NANO LETTERS
Anomalous Hydration Shell Order of Na+ and K+ inside Carbon Nanotubes
2009 Vol. 9, No. 3 989-994
Qing Shao,† Jian Zhou,‡ Linghong Lu,† Xiaohua Lu,*,† Yudan Zhu,† and Shaoyi Jiang§ State Key Laboratory of Materials-oriented Chemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, People’s Republic of China, School of Chemistry and Chemical Engineering, South China UniVersity of Technology, Guangzhou 510640, People’s Republic of China, and Department of Chemical Engineering, UniVersity of Washington, Seattle, Washington 98195 Received October 7, 2008; Revised Manuscript Received January 3, 2009
ABSTRACT We performed molecular dynamics simulations of the hydration of Na+ and K+ in infinitely long single-walled armchair carbon nanotubes (CNTs) at 298 K. Simulation results indicate that the preferential orientation of water molecules in coordination shells of these two cations presents an anomalous change in the CNTs and causes a diameter-dependent variation for the interaction energy between the cation and water molecules in its coordination shell. In the five CNTs of this work, it is energetically favorable for confining a hydrated K+ inside the two narrow CNTs with diameters of 0.60 and 0.73 nm, whereas the situation is reverse inside the wide CNTs with diameters of 0.87, 1.0, and 1.28 nm. This finding is important for CNT applications in ionic systems that control the selectivity and the ionic flow.
Ionic hydration inside carbon nanotubes (CNTs) is a subject of multidisciplinary interest. There is an increasing interest in applications of CNTs in nanofluidic systems that control the selectivity and the ionic flow. The nanopore of CNT offers advantages over traditional materials in the nanofluidic apparatus because its nearly frictionless wall and wellcontrolled pore size provide the combination of extremely fast flux and high selectivity.1-3 Various CNT-based nanofluidic systems have been envisioned.4-11 The hydrophobic nanopore of CNT is also considered as model of biological channels.12,13 Understanding the ionic hydration in CNTs can contribute to the elucidation about the ionic transfer and selectivity mechanisms inside the ion channels. Among various ions, Na+ and K+ have received special attentions because of their important role in biological and chemical fields. The separation of these two cations is critical in many applications. The hydration of Na+ and K+ is quite similar, making it very difficult to separate them. However, an ion channel filled with water such as KcsA channel can separate K+ from Na+ with extremely high selectivity and fast flux. This high performance of ion channel is recognized to attribute to the characteristic hydration of these two cations in the nanometric channel.14 Furthermore, although the size of K+ is larger than that of Na+, Na+-selective channels are * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +86-25-83588063. Fax: +86-25-83588063. † Nanjing University of Technology. ‡ South China University of Technology. § University of Washington. 10.1021/nl803044k CCC: $40.75 Published on Web 02/10/2009
2009 American Chemical Society
generally wider than K+-selective channels.15 This phenomenon is also suggested to have close relationship with the hydration of these two cations inside nanoscale confinement.16 Considerable researches14,16-28 have been carried out to study the hydration of Na+ and K+ in various biological and synthetic nanopores. Mackinnon and his co-workers29,30 observed that K+ has to lose part of its surrounding water molecules inside the filter of KcsA channel. Their studies suggest that this stripping of the coordination shell is important for the high K+-selectivity of this channel. Several groups found the similar stripping for the coordination shells of Na+ and K+ inside CNTs and other nanopores.16,21,31-33 This stripping induces the enthalpy and entropic changes that affect the ion selectivity and flux inside the narrow nanopore.33,34 They also found that this type of stripping only occurs in quite narrow CNTs. A CNT with diameter close to 1.0 nm is already large enough for an ion such as Na+ or K+ to enter with no water molecules leaving the coordination shell.33,34 These studies have improved our understanding about the hydration of Na+ and K+ and the mechanisms of transport and separation of these two cations in channels. However, several important issues about the hydration of Na+ and K+ in CNTs remain unaddressed. One of our recent simulations has shown that in a (10, 10) CNT the preferential orientation of water molecules in the coordination shell of these two cations differs considerably from that in bulk solution.28 Previous studies have shown that this shell order
Table 1. The Lennard-Jones Parameters and Partial Charges for Ions,38 Water Molecule (SPC/E),37 and Carbon Atom of CNT28 ions
site
σ/nm
ε/kJ mol-1
q/e
Na+ K+ Cl-
0.333 0.493 0.442
0.0116 0.00137 0.493
1.000 1.000 -1.000
OW HW
0.317 0.000
0.650 0.000
-0.8476 0.4238
C
0.355
0.293
0.000
water
CNT
is relevant to the hydration of Na+ and K+.35,36 Then this shell order variation of Na+ and K+ could affect their hydration significantly. Furthermore, it has to be noted that the (10, 10) CNT in which we discovered the shell order variation is in the scale of CNTs where the hydration of Na+ and K+ were suggested to remain intact.27 Thereby, although the energy barrier for the ion entering is nearly zero in the CNTs with diameters around 1.0 nm,33,34 the interaction energy between the ion and water molecules may change profoundly due to the confinement, which may be affected by the CNT diameter and ion type. The goal of this study is to understand the hydration of Na+ and K+ inside the CNT with diameter around 1.0 nm, especially the diameter effect on the shell order variation and its related consequence on the interaction energy between the ion and water molecules. We are also interested in comparing the shell order variations of Na+ and K+ inside CNTs, and the related impacts on the hydration of these two cations. To tackle these issues, we performed molecular dynamics (MD) simulations of hydration of Na+ and K+ inside five single-walled infinite armchair CNTs with diameters of 0.60, 0.73, 0.87, 1.0, and 1.28 nm at 298 K. We used the SPC/E model37 for water molecule and the ions are treated as the charged Lennard-Jones (L-J) sites.38 The single-walled CNT is formed by folding a graphite sheet to a cylinder with each carbon atom of the nanotube treated as a neutral L-J interaction site. The potential energy of intermolecular interactions is described as a combination of L-J 12-6 potential and a columbic potential
[( ) ( ) ]
U(rij) ) 4εij
σij rij
12
-
σij rij
6
+
qiqj rij
(1)
where rij is the distance between atoms i and j, qi is the partial charge assigned to atom i, and εij and σij are energy and size parameters obtained by Lorentz-Berthelot combining rules, where σij ) (σi + σj)/2 and εij ) (εiεj)1/2. Table 1 lists the L-J parameters and the partial charges used in this study. The exact description of solvent density in the CNT is an important issue for the simulation. Several previous studies applied the bulk density in their simulations.21,31 However, our recent simulation showed that the aqueous density inside CNTs differs from the bulk phase and is dependent on the CNT diameter.39 Our recent simulation also showed that the assumption of bulk density may affect simulation results profoundly.28 Because the study of Lakatos et al.24 showed 990
that the adsorption amount of water molecules inside the CNT is not affected by the ion existence at infinite dilution at ambient condition, we gained the equilibrium solvent density in the CNT at 298 K from the simulation of pure water-CNT systems. It can be found that the solvent densities are different inside the CNTs with different diameters, as listed in Table S1 in Supporting Information. It is known that in high concentration solution, an ion pair is easier to form, which may make the observations of hydration of the individual ion challenge. To avoid this effect, the lengths of CNTs with different diameters were different, making sure that every CNT contains considerable number of water molecules and the low ionic concentration inside. The corresponding lengths of the CNTs with diameters of 0.60, 0.73, 0.86, 1.0, and 1.28 nm are 24.6, 27.1, 20.0, 14.2, and 8.4 nm, respectively. The corresponding ionic concentrations in the five CNTs are listed in Table S1 in Supporting Information. The length of z dimension of the simulation cell equals the length of CNT. The lengths of x and y dimensions of the simulation cell are both 7.5 nm. The whole CNTelectrolyte system, including the CNT and the confined electrolyte solution, was placed in the middle of the simulation cell with the axial direction of CNT align with the direction of z dimension of the simulation cell and the rest space of the simulation cell is filled with vacuum. The periodic boundary conditions in the x and y dimensions do not really work because there are no interactions between mirrors in these two dimensions. The periodic boundary condition works only in the z dimension. The long-range electrostatic interactions were computed with particle mesh Ewald method,40 and the short-range van der Waals forces were calculated within a cutoff distance of 1.0 nm. Cl- is used to keep the system neutral. The initial distance between the cation and the anion is at least 4.0 nm to avoid the formation of ion pair. Figure S1 in Supporting Information shows the schematic for the simulation cell of NaCl in the (10, 10) CNT as an exemplary. Table S1 n Supporting Information lists the details of all 10 simulation systems. MD simulations were performed in a NVT ensemble with GROMACS (version 3.3.1).41 For all simulated systems, after the energy minimization and 1.0 ns MD run with integral step of 2.0 fs for equilibrium, another 3.0 ns MD run was carried out with integral step of 2.0 fs and the coordinates were saved every 0.1 ps for the further analysis. No ion pair was observed during the simulation. The other simulation details are the same as our previous work.28 Figure 1 shows the ion-oxygen radial distribution functions (RDFs) of Na+ and K+ inside the five CNTs and bulk solutions. We can observe that for both Na+ and K+, although the profile shape varies inside various CNTs, there are always an obvious first maximum and a nearby minimum for each profile. This maximum and minimum indicate that the coordination shell of these two cations exists inside CNTs. Table 2 lists the positions of the first maximum (rmax) and minimum (rmin) of profiles inside the five CNTs and bulk solution. We can find that, in all the five CNTs, rmax and rmin for Na+ are 0.25 and 0.32 nm, respectively, agreeing Nano Lett., Vol. 9, No. 3, 2009
Figure 1. Ion-oxygen RDFs for (a) Na+ and (b) K+ inside various CNTs and bulk solution.
Table 2. Position of First Maximum (rmax), First Minimum (rmin) for the Ion-Oxygen RDFs for Na+ and K+ and Coordination Number (Nc) of Their First Coordination Shells in CNTs and Bulk Solutions Na+ diameter/nm 0.60 0.73 0.87 1.00 1.28 bulk
K+
rmax/nm
rmin/nm
Nc
rmax/nm
rmin/nm
Nc
0.23 0.23 0.23 0.23 0.23 0.23
0.32 0.32 0.32 0.32 0.32 0.32
4.5 5.6 5.4 5.6 5.7 5.2
0.27 0.27 0.27 0.27 0.27 0.27
0.34 0.34 0.34 0.34 0.34 0.34
4.0 5.6 6.7 6.6 6.2 6.2
well with the corresponding bulk values observed in this work and the simulation results of others.35,36 The same feature is observed for the confined K+. This consistency indicates that the coordination shell sizes of these two cations inside CNTs are the same as that in the bulk solution and inert to CNT diameter. Table 2 also lists the coordination numbers (Nc) of Na+ and K+ in CNTs and bulk solution, which are calculated according to the numeric integration of the corresponding RDF profiles in Figure 1. Consistent with the simulation of Corry,33 we only find the significant reduction of Nc for Na+ inside the (7, 7) CNT with diameter of 0.60 nm. Nc of Na+ is 4.5 inside this CNT, 0.7 smaller than that in the bulk solution. The diameter of the widest CNT in which Nc of K+ reduces significantly is 0.73 nm, larger than that for Na+, probably due to the relative larger coordination shell size of K+. As listed in Table 2, Nc of K+ are 4.0 and 5.6 inside the CNTs with diameters of 0.60 and 0.73 nm, respectively, 2.2 and 0.6 smaller than the bulk counterpart. In the other CNTs, Nc of either cation is similar to that in bulk solution. This observation indicates that the incomplete first coordination shell, considered as one of the main contributions of energy change and ion-related function,33,34 does not occur in the CNT with diameter larger than 0.73 nm for these two cations. On the basis of the above investigation, the hydration of Na+ and K+ in CNT with diameter around 1.0 nm seems to be identical to that observed in bulk solution, as suggested by Shannon et al.27 However, we observe a diameter-dependent variation for the preferential orientation distributions of water molecules Nano Lett., Vol. 9, No. 3, 2009
in the coordination shell of Na+ and K+ inside these five CNTs. To study this shell order, we defined an angle R between the dipole moment of water molecule and the ion, as illustrated in Figure 2a. Figure 2b,c shows the distributions of cos R for the shells of Na+ and K+ inside the five CNTs and bulk solution. Consistent with previous simulation,36 the distribution profiles for the two cations in bulk solution have maxima at -1, implying that the water molecules in the coordination shell have their oxygen atoms point to the ion and hydrogen atoms away from the ion. For either Na+ or K+, the profile maximum positions in all the five CNTs are the same as that in the bulk solution, indicating that the water molecules still prefer to have their oxygen atoms point to the ion inside CNTs. Although with the same position, the maximum value varies considerably inside the five CNTs. As shown in Figure 2b, the maximum values of Na+ inside the five CNTs with diameters of 0.60, 0.73, 0.87, 1.0, and 1.28 nm are 0.168, 0.105, 0.069, 0.066, and 0.075, respectively. Comparing with that in bulk solution (0.092), we can find that the maxima inside the CNTs with diameters of 0.60 and 0.73 nm are larger than that in bulk solution, whereas those inside CNTs with diameters of 0.87, 1.0, and 1.28 nm are smaller. As to K+, we can observe in Figure 2c that maximum values in the CNTs with diameters of 0.60, 0.73, 0.87, 1.0, and 1.28 nm are 0.145, 0.085, 0.030, 0.018, 0.026, and the one in bulk solution is 0.056. The same as that of Na+, the maxima of K+ inside the two narrow CNTs are larger than that in bulk solution, and those inside the three wide CNTs are smaller than the bulk one. This observation indicates that there might be two types of CNT confinement effects on the shell order. Inside the three relatively wider CNTs, the confinement decreases the shell order, while the shell order is enhanced inside the two narrow CNTs. Additionally, we find that the maximum values of both Na+ and K+ are smallest inside a moderate CNT with diameter of 1.0 nm, indicating that there might be a nonmonotonically diameter-dependent variation for the shell order in the CNTs. To further investigate the variation of shell order, we applied the parameter named hydration factor (F) proposed by Zhou et al.,36 as defined in eq 2. According to the definition, a random orientation distribution of water mol991
Figure 2. The coordination shell order. (a) Definition of angle R; (b) distributions of cos R for Na+ in CNT and bulk solution; (c) distributions of cos R for K+ in CNTs and bulk solution; (d) hydration factor F for Na+ and K+ inside CNTs as a function of diameter. The corresponding F for Na+ and K+ in bulk solution are 0.73 and 0.56, respectively, agreeing well with the previous simulation results.28,36
ecules would result in a value around 0.14 for F, and closer to 1 indicates higher order of coordination shell. F)
firstshell N-1
