Coupling Transport of Water and Ions Through a Carbon Nanotube

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Coupling Transport of Water and Ions Through a Carbon Nanotube: The Role of Ionic Condition Jiaye Su, and Decai Huang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01851 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 14, 2016

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The Journal of Physical Chemistry

Coupling Transport of Water and Ions Through a Carbon Nanotube: The Role of Ionic Condition Jiaye Su*, Decai Huang Department of Applied Physics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China. *

Electronic mail: [email protected]; [email protected]

Phone:+86-025-84315875 ABSTRACT:

Control of water and ion transport through nanochannels is of

primary importance for the design of novel nanofluidic devices. In this work, we use molecular dynamics simulations to systematically analyze the coupling transport of water and ions through a carbon nanotube in electric fields. We focus on the role of ionic conditions, including the salt species and concentration, which can significantly regulate the ion and further the water transport. We find that the coupling of water-anions is stronger than water-cations, and thus anions play a dominant role in determining the water transport. Specifically, the water and ion flux both exhibit a linear increase with the field strength, in agreement with recent experimental observations; while the water and ion translocation time show a linear and power law decrease, respectively, yielding to the Langevin predictions. These results strongly depend on the salt species, demonstrated by the ion binding. More surprisingly, with the increase of salt concentration, the anion flux displays a maximum behavior, inducing a similar maximum for water flux; while the cation flux increases almost linearly. Our results reveal deep insights into the coupling transport of water and ions, especially the important role of ionic condition, and are helpful for the design of desalination, ion separation and high flux nanofluidic devices.

INTRODUCTION Water is not only the matrix of life but also the matrix of life itself, since it plays a key 1

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role in biological activities. It has been well-recognized that water is transported in and out of cell membranes by specific protein channels, governed by their charged residues.1 During the past decade, considerable effort has been made on the dynamics and thermodynamics of water transportation based on carbon nanotube (CNT) models, both in simulations2-8 and experiments.9-12 The water flow rate through CNTs is found to be several orders of magnitude faster than the conventional Hagen-Poisseuille prediction, depending on the CNT diameters13 This is because CNTs not only have regular structures with controllable size but also have frictionless interior surface,14,15 making themselves as fast water transporters. Meanwhile, the water-water interaction is stronger than that of water-CNT, which could be a partial reason for fast transportation, since the liquid-channel interaction plays a nontrivial role during the liquid transport.16,17 Ions are also essential elements for biological activities. Similar to water but more surprisingly, some ions are also expected to transport through protein channels in single-file, rather than hydrated clusters.18 However, in a general sense, ions should be hydrated and the transport of ions in nanochannels can be described by the known Poisson-Nernst-Plank (PNP) equation.19 In some recent experimental studies, the translocation of single DNA20 or nanoparticle21 through a nanochannel has been successfully detected by ion current signals. This is because when a molecule enters the nanochannel, it displaces an amount of electrolyte solution equivalent to the molecule volume, leading to a detectable pulse in the current−time recordings, which makes single molecule detection feasible. Therefore, understanding the transport dynamics of ions is not only helpful for us to uncover some biological phenomenon but also useful for the design of novel molecular detection devices. Normally, when ions are presented in water, the motion of ions should be coupled to water molecules due to the Coulomb drag.22 Inevitably, when a hydrated ion moves through a nanochannel, some water molecules will be also driven through it.23,24 A recent theoretical study showed new mechanism on the blockage of water flow through narrow CNTs by cations,25 which agrees well with experimental observations.26 Actually, the electroosmotic phenomenon has been paid great attention 2


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in recent years due to its huge applications.27 In particular, previous experimental work have made great effort on the ion transport through CNTs, where some common results are established, such as the linear relation between ion current and electric field, as well as power behaviors for the current and salt concentration.20,26,28 A very recent experiment showed detailed power law scaling behaviors for current and salt concentration in different CNT geometries.29 Simulation work also revealed similar linear and power law behaviors for ion current.24,30 Although previous experiments and simulations greatly enhanced our knowledge on the transport of water and ions, as far as we know there are still some fundamental problems unclear. For example, most of previous work focus on the transport of monovalent salts, such as NaCl and KCl, polyvalent salts are rarely considered. Furthermore, our understanding on the coupling relation between water and ions is still rather poor. Actually, if we can control the ion transport we may also control the water transport and even design water pumps. Herein, we will show by molecular dunamics simulations that, the water transport is strongly coupled to ions through a carbon nanotube in electric fields. We focus on the role of ionic conditions, including the salt species, from monovalent to polyvalent and concentration, which can well regulate the ion and water transport.

MODEL AND SIMULATION METHOD As shown in Figure 1, the simulation system contains a CNT (10,10) with length of 2.56 nm and diameter of 1.35 nm, embed in two graphite sheets (5.1×5.1 nm2), 3136 water molecules and some ions. An external electric filed along the channel direction (+z) was applied to drive the ion through the channel and water will be dragged by ions. Herein, we focus on the role of ionic conditions, such as the salt species and concentration. To consider salt species, we simulated three different salt solutions, from monovalent to polyvalent, namely NaCl, CaCl2 and LaCl3, where the number of Cl- is fixed as 60, and Na+, Ca2+, La3+ are 60, 30, 20, respectively. We also changed the field strength for these three systems. To consider the salt concentration, we used NaCl system under a given field strength. It appears that the transport properties of 3



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water and ions should strongly depend on the CNT size, as shown by previous work.13,16,24,29,30 Our current work focus on the effect of ionic conditions, and thus we do not study the CNT size further, which needs huge computational resources. We have actually made some tests before choosing the present CNT size, especially the CNT diameter. For smaller CNTs, ions can hardly enter and we may not have good statistics, and for larger CNTs when ions can freely enter, the confinement effect will almost disappear, similar to bulk solution. Thus, we chose a moderate CNT that could have appropriate confinement effect on hydrated ions. All MD simulations were carried out at constant volume and temperature (Nose-Hoover coupling) with Gromacs 5.0 simulation package.31 The TIP3P water model was used.32 Amber 03 force field was used to describe the carbon and ion interactions33 and the missing parameters for La3+ was from a previous work.34 The particle-mesh Ewald method was used to treat the long-range electrostatic interactions.35 Periodic conditions were applied in all directions. A time-step of 2 fs was used, and data were collected every 1 ps. The carbon nanotube and two graphite sheets were held fixed during the simulations. For each set of system (21 in total), we conducted two independent 125 ns MD runs, and the last 120 ns trajectory was used for data analysis. Standard error bars were estimated by two data points.

RESULTS AND DISCUSSION We show in Figure 2 the water and ion flux as a function of the field strength. Similar to previous work,3-5,16,17 we defined the upflux/downflux as the total number of water molecules or ions per nanosecond conducted through the CNT from bottom/top (-z/+z) to top/bottom (+z/-z), respectively. The net flux is the difference between upflux and downflux. Clearly, ions will only transport either along or against the field direction. Water molecules can be dragged through the channel by both cations and anions, and thus the flux direction depends on the competition between them. Interestingly, as presented in Figure 2a, for the three ionic systems of NaCl, CaCl2 and LaCl3, the water flux have a linear relation with the field strength, which should be due to the same behaviors of ion flux in Figure 2b, since the net water flux is induced by the 4


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dragging of ions. The linear behavior of ion flux is in good agreement with recent experiments20,26,28 and simulations24,30 for NaCl or KCl. We should note that in Figure 2a, the slopes of CaCl2 (97.3+7.1) and LaCl3 (50.6+1.4) are clearly smaller than that of NaCl (218.2+29.2). A larger slope means a higher impact of ion motion on the water transport. As NaCl can be well solved in water, Na+ and Cl- have less binding ability (discussed later), they should have a more profound influence on the water flux. A direct proof is the large slope of Cl- in Figure 2b. It deserves to note that for the three ionic systems, the direction of water flux is always same as Cl- flux, suggesting the dominant role of Cl- in the water flux contribution. There should be at least two reasons for the high impact of Cl- on the water flux. Remarkably, one is the larger Cl- flux compared to cation flux for each of the ionic system. The other is that Cl- itself has more capability of dragging water molecules. For example, for the NaCl system at E=0.1 V/nm, even Na+ flux (0.93 ns-1) is slightly larger than Cl- (0.85 ns-1), the water flux is also in the Cl- flux direction. The larger hydration number of Cl- (7.2 while it is 5.82 for Na+) can well interpret this phenomenon.36 Although the mobility of Cl- is larger than Na+ in bulk solution, according to a previous work,24 inside the CNT (10,10) the ion mobility depends on the field strengths, and Na+ can also has slightly larger value than Cl- at E=0.1 V/nm. For stronger field strengths, the Cl- mobility becomes larger. Thus, some dynamic properties of ions inside nanochannels will exhibit different behaviors from bulk solution. As Cl- plays the dominant role in inducing the water flux, the overall decreasing water flux with the increase of cation valence in Figure 2a can be thus well ascribed to the same behaviors of Cl- flux in Figure 2b. The ultimate reason for the dependence of ion flux on the salt species should be due to different ion binding ability (discussed later). One may also note that at E=0.1 V/nm, the water flux for CaCl2 system is clearly larger than that of NaCl. This should be clearly due to the low value of Ca2+ flux; while for the NaCl system, the Na+ flux is very close to Cl-, where the opposite water flux induced by Na+ greatly reduces the net water flux. Specifically, for the LaCl3 system, La3+ flux is completely zero due to the strong interaction of La3+-Cl5



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and La3+-water. Thus, the water flux is completely induced by the Cl- flux; however, the Cl- flux (or water flux) is at low levels because of the strong binding of La3+-Cl-. Through the above discussion, we should be partially aware of the nontrivial role of ionic condition in the coupling transport of water and ions through the CNT. First, for the three ionic systems, Cl- regulates the water flux and determines its direction. Second, with the increase of cation valence, the overall ion and water flux both decrease and have a linear response to the field strength. Third, La3+ fails to go through the channel and thus, the water flux therein is completely determined by the Cl- flux. We also note that a recent combined MD simulations and density functional theory (DFT) calculations demonstrate new physical mechanism for the ion and water transport through CNTs.25 They found that cations block water flow through (6,6) type CNTs because of interactions between cations and aromatic rings in CNTs; while in wide CNTs, these interactions trap the cations in the interior of the CNT, inducing unexpected open or closed state switching of ion transfer under a strong electric field, which can well interpret recent experimental observations.26 Consequently, besides the ionic conditions in our current work, the ion or CNT diameter should be also a key parameter for the design of novel ion/water nanofluidic devices.24,29,30 The coupling between water and ions suggests the possible usage of given salts to achieve net water transport, which should be helpful for the design of unidirectional nanofluidic devices. In an effort to further elucidate the transport dynamics of water and ions, we present in Figure 3 the average translocation time of individual water and ion as a function of the field strength. Interestingly, the water translocation time exhibits linear decrease or increase with the increase of field strength, in analog to the flux behavior. However, the ion translocation time displays a power law decrease. We have to point out that the water translocation time is averaged from all the water permeation events, i.e., the sum of upflux and downflux (namely the water flow). Thus, the dragging of ion should only have partial effect on the value, since without any ion involved there will be also a large amount of water flow. For example, as shown in Figure 2a, for the LaCl3 system, the induced water flux is only 1.9 ns-1 at E=0.1 V/nm, while the water 6


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flow is 93.2 ns-1. Thus, for this case the effect of ion dragging can be clearly neglected. Remarkably, for the LaCl3 system, Cl- should not have profound impact on the water translocation time or the impact should be covered by the effect of electric field, as translocation time slightly increases with the field strength. For the NaCl and CaCl2 systems, the water translocation time is obviously affected by the ions, since the decreasing behavior follows the ion translocation time. This is because there are large amount of water flux induced by ions. We should note that differs from the LaCl3 system, where the La3+ flux is zero, Na+ and Ca2+ also induces many water flux in the downflux. Hence, the water transport can be more affected by the ions, and the decrease of ion translocation time leads to the decrease of water translocation time. Of particular interest is that, the power law behavior of ion translocation time with the field strength can be actually deduced from the Langevin dynamics. The motion of ion inside the CNT channel along the channel axis direction should obey the one-dimensional Langevin equation = − + () Where m is the ion mass, f=Eq is the electric force on the ion, is the friction coefficient that reflects dissipative forces, and R(t) is the random force exerted by the collisions of solvent molecules with zero mean < R(t)>=0. In a steady state, the averaged acceleration should be close to zero, and thus we have Eq ≈ / ≈ /, where L and denote the channel length and translocation time, respectively. We finally have ~ . As shown in Figure 3b, the five slopes from the power law fittings of the simulation data are close to the Langevin value of -1. Specifically, the slopes of anions are more close to the idea value. The slight larger deviation of cations may be relevant to the complex blocking effect inside the channel.25,26 As we have mentioned above that the dependence of water and ion flux on the ionic condition should be relevant to the binding ability between cations and anions, we counted the ion binding number and present them in Figure 4 as a function of the field strength, where the water and ion occupancy are also given. Note that we calculated the ion binding number for the whole simulation box, since the ion occupancy inside 7



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the channel is very low. Roughly, we define an ion couple when the distance between two nearby ions is smaller than 0.5 nm. As seen in Figure 4a, the ion binding number does not show appreciable dependence on the field strength. With the increase of cation valence, the ion binding number increases remarkably, which affects the ion and water flux significantly, since only free ions can mostly have the opportunity to transport through the channel. As La3+ has 3e charge, the strong binding of La3+-Cl-1 can be well understood. The water occupancy in Figure 4b almost increase linearly with the field strength, since the electric field facilitates filling of hydrophobic channels with water. This result is similar to the previous work on single-file water transport in electric fields,3 and can be well supported from experimental results.10 Therefore, we believe the electric field should be the major reason for the occupancy increase herein. Actually, the electric field can affect the water dipole orientation and arrangement. The water occupancy slightly bifurcates for the three ionic systems, which should be codetermined by the electric field and ion occupancy. This is because at high field strengths, the order of water occupancy for the three systems can be well interpreted by the opposite order of ion occupancy (see Figure 4c). In contrast, at low field strengths, the same order of ion occupancy exists, while the water occupancy are almost same. Thus, the bifurcation of water occupancy should not be solely due to the competition between water and ion. Perhaps high field strength changes the water dipole orientation and arrangement, and then enhances the effect of ion occupancy. As shown in Figure 4c, the overall ion occupancy is rather low, indicating the existence of energy barriers. Actually, the free energy barrier of dragging a hydrated ion into a nanochannel will become zero only if the effective channel diameter is larger than 1.4 nm.37 Consider the Lennard-Jones diameter of water-carbon (0.3275 nm) in the present work, the CNT diameter should exceed 2.0 nm for ions to permeate into the channel freely. Thus, for the current channel (1.35 nm in diameter), the existence of free energy barrier leads to the low ion occupancy. In particular, for the NaCl system, the ion occupancy decreases and saturates with the increase of field strength, since high field strengths result in fast translocation. Therefore, ions will only stay inside 8


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the channel for short durations. However, because of the extremely low occupancy for the CaCl2 and LaCl3 systems, the same phenomenon is not appreciable, where the values for La3+ are completely zero. We further calculated the radial density profiles for water and ions inside the CNT, shown in Figure 5(a). As a whole, the density distributions agree with previous work for partially existed data.38,39 Specifically, the two peaks for water indicates water layer structures inside the CNT, and systematic distributions and water structures for various CNT diameters can be found in the previous work.38 An interesting phenomenon is that all the ion densities have a single peak locating between the two water peaks. Thus, ions will mostly stay away from the channel center and wall. We show in Figure 5(b) the axial density profiles for ions, which can well elucidate the ion concentration polarization (ICP). ICP is a rearrange of ions near membrane surface in electric fields, which is believed to have profound impact on the transport of charged molecules, including water, ions and macromolecules. However, as far as we know, the detailed effect of ICP on the transport of charged species is still a challenge.40-43 This is because the ICP is a result rather than a preset parameter or condition in simulations and experiments, although this phenomenon can be identified easily in experiments. Remarkably, Figure 5(b) demonstrates that the ion density exhibits asymmetric distributions at the two sides of graphene membrane, suggesting an ICP formation. Normally, Cl- has higher density near the upper membrane (z=4.16 nm) for NaCl and CaCl2; however, Cl- for LaCl3 has abnormal higher density near the lower membrane (z=2.0 nm), which should be caused by the strong dragging of La3+. All the three cations have high density near the lower membrane. Thus, the symmetry of ICP can be highly affected by polyvalent ions. Up to now, we have discussed the effect of salt species on the coupling transport dynamics of water and ions. We further investigated the role of salt concentration, since it has a nontrivial impact on the transport of ions and DNAs in experimental work.20,26-29 Because of strong binding effect of Ca2+-Cl- and La3+-Cl-, we then chose the NaCl system at E=0.5 V/nm. We show in Figure 6 the water and ion flux as a function of the NaCl concentration. Surprisingly, the water and Cl- flux both exhibit a 9



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maximum with the same location at around 2 M, suggesting again the dominant role of Cl- in inducing the water flux. The Na+ flux increases almost linearly with the concentration. Remarkably, the transport of Cl- and Na+ should have a complex competition, since they move in the opposite direction. Specifically, as we have discussed above, there should be a free energy barrier for ions to enter the present CNT, which indicates the breakdown of the ion hydration shell, and thus Cl- and Na+ are almost unlikely to pass through each other when they meet inside the channel. We can actually compare the ion flux herein with our previous work for a wider CNT (15,15) with the same length (2.02 nm in diameter), although a charged nanoparticle is involved therein,44 shown in Figure S1 of the supporting information. Note that Figure S1 is not a directly reuse of our previous data, where we showed ion flux as a whole (Cl- and Na+ flux are not divided). The ion flux therein is almost an order larger than the current value, since the free energy barrier for ions to enter CNT (15,15) should be close to zero. Remarkably, for the CNT (15,15), Cl- and Na+ flux have almost same behaviors (power law like), where Cl- flux is also the larger one. Consequently, the thoroughly different flux behavior of Cl- and Na+ in the present work, especially the maximum behavior of Cl- flux should be clearly due to the CNT confinement and complex competition between Cl- and Na+. Theoretically, the ion transport can be described by the known PNP equation19 and in one-dimensional approximation we have:24

Ji = −qi ci µi ENA exp(−∆Fi / kBT) where

qi is the ion charge, ci is the ion concentration, µi is the ion mobility, NA

is the Avogadro constant and

∆Fi is the free energy difference of ion in bulk solvent

and the channel. Herein, if we assume

∆Fi is independent of the salt concentration,

we obtain a linear relation between the ion flux and concentration

Ji ~ ci .

Interestingly, the Na+ flux in Figure 6 yields to this linear behavior. Actually, some previous work obtained similar linear relation but contain the channel geometry.45,46 Nonetheless, some experimental20,28,29,45,47 and theoretical studies24,46 demonstrated 10


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nonlinear behaviors, where a power law is suggested.20,24,28,29 As in these studies the salt concentration is always below 2 M, an exponential relation is suggested in our previous work for similar high concentration range as present, where a power law can also be included for the data before 2 M.44 The power law exponent from experiments is around 1/3,20,28,29 while the simulation value is about twofold larger.24,44 This is because some conditions in experiments and simulations are quite different, e.g., the CNT length in experiments is always up to micrometers that is three orders larger than simulation models. Technically, it is still difficult for MD simulations to consider dilute solutions, such as 0.01 M and below, because the system size is limited by computational abilities. For example, our current system contains 3136 water molecules, when we just add one pair of NaCl, the concentration will be 0.018 M. Thus, in the present work we focus on the range of 0.2~5 M, under which we can well observe the abnormal water and ion flux behaviors. To be concluded, we believe the power law should be a general rule between the ion flux and concentration for the concentrations below 2 M and wider channels. When the channel has confinement effect on the hydrated ions, the flux behaviors will be thoroughly different for cations and anions. The water flux behavior is determined mostly by anions. Specifically, the existence of flux maximum has profound implication on the design of high flux water or ion devices. We also calculated the average translocation time for individual water and ions, shown as a function of the NaCl concentration in Figure 7. The water translocation time exhibits a minimum at around 1 M and then increases linearly with the salt concentration; while both the ion translocation time increase almost linearly. The increasing behavior for ion translocation time should be due to the high binding probability of Na+-Cl- at high salt solutions (shown later). The formations of ion couples should slow down the motion of cations and anions in electric fields. The minimum translocation time for water can be understood since at low salt concentrations, Na+ and Cl- are less binding, and thus their fast conduction can speed up the water transport; however, with the concentration increase Na+ and Cl- become more binding, and the increase of ion translocation time leads to the increase of water 11



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translocation time. We finally present the ion binding number as well as the water and ion occupancy in Figure 8 as a function of the NaCl concentration. As shown in Figure 8(a), the ion binding number demonstrates an excellent power law increase with the salt concentration. The large amount of ion binding number significantly hinders the motion of ions in electric fields, which well supports the results of Figure 7. The power law increase behavior should be due to the fact that at the high salt concentration range in simulation each cation/anion will be binding to more than one anion/cation, where the power law index of 1.86+0.01 may imply the average number. Clearly, in dilute solutions, if each cation/anion is binding to one anion/cation, the ion bound number should increase linearly with the concentration. The opposite change of water and ion occupancy in Figure 8(b) can be well interpreted by the occupancy competition between them, where the increasing behavior of ion occupancy with salt concentration can also be self-evident.

CONCLUSIONS In summary, we have systematically investigated the coupling transport of water and ions through a carbon nanotube in electric fields by the use of molecular dynamics simulations. We focus on the role of ionic conditions, including the salt species (NaCl, CaCl2 and LaCl3) as well as the salt concentration (NaCl). The ionic condition holds great likelihood in the control of ion transport. Due to the strong coupling between water and ions, the transport of water can be thus well tuned. Of particular interest is that the stronger coupling of water-anion leads to the dominant role of anions in the control of water transport. Specifically, both the water and ion flux exhibit linear increase with the field strength, in agreement with the experimental linear behavior of current-voltage;20,26,28 while their translocation times exhibit a linear and power law behaviors, respectively, depending on the salt species. The remarkable dependence of ion binding on salt species should be responsible for these results. The power law behavior of ion translocation time can be well interpreted by the Langevin analysis. 12


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More surprisingly, for the system of NaCl, the flux of Cl- shows a maximum behavior with the increase of salt concentration, inducing a similar maximum of the water flux, where the Na+ flux increases almost linearly. This is thoroughly different from our previous work for a wider CNT channel,44 where the ion flux exhibits a power law or exponential behaviors. Thus the effect of CNT confinement and/or the complex competition between Cl- and Na+ should be the major reason for present results. We also note that in experimental work the salt concentration is mostly below 2 M, and the power law behavior for the current-concentration is a common result.20,28,29 In the present work, we consider the salt concentration up to saturation value, which allow us to observe abnormal transport dynamics. We also presented detailed discussion based on the PNP equation for ion transport. With the increase of slat concentration, the ion translocation time increases linearly; while the water translocation time has a small minimum. The power law increase of ion binding number with salt concentration can interpret these results. As a whole, our simulation results demonstrate the nontrivial role of ionic conditions in the coupling transport of water and ion, which is helpful for the design of novel water or ion nanofluidic devices.

ASSOCIATED CONTENT Supporting Information An additional plot. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGEMENTS This work is financially supported by the National Natural Science Foundation of China (21204093, 21574066, 11574153). The allocated computer time at the National Supercomputing Center in Shenzhen is gratefully acknowledged.

REFERENCES (1) De Groot, B. L.; Grubmuller, H. Water Permeation across Biological Membranes: 13



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Mechanism and Dynamics of Aquaporin-1 and GlpF. Science 2001, 294, 2353– 2357. (2) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water Conduction Through the Hydrophobic Channel of a Carbon Nanotube. Nature 2001, 414, 188–190. (3) Su, J. Y.; Guo, H. X. Control of Unidirectional Transport of Single-File Water Molecules through Carbon Nanotubes in an Electric Field. ACS Nano 2011, 5, 351–359. (4) Li, J. Y.; Gong, X. J.; Lu, H. J.; Li, D.; Fang, H. P.; Zhou, R. H. Electrostatic Gating of a Nanometer Water Channel. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 3687–3692. (5) Wan, R. Z.; Li, J. Y.; Lu, H. J.; Fang, H. P. Controllable Water Channel Gating of Nanometer Dimensions. J. Am. Chem. Soc. 2005, 127, 7166–7170. (6) Liu, B.; Li, X. Y.; Li, B. L.; Xu, B. Q.; Zhao, Y. L. Carbon Nanotube Based Artificial

Water

Channel

Protein:

Membrane

Perturbation

and

Water

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Figures and captions

Figure 1. Snapshot of the simulation system. A carbon nanotube with length of 2.56 nm and diameter of 1.35 nm, combined with two graphite sheets (5.1×5.1 nm2), is embedded in a periodic water box with 3136 water molecules and varying number of ions. Ions are driven through the channel by external electric fields, and water 18


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molecules will be dragged by ions.

(a)

(b) Figure 2. Average (a) water flux and (b) ion flux as a function of field strength. There are three independent simulated systems of NaCl, CaCl2 and LaCl3. The number of Cl- is fixed as 60, and thus the number of Na+, Ca2+ and La3+ are 60, 30 and 20, respectively. The flux is the net number of water or ion transporting through the whole 19



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channel in one direction (either +z or –z). Lines are corresponding linear fittings for data points. Data for La3+ are completely zero. Error bars are shown for two data points (same for the other figures).

(a)

(b) Figure 3. Average translocation time of individual (a) water and (b) ion as a function of field strength. The translocation time indicates the mean traveling duration for water or ion through the whole channel. The black line is corresponding linear fitting for same color data points. Data for La3+ are unavailable due to its zero flux. 20


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(a)

(b)

(c) Figure 4. Average (a) ion binding number, (b) water occupancy and (c) ion occupancy as a function of field strength. The ion binding number is counted for the whole simulation box and roughly two nearby ions is binding when their distance is smaller than 0.5 nm. The ion and water occupancy are referred to the channel interior. Lines in (a) are the average values of data. 21



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(a)

(b) Figure 5. (a) Radial density profiles for water ( / ) and ions ( / ) inside the channel as a function of radial position, and (b) axial density profiles for ions ( / ) as a function of axial position at E=0.5 V/nm. =1.0 g/cm3 is the bulk water density and r=0 denotes the channel center. The position of two graphene sheets are z=2.0 nm and 4.16 nm, respectively.

22


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Figure 6. Average water and ion flux as a function of NaCl concentration. The field strength is fixed as E=0.5 V/nm (same for the following figures). Note that at room temperature the saturation concentration of NaCl is about 5 M.

23



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Figure 7. Average translocation time of water and ions as a function of NaCl concentration.

24


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(a)

(b) Figure 8 Average (a) ion binding number, (b) water and ion occupancy as a function of NaCl concentration.

25



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TOC Graphic

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Coupling Transport of Water and Ions Through a Carbon Nanotube

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