous graphene [51] the membrane porosity is assumed to be 10%, which is much higher than the experimental value. [52]Thus, the water permeability of the CHC membrane is several times higher than that of other C-based membranes and around 1000 times higher than that of the polyamide membranes currently in use.The ability to achieve 100% salt rejection with high water permeability points to extraordinary potential of functionalized CHC membranes.100% salt rejection is achieved with two -COO − groups per pore.When there is only one −COO − group per pore, the salt rejection rate of the surface-functionalized membrane decreases to 77% and 65% while the water permeability increases to 8990 and 10 070 l m −2 h −1 bar −1 at 1000 and 1500 bar, respectively, and the salt rejection rate of the wall-functionalized membrane decreases to 98% and 95% while the water permeability increases to 6540 and 6740 l m −2 h −1 bar −1 .Three more -COO − groups per pore, on the other hand, will reduce the water permeability but cannot further improve the salt rejection rate of the wall-functionalized membrane.Therefore, the choice of two functional groups is optimal.
We next analyze the interaction between the salt ions and −COO − groups to understand the mechanisms of the desalination.Figure 2b-d shows the distributions of the salt ions' mass densities along the z-axis (Figure 1d).Broad peaks appear just before the entrance to the pores, accumulation of salt ions in this region.In the absence of functional groups (Figure 2b), the membrane is the only barrier that the salt ions face and, therefore, due to the large pore diameter, many salt ions can pass through, resulting in a low salt rejection rate.In the case of surface functionalization, many Na + ions are trapped at the entrance to the pores due to interaction with the −COO − groups (Figure 2c), realizing an average distance of 2.2 Å (Figure 3a).The −COO − groups at the surface thus work as an additional barrier, both physical and electrostatic, resulting in enhanced salt rejection.However, this barrier is not enough to completely prevent the passage of salt ions.In the case of wall functionalization, the Na + ions enter the membrane, while the Cl − ions are repelled by the -COO − groups.The Na + ions become electrostatically trapped inside the membrane by the −COO − groups (Figure 2d) and further block the Cl − ions from entering the membrane due to reduction of the effective pore size.The maximum of the radial distribution function between the Na + ions and O atoms of the −COO − groups appears at the same radius as in the case of surface functionalization (Figure 3a).However, the value is lower, indicating that fewer Na + ions interact with the -COO − groups.In the case of wall functionalization, the -COO − groups have less freedom of motion than in the case of surface functionalization (see Videos S2 and S3, Supporting Information) due to the constraints by the walls, resulting in a smaller effective pore size near the -COO − groups.The minima of the water mass density near the -COO − groups in the case of wall functionalization (Figure 3b) supports the conclusion of effective pore size reduction.The -COO − groups and trapped Na + ions block the water, which gives rise to two peaks near these minima.Therefore, both the presence and the location of the -COO − groups control the effective pore size.A shift of the curves in Figure 3b with respect to the initial boundaries of the membrane is due to deflection of the membrane under high pressure (see Video S1, Supporting Information).The mass density of water in Figure 3b is similar to that of salt water in the feed zone.The fact that it is less than 1 g cm −3 in the permeate zone while there are no salt ions is due to the interaction of water with the membrane and piston.The geometrical criteria of ref. [56] are used to calculate the number of hydrogen bonds per water molecule in the feed zone as well as inside the pristine and wall-functionalized membranes after equilibration.We obtain 1.7 in the feed zone, and 1.4 and 1.2 inside the pristine and wall-functionalized membranes, respectively, in agreement with a recent study of water confined in (7, 7) and (14, 14) carbon nanotubes that reported 0.9 and 1.2 hydrogen bonds per water molecule, respectively. [57]ypically, the water flux is inversely proportional to the thickness of the membrane.According to Table 3, we find for the pristine CHC membrane that the water permeability is reduced by 12% when the thickness is doubled from 1.2 to 2.4 nm and by 38% when the thickness is increased by a factor of 5 from 1.2 to 6.0 nm.Experimentally, typical thicknesses are 8 to 10 nm. [34]oth the surface-functionalized and wall-functionalized membranes show a similar trend, with 14% and 8% decrease of the water permeability, respectively, when their thickness is increased from 1.2 to 2.4 nm.

Conclusions
Using molecular dynamics simulations, functionalization of CHC membranes by -COO − groups is demonstrated to be an effective method to control the pore size for water desalination.The water permeability turns out to be several times higher than that of existing C-based membranes and around 1000 times higher than that of conventional polyamide membranes.Importantly, we find that both the presence of functional groups and their location control the effective pore size.The salt rejection rate increases from 56% for the pristine membrane to 90% and 100% for the surfacefunctionalized and wall-functionalized membrane, respectively, at 1000 bar pressure.Wall-functionalization, therefore, is a particularly effective approach for combining 100% salt rejection with ultrahigh water permeability to guide future experimental efforts.

Figure 2 .
Figure 2. a) Number of water molecules that passed through the membrane as a function of the simulation time at 1000 bar.b-d) Mass density of the salt ions across the system.The values are averaged over the last 100 ps before the time t h (p = 1000 bar).The center of the membrane is located at z = 0.The black dashed lines indicate the initial boundaries of the membrane.

Figure 3 .
Figure 3. a) Radial distribution function between the Na + ions and O atoms of −COO − .The values are averaged over the last 100 ps before the time t h (p = 1000 bar).b) Mass density of water across the system.The values are averaged over the last 100 ps before the time t h (p = 1000 bar).The center of the membrane is located at z = 0.The black dashed lines indicate the initial boundaries of the membrane.

Table 2 .
Salt rejection rate and water permeability.

Table 3 .
Effect of the membrane thickness on the water permeability at p = 1000 bar.