Effect of Hydrogen Bonding Interaction on Arrangement and Dynamics

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Effect of Hydrogen Bonding Interaction on Arrangement and Dynamics of Water Confined in Polyamide Membrane: A Molecular Dynamics Simulation Ning Zhang, Shaomin Chen, Boyun Yang, Jun Huo, Xiaopeng Zhang, Junjiang Bao, Xuehua Ruan, and Gaohong He J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b12790 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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The Journal of Physical Chemistry

Effect of Hydrogen Bonding Interaction on Arrangement and Dynamics of Water Confined in Polyamide Membrane: A Molecular Dynamics Simulation Ning Zhang, Shaomin Chen, Boyun Yang, Jun Huo, Xiaopeng Zhang, Junjiang Bao, Xuehua Ruan, Gaohong He* State Key Laboratory of Fine Chemicals, School of Petroleum and Chemical Engineering, Dalian University of Technology, Panjin, 124221, China *Corresponding author.

Tel.: +86-411-84708774. Fax: +86-411-84708460. E-mail: [email protected]

Abstract: Increasing demand for freshwater inspires further understanding the mechanism of water diffusion in reverse-osmosis membrane for developing high-performance membrane in desalination. Water diffusion has close relationship with the structural and dynamical characteristics of hydrogen bonds, which is not well understood for the confining environment inside the polyamide membrane at the molecular level. In this work, an atomistic model of highly crosslinked polyamide membrane was built with an equilibrated mixture of m-phenylenediamine and trimesoyl chloride monomers. The structure and dynamics of water in the regions from bulk phase to membrane interior were investigated by molecular dynamics simulation. Explicit hydrogen bonds criteria were determined for hydrogen bonding analysis. Local distribution and orientation of water reveal that the hydrogen bonding affinity of the hydrophilic functional groups of polymer inhibits water diffusion inside the membrane. The affinity helps produce percolated water channel across the membrane. Hydrogen bonding structures of water in different regions indicate dehydration is required for the water entry into the polyamide membrane, which dominates water flux across the membrane. This paper not only deepens the understanding of the structure and dynamics of the water confined in the polyamide membrane but also stimulates the future work on high-performance reverse-osmosis membrane. 1

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1. Introduction The past several decades have witnessed a dramatic industrial development and population explosion all over the world, resulting in a series of problems including pollution, climate change and food shortage.1 The problems inevitably lead to the shortage of freshwater available for residential, commercial and industrial consumption. The earth is covered by water which is mainly in the forms of the oceans and seas. Therefore, seawater desalination is an extremely promising way to address the shortage of freshwater.2-3 Reverse osmosis (RO) is currently considered as an important technology for desalination due to its simplicity and low energy consumption. Recent report shows that RO technology has been applied to more than 50% of the installed worldwide desalination factories.4 The core component of RO process is the selective semi-permeable membrane between the feed and permeate sides, which permits water to pass through but blocks salt ions. The properties of RO membrane determine the efficiency of the desalination process. Nowadays, the widely used commercial RO membrane is the aromatic polyamide (PA) composite membrane, which has good chemical and mechanical stability and wide operating temperature range.5 Extensive studies have been implemented to enhance the water flux and ion rejection of PA membranes.6-11 Despite of the large efforts, there is still a long way to develop high-performance RO membrane for desalination. This is mainly due to the fact that the morphology of the membrane at the molecular level and the mechanisms of water and ion diffusion in the membrane are not well understood.12 Therefore, it is significant to explore the microscopic structure of membrane and the interactions between membrane and water in the application of desalination. In recent years, the development of molecular simulation has made it possible to investigate the structure of RO membrane at the molecular level by using molecular dynamics (MD) simulation, which can compensate for the shortcomings of conventional experiment. Kotelyanskii et al.13-14 carried out the pioneering work on the water and ion mobility inside PA membrane. It was found that in the membrane 2


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water presents a jump-diffusion motion rather than Brownian motion. Harder et al.12 used a heuristic approach to mimic the polymerization process and obtained a reasonable model of PA membrane, which could be used in MD simulation within a practical simulation time. Luo et al.15 constructed a membrane topology and calculated water flux and ion rejection using equilibrium molecular dynamics (EMD), which is in agreement with experimental values. Ding et al.16-18 employed EMD to investigate the structural and dynamic properties of water and membrane structure. There are also numerous MD studies on water dynamics and ion transport19-21 and membrane local structure.22 The studies confirm that MD simulation is a useful way to help explore RO membrane development. Water transport through RO membrane could be well described by the solubility-diffusion

mechanism23:

(i)

water

diffuses

from

bulk

phase

to

bulk/membrane interface and dissolves into the membrane; (ii) the dissolved water permeates through the membrane dense region from one side to the other; (iii) the permeated water dissolves from the other bulk/membrane interface to the bulk phase of the other side. The transfer resistance of water through the membrane is then resulted from the interfacial and interior regions, where the functional groups of PA membrane have significant effect on water transfer.24 It is necessary as well as vital to investigate the influence of functional groups. Gai et al.24 carried out MD simulation to study the interaction between water and PA membrane. It was found that the hydroxyl and carbonyl groups have strong affinity to water and increasing of hydroxyl and carbonyl groups may help improve the adsorption capacity of the membrane to water. Song et al.25 investigated the residence time of water around different functional groups inside PA membrane. It was found that water transports faster around benzene rings than carboxyl and amino groups due to the relatively high hydrophobic effect of benzene rings. However, the previous studies mainly focused on the water transport inside the membrane. It is still important to further investigate water transport in the process of bulk-membrane-bulk with considering the effect of bulk/membrane interface. In this work, we carried out MD simulation on hydrated PA membrane (the FT-30 3



RO membrane26-27) without the polysulfone support layer in order to shed light on the structural and dynamical properties of water inside the membrane. The membrane was initially constructed using an efficient approach. Subsequently, several radial distribution functions and the water self-diffusion in different regions were estimated to compare with the previous reports.16-18 Based on the validation, structural properties were explored by means of water orientation, and hydrogen bonding analysis in order to characterize the interaction between membrane and water. Finally, the cluster size distribution was estimated to explore the channel connectivity inside the PA membrane. The present study helps to understand the mechanism of water diffusion inside the PA membrane and develop RO membrane with high water flux and ion rejection.

2. Methodology 2.1 Construction of crosslinked polymer MD simulations were carried out based on the system comprised of the crosslinked PA membrane and two water reservoirs. The chemical structures of the monomers (i.e. m-phenylenediamine (MPD) and trimesoyl chloride (TMC)) considered here are shown in Fig. 1a. Initially, 448 MPD and 294 TMC monomers were adopted to construct a solution system with the size of 52.7 Å × 52.7 Å × 52.7 Å. There is strong intermolecular interaction between the monomers, annealing was used to accelerate the relaxation of the system in canonical (NVT) ensemble: (i) the temperature of the system is gradually elevated from 340 to 1000 K within a time period of 100 ps; (ii) the heated system is equilibrated at 1000 K for 1 ns; (iii) the system is cooled down to 340 K within 100 ps; (iv) the system is equilibrated at 340 K for 1 ns. During the crosslinking process, periodic boundary conditions (PBCs) were used in three dimensions with the size of the MPD/TMC mixture.

4


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Fig. 1 (a) The chemical structure of m-phenylenediamine (MPD), trimesoyl chloride (TMC) and crosslinking reaction. (b) Intermolecular RDF between the carbonyl carbon of TMC and the amino nitrogen of MPD. Luo et al.15 encouraged further crosslinking to achieve high degree of crosslinking by a heuristic simulation method with additional potential. Besides, shen et al.28 obtained high degree of crosslinking by extending the distance criterion from 3.5 Å for the initial crosslinking stage to 4.5 Å for the final crosslinking stage. In this work, it was found that the initial annealing process for system relaxation helps to obtain high degree of crosslinking with only one distance criterion. Subsequently, MPD and TMC monomers in the equilibrated mixture were artificially polymerized at 340 K according to the crosslinking criterion, which is defined as the C-N radial distribution function between the carbon atom of a free acyl chloride group (‒COCl) of TMC and the nitrogen atom of a free amine group (‒NH2) of MPD. Thus the crosslinking criterion was determined as LC = 5.0 Å, as shown in Fig. 1b. If the C-N distance 5



between one MPD monomer (or residue) and one TMC monomer (or residue) is smaller than the crosslinking criterion, a amide bond will be artificially built between the acyl carbon and the amino nitrogen while the chlorine atom of ‒COCl and one hydrogen atom of ‒NH2 are deleted. Each produced amide bond was carefully checked in order to eliminate the unrealistic formation of ring catenation and spearing.24 Based on the crosslinking protocol, the equilibrated system was run in NVT ensemble but interrupted every 200 ps for producing new amide bonds until there is no amide bond formed. PBCs were used in three dimensions with 52.7 Å × 52.7 Å × 52.7 Å during the crosslinking process. After the crosslinking process, the unreacted TMC and MPD monomers were removed from the system and the remaining acyl chloride groups were replaced by the carboxyl groups (i.e. ‒COOH) as a result of the hydrolysis reaction. Finally, the mixture containing 410 MPD and 287 TMC monomers produced a three-dimensional crosslinked PA membrane with the crosslinking degree of 79.9 %, which is defined as the ratio of the number of amino groups to the total number of carboxyl and amino groups. Then the crosslinked membrane was annealed between 300 and 600 K for four times according the abovementioned annealing protocol. Subsequently, the annealed PA membrane was equilibrated for 10 ns in isothermal-isobaric (NpT) ensemble under 300 K and 1 bar. The simulated density of dry membrane is calculated to be 1.2 g/cm3, which is consistent with previous results.21, 28

2.2 Construction of hydrated membrane As for the construction of hydrated membrane, water molecules were randomly inserted into the vacancy of the crosslinked polymer to achieve a water content of 23 wt%.13 This is in accordance with the experimental water content of the TMC/MPD polymeric membranes.29 The hydrated membrane was equilibrated in NpT ensemble (300 K, 1 atm) for 10 ns. After equilibration, the membrane was exposed to two external water reservoirs on the z-axis direction, as shown in Fig. 2. Ensuring the water movement either in the reservoir or in the membrane, each water reservoir in x6


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y dimensions should be set smaller than that of the membrane. Thus the two water reservoirs were produced with the size of 45 Å × 45 Å × 60 Å.

Fig. 2 Snapshot of the water/membrane/water system, where atoms can be recognized by colors (i.e. yellow-carbon; blue-nitrogen; red-oxygen; white-hydrogen).

2.3 Computational details MD simulations using the package NAMD 2.930 were carried out in the NpT and NVT ensembles for the modeling and producing processes. TMC and MPD monomers were constructed using the generalized AMBER Force Field (GAFF).31 The force field of crosslinked polyamide was taken from a previous study.15 Water molecule was modeled by the TIP3P model.32 PBCs were applied in three dimensions with the size of 45 Å × 45 Å × 172.7 Å. SHAKE algorithm was adopted to constrain the covalent bonds involving hydrogen atoms around the equilibrium length. The particle mesh Ewald (PME) method33 was used to solve the Coulombic forces with the grid spacing of 1.0 Å. The long and short range forces of electrostatic interactions were separately calculated at the distance of 12 Å. The interactions of van der Waals smoothly approach to zero from 10 to 14.5 Å. The water/polymer/water system was performed in NpT (300 K, 1 atm) ensemble with 8 ns for equilibration and a subsequent 2 ns for data sampling. The sampling frequency was 1000 time steps with a time step of 1 fs. The density of the hydrated membrane at 300 K was measured to be 1.30 g/cm3, which is similar to the results of experiments29, 34 and simulations.13, 15, 18

7



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3. Results and discussion 3.1 Local structure of water For exhibiting the confinement effect of PA membrane on the water molecules, it is necessary to compare the local structures of the bulk water and the confined water. The local structure of water can be characterized by radial distribution function (RDF), which is defined as follows

g12 (r) =

dN2 ρ 4πr 2dr

(1)

where dN2 is the amount of atom 2 in a spherical shell of the thickness dr with a distance r from atom 1, and ρ is the number density of atom 2 in the focused area. This section presents the RDFs of the Ow-Ow, Ow-Hw, Ow-NF, Ow-NA, Ow-OF, Ow-OE, Ow-OA pairs over the trajectory of 2 ns, where Ow and Hw represent the oxygen and hydrogen atoms of water, and NF, NA, OF, OE and OA represent the amide nitrogen, amino nitrogen, amide oxygen, carboxyl oxygen and hydroxyl oxygen, respectively. 3.1.1 Local water distribution Fig. 3 shows the RDFs of the intermolecular Ow-Ow and Ow-Hw pairs for confined and bulk water, respectively. For the RDFs of confined water, the average density of water in the membrane is adopted as the reference density ρ. As for the RDFs of bulk water, the average density of water in the reservoir is used as the reference density ρ. It is shown in Fig. 3a that both confined and bulk water occupies the first peaks at 2.8 Å. This is consistent with the previous study.16 It indicates that local water aggregation exists in both bulk and confinement environments. Notably, the first peak height for confined water is almost twice than that for bulk water. According to Eqn. (1), it might be due to high local distribution or low density of the confined water in the PA membrane. It is necessary to compute the coordination numbers of the bulk and confined water by integrating the two gOw-Ow(r) RDFs. It is shown in Fig. 3a that the coordination number of confined water is obviously less than that of bulk water. Thus, the apparent high peak of gOw-Ow(r) for confined water is resulted from the rare 8


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water density in the membrane. The nanochannel of the PA membrane restricts the arrangement of the confined water and decreases the local distribution of the water molecules in the membrane. This will definitely weaken the intermolecular interactions between the confined water molecules.

Fig. 3 (a) RDFs for the Ow-Ow pairs and the corresponding coordination numbers (Nc) for bulk and confined water; (b) RDFs for the intermolecular Ow-Hw pairs for bulk and confined water. Fig. 3b presents the gOw-Hw(r) RDFs with bimodal characteristics for bulk water and confined water. The first and second peaks and the local minimum of the gOw-Hw(r) RDFs have the similar positions in bulk water and inside the PA membrane. It is observed that the two peaks are located at 1.9, 3.3 Å, and the local minimum at 2.45 Å, 9



respectively. It indicates that the overall hydrogen bond (H-bond) structure of water could maintain well in the confinement. This is also confirmed by the gOw-Ow(r) RDFs of bulk water and confined water. Both gOw-Ow(r) and gOw-Hw(r) RDFs are decisive characteristics in determining H-bonds between water molecules either in bulk phase or inside the membrane.35-36 The RDFs depicted in Fig. 4 characterize the interactions between water and the functional groups. The functional groups are represented by the corresponding core atoms (i.e. oxygen and nitrogen atoms) as shown in the top panel. Fig. 4a depicts the gNA-Ow(r) and gNF-Ow(r) RDFs as a function of distance r. The first peak of the gNA-Ow(r) RDF located 3.1 Å reflects the high aggregation of water around the amino groups. It indicates that there is close interaction between the amino groups and water. There is no obvious peak in the gNF-Ow(r) RDF, which might be ascribed to the steric effect of the benzene rings of the polymer. Fig. 4b depicts the gOA-Ow(r), gOE-Ow(r) and gOF-Ow(r) RDFs with the first peaks located at 2.9, 3.0 and 3.0 Å, respectively. It implies that there also exists affinity between the reacted/unreacted carboxyl groups and water.

Fig. 4 RDFs between the confined water and the functional groups of the PA membrane. The top panel depicts the representative atoms of the functional groups. 10


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3.1.2 Water orientation

Fig. 5 Profiles of the water orientation (θ) and the number density (ߩ୊ୋ) of the unreacted functional groups along the direction normal to the membrane surface. It was reported that the interaction between nanochannel wall and the confined water has great effect on the water transport behavior in the channel, which can be characterized by the ordering of dipole moment.37 In this work, in order to reflect the confinement of the PA membrane to the diffusion behavior of the confined water, it is necessary to investigate the distribution of the water orientation along the z-axis (i.e. the membrane thickness direction). It also helps to understand the mechanism of water transport in the membrane. It is known that the crosslinked membrane possesses the unreacted groups of ‒COOH and ‒NH2, which have attraction to the confined water molecules.24 A clear evidence of this fact is the orientation of the confined water in the PA membrane. Fig. 5 depicts the profiles of water orientation and the unreacted functional groups along the z-axis. For the sake of convenience, the water orientation is defined as a characteristic angle θ, which is the angle between the vector of water dipole and positive z direction. It is observed that the angle θ slightly fluctuates around 90ºin the bulk phase. This suggests that water molecules have no preferential orientation in bulk phase. However, the angle θ presents a sharp fluctuation around 90° near the membrane surface and inside the membrane. The profile of the unreacted functional groups shows obvious fluctuation throughout the entire membrane, of which the tendency is similar with the water orientation profile. It indicates that the 11



water motion is affected by the functional groups. In order to further elucidate the effects of the unreacted groups of ‒COOH and ‒NH2, it is necessary to observe the hydrogen bonding (H-bonding) interaction between the functional groups and the water confined in the PA membrane.

3.2

H-bonding analysis

It was previously reported that H-bonding network plays an important role in water diffusion either in bulk phase38 or inside the membrane,36 which has close relationship with water flux in the process of desalination.34, 39 It is known that there is hydrogen bond interaction between water and the hydrophilic groups of PA membrane, which is believed to have great effect on the water diffusion motion in the membrane. Therefore, it is of significant importance to study the hydrogen bond properties of water, including hydrogen bonding states, dynamics and cluster, to deepen our understanding of the mechanism of water transfer in PA membrane. For convenient H-bonding analysis, it should be priority to define the H-bond criteria for different types of H-bonds. 3.2.1 Hydrogen bond criteria

Fig. 6 Distributions of the angle α represented by the snapshot for bulk water and confined water. H-bond is widely recognized as the intermolecular interaction between an 12


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electronegative atom and a hydrogen atom covalently bonded to another electronegative atom. Geometric criterion36,

40

has been widely used due to its

convenience and effectiveness. In this study, the geometric criterion for identifying one H-bond, such as O–H⋯O, involves the hydrogen bond length O⋯H, the distance O⋯O and the angle O⋯O–H. The symbols ‘‘–’’ and “⋯” correspond to the covalent bond and the intermolecular interaction, respectively. The geometric criterion adopted in this work is specified as follows: C

(1) The distance ROH of the H-bond length is less than ROH ; C (2) The distance ROO between the H-bond donor and acceptor is less than ROO ;

(3) The O⋯O–H angle α is less than αc. C

C where, the threshold values ROO and ROH are identified by the first minimum

positions of the corresponding RDFs, and αc is estimated by the angle α distribution. Table 1 Geometric criteria of different types of the H-bonds between polymer and water H-bond type

C ROO /Å

C ROH /Å

αc / °

NA-Ow

4.3

2.5

40

OA-Ow

4.5

2.5

40

OE-Ow

4.5

2.5

40

OF-Ow

3.3

2.5

40 C

C

According to the gOw-Ow(r) and gOw-Hw(r) RDFs as shown in Fig. 3, ROO and ROH are respectively determined as 3.5 and 2.45 Å for the water-water (W-W) H-bonds in bulk phase and inside the membrane. Fig. 6 presents the distribution of the angle α composed of the water pairs with ROH less than 2.45 Å. It is observed that only a small percentage (less than 12%) of water pairs produce the angle α greater than 30°. It is reasonable to define the angle threshold as the widely used value of αC = 30°.41 Thus C

C

the criterion of the W-W H-bonds is defined as ROO ≤ 3.5 Å, ROH ≤ 2.45 Å, αC ≤ 30°. It is known that there exits water-polymer (W-P) H-bonds by means of the 13



H-bonding interactions between water and the functional groups (i.e. amino, acylamino and carboxyl groups), as shown in Fig. 4. According to the above statement, the geometric criteria of the W-P H-bonds can be obtained and listed in Table 1. 3.2.2 Hydrogen bond statistics

Fig. 7 Profiles of the average numbers of the W-W and W-P H-bonds per water molecule along z-axis. According to the identified H-bond criteria, the H-bonding structure of the water confined in the membrane can be determined. Fig. 7 shows the profiles of the average H-bond number of the water at different positions along z-axis, where the W-W and W-P H-bonds are considered. It is shown that the quantity maintains at 3.0 in bulk phase, and has a sharp decrease to about 1.8 from the surface to the interior of the PA membrane. As stated above, this might be due to the attraction by the functional groups of the polymer. Thus, the W-P H-bonds are estimated for further elucidating the interaction between the functional groups and the confined water. It is shown in Fig. 7 that increases within the bulk/membrane interface, and fluctuates in the membrane interior. In order to elucidate the variation of the H-bond structure of water, we also calculated the W-W H-bonds of the water molecules within the first hydration shell of the functional groups near the bulk/membrane surface. It is found that on average, one water molecule possesses 1.5 W-W H-bonds, which is only 14


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half of the bulk water. The focused water molecules account for 24.8 to 63.1 % of the water across the surface region. Thus a decreasing trend of is observed near the bulk/membrane surface.

Fig. 8 Percentages of bulk and confined water with different H-bonding states fn (n = 0~6). The solid lines are drawn as a guide to the eye. The above-mentioned H-bond statistics only characterize the mean H-bonding ability of water in bulk and confined phases. It is known that H-bonding states has great effect on the dynamic behaviors of water.35, 38, 42 Thus, it is still necessary to describe the local structure of water with different H-bonding states, which are defined according to the H-bond constituents. The H-bonding state of one water molecule is characterized by a quantity fn (n = 0~6), which denotes that the water molecule forms n W-W H-bonds. Fig. 8 shows the percentages of confined and bulk water with the H-bonding states from f0 to f6. It is shown that bulk water prefers to form 3 and 4 H-bonds with the percentages of 35 % and 24.2 %, respectively. This indicates that the bulk water of the system retains the local tetrahedral structure, which is in agreement with previous study43. The confined water inside the membrane mainly forms 1 and 2 H-bonds. The confined water molecules with f2 take the dominant role and possess the percentage of 35 %. It implies that the water molecules confined in the PA membrane prefer to produce linear H-bond structure. The confined water molecules with f3 and f4 only occupy the percentages of 18.8 and 4.0 %, 15



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respectively. This is due to the strong confinement of the nanochannels of the PA membrane and the H-bonding attraction by the functional groups. 3.2.3 Hydrogen bond dynamics Intermolecular H-bond is usually short-time and dynamic interaction resulted from the fast vibrational and librational motions of the hydrogen bonded molecules. H-bonding dynamics can be characterized by H-bonding lifetime in terms of the continuous time autocorrelation function of the H-bond amount,44-45 which is defined as, c(t ) =

h (t ) ⋅ h(0) h ( 0) 2

(2)

where h(0) is the instantaneous amount of H-bonds at the initial time t = 0, and h(t) is the amount of the unbroken H-bonds from 0 to t. The function characterizes the structural relaxation of H-bond network. On the basis of the time autocorrelation function, the average H-bonding lifetime (߬ୌ୆ ) is evaluated by the time integral of c(t) as follows: ∞

τ HB = ∫ c(t )dt

(3)

0

Fig. 9 Autocorrelation functions c(t) of the W-W and W-P H-bonds. (CO)OH and CO(OH) denote hydroxyl and carbonyl of the carboxyl group, respectively; (NH)CO denotes carbonyl of the amide group. 16


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As shown in Fig. 9, the confined W-W H-bonds decay slower than that in bulk phase. According to Eq. (3), the lifetimes of the W-W H-bonds in the two phases are estimated to be 0.38 and 0.25 ps, respectively. This is born out from the confinement of the membrane channels. The (CO)OH-water H-bonds present the longest lifetime of about 1.14 ps, which is followed by the (NH)CO-water and NH2-water H-bonds with the lifetimes of 0.89 and 0.66 ps, respectively. And the shortest lifetime, 0.42 ps, belongs to the CO(OH)-water H-bonds. Moreover, the c(t) functions for the (CO)OH-water, (NH)CO-water and NH2-water H-bonds decay more slowly than the water-water H-bonds, and the CO(OH)-water H-bonds have comparable relaxation tendency with the confined W-W H-bonds. The W-P H-bonds are more stable than the W-W H-bonds. It indicates that there exists close interaction between water and the hydrophilic functional groups of PA membrane. Consequently, the hydrophilic functional groups located in the bulk/membrane interface help to facilitate the access of water into the membrane, enhancing the water flux.46 It was previously reported by Kulkarni et al.47 that increasing the amino and carboxyl groups of the membrane surface could enhance water flux through the membrane. There are also several experimental studies48-51 which support the relationship between the hydrophilicity of membrane surface and water flux. Conversely, high hydrophilicity of the membrane interior will definitely inhibit the water transport inside the PA membrane. This is consistent with the previous report that increasing the interior hydrophobicity of the PA membrane helps enhance the water flux.7

3.3

Water self-diffusivity Self-diffusivity could reflect the thermodynamic motions of water in bulk and

confined phases. In this section, the mean square displacement (MSD) is employed to obtain the self-diffusion coefficient of water Dw, which is produced by the slope of MSD as a function of time t.

1 dMSD(t ) D = lim 6 t →∞ dt where MSD(t) is the mean square displacement: 17


(4)


MSD(t ) =

1 NW

N

∑ r (t ) − r (0) i

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2

i

(5)

i =1

where ri (t ) is the position vector of the ith molecule at time t; the bracket < ··· > denotes the ensemble average.

Fig. 10 MSDs of water in different regions from bulk water to membrane interior Here, we focus on the water diffusivity in three regions (i.e. bulk region, bulk/membrane interface, and membrane interior). The MSDs of water in different regions are obtained using Eq. (5) and shown in Fig. 10. It shows an increasing order of self-diffusivity of water in membrane interior, bulk/membrane interface and bulk phase. Water diffuses much faster in bulk phase than that in other regions. According to Eq. (4), the self-diffusion coefficients of water in different regions can be obtained. In bulk phase, the diffusion coefficient of water Db is about 3.08×10-5 cm2/s, consistent with the experimental result.52 In the bulk/membrane interface region, water has much smaller self-diffusion coefficient (Df = 0.58×10-5 cm2/s). This is mainly due to the attraction of the functional groups as well as the block of the polymer chains. Inside the PA membrane, the self-diffusion coefficient of water (Di = 0.24×10-5 cm2/s) is about half of that in the bulk/membrane interface region, and an order of magnitude less than that in bulk water. This is further attributed to the confinement and attraction in the membrane. The simulated water self-diffusion coefficients are similar with the previous studies.14, 18-19, 53 It should still be clear that 18


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different results presented in different reports could be attributed to some degree to the heterogeneity of the water channels and local membrane structures as well as the adopted model and simulation details.

3.4

Cluster analysis Spatial distributions of the monomers and crosslinking sites are closely related to

the degrees of tortuous pores or channels in the membrane at the molecular level. It is known that only percolated pores guarantees effective water transport across the membrane, while dead-end pores can be occupied by water but have no contribution to water transport.28 The morphology of the water channels in the PA membrane has great effect on water transport. Hence, in order to better understand the morphology of the water channels, it is necessary to investigate the structural properties of the water clusters in the PA membrane.

Fig. 11 Probability distribution of the size of the largest water cluster inside the PA membrane. A water cluster is depicted as a group of water molecules which are directly or indirectly hydrogen bonded. In other words, the water molecules of the same cluster are involved in a continuous H-bonding network, which is identified by the geometric criterion as mentioned above. And the size of one cluster is characterized by the water amount in the cluster. Fig. 11 shows the probability distribution of the size of the biggest water cluster inside the PA membrane. The highest distribution is observed at 19



the cluster size of around 300. The size of the largest water cluster exhibits a relatively wide variation range from 120 to 678. The average size of the largest water cluster is estimated to be about 350. However, it is still unclear whether the membrane is spanned or not by the confined water molecules. The insets of Fig. 11 illustrate the morphology snapshot of the corresponding size of the largest water cluster. It is shown that when the largest water cluster grows to the size of 300, the PA membrane is spanned by the confined water molecules. In order to characterize the degree of the water percolation, we introduced the spanning length Lc along membrane thickness, which is defined as the length in the z-axis direction of the largest cluster inside the membrane. It is found that the largest cluster has a mean spanning length of 44.2 Å, accounting for about 96% of the membrane with the thickness of 46 Å. It implies that the water channels are well connected in the direction of membrane thickness, which definitely contributes to water transport in the PA membrane.

4. Conclusion In this work, we have successfully constructed an atomistic model of the crosslinked polyamide membrane and performed a series of MD simulations to study the structural and dynamical properties of water confined in PA membrane. Radial distribution function and orientation were used to characterize the local structure of water, which indicates that the carboxyl and amino groups as well as the amide group have affinity to water in the water/membrane/water system. This could affect the self-diffusion motion of the confined water in the membrane. H-bonding analysis was employed to further investigate the effect of membrane on the structural and dynamical properties of water in the PA membrane. H-bond criteria for different H-bonds were defined to explicitly describe the H-bond network. When one water molecule enters into the PA membrane, part of its W-W H-bonds would break down and replaced by the W-P H-bonds. This is due to the membrane confinement and the affinity of the functional groups. In general, the W-P H-bonds are more stable than the W-W H-bonds ether in bulk or confining phase. Comparing with 20


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other W-P H-bonds, the H-bonds between water and –COOH present the longest lifetime. It implies that the –COOH group of the PA membrane has strong attraction to the surrounding water molecules. Additionally, the self-diffusion coefficients of water molecules in three regions (i.e. bulk region, bulk/membrane interface, membrane interior) were estimated in the decreasing order of Db > Df > Di. This verifies the effects of the functional groups on water self-diffusion motion. Well-connected channel guarantees the easy pass of water through the membrane. Thus, the size distribution of water cluster was adopted to characterize the connectivity of water channel inside the PA membrane. There appear percolated water channels in the PA membrane, which is critical to water transport through the membrane. It was shown that the membrane is spanned by the confined water molecules when the largest water cluster grows to the size of 300. In summary, hydrophilic groups in the bulk/membrane interface facilitates the access of water into the PA membrane, reducing the transfer resistance of the dissolve process. However, high hydrophilicity of the membrane interior definitely blocks the transport of water in the PA membrane. As previously reported, increasing the interior hydrophobicity of the PA membrane enhances the water flux.7 From the view point of intermolecular interaction, enhancing the interfacial hydrophilicity and the interior hydrophobicity of the PA membrane could reduce the water transfer resistance and facilitate water flux through the membrane. Therefore, it is recommended that maintaining the appropriate mechanical strength, there should be heterogeneous hydrophilicity in the PA membrane along the direction vertical to the surface, which could be achieved by creating a gradient of crosslinking degree from the membrane interior to the surface. This paper deepens our understanding of the fundamental properties of water confined in the PA membrane and guides our future work on developing high-performance RO membrane.

Acknowledgements This research has been supported by National Natural Science Foundation of China (Grant No. 21506019), the Fundamental Research Funds for the Central 21



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Universities (Grant No. DUT16QY43), the Program for Changjiang Scholars (T2012049).

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Effect of Hydrogen Bonding Interaction on Arrangement and Dynamics

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