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Pressing Carbon Nanotube Triggers Better Ion Selectivity Lijun Liang, Zhisen Zhang, Jia-Wei Shen, and Xiang Yang Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06637 • Publication Date (Web): 15 Aug 2017 Downloaded from http://pubs.acs.org on August 20, 2017

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The Journal of Physical Chemistry

Pressing Carbon Nanotube Triggers Better Ion Selectivity Lijun Liang†, *, Zhisen Zhang‡, *, Jia-Wei Shen§, Xiang-Yang Liu⊥, ‡, * †

College of Life Information Science and Instrument Engineering, Hangzhou Dianzi

University, Hangzhou, People's Republic of China ‡

Research Institute for Biomimetic and Soft Matter, Fujian Provincial Key Laboratory of Soft

Functional Materials, Department of Physics, Xiamen University, Xiamen, 361005, People’ s Republic of China School of Medicine, Hangzhou Normal University, Hangzhou 310016, People’s Republic of

§

China ⊥

Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore,

117542, Singapore



Corresponding authors.

Tel: +65-6516 2812; Fax: +65-6777 6126 (X. Y. Liu) E-mail addresses: [email protected] (L. Liang) [email protected] (Z. Zhang) [email protected] (X. Y. Liu)

ACS Paragon Plus Environment


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Abstract The selective transport of K+ or Na+ in acqueous solutions by biomembrances is highly efficient in ion separation, but hardly achieved by artificial devices. Inspired by the gates in voltage-gated potassium channels, our computational modeling indicate that biomimetic ion selectivity via nanopores can be achieved by membrane-spanning single-walled carbon nanotubes (CNTs) functionalized with carboxyl groups. It follows that the ion selectivity of the membrane-spanning CNTs can be acquired by pressing the functionalized CNT nanopores in the deformable biomimetic nanopores. According to free energy calculations by umbrella sampling, the free energy barrier difference between the permeation of K+ and Na+ through the functionalized CNT nanopores can be up to about 14.0 kJ/mol, resulting in a K+/Na+ conduction ratio around 260:1. The membrane-spanning single-walled carbon nanotubes with mechanically deformable nanopores may be of critical importance in design and fabricate many nanoscale devices and nanofiltration membranes etc.


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1. Introduction Many remarkable biological and ion separation properties have been evolved in biological ion channel through millions of years’ evolution1-3. It provides a great source of natural ion channel to develop bioinspired nanopores with remarkable properties4-7. Biological ion channel could achieve extremely high ion permeability and selectivity by precisely arranged amino acids8-10, which is essential to the life activity. For example, the aquaporin could rapidly transport water molecules but not ions11-13. In the view of the superior ion selectivity in biological nanopores, many attentions have been paid on mimicking these properties in technical applications of protein and DNA by experiments and theoretical calculations14-19. Although there are lots of advantages of biological nanopores with chemical/biological engineering, the biological nanopores always lose their bioactivity outside of the biological settings. Due to the delicate sensitivity of the lipid membrane to the temperature, pH value and salt concentration, the technical applications made from biological nanopores have been strictly limited ex vivo. Nanopore designed from non-biological materials is another promising choice to achieve the function of biological nanopores20-25. For example, the biomimetic graphene nanopores show excellent properties on the selective transportation of the K+ and Na+ ions4, 26. However, these biomimetic nanopores from graphene nanopore could not be directly used in biological system since the membrane structure of lipid could be disrupted by graphene27, 28. Compared to other biomimetic nanopores, the biomimetic nanopores based on CNTs exhibit their special superiority. Sansom et al designed a biomimetic pore via CNTs based on Cav and NavAb channels, which showed Ca2+ favored selectivity29. CNTs functionalized with charged molecular tethers have exhibited voltage gated control of ion transport30. Zhou et al found that the ion conduction could be controlled by a mechanical nanogate based on CNTs 31. Remarkably, the prediction that short CNTs could spontaneously inserted into lipid bilayers and form channels has recently been confirmed in experiment32. Moreover,



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this study showed that CNT channel could transport water, protons, small ions and DNA molecules32. It thus represents a step forward towards the real application of CNTs used as biomimetic nanopore. To realize the functions of ion channel by biomimetic nanopore based on CNT, the molecular level transportation mechanism of ions through functional filter core in ion channel must be well understood. Based on our previous work4, the potassium channel from Streptomyces lividans (KcsA, PDB ID: 1BL8) was selected as a model protein for its relatively simple structure and high selectivity for K+ ions over Na+ ions8. More specifically, KcsA potassium channel has up to 3 order magnitude selectivity for K+ over Na+. Besides experiments, molecular dynamics (MD) simulation has been successfully used to study the solid state nanopore on biology33-37. In this study, MD simulation has been used to explore nanopore with ion selective function and investigate their ion selectivity mechanism. In KcsA channel, the ion filter core is composed by the polarized carbonyl groups from the glutamic acids. Therefore, the bioinspired nanopores based on membrane-spanning CNT (14, 14) was constructed by functionalization with two carboxyl groups. With a stronger polarity, the CNT functionalized with carboxyl groups is expected to show functionality similar to KcsA channel. To construct the biomimetic nanopore with high ion permeation and selectivity, the distance between two carboxyl group was tuned by an external force as described in simulation details part, which can be exerted by an atomic force microscope (AFM) tip in experiment. All performed simulations are summarized in Table 1.

2. Methods 2.1 Modeling and system setup CNT (14, 14) with a length of 4.0 nm was selected to make the length comparable to the thickness of lipid bilayer membrane. To mimic the structure of filter core in


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KcsA channel, two carbonyl groups were covalently linked to two carbon atoms in the center of CNT (14, 14) (Figure 1). The functionalized CNT (f-CNT) was inserted into a POPC lipid membrane with 128 lipids. After a 20-ns equilibrium simulation (refer to Figure S1 in Supporting Information for interaction energy between f-CNT and POPC), they were immersed into a TIP3P38 water box (with a density of 1 g/cm3). To create f-CNTs with different pore sizes, constant velocity steered molecular dynamics (SMD) simulations39 were applied to the carbon atoms covalently linked to one carbonyl group, with the carbon atoms covalently linked to the other carbonyl group fixed (Figure 1). Totally 20 systems, in which the distance between two carbonyl groups in f-CNTs varies from 1.41 nm to 0.36nm, were constructed (Table 1 and Figure 2). After that, 0.5 M NaCl and 0.5 M KCl were added into the systems to investigate the K+/Na+ selectivity of the f-CNTs. The total number of atoms was about 41700 for each system, which were contained in a 7.47 × 6.27 × 8.54 nm3 simulation box. After energy minimization and equilibration simulations, 20 ns MD simulation were carried out for each system. The NpT ensemble was used in the simulation with the constant temperature of 310K imposed by Berendsen thermostat40 and the pressure of 1 bar controlled by a semi-isotropic Parrinello-Rahman barostat. A strong electric field with the strength of 40 mv/nm along the z axis was applied to accelerate the transport process of K+/Na+ through the f-CNTs. In all simulations, the partial charges and parameters for the carboxyl groups were taken from the side carboxyl groups of glutamic acid in CHARMM27 force field41. The parameters of carbon atoms that covalently connect to carboxyl group are from reference29, and the parameters for other carbon atoms in CNTs are from previous work42-44

Besides

the

carboxyl

groups,

all

carbon

atoms

in

CNT are

electrically-neutral. Gromacs 4.6.3 package was used to perform all simulations in this study45. The LINCS algorithm and Particle Mesh Ewald methods46 were used in all simulation.



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2.2 Free energy calculations According to the structural symmetry of the f-CNTs, the PMF profiles should present

the

same

symmetry

as

the

structure

of

f-CNTs,

which

is

PMF ( )  PMF ( ) (see Figure S3). The free energy profile (represented by

potential of mean force, PMF) of Na+ and K+ ions passing through four nanopores (Conf-1, Conf-8, Conf-15 and Conf-20) were calculated by umbrella sampling47 along the z axis from -0.2 nm to +2.0 nm (distance to -COO- groups in z axis)48. And the free energy profile for -2.0 nm to 0.0 nm was generated from that of 0.0 nm to +2.0 nm by PMF ( )  PMF ( ) . In each system, 55 equidistant windows with width of 0.04 nm were extracted and a harmonic force constant of 1000 kJ∙mol-1∙nm-2 was used to restrain the ion in each window. For each window, 5 ns simulation was performed. After carefully analysis, the first 2 ns was removed in each umbrella simulation for thermodynamic equilibration, followed by a 3 ns of production run. The PMFs were then unbiased and combined via the weighted histogram analysis method (WHAM)49, 50

. Additional MD simulations only including ions and water molecules were

performed to calculate the binding affinity between K+/Na+ and water molecule. According to the relationship between probability distribution and free energy profile, the binding affinity of K+/Na+ to water molecule was estimated based on the RDFs (g(r)) of water molecules to ions, as expressed in eq.1:

G(r )   RT ln( g (r ) / g (r )max )

(1)

In the eq.1, the global maxima in RDF profiles g(r) max was chosen to be the zero point of free energy, which were g(r)(0.27 nm) and g(r)(0.23 nm) for K+ and Na+, respectively.

3 Results and discussion 3.1 Design of mechanically deformed bioinspired pores


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As mentioned above, many reports have shown that CNT could perform as an excellent candidate for desalination, in which the desalination performance highly depends on the filter size. However, the radius of CNT (m,n) is discrete due to the limitation of CNTs topology. To obtain CNT-based biomimetic nanopores with continuous sizes, pressed f-CNT (14, 14) was used as a model nanopore. The main constituents of ion selective filter core in KcsA channel are carbonyl oxygen atoms. As seen in Figure 1, CNT (14, 14) were functionalized by two carboxylic groups. It’s known that the distance between the nearby oxygen atoms in natural KcsA channel is about 0.31 nm (the smallest nanopore) to 0.42 nm (the largest nanopore)4,6. To acquire the similar function of KcsA channel, the reduction of distance between two carboxylic groups in the f-CNT (14, 14) is necessary since it is around 1.41 nm in the initial structure (Conf-1). Under the external force, f-CNT was deformed and a constriction was formed (Figure 2a). The relationship between the applied force and the distance between the two carboxylic groups are depicted in Figure 2b, which is almost linear in the range that varied from 1.41 nm to 0.36 nm, where the force changes from 0 to 1.2 × 104 kJ∙mol-1∙nm-2. To understand the effect of distance between carboxylic groups on the ion selectivity, 20 conformations with distance interval close to 0.05 nm were extracted (Table 1).

3.2 Primary test of ion conduction in f-CNTs under strong electric field To primary explore the ion-selective performance of f-CNTs, 50 ns MD simulations were performed for each of the 20 systems with an extremely strong electric field (40mV/nm), in which the electric field was used to accelerate the conduction process of K+/Na+ in the f-CNTs. Then, the ions permeation numbers are extracted (Table 2). In the largest one (Conf-1), the ion conduction for K+/Na+ is 15:11, and it increases to 9:2 in the smallest one (Conf-20). The results in Table 2 indicates that the K+/Na+ conduction bias turns into significant when the distance reaches 0.66 nm (Conf-14, 16:5). With the deceasing of pore size in f-CNTs, most of the f-CNTs become more



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favorable to the conduction of K+ than that of Na+. It should be pointed out that the K+/Na+ ratio in Table 2 is provided by 50-ns trajectories, which is due to insufficient sampling of ion conduction events. To further confirm the ion conduction bias of f-CNTs, 200-ns simulations were carried out for the following four systems: Conf-1(1.41nm), Conf-8 (0.95nm), Conf-15 (0.58nm) and Conf-20 (0.36nm). As seen in Figure 3, the ion permeation events of K+ and Na+ ions conduction in Conf-1 is 69 and 31. It is 64 and 28 permeation events for K+ and Na+ passing through Conf-8. With the decrease of distance to 0.58 nm, the ion permeation events of K+ and Na+ is 6 and 3 in Conf-15. With further reduction of distance to 0.36 nm, the ion permeation events for K+ and Na+ is 10 and 2 in Conf-20. The long time trajectories confirmed that the ion permeation events roughly decreased with the decrease of the distance between two carboxylic groups in f-CNT. The ion selectivity for K+/Na+ slightly changes with the decrease of the distance from 1.41 nm to 0.58nm. However, the ion conduction bias increased when the pore size decreased (Conf-20). Thus, it’s confirmed that Conf-20 exhibits a discrimination between K+ and Na+. The ion discrimination is close to the biomimetic nanopore from O-doped graphene sheet4. In the filter core of KcsA channel, the distance between oxygen atoms is from 0.31 nm to 0.42 nm in four binding layers. In this work, the distance between two carboxylic groups in Conf-20 is 0.36 nm, making it possible that the f-CNT Conf-20 could exhibit the similar ion selective function of KcsA channel. Further investigation shows that the permeation processes of K+ and Na+ passing through Conf-20 are different. In Figure 4, the conduction processes of K+ and Na+ passing through Conf-20 are captured. From Figure 4a to 4c, it could be found that a single K+ ion could relatively easily permeate through Conf-20. However, a single Na+(i) ion would be trapped (Figure 4d) by the carboxylic groups in Conf-20, which could attribute to the strong attraction between oxygen atoms and Na+ ion4. The Na+(i) could not get through of the filter in Conf-20 until the Na+(ii) ion knocking on it (Figure 4e). Under the knock-on effect, the Na+(i) ion could get rid of the attraction of the oxygen atoms in Conf-20 (Figure 4f). This knock-on permeation mechanism of


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Na+ ion has been uncovered in the permeation of Na+ ion through Na+ ion channel53,54. The conduction trajectories of K+/Na+ are also extracted to illustrate the conduction difference between K+ and Na+ in f-CNTs (Figure S2 in Supporting Information). It should be reminded that the ion conduction ratio in this section is not the actual ion selectivity of the f-CNTs, since there is an extremely strong electric field applied to the system. The results in Table 2 and Figure 3 do suggest that the discrimination between K+ and Na+ becomes more distinct when the pore size of f-CNTs changing from 1.41 nm (Conf-1) to 0.36 nm (Conf-20). With the ion conduction free energy barrier, the ion selectivity of f-CNTs will be discussed in further details in the following section.

3.3 Free energy profiles of ion conduction in f-CNTs The ion conduction bias of f-CNTs has been shown in above section. It should be noticed that there are fluctuations in the ratio of K+/Na+ permeation events, which could be attributed to the inadequate sampling of ion conduction events. Although the simulation time was then extended to 200 ns for several cases, the permeation events of K+/Na+ are still insufficient for statistical analysis. To obtain a more statistic and quantitative understanding, the free energy profiles of K+ and Na+ conduction in f-CNTs (Conf-1, Conf-8. Conf-15 and Conf-20) were calculated. And the K+/Na+ selectivity of different f-CNTs were then estimated by the difference in free energy barrier. The PMF profiles are shown in Figure 5, Figure S4, S5 and S6. Varied by pore size in f-CNTs, the free energy barrier for K+ and Na+ ions passing through the f-CNT is different. With the largest difference between free energy barrier of K + and Na+, Conf-20 was taken as an example for further analysis. The free energy barrier for Na+ passing through the biomimetic nanopore Conf-20 is 43.4  0.8 kJ/mol, and 29.1  1.0 kJ/mol for K+ (Figure 5 and Figure S5). The difference in free energy barrier is about 14.3 kJ/mol, indicating that there is a remarkable selectivity of K+ over Na+ in Conf-20 f-CNT. Since the initial number of K+ and Na+ is same in our simulation, the



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reaction rates for conduction of K+/Na+ through f-CNT (Conf-20) could be assumed to proportional to their reaction rate constant. Thus, the relationship between ions selectivity and the free energy barrier difference could be described as eq.2, where k is the reaction rate constant, T is temperature (here is 310K), and R is 8.314 J/(mol·K). With a free energy barrier difference of 14.3 kJ/mol, the estimated ratio of selectivity of Conf-20 for K+/Na+ is around 260:1, indicating that the similar ion selective function of KcsA protein could acquire by the f-CNT system. 

G ( Na ) G ( K k (K  ) RT  e  k ( Na )



)

(2)

3.4 Ion selective mechanism of f-CNTs Based on the study of ion selectivity in above section, Conf-20 with high ion selectivity was further investigated to explore the mechanism of ion selective. To illustrate the mechanism, the binding affinity between ions and water and carboxyl group barrier

, ions

in f-CNT Conf-20, and the conduction free energy were introduced, in which the conduction free energy barrier is

caused by the binding affinity difference between ion-water and ion-carboxyl (eq.3). Gconduction  Gcarboxyl  Gwater

(3)

The thermodynamic preferred configurations for K+ and Na+ near the carboxylic groups in Conf-20 are shown in Figure 6. With the small pore size of Conf-20, the ions could bond to more oxygen atoms in carboxyl groups. In the radial distribution function (RDF) profiles of ions to oxygen atoms of carboxylic groups (Figure 6a), the favorable distance between K+ and the oxygen atoms of carboxylic groups is 0.257 nm, and 0.215 nm for Na+. And the configuration details are shown in Figure 6c and 6d. For ion-water system, the favorable distance between K+ and oxygen atom of water molecule is 0.27 nm, and 0.23 nm for Na+ (Figure 6b)4. With a shorter binding distance, the binding affinity of Na+ (11.3 kJ/mol) to water is much larger than that of


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K+ (6.0 kJ/mol). It’s also found that the binding distance between ions and carboxyl group is smaller than that of ion-water, and the binding distance of Na+ is smaller than K+ in the ion-water and ion-carboxyl systems. This is due to the stronger polarity of carboxyl group (than water molecule) and smaller size of Na+ (than K+). With a stronger polarity, the K+/Na+ ions are more favorable to bond with carboxyl groups in Conf-20 than water molecules, resulting in the global minima in PMF profiles (Figure 5), which are the conduction free energy barriers for K+/Na+ (eq.3). Meanwhile, the size of Na+ is smaller than K+, consequently the binding distance between Na+ and oxygen atoms (both in water and carboxyl group) is shorter than that of K+. It should be noticed that the binding distance changes (from water to carboxyl group) of Na+ (0.015 nm) is larger than K+ (0.013 nm). And the electrostatic interaction is inverse correlation with the square of distance, which would cause a larger difference between the binding affinities of Na+-carboxyl (

) and Na+- water (

) for Na+ than K+. Thus,

according to eq.3, the conduction free energy barrier (

) of Na+ should be

larger than that of K+, which is well matched with the free energy profiles in Figure 5. The results suggest that it’s the strong polarity of carboxyl group and binding distance difference (or ion size) of K+/Na+ inducing the ion selectivity function in f-CNT.

Conclusions Bioinspired by the natural potassium ion channel, a series of f-CNTs were obtained under the external force based on the spanning-membrane CNTs in this study. Our results suggest that the ion selectivity function can be achieved from biomimetic f-CNTs. Conf-20 with 0.36 nm distance between two carboxylic groups provides significant K+/Na+ selectivity. Evaluated by free energy profiles, the selectivity of K+/Na+ is around 260:1 in Conf-20. The study revealed that the ion selectivity was mainly affected by the filter size of Conf-20, the strong polarity of carboxyl group and binding distance (or size) difference of K+/Na+. It suggests that the functionalized CNT nanopores could gain similar ion selective function as ion channels. As more



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emerging of ion channel structure and further development of nanopore synthesis method, biomimetic nanopores with desired excellent biological, physical and chemical properties could be expected. Supporting Information Available The interaction between CNT and POPC membrane in the equilibrium MD simulation. The conduction process of K+ (Left) and Na+ (Right) in Conf-20. PMFs with error bar of K+ and Na+ passing through f-CNT (Conf-20). PMFs of Na+ and K+ ion permeating through different f-CNTs: Conf-1 (1.41nm), Conf-8 (0.95nm), Conf-15 (0.58nm) and Conf-20 (0.36nm) are described in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgement We acknowledge the financial support by the National Natural Science Foundation of China (Grant Nos. 21503186, Nos. 21403049 and No. U1405226), China Postdoctoral Science Foundation (2016M592090), “111” Project (B16029), Natural Science Foundation of Fujian Provincial Department of Science & Technology of China (Grant Nos. 2014H6022, 2017J05028), The 1000 Talents Program from Xiamen University, Start Funding of Hangzhou Normal University (Nos. PE13002004041).

Notes The authors declare no competing ﬁnancial interest.

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Figures

Figure 1. (a) Section view of the KcsA channel filter core structure, herein the filter of protein is shown by licorice model, and other part is shown by surf model (white). The potassium ions are shown in pink VDW model. (b) The mechanically deformed f-CNT nanopore based. Carbon nanotubes are shown in licorice model, and carboxylic groups are shown in VDW model.

Figure 2. The deformed f-CNTs with different distance between two carboxylic groups are generated with the change of the force. (a) The schematic of deformed f-CNTs in system. f-CNT is shown by licorice model, the carboxylic groups in CPK model, and the ions in vdW model: K+ (yellow) and Na+ (red). (b) The applied force on f-CNT as the function of the distance between the center of mass of two oxygen atoms in each carboxylic group.



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Figure 3. The number of penetrated ions and water molecules in different f-CNTs as a function of simulation time. The blue square represents the water molecules, the red triangle for K+ ions, and the green triangle for Na+ ions. (a) Conf-1; (b) Conf-8; (c) Conf-15; (d) Conf-20.


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Figure 4. The conduction process of K+ and Na+ in Conf-20. The left part is the conduction process of K+ ion: (a) One K+ in the filter of nanopore; (b) K+ leaves the filter of nanopore; (c) K+ transport through the nanopore. The right part is the conduction of Na+ ion: (d) Na+(i) ion in the filter of nanopore; (e) Na+(ii) ion enters into the filter of nanopore; (f) Na+(i) ion transports through the filter of nanopore under the knock-on effect of Na+(ii).

Figure 5. Potential of mean force of ions passing through f-CNT (Conf-20): the red line represents the free energy profile of K+, and the black one for Na+.



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Figure 6. (a) The radial distribution function (RDF) of Na+ (black line) and K+ ion (red line) to oxygen atoms of carboxylic groups in Conf-20. The 2nd peak at 0.335 nm in RDF of Na+ was caused by the knock-on process, which is consist with Figure 4d-f. (b) The dehydrate PMF of Na+ ion (black line) and K+ ion (red line). The snapshots of stable configuration of K+ (pink) and Na+ (yellow) around carboxylic groups: (c) K+ ion; (d) single Na+ ion; (e) two Na+ ions.


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Table 1. All performed simulations in this study. unbiased MD simulations System

Distance (nm)

Simulation

System

Distance (nm)

Time (ns)

Simulation Time (ns)

Conf-1

1.41

200

Conf-11

0.82

50

Conf-2

1.36

50

Conf-12

0.76

50

Conf-3

1.29

50

Conf-13

0.73

50

Conf-4

1.18

50

Conf-14

0.66

50

Conf-5

1.13

50

Conf-15

0.58

200

Conf-6

1.06

50

Conf-16

0.55

50

Conf-7

0.98

50

Conf-17

0.48

50

Conf-8

0.95

200

Conf-18

0.46

50

Conf-9

0.90

50

Conf-19

0.39

50

Conf-10

0.84

50

Conf-20

0.36

200

PMF calculation System

Ion

Simulation

System

Ion

Time (ns)

Simulation Time (ns)

Conf-1

Na+

55*5

Conf-1

K+

55*5

Conf-8

Na+

55*5

Conf-8

K+

55*5

Conf-15

Na+

55*5

Conf-15

K+

55*5

Conf-20

Na+

55*5

Conf-20

K+

55*5



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Table 2. The ratio of K+ to Na+ passing through different f-CNTs in 50 ns simulation. System

d/nm

K+:Na+

System

d/nm

K+:Na+

System

d/nm

K+:Na+

System

d/nm

K+:Na+

Conf-1

1.41

15:11

Conf-6

1.06

18 : 7

Conf-11

0.82

23 : 10

Conf-16

0.55

4:5

Conf-2

1.36

20:12

Conf-7

0.98

22 : 8

Conf-12

0.76

9:8

Conf-17

0.48

11 : 6

Conf-3

1.29

20:12

Conf-8

0.95

8:6

Conf-13

0.73

20: 9

Conf-18

0.46

9 : 10

Conf-4

1.18

12:10

Conf-9

0.90

21 : 9

Conf-14

0.66

16 : 5

Conf-19

0.39

6:2

Conf-5

1.13

13:11

Conf-10

0.84

13 : 7

Conf-15

0.58

2:1

Conf-20

0.36

9:2


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TOC Graphic



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Figure 1. (a) Section view of the KcsA channel filter core structure, herein the filter of protein is shown by licorice model, and other part is shown by surf model (white). The potassium ions are shown in pink VDW model. (b) The mechanically deformed f-CNT nanopore based. Carbon nanotubes are shown in licorice model, and carboxylic groups are shown in VDW model. 49x15mm (600 x 600 DPI)


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Figure 2. The deformed f-CNTs with different distance between two carboxylic groups are generated with the change of the force. (a) The schematic of deformed f-CNTs in system. f-CNT is shown by licorice model, the carboxylic groups in CPK model, and the ions in vdW model: K+ (yellow) and Na+ (red). (b) The applied force on f-CNT as the function of the distance between the center of mass of two oxygen atoms in each carboxylic group. 49x17mm (300 x 300 DPI)



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Figure 3. The number of penetrated ions and water molecules in different f-CNTs as a function of simulation time. The blue square represents the water molecules, the red triangle for K+ ions, and the green triangle for Na+ ions. (a) Conf-1; (b) Conf-8; (c) Conf-15; (d) Conf-20. 102x71mm (600 x 600 DPI)


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Figure 4. The conduction process of K+ and Na+ in Conf-20. The left part is the conduction process of K+ ion: (a) One K+ in the filter of nanopore; (b) K+ leaves the filter of nanopore; (c) K+ transport through the nanopore. The right part is the conduction of Na+ ion: (d) Na+(i) ion in the filter of nanopore; (e) Na+(ii) ion enters into the filter of nanopore; (f) Na+(i) ion transports through the filter of nanopore under the knock-on effect of Na+(ii). 111x77mm (300 x 300 DPI)



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Figure 5. Potential of mean force of ions passing through f-CNT (Conf-20): the red line represents the free energy profile of K+, and the black one for Na+. 56x39mm (600 x 600 DPI)


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Figure 6. (a) The radial distribution function (RDF) of Na+ (black line) and K+ ion (red line) to oxygen atoms of carboxylic groups in Conf-20. The 2nd peak at 0.335 nm in RDF of Na+ was caused by the knock-on process, which is consist with Figure 4d-f. (b) The dehydrate PMF of Na+ ion (black line) and K+ ion (red line). The snapshots of stable configuration of K+ (pink) and Na+ (yellow) around carboxylic groups: (c) K+ ion; (d) single Na+ ion; (e) two Na+ ions. 82x47mm (300 x 300 DPI)


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