Anomalous Dynamics of Water in Polyamide Matrix - The Journal of

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B: Biomaterials and Membranes

Anomalous Dynamics of Water in Polyamide Matrix Fengchao Cui, Wenduo Chen, Xiangxin Kong, Lunyang Liu, Ce Shi, and Yunqi Li J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 18 Mar 2019 Downloaded from http://pubs.acs.org on March 18, 2019

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The Journal of Physical Chemistry

Anomalous Dynamics of Water in Polyamide Matrix Fengchao Cui†, Wenduo Chen†,‡, Xiangxin Kong†, Lunyang Liu†, Ce Shi† and Yunqi Li*,† †Key

Laboratory of High-Performance Synthetic Rubber and its Composite Materials,

Changchun Institute of Applied Chemistry (CIAC), Chinese Academy of Sciences, Changchun 130022, P. R. China. ‡School

of Materials, Sun Yat-Sen University, 135 Xingang West, Guangzhou 510275, P. R.

China.

*To whom correspondence should be addressed. Tel: +86-0431-85262535. Email: [email protected].

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Water in polymer matrixes is likely to show anomalous dynamics, a problem has not been well understood yet. Here we performed atomistic molecular dynamic simulations to study the water dynamics in polyamide (PA) matrix, the bulk phase of well-known reverse osmosis membranes. For time-dependent ensemble average, water molecules experienced ballistic diffusion at shorter time scale, followed by a crossover from sub-diffusion to Brownian diffusion at time scale around 10 ns, and non-Gaussian diffusion, an indication of anomalous dynamics, sticks on even at the Brownian diffusion region. The anomalous dynamics mainly originate from two distinct motions including small-step continuous diffusion and jumping diffusion. The jumping motion has mean length of 3.08 ± 0.31 Å and characteristic relaxation time of 0.218 ± 0.040 ns, dominates the water diffusion in fully hydrated PA matrix. It was comprised by low- and high-frequency jump, the former is almost unchanged and the latter remarkably increases with the increase of hydration level. Surrounding neighbors of water strongly affect the jumping frequency which exponentially or linearly decays with the increase of atoms from PA matrix. Though the PA matrix is flexible associated with water dynamics, the translocation of water is mainly through either tracing the position of neighboring water or jumping into the adjacent accommodation space.


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1. Introduction Reverse osmosis (RO) membranes have become the core materials for large-scale desalination of seawater and brackish groundwater, which is the leading solution for the shortage of fresh water resources all over the world.1,2 Polyamide (PA) active layer built through the interfacial polycondensation between metaphenylene diamine (MPD) and 1,3,5-Benzenetricarbonyl trichloride (TMC) monomers3 is comprehensively applied as the heart of RO membranes. Although remarkable progress has been achieved in promoting the water permeability and salt rejection of PA membranes, further improvements for its performance has become extremely slow due to the lack of a deep understanding for the water dynamics in the polymer matrix. To understand the dynamics of water in polymer matrix, the solution-diffusion model4 has been extensively applied to qualitatively interpret the macroscopic water flux through membranes under given operational conditions.5 This model has also been criticized due to the deficiency in understanding microscopic details that can facilitate the fine design and regulation of membranes with expected distribution of polarity and defects etc. Alternative models and important influencing factors based on elaborate observations from experiments and simulations have been reported. Based on quasi-elastic neutron scattering (QENS) measurements, Sharma et al. proposed a random jump-diffusion model6 to describe water diffusion in PA membranes. A number of equilibrium and non-equilibrium molecular dynamics (MD) simulations (EMD and NEMD) have been exploited trying to reveal the transport of water and ions associated with the surrounding structural characteristics in PA matrixes.7-20 Pioneering works using MD simulations reported by Kotelyanskii et al., where



distinct “jump-like” motion of water was directly observed.8,14 Gao et al. revealed that the dynamic regimes of water permeation include Brownian diffusion, flush and jump diffusion.19 While in contrast to these studies, EMD and NEMD simulations conducted by Ding et al.12,21 suggested that there is no sudden translational “jump” of water in PA matrix at all. Wei and co-workers7 further pointed out that the heterogeneity of local structure gave rise to the heterogeneous dynamics of water molecules in PA matrix and less cross-linked pathway resulted in the fast translocation of water molecules. Although these studies are gradually deepening the cognition for the water dynamics in PA membranes, clear statement accounting for the heterogeneous structure and the anomalous dynamics is still absent. The dynamics of water is quite different to that in bulk phase, where the mean squared displacement (MSD) exhibits a linear relation with elapsed time t and Gaussian statistics can be applied to describe the distribution of displacement. It is well-known that the structures of PA membranes are heterogeneous and cross-linked morphological structures.22 In such heterogeneous medium, anomalous dynamics is ubiquitous in nature.23-26 The anomalous dynamics can be typically characterized by a sublinear increase of the MSD or “Brownian but not non-Gaussian” behavior.26-28 The complex geometrical confinement and energy landscape of PA matrixes may result in the deviation of water dynamics from the normal one like as in the bulk phase. Kotelyanskii et al.14 reported the anomalous characteristics of water dynamics in PA matrix within 1.0 ns time scale. A well-defined description for water anomalous dynamics is still scare at longer time scale and the synergistic structure relaxation is still far away clear. In this investigation, we firstly constructed PA matrixes by the polycondensation


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between MPD and TMC using MD simulations with heuristic distance criterions. Based on the product structures, we explored water dynamics in the flexible PA matrix. Water molecules exhibit anomalous dynamics characterized by the presence of sub-diffusive regime and the non-Gaussian displacement probability distributions. We further revealed the microscopic origin of anomalous dynamics and the translocation pathway of water molecules. We believe this study can significantly deepen the understanding of water transport through PA matrix at the microscopic level. 2. Computational details 2.1 Protocols of Polycondensation Figure S1 displays the simulation timeline of the generation and swelling of PA matrix and analysis of water dynamics in PA matrix. Three parallel aromatic polyamide (PA) matrixes (M1-3) were created by imitating the interfacial polycondensation of MPD (Figure S2a) and TMC (Figure S2b) using molecular dynamics simulations. For each system, 600 MPD and 400 TMC monomers were randomly assigned into a larger box of 78.0 * 78.0 * 78.0 Å3 to avoid the steric clashes. Three simulation boxes were gradually compressed to the target volumes (60.0 * 60.0 * 60.0 Å3) by 0.5 Å decrements with conjugate gradient minimization of 2000 steps, followed by 4 ps MD simulations under NVT ensemble, in which the only exclude volume term is included. Atomic interactions was described by GAFF29, and R.E.D. tools30 with restrained electrostatic potential (RESP) approaches were used to obtain the partial charges. The highly cross-linking aromatic PA matrixes were constructed by a consecutive polycondensation of MPD and TMC monomers using the



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heuristic method,11,15 in which the distances between a free amine group and the carbonyl carbon of a free acyl chloride group are usually used to determine the occurrence of the interfacial polycondensation. The distance criterions were gradually increased from 3.25 to 5.0 Å with the increments of 0.25 Å to weaken the hindrance of reactive group diffusion. For every distance criterion, 1 ns MD simulations of the interfacial polycondensation were continuously carried out at the experimental temperature of 303 K, but were broken off every 10 ps so that the free amide and acyl chloride groups within the distance criterions were bonded. At the same time, a hydrogen atom in the amide group and a chloride atom in the acyl chloride group were removed. Parameters involving nitrogen (N) and acyl carbon (AC) were updated once the polycondensation reaction occurred and the partial charges of atoms bonded to N or AC before and after polycondensation are depicted in Figure S2c. After the 5.0 Å distance criterion corresponding to 7 ns MD simulations, the polycondensation reactions were almost finished and no more amide bonds were formed even more long MD simulations time. The unreacted MPD and TMC monomers were removed from the system to give the final structure. After that, the PA matrixes were compressed and relaxed using 21-step compression and relaxation scheme proposed by M. Colina et al.,31 followed by 10 ns equilibration simulation at 303 K and 1 atm with NPT ensemble. The final aromatic PA matrix was shown in Figure S3a with the distribution of void space. It need to be mentioned that periodic boundary condition was considered in the whole polycondensation reaction, that is, amide bonds could form between the primary unit cell and image cell, as reported by Suzuki et al..32 The degrees of polymer cross-linking (DPC) of final PA membranes were calculated

based

on

the

pending

carboxylic


groups

(COOH)

with

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100(COOHinitial-COOHfinal)/COOHinitial.12,18,21 The pore size distributions were evaluated by Zeo++ program.33 PA matrixes were swollen with water molecules by randomly inserting TIP3P H2O molecules one by one into the void space. The insertion is repeated until a desired moisture content (the mass fraction wt% =mass of H2O/mass of hydrated PA matrix). After every insertion, conjugate gradient minimization of 2000 steps followed by 10 ps MD simulations under 303 K and 0 atm were run to relax the hydrated PA matrix. In this investigation, 5.0, 10.0, 15.0, 23.0 wt% water uptakes were considered, and then the systems were equilibrated for 2 ns with NPT ensemble under constant 303 K and 1 atm. Subsequently, the 200 ns production for all systems were carried out to shed light on water dynamics in aromatic PA matrix under NVT ensemble. The trajectories were recorded in every 20 fs before 5 ns and 200 fs after 5 ns. In the process of compression and swollen PA matrixes, NPT ensemble was used to adjust the volume of dry or hydrated PA matrixes, and NVT ensemble was employed in the constructed PA matrixes and the investigation of water dynamics. Langevin thermostat was used to maintain the temperature at 303 K with the dampening coefficient of 5 ps-. Pressure was scaled at 1 atm with Nosé-Hoover Langevin piston method 34-37 with the piston period of 100 fs, the piston decay of 50 fs, and the piston temperature at 303 K. Periodic boundary conditions were applied and long-range electrostatics were treated using the particle-mesh Ewald (PME) method.38,39 Non-bonded interactions were calculated using a cutoff of 12 Å without switch function, and a 14 Å neighbor list was updated every 10 steps of the dynamics. The integrated time step is set to 2 fs. All covalent bonds involving hydrogen atoms were



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confined by SHAKE algorithm.40,41 All MD simulations were performed with NAMD 2.9 program.42 2.2 Analysis of water dynamics To examine water motion, we firstly determined the time dependence of quantities, i.e., the mean-squared displacement (MSD) with the following equation (Eq. 1):

  MSD( t )  | ri ( t )  ri (0) |2

(1)



where ri ( t ) denotes the position of the particle i at time t, and the represents the moving time average over molecules and time origins. The diffusion coefficients (DE) can be obtained from the Einstein relation in the long time limit, i.e., the Brownian regime. Whether or not water diffusion within PA matrix obeys Gaussian statistics can be determined by so-called non-Gaussian parameter which is given by Eq. 2

α 2 (Δt ) 

3  Δr 4 (Δt )  5  Δr 2 (Δt ) 

1

(2)

This quantity should be strictly zero for standard Gaussian process, and non-zero value indicates a non-Gaussian behavior. The microscopic source that gives rise to non-Gaussian behavior can be identified by looking directly the displacement distribution within a given time, i.e., the self-part of the van Hove correlation function (VHCF) 43 given by Eq. 3

1 Nw    G s (r, t )   δ( r  | ri ( t )  ri (0) | N w i 1

(3)

where the denotes ensemble average, δ is the Dirac delta function, Nw is the number of



water molecules, and ri ( t ) is the position vector of atom i at time t. This function represents


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the probability that a molecule has moved a distance r during time t. For the tagged particles undergoing Brownian motion, the self-part of VHCF should be a Gaussian form (Eq. 4)

G sg (r, t )

r2  exp( ) 3/ 2 4 Dt (4 πDt ) 1

(4)

where D is the diffusion constant. Random jump-diffusion model plus small-step continuous diffusion model (Eq. 5) proposed by Molinero and coworkers44 can perfectly describe the diffusive behavior of water in PA matrix.

Q 2 l 02 1 1 2  ( )  D Q C τ τ 0 6  Q 2 l 02

(5)

where, the first term at the right represents the random jump-diffusion model,

τ0

is the

residence time between jumps and l0 is the jumping length. The second term represents small-step continuous diffusion, which is considered as Brownian diffusion described by Fick’s law, and DC is the continuous diffusion constant. dependent on the wave vector Q2.

τ

τ

is the characteristic time constant

can be evaluated with the following equation (Eq. 6),

τ 1 τ  Γ( ) β β

(6)

where, Г is the gamma function, and τ and β are determined by fitting the self-intermediate scattering function (SISF) using the Kohlrausch-Williams-Watts function (KWW).45 SISFs were calculated using 18 equispaced

 Q values

in the range of 1.820.0 nm-1. Here,

LiquidLib toolbox46 is employed to analyze water dynamics in PA matrix. 3. Results and Discussion



3.1 Structure of Polyamide Matrix Atomistic models of PA matrixes were manufactured by the polycondensation of MPD and TMC with the modified heuristic distance criterion,11,15 which can overcome the fast slowdown of polycondensation reaction, resulting from the diffusion of reactive site is impeded as the growth of crosslinking clusters. Figure 1 shows the kinetics of polycondensation reaction of MPD and TMC, the changes of local topology structure, the structure of saturated swollen PA matrix, and the pore size distribution. As shown in Figure 1a, the evolution of fraction against polycondensation time is highly non-linear, comprising an initial fast regime followed by a much slower and asymptotic growth stages. Detailedly, film growth went through four distinct stages, i.e., random collision(mont2.0), the random growth (mont1/2), the confined diffusion (mont1/3) and the mergence of some clusters (mont0), being reasonable agreement with the report of Srebnik et al.47. It can be seen from Figure 1b that a plenty of oligomers were quickly formed at the initial stage, as observed by Muscatello et al,48 and the maximum appears at the stage 3 with mont1/3, followed by the exponential decay of the amount of clusters. Figure 1c shows that the local topology structures convert from low coordination to high coordination. The final PA membrane is made of a larger crosslinking cluster and a spot of short fragments composing of several MPD and TMC monomers. An oxygen to nitrogen ratio of 1.33 of so-constructed dry membrane is close to the experimental value of commercial membranes22,49-51 and the previous simulation reports.7,12 The degree of polymer cross-linking of final PA membrane is 86.0%, which is in line with the values reported by those simulations12,13 and experiments measured.22,50 We also quantified the average number


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of monomer units between cross-link junctions with Nx=4.0, which is lower than semi-aromatic PA network (Nx=5.0) anticipated by Chan et al.52 and is relatively consistent with the later experimental value (Nx=3.6).53 The density of dry and hydrated PA matrix (1.28 and 1.30 g/cm3) is close to the reported values in the literature.7,8,13 The calculated pore size distributions (PSDs) is qualitatively consistent with PALS54 and SAXS experiments55 and the results reported by the others’ researcher.15,21 As the increase of water content, the PSDs gradually broaden, indicating the increase of the amount of the pore with larger size. Figure S4 depicts the total structure factors of the dry PA matrix and hydrated PA matrixes with the different water uptake. The structure factors were calculated with the Debye equation using the ISAACS program.56 Evidently, the plots indicate that PA matrixes primarily are amorphous without evident periodicity. At the higher q (~1.5 Å-1), a broad correlation peak of intra-molecular chains of PA membrane was obtained, which is good agreement with the experimental SAXS55 curve and the calculated X-ray scattering intensities.8 These results verify that the fabricated PA matrix could represent the real micro-structure in the most densest interior region of PA membrane. 3.2 Water Dynamics To examine the water motion in PA matrix, we firstly evaluated the mean-squared displacement (MSD) of the oxygen of water. Figure 2a depicts the curves of MSD against long time scale for different water content. The dynamic behavior of water at the shorter time was emphasized in Figure S5. The motions of water are characterized by the presence of three regimes distinguished with the different slopes. For all water contents, water molecules



undergo the so-called ballistic region (MSD  Δt2) corresponding to the local vibration at the shorter time scale (

Anomalous Dynamics of Water in Polyamide Matrix - The Journal of

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