Fast water transmission of zigzag graphyne-3 nanotubes

Abstract

We report the molecular dynamics simulation of water molecules permeating quickly through the wall of zigzag graphyne-3 nanotubes (G3NT (N, N) (N = 2, 3, 4, and 6)), the water fluxes are about 5 orders of magnitude higher than that of the commercial forward osmosis membranes. High water fluxes are attributed to the capillarity of G3NT (N, N) nanotubes and the huge osmotic pressure difference between feed solution and draw solution. Furthermore, the nanotube walls can highly intercept salt ions. The counter diffusion phenomenon, where water molecules permeate through the nanotube wall from draw solution side (inside) to feed solution side (outside) of G3NT (N, N) nanotubes, is much weaker than that of two-dimensional monolayer graphyne-3, so higher net water fluxes can be achieved. Besides, the diffusion rates of water molecules along the axis of G3NT (N, N) nanotubes are about 2 orders of magnitude higher than that of water molecules without limited space owing to the formation of a hydrogen bonding network. G3NT (N, N) nanotubes are promising to be used in water treatment or controlled drug release.

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1 Introduction

The excellent properties of carbon nanotubes (CNTs) have motivated substantial research efforts.^1,2 Due to the potential applications of carbon nanotubes in drug delivery, biomimetic selective transport of ions, etc., dramatic enhancement of pressure driven flows of water through CNTs has gained considerable attention. The pressure driven flow velocities of water in multiwalled carbon nanotube (MWNT) membrane pores of 7 nm inner diameter are about 5 orders of magnitude higher than that predicted from Newtonian Flow using the Hagen–Poiseuille equation,^3,4 while the measured water flow exceeds the values calculated from continuum hydrodynamics models by more than 3 orders of magnitude in double walled carbon nanotube (DWNT) pores with an inner diameter of 1.6 nm.⁵ Many molecular dynamic (MD) studies have investigated the diffusion and filling mechanism in CNTs as well as the velocity profiles under an external driving force.⁴ A substantial amount of work has been carried out with the impregnation of CNTs in polymer host matrix to act as flow channels.^6–10 However, there are still significant challenges that have to be addressed to align the CNTs, to reinforce it in a suitable host matrix without disturbing the alignment and inhibiting the agglomeration, to open the tips preferentially and to scale up favorably.

Graphyne, with natural form of regular holes, is thermally and chemically stable, and the mechanical properties of monolayer graphyne are high enough to endure the stress and deformation in clamping process and the external pressures in reverse osmosis (RO).^11,12 Compared with graphene, regular triangle holes distribute uniformly on graphyne, size of these holes can be precisely controlled by increasing specified numbers of acetylenic bonds among adjacent six-membered rings. Particular electronic properties of graphyne have motivated previous theoretical, experimental and quantum-scale studies,^13–16 and its mechanical properties have also been explicitly determined.^17–21 Characteristics in structure and excellent physicochemical properties of monolayer graphyne have motivated researchers to study its separation performance for desalination, nanofiltration or other membrane separation processes. Some reports have shown successful synthesis of flake graphyne structures.^22–24 Most strikingly, Li et al.²⁵ reported that graphdiyne films with the area of 3.61 cm² have been successfully fabricated on the surface of copper via a cross-coupling reaction using hexaethynylbenzene. Just as the rapid development in synthesis and fabrication of large-area graphene,^26–29 successful fabrication of larger single-layer graphyne with higher quality and lower energy consuming is also promising. Existing researches on separation performance of graphyne are mainly by molecular simulations due to vacancy of large-area graphyne. Several researchers^30–33 have studied the separation mechanism of monolayer graphyne-N for N = 3, 4, 5 or 6. Their results show that the main factors affecting water permeability and salt rejection rate include nanopore diameter, hydrogen bond formation, salt concentration of the solution, hydrostatic pressure, and hydrophilic–hydrophobic property of the membrane and salt ions.

As CNTs can be regarded as the rolling up of two-dimensional graphene through different ways, graphyne nanotubes (GNTs) can also be regarded as the rolling up of two-dimensional graphyne. Compared with CNT, the wall of GNT is with natural form of regular triangle holes, so the doping of the wall is possible and some molecules can permeate through the wall.^34,35 Some researchers have studied the mechanical strength, electrical performance,^34–36 thermal conductivity,^37,38 hydrogen storage performance,³⁹ or electrochemical properties⁴⁰ of graphyne nanotubes. However, transmission of water molecules or salt ions through graphyne nanotube has not been studied. Li et al.⁴¹ have successfully prepared graphdiyne' nanotube (GDNT) arrays through an anodic aluminum oxide template catalyzed by Cu foil. Other types of graphyne nanotubes are also promising to be prepared in the near future. Graphyne nanotubes are promising to be used as support substrate of filter membranes for water treatment,⁴² used as carriers in controlled drug release just as CNTs⁴³ or used in other fields. In this paper, we studied the transmission characteristics of graphyne-3 nanotubes for water molecules and salt ions with different nanotube diameters and the mass concentrations of draw solutions.

2 Simulation details

Graphyne-3 membranes were rolled to be nanotubes, diameters of zigzag (N, N) graphyne-3 nanotube, shorthand for G3NT (N, N) (N = 2, 3, 4, and 6), were respectively 12.4 Å, 19.3 Å, 25.0 Å, and 37.4 Å. Pure water was chosen as feed solution, sodium chloride solutions of different mass concentrations were adopted as draw solutions. Draw solution was filled inside of G3NT (N, N) nanotube, while feed solution was filled outside. Unit cell of graphyne-3 and a snapshot of the simulation system have been shown in Fig. 1.

Fig. 1 (a) Unit cell of graphyne-3; (b) side view of the simulation system; (c) front view of the simulation system (note: gray balls are on behalf of the carbon atoms, sodium ions and chloride ions are displayed as purple and green balls, all of them are demonstrated in the form of CPK; the oxygen atoms and hydrogen atoms of water molecules are respectively displayed as red balls and white balls).

Smart Minimizer method was used to perform energy minimization for 5000 steps so as to get the lowest-energy conformation. Smart Minimizer method combines the steepest descent, conjugate gradient, and Newton methods in a cascading manner. Molecular dynamics simulation was running for 2 ns with the time step of 1 fs. To try to meet actual FO (forward osmosis) operating conditions, NPT ensemble was chosen and thermostat was used to keep the temperature constant at 298 K. Nose mode was adopted to perform the fixed temperature calculation. Berendsen method was adopted to keep external pressure constant at 1 atm. COMPASS force field⁴⁴ was used and charges were distributed by forcefield assigned method, Ewald method was used to calculate electrostatic and van der Waals effects.

COMPASS is an ab initio force-field. The condensed-phase properties for most covalent models and ionic models (such as graphene, NH₄⁺, HCO₃⁻, CO₃²⁻, H₂O, Na⁺, K⁺ and Cl⁻)^45–48 can be predicated accurately using this force-field. Moreover, the water properties calculated from COMPASS force-field were in good agreement with the experimental results and the calculated results based on the SPC/E model which can accurately reproduce the structure of liquid water in a wide range of temperature.⁴⁹ Hence this force-field was used to predict the structure and properties of the systems in this work.

3 Results and discussion

3.1 Water flux and rejection rate

Fig. 2 shows that when the inside and the outside of G3NT (2, 2) nanotube are both filled with pure water, water molecules can still permeate through the nanotube wall from the outside to the inside of the nanotube. It is capillarity^50,51 of G3NT (2, 2) nanotube that leads to this phenomenon and the corresponding water flux is as high as 66.29 L cm⁻² h⁻¹. Pure water is filled outside of the G3NT (2, 2) nanotube and sodium chloride solution is filled inside. The mass concentrations of the sodium chloride solutions are respectively 5%, 10%, 15%, 20% and 26.5%. The calculated water fluxes that water molecules permeating through the wall from the outside to the inside of G3NT (2, 2) nanotube are all higher than 100.00 L cm⁻² h⁻¹, which are about 5 orders of magnitude higher than that of commercial forward osmosis membranes.^52–54 The water fluxes are much higher than that of two-dimensional graphyne-3 membranes when same feed solution and draw solutions are used. It can be concluded that the presence of sodium ions and chloride ions has a significant effect on water molecules permeating through the wall of G3NT (2, 2) nanotube from its outside to inside.

Fig. 2 Water fluxes and rejection rates of Na⁺ and Cl⁻ through the wall of G3NT (2, 2) nanotube when different mass concentrations of draw solutions are respectively filled in the nanotube.

Fig. 3 shows that the water flux of G3NT (3, 3) nanotube is as high as 203.69 L cm⁻² h⁻¹ and it is much higher than that of G3NT (2, 2) nanotube, the water fluxes of G3NT (4, 4) nanotube and G3NT (6, 6) nanotube are respectively 176.83 L cm⁻² h⁻¹ and 175.41 L cm⁻² h⁻¹. The changing trend of water fluxes is mainly attributed to the different osmosis pressure differences between the outside and the inside of the nanotube. It can be seen from Fig. 2 and 3 that the wall of G3NT nanotube can achieve a rejection rate of 100% for both Na⁺ and Cl⁻.

Fig. 3 Water fluxes and rejection rates of Na⁺ and Cl⁻ through the wall of G3NT (N, N) (N = 2, 3, 4, and 6) nanotubes when draw solutions are all sodium chloride solutions of the mass concentration of 5%.

3.2 Counter diffusion of water molecules

When sodium chloride solution with the mass concentration of 5% was used as draw solution, molecular dynamics simulation lasted for 2 ns and the areas of the G3NT (N, N) (N = 2, 3, 4, or 6) nanotube wall for water transmission are the same with each other, the numbers of water molecules passing through the G3NT (N, N) nanotube wall in forward diffusion (from the outside to the inside of G3NT (N, N) nanotube) and in counter diffusion (from the inside to the outside of G3NT (N, N) nanotube) as well as their ratios were listed in Table 1. It shows that these ratios are all within 0.1, which are much smaller than that of the two-dimensional graphyne-3 while the value of the latter is larger than 0.5. It can be concluded that the capillarity of G3NT (N, N) nanotube and the pressure difference between feed solution and draw solution can inhibit the counter diffusion of water molecules. So, the G3NT (N, N) nanotube systems have high water fluxes.

Table 1 Ratios of the numbers of water molecules passing through the G3NT (N, N) (N = 2, 3, 4, or 6) nanotube wall in forward diffusion and counter diffusion

G3NT (N, N)	Forward diffusion	Counter diffusion	Counter diffusion/forward diffusion
G3NT (2, 2)	459	44	0.10
G3NT (3, 3)	709	19	0.03
G3NT (4, 4)	624	25	0.04
G3NT (6, 6)	639	44	0.07

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3.3 Hydrated ions and coordination number

Fig. 4 shows the radial distribution function of water molecules relative to sodium ions or chloride ions. The radial distribution function gives a measure of the probability that, given the presence of an atom at the origin of an arbitrary reference frame, there will be an atom with its center located in a spherical shell of infinitesimal thickness at a distance, r, from the reference atom. This concept also embraces the idea that the atom at the origin and the atom at distance r may be of different chemical types, say α and β. The radial distribution function iswhere x_i is the mole fraction of chemical type i, N_i is the number of atoms of chemical type i, N is the total number of atoms, and ρ is the overall number density.

Fig. 4 Radial distribution function: (a) water molecules around sodium ions (b) water molecules around chloride ions, in G3NT (N, N) (N = 2, 3, 4, or 6) nanotube.

Calculate the coordination numbers of hydrated sodium ions and hydrated chloride ions using formula (2) and list them in Table 2.

Table 2 Coordination numbers of the first and the second hydration layer of the hydrated sodium ions and hydrated chlorine ions in G3NT (N, N) nanotube for N = 2, 3, 4, or 6

G3NT (N, N)	Hydration layer	Coordination number
		(Na^+)	(Cl^−)
(2, 2)	First	4.15	4.98
	Second	9.34	11.56
(3, 3)	First	5.10	6.25
	Second	12.89	18.01
(4, 4)	First	5.37	6.79
	Second	14.38	19.16
(6, 6)	First	4.27	5.76
	Second	13.05	16.93

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Results show that both the coordination number of the first hydration layer and the second hydration layer of hydrated sodium ions are smaller than that of the hydrated chloride ions. Limited space of G3NT (N, N) (N = 2, 3, 4, or 6) nanotube have different effect on the distribution of water molecules around sodium ions and chloride ions. Changing the diameter of G3NT (N, N) nanotube will lead to the change of the coordination numbers of hydrated sodium ions and hydrated chloride ions in the first hydration layer and in the second hydration layer.⁵⁵

3.4 Transmission of water molecules and salt ions along the axis

Based on the mean square displacement curves of water molecules, sodium ions and chloride ions, as shown in Fig. 5, we calculate the diffusion coefficient using formula (3) and formula (4), and list the results in Table 3. Results show that the diffusion coefficient of water molecules along the axis of G3NT (N, N) (N = 2, 3, 4, or 6) nanotube is ∼2 orders of magnitude higher than that of water molecules without limited space (the diffusion coefficient of water molecules without limited space is about 2.09 to 2.66 × 10⁻⁹ m² s⁻¹ (ref. 56)). The diffusion coefficient of sodium ions and chloride ions along the axis of G3NT (N, N) nanotube are a little less than that of sodium ions and chloride ions without limited spaces (the diffusion coefficient of sodium ions and chloride ions without limited spaces are about 1.35 × 10⁻⁹ m² s⁻¹ and 2.06 × 10⁻⁹ m² s⁻¹, respectively^57–59).

Fig. 5 The MSD–time curves when water molecules or salt ions diffuse along the axial direction of the G3NT (N, N) (N = 2, 3, 4, or 6) nanotube: (a) water molecules (H₂O); (b) sodium ions (Na⁺); (c) chloride ions (Cl⁻).

Table 3 Diffusion coefficient of water molecules (H₂O), sodium ions (Na⁺), and chloride ions (Cl⁻) along the axis of G3NT (N, N) (N = 2, 3, 4, or 6) nanotube

G3NT (N, N)	Diffusion coefficient (10^−9 m^2 s^−1)
	H2O	Na^+	Cl^−
G3NT (2, 2)	51.98	1.09	1.04
G3NT (3, 3)	35.10	0.02	0.01
G3NT (4, 4)	115.54	1.13	1.64
G3NT (6, 6)	64.88	0.20	0.25

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As the extension of simulation time, water molecules in the fill space gradually diffuse to the two ends of G3NT (N, N) nanotube. We take a snapshot showing the transmission of water molecules inside the fill space in G3NT (2, 2) nanotube when molecular dynamics simulation has lasted for 1 ns, as shown in Fig. 6(a) and (b). Fig. 6(a) shows that when the inside of the G3NT (2, 2) nanotube is filled with sodium chloride solution of which the mass concentration is 5% and the outside is filled with pure water, water molecules are connected by hydrogen bonding network and diffuse continuously along the axis to one end of G3NT (2, 2) nanotube. Fig. 6(b) shows that when the inside and the outside of the G3NT (2, 2) nanotube are both filled with pure water, water molecules are far away from each other and cannot form hydrogen bond network. So it can be concluded that the capillary of G3NT (N, N) nanotube and the pressure difference between feed solution and draw solution are beneficial to the formation of hydrogen bonding network among water molecules in G3NT (N, N) nanotube and so lead to fast transmission of water molecules along the axis of G3NT (N, N) nanotube.

Fig. 6 A diagram which shows how water molecules diffuse along the axial direction of the G3NT (2, 2) nanotube. (a) The inside of the G3NT (2, 2) nanotube is filled with sodium chloride solution of which the mass concentration is 5% and the outside is filled with pure water; (b) the inside and the outside of the G3NT (2, 2) nanotube are both filled with pure water.

4 Conclusions

We have shown that water molecules can permeate fast through the walls of G3NT (N, N) (N = 2, 3, 4, and 6) nanotubes, the water fluxes are all higher than 100.00 L cm⁻² h⁻¹, which are ∼5 orders of magnitude higher than that of commercial forward osmosis membranes. Both the capillarity of G3NT (N, N) nanotube and the pressure difference between feed solution and draw solution lead to these high water fluxes. The counter diffusion phenomenon that water molecules permeate through the nanotube wall from the inside (filled with draw solution) to the outside (filled with feed solution) of G3NT (N, N) nanotube is much weaker than that of monolayer graphyne-3 and that is beneficial to high water flux. Limited space of G3NT (N, N) nanotube has effect on the coordination numbers of hydrated sodium ions and hydrated chloride ions. The diffusion coefficient of water molecules along the axis of G3NT (N, N) nanotube is about 2 orders of magnitude higher than that of the water molecules without limited space. Therefore, G3NT (N, N) nanotubes are promising candidates for support substrate of forward osmosis or to be used in nanoscale molecule transport device.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51473097), (51003067).

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