Unidirectional Transport of Water through an Asymmetrically Charged

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Unidirectional Transport of Water Through an Asymmetrically Charged Rotating CNT Milad Khodabakhshi, and Ali Moosavi J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 9, 2017

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The Journal of Physical Chemistry

Unidirectional Transport of Water through an Asymmetrically Charged Rotating CNT Milad Khodabakhshi and Ali Moosavi* Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P. O. Box 11365-9567, Tehran. *Email: [email protected]

ABSTRACT Achieving a high speed, unidirectional water flow through Carbon nanotubes (CNTs) is a key factor in designing novel nanofluidic devices. In this study, utilizing molecular dynamics (MD) simulations, we propose a novel nanoscale water pump for directed water transportation using charged rotating CNT. Two basic conditions for stable water flow, including thermodynamic nonequilibrium and spatial asymmetry, are provided by introducing partial charges on carbon atoms of the channel with asymmetric patterns and its rotation, respectively. We demonstrate that the performance of the water pump is proportional to the gradient of a linear charge distribution and angular velocity of the rotation. Our results indicate that in a constant total charge, there is a linear relationship between water flux and charge difference of the nanotube ends. In addition there is a logarithmic relationship between the water flux and the nanotube angular velocity. In fact, there is no considerable flux when the nanotube is rotating with low angular velocities. However, increasing the angular velocity first increases the flux rate and then leads to its saturation. Furthermore, relationship between the water flux and charge density is investigated. The results can be used in designing future CNT-based pumps and high-flux nanoscale systems for practical applications.

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1. INTRODUCTION

Directed transport of fluid through nanochannels plays an important role in a wide range of industrial applications including nanofiltration,1–7 seawater desalination8–14 and drug delivery.15–18 Due to high surface to volume ratio, confined water molecules in nanoenvironments, usually exhibit different behaviors compared to those of bulk systems.19–21 Consequently, CNTs have attracted extensive attentions due to their small size and exclusive characteristics. For the first time, in 2001, Hummer et al.22 found that water molecules could pass through a hydrophobic (6, 6) CNT. Since then, the hydrodynamics properties of CNTs turned into an interesting subject for researchers. In particular, there are several studies on the conduction of water23 and ionic solutions24–26 through the CNTs. Water transportation through CNT based water pumps is of great importance for designing molecular machines and devices. However, in order to continuously transport water, the equilibrium and spatial symmetry of the system should be broken properly.27,28 Because of the problems arising from their nanoscale dimension, it is hard to engage a suitable method with the ability to pump fluid across CNTs. Both hydrostatic29 and osmotic30 pressure gradients are wellknown approaches for pumping water through nanochannels. In such approaches, the need for a large water reservoir or mechanical pumps as a pressure gradient provider is inevitable. Therefore, because of the problems arising from the small size of the carbon nanotubes, these methods fail in CNTs. In recent years, various novel methods have been developed for water pumping in order to solve the problems associated with these conventional methods. Although a water molecule is neutral as a whole, considering the partial charges on O and H atoms, it is a dipolar molecule. Accordingly, using MD simulations, numerous methods have been proposed to pump water by

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applying external electric fields. Rinne et al.31 used a time dependent electric field, generated by electrodes with oscillating charges adjacent to the CNT in order to pump water. Wang et al.32 examined water pumping through a single-walled carbon nanotube in the presence of a linear electric field gradient. A vibrating charge adjacent to a CNT, with an off-center deformation will satisfy the asymmetry and nonequilibrium of the system, and leads to water pumping.33 Zhu et al.34 investigated the relationship between the direction of a uniform external electric field and the flux rate. They demonstrated that there is a critical angle (θC) between the external field and the nanochannle axis, which optimizes the pumping ability. In addition, molecular dynamics studies have predicted that using various mechanical motions in a proper way can provide the required conditions for water pumping. Water pumping is feasible by means of nanoscopic propellers with molecular blades decorated on the outer surface of a rotating CNT.35 A small portion of the pretwisted wall of a CNT can also be used for the purpose of water transportation.36 Zhou et al.37 developed a nanoscale water pump driven by mechanical vibrations where both the equilibrium and the spatial symmetry of the system are broken by a periodic excitation at an off-center position. Besides, nanopumping is also achieved by surface Rayleigh travelling waves of CNT.38 Other approaches are also reported for water pumping such as chemical gradient,39 thermal gradient,40,41 rotating electric and magnetic fields42 and revolving charges.43 Apart from the above mentioned methods, water pumping can also be achieved by the rotation of a CNT. In an experiment, the rotational motion of nanoparticles in an aqueous solution could be achieved using optical tweezers.44,45 When rotation is used to pump water, the symmetry of the system must be broken properly. Feng et al.46 found that a rotating chiral CNT can be used as a water pump. Similarly a rotating chiral CNT modified by vacancies, is used for seawater desalination.47 However, it is worth mentioning that the poor performance of pristine CNTs in 3



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fluid transportation restricts their applications in many crucial fields such as water purification. Therefore, finding a more appropriate way to satisfy the asymmetry of the system could improve the pumping efficiency and its potential applications. The present study purposes a novel efficient nanosized system to drive a controllable unidirectional water flow, such that no external pressure gradient is required, using MD simulations. Compared to energy-intensive conventional methods, which are costly to maintain, water pumping could be achieved by this design more efficiently. The equilibrium and symmetry of the system are broken by the rotation of an armchair CNT and an asymmetric charge distribution, respectively. The dependence of the flux rate on the charge distribution and angular velocity is investigated. The findings help to elucidate the connection between various surface charge patterns and the pumping capacity of a rotating CNT.

2. METHODOLOGY

Using MD simulations, this study investigates the effective parameters on water conduction through charged rotating CNTs. The simulation box is presented in Figure 1a with a volume of 3

60 60 73 Å containing 4794 water molecules. The number of water molecules is chosen such that the water density inside the occupied volume is equal to 0.997 gr⁄cm3 . The atoms of both graphene sheets have been kept fixed in all the directions and are electrically neutral. A (9, 9) armchair CNT with length and radius about 30 Å and 6.104 Å, is positively charged. In practice, charging nanotubes could be achieved through the controlled functionalization methods.48,49 The charge distribution satisfies the relation, qi

q1

i

1 qd , where q1 is the first term and qd is

the general term of the arithmetic progression and qi is the charge of each carbon atom of the i-th ring counter from the left. The CNT has 26 rings. The charge difference between the two ends of

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the CNT is equal to Δq

q26

q1 . The CNT is rotating around its central axis, with angular

velocity ranging from 0 ps-1 to 3.181 ps-1. All MD simulations are performed using LAMMPS package.50 Periodic boundary conditions are employed in all directions. Here, water molecules are modeled using the CHARMM version of the TIP3P model,51 where the charge quantities on O and H atoms are -0.834e and +0.417e, respectively.

Figure 1. (a) Snapshot of the simulation framework. Two reservoirs are connected by an uncapped (9, 9) CNT embedded between two graphene sheets. The water molecules are depicted by balls in red and white for oxygen and hydrogen, respectively. (b) Zoomed side view of the CNT used in the simulations. The graph above the diagram indicates the charge on each carbon atom of the corresponding ring of charged carbon atoms below. The CNT has 26 rings. The quantity of charge and angular velocity are denoted as q and ω, respectively.

Internal geometry of each water molecule is fixed using the SHAKE algorithm. The CHARMM27 force field52 is used to calculate the interatomic interactions between O and H atoms. In this study interactions between all particles are calculated based on following relationship 5



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4

(1)

where k is Coulomb’s constant, q represents the signed magnitude of the charges, r denotes the interatomic distance, ε stands for the potential energy well, and finally σ is the zero-across distance of the potential. The values for ε and σ are supposed to be εO-O 3.15 Å, εO-H

0.0836 kcal mol-1 , σO-H

1.77 Å, εH-H

0.1521 kcal mol-1 , σO-O

0.0461 kcal mol-1 , and σH-H

considering pair interaction between H and O atoms. While they are defined as εC-O mol-1 and σC-O

0.4 Å

0.0937 kcal

3.19 Å for the C-O interaction, based on experimental observations.53 The cutoff

distance is considered as 10 Å for the Lennard-Jones (LJ) interactions. The particle-particle particle-mesh (PPPM) method is used when computing the long-range electrostatic interactions with a cutoff distance equal to 12 Å and a root mean square accuracy of 10-4. It should be noted that in this method the introduced uniformly distributed background charges do not affect the net force acting on charged particles in such systems.54 Therefore, PPPM method can be used to investigate water transportation in this study. All the simulations are carried out in the constant volume and temperature (NVT) ensemble. A Nosé-Hoover thermostat is used to keep the water temperature at 300 K. The velocity of the center-of-mass is subtracted before calculating the temperature. The neighbor list is updated every time step. A time step of 2 fs is used and the data are collected every 4 ps. Duration of each simulation is 25 ns where the last 20 ns are used for the analysis.

3. RESULTS AND DISCUSSION

3.1. Potential Energy Surface (PES) Between Water and the CNT. When the CNT is electrically neutral, the hydrodynamics behaviors of water are dominantly affected by LJ 6


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interactions. In the case of charged CNTs, Coulomb electrostatic interactions also affect the water behaviors. In order to gain a better understanding of the water behavior inside a charged CNT we first need to calculate the potential energy of water inside the CNT. Considering that the CNT is electrically charged, the water molecules should be considered as dipole moments. The potential of a water dipole induced by the charge of each carbon atom, can be calculated by superposing the point charge potentials between carbon atoms and the charges of the water cos β

.

(2)

where qC represents the charge of the carbon atoms, m stands for the dipole moment per water molecule, rCW is the distance between carbon atoms and water molecule, β denotes the angle between the dipole moment and rCW and U represents the electric potential of the carbon atoms inside the CNT. Here, to investigate the effect of the system asymmetry, we take four different charge patterns into account. Parameters for the charge distribution are selected based on Table 1 where q increases by +0.025e in each step. The distribution of water orientation inside the CNT, which is the averaged value for the angle between the water dipole vector and the Z direction, was obtained from the MD simulations. The water orientation with respect to the nanotube axis depends on the surface charge density. Therefore, the PES averaged over the distribution of water orientations is plotted at angular coordinate in the cylindrical coordinate system of the CNT, θ 0, as a function of axial, Z, and radial, R, coordinates in Figure 2. To this purpose, a water molecule is moved inside the inner space of the channel and the net potential energy is measured. As shown in Figure 2, when the CNT is uniformly charged the PES is symmetric along the CNT. By increasing the charge difference, the minimum of the landscape becomes deeper and shifts toward the right-side of the CNT. Therefore, the potential difference along the CNT increases, as a result,

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system symmetry is broken. Furthermore, analyzing the water density profile inside the CNT for maximum value of q reveals that it reaches its maximum at the radius of 3.0 Å, which is consistent with the radius of minimum potential energy. Thus, the PES is also presented at this radius as a function of θ and Z (see Figure 2e). It is observed that there is a sinusoidal relationship between the potential energy and , due to the hexagonal lattice structure of the CNT. Table 1. Charge distribution parameters for the (9, 9) CNT with the length of 30 Å at the same total charge. The total charge is equal to Sq 18.954e. q1 (e)

qd (e)

0.0405 0.0280 0.0155 0.0030

0.000 0.001 0.002 0.003

Δq (e) (q26 q1 ) 0.000 0.025 0.050 0.075

3.2. Dynamics of the System. Here, we employ the dragging theory to investigate the pumping behaviors induced by the rotation of an asymmetrically charged CNT. In general, we can assume that Udip r,θ,z,ω,t, q1 , qd is the potential energy of a water dipole inside the CNT. Since the Coulomb interaction is long-ranged, all the water molecules inside the CNT should be considered in the calculations. However, water always forms layered structures inside the CNT. Therefore, for simplifying the calculations, we can calculate the potential energy of the water molecules only for the radial positions of these layers. The number and position of the layers depend strongly on the radius of CNT and the amount of charge on it. The force acting on water molecules can be calculated by differentiation the potential with respect to the Z axis.

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Figure 2. PES as a function of R and Z at θ 0 for (a) Δq 0e, (b) Δq 0.025e, (c) Δq 0.050e and (d) Δq 0.075e. (e) PES as a function of Z and θ at R 3.0 Å for Δq 0.075e.

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, , , ,

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(3)

The total force on the water molecules due to the nanotube is calculated by

(4) where j is the number of the water layers inside the CNT, L is the length of the CNT and ρ is the number density of water molecules, which can be obtained from the profile density of water in the simulations. When the CNT rotates, it makes the adjacent water molecules rotate because of the friction between water and CNT. Considering the rotation of the CNT, the dipole moment per water molecule, can be assumed as

(5) where α represents the polarizability per water molecule and τ stands for the water relaxation time. It should be noted that the final expression for the total force should be time independent after the steady state condition. Assuming a linear relationship between total force and axial velocity, we obtain

,

,

,

,

(6)

where γ is the friction coefficient of the channel per unit length. It is worth-mentioning that γ depends on the interaction strength between water and the CNT. As a result, by increasing the charge density, the friction coefficient increases too. The cumulative flux, defined as the difference between the number of water molecules that exit from one side of the CNT and the other side (they have entered previously through the opposite side), is calculated based on

10


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, ,

,

(7)

where N is the average number of water molecules inside the nanotube. The flux rate, defined as the difference between the number of water molecules per nanosecond that exit from one side of the CNT and the other side (they have entered previously through the opposite side), is formulized by

,

,

25

5 20

(8)

The average friction coefficient was measured by applying an external force to all of the water molecules

(9)

3.3. Water Transportation Behaviors inside the CNT

3.3.1. Charge Difference Effects. In this section, we examine the effects of the charge difference of the CNT ends on the flux rate in a constant total charge. The angular velocity of the rotation is ω

0.628 ps-1 and the total charge, Sq , is equal to +18.954e. Parameters for the charge

distribution are selected based on Table 1.

By rotation of the CNT, the inside water molecules rotate consequently and the axial force which comes from the derivative of the potential energy drives them inside the CNT. The water molecules always tend to move toward the direction of the potential energy decrement. The potential energy along the CNT is symmetric, when it is charged uniformly. Therefore, the water flux is equal for both directions and the net water flux is zero. In contrast, by increasing the charge

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difference, the system symmetry will be broken and the resultant potential difference leads to a directed water flow.

Figure 3. (a) Cumulative flux inside the (9, 9) CNT with a length of 30 Å with an angular velocity of 0.628 ps-1 as a function of time for different charge differences between the two ends of the CNT. (b) Flux rate inside the (9, 9) CNT with a length of 30 Å with an angular velocity of 0.628 ps-1 as a function of charge difference between the two ends of the CNT.

According to Figure 3b, the water flux increases linearly with Δq. In general, the water flux depends on the average number, N, of water molecules, the average water nanotube friction coefficient and the total axial force QR ∝ NF z ⁄γ . As shown in Figure 4a, the first peak of the water density profile sharpens as Δq increases. This indicates that the water molecules would prefer to stay in vicinity of the CNT wall at stronger radial interaction strengths. Therefore, it is expected that both the average number, N, of water molecules and the average friction coefficient increase. It was found that N increases linearly with Δq, approximately 1.83% in each step. Moreover, as shown in Figure 4b, the average friction coefficient increases also linearly with Δq. Generally, the friction coefficient increases quadratically with surface charge density.55 Therefore, 12


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by increasing Δq, the friction coefficient increment in the right-side of the CNT is slightly more than the friction coefficient decrement in the other side. As a result, despite of the constant total charge of the CNT, the average friction coefficient is expected to increase with Δq for the range of Δq studied.

Figure 4. (a) Water density profiles inside the (9, 9) CNT for different charge differences between the two ends of the CNT. (b) Average friction coefficient per unit length of the (9, 9) CNT as a function of charge difference between the two ends of the CNT.

The final factor is driving force, which could be characterized by the angular velocity of water and the behavior of the potential energy surface. The angular velocity of the adjacent water molecules increases as the partial charge of each ring increases. Therefore, as shown in Figure 5a, by increasing Δq, the angular velocity of water molecules in the left-side of the CNT decreases, and it increases for those of the right-side of the CNT. Nevertheless, since the total charge of the CNT is fixed, the average angular velocity of water molecules inside the CNT is the same for all situations (see Figure 5b). Therefore, the energy transferred to the fluid is approximately the same for all systems. However, the net force, F tot z , acting on the water molecules in the flow direction 13



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depends on the behavior of the potential energy surface. According to Figure 5c, the magnitude of the potential difference along the CNT changes linearly with Δq which causes the driving force to increase linearly with Δq. Thus, since all the effective factors changes linearly with Δq, the assumption of the linear relationship between the water flux and Δq is totally reasonable. Finally, we should note that the total change in N⁄γ is only 3.3% in each step. Therefore, the flux rate dominates by the driving force increment under the conditions studied.

Figure 5. (a) Angular velocity of water along the nanotube length for different charge differences between the two ends of the CNT. (b) Average angular velocity of water molecules as a function

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of charge difference between the two ends of the CNT. (c) Potential energy difference along the CNT as a function of charge difference between the two ends of the CNT.

3.3.2. Effects of Angular Velocity. The rotation of CNT with high angular velocities is a difficult task in practice.44 Therefore, investigating the effect of angular velocity on the water flux to derive the best condition for the nanopump is necessary. In this section, we take a charge distribution with q1

qd

0.002e into account. The dragging theory was used to reproduce the

angular velocity dependence of the flux rate. The equations for ρ, U and then Udip were obtained using numerical approach by fitting the equivalent dada in each layer (at first, U was measured independently in each layer). As the theory predicted, the water flux equals to zero when the CNT is fixed. The reason is that in despite of the asymmetric charge distribution, the system is in equilibrium and the water molecules are positioned in a way that the attractive and repulsive forces between H, O and C atoms are balanced and the total force on water will be zero. When the CNT is rotating, the inside water molecules rotate consequently. A rotating water molecule is always attracted by the stronger interaction and tends to change its pass to the region with lower potential energy. However, the water flux does not increase with the angular velocity and remains negligible in the range of 0 ps-1 to 0.187 ps-1. This is because of the partial charges on carbon atoms. Although the asymmetric charge distribution provides the required conditions for destroying the system symmetry, it increases the interaction strength between water and the CNT. As a result, water molecules are absorbed to the wall strongly and the friction increases. Therefore, rotation of the CNT with low angular velocities cannot provide the required energy to conquer the friction and the flux rate remains negligible. However, according to Figure 6b, the water flux improves by continuing to increase the angular velocity in the range of 0.187 ps-1 to 2 ps-1. As Figure 7a illustrates, the angular velocity of water molecules increases with the increase of the angular 15



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velocity of the CNT in this range. Therefore, the kinetic energy of the water molecules increases in a way that provides the required energy for cancelling the friction force between the CNT and water. However, based on the theory, continuing to increase the angular velocity, leads to reduction in water flux increment rate. By fitting the theory parameters to the results in Figure 6b we can obtain τ

0.17 ps, which considering the lattice structure of the CNT, is approximately in

accordance with the velocity of the rotation at which the pumping becomes inefficient. According to Figure 7b, we also observe a similar behavior in the angular velocity of water for high values of ω. In fact, in high angular velocities, water molecules do not have enough time to respond to the environment and it makes the conditions difficult for water molecules to adapt themselves with the rotating carbon atoms. Therefore, not only achieving high angular velocities is very difficult experimentally, but it also makes the nanopump less-efficient.

Figure 6. (a) Cumulative flux inside the (9, 9) CNT with a length of 3.0 Å as a function of time for different angular velocities. (b) Flux rate inside the (9, 9) CNT with a length of 30 Å as a function of angular velocity, from the simulation (points) and dragging theory (line).

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3.3.3. Charge Density Effects. In this section, we discuss about flux rate inside CNTs under 0.628 ps-1. We take q1

different charge densities for ω

qd into consideration for the charge

distribution where q1 varies from 0e to +0.013e with a step of +0.001e. As shown in Figure 8b, because of the symmetry, water flux is zero for pristine CNTs. In cases of charged CNTs, spatial asymmetry is satisfied and the directed transport of water is achieved. There exists an optimized value of charge density at which the flux rate reaches its maximum value at q1 However, continuing increment in

0.004e.

reduces the pumping efficiency.

Figure 7. (a) Angular velocity of water along the nanotube length for different angular velocities of the CNT. (b) Average angular velocity of water molecules as a function of angular velocity of the CNT.

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Figure 8. (a) Cumulative flux inside the (9, 9) CNT with a length of 3.0 Å with an angular velocity of 0.628 ps-1 as a function of time for different charge densities. (b) Flux rate inside the (9, 9) CNT with a length of 30 Å with an angular velocity of 0.628 ps-1 as a function of charge density. By carefully analyzing the data, it was found that when the charge density increases, four basic factors determine the flux rate through the CNT, i.e. (1) increase in friction, (2) increase in water density, (3) increase in potential difference along the CNT, and (4) increase in, then saturation, of water angular velocity. We explain this part in details in following paragraphs. Figure 9a shows water density profile inside the CNT for different charge densities. The peaks of the density profile sharpen as

increases. This indicates that the water molecules would prefer

to stay in vicinity of the CNT wall at stronger radial interaction strengths. Besides, the radial position of the peaks gets also closer to the wall. It can be observed in Figure 9a that the average distance of the water molecules from the wall decreases gradually with the increase of charge density. With decrement in the distance to the wall, the energy barrier for the water molecules is larger to escape from the channel and, as a result, the water flux decreases. Therefore, by increasing the charge density, both the increment in the charge magnitude of the carbon atoms and the

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decrement in distance of water layers to the wall, lead to lateral force increment between water and CNT. Therefore, as shown in Figure 10, the water nanotube friction coefficient increases nonlinearly with the surface charge density.56 Figure 9b shows the average number, N, of water molecules inside the CNT for different charge densities. Increasing

from 0e to +0.013e results in the increment in the number of water

molecules inside the CNT which contributes in the flux rate increment (eq 8). Under the conditions studied, the pumping force dominates by the water-carbon electrostatic interaction and the rotation of the nanotube. The charge of each carbon atom, qi , increases linearly with increasing q1 . Furthermore, the charge difference between the two ends of the CNT increases by a fixed step of +0.025e. We obtained the average distribution of water orientations along the CNT for different values of q1 from the MD simulations. Therefore, considering the water orientations, we calculated the potential energy of water inside the CNT. It was found that the potential difference along the CNT also increases linearly with increasing the amount of total charge on the CNT. When the charge density increases, slip velocity of water molecules decreases, since the interaction strength between water and the CNT increases. As a result, water molecules rotate faster and the transferred energy to the fluid increases which tends to enhance the flux rate. However, it is obvious that the maximum possible value for the angular velocity of water could be equal to the angular velocity of the CNT. Figure 11a shows the angular velocity of water along the CNT for different charge densities. The angular velocity of water and its change of slope have a higher value in the right-side of the CNT. Therefore, the angular velocity of water increases in the total length of the CNT, until it reaches to the angular velocity of the CNT in the more-charged 19



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half of the CNT. After that, continuing to increase the charge density makes no change in angular velocity of water in this part and only affects the angular velocity of water in the other side. As shown in Figure 11b average angular velocity of water increases with q1 in the range of 0 e to +0.004e. However, there is a reduction in the slope of diagram when we continue to increase q1 .

Figure 9. (a) Water density profiles inside the (9, 9) CNT for different charge densities. (b) Average number of water molecules inside the (9, 9) CNT with the length of 3.0 Å and an angular velocity of 0.628 ps-1 as a function of charge density.

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Figure 10. Average friction coefficient per unit length of the (9, 9) CNT as a function of charge density.

Figure 11. (a) Angular velocity of water molecules along the nanotube length for different charge densities. (b) Average angular velocity of water molecules as a function of charge density.

When q1 increases in the range of 0e to +0.004e, only the first factor reduces the pumping efficiency and the other ones tend to increase the water flux. Thus, the water flux increases. However, with the higher values of q1 , the angular velocity of water molecules becomes saturated. Therefore, an important factor loses its effect on the flux rate increment. Thus, considering the 21



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effect of friction increment, the water flux decreases. Finally, we should note that the water flux has a local increment at q1

0.008e. By analyzing the water density profile from Figure 9a, we 0.008e. In fact, by increasing the interaction

see that the second peak starts to sharpen at q1

strength between water and the CNT, the correlations between the water molecules and CNT surface become longer ranged, which causes the second water layer becomes larger. It can be understood from Figure 2 that the water-carbon interaction decreases by increasing the distance from the wall. Therefore, the friction force in the second layer is less than in the first layer. Moreover, by increasing the charge density, the potential difference along the CNT in the second layer increases. Therefore, by increasing the number of water molecules in the second layer, where the energy barrier for the water molecules to conduct through the CNT is less than the first layer, the water flux improves. As a result, there is a local increment in the flux rate at the point associated with this charge density.

4. CONCLUSION

To summarize, our study revealed that rotating armchair CNTs which have been previously charged with asymmetric patterns could drive water continuously without external pressure gradients. It was found that both the charge pattern and nanotube angular velocity have crucial impacts on pumping behaviors of the nanosized water pump. We investigated that in a constant total charge, due to the direct relationship between water velocity and charge difference along the CNT, water flux increases linearly with the charge difference of the CNT ends. Since decorating the CNT with partial charges enhances the friction of the wall, a specific minimum required force is needed to produce water flux though the CNT. Therefore, with a charged CNT, angular 22


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velocities less than 0.187 ps-1 are not able to create a considerable water flux. While, increasing the angular velocity of the CNT causes increment in water flux. Nevertheless, increasing angular velocity to very high values will not provide enough time for water molecules to adapt themselves with the quick environmental changes and water flux decreases. The water flux increases with the increase of the charge density in the range of q1

qd

0.004e. While, with the higher values of

q1 , surface friction increases and angular velocity of water molecules will also converge to its maximum value. As a result, the performance of the nanotube drops. In addition to water pumping, this mechanism can also be used to pump more general fluids such as salty water, water-methanol solution and drugs. Considering the different behaviors of different kinds of materials inside the charged CNT, it is expected that the designed nanopump system can be applicable in a wide range of different subjects including seawater desalination, drug delivery and nanofiltration.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the Sheikh Bahaei National High Performance Computing Center (SBNHPCC) for providing computing facilities and time. SBNHPCC is supported by scientific and technological department of presidential office and Isfahan University of Technology (IUT). We would like also to thank and appreciate Sharif University of Technology Supercomputer Center and for their support and permission to access supercomputers to perform advanced computations and simulations of the present study.

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TOC GRAPHIC

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Unidirectional Transport of Water through an Asymmetrically Charged

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