Accepted Manuscript Multiwalled Carbon Nanotube Membranes for Water Purification Carmen Rizzuto, Giovanni Pugliese, Mohammed A. Bahattab, Saad A. Aljlil, Enrico Drioli, Elena Tocci PII: DOI: Reference:
S1383-5866(17)33279-3 https://doi.org/10.1016/j.seppur.2017.10.025 SEPPUR 14107
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Separation and Purification Technology
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13 August 2017 9 October 2017 15 October 2017
Please cite this article as: C. Rizzuto, G. Pugliese, M.A. Bahattab, S.A. Aljlil, E. Drioli, E. Tocci, Multiwalled Carbon Nanotube Membranes for Water Purification, Separation and Purification Technology (2017), doi: https:// doi.org/10.1016/j.seppur.2017.10.025
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Multiwalled Carbon Nanotube Membranes for Water Purification Carmen Rizzuto1, Giovanni Pugliese2, Mohammed A. Bahattab3, Saad A. Aljlil3, Enrico Drioli1,3,4and Elena Tocci1*
Institute on Membrane Technology, ITM-CNR, Via P. Bucci, 17/C, 87030 Rende (CS), Italy 2
University of Rostock, Schillingallee 70, 18051 Rostock, Germany
King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia
WCU Department of Energy Engineering, College of Engineering, Hanyang University, Seoul, 133-791, Korea
*Corresponding authors: E. Tocci E. Tocci (Tel: +39-0984-49-2038; Email: [email protected]
Prepared as a manuscript for Separation and Purification Technology Abstract
For the development of advanced membrane technologies, a good understanding of the materials properties and their transport mechanisms, as well as the realization of innovative functional materials with improved properties, are key issues. Due to their attractive permeability characteristics, various nano-structured RO membranes were proposed with the incorporation of carbon nanotubes. The growth in computational power has now made possible simulating tubes with characteristics closer to the real material, providing novel insights in the water flux to tube structure relationship. However, the understanding of the effect of the different number of walls, remains challenging and as a result, a deeper understanding is needed of how these changes can affect the performance of the membrane at the molecular level. To address this issue, molecular dynamic simulation (MD) is well known to be a powerful tool to enhance the understanding of nanoscale systems. This theoretical work provides new insights on the effect of walls in Multi Walled Carbon nanotube membranes, as model case of a CNT nanocomposite RO membrane, for desalination applications. Specifically, two
types of vertically aligned multi Walled Carbon Nanotube membranes, MWCNT (6,6) and MWCNT (8,8), were analyzed theoretically by means of non-equilibrium Molecular Dynamics simulations, in order to study the influence of the number of walls on permeation of reverse osmosis simulations. A comparison of the two membranes formed by using differently sized tubes give us the estimation of the level of desalination and efficiency. The carbon nanotube membranes were modeled using two graphene sheets and single walled (SW), double walled (DW), three walled (TW) for both (6,6) and (8,8) configurations, and six walled (6W) for (6,6). Simulations were conducted with a hydrostatic pressure difference to investigate the ion rejection and water conductance in each membrane system. MWCNT (6,6) are very selective to ions whilst MWCNT (8.8) were more permeable to water. The different behaviour was justified in terms of the different size of entrance of CNT with a cooperative effect due to numbers of walls of CNT and the hydrophobic effect of the graphene layers. A good agreement is found if we compare our system with some functionalized SWCNT (8,8)  and with that of protein aquaporin-1 . As the number of walls is augmented, the water conductance followed the same trend with a general performance greater than commercial reverse osmosis membranes . Under the conditions of our simulations, it appears that the MWCNT (8,8), particularly with DW (8,8) and TW(8,8) could offer an improvement over
membranes in terms of water conductance with a relatively good compromise between water conductance and salt rejection.
Keywords: Non-Equilibrium Molecular Dynamics (NEMD), Reverse Osmosis, Desalination, MWCNTmembranes, Graphene, Ion rejection, Water conductance
1. Introduction Fresh water scarcity has emerged as a big challenge of current era. Desalinations of sea water has long been utilized to produce fresh water suitable for human consumption and irrigation in areas of water lack, and its use is becoming more widespread across the globe. According to the United Nations World Water Development Report 2015, unsustainable development pathways and governance failures have affected the quality and availability of water resources, compromising their 2
capacity to generate social and economic benefits. Around the world, 748 million people lack access to an improved drinking water source, at the same time many emergent nations are undergoing rapid industrialization without appropriate wastewater management system . Actually, the principal desalination technology is based on membrane separation via reverse osmosis (RO) , but also new desalination technologies such as geothermal desalination , solar desalination  and membrane distillation  were developed. For the growth of advanced membrane technologies, a good understanding of the materials properties and their transport mechanisms, as well as the realization of innovative functional materials with improved properties, are key issues. Due to their attractive permeability characteristics, various nano-structured RO membranes were proposed and the incorporation of carbon nanotubes (CNTs)[1,9] and nanoporous graphene [10,11] into membranes shows a promising and scalable production technique. In particular, carbon nanotubes since their discovery in 1995  have received considerable interest due to their unique mechanical, optical, and electrical properties that make them amenable to a range of applications as sensor, filters, actuators, reactors, drug delivery, gas storage and channel [13–15]. CNTs were also demonstrated as a useful material for manufacturing electrodes for use in desalination of water using a flow through capacitor [16,17]. CNT membranes were used for direct water desalination or to remove salts without affecting the flow rate of water molecules . Filtration applications have benefited from the implementation of new technologies able to produce controlled size membranes containing CNTs of various types. Among the various methods for fabricating CNT membranes, the vertically aligned carbon nanotube (VA-CNT) membranes, manufactured using an aligned array of CNTs, are truly interesting for their applications in desalination [19–21]. In literature, many theoretical studies have shown how the transport of molecule of water inside single CNTs is possible. Although a full understanding of the origin of the flow enhancement in CNTs was not reached, some aspects are now accepted: movement of water through very narrow membrane channels is different from Poiseuillian flow through macroscopic tubes. The diffusive nature is of single-file transport and it is may governed by interactions with the channel wall or limited by water dehydration at the channel entrance . The growth in computational power has now made possible simulating tubes with characteristics closer to the real material, providing novel insights in the water 3
flux to tube structure relationship. However, the understanding of the effect of the different number of walls, remains challenging for which theoretical approaches can provide some insight. The aim of this work is to study the effect of different nanotubes, examining the influence of the number of walls in vertically aligned carbon nanotube membranes (Multi Walled Carbon Nanotube (MWCT)) on permeation by means of the computational tool of non equilibrium molecular dynamics simulation (NEMD). The effect of the pore size and number of walls, which play a key role for the ions rejections and water transport, was studied. Moreover, our scope was also to examine the best combination of graphene and multi walled carbon nanotubes (MWCNT) as membrane to increase the ion rejection. The aim is to provide a computational strategy to design CNT membranes for specific desalination applications maximizing selectivity.
Carbon nanotube membrane simulations
The first study conducted by Hummer et al in 2001 indicated how water can permeate through relatively narrow carbon nanotubes by the formation of single “water wires” through CNTs, with water molecules connected all by hydrogen bonds. This result was very surprising as it was thought that the nonpolar interior of narrow nanotubes would provide an unfavorable home for polar water molecules passing through the tube. Carbon nanotubes are non-polar system and therefore relatively hydrophobic. The understood filling mechanism depends on the water solution polarity, ion concentration and the van der Waals forces between water molecules and the CNT. When water was in the interior of the CNT, could have a lower chemical potential than it would in the bulk, it fills the CNT. CNTs are polarizable material, so this polarizability allowed for van der Waals forces between the water and the membrane walls, attracting the water molecules into the structure . Corry  in his paper on reverse osmosis in 2008, has indicated that membranes comprising sub nanometer diameter carbon nanotubes provided an efficient means of water desalination when used also in reverse osmosis. Although these narrow pores rejected ions extremely well, they conducted water at high rates being many times more efficient than existing membranes. Then various kind of 4
researches were conducted to analyze water conducting processes and desalination. MD simulations have used to investigate the transportation of different ions through functionalized pore graphene under the application of electric field. A mono-atomic layer of graphene as a membrane was already used [10,26–28] for desalination process and such as graphene-carbon nanotube membranes  were considered as an ideal membrane. Really, pure graphene membrane without pore is impermeable to small molecules due to the closely packed carbon atom in the lattice and repulsion of molecules by electron density of its hexagonal rings . Shi et al.  analyzed the separation of ethanol/water mixture though functionalized graphene membranes with hydrophobic and hydrophilic pores, to examine the effect of the pore size. They found that the flow rates of water and ethanol molecules are dependent on the pore size. For hydrophobic and larger pores (8.2Å), water molecules had higher flow rate that ethanol one due to the smaller size of water molecule. When the pore size become more close to kinetic diameter of water (3Å) , the chemical nature of the functional group plays a dominate role in water permeation, so water molecules pass very fast where effect of pore affinity is insignificant. In order to confirm the predictions of the no-slip Poiseuille flow relation, MD simulations are used for the prediction of water flow though circular pores with diameter about 1 nm . At the tube size of ~ 8 Å, water molecules are able to penetrate through the pore, whereas ions do not . Increasing tube diameter, as a recommended method to improve water permeability, decreases ion rejection. Functionalization of CNT entrance , ,   could not solve the problem completely because of reducing desalination efficiency. A solution was proposed by Razmkhah  by using CNTs with tight and wide diameters. The authors considered two different shapes of “expanded tube end” in addition to tubular CNT. They concluded that very large flux was found in all the simulated CNT membranes in comparison to existing semipermeable membranes. 2. Simulation details Simulations of the water transport through the carbon nanotube membranes were carried out using the Material Studio (7.0) package of BIOVIA  The selected force field was Dreiding , which was proven to be useful for CNTs . Dreiding is a force field is a purely diagonal force field with
harmonic valence terms and a cosine-Fourier expansion torsion term. The van der Waals interactions are described by the Lennard-Jones potential and electrostatic interactions are described by atomic monopoles and a Coulombic term. Hydrogen bonding is described by an explicit Lennard-Jones potential. Our systems were composed of three different sections as schematically shown in the Figures 1. The first section was made by a saltwater reservoir. The saltwater solution contains H 2O molecules, Na+ and Cl- ions. Ions were randomly placed to yield a salt concentration of 0.55 M which match seawater salinity . The second section consisted of multi wall carbon nanotube MWCNT membranes, in which three H-terminal carbon nanotubes are packed perpendicular to two regular sheets of graphene representing model of barrier membrane. The carbon nanotube membranes were modeled in single walled (SW), double walled (DW), three walled (TW) or six walled (6W) configurations. The third section was made of a reservoir of water, which contains only a specific number of water molecules according to the densities of the systems. The impermeability of the graphene sheets allow us to use high hydrostatic pressure that is uniformly distributed across the membrane. Non-equilibrium molecular dynamic  was used for all systems in NVT ensemble at a constant temperature of 300 K with the application of the Berendsen thermostat . Then, we analyzed some important properties of MWCNT-membranes (6,6) and (8,8) such as, conductance of the water during the simulation time, the salt rejection of a NaCl solution, the radial distribution of Na+ and Cl- during their passage inside the innermost carbon nanotube.
Figure 1: MWCNT membrane with SW (6,6). Armchair CNTs and two graphene sheets compose the membrane. Carbon atoms are shown in grey, oxygen atoms in red and hydrogen atoms in white. Clions are colored in green and Na+ are in violet.
Armchair type carbon nanotubes with indices n and m of (6,6) and (8,8) were simulated. Following Hummer et al. [23,44], all carbon atoms of CNTs and of graphene sheets were simulated as are neutral systems with physically realistic terminations, in which all terminal carbons have hydrogens as in the paper of Hughes . Although recent studies suggest that the atoms at the very end of the tube are likely to have slightly more charge than those in the center, we expect this to have only a minor influence on the conduction and ion exclusion properties of the nanotubes . Previous simulation studies have indicated that water flow is independent of the length of the pores: the center of the tubes are almost frictionless and we should expect the conductance of water through these CNTs to be largely independent of their length [33,44,47]. For simplicity, we examined CNTs of a single length, 19.68 Å. Corry  has shown for an aqueous solution containing Na + and Cl- ions their travel through CNTs of different diameter and length. Single columns of water molecules were formed in (5,5) and (6,6) CNTs, while (7,7) and (8,8) systems had two or in case four rows of water molecules. The C-C diameters of the nanotubes are 8.14 Å for MWCNT-membranes (6,6) and 10.85Å for MWCNT-membranes (8,8) type. The diameters of nanotubes were measured between the carbon centers as well as the effective internal diameter assuming a carbon atom van der Waals radius of 1.7 Å. The wall separation in multiwalled nanotubes is 3.35 Å such as the molecular diameter of water (2.75Å) and there is no passage of water outside the innermost CNT . The system was made by Amorphous Cell module of BIOVIA software  and the 3D -periodic boundaries were employed to form a continuous 3-dimensional membrane. All carbon atoms for each MD simulation are fixed, so their effects on the adjacent water are very little. The carbon nanotubes are open at both ends. The geometric parameters of all systems are, respectively summarized in the following Table 1.
Table 1: Geometric parameters of the systems. CNTs type
SW (6,6) DW (6,6) TW (6,6) 6W (6,6)
Area of graphene
Å 54.00×54.00×51.37 54.00×54.00×52.69 68.00×65.00×41.92 72.40×70.70×40.14
Å2 2916.00 2916.00 4420.00 5118.68
Inner diameter of CNT Å 8.14 8.14 8.14 8.14
Outer diameter of CNT Å 11.48 15.53 26.33
Length of Water CNT Thickness in the model Å Å 19.68 50.149 19.68 51.925 19.68 41.036 19.68 34.574 7
SW (8,8) DW (8,8) TW (8,8)
54.00×54.00×41.84 54.00×54.00×52.54 69.30×81.35×44.80
2916.00 2916.00 5637.55
10.85 10.85 10.85
19.68 19.68 19.68
44.493 46.866 45.871
All the systems were energy minimized and then equilibrated for 200 ns under a constant volume and temperature of 298 K in the NVT-ensemble. For all simulations, time step was 1 fs. The temperature control method was Nosé . Ewald Summation method  was used for the electrostatic terms with accuracy of 0.001 kcal/mol. After the equilibration stage, Non-Equilibrium Molecular Dynamic simulations were carried out for 10 ns at 300 K in order to simulate water and ions permeation under hydrostatic pressure. Time step was 1 fs in the NVT- ensemble . As in the method used by Joseph  the hydrostatic pressure difference in the simulation system was induced, in the z direction to drive the flow, by applying an external force, F, to the bulk water molecules, proportional to desired pressure to the system. The control of the temperature was conducted by Berendsen thermostat . The impermeability of the graphene membrane allows us to use pressure difference to apply a large well-defined force that is uniformly distributed across the entire surface of the membrane . In this case, the application of a hydrostatic pressure like an external force was applied to the oxygen atoms of the water molecules to allow the passage through the CNT membrane. The value of the external force was set finally on 200 kcal/mol Å. The actual hydrostatic pressure  in each simulation is determined from the Equation (1):
(1) Where n is the average number of oxygen atoms to which these additional force is applied during the simulation, f is the force applied to each oxygen atom and A is the cross sectional area of the membrane. The hydrostatic pressure was constant and fixed at a value of 497 MPa. Although, most experimental pressure of reverse osmosis in seawater desalination operate at pressure of 60-80 bar (6 – 8 MPa) , we conducted our simulation under a larger pressure difference of 400 MPa, because this allows to observe a great number of events in our limited simulation time as reported also in . 8
The radial distribution function (RDF) indicates the local probability density of finding B atoms at a distance r from A atoms averaged over the equilibrium density, as follows:
where nB is the number of B atoms at a distance r in a shell of thickness dr from atom A, NB is the total number of B atoms in the system, and V is the total volume of the system. The probability is normalize to the probability expected for a completely random distribution at the same density.
Then, in order to estimate the number of different water molecules coordinated to a selected ion, values of g(r) were converted into coordination numbers with the following expression:
(r) r 2 dr
where nxz (r ) is the number of x particles coordinated to particle z within a radius r, V the cell volume, Nz the total number of particles z in the system, and
g xz (s)
the radial distribution function between x and z.
3. Results and Discussion
To determine the suitability of MWCNTs for water desalination, the ion rejection capabilities were investigated by counting the number of ions passing through the CNT pore during the simulation. The percentage (%) of Ion Rejection normalized on number of nanotubes, nanoseconds and pressure is indicated in Table 2. The membrane rejection
was calculated using the Equation (4):
is the feed concentration,
is the permeate concentration of the salt respectively.
Table 2 and Figure 2: Na+ and Cl- rejection in MWCNT membranes
Na+, MWCNT (6,6) Na+, MWCNT (8,8) 100.5 100.0
99.0 98.5 98.0 97.5 97.0
Number of walls
Cl-, MWCNT (6,6) Cl-, MWCNT (8,8) 100.5 100.0 99.5
% Ion rejection
SW (6,6) DW (6,6) TW (6,6) 6W (6,6) SW (8,8) DW (8,8) TW (8,8)
% Ion Rejection Na+ Cl100 100 100 100 100 100 100 100 99.8 99.9 98.2 98.2 99.6 99.3
% Ion rejection
99.0 98.5 98.0 97.5 97.0
Number of walls
For the smaller MWCNT membranes (6,6) we have found high ion rejection of 100% for both ions, while for the larger MWCNT-membranes (8,8), the % ion rejection decreased in almost the same trend. The salt rejection also follows a direct tendency with the coordination numbers of water molecules of the first shell of the ions as noted previously . The larger anion, Cl- requires more water molecules to be removed from its solvation shell to enter the CNTs than Na+. The Figure 3 shows the hydration shell of the two ions of the SW membrane system.
Figure 3: Snapshots indicating the solvation shell for Na+ and Cl- ions in SW (8,8) system in the bulk and in the innermost CNT.
This figure is a snapshot summarizing the state of water molecules and ions outside and inside the nanotube. The molecular orientation of water molecule towards to Cl- and Na+ ions have been analyzed by the comparison of the calculated RDF for (O) water-ion and (H) water-ion, in Figure 4 a-b.
10 Cl-- (H) water
Cl-- (O) water
Na+- (O) water
Na+- (H) water
2 0 0
6 r, Å
b) Figure 4 a-b: Radial Distribution Functions of (O) water-ion and (H) water-ion in SW (8,8)
The Figure 4 a-b indicate the g(r) functions show the first peak (Figure 4 a) for the interactions between Cl- ions and hydrogen atoms of water molecules. As well in Figure 4 b, the first peak is indicating the interactions 11
between Na+ and the
water molecules that
orientation of water +
towards the positive
Na bulk Na + confined Cl- bulk Cl- confined
Average 4.9 2.57 4.3 0.86
Range 2-8 0.9 – 5.8 2-7 0.8 – 1.9
molecules with their charge
Moreover, we have calculated (see Table 3) the coordination number of ions from the radial distribution function g(r) of Na+ and Cl- in the bulk and inside the nanotube from Equation (3). The first peak identifies the first coordination-shell around the ions and the correspondent strong interaction. Table 3 indicated that the average number of water molecules surrounding Na+ and Cl− decreased from bulk to the nanotube with confined environment. The general observation is that when the ions are in the bulk, the first solvation shell is much larger and stable compared to that observed in the nanotube, because there are a large number of first coordination water molecules, which creates a dense network of hydrogen-bonds . When ions are in the innermost nanotube, Cl- preferentially moves alone or just with one molecule whilst Na+ is almost all the time, surrounded in average by 3 water molecules. We have compared the g(r) for MWCNT with TW (8,8) and DWCNT (8,8): the peak interactions were in the same range indicating that there was no effect of increasing number of the CNT walls.
Table 3: Coordination numbers
In the hydrophobic environment of the CNT, a low number of water molecules coordinate the ions and they can traverse the membrane interface. The comparison of the different behavior of the Cl- and Na+ in the bulk and in the innermost CNT has indicated that the intensities of the peaks are not the same because they depend on the hydration number of the ions. The radial distribution functions both in the bulk and inside the nanotubes indicated that the interactions of the chloride ion with the hydrogen atoms of water molecules are 12
at 2.1 Å, while for the sodium ions, fall at 2.01 Å. During the MD runs the passage of water molecules through the innermost CNTs was observed for all systems and the water conductance (the average number of water molecules through the CNTs) per nanotube per nanosecond per pressure was calculated. The results of the NEMD simulations are summarized in Table 4. Table 4: Water Conductance.
pnt = per nanotube, pns = per nanosecond of simulation, ppress = per pressure applied
The water flux in independent of the length of the tube at pressure differences larger than 200 MPa  and Systems
density in CNT,
Conductance *102 (pnt pns ppressa))
SW (6,6) DW (6,6) 6W (6,6) SW (8,8) DW (8,8) TW (8,8)
8.14 8.14 8.14 8.14 10.85 10.85
1.88 0.98 0.40 2.89 14.7 17.1
0 0 0 0.014 0.107 0.050
0 0 0 0.009 0 0.100
generally, increases with the increasing pore size again. Comparing our data with that of Corry  for the relatively similar system but without the impermeable graphene sheet and normalizing for the pressure that the author applied in the paper, the results are of about 4,3 (our value) vs 23 (Corry) for SW (6,6) and 6,6 vs 82 (Corry) for SW (8,8), water molecules per nanosecond and nanotube, respectively. The discrepancy of about 5 times for SW (6,6) and of 13 times for SW (8,8) can be related to the to the presence of the graphene 13
barrier. A good agreement is found if we compare our system with some functionalized SWCNT (8,8)  and with that of protein aquaporin-1 that is of 5.8 water molecules per nanosecond and channel . As the number of walls is augmented, the water conductance followed the same trend with a general performance greater than commercial reverse osmosis membranes . The average conductance of SW (8,8) is roughly double of the conductance of SW (6,6) , while that DW (8,8) and TW (8,8) are fifteen and thirty-times the conductance of DW (6,6) and TW (6,6), respectively. We can explain this different behaviour of MWCNT membranes (6,6) and (8,8) as a function of the different size of entrance of CNT. There will be a cooperative effect between the growing numbers of walls of CNT combined with the hydrophobic effect of the graphene layers, i.e. the impermeable barrier of sp2 carbon to polar molecules. The dimensions of the entrance of the nanotubes is the determining factor for different behaviors of MWCNT (8,8) and MWCNT (6,6). A larger cavity of the CNTs allows the passage of a greater number of water molecules, because it was assisted by the interactions with terminal hydrogens of the walls of CNTs. The affinity of water in the bulk with the entrance of CNTs was evidenced by Thomas who analysed the influence of the orientation of water molecules near the carbon surface whilst inside CNTs of larger diameters, water molecules have no affinity toward any carbon atoms . Moreover, the smallest SWCNT (6,6), among MWCNT with DW(6,6), TW(6,6) and 6W(6,6), revealed the highest conductance of water molecules due to the lowest hydrophobic contribution of the nanotube walls. MWCNT with DW (6,6), having a greater number of walls combined with a small dimension of the entrance allowed the passage of a reduced number of water molecules. Consequently, MWCNT with TW (6,6) and MWCNT with 6W(6,6) showing the greatest hydrophobic character for the increased number of walls, revealed almost zero conductance. For MWCNT-membranes (8,8) the larger cavity effect was relevant in comparison to the relatively smaller dimension of graphene layer (reduced hydrophobic character) and to the number of walls, justifying a higher conductivity of water. 14
The water molecules in MWCNT (6,6) organized themselves in single-file configuration, forming a chain like network connected with hydrogen bonds. This give rise to the unique phenomenon of ultra-efficient transport of water through these ultra-narrow molecular pipes. The reason being the organization of water molecules in H-bond wires that lowers the chemical potential energy of the water inside the nanotube . Moreover, the missing interactions between sp2 carbon atoms of CNT and water, due to the hydrophobic interior of CNTs, facilitate the formation of the one-dimensional hydrogen-bonded water chains  . The water wires increase the water flux and when they are highly ordered the small number of molecules forming a chain prevents the decrease in entropy from being prohibitive. The individual water molecule that has a high number of hydrogen bonds in the bulk, when moves inside the pore, it is surrounded by a few hydrogen bonds (this means that some of these bonds are broken). As already indicated, water molecules are attracted in the pore by favorable van der Waals attractions with the narrow nanotubes and with an attraction from the water molecules in the pore whose aligned dipoles . In Figure 6 (a, b) the different configurations of water wires for the two types of MWCNT studied are reported.
Water Flow direction
Figure 6: Water wires in SW (6,6) and SW (8,8) CNTs. Blue lines indicate hydrogen bonds. White atoms are hydrogen and red ones are oxygens
As we can see, in the MWCNT-membranes (6,6), water molecules are organized in a single file chains oriented along the nanotube axis whilst in MWCNT with DW (8,8) and TW (8,8) the wires are composed, in average, by three - four chains. Water wires were stabilized by hydrogen bonds in both systems. For these visualization a maximum hydrogen-acceptor distance of 2.5 Å and minimum donor-hydrogen-acceptor angle of 90° were considered. The configuration of water wires depends on the CNT type. In single walled (6,6) the water wires are organized in single chains for the total duration of the simulation. In DW(6,6) and much more in TW (6,6) the results from simulations indicated fluctuations between filled and empty states (bi-stable states) of the CNT cavity confirming the results of Hammer that nanoscale confinement leads to a lowering of the chemical potential .
This theoretical work provides new insights on the effect of walls in Multi Walled Carbon nanotube membranes, as model case of a CNT nanocomposite RO membrane, for desalination applications. Here, we have analyzed theoretically two types of vertically aligned Multi Walled Carbon Nanotube membranes, MWCNT (6,6) and MWCNT (8,8), by means of non-equilibrium Molecular Dynamics simulations, in order to study the influence of the number of walls on permeation of reverse osmosis simulations. A comparison of the two membranes formed by using differently sized tubes give us the estimation of the level of desalination and efficiency. MWCNT (6,6) and
MWCNT (8,8), to
investigate the ion rejection and water conductance in each membrane system. The dimension of CNT’s pores is responsible for Na+ and Cl- rejection. For MWCNT membranes (6,6) we have found high ion rejection of 100% for both ions, while for the larger MWCNT-membranes (8,8), the % ion rejection decreased. Water molecules surrounded in different amount the ions inside the CNT as well in bulk phase. Both membrane conduct water at relatively high rates; in particular, membranes containing CNTs with larger radii are characterized by larger water conductance. The configuration of water wires depends on the CNT type. The water molecules in MWCNT (6,6) organized themselves in single-file configuration, forming a chain like network connected with hydrogen bonds. In single walled (6,6) the water wires are organized in single chains for the total 16
duration of the simulation. In DW(6,6) and much more in TW (6,6) the results from simulations indicated fluctuations between filled and empty states. Larger pores in MWCNT (8,8) allow for more chains of hydrogen bonded water molecules to cross the CNT with a non - continue flux of water. The different behaviour of MWCNT membranes was justified in terms of the different size of entrance of CNT with a cooperative effect due to numbers of walls of CNT and the hydrophobic effect of the graphene layers. Under the conditions of our simulations, it appears that the MWCNT (8,8), particularly with DW (8,8) and TW(8,8) could offer an improvement over current generation membranes in terms of water conductance  with a relatively good compromise between water conductance and salt rejection. It also demonstrated that molecular dynamic simulation are powerful tool to enhance the understanding of nanoscale systems and to predict the performance these materials.
This work was partially supported by the King Abdulaziz City for Science and Technology (KACST) Project “CNT-RO and NF membranes for the treatment of aqueous solutions and desalinations”.
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Highlights MWCNT (8,8) are characterized by larger water conductance than MWCNT (6,6) The dimension of CNT’s pores is responsible for Na+ and Cl- rejection. MWCNT (8,8) could offer an improvement over current generation membranes in terms of water conductance.