Effects of ions on the diffusion coefficient of water

Effects of ions on the diffusion coefficient of water in carbon nanotubes Xiang Gao, Tianshou Zhao, and Zhigang Li Citation: Journal of Applied Physics 116, 054311 (2014); doi: 10.1063/1.4892484 View online: http://dx.doi.org/10.1063/1.4892484 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The effect of hydrogen bonds on diffusion mechanism of water inside single-walled carbon nanotubes J. Chem. Phys. 140, 214507 (2014); 10.1063/1.4879796 Entropy of single-file water in (6,6) carbon nanotubes J. Chem. Phys. 137, 044709 (2012); 10.1063/1.4737842 Highly selective adsorption of methanol in carbon nanotubes immersed in methanol-water solution J. Chem. Phys. 137, 034501 (2012); 10.1063/1.4732313 The environmental effect on the radial breathing mode of carbon nanotubes in water J. Chem. Phys. 124, 234708 (2006); 10.1063/1.2205852 Transport of a liquid water and methanol mixture through carbon nanotubes under a chemical potential gradient J. Chem. Phys. 122, 214702 (2005); 10.1063/1.1908619

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JOURNAL OF APPLIED PHYSICS 116, 054311 (2014)

Effects of ions on the diffusion coefficient of water in carbon nanotubes Xiang Gao, Tianshou Zhao,a) and Zhigang Lib) Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

(Received 6 July 2014; accepted 26 July 2014; published online 6 August 2014) In this work, we investigate the ion effects on the diffusion of water in carbon nanotubes through molecular dynamics simulations. The diffusion coefficient of water molecules Dw in the presence of cations (Naþ and Kþ) and anions (F, Cl, and Br) are calculated by changing the ion concentration. The dependence of Dw on the ion concentration is found highly nonlinear and distinct for different ions. For positively charged systems, as the ion concentration is varied, Dw assumes a maximum under the competition between the number and orientation changes of free OH bonds and the effects of ionic hydration. For negatively charged systems, however, Dw decreases monotonously with increasing ion concentration for F. For Cl and Br, Dw reaches the minima at certain ion concentrations and then gently increases. The different behaviors of Dw in the presence of different anions are caused by the stability change of water hydrogen bonds due C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892484] to ionic hydration. V

I. INTRODUCTION

Fluid flows in nanoconfinements play essential roles in many applications in engineering and science due to the unique properties offered by the fluid-surface interactions.1–5 Water transport in carbon nanotubes (CNTs) is one of the most popular nanofluidic systems and can be used to perform different functions in a variety of systems or processes, such as fuel cells, super capacitors, seawater desalination, and biomolecule separation.6–10 In many applications, water transport is associated with the migration of ions, which could be the products of chemical reactions or generated by the dissolution of electrolytes.11,12 In bulk solutions, ions can significantly change the static structure, hydrogen bond dynamics, and reorientation dynamics of water molecules.13–17 The interaction between ions and water molecules can also lead to the phenomenon of ionic hydration, where an ion is surrounded by a group of oriented water molecules.13 In nanoconfinements, these effects may be coupled with the solid surface and greatly affect the diffusion of water molecules. Previous studies on water and ion transport in nanoconfinements are for neutral systems and mainly focused on the effects of surface and pore size on the diffusion of water and ions, osmosis transport, and electro-osmotic phenomena in nanochannels.1,6,18–36 However, little work has been conducted to understand how the presence of ions changes the diffusion of water molecules in charge non-neutral systems, such as the proton exchange membranes in fuel cells and electrodes in supercapacitors. In these applications, water transport is a critical issue and the role of ions in affecting the diffusion of water molecules requires intensive explorations. In this work, we investigate how ions affect the diffusion coefficient of water Dw in CNTs through molecular dynamics simulations. Systems with pure cations (Naþ and Kþ) and anions (F, Cl, and Br) are studied and Dw at

different charge concentrations are calculated. It is found that the diffusion coefficient of water changes nonlinearly as the ion concentration is varied. For positively charged systems, Dw assumes a maximum, which is higher than that of bulk water, when the cation concentration is increased. For negatively charged systems, the presence of anions reduces the diffusion coefficient of water and the dependence of Dw on the anion concentration depends on the species of the anion. The nonlinear change of Dw is caused by the changes in the number and orientation of free OH bonds near the water-CNT interface and the stability of water hydrogen bond network caused by the formation of ionic hydration shell in the presence of ions.

II. MOLECULAR DYNAMICS SIMULATION

The molecular dynamics (MD) simulations are performed using the LAMMPS package.37 A typical MD system consists of a (16, 16) CNT (2.2 nm in diameter) with length of 36.9 nm, which is filled with 3276 water molecules. The axis of the CNT is in the z-direction, as shown in Fig. 1. Initially, water molecules are placed at face-centered cubic lattice sites inside the CNT. A certain number of cations (Naþ or Kþ) or anions (F, Cl, Br) are introduced into the system by replacing an equal number of water molecules at random locations. The SPC/E model is used for water molecules.38 Ions are treated as charged Lennard-Jones (LJ)

a)

Email: [email protected] Email: [email protected]

b)

0021-8979/2014/116(5)/054311/6/$30.00

FIG. 1. A snapshot of a typical MD simulation system. 116, 054311-1

C 2014 AIP Publishing LLC V


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particles. The water-water and water-ion interactions are described by the LJ and Coulomb potential, ( " ) 6 # XX rij 12 rij qi qj þ ; (1) U¼ 4eij rij rij rij i j where e is the binding energy, r is the collision diameter, r and q are the distance between and charge carried by the interacting oxygen, hydrogen, and ions. The interactions between carbon atoms and water molecules/ions are also modeled by the LJ potential. The Lorentz-Berthelot mixing rule is used to obtain the LJ parameters, for which e ¼ 0:086 kcal/mol and r ¼ 0:34 nm are employed for carbon atoms.39 The parameters for the ions, oxygen, and hydrogen are obtained from Ref. 40. Periodic boundary conditions are employed in all the directions. To prevent the interactions between periodic CNT images in the x and y directions, the CNT is located in a cubic simulation cell, which is 8 nm in the x and y directions. In the z direction, the length of the simulation cell is the same as that of the CNT. The SHAKE algorithm is applied to constrain the angles and bonds of water molecules. The cut-off distance for the LJ and Coulomb potentials is set at 1 nm. The Particle-Particle Particle-Mesh (PPPM) method is used to account for the long range Columbic force. It is noted that this method introduces uniformly distributed background charges in non-neutral systems, which may affect the energy and pressure calculation but do not change the net force on charged particles.41 Hence, PPPM method can be used to study water diffusion in non-neutral systems. Simulations are performed in the (N, V, T) ensemble, where the temperature is maintained at 300 K through a Nose-Hoover thermostat with a time constant equal to 0.1 ps. The time step is 1 fs for all the simulations. After the initialization, the system is relaxed for 200 ps, which is followed by data collection for 2 ns. A snapshot of a typical MD system is shown in Fig. 1. III. WATER DIFFUSION COEFFICIENT

The diffusion coefficient of water molecules is calculated through Dw ¼ lim h½zðtÞ zð0Þ2 i=2t; t!1

(2)

where t is time and h½zðtÞ zð0Þ2 i is the mean square displacement (MSD) of water molecules in the axial direction. Due to the non-wetting property and low friction of the CNT surface, the drift of the center of mass (COM) of water and ions is observed in the simulations. In calculating the MSD, the displacement of COM is considered and the peculiar motion of water molecules is used. The MSD is computed as a function of time and the diffusivity is obtained by linearly fitting the MSD, which is the average of all the water molecules in ten simulations with different initial conditions. Using Eq. (2), Dw of bulk water and that in (16, 16) CNTs are obtained as 2:62 109 m2 =s and 2:33 109 m2 =s, which are consistent with previous work.19,26,38 The diffusion coefficient of water as a function of ion concentration Cion for positively (Naþ and Kþ) and negatively

FIG. 2. Diffusion coefficient of water molecule as a function of ion concentration in the presence of different cations (Naþ and Kþ) and anions (F, Cl, and Br).

(F, Cl, and Br) charged systems are shown in Fig. 2. As Cion is varied from 0 to 5.5 M, which is within the range of electrolyte concentration in some supercapacitors,42 it is seen that Dw behaves quite different for differently charged systems. In the presence of cations, Dw increases with increasing ion concentration at low Cion and then assumes a maximum, which is about 13% and 30% higher than that of pure water for Naþ and Kþ, respectively. After the maximum, Dw keeps dropping as Cion continues to increase, as shown in Fig. 2(a). For negatively charged systems, however, Dw decreases greatly as Cion is increased up to 2.65 M for all the anions. For Cl and Br, Dw reaches the minima at Cion ¼ 2:65 and 3.71 M, respectively, and then slightly increases as Cion is further increased. For F, however, Dw shows a monotonous decrease with increasing Cion , as shown in Fig. 2(b). To understand the nonlinear dependence of Dw on the ion concentration, it is necessary to look into the structural change of water brought about by the CNT surface and ions. Without the presence of ions, it is known that most water molecules interact weakly through hydrogen bonds, which form hydrogen bond networks, as illustrated in Fig. 3(a). Due to the weak interactions, hydrogen bond networks are unstable and always dynamically switch between the formation and breakdown processes. The stability of hydrogen


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FIG. 3. Schematic of hydrogen bond network (a) and the phenomenon of ionic hydration (b) and (c).

bond networks can be measured by the relaxation time of hydrogen bonds, as will be discussed later. Hydrogen bond networks can constrain the motion and therefore reduce the diffusion coefficient of water molecules. There are also dangling oxygen and hydrogen atoms forming free OH bonds, which have higher mobility compared with those involved in the hydrogen bond networks and can enhance water diffusion. Due to the surface effect, the number of free OH bonds per water molecule is usually higher near the wall than that

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around the center of the CNT, as will be shown later. In addition, the orientation of the free OH bonds at the water-CNT interface also affects the mobility of water molecules. When the OH bond vectors are in the radial direction (perpendicular to the CNT surface), the diffusivity of water molecules is promoted because oxygen atoms are far from the CNT surface and the friction at the interface is small compared with the case where OH bond vectors are opposite to the radial direction and oxygen atoms are close to the CNT surface. When ions are introduced into the system, they will interact with water molecules and each ion will be surrounded by a layer or more oriented water molecules, which is termed ionic hydration, as illustrated in Figs. 3(b) and 3(c). The interaction between an ion and its hydration shell (water molecules around the ions) is usually stronger than that of water hydrogen bonds and can greatly reduce the mobility of water molecules. Therefore, for confined water in the presence of ions, the coupled effects of hydrogen bond dynamics, free OH bond distribution, and ionic hydration determine the diffusion of water molecules. In Fig. 2, as the ion concentration is increased, the ionic hydration tends to reduce the water diffusion coefficient. However, the formation of hydration shells also affects the number and orientation of free OH bonds and the stability of hydrogen bond networks. The average free OH bond number per water molecule and the orientation distribution of the free OH bonds close to the surface are shown in Fig. 4 for Kþ and Cl. It is seen that the free OH bond number per water molecule increases with increasing Kþ concentration, especially near the interface, where most of the free OH bonds are located (Fig. 4(a)). Furthermore, the number of OH bonds perpendicular to the CNT surface tends to be dominant as Kþ concentration is increased, as shown in Fig. 4(b). For Cl, however, the number of free OH bonds per water molecule decreases with increasing Cl concentration and the orientation of OH bonds tends to increase the friction at the interface because oxygen atoms are close to the CNT surface (Figs. 4(c) and 4(d)). This is understandable because Cl likes to interact with hydrogen and repels oxygen toward the surface (Fig. 3(c)). Hence, at low ion concentrations, the changes in the number and orientation of free OH bonds due to the presence of cations will enhance the water mobility, while that caused by anions will reduce the diffusion coefficient of water molecules. The distinct dependence of Dw on Cion at low ion concentrations is also consistent with the change of the hydrogen bond network dynamics caused by the ions. In the presence of ions, the stability or the relaxation time of the hydrogen bond network may be changed. A long relaxation time indicates a relatively stable hydrogen bond network and therefore reduced water diffusion coefficient. The relaxation time of hydrogen bonds can be calculated through sr ¼ tc =ln CHB ðtc Þ;

(3)

where tc is the cut-off time and CHB is the correlation function of the hydrogen bond given as16 CHB ðtÞ ¼ hhð0ÞhðtÞi=hhð0Þi;

(4)

where hðtÞ is the hydrogen-bond population variable. hðtÞ¼1 if a tagged pair of molecules are hydrogen bonded at time t,


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FIG. 4. Number of free OH bonds per water molecule at different radial positions and the probability distribution of free OH bond orientation near the CNT surface. (a) and (b) are for Kþ; (c) and (d) are for Cl. The vector r in the insets of (b) and (d) denotes the radial direction.

otherwise hðtÞ¼0. The correlation function represents the probability that a hydrogen bond is intact at time t. The relaxation time of the hydrogen bonds at various Cion values for different ions is shown in Table I. For cations, it decreases first and then starts to increase at Cion ¼1:64 and 3.27M for Naþ and Kþ, respectively, which are consistent with the Cion values at the maxima in Fig. 2(a). For anions, however, sr keeps increasing for Cion up to 2.65M for F, Cl, and Br, which is in line with the drop of Dw at low ion concentration in Fig. 2(b).

TABLE I. The relaxation time sr (in ps) of hydrogen bonds at different ion concentrations. Cion

Naþ

Kþ

F

Cl

Br

0 0.17 1.0 1.64 2.65 3.27 4.6 5.5

7.34 7.11 6.41 6.38 6.44 6.40 6.74 7.18

7.34 7.09 6.41 6.23 6.05 6.01 6.32 6.57

7.34 7.63 9.14 9.93 10.86 11.49 12.27 12.70

7.34 7.59 9.14 9.86 10.29 10.08 9.19 8.45

7.34 7.63 9.14 9.92 10.23 9.98 9.05 8.19

Therefore, at low ion concentrations, although the ionic hydration is apt to reduce the water diffusion coefficient, its direct influence is relatively weak compared with the combined effects due to the changes in the free OH bond and hydrogen bond network caused by ionic hydration. The latter explains why Dw increases and decreases with increasing cation and anion concentrations, respectively, at low ion concentrations, as shown in Fig. 2. As the ion concentration is further increased, the free OH bond number per water molecule appears to be independent of Cion for both cations and anions, especially near the CNT surface, as depicted in Figs. 4(a) and 4(c). This makes the free OH bond effect a minor issue. Hence, the dependence of Dw on Cion , in this case, is mainly determined by the competition between the ionic hydration and the change in hydrogen bonds. It is known that the water hydrogen bond is stronger than the van der Waals interaction but much weaker than the ionic bonds.43 For ionic bonds, the binding strength depends on the species of ions. Following the analyses in Refs. 44 and 45, we calculate the binding energies of hydrogen and different ionic bonds, which are shown in Fig. 5. It is seen that ionic bonds are stronger than the hydrogen bond, indicating that the ionic hydration tends to dominate over the hydrogen bonds in affecting Dw at high


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help the design of nanofluidic systems in certain applications to promote water diffusion. ACKNOWLEDGMENTS

This work was supported by the Collaborative Research Fund of the Hong Kong Special Administrative Region under Grant No. HKUST9/CRF/11G. X. Gao was partly supported by the Postgraduate Scholarship through the Energy Technology Concentration at HKUST. 1

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FIG. 5. Binding energies for hydrogen and ionic bonds.

ion concentrations. For cations, the ionic bond of Naþ is stronger than that of Kþ. This explains why the Cion value at the maximum for Naþ is smaller than that for Kþ in Fig. 2(a). For anions, the ionic bond strength for F is much higher than that of Cl and Br, this justifies the monotonous decrease of Dw for F in Fig. 2(b) as ionic hydration becomes important at high ion concentrations. It is worth mentioning that the radii of the first hydration shell of F, ˚ , respecCl, Br, Naþ, and Kþ are 3.25, 3.9, 4.0, 3.2, 3.8 A tively. Considering the binding energies in Fig. 5, the ions can affect the mobility of molecules within a spherical shell ˚ in radius. of 5 A In Fig. 2(b), the minima and subtle increase in Dw for Cl and Br are related to the relaxation of water hydrogen bond networks. As shown in Table I, sr reaches the maxima at Cion ¼ 2:65 M for Cl and Br, after which sr decreases, indicating that the ion-ion interactions gradually become important and make the hydrogen bond network less stable. This enhances the diffusion of water molecules, considering that the ionic bond strength for Cl and Br is comparable to that of hydrogen bonds. This is why Dw increases slightly for Cl and Br after the minima in Fig. 2(b). It is noted that the ion effects on the water diffusivity in neutral systems are different from the nonlinear behaviors in Fig. 2. In neutral systems, Dw decreases monotonously with increasing ion concentration because the ionic hydration effect dominates and the interaction between the hydration shells of cations and anions reduces the mobility of water molecules.24,27 IV. CONCLUSIONS

We have studied the effect of ion concentration on the diffusion coefficient of water in CNTs. For positively charged systems, Dw assumes a maximum at certain ion concentration. For negatively charged systems, however, Dw decreases monotonously with increasing ion concentration for F. For Cl and Br, Dw reaches the minima at Cion ¼ 2:65 and 3.71 M, respectively, and then increases slightly. The nonlinear changes of Dw were explained based on the variations of free OH bonds and hydrogen bond dynamics caused by ionic hydration. The findings in this work may


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