Original Article | Published:

Hydration structure of reverse osmosis membranes studied via neutron scattering and atomistic molecular simulation

Polymer Journalvolume 50pages327336 (2018) | Download Citation

Abstract

Reverse osmosis (RO) membranes are becoming popular as energy saving and environmentally friendly materials for the desalination of water. Toward the rational design of RO membranes, we performed contrast-variation neutron scattering measurements and atomistic molecular dynamics (MD) simulations on polyamide/water systems with various water contents and deuteration ratios. The experimental and computational structure factors showed good agreement for all the systems examined. The structure of the water-rich polyamide/water system obtained from MD calculation showed that the water clusters are well connected to each other, and a relatively large number of water molecules are present at a distance over 3 Å from the polyamide. The partial radial distribution functions were calculated, and strong interactions were observed between water and the carboxyl group in polyamide. Thus, the water permeability of the RO membrane can be expected to improve when more carboxyl groups are introduced. In addition, the polyamide–polyamide interaction was found to be equal to or smaller than the polyamide–water interactions and relatively weak in the water-rich system.

Introduction

Due to global water shortages and water quality deterioration, there is increasing demand for the production of potable water. Consequently, the market for water treatment is growing considerably. Reverse osmosis (RO) membranes are rapidly becoming popular materials for desalination, being both energy saving and environmentally friendly [1,2,3,4]. Most current RO membranes are thin-film composite polyamide membranes, which are composed of a functional layer for separation, a supporting layer, and a substrate [5, 6]. The functional layer, which separates the solutes from the feed water, is made of crosslinked aromatic polyamide. There are several characteristics required for RO membranes: water permeability, a high rejection rate for salt and other solutes like boric acid, chemical stability, and low-fouling properties. The control of these characteristics by controlling the membrane morphology (nanometer scale) and pore structure (sub-nanometer scale) of the functional layer is important, and several investigations in this area have been conducted [7,8,9,10,11,12,13,14]. From transmission electron microscope (TEM) studies, protuberance structures have been observed on the functional layer, and the surface area and number density of the protuberances were found to be positively correlated with the water permeability, whereas the thickness of the protuberances estimated from TEM images found to be negatively correlated with the permeability [9, 14]. In addition, an analysis of the pores using positron annihilation lifetime spectroscopy revealed that the pore size is positively correlated with the water permeability and negatively correlated with the rejection rates of the solutes, respectively [9, 14].

In the functional layer, polyamide and water are thought to form a hydrogel-like structure, and this structure affects the permeation of water and the rejection of solutes. However, the details of the hydration structure at a molecular level are still unclear. Because the pore sizes in the functional layer are very small (sub-nanometer scale), it is challenging to obtain reliable information about the hydration structure using indirect methods, as well as direct observation using TEM. Regarding the pores in the functional layer, it is possible to form design guidelines for RO membranes assuming a phenomenological model, such as Hagen–Poiseuille flow [15]. However, the phenomenological understanding is limited because the interactions between water and polyamide are not considered, and the permeation phenomenon through small pores of sub-nanometer scale is often different from that of the phenomenological model.

However, by obtaining a clear understanding of the structure and dynamics of water molecules in the membranes and by controlling them precisely, the performance of RO membranes, especially the water permeability, can be drastically improved. Toward the rational design of RO membranes, we have used neutron scattering experiment and molecular dynamics (MD) simulations to obtain information on the hydration structure in the functional layers at atomic resolution. Because X-rays interact with the electron cloud of the scattering atoms, the scattering ability depends on the atomic number, and the sensitivity to light elements such as hydrogen is low. Because neutrons are scattered by the atomic nucleus, the scattering ability is not dependent on the atomic number, and even hydrogen can be observed with high sensitivity. Therefore, neutron scattering is suitable to analyze the hydration structure of polymers.

First, we describe the study of the saturated water content using the adsorption isotherm of the functional layer. Because the water content is thought to be an important parameter affecting the water permeability of RO membranes, polyamide/water systems with various water contents, including saturated membranes, can be used for the analysis described in the following sections. Second, the structure factors obtained from the neutron scattering and the MD simulations are compared. In complex systems consisting of polyamide and water, the sum of the scattering contributions arising from the interactions between multiple components is observed. To separate these contributions, we applied the contrast variation method [16, 17] for the neutron scattering experiments, and polyamide/water systems with various deuteration ratios were examined. Finally, the functional groups of the polyamide that are closely related to the water permeation are discussed to provide guidelines for improving the performance of RO membranes.

Methods

Contrast variation method

The static structure factor S(Q) observed by neutron scattering is related to the partial structure factor S ij (Q) and the partial radial distribution function g ij (r), as shown in Eqs. (1) and (2).

$$S(Q) = \mathop {\sum}\limits_i \mathop {\sum}\limits_j w_{ij} S_{ij} (Q)$$
(1)
$$S_{ij}(Q) = 4\pi \rho {\int} r^{2}{(g_{ij}(r) - 1)} \frac{\sin {(Qr)}}{Qr}dr + 1$$
(2)

Here, ρ is the atomic number density, and w ij is the weight factor for a pair formed by the atomic species i and j and is expressed as:

$$w_{ij} = \frac{{c_ic_jb_ib_j}}{{\left\langle b \right\rangle ^2}}.$$
(3)

Here, c i and b i are the number concentration and coherent neutron scattering length for atomic species i, respectively, and <b> is the average of coherent neutron scattering lengths (Σc i b i ). In the present study, c i was obtained from the molecular model of polyamide shown in Fig. 1 and the composition of the system listed in Table 1. b i was taken from the National Institute of Standards and Technology database [18]. The molecular model and composition will be described in detail in the subsection concerning MD calculations.

Fig. 1
Fig. 1

Molecular model of the aromatic polyamide used for the MD calculations. (Color figure online)

Table 1 System name, water content, the numbers of polyamide, and water molecules in the MD unit cell, and the initial density

In a complex system consisting of polyamide and water, the sum of the scattering contributions arising from the interactions of multiple components, such as polyamide–polyamide, water–water, and polyamide–water interactions, is observed. To separate these contributions, we applied the contrast variation method [16, 17]. For this method, we examined systems with various deuteration ratios to vary the weight factor, w ij . Figure 2 illustrates the weight factors wpp, www, and wpw as a function of the deuteration ratio for the system with 26 wt.% water content; wpp, www, and wpw are the weight factors related to polyamide–polyamide, water–water, and polyamide–water interactions, respectively, and detailed definitions concerning these are provided in the caption of Fig. 2. Because www and wpw are ~0 at the deuteration ratio indicated by the arrow in Fig. 2, only the scattering contribution from wpp can be observed.

Fig. 2
Fig. 2

Weight factors wpp, www, and wpw vs. the deuteration ratio of the system with 26 wt.% water content. wpp, www, and wpw are the sum of w ij in Eq. (3) over the pairs formed by the pairs of atoms p and w. The set of atoms p consists of the atoms in the polyamide without the hydrogen atoms in the amide, amine, and carboxyl groups. The set of atoms w consists of the hydrogen and oxygen atoms in water and the hydrogen atoms in the amide, amine, and carboxyl groups of the polyamide. (Color figure online)


Separation of the functional layer

The functional layer was separated from an RO membrane that had been manufactured by our production machine. The porous supporting layer including functional layer was peeled off from the nonwoven fabric, and the supporting layer was dissolved and washed off using organic solvents. During the operation, the sample of functional layer was carefully treated to maintain it in a wet state (for a detailed experimental scheme, see the Supplementary Information).


Adsorption isotherm measurement

A functional layer of ca. 15 g was placed on a digital balance in a glove box maintained at 25 °C, and a small ultrasonic humidifier was also placed in the glove box to control the humidity at a constant value. The equilibration of the system continued until the weight change over 5 h converged to within 5%. This procedure was conducted at various humidities, and the equilibrium weight of the wet sample, W1, was measured. After completion of all measurements, the functional layer was vacuum dried at 100 °C in a vacuum dryer, and the weight of the absolutely dry sample, W0, was measured. The water content, W, at each humidity level was calculated using Eq. (4).

$$W( {wt.\% } ) = \{ (W_1 - W_0 \}/ W_1\} \times 100$$
(4)

Moisture conditioning

The moisture conditioning of the samples was carried out as follows. The functional layer was hydrated in a glove box under atmospheric conditions determined based on the adsorption isotherm and sealed in cylindrical vanadium cells of 6 mm inner diameter and 50 mm length. The water contents of the samples were adjusted to be 9, 16, and 26 wt.%. The saturated water content of the functional layer was found to be ca. 16 wt.%, and this is described in detail in the “Results and discussion” section. The sample with 26 wt.% water content was prepared by the evaporation of the excess water. For the moisture conditioning of the samples, H2O, D2O, and H2O/D2O (denoted M2O) mixtures were used. For the samples obtained, the system (sample) name, water content, deuteration ratio, and weight factors are listed in Table 2. For the M2O system, www and wpw were found to be ~0, as shown in Table 2. This indicates that the scattering contributions related to the water–water and polyamide–water interactions are zero, and the contribution relating to the polyamide–polyamide interactions is dominant.

Table 2 System name, water content, deuteration ratio, and weight factors

Neutron scattering measurements

Neutron scattering measurements were carried out on polyamide/water systems in the vanadium cell, an empty cell, a vanadium standard sample, and background using the pulsed time of flight instrument iMATERIA installed at Materials and Life Science Experimental Facility. The raw data for each run were collected at scattering angles (2θ) of 35°, 90°, and 155°. The duration of each measurement was 5 h. Corrections for the attenuation and subtraction of the scattering from the empty cell and background were made. The data were normalized using corrections for multiple scattering, detector efficiencies, and factors of the energy spectrum of the incident neutron beam. A recoil correction was performed using cubic spline interpolation method to estimate the recoil effect baseline.


MD calculations

A molecular model of the aromatic polyamide used for the MD calculations was determined based on structural analyses by solid-state 13C-NMR spectroscopy [19]. The chemical structure of this model is shown in Fig. 1. The molecular weight of the polyamide is 3573 g/mol. The system name, water content, numbers of polyamide and water molecules in the MD unit cell, and initial density are listed in Table 1. These system names and water contents correspond to those in Table 2. The initial density of the system was set to 0.2–0.3 g/cm3 to ensure rapid convergence to the (local) equilibrium state. The initial structure of the polyamide/water system was constructed using the following scheme. After the torsion angles of each polyamide chain had been generated randomly, the polyamide and water molecules were placed randomly into the MD unit cell with the number of molecules listed in Table 1. The periodic boundary conditions were applied. After energy optimization at constant volume, 2-ns MD calculations were conducted for further equilibration under the conditions listed in Table 3 to relax the initial stress in the system. The 2-ns duration was partitioned into four steps to accelerate the relaxation. At step 1, the NVT ensemble was employed to suppress abrupt changes in the MD unit cell. At step 3, simulated annealing was conducted by varying the temperature from 300 to 600 K with five repeated heating–cooling cycles. The temperature and pressure were maintained by the Nosé-Hoover thermostat [20] and the Andersen barostat [21], respectively.

Table 3 MD conditions for structural relaxation

Ten-ns MD calculations were carried out for the production runs in NPT ensemble at 1 atm and 300 K. The MD simulations were performed on four different initial structures for each system to reduce the statistical error arising from the choice of the initial structure. The properties obtained from these four MDs were averaged. The molecular modeling and energy optimization of the initial structures were conducted with Materials Studio (BIOVIA Inc.) [22]. The MD calculations were performed with our own MD code. Detailed descriptions of the simulation conditions and potential parameters for the MD calculations are provided in the Supplementary Information.

Results and discussion

Adsorption isotherm and saturated water content

The adsorption isotherm obtained from the experiment is shown in Fig. 3. Water content (W) of the functional layer increased to ca. 16 wt.% as the relative humidity approached 100%. Based on this result, the saturated W was determined to be ca. 16 wt.%. In the actual composite RO membranes, the functional layer is saturated with water; hence, the study of the hydration structure of the polyamide/water system around the saturated water content is particularly important.

Fig. 3
Fig. 3

Water content (W) of the functional layer vs. relative humidity

Comparison between the experimental and computational structure factors

Here, we compare the computational and experimental structure factors and discuss the water content and deuteration ratio dependencies of the structure factors. The structure factors, S(Q), obtained from experiment and the MD calculations are shown in Fig. 4. The computational S(Q) values were evaluated from the partial radial distribution functions, g ij (r), using Eqs. (1)–(3), and g ij (r) was obtained from the 10-ns MD run. As shown in Fig. 4, the experimental and computational structure factors show good agreement for all the systems examined. Despite using the small unit cell in the MD calculations (ca. 30 Å), the agreement is found even in the low-Q region. This result indicates that polyamide/water systems in the experimental samples have a uniform structure. A possible reason for the difference in the first maximum of S(Q) for the D2O system containing 26 wt.% water is existence of relatively large structural fluctuations in the water-rich system.

Fig. 4
Fig. 4

Comparison between the structure factors, S(Q), obtained from experiment and MD calculation for systems containing a 9, b 16, and c 26 wt.% water. Top: H2O, middle: D2O, and bottom: M2O mixtures

Because the weight factors www and wpw are 0 and wpp is not 0 for the M2O system, as shown in Table 2, the agreement between the computational and experimental S(Q) for M2O system indicates that the scattering contributions related to the polyamide–polyamide interactions are well reproduced by the MD calculations. Because the water–water and polyamide–water interactions for D2O and H2O systems further contribute to S(Q), the reliability of the hydration structures obtained from MD calculations is demonstrated by the agreement between the computational and experimental S(Q) for both D2O and H2O systems.

The water content and deuteration ratio dependencies of the structure factors are discussed below. In Fig. 4, no significant dependence is shown in the first maximum at Q = 1.6 Å−1 for all the systems examined. At higher water contents, the first minimum at Q = 2.3 Å−1 is lower, and the maximum at 5.4 Å−1 is higher for the H2O and M2O systems, indicating that different hydration structures are formed depending on water content.

Partial structure factors obtained from MD calculations

Here, we discuss the maxima and minimum at Q = 1.6, 2.3, and 5.4 Å−1 of the structure factor S(Q) shown in Fig. 4 with the partial structure factors obtained from the MD calculations. Figure 5 shows the partial structure factors with a weight factor (2-δ ij )w ij S ij (Q) obtained from the 10-ns MD runs, where δ ij is the Kronecker delta. As shown in Eq. (1), S(Q) is sum of the partial structure factors with weight factor (2-δ ij )w ij S ij (Q). S ij (Q) evaluated from the partial radial distribution functions g ij (r) using Eq. (2), and w ij was calculated using Eq. (3).

Fig. 5
Fig. 5

Partial structure factor with weight factor (2-δ ij )w ij S ij (Q) obtained from MD calculations on systems containing a 9, b 16, and c 26 wt.% water, where δ ij is the Kronecker delta. Top: H2O, middle: D2O, and bottom: M2O mixtures. HW hydrogen in water, HP hydrogen in phenyl group, CP carbon in phenyl group, CA carbon in amide and carboxyl groups, NA nitrogen in amide group, OA oxygen in amide and carboxyl groups, OW oxygen in water

For the first maximum at Q = 1.6 Å−1 of S(Q), the water content and deuteration ratio dependencies of (2 ij )w ij S ij (Q) are described below. For the H2O and M2O systems shown at the top and bottom of Fig. 5, the water content dependence of the (total) S(Q) is canceled by the positive and negative (2 ij )w ij S ij (Q). The largest (2 ij )w ij S ij (Q) is that for the CP–CP (carbon in phenyl group–carbon in phenyl group) pair, followed in order by those for HW–OW (hydrogen in water–oxygen in water), CP–HW (carbon in phenyl group–hydrogen in water), CP–HP (carbon in phenyl group–hydrogen in phenyl group), and CP–OW (carbon in phenyl group–oxygen in water) pairs in descending order. (2 ij )w ij S ij (Q) for the CP–CP pair is positive and does not change when the water content increases. For the HW–OW and CP–HW pairs, (2 ij )w ij S ij (Q) are negative and decrease with increasing water content. For the D2O system shown in the middle of Fig. 5, in contrast, (2 ij )w ij S ij (Q) for the CP–CP pair is positive and decreases with increasing water content. For the HW–OW pair, (2 ij )w ij S ij (Q) is positive and increases with increasing water content.

For the first minimum at Q = 2.3 Å−1 of S(Q), the water content and deuteration ratio dependencies of (2 ij )w ij S ij (Q) are described below. For the H2O and M2O systems, the largest (2 ij )w ij S ij (Q) is that for the HW–OW pair, followed in order by those for the CP–HW, CP–HP, and CP–OW pairs in descending order. For the HW–OW pair, (2 ij )w ij S ij (Q) is negative and decreases significantly as the water content increases. This is the reason why S(Q) at Q = 2.3 Å−1 in Fig. 4 is lower at higher water contents. For the D2O system, in contrast, (2 ij )w ij S ij (Q) for the HW–OW pair is positive and increases as the water content increases.

For the maximum at Q = 5.4 Å−1 of S(Q), the water content and deuteration ratio dependencies of (2 ij )w ij S ij (Q) are described below. For the H2O and M2O systems, the largest (2 ij )w ij S ij (Q) is that for CP–CP pair, followed in order by those for the CP–NA (carbon in phenyl group–nitrogen in amide group), CP–HW, CA–CP, and CP–OW pairs in descending order. For the CP–CP and CP–OW pairs, (2 ij )w ij S ij (Q) are positive and increase with increasing water content. This is the reason why S(Q) at Q = 5.4 Å−1 in Fig. 4 is higher when the water content is higher. For the D2O system, on the other hand, the largest (2 ij )w ij S ij (Q) is that for the CP–CP pair, followed in order by those for CP–HW, CP–NA, CA–CP, and HW–HW pairs in descending order. When water content increases, the (2 ij )w ij S ij (Q) for CP–CP, CP–NA, and CA–CP pairs decrease and those for the CP–HW and HW–HW pairs increase.

Hydration structure of polyamide obtained from MD calculations

In this subsection, we describe the hydration structure of the polyamide/water system obtained from MD simulations. A snapshot structure for the system (b) with 16 wt.% water content is illustrated in Fig. 6. The complex hydrogen-bonded network formed between polyamide–polyamide, water–water, and polyamide–water are shown as solid yellow lines in Fig. 6. The water molecules bound to polyamide may play an important role in structure formation of the polyamide/water system.

Fig. 6
Fig. 6

Snapshot for system (b) (16 wt.% water). The hydrogen bonds are displayed based on geometric criteria (rhydrogen–acceptor ≤ 3.0 Å, θdonor–hydrogen−acceptor ≥ 150°). Hydrogen atoms connected to a carbon atom are not shown

The state of the water in the polyamide is discussed below. Various expressions and definitions for the state of the water in polymer have been suggested based on differential scanning calorimetry, NMR, and X-ray diffraction studies [23,24,25,26], for example, free, bound, hydrated, nonfreezing, and intermediate water. In the present study, we classified the water molecules at a short distance from polyamide as bound water, whereas others are classified as free water. The distance threshold for the classification was set at 3 Å based on the first peak end positions of the radial distribution functions, as shown in Fig. 7. The distribution of free and bound water molecules in polyamide are shown in Fig. 8. The structure of system (c), which contains more water than the saturated value (ca. 16 wt.%), shows that the water clusters are connected to each other. In contrast, the water clusters in system (a), which has a lower water content than the saturated value, are not well connected. System (b), which has a water content near the saturated value, exhibits intermediate behavior. The amount of free and bound water molecules in the polyamide is also shown in Fig. 9. A relatively large amount of free water is observed in system (c). In contrast, there is almost no free water in system (a). In addition, a small amount of free water exists in system (b).

Fig. 7
Fig. 7

Partial radial distribution functions g ij (r) for pairs formed by the atoms in polyamide and water for the systems containing a 9, b 16, and c 26 wt.% water. HC hydrogen in carboxyl group, OW oxygen in water, OA oxygen in amide group, HW hydrogen in water, HM hydrogen in amine group, HA hydrogen in amide group, HP hydrogen in phenyl group, OC hydroxyl oxygen in carboxyl group, NM nitrogen in amine group, NA nitrogen in amide group, CP carbon in phenyl group. g ij (r) for HA–OA was obtained without the pair formed by the atoms within the same amide group

Fig. 8
Fig. 8

Distribution of free and bound water molecules in polyamide for systems containing a 9, b 16, and c 26 wt.%. The water molecules within 3 Å from polyamide are defined as bound water. The others are defined as free water

Fig. 9
Fig. 9

Amount of free and bound water in polyamide for the systems containing a 9, b 16, and c 26 wt.% water. The water molecules within 3 Å from polyamide were classified as bound water. The others were classified as free water. (Color figure online)

Figure 7 shows the partial radial distribution functions, g ij (r), for pairs formed by the atoms in polyamide and water for the systems containing 9 (a), 16 (b), and 26 wt.% water (c). There are peaks at distances of 1.8–2.1 Å (hydrogen–acceptor) and 2.7–3.1 Å (donor–acceptor), which can be explained by the hydrogen bonds in the polyamide–water and polyamide–polyamide pairs. In terms of the strength of the polyamide–water interaction estimated by the height of the first peak for the hydrogen–acceptor pair, the strongest interaction is observed between the hydrogen atoms in the carboxyl groups and the oxygen atoms in water (HC–OW), followed in order by amide oxygen in carboxyl groups and hydrogen in water (OA–HW), hydrogen in amine and amide groups and oxygen in water (HM–OW and HA–OW), and hydrogen in phenyl group and oxygen in water (HP–OW) in descending order. For the HP–OW pair, the peak derived from hydrogen bonding (1.8–2.1 Å) is not observed, and the peak at distance of 2.8 Å is considered to be derived from water molecules interacting to the neighboring amide, amine, and carboxyl groups. The strength of interaction between hydrogen and oxygen in the amide groups (HA–OA) is considered to be the major component in the polyamide–polyamide interactions and is found to be almost equal to those of HM–OW and HA–OW but smaller than those of HC–OW and OA–HW. At a higher water content, the peaks of g ij (r) are lower except for the amide–amide pair (HA–OA). This indicates that the water molecules, which weakly interact with polyamide, increase in the water-rich system.

Figure 10 shows the integrated coordination number, N, from the radial distribution function for the donor–acceptor pair in the range of r ≤ 3.5 Å. As the number of water molecules increases, the coordination of water molecules with atoms in the functional groups in polyamide increases, thus N increases. This trend is consistent with that of the amount of bound water shown in Fig. 9. The water content dependency of the integrated coordination number is remarkable for the carboxyl and amine groups, indicating that water molecules coordinate preferentially around the carboxyl and amine groups as the number of water molecules increases. As the number of water molecules increases, in contrast, the amide–amide coordination number decreases. These results suggest that the amide–amide hydrogen bonds break and those of amide–water form as the number of water molecules increases.

Fig. 10
Fig. 10

Integrated coordination number N (r ≤ 3.5 Å) from the radial distribution function for pairs formed by the atoms in polyamide and oxygen in water for the systems containing a 9, b 16, and c 26 wt.% water. OC hydroxyl oxygen in carboxyl group, OW oxygen in water, OA oxygen in amide group, NM nitrogen in amine group, NA nitrogen in amide group, CP carbon in phenyl group. N for HA–OA was obtained without the pair formed by the atoms within the same amide group. (Color figure online)

Conclusions

Toward the rational design of RO membranes, we performed neutron scattering measurements and atomistic MD simulations on polyamide/water systems to study the hydration structure of the functional layer in RO membranes at atomic resolution. From the adsorption isotherm obtained by experiment, the saturated water content of the functional layer was found to be ca. 16 wt.%. Thus, the water contents of the systems were set to be 9, 16, and 26 wt.% for the structural analyses. To separate the scattering contributions related to the polyamide–polyamide, water–water, and polyamide–water interactions, we used the contrast variation method for the neutron scattering, and polyamide/water systems with various deuteration ratios were examined. The experimental and computational structure factors showed good agreement for all the systems examined. This result indicates that the MD calculations well reproduce each interaction in the polyamide/water systems.

The structure of water-rich polyamide/water system obtained from MD calculation showed that the water clusters are well connected to each other, and a relatively large amount of free water, classified by the distance from polyamide, was observed. It is important to control both the channel structure of water and the amount of free water to improve the permeability and selectivity of the RO membrane. The partial radial distribution functions were calculated, and strong interactions were observed between water and the carboxyl groups in polyamide. The water permeability of RO membranes can be expected to improve when carboxyl groups, which strongly interact with water, are introduced. In addition, the amide–amide interaction, which is a major component of the polyamide–polyamide interactions, was found to be equal to or smaller than the polyamide–water interactions and relatively weak in the water-rich system. The production, operation, and washing processes are considered to influence these interactions, and the change in these interactions may affect the mobility of water molecules in the channels. In subsequent work, we will analyze the dynamics of polyamide/water systems by using quasielastic neutron scattering measurements and atomistic MD simulations.

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Acknowledgements

The authors greatly acknowledge Prof. Osamu Yamamuro (The University of Tokyo), Prof. Kenji Maruyama (Niigata University) and Prof. Toru Ishigaki (Ibaraki University) for the technical advice about the data analysis of neutron scattering. The neutron experiments at the Materials and Life Science Experimental Facility of the J-PARC were performed under the user programs (Proposal No. 2014AM0006, 2014AM0007).

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Affiliations

  1. Advanced Materials Research Laboratories, Toray Industries, Inc., 2-1 Sonoyama 3-chome, Otsu, Shiga, 520-0842, Japan

    • Tomonori Kawakami
  2. Material Science Laboratories 2nd Material Science Laboratory, Toray Research Center, Inc., 3-7 Sonoyama 3-chome, Otsu, Shiga, 520-0842, Japan

    • Masaru Nakada
    •  & Kazuyuki Okada
  3. Global Environment Research Laboratories, Toray Industries, Inc., 2-1 Sonoyama 3-chome, Otsu, Shiga, 520-0842, Japan

    • Harutoki Shimura
    •  & Masahiro Kimura

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Conflict of interest

The author declares that they have no competing interests.

Corresponding author

Correspondence to Harutoki Shimura.

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DOI

https://doi.org/10.1038/s41428-017-0019-1