Water desalination through rim functionalized carbon nanotubes

Yang Hong a, Jingchao Zhang b, Chongqin Zhu *c, Xiao Cheng Zeng *a and Joseph S. Francisco c
aDepartment of Chemistry, University of Nebraska-Lincoln, Lincoln, NE 68588, USA. E-mail: xzeng1@unl.edu
bHolland Computing Center, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
cDepartment of Earth and Environmental Science, Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USA. E-mail: chongqin@sas.upenn.edu

Received 14th November 2018 , Accepted 30th December 2018

First published on 31st December 2018

Carbon nanotubes (CNTs) are promising media for seawater desalination due to their high water flow rate. Currently, narrow CNT membranes cannot be mass-produced for salt rejection purposes. Hence, introducing chemical functional groups at the rims of comparatively wider CNTs is an alternative strategy to enhance the ion exclusion performance. Although the dipole moment between the CNT rim and locally anchored functional groups is expected to have an important impact on desalination performance, its specific effects have not been systematically investigated. Herein, we present a comprehensive study of the water permeability and salt rejection of CNTs with various dipole moments anchored at their rims using classic molecular dynamics (MD) simulations. Compared to their bare CNT counterparts, CNTs with a low dipole moment at the rim can slightly increase the water flow and salt rejection rate, and CNTs with a high dipole moment can significantly improve the salt rejection efficiency, although water passage is slowed. In general, introducing functional groups with a high dipole moment on wider CNT rims can filter more than 95% of salt ions while maintaining a high water permeability of 10.2 L cm−2 day−1 MPa−1. The calculated potential of mean force for water molecule and salt ion passage through the CNTs, oxygen and hydrogen density maps, radial distribution functions, and snapshots of water molecules and salt ions in the CNTs offer in-depth insights into the mechanism of seawater desalination by CNTs. Our study offers guidelines for an alternative design of CNTs to achieve both high salt rejection and fast water flow.


Freshwater is an essential element of human society. With the rapidly growing global population, freshwater storage has deteriorated dramatically due to agricultural, industrial, domestic and municipal water withdrawals. The fast-growing freshwater demand and the limited renewable water supply render freshwater shortage a serious global challenge. Currently, approximately one-third of the global population lives under freshwater stress.1–3 Since seawater and saline aquifers account for ∼98% of the world's water storage, seawater desalination has become one of the most promising supply-side measures to address the global freshwater shortage.4 The two most widely used desalination techniques are reverse osmosis (RO) and thermal distillation (including multi-stage flash and multi-effect distillation).5 In the Arabian Gulf and adjoining areas, mainly thermal distillation has been used in desalination plants. Such an approach demands a substantial energy supply and, as a result, could aggravate the greenhouse effect.6,7 Outside the Gulf area, RO is the most widely applied desalination technique and constitutes ∼50% of the global market.8 RO membranes are several times more efficient than the thermal distillation method. Seawater desalination efficiency is mainly characterized by two factors, i.e., water permeability and salt rejection. RO membranes can separate and collect desalinated water from seawater with a salt rejection rate of ∼98%. However, RO still has several drawbacks, such as low water flow rate and high cost of water conveyance, pretreatment and equipment maintenance.8,9 Since all state-of-the-art plants are energy- and capital-intensive, their applications in the world's freshwater supply are still limited.10,11

Nanoporous membranes open up new perspectives for seawater desalination due to their fast convective water transport and very small pore dimension. Nanostructures, including carbon nanotubes (CNTs), graphyne, graphene, graphene oxide, single-layer MoS2 and zeolite thin-film nanocomposite membranes, have shown excellent desalination performances, either in laboratory tests or from molecular dynamics (MD) simulations.12–20 Among these media, CNT membranes stand out due to their excellent water transport and unique mechanical properties.21,22 Holt et al.22 reported that aligned double-walled CNT membranes with a sub-2 nm pore diameter exhibit extremely fast water flows up to ∼6 × 103 L cm−2 day−1 MPa−1, which is five orders of magnitude greater than those of RO membranes (∼2.6 × 10−2 L cm−2 day−1 MPa−1).23,24 The excellent flow rate of CNT membranes is attributed to the smooth inner hydrophobic surface, which lubricates and speeds up near-frictionless water transport.25 However, the Na+ ion rejection rate for non-functionalized sub-2 nm CNT membranes is typically lower than 40%[thin space (1/6-em)]12,26 due to the slightly larger pore size than the size of hydrated sodium ions. To achieve nearly complete salt ion exclusion, previous MD simulations have suggested that the diameter of CNTs has to be <0.9 nm (sub-1 nm), based on computations of salt ion desolvation energy barriers.27,28 However, typical experimentally synthesized CNTs exhibit a wide range of diameter distributions, making the massive production of sub-1 nm CNTs with nearly uniform size a substantial challenge. Introducing functional groups at wider CNT (diameter > 0.9 nm) ends is an alternative approach to control the ion exclusion capability. For example, Fornasiero et al.12,13 experimentally demonstrated that the solution ionic strength, pH value and ion valence could affect the ion exclusion capabilities of functionalized CNT membranes. They found that the Donnan-type rejection mechanism is dominated by the interaction between negatively changed carboxylic functional groups at CNT tips and mobile ions in seawater solutions. Chen et al.29 designed an asymmetric tip-functionalized CNT membrane with hydrophilic groups (carboxyl) on one tip and hydrophobic groups (trifluoromethyl) on the other. The driving force produced by the hydrophilic–hydrophobic groups facilitated water transport and effectively blocked salt ions for pore sizes of 0.81 and 1.09 nm. However, functional groups do not always incur positive effects on the ion-blocking performance of CNT membranes. Corry et al.26 examined a range of functional groups with different charges and polarities on the tip of a 1.1 nm-diameter CNT. They found that 8 negatively charged carboxylic groups prevent the passage of both Na+ and Cl ions, resulting in a 100% salt rejection rate. However, the addition of 4 OH groups unexpectedly facilitates the passage of Na+ ions. Qin et al.30 showed that Na+ ion can easily bind with the rim functionalized CNTs by OH, and block the water flow. In contrast, the hydrophobic C2H5 functionalized CNTs exhibit weak binding with Na+ ions in moderate density, and the water flow is thus resumed. Hence, careful design of chemical functionalization is required to optimize the desalination performance of CNT membranes.

In this work, our focus is placed on the effects of a dipole moment at the CNT rim on the water desalination performance. The CNTs are first functionalized by hydrogen atoms; the charge of carbon atoms at the CNT rim is −0.115e, and the charge of hydrogen atoms used to passivate these carbon atoms is +0.115e. We can tune the charges of carbon and hydrogen atoms to mimic the dipole moment changes between C–H bonds. Using classic MD simulations, both the salt rejection and water permeability performance of CNTs are examined, with charge variations from −0.515e to +0.515e. In addition to the dipole moments, two different pore sizes and four different pressures are also investigated. Our simulation results show that the water permeability of (9,9) CNTs is 5-fold greater than that of (7,7) CNTs. While a low dipole moment can facilitate water transport in CNTs, a high dipole moment blocks the passages of both water molecules and salt ions through the CNT due to the enlarged energy barriers, which lead to enhanced salt rejection efficiency and reduced water flow. Overall, the (9,9) CNTs with high dipole moments give rise to the best water desalination performance, with more than 95% of ions being blocked at 200 MPa, and a high water permeability of 10.2 L cm−2 day−1 MPa−1.


A schematic of the system is shown in Fig. 1(a). The axial direction of the CNT is set along the z-axis, and both CNT ends are connected with graphene (perpendicular to the z-axis). Every other carbon atom on the left rim of the CNT is passivated by hydrogen atoms, as shown in Fig. 1(b) and (c). The simulated water solution contains 33 Na+ ions, 33 Cl ions and 998 water molecules, corresponding to a salt concentration of 123 g L−1. This higher concentration than that of seawater (∼35 g L−1) was chosen to increase the encounter probabilities between salt ions and CNTs during the MD simulations. The simulation box has dimensions of 6.0 × 6.1 × 10.0 (x × y × z) nm.3 Periodic boundary conditions are applied in all directions. A rigid piston (monolayer graphene) is placed on the left side of the CNT and is used to push the water towards the CNT. Initially, half of the water molecules and all salt ions are located in the left portion of the system between the rigid piston and CNT. The other half of the water molecules are placed on the right side of the CNT. A (9,9) armchair CNT with a length of 1.1 nm and a diameter of 1.2 nm is studied first. For comparison, a narrower (7,7) CNT with a 0.95 nm diameter is also investigated. Both diameters are comparable to the size of hydrated sodium (with a diameter of ∼0.76 nm). Convergences of water flux and salt rejection rate with membrane thickness are examined. As shown in ESI Fig. S1, the membrane thickness (in nanoscale) has negligible impact on the desalination behavior. Therefore, to save the computational cost, the CNT length is fixed at 1.1 nm in all simulations. To further explore the dependence of desalination performance on external pressure, the pressure applied to the rigid piston is varied from 200 MPa to 800 MPa with 200 MPa intervals.
image file: c8ta10941a-f1.tif
Fig. 1 Schematics of the simulation system. (a) Snapshot of the (9,9) CNT system after a 200 ps equilibration run in the NVT ensemble without applying external pressure. The red and white colours represent oxygen and hydrogen atoms, respectively, in the water molecule. The turquoise and yellow balls represent carbon atoms and hydrogen atoms at the CNT rim, respectively. Na+ and Cl ions are denoted by green and blue, respectively. After the equilibration run, external pressure is applied to the seawater as denoted by the blue arrow. A top view of the (b) (9,9) and (c) (7,7) CNT rims passivated with hydrogen atoms.

The carbon–carbon interactions in graphene layers are described by a second-generation reactive empirical bond order (REBO) potential.31 The water molecules are modelled by SPC/E potential. The rest of the system, including the CNT, the salt ions and the pairwise interactions between each species, are described by the 12-6 Lennard-Johns (LJ) potential with the coulombic interaction term; the parameters are summarized in ESI Table S1.32–34 The cutoff distances for both the Coulomb and LJ energy terms are set as 9.8 Å. Previous studies have shown that the dipole moment of functional groups attached to the CNT rim plays a key role in desalination performance.26,30,35–37 To understand the effect of dipole moment on desalination performance across CNTs, the charge parameter q of the rim carbon atoms (CCH) and the passivation hydrogen atoms (HCH) is adjusted to implement the dipole moment change. Originally, the charge of CCH (QC) is −0.115e, while the charge of HCH (QH) atoms is +0.115e, as shown in ESI Table S1 with underlines. For later modelling purposes, QC is modified from −0.515e to +0.515e, and QH is changed from +0.515e to −0.515e accordingly. Meanwhile, the bond length and tilt angle of C–H bond are kept at 1.09 Å and 0°, respectively.

All MD simulations in this work are performed by using the large-scale atomic/molecular massively parallel simulator (LAMMPS).38 The system is first equilibrated in the canonical ensemble (NVT) at 300 K for 200 ps with no external pressure. Next, a constant and continuous external pressure is applied to the rigid piston to push the water molecules through the CNT until at least half of the water molecules from the solution side are moved to the permeate side. When water molecules move to the permeate side, the concentration in the solution side keeps increasing. The concentration difference between two sides will cause an osmotic pressure and making the water molecules prefer to move from the right side to the left side. The magnitude of the osmotic pressure can be estimated by eqn (S1) in ESI, by using the initial concentration of the salt solution. The result is 5.25 MPa. Hence, to remove the influence of increased concentration on the simulation results, a very large external pressure (at least 200 MPa), about 2 orders of magnitude higher than the osmotic pressure, is applied to the graphene piston in the forward direction. The simulation time step is 0.5 fs unless otherwise stated, and the simulation time varies according to the CNT size, applied pressure, and charge. Two independent MD simulations with different initial velocity seeds are performed, and the results are averaged to suppress statistical noise.

The potential of mean force (PMF) is used to evaluate the water desalination performance of CNTs under different conditions. The PMF of moving a salt ion or a water molecule along the z direction is calculated based on the umbrella sampling method. A restoring force in the z direction is applied to each atom in the target group; this force is expressed as

Fz = Kz(zz0)mi/m,(1)
where Kz is the spring constant, mi is the mass of the ith atom in the target group, m is the total mass of the target group, z0 is the target position for each umbrella sampling window, and z denotes the z-direction coordinate of the target group mass center.39 For the (9,9) CNTs, Kz is set as 2 kcal mol−1 Å−2, while for the (7,7) CNTs, Kz is 4 kcal mol−1 Å−2. The spring constants in the x and y directions are kept at 2 kcal mol−1 Å−2 to keep the target particle moving along the central axis of the CNT. The umbrella sampling windows are separated by 1 Å intervals in the span of 14 to 30 Å, which cover the range from the bulk water to the center of the CNT. Simulations are performed for 6 ns with a time step of 2 fs. Data from the last 4 ns are collected and analysed by the weighted histogram analysis method (WHAM) to obtain the PMF.40

Results and discussion

Water permeability

First, CNTs with zero dipole moment at the rim are studied; both QC and QH are set to 0. Once external pressure is applied, water molecules start moving from the solution side to the permeate side. During this process, the number of water molecules filtered by the CNT is monitored, and the results are presented in Fig. 2(a). At the beginning of the simulation, for both pore sizes, the number of filtered water molecules shows a linear increase with simulation time. When the simulation time is sufficiently long, the water profile levels off, which means that all water molecules have moved to the permeate side. By fitting the linear region, the water flow rate per unit time for the (9,9) CNT is 182 molecules per ns under 800 MPa. In contrast, the flow rate per unit time for the (7,7) CNT is only 32 molecules per ns, which is more than 5 times slower than that obtained for the wider CNT. The difference in the flow rate per unit time for the (7,7) CNT and (9,9) CNT is due to the different local structures of water molecules inside the CNTs, as shown in Fig. 2(b) and (c). The water transport in bare (7,7) CNTs is limited to single- or double-chain passages, while in bare (9,9) CNTs, the water molecules are allowed to transport through more than four pathways, resulting in a much faster water flux.
image file: c8ta10941a-f2.tif
Fig. 2 (a) The cumulative number of water molecules filtered in (9,9) and (7,7) CNTs with zero dipole moment at the rim vs. simulation time under an external pressure of 800 MPa. The linear region, as denoted with brackets, is fitted for the water flux calculation. Front and top views of water molecules inside the (b) (9,9) CNT and (c) (7,7) CNT at 200 MPa. The red and white balls represent water molecules. The turquoise and yellow balls represent carbon atoms and hydrogen atoms at the CNT rim, respectively.

Second, the effects of external pressure on the water flux of (9,9) and (7,7) CNTs are studied. The results are shown in Fig. 3(a). For both CNTs, the water flux increases linearly with external pressure. As such, we can predict the water transport behaviour at low pressures, such as those in commercial RO plants (1–10 MPa). The water permeability (Am) of CNTs, a pressure-independent variable, is defined as41

image file: c8ta10941a-t1.tif(2)
where ν represents the volume of a single water molecule, P is the applied pressure, Ng is the water flux, and Ng/P is the slope of the linear fitting profile in Fig. 3(a), which represents the normalized water flux per unit pressure. When the CNT pore density ρ is set to the experimental pore density achieved by Holt et al.22 (2.5 × 1011 cm−2), the Am of (9,9) and (7,7) CNTs is 0.170 and 0.0201 L cm−2 day−1 MPa−1, respectively. If the pore density reaches the theoretical maximum calculated by Sotomayor et al.42 (5.8 × 1013 cm−2), the Am for (9,9) and (7,7) CNTs amounts to 39.4 and 4.9 L cm−2 day−1 MPa−1, respectively. The latter density is used in the following analyses.

image file: c8ta10941a-f3.tif
Fig. 3 (a) Water flux vs. applied pressure for (9,9) and (7,7) CNTs with zero rim dipole moment. Water permeability in (b) (9,9) and (c) (7,7) CNTs vs. the rim charge. The error bars are calculated based on the standard errors of linear fitting.

Third, to evaluate the effect of dipole moment, QC is adjusted in the range of −0.515e to +0.515e. The charge of QH has the same magnitude as QC but the opposite sign. The water flux versus the external pressure at different QC values and pore sizes is shown in ESI Fig. S2. For both uncharged and charged CNTs, the water flux has a positive correlation with the applied pressure. Thus, we can predict the water permeability of charged CNTs based on eqn (2). The relationship between the added charge and water permeability is presented in Fig. 3(b) and (c), where the water permeability profiles for the (9,9) and (7,7) CNTs exhibit similar overall trends. For both CNTs, the water permeability curves are not completely symmetric with respect to the zero-charge point. In general, when carbon atoms hold a partial negative charge and hydrogen atoms hold a positive charge, the water flux is slightly faster than in the opposite charge arrangement. The water permeability performance is usually better with a small charge than in uncharged conditions. When the charge magnitude is greater than 0.215e, regardless of the sign of the charge, the water flow in the (9,9) CNT declines sharply with increasing charge. For (7,7) CNTs, the water permeability curve starts to drop at QC = +0.215e. The maximum water permeability Am is 40.6 L cm−2 day−1 MPa−1 for a (9,9) CNT with a −0.115e charge on the rim carbon atoms. This permeability is much higher than that for commercial RO membranes (∼2.6 × 10−2 L cm−2 day−1 MPa−1) and is comparable to the maximum water permeability achieved by other low-dimensional carbon materials, such as nanopore-containing graphene (129 L cm−2 day−1 MPa−1) and graphyne-4 membranes (13.1 L cm−2 day−1 MPa−1).16,17

Salt rejection

In addition to water permeability, we also compute the salt rejection rate, defined as
R = 1 − N1/2/N0,(3)
where N0 is the number of salt ions in the solution before pressure is applied; and N1/2 is the number of salt ions passed through the CNT when half of the water molecules have moved to the permeate side.16,17 Here, R = 100% means that all salt ions are rejected by the CNT and the permeate-side salinity is zero, and R = 0 means that the CNT has no salt rejection function. Fig. 4(a) shows the pressure effect on salt rejection for zero-charged CNTs. For both CNTs, the salt rejection rate decreases with increasing pressure. Specifically, the salt rejection in the (7,7) CNT reaches 100% below 400 MPa but reduces to 85% at 800 MPa. The salt rejection performance of the (9,9) CNT is not as good as that of the (7,7) CNT since salt ions can pass through the former more easily. The salt rejection rate decreases from 80% to 53% when the pressure increases from 200 to 800 MPa.

image file: c8ta10941a-f4.tif
Fig. 4 (a) The salt rejection rate vs. the external pressure for (9,9) and (7,7) CNTs with zero dipole moment. The salt rejection rate vs. the rim charge for (b) (9,9) and (c) (7,7) CNTs under external pressures of 200 MPa and 800 MPa.

As shown in ESI Fig. S3, for charged CNTs, the salt rejection rate generally decreases with applied pressure. The salt rejection rate versus QC is shown in Fig. 4(b). All charged (7,7) CNTs can block nearly 100% of the salt ions when the external pressure is <400 MPa. For higher pressures, only CNTs with a large QC can still filter all salt ions, whereas for CNTs with a small QC, the salt rejection rate can be as low as 73%. For wider CNTs, the situation is even worse. Under 200 MPa external pressure, the (9,9) CNT can only filter more than 95% of the salt ions (a condition for drinkable seawater) if QC > 0.315e. Under high pressure, none of the charged (9,9) CNTs can meet the salt-rejection requirement for desalination.

Mechanistic investigation of dipole moment effect

To further understand the effect of dipole moment on water desalination performance, oxygen and hydrogen density maps at the pore ends were generated and are given in Fig. 5. The CNT dipole moment and pore size can significantly affect the water distribution near the pore rim. For (9,9) CNTs with QC = +0.515e, the water molecules are distributed in a circular pattern, while for QC = −0.515e, the oxygen atoms are arranged in one-to-one correspondence with rim H atoms; however, the maximum density area is located in the CNT center due to the strong repulsion between the −0.515e-charged C atoms at the CNT rim and the oxygen atoms in water molecules. In addition, when the pore rim has zero dipole moment, the distribution of oxygen atoms is a mixture of the above patterns, where water molecules are scattered uniformly over the edge and center. In contrast, the oxygen density map in (7,7) CNTs with QC = −0.515e or +0.515e exhibits circular shapes with highlighted spots facing towards the rim H atoms. However, the hydrogen density maps for the two cases exhibit different shapes. In CNTs with QC = +0.515e, the −0.515e-charged hydrogen atoms at the rim are tightly surrounded by the hydrogen atoms of nearby water molecules owing to strong attractive interactions. Since the water molecules are confined by the pore rim, the water permeability in this case is even lower than that in the case of the (7,7) CNT with QC = −0.515e. For wider (9,9) CNTs, water molecules in the centers of the CNTs experience less constraint from the dipole moment at the rim, so a similar phenomenon is not observed. In general, CNTs with large dipole moments can facilitate the breaking of in-plane hydrogen bonds in water networks close to the pore rim and the partial stabilization of water molecules near the rim. Hence, water transport in these CNTs encounters a high energy barrier and has a small flow rate. In addition, for CNTs with small dipole moments, such as QC = −0.115e, the water molecules show similar patterns to those observed for zero-dipole-moment CNTs, suggesting that even small dipole moments can promote the breaking of hydrogen bonds, but water molecules are not retained around the CNT rim. Thus, CNTs with small dipole moments result in faster water flux than zero-charged CNTs due to the reduced energy barrier for water passage.
image file: c8ta10941a-f5.tif
Fig. 5 Oxygen (–O–) and hydrogen (–H–) density maps at the pore rim of (a to h) (9,9) and (i to p) (7,7) CNTs with QC = +0.515e, −0.515e, 0 and −0.115e at 200 MPa. A cold colour represents a lower density, and a warmer colour indicates a higher density.

To further elucidate the physical mechanism regarding water and salt ion passage in CNTs, the potential mean forces (PMFs) of moving a single water molecule, a Na+ ion, or a Cl ion, through the (9,9) and (7,7) CNTs are calculated. As shown in Fig. 6(a) and (b), for the CNTs with zero dipole moment at the rim, the energy barrier of moving a single water molecule through either (9,9) or (7,7) CNTs is extremely low. Similar results have been found by Corry et al.,28 who observed that water-molecule passage encounters negligible energy barriers in bare (n, n) CNTs for n > 5. Such a low energy barrier is consistent with fast water flow in CNTs. Likewise, the energy barrier for Na+ ions is only 0.8 kcal mol−1 in (9,9) CNTs, as the CNT allows the entire hydrated sodium to pass through without distorting its first solvation shell. In other words, Na+ ions transport almost barrier-free in wide CNTs.28 In contrast, Cl ion passage in (9,9) CNTs encounters a high energy barrier of ∼2.5 kcal mol−1 due to the larger hydration shell than that of Na+. When the pore becomes narrower, the energy barrier for both ions greatly increases. The energy barrier of Cl ions in (7,7) CNTs is nearly 3 times greater than that in (9,9) CNTs, and the energy barrier of Na+ ions also increases to 2 kcal mol−1. This illustrates the reason why the salt rejection is only 53% through (9,9) CNTs at 800 MPa but reaches 85% in (7,7) CNTs. Fig. 6(c) and (d) present the PMFs of moving a Cl ion through (7,7) and (9,9) CNTs with different dipole moments. For a small charge of QC = +0.05e, both CNTs entail similar energy barriers as that in the case of zero dipole moment, and thus, the salt rejection efficiency for the QC = +0.05e-charged CNTs is similar to that for the non-functionalized CNTs. The (7,7) CNT only requires a charge of QC = −0.215e to approach 100% salt rejection, as reflected by the sharp PMF increase in Fig. 6(d). In contrast, for (9,9) CNTs, the rim charge must be reduced to QC = −0.515e to reach the same energy barrier and achieve a ∼100% salt filtration efficiency at 200 MPa. We also computed the PMFs of water molecules in (9,9) CNTs with different dipole moments, as shown in ESI Fig. S4. Regardless of the CNT charge, water transport always encounters small energy barriers of less than 0.7 kcal mol−1.

image file: c8ta10941a-f6.tif
Fig. 6 Computed PMFs of moving a single water molecule or salt ion through (7,7) and (9,9) CNTs with differently charged rims.

The number of hydrogen atoms anchored at (9,9) CNT rims are 9, while the (7,7) CNT rims have 7 hydrogen atoms. Effects of hydrogen atom number and dipole moment densities on PMFs are studied. The PMFs of moving a single Cl ion through (9,9) CNT with different dipole moment magnitude and density are shown in ESI Fig. S5. Regardless of the dipole moment magnitude, the PMFs through CNT with smaller dipole moment density at the pore rim are lower than those with larger density. The reason can be explained from two perspectives: (1) as shown in the non-dipolar cases (QC = 0), removing hydrogen atoms at the pore rim increases the effective pore area, and thus can reduce the cost of energy to pass through the CNTs; (2) with large pore dipole moment (QC = −0.515e), CNTs with the less dipole moment density exert smaller repulsion forces on the incoming Cl ions, resulting in a lower PMF compared to the case with a denser dipole moment.

The salt rejection behaviour can also be explained by the radial distribution function (RDF), computed by quantifying the occurrence probabilities of water molecules in the vicinity of a single salt ion. A series of RDFs along the z-axis were calculated, covering the entire CNT length. An RDF example is shown in ESI Fig. S6. The salt ion hydration coordination number can be calculated by integrating the first peak. In Fig. 7, the salt ion coordination numbers in narrower CNTs exhibit larger drops in the rim region, indicating higher energy consumption to enter the (7,7) CNTs. For narrow CNTs, more water molecules associated with the salt ion hydration shell need to be stripped off when the salt ion passes through the CNT, giving the higher salt rejection rate in (7,7) CNTs. This phenomenon is clearer for Cl ions because hydrated Cl ions have a larger size and can less easily enter narrow CNTs than Na+ ions. The maximum coordination-number drop for the (7,7) CNTs is 3.1, whereas for (9,9) CNTs, the coordination number is only lowered by 2.1. For Na+ ions, the (7,7) CNTs result in a greater coordination-number decrease than (9,9) CNTs, but the drop is not as conspicuous as that observed for Cl ions.

image file: c8ta10941a-f7.tif
Fig. 7 The ion coordination number along the z-axis for (a) Cl and (b) Na+ ions passing through (7,7) and (9,9) CNTs with zero external pressure and with a rim charge of QC = +0.515e. The shadow area represents the position of the CNT.

Two snapshots of Cl ions are presented in Fig. 8(a) and (d), where the salt ion enters the (7,7) CNT with QC = +0.515e at the rim. To make the transport process clearer, two extra figures with more details were generated based on Fig. 8(a) and (d). Initially, the Cl ion holds 7 water molecules in its first water shell when it enters the pore. However, three water molecules are stripped off from the hydration shell and form new hydrogen bonds with surrounding water molecules. Simultaneously, two water molecules in the center of CNT drag the Cl ion to the permeate side by forming new hydrogen bonds with the remaining water molecules in the first hydration shell. Last, as shown in Fig. 8(d), the Cl ion is only surrounded by four water molecules within the CNT. The transport process is consistent with the Cl ion coordination-number change, as shown in Fig. 7(a).

image file: c8ta10941a-f8.tif
Fig. 8 Snapshots of a Cl ion passing through a (7,7) CNT with no external pressure. The yellow hydrogen atoms hold −0.515e charges (QC = +0.515e), with which hydrogen bonds can be formed with the hydrogen atoms (white colour) of water molecules. (a) A Cl ion with 7 water molecules before entering the CNT. (b) Three water molecules, denoted with a grey colour, move away from the first water shell of the Cl ion due to the interaction with nearby water molecules and the CNT rim. (c) Three water molecules move away, and water molecules in the CNT drag Cl ions along by forming hydrogen bonds with remaining water molecules in the hydration shell. (d) The Cl ion ends up with surrounding water molecules within the CNT.


In this work, the desalination performance of CNTs with tube diameters > 1 nm and with different dipole moments at the pore rim is systematically studied by using classic MD simulations. To investigate the effect of the dipole moment at the rim, the charge values on the carbon atoms at the pore rim and on adjacent hydrogen atoms are systematically changed. CNTs with low dipole moments at the rim have little effect on the improvement in water transport and salt rejection efficiency, whereas CNTs with high dipole moments at the rim yield much better salt rejection performance but reduce water flow. A series of other physical properties, including the PMF, RDF, and oxygen and hydrogen density maps, are computed to further understand the mechanism of water flow and salt ion passage. The effects of pore size and external pressure on desalination performance are also investigated. High pressure is found to have positive effects on water permeability but negative effects on salt rejection efficiency. Water transport in (9,9) CNTs is much faster than that in (7,7) CNTs. However, the salt rejection ability of wider CNTs is worse than that of narrower CNTs. Considering the need for balance between water permeability and salt rejection in the design of membranes, the (9,9) CNTs with large dipole moments at the rim seem to be a better choice. At a high pressure of 200 MPa, the (9,9) CNTs could block more than 95% of NaCl salt ions yet maintain a high water permeability of 10.2 L cm−2 day−1 MPa−1. Under practical working conditions, introducing high-dipole-moment functional groups at the rim of CNTs not only maintains superfast water flow but also provides better salt rejection performance, rendering the functionalized CNTs a promising candidate for seawater desalination.

Conflicts of interest

There are no conflicts to declare.


This work was completed utilizing the Holland Computing Center of the University of Nebraska, which receives support from the Nebraska Research Initiative.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/c8ta10941a

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