continuous water-water hydrogen bonding network across the ...here, using nonequilibrium molecular...

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Continuous water-water hydrogen bonding network across the rim of

carbon nanotubes facilitating water transport for desalination Yaqi Hou1, Miao Wang2, Xinyu Chen1, and Xu Hou1,2,3,4,5 () Nano Res., Just Accepted Manuscript • https://doi.org/10.1007/s12274-020-3173-2 http://www.thenanoresearch.com on Oct. 12, 2020 © Tsinghua University Press 2020 Just Accepted

This is a “Just Accepted” manuscript, which has been examined by the peer-review process and has been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall TUP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI®), which is identical for all formats of publication.

Address correspondence to First A. Firstauthor, email1; Third C. Thirdauthor, email2

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TABLE OF CONTENTS (TOC)

Continuous water-water hydrogen

bonding network across the rim of

carbon nanotubes facilitating water

transport for desalination

Yaqi Hou1, Miao Wang2, Xinyu Chen1,

Xu Hou1,2,3,4,5*

1State Key Laboratory of Physical

Chemistry of Solid Surfaces, College of

Chemistry and Chemical Engineering,

Xiamen University, Xiamen 361005,

China

2Research Institute for Biomimetics and

Soft Matter, Fujian Provincial Key

Laboratory for Soft Functional

Materials Research, Jiujiang Research

Institute, College of Physical Science

and Technology, Xiamen University,

Xiamen 361005, China

3Collaborative Innovation Center of

Chemistry for Energy Materials,

Xiamen University, Xiamen 361005,

China

4Tan Kah Kee Innovation Laboratory,

Xiamen 361102, Fujian, China

5CAS Key Laboratory of Bio-inspired

Materials and Interfacial Sciences,

Technical Institute of Physics and

Chemistry, Chinese Academy of

Sciences, Beijing 100190, China

*To whom correspondence should be

addressed.

A new mechanisms of water-water hydrogen bonding network facilitating water transport through carbon nanotubes at liquid-gas interface is presented and confirmed, which could potentially spark further experimental and theoretical efforts to design and explore advanced carbon nanotube systems with more beneficial performance in water desalination and purification.

Xu Hou, E-mail: [email protected]; Website: https://xuhougroup.xmu.edu.cn/

mailto:[email protected]://xuhougroup.xmu.edu.cn/

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Continuous water-water hydrogen bonding network across the rim of carbon nanotubes facilitating water transport for desalination

Yaqi Hou1, Miao Wang2, Xinyu Chen1, Xu Hou1,2,3,4,5 () 1 State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China 2 Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Jiujiang Research Institute, College of Physical Science and Technology, Xiamen University, Xiamen 361005, China 3 Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen 361005, China 4 Tan Kah Kee Innovation Laboratory, Xiamen 361102, Fujian, China 5 CAS Key Laboratory of Bio-inspired Materials and Interfacial Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China © Tsinghua University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Received: day month year / Revised: day month year / Accepted: day month year

ABSTRACT The development of membranes featuring carbon nanotubes (CNTs) have provided possibilities of next-generation solar desalination technologies. For solar desalination, the microstructures and interactions between filter membrane and seawater play a crucial role in desalination performance. Understanding the mechanisms of water evaporation and ion rejection in confined pores or channels is necessary to optimize the desalting process. Here, using non-equilibrium molecular dynamics simulations, we found that continuous water-water hydrogen bonding network across the rims of CNTs is the key factor in facilitating water transport through CNTs. With the continuous hydrogen bonding network, the water flux is two times of that without the continuous hydrogen bonding network. In CNT arrays, each CNT transports water molecules and rejects salt ions independently. Based on these observations, using CNT arrays consisted with densely packed thin CNTs is the most advisable strategy for evaporation desalination, possessing high transport flux as well as maintaining high salt rejection.

KEYWORDS carbon nanotubes, hydrogen bonding network, facilitated water transport, salt rejection, desalination

1 Introduction Solar desalination that can directly harvest solar-thermal energy from sunlight to create fresh water from seawater is considered to be one of the most promising and sustainable water purification technologies for tackling fresh water shortage [1-4]. Recently, lots of improvements have been made on solar desalination with the developments of membranes consisting of carbon nanotubes (CNTs) that have structural features leading to efficient light absorption and thermal conversion ability, and natural nanoscale channels for water transport and salt rejection [5-11].

The development of membranes with specialized channels that enable fast water transport while remaining high salt rejection has always been a motivation for research in the area of desalination due to the specific interface of nanochannels [12-14]. With the unique structures, the fast water transport through CNTs has attracted increasing attention to exploring on the mechanisms resulting in the fast transport properties of water molecules [15-19] and the high efficiency of salt rejection [16, 20, 21]. For instance, the hydrophobicity and atomistic smoothness of CNT walls result in nearly frictionless and enhanced water flow [22-25]. Dissolved salt ions need to be partially dehydrated when they go into CNTs,

resulting in an increasing energy barrier for them to pass through, and it is sensitive to changes in diameters of CNTs [16, 26, 27]. After being modified with charged functional groups on the tips, CNTs can further achieve a high salt rejection capability or ion selectivity through the interactions of electrostatic repulsion [28-30]. Other influence factors, like cation-π interactions [31], the interaction strength between tube wall and water molecules [32], asymmetric thermal fluctuation [33], vibration [34], electric field [21, 35], magnetic field [35], etc., will either pump or block the water molecules flowing across CNTs.

Among the pioneering computer simulations and experimental studies of water and ion transport through CNTs, the hydrogen bonding (H-bonding) interactions have been reported to be a critical key player, and the unusual properties of single-file water arrangement in single CNT can be attributed to the particular H-bonding topology [36, 37]. The H-bonding interactions at the water-nanotube interface also significantly affects the flow speeds [15], while the intermolecular H-bonding rearrangement dominates the energy barrier and can be manipulated to enhance water transport speeds [38].

The abovementioned mechanisms have raised the possibilities to interpret the behaviors of aqueous solution inside CNTs. However,

Address correspondence to First A. Firstauthor, email1; Third C. Thirdauthor, email2

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during the practical solar desalination, instead of that CNT membranes are immersed in the liquid phase, CNTs are placed at the liquid-gas interface, and the filtration is taking place during liquid-gas phase transition. Thus, the influence of liquid-gas interface can be influential but was seldom discussed [39]. From a microscale view, the liquid-gas interface contains several layers of water molecules that is at nano- or even sub-nano scales, which makes the qualitative observation and quantitative analysis very difficult by current experimental techniques. Additionally, the end-effect of CNTs for water entering and exiting are also overlooked in most discussions. However, this end-effect exists in reality. It has been reported that the mechanism is not clear, but the end-effect has a significant impact on the confinement transport of water molecules for sure [40, 41]. When water molecules pass through CNTs, whether the H-bonding network generated by the aggregation of water molecules across the rim of CNTs influence the water transport in the same way as the interior H-bonding network remains unsolved. And, the water transport and salt rejection mechanisms for seawater passing through CNTs at liquid-gas interface during phase transition remains unclear. Therefore, more in-depth understanding on the fundamental flow mechanisms through CNTs can be helpful for the future progresses of utilizing CNTs in various water treatments.

Here we focus the efforts on studying the end-effects on the water flow and salt rejection through CNTs with different diameters at liquid-gas interface. The CNT with diameter of 0.95 nm shows discontinuous H-bonding network across the rim of exit end, resulting in lower flux. Notably, we observe significant enhancement of water transport in the larger 2.98-nm-diameter CNT channel that has continuous H-bonding network across the

rim around the exit end, implying that facilitating water transport requires the strong and continuous H-bonding network. We also find that the transport abilities of individual CNTs in CNT arrays are independent from each other, making these channels possible in scale up practically. These findings could potentially spark further experimental and theoretical efforts to design and explore advanced CNT array systems with more beneficial performance in water desalination and purification. 2 Results and discussions Figure 1 shows a representative CNT membrane system for solar desalination. As the temperature rises above the vaporization temperature, for example 393.15 K in this work, water molecules tend to pass through the CNTs in a continuous phase and gather at the exit end of CNTs. Afterwards, the liquid-gas phase transition happens, and only a few water molecules evaporate into small and independent clusters. It is because the water-water hydrogen bonds (H-bonds) consist the main part of the interactions among water molecules; therefore, it needs continuous H-bonding network to maintain the continuous transport of water molecules. Surprisingly, the gathered water at the exit end would not hinder the smooth passage of subsequent water molecules, but would help to form a stronger and more continuous H-bonding network across the rim, which induce more subsequent water molecules passing. The bigger the diameter of CNT is, the more the water molecules gathered, leading to a stronger and more continuous H-bonding network and a higher flux during the same period, despite the friction increases with the increase of CNT diameters [42].

Figure 1 Schematics of solar desalination using CNT array membrane. CNTs absorb solar energy to heat up and accelerate the evaporation of seawater. During the

evaporation process, the water molecules/salt ions show different transport behaviors which are dependent on the diameters of CNTs and the topologies of the

H-bonding networks across the rims of CNTs. In the CNT with bigger diameter (~3.0 nm) on the left, there are more water molecules inside and aggregating at the

exit end of CNT, which makes the H-bonding network stronger and more continuous across the rim than that in CNT with the smaller diameter (~1.0 nm) on the right,

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resulting in higher water flux but lower salt rejection. While the smaller CNT can prevent almost all the ions from passing through. Therefore, finding a way to

balance these two competitors to achieve high filtration speed and high salt rejection at the same time is a key point.

2.1 Filtration flux and salt rejection in single CNTs. We use a single CNT to analyze the fundamental mechanism for the convenience of avoiding more influence factors. A typical single CNT model for evaporation desalination is shown in Figure 2a. The bottom part is the bulk phase of 1.0 mol/L NaCl solution, and the middle part is the single CNT. The blank space on the top is to collect the water molecules and salt ions passing through. Five single CNT systems with different diameters (d = 0.95 nm, 1.22 nm, 1.49 nm, 2.03 nm, and 2.98 nm) are simulated, and the total number of passing water molecules (

tot_waterN ) within a certain

period of time are shown in Figure 2b. Initially, the number of water molecules passing through increases linearly over time and the slope shows the speed of transport and evaporation. Then, the transport speed slows down and the total number of water molecules gradually approaches to a certain equilibrium value. For thinner CNTs with the diameters of 0.98 nm and 1.22 nm, the simulations were prolonged, the

tot_waterN are still less than those

through the thicker CNTs (Figure S7).

The results show that the bigger the CNT diameter is, the bigger slope the curve has, which represents the filtration happening at a higher speed and reaching the equilibrium value with more water molecules passing. The total number of passing water molecules also has a limit value as the CNT diameter increases (seen in the inset of Figure 2b). To quantitively compare the differences, we use formula time/

tot _ water (1 )N A et−= ⋅ − to fit the data. Two fitting

parameters, A and 1 t , quantitatively reflect the difference of the final number

tot_waterN and filtration speed of water molecules

in CNTs with different diameters. The specific values of the fitting parameters are listed in the Electronic Supplementary Material (ESM) (Table S1). Therefore, increasing the diameters of CNTs has a positive effect on facilitating the water transport; however, the number of salt ions passing through the CNT also increases (Figure 2c), so the salt rejection drops significantly (Figure 2d), which is not desirable in desalination.

Figure 2 The water/ion transport behaviors passing through the single CNTs. (a) A typical illustration of simulation model used for single CNT systems. (b) Different dependence between CNT diameters and the total numbers of water molecules (

tot_waterN ) passing through single CNTs over time. The circles are simulation data

and the solid curves are fitting lines. The final numbers of tot_waterN within different CNTs are shown in the inset. (c) Total numbers of Na

+ (tot_Na

N + ) passing

through single CNTs with different diameters, which have similar trends as water molecules. The bigger the CNT diameter is, the faster and more ions pass. (d) Salt

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rejection of Na+ and Cl- are almost identical and decrease as the CNT diameters increase. The outlier of CNT with the diameter of 2.98 nm is caused by the size

limitation of the simulation system, but it does not affect the full analysis in this work.

2.2 Continuous H-Bonding Network Facilitating Water Transport. Based on the observation of micro dynamic processes of water molecular transport through CNTs with different diameters, we found that water molecules will form a continuous water phase instead of in the form of small and individual vapor clusters to realize continuous transport and pass through the CNTs even at a high temperature (393.15 K). That is to say, the liquid-gas transition does not occur inside the CNTs. Compared to bulk water phase, the water inside CNTs has a smaller density (~0.72 g/cm3), and each water molecules have less coordination numbers, shown in Figure S4. Thus, the inside water is neither water vapor nor liquid water, it is in totally different state from the bulk phase. The real vaporization process occurs at the liquid-gas interface after the water molecules having passed through the CNTs. Therefore, some small and individual clusters can only be found in the upper vacuum region. Based on the geometrical characteristics of hydrogen bonding (Figure S1) [43-45], inside CNTs, H-bonds are continuous and form a H-bonding network (Figure S2), which is the key to guarantee the continuous transport of water molecules through CNTs.

As shown in Figure 3a, after water molecules passing through CNTs, the proportion of the number of water molecules gathered at the exit end of CNT ( exitN ) to tot_waterN increases as the

diameter increases. In the initial state, the majority of passing water molecules aggregate at the exit end of CNT, with the proportion reaching 1.0. As the transport continues to the equilibrium state, a low proportion (< 0.04) of water molecules will stay near the exit end of thin CNTs, while higher proportion (~ 0.11) of water molecules will stay near the exit end of thick CNTs (seen in the inset of Figure 3a). Contour maps in Figure 3b are the top-view of the simulation systems. It shows intuitively that during the initial stage of transport, water molecules of all systems gather near the exit end of CNTs, but when it comes into the equilibrium state, only a small part of water molecules are left at the exit end of thin CNT, while a big part of water molecules are still stay around the exit end of thick CNT. The water molecules near the exit end can further form a H-bonding network together with the water molecules inside the CNTs and generate a stronger continuous H-bonding network across the rim of CNTs, thus facilitating the subsequent transport of water molecules, which is the micro mechanism why water molecules in thicker CNT can transfer more water molecules at a higher speed. Figure 3c and 3d further show the distributions and microstructures of H-bonding networks across the rims of thin CNT and thick CNT, from which we can see the H-bonding network in thin CNT system is sparse and not continuous, while the H-bonding network in thick CNT system is dense and continuous, intuitively proving the facilitating effect of the continuous H-bonding network on water transport.

Figure 3 Significant facilitating effect of continuous H-bonding network on water transport through a single CNT. (a) The proportion of the amount of passing water

molecules staying around the exit end of CNT ( exitN ) to the total amount of passing water molecules ( tot_waterN ) over time. Inset of a is the enlarged view of this

proportion during equilibrium states. (b) Contour maps of the distribution of passing water molecules in different systems. The red dashed circles represent the exact

position of the rims of CNT exit ends. The scale bar color represents the number of passing water molecules at different positions, waterN . (c, d) Microstructures of

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water molecules and H-bonding networks across the rims of thin and thick CNTs with bird’s eye view (left) and zoom-in top view (right). Water-water H-bonds are

drawn in light green dash.

2.3 Filtration flux and salt rejection in CNT arrays. The above study on single CNTs can clearly analyze the micro mechanism of water transport in the CNT, but the flux of a single CNT is limited, which will be solved by using the CNT array. As shown in Figure 4a, three different CNT arrays have been designed: ten of CNTs with the diameter of 0.95 nm, six of CNTs with the diameter of 1.22 nm, and four of CNTs with the diameter of 1.49 nm. They all have the similar cross-section area with one of CNT with the diameter of 2.98 nm. Here, choosing the similar cross-section area for each CNT array is to eliminate the difference of internal volume of CNT channels which can not be eliminated in the single CNT models. The analysis of the total numbers of passing water molecules and ions over time were also made. We can see that using arrays can significantly accelerate the filtration speed of water molecules (Figure 4b), and the arrays consisted with thin CNTs can almost achieve the same filtration speeds as those of thick CNTs. Two fitting parameters, A and 1 t , also quantitatively reflect the similarity in

tot_waterN and filtration speed

with different CNT arrays (Table S2). It is worth mentioning that even if the number of CNTs for filtration is increased, the number of ions passing through the array still remains very similar to that of a single CNT with the same diameter (Figure 4c). With the increase of CNT diameter in the array, the salt rejection decreases significantly. Further comparing the salt rejection of single CNT

and CNT array (Figure 4d), it is found that in our system, the CNT diameter is the only factor that decides the salt rejection. If the diameter of CNT is equal, both single CNT and CNT array have almost the same salt rejection ability, which indicate that each CNT in CNT array can transport water molecules and reject salt ions independently.

When focusing on the CNT array of ten of CNTs with the diameter of 0.95 nm, we found that CNT No.1 passes the most water molecules, while CNT No.10 passes the least water molecules (Figure 4e). Further analysis of the causes of this amount differences shows that after water molecules passing through the CNT array, more water molecules gather near the exit end of CNT No.1, while there is no water molecule gathering near the exit end of CNT No.10 for a long period of time (Figure 4f, see dynamic processes from Movie S1 and Movie S2 in ESM). Therefore, the passing water molecules can form a more continuous H-bonding network with the water molecules inside the CNT No.1, so as to promote more water molecules to pass through the CNT No.1; while the H-bonding network across the rim of CNT No.10 is discontinuous, which hinders the continuous transport of water molecules. This phenomenon reinforces once again our conclusion of the facilitating effect of the continuous H-bonding network on the water transport.

Figure 4 The water/ion transport behaviors through CNT arrays. (a) Three CNT array models with the same transport cross-section area. (b) Total numbers of water molecules (

tot_waterN ) passing through different CNT arrays have similar trends as those in single CNT systems, but the filtration speed of thin CNT array has been

greatly speeded up because more CNTs have taken part in the transport. The circles are simulation data and the solid curves are fitting lines. The specific values of the

fitting parameters are listed in Table S2. (c) Total numbers of Na+ (+tot_Na

N ) passing through CNT arrays with different diameters, and the bigger the CNT

diameters are, the more ions pass. (d) Comparison of salt rejections of single CNT and CNT arrays. With more CNTs taking part in the transport in CNT array

systems, the filtration is accelerated, and the key performance of their salt rejections is not reduced. (e) Number of water molecules passing through each CNTs in the

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same CNT array (10×CNT (0.95 nm)). The green label is the serial number of each CNT. (f) Snapshots of water molecules and H-bonding network across the rim of

CNT No.1 and CNT No.10 during transport.

2.4 Advisable design strategies of CNT arrays for desalination. The performance indicators including the filtration speed ( dv ) and salt rejection ( dr ) of CNT arrays during desalination are averaged on each CNT and compared with those of the single CNTs of the same diameters. The results are shown in Figure 5a. The data show that the performance indicators of the individual CNT in the array are very close to those of the single CNT with the same diameter, furthermore, changing the distance among CNTs in the array will slightly influence the desalination performance (Figure S5). That is to say, every CNT in the array can transport water molecules and reject ions independently free of impact from others. The performance indicators ( dv and dr ) will become the characteristic parameters which are only related to the CNT diameters, as listed in Figure 5b. Based on these characteristic parameters, the filtration speed and salt rejection of any CNT array consisted with above five kinds of CNTs can be calculated and predicted based on the following equation:

array d d array dd

, d = 0.95, 1.22, 1.49, 2.03, 2.98 nmV N v R r= =∑ ， (1) in which, dN represents the number of CNTs with the diameter of d nm . Based on Eq. (1), we predicted the theorical desalination

indicators of single CNTs and CNT arrays (displayed in red squares in Figure 5c), and compared them with the molecular dynamics (MD) simulation results (displayed in black dots in Figure 5c). The predicted values are highly consistent with the simulation values, which means our prediction model is reliable and can be extended to predict other CNT array systems with larger scale and more complex structures. In addition, Eq. (1) is transplantable and can be extended to other CNT systems with different diameters, if the characteristic parameters dv and dr that are related to the specific diameters were calculated in advance through MD simulations.

In this way, according to the characteristic performance indicators and Eq. (1) given in this paper, any CNT array structure with expected filtration speed and salt rejection can be designed and evaluated. Figure 5c divides design strategies into different levels: rational designs which have high

arrayV and high arrayR ,

ordinary designs which have medium performance, and inadvisable designs which should be avoid in real design of CNT arrays. The most advisable design strategy is using the compact arrangement of thin CNTs, ten of CNTs with the diameter of 0.95 nm for example, which will achieve high

arrayV and arrayR at the same time. This

design strategy is of great significance for further system scale-up.

Figure 5 Design strategies of CNT arrays with different filtration speeds and salt rejections. (a) Comparison of filtration speeds and salt rejection performance of

single CNT and CNT arrays. Each CNT can transport independently in arrays and the transport performance is only related to the diameters of CNTs. (b) Each CNT

with a certain diameter has its characteristic desalination performance indicators. (c) Performance prediction matrix of different CNT array designs. The black dots

are values calculated from non-equilibrium molecular dynamics (NEMD) simulations, and the red squares are predicted values calculated based on Eq. (1). Regions

with different background colors show the overall performance evaluation of the CNT array designs: rational designs, ordinary designs, or inadvisable designs.

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3 Conclusions Designing CNT membranes with fast filtration speed and high salt rejection for desalination has always been the focus of researches. In this work, employing the most fundamental structural unit, the single CNT, we study the key factors affecting the transport behaviors of water molecules and ions in the process of desalination by means of NEMD simulations. It is found that the continuous H-bonding network plays an important role in the rapid and continuous transport of water molecules, and the salt rejection is mainly controlled by the CNT diameter. Moreover, each CNT can maintain its own desalination performance relatively independent from its peers in CNT array. Also, motivated by the simulation data, the paper showcases different design strategies. The discovery in this work lays the foundation of basic mechanism in water transport within CNTs at liquid-gas interface, based on which the desalination performance of CNT array with different structural characteristics can be predicted, and it hopes to spark more interests in CNT array design, as well as the scale-up design for practical desalination. 4 Theoretical methods NEMD simulations were performed using LAMMPS molecular dynamics simulator [46]. As shown in Figure 2a, three layers of graphene were built to delimit the accessible area of water molecules and salt ions. Between the upper two layers of graphene, single CNTs and CNT arrays were built as the only channels for water molecule/salt ion transport. All the graphene layers and CNTs are frozen during the entire simulations. Between the lower two layers of graphene, bulk of well mixed 1.0 mol/L NaCl salt solution was set. All the models were created by PACKMOL [47]. The sizes of simulation boxes and their contents are summarized in Table S3 in the ESM. The simulation boxes used in all cases were periodic in three dimensions. The carbon force field parameters were taken from the original Amber force field set [48], OPC3 model for water molecules [49] and the force field for salt ions were taken from ClayFF, whose reliability has been proved in previous studies [50]. All force field types and parameters have been summarized in Table S4 in the ESM. Before the evaporation simulation, the bulk salt solution was equilibrated in NPT (constant number of particles (N), pressure (P), and temperature (T)) ensemble for 1 ns at a pressure of 1 atm and a temperature of 300.15 K to make it mix evenly and achieve the real density. The calculated mean square displacement (MSD) is shown in Figure S3 and the diffusion coefficient is 5.42×10-9 m2/s, which is close to the results from other simulations and experiments [51, 52]. This means the current method and parameters can correctly reflect and describe the dispersion and diffusion behaviors of water molecules, which lays a model foundation for the further study of the evaporation behavior in this work. Then the production non-equilibrium simulations were carried out in NVT (constant number (N), volume (V), and temperature (T)) ensemble at a high temperature (393.15 K) for evaporation filtration using a Nose–Hoover thermostat for 12 ns with a time step of 1 fs. For all simulations, long-range interactions were computed using the Ewald method as implemented in LAMMPS. All the analysis and visualization of dynamic trajectory were performed by VMD [53]. Each simulation has been performed for three times with different

initial velocities to ensure the repeatability of the simulation results.

Acknowledgements The authors gratefully acknowledge supports from the National Natural Science Foundation of China (Grant No. 21975209, 21673197, 51706191, 21621091), the National Key R&D Program of China (Grant No. 2018YFA0209500), the 111 Project (Grant No. B16029), the Fundamental Research Funds for the Central Universities (Grant No. 20720190037), the Natural Science Foundation of Fujian Province of China (Grant No. 2018J06003), and CAS Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences.

Electronic Supplementary Material: Supplementary material that includes (1) Two geometrical criteria for hydrogen bonds. (2) Hydrogen bonding networks inside the CNTs with different diameters. (3) Mean square displacement (MSD) of water molecules in bulk phase. (4) Radial distribution function (RDF) and coordination number of each water molecules in both confinements and bulk phase. (5) The influence of the distance among CNTs on the filtration speed of CNT arrays. (6) The water transport behaviors passing through the single CNTs with 0.1mol/L NaCl. (7) Total numbers of water molecules passing through two thin CNTs over prolonged duration of 24 ns. (8) Snapshots of two water molecules transport trajectory in CNT array. (9) The fitting values of the parameters A and 1 t for single CNTs. (10) The fitting values of the parameters A and 1 t for CNTs arrays. (11) Atomic parameters for models used in the simulations. (12) Force field types and parameters of bonded and nonbonded interactions. (13) Density and ion concentration of the bulk aqueous solution at different time points through simulations. (14) Top view of dynamic water-water hydrogen bonding networks during desalination with 10×CNT (0.95 nm) array. (15) Comparison of continuous and discontinuous hydrogen bonding networks is available in the online version of this article at http://dx.doi.org/10.1007/s12274-***-****-*.

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Electronic Supplementary Material

Continuous water-water hydrogen bonding network across the rim of carbon nanotubes facilitating water transport for desalination

Yaqi Hou1, Miao Wang2, Xinyu Chen1, Xu Hou1,2,3,4,5 () 1State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China 2Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Jiujiang Research Institute, College of Physical Science and Technology, Xiamen University, Xiamen 361005, China 3Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen 361005, China 4Tan Kah Kee Innovation Laboratory, Xiamen 361102, Fujian, China 5CAS Key Laboratory of Bio-inspired Materials and Interfacial Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China Supporting information to DOI 10.1007/s12274-****-****-*

Figure S1 Two geometrical criteria for hydrogen bonds. Two-parameter geometrical definition ( oor and α ) imposes constraints on relative orientation of the

interacting water molecules. A hydrogen bond is formed if the distance between two O atoms oo 0.35 nmr < and the angle 30α <

Address correspondence to [email protected]

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Figure S2 Hydrogen bonding networks inside the CNTs with different diameters of (a) 0.98 nm and (b) 2.98 nm. Water-water H-bonds are drawn in light green

dash.

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Figure S3 Mean square displacement (MSD) of water molecules in bulk phase.

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Figure S4 (a) Radial distribution function (RDF), and (b) coordination number of each water molecules in both confinements and bulk phase.

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Figure S5 The influence of the distance among CNTs on the filtration speed of CNT arrays. (a) Different CNT arrays with different distances among CNTs. (b)

The distance among CNTs will slightly influence the filtration speed of the CNT arrays. The CNT array with tight distribution has a slightly higher filtration

speed than that of CNT array with loose distribution, which can be attributed to the more continuous H-bonding network. With tight distribution, the passing

water molecules can form a denser aggregation at the exit ends of CNTs, which makes it easier to form a continuous H-bonding network across the rims.

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Figure S6 The water transport behaviors passing through the single CNTs with 0.1 mol/L NaCl. Compared to the water transport behaviors with 1.0 mol/L NaCl

solution in the main text, the change of concentration will not change the tendency of water transport through the single CNTs with different diameters.

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Figure S7 Total numbers of water molecules (tot_waterN ) passing through two thin CNTs over prolonged duration of 24 ns.

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Figure S8 Snapshots of two water molecules transport trajectory in CNT array. Due to the thermal movement of molecules, water molecules exist reciprocating

motion passing through CNTs.

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Table S1 The fitting values of the parameters A and 1 t for single CNTs.

CNT diameter (nm) A 1 t

0.95 3708 0.08701

1.22 4042 0.2563

1.49 4122 0.5795

2.03 4208 1.827

2.98 4197 6.753

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Table S2 The fitting values of the parameters A and 1 t for CNTs arrays.

CNT arrays A 1 t

10×CNT (0.95 nm) 3912 0.6621

6×CNT (1.22 nm) 3766 1.058

4×CNT (1.49 nm) 3589 1.888

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Table S3 Atomic parameters for models used in the simulations.

System x/Å y/Å z/Å

No. of

water

molecules

No. of Na+ No. of Cl-

1.0 mol/L NaCl 119.3 117.2 201.0 33550 610 610

0.1 mol/L NaCl 119.3 117.2 201.0 33550 61 61

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Table S4 Force field types and parameters of bonded and nonbonded interactions.

Element Mass (AMU) Charge (e)

CNT C 12.0107 0.0000

Graphene C 12.0107 0.0000

Water O 15.9994 -0.8952

Water H 1.00800 0.4476

Na+ 22.9900 1.0000

Cl- 35.4530 -1.0000

Lennard-Jones potential for all atoms

( )12 6

4vWU rr rαγ αγ

αγ αγ

σ σε

= −

Mixing rules: , 2αγ α γ αγ α γε ε ε σ σ σ= = +

Parameters ε (kcal/mol) σ (Å)

CNT C 0.1200000 3.29630

Graphene C 0.1200000 3.29630

Water O 0.1633335 3.17427

Water H 0.0000000 0.00000

Na+ 0.1301000 2.35020

Cl- 0.1000000 4.40000

Bond coefficients ( ) ( )20b bV r k r r= −

Parameters bk (kcal/Å2) 0r (Å)

Water O-H 554.135 0.9789

Angle coefficients ( ) ( )20aV kθθ θ θ= −

Parameters kθ (kcal/2θ ) 0θ (°)

H-O-H 45.7696 109.47

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Table S5 Density ( bulkρ ) and ion concentration ( bulkc ) of the bulk aqueous solution at different time points through

simulations.

Time (ns) ρbulk (g/cm3) cbulk (mol/L)

0 1.025 1.000

6 0.919 0.970

12 0.917 0.944

From the data in the table, it can be seen that the density and ion concentration of the bulk phase at the entrance side are kept at a relatively stable value, which means the size of the current simulation system is a size that can provide a stable osmotic pressure state and enough water molecule offering for the whole simulation processes.

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Movie S1. Top view of dynamic water-water hydrogen bonding networks during desalination with

10×CNT (0.95 nm) array.

Movie S2. Comparison of continuous and discontinuous hydrogen bonding networks.

3173Manuscript_R11 IntroductionAcknowledgementsReferencesElectronic Supplementary MaterialFigure S6 The water transport behaviors passing through the single CNTs with 0.1 mol/L NaCl. Compared to the water transport behaviors with 1.0 mol/L NaCl solution in the main text, the change of concentration will not change the tendency of water tra...Figure S8 Snapshots of two water molecules transport trajectory in CNT array. Due to the thermal movement of molecules, water molecules exist reciprocating motion passing through CNTs.Table S2 The fitting values of the parameters and for CNTs arrays.Movie S1. Top view of dynamic water-water hydrogen bonding networks during desalination with 10×CNT (0.95 nm) array.Movie S2. Comparison of continuous and discontinuous hydrogen bonding networks.

continuous water-water hydrogen bonding network across the ...here, using nonequilibrium molecular...

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