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An investigation of proton conductivity of PVA, PBI and SPEEK polymer membranes using molecular dynamics simulation
Journal of Molecular Liquids 296 (2019) 111781
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
An investigation of proton conductivity of PVA, PBI and SPEEK polymer membranes using molecular dynamics simulation Mahmoud Rahmati a, *, Marjan Jangali b, Hossein Rezaei c, d a
Department of Chemical Engineering, Graduate University of Advanced Technology, Kerman, Iran Department of Chemical Engineering, Shahid Bahonar University of Kerman, Iran c Petroleum Engineering and Development Company (PEDEC), National Iranian Oil Company (NIOC), Tehran, Iran d Chemical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 January 2019 Received in revised form 8 September 2019 Accepted 19 September 2019 Available online 8 October 2019
The conductivity and diffusion of hydronium ions at 298 K in PVA (Polyvinyl alcohol), PBI (Polybenzimidazole) and SPEEK (Sulfonated polyether ether ketone) as known membranes of PEMFCs have been investigated using molecular dynamics simulation method throughout this work. The simulation results show that the diffusion of hydronium ions in these polymer membranes depends on the polymer structure and water concentration in the membrane. On the other hand, RDF analysis results also show that the tendency of hydronium ions to polymer atoms strongly depends on the water concentration. So their tendency to polymer chains decreases with increasing the water concentration in PBI and PVA. Based on the results of this investigation, the conductivity of hydronium ions in PVA is more than the two other membranes (¼19.83 ms/cm in 30 wt % of water). © 2019 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics simulation Polymer membrane Proton conductivity PEMFCs
1. Introduction Proton exchange membrane fuel cells (PEMFCs) convert chemical energy into electrical energy which has high efficiency, high energy and low impact on environmental pollution as environmentally friendly energy resource [1e4]. Recently, PEMFCs have attracted much attention due to its simplicity of operation, high efficiency and low cost. Proton exchange membrane (PEM) which conducts the proton flow from anode to cathode plays an important role in PEMFCs [4e6]. Based on previous studies, the polymer chain structure which has an important effect on the proton conduction process in PEM [7e12] can be investigated with experimental and simulation methods [13e19]. Molecular dynamics (MD) simulation as a powerful method can precisely predict the physical and thermodynamic properties of materials. This method can be used to study the mechanism of the processes in atomic and molecular scales. It is also usable for atomic study of proton permeability through the polymer membranes which has been attractive for researchers and there have been many studies in this field. Bahlakeh et al. [19] have used molecular dynamics simulation in order to compare transport
* Corresponding author. E-mail address: [email protected] (M. Rahmati). https://doi.org/10.1016/j.molliq.2019.111781 0167-7322/© 2019 Elsevier B.V. All rights reserved.
properties of hydronium ions in non-sulfonated and fully sulfonated poly ether ketone (SPEEK) membranes. They have observed that the diffusion coefficient and conductivity of hydronium ions enhance with increasing degree of sulfonation and temperature in non-SPEEK and fully SPEEK membranes. Pahari et al. [20] have characterized the structural and dynamical properties of phosphoric acid doped polybenzimidazole (PBI) membrane at various concentrations of phosphoric acid using MD simulation. They have reported the contribution of different atoms in bonding with hydrogen in this membrane. The simulation performed by Zhu et al. [21] shows that the hydrogen bonds have effect on proton mobility in PBI membrane which is dependent on the polymer structure. The mobility of water molecules in blend membranes of polyvinyl alcohol (PVA) and its relation to polymer structure have been studied using MD simulation by Wang et al. [8] and Wei et al. [10]. In this investigation, the proton mobility in PVA, SPEEK and PBI as the most common proton exchange membranes has been investigated using MD simulation. For this purpose, mean square displacement (MSD) and diffusion coefficients of hydronium ions and water molecules were calculated in different conditions. In addition, the effect of hydrogen bonds on mobility of hydronium ions in these membranes was also investigated. Then, a comprehensive analysis of radial distribution function (RDF) was performed to study the behavior of hydronium ions and water
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molecules in polymer chains. And finally, the simulation results were compared with the results of the previous studies.
2. Models and methods 2.1. Molecular structure The structure of monomer, polymer chain and polymer membrane were constructed to perform MD simulation and calculate diffusion coefficient and proton mobility of hydronium ions and water molecules. The molecular structures of PVA, PBI and SPEEK monomers are shown in Fig. 1. PVA, PBI and SPEEK polymer chains with 50, 15 and 15 monomers consist of different types of atoms. The oxygen and sulfur atoms in SPEEK, nitrogen atoms in PBI and oxygen atoms in PVA have an effect on mobility of hydronium ions in these membranes. The degree of sulfonation (DS) of 60% was chosen for SPEEK polymer chains.
2.2. Calculation methods In this investigation, the mobility of hydronium ions and water molecules was estimated using mean square displacement (MSD) which calculates average distance of molecules passing during simulation. The MSD is defined as equation (1) [19,22]:
MSDðtÞ ¼ ðri ðtÞ ri ð0ÞÞ2 ¼
N h i 1 X ðri ðtÞ ri ð0ÞÞ2 N
(1)
i¼1
where N is the total number of particles, ri(t) is the position of particles at time t and ri(0) is their position at the beginning of dynamic calculations. The diffusion coefficient of hydronium ions and water molecules was also calculated using Einstein relation which is defined as following equation [19,22]:
D¼
1 dMSDðtÞ 1 d lim ¼ lim 6 t/∞ dt 6N t/∞ dt
N h X
ðri ðtÞ ri ð0ÞÞ2
i
(2)
Fig. 1. The chemical structure of SPEEK, PBI and PVA monomers (blue, red, yellow, white and gray stand respectively for nitrogen, oxygen, sulfur, hydrogen and carbon) and a schematic of PBI, SPEEK and PVA membranes with 10 wt % of water after the MD simulation under NPT ensemble.
i¼1
The conductivity of hydronium ions ðsÞ in the polymer membrane was estimated using equation (3) [19,23]:
Nz2 e2 D s¼ VkT
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DHvap RT V
nB 4pr 2 Dr
gAB ðrÞ ¼
(5)
NB V
(3)
where N is the number of hydronium ions per cell volume, z is charge number and e is the elementary charge. D, V, k and T are, respectively, the diffusion coefficient of hydronium ions, the total volume of the polymer membrane, Boltzmann constant and Kelvin temperature. The solubility parameter (d) is the square root of the cohesive energy density. The cohesive energy is closely related to the enthalpy of vaporization (DHvap) which is the amount of heat that must be added to a substance in order to change from a liquid to a gas state. The solubility parameter was calculated by the following equation [10]:
d¼
where nB is the number of atoms B around atoms A that are located inside a spherical shell of thickness Dr, NB is the total number of atoms B and V is the total system volume. The coordination number (CN) is defined as the average number of molecules around the molecule of interest, which is good method to characterized local structure. CN can be obtained by integrating the corresponding gA-B(r) with the following equation [24]:
ðr CN ¼
r4pr2 gðrÞdr
(6)
0
(4)
where R is the gas constant, T is Kelvin temperature, and V is the total volume. The radial distribution function (RDF) shows the probability of finding atoms A from atoms B at the distance r (gA-B(r)) which was averaged over the MD trajectories using equation (5) [19,22]:
where dr is the thickness of the spherical shell and r stands for the average number. 2.3. Molecular simulation details The Amorphous Cell module in the Materials Studio software (Version 4.3) [25] was used for generating simulation box
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781
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Table 1 Simulation boxes details for the PVA, SPEEK and PBI polymer membranes. Water concentration (wt. %) PVA
SPEEK
PBI
H3Oþ H2O Polymer chains Density (g/cm3) H3Oþ H2O Polymer chains Density (g/cm3) H3Oþ H2O Polymer chains Density (g/cm3) 10 20 30 40
30 30 30 30
126 285 486 756
9 9 9 9
1.12 1.09 1.09 1.09
30 30 30 30
289 650 1113 1730
9 9 9 9
1.30 1.29 1.25 1.19
30 30 30 30
261 585 1002 1560
9 9 9 9
0.98 1.12 1.18 1.17
Table 2 Physical properties (densities and solubility parameters) of PVA, SPEEK and PBI polymers at 298 K. Polymer
PVA SPEEK PBI
Density (g/cm3)
Solubility parameter ((J/cm3)1/2)
Simulation
Experimental
Simulation
Experimental
1.26 1.27 1.16
1.24e1.27 [8,10] 1.26e1.32 [40] 1.17e1.33 [21,38,44]
23.01 20.92 19.59
23.54 [8,10] e e
Fig. 2. Mean square displacements of H3Oþ in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
[7,8,26e30]. The initial density of simulation box is 0.3 g/cm3 in which polymer chains, water molecules and hydronium ions have been dispersed randomly [19,22]. The details of simulation box for three polymer membranes are summarized in Table 1. After the construction of simulation box, the minimization was performed using the smart method for 5000 steps with the convergence criterion of 0.001 (kcal mol1/Å) [22]. In the next step, a 500 ps of MD equilibration was run on the simulation box in NPT ensemble to obtain the final equilibrium density at 298 K and 1 bar. Afterward, an MD equilibration run on the membranes were performed by annealing procedure and the temperature cycle method [31].
During annealing process, the membranes were heated from 298 to 498 K with intervals of 20 K and then were cooled with the same intervals. At each step of annealing process, a 100 ps of NPT ensemble was imposed to the system. Afterward, a 200 ps of MD equilibration run on the membranes were performed in NPT ensemble to obtain the final equilibrium density at 298 K and 1 bar [31]. Finally, MD simulation of NVT ensemble under periodic boundary condition at 298 K was used to investigate the mobility of hydronium ions in the membranes. The atomic trajectory which is suitable for the structural and equilibrium thermodynamic properties analysis was recorded every picosecond.
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Fig. 3. Mean square displacements of H2O in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
The pervious molecular simulation studies show that COMPASS1 force field [32] is appropriate for the simulation polymers, water molecules and hydronium ions in PVA [10,11,14,26,27,33e37], SPEEK [19,28], PBI [20,21,38] and PEM [7]. So COMPASS force field was used in all of MD simulations which were done using 4.3 version of Materials Studio software with 1 fs time step till 20 ns run times for all calculation [30,39]. The Berendsen thermostat and barostat were used to control temperature and pressure during the simulations with a decay constant of 0.1 ps [22]. Ewald summation method with the accuracy of 0.001 kcal/mol was used for longrange Coulomb interactions [23,28e30]. The cutoff distance of 1.25 nm was considered for van der Waals (vdW) interaction [28,29]. Furthermore, each proton in the form of hydronium ion (H3Oþ) was assumed to be hydrated with a water molecule during MD simulation.
3. Results and discussion 3.1. Density and solubility parameter Density and solubility parameter of PVA, PBI and SPEEK polymers were calculated using MD simulation and its results were
1 Condensed-phase Optimized Molecular Potential for Atomistic Simulation Studies.
compared to available experimental data. The average density of these polymers was calculated from the equilibrium time. The calculated density for pure PVA, PBI and SPEEK polymers are 1.26, 1.16 and 1.27 g/cm3, respectively. Based on the results that have been displayed in Table 2, the simulation results are in good agreement with the experimental data. The solubility parameter of PVA polymer which was calculated by MD simulation and equation (4) is 23.01 (J/cm3)1/2 which is close to the experimental data 23.54 (J/cm3)1/2 [8,10]. Therefore, it can be said that the COMPASS is an appropriate force field for MD simulation because of its acceptable results. In the following, this force field has been used in order to do all calculations. In this investigation, MD simulation was used to investigate the effect of water concentration on the proton mobility in PVA and PBI membranes. For this purpose, simulation boxes with different water concentration were constructed for PVA, SPEEK and PBI Table 3 The diffusion coefficients of hydronium ions (DH) and water molecules (DW) in the PVA, SPEEK and PBI membranes. Water concentration (wt. %)
DH ( 1010 m2/s)
DW ( 1010 m2/s)
PVA
SPEEK
PBI
PVA
SPEEK
PBI
10 20 30 40
0.31 1.83 4.85 5.63
0.24 1.34 4.10 8.26
0.37 2.40 4.50 6.50
1.84 6.20 7.58 14.96
1.16 4.37 8.69 16.02
3.31 5.48 10.45 14.75
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781 Table 4 The conductivity of hydronium ions in the PVA, SPEEK and PBI membranes. Water concentration (wt. %)
The conductivity of hydronium ions(ms/cm) PVA Sim.
10 20 30 40
PBI Exp.
1.67 2e25 8.63 [45] 19.83 19.91
Sim.
SPEEK Exp.
0.54 1-8 3.13 [46] 8.82 15.05
Sim.
Table 5 The hydrogen bond energy of PVA, SPEEK and PBI membranes. Water concentration (wt. %)
Number of Hydrogen bonds
Hydrogen bond energy (kcal/mol)
PVA
PBI
SPEEK
PVA
PBI
SPEEK
10 20 30 40 Number of O and N atoms of polymer membrane
269 373 482 676 e
176 352 645 1007 e
264 521 841 1284 e
372.5 587.2 855.6 1229.4 450
291.2 682.8 1268.2 2055.1 540
444.6 954.3 1622.1 2532.6 810
Exp.
0.94 0.9e12 [19,47e49] 5.42 8.57 10.10
membranes (see Table 1) which were equilibrated using NPT ensemble. A schematic of PVA, SPEEK and PBI as equilibrated membranes with 10 wt % of water is shown in Fig. 1. The equilibrium density of these membranes is also listed in Table 1. The results indicate that the density of SPEEK decreases with increasing the concentration of water. The previous studies also show the same results [19,40].
3.2. Mean square displacement (MSD) The mobility of hydronium ions and water molecules in PVA, SPEEK and PBI membranes were calculated using MSD and equation (1). The study results of systems with different water concentrations are shown in Fig. 2. These results indicate that increasing water concentration (wt. %) in polymeric membranes increases MSD of hydronium ions. On the other hand, increasing the number of water molecules in membranes causes these molecules to surround the polymeric chains and leads to decreasing of
Fig. 4. A schematic illustration of the simulation box of PBI, SPEEK, and PVA membranes with 40 wt % of water and the hydrogen bonds in these membranes.
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attraction between polymers and hydronium ions and also polymers and other water molecules that is due to their hydrogen bonds. Therefore, hydronium ions can easily move around. Based on MSD results in 10 wt % of water (in Fig. 2a), maximum MSD of hydronium ions is in PBI membrane and its minimum is in SPEEK membrane. On the other hand, MSD results of 20 wt % of water (Fig. 2b) indicate that movement of hydronium ions in PBI membrane is more than the two other membranes which is almost twice of hydronium ions movement in SPEEK membrane. In addition, the simulation results (Fig. 2c) show that MSD of hydronium ions in PBI membrane is close to that reported for SPEEK membrane. In other words, attraction and repulsion between polymer chains and hydronium ions in 30 wt % of water in these two membranes are the same. Finally, the maximum MSD of hydronium ions in SPEEK membrane is in 40 wt % of water concentration and its minimum is in 10 wt % of water. Based on the results illustrated in Fig. 3, it can be said that water concentration in SPEEK, PVA and PBI strongly influence MSD of hydronium ions in these membranes. Fig. 3 represents MSD of water molecules in PVA, SPEEK and PBI with different water concentrations. Increasing water concentration in these membranes increases MSD of water molecules based on Fig. 3 results. The presence of more water molecules in these membranes decreases interactions between polymer chains and water molecules in a way that they can easily move. The results from Fig. 3 indicate that maximum and minimum MSD of water molecules are in 10 wt % of water both in PBI and PVA. The number of oxygen atoms in PVA polymer chains is more than the other polymers so the hydrogen bonds between water molecules and the PVA polymer chains are the strongest. The MSDs of water molecules in PVA, PBI, and SPEEK with 30 wt % of water (Fig. 3c) are similar to those with 10 wt % of water. MSD of water molecules for 40 wt % of water concentration in PVA, PBI, and SPEEK are close together (see Fig. 3d) that is due to the presence of more water molecules around polymer chains which decrease interactions of water molecules and polymer chains. So effect of molecular structure of polymer chains on water molecules mobility is not significant. Also, the simulation results, in Figs. 2 and 3, show that the MSD of water molecules is almost 2e9 times as much as the MSD of the hydronium ions that is because of the strong attraction between H3Oþ and the polymer chains. For example, in the SPEEK membrane, the maximum MSD of hydronium ions with different water concentrations (10, 20, 30 and 40 wt %) is 420, 1500, 4800 and 1050 Å2 while it is 2375, 5280, 10720 and 19150 Å2 for water molecules, respectively. It can be concluded that depending on the molecular structure of polymeric chains in PVA, PBI and SPEEK, hydrogen bonds have a significant role in movement and conductivity of hydronium ions in these membranes. There is a direct relation between this role of hydrogen bonds and the number of water molecules (water concentration) in these membranes.
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Fig. 5. RDFs of the hydronium ions (H3Oþ-H3Oþ) together in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
3.3. Diffusion coefficient The diffusion coefficient of hydronium ions (DH) and water molecules (DW) in different polymer membranes which was calculated using Eq. (2) are listed in Table 3. The results from this table show that increasing wt. % of water is effective on increasing DH in all these membranes which is consistent with the previous results obtained by MD simulations [41]. DH in PBI and PVA with 40 wt % of water is almost 20 times of DH with 10 wt % of water in these membranes. However, the ratio of DH for 40 wt % and 10 wt % of water in SPEEK membrane is almost 34. Its reason is the presence of more water molecules around polymer chains which decreases interactions between hydronium ions and polymer atoms and makes the transport of hydronium ions easier. Generally, the maximum amounts of diffusion coefficients of hydronium ions in PBI are for 10 and 20 wt % of water. The maximum amounts of (DH) in PVA and SPEEK are for 30 and 40 wt % of water, respectively. As seen in Table 3, Dw is a function of water concentration in membrane and it depends on hydrogen bonds between water molecules and polymer chains. Also the simulation results show that the maximum DW corresponds to PBI, PVA, PBI and SPEEK membranes with 10, 20, 30 and 40 wt % water concentrations, respectively. It is also clear that the mobility of hydronium ions is related to the mobility of water molecules and the self-diffusion coefficient of them increases as a function of water concentration and finally they will be close to the bulk water. It is important to note that the self-diffusion coefficient of water is 22.9 1010 m2/s at 298 K [42]. 3.4. Proton conductivity The conductivity of hydronium ions in PVA, SPEEK and PBI polymer membranes which listed in Table 4 was calculated using MD simulation and equation (3). The conductivity of hydronium ions by using MD simulation is 1.67e19.91, 0.54e15.05 and
0.94e10.10 ms/cm in the PVA, SPEEK and PBI membranes, respectively, which are dependent on water content and degree of polymerization. A Comparison between simulation results and available experimental data (2e25, 1e8 and 0.9e12 ms/cm for PVA, SPEEK and PBI membranes, respectively) in relation to conductivity of hydronium ions in Table 4 shows that there is an acceptable agreement between them. However, the amount of discrepancy can be due to the operating conditions and membrane purity in the molecular simulation and the experiment is not the same. Therefore, it can be said that molecular dynamics simulation is a useful tool for analyzing proton conductivity in polymer membranes. In addition, simulation results show that proton conductivity depends on water concentration in polymer membrane and it is increased with increasing water concentration. Based on the results from Table 4, the maximum conductivity of hydronium ions occurs in PVA membrane that is due to the presence of highly regulated groups of OH in polymer chains and hydrogen bonding between them which causes easier movement of hydronium ions in this membrane. The hydrogen bonds between water molecules and OH groups in polymer chains are increased with increasing water concentration in PVA membrane which causes less attraction of hydronium ions in polymer chains of this membrane and more conductivity of them. Fig. 4 represents a schematic illustration of simulation boxes for PBI, SPEEK, and PVA with 40 wt % of water. The results from Fig. 4 which are related to hydrogen bonds between hydronium ions and polymer chains in PBI, SPEEK, and PVA confirm that a small number of hydronium ions are located near PVA polymer chains and the proximity of OH groups in these chains has an effect on the transport of hydronium ions in this membrane. It can be said that polymer chains in SPEEK and PBI contain more number of donor or acceptor groups of hydrogen bonding in comparison with PVA polymer chains (Table 5). The hydrogen bonds in these two membranes are stronger too. In addition, their distance is high in polymer chains and hydronium ions cannot
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781
Fig. 6. RDFs of water-water molecules in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
easily transfer because they are attracted to polymer chains by hydrogen bonds. In conclusion, hydronium ions diffusion in SPEEK and PBI membranes is less than their diffusion in PVA. This behavior can clearly be seen in Fig. 4. Generally, PVA is the best polymer membrane with the highest amount of proton conductivity at room temperature.
3.5. Hydrogen bonds It should be noted that due to the presence of water molecules, oxygen and nitrogen atoms in polymer chains and hydronium ions, a hydrogen bond plays an important role in mobility and conductivity of protons which is electrostatic interaction between two polar groups that occurs when a hydrogen atom (H) covalently
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Fig. 7. RDFs of HW-HW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
bonds to atoms of nitrogen (N), oxygen (O), or fluorine (F). This bond is stronger than van der Waals interaction, but weaker than covalent or ionic bonds. Therefore, it is necessary to study the hydrogen bonds in the polymer membrane. The energy of hydrogen bonds in PVA, SPEEK and PBI membranes with different water concentrations which listed in Table 5 were calculated using Deriding force field during MD simulation. The results from Table 5 show that the maximum numbers of oxygen and nitrogen atoms in polymer chains exist in SPEEK membrane so the energy of hydrogen bond in this membrane is more than the other membranes. The low mobility of hydronium ions and water molecules in this membrane with 10, 20 and 30 wt % of water is due to their strong interactions (hydrogen bonds) with polymer chains. The results show that the number of hydrogen
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Fig. 8. RDFs of HW-OW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
bonds increases by the increasing water concentration in the membrane, and this exhibits that the similar hydration structures with that in bulk water. It was also observed that the energy of hydrogen bond depends on the kind of polymer chains and water concentration in the polymer membrane. Furthermore, the review of Fig. 4 related to the hydrogen bonds in PBI, SPEEK, and PVA confirms that the strength of hydrogen bond between hydronium ions and polymer chains in theses membrane can be shown in this way: SPEEK > PBI > PVA. The hydrogen bonds in PBI, SPEEK, and PVA membranes include hydrogen bonds of (1) (hydronium-hydronium ions, (2) waterwater molecules, (3) water-hydronium ions, (4) hydroniumpolymer atoms, (5) water-polymer atoms and (6) polymerpolymer atoms. Geometric and energetic criteria are two methods
Fig. 9. RDFs of OW-OW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
widely used to identify hydrogen bonds [41,43]. Herein, we focus on geometric criterion method to study of hydrogen bonds in the polymer membrane. In the geometric criterion method the hydrogen bonds among water molecules are identified when ROwOw 0.40 nm, and ROw-Hw0.23 nm which R is the minimum position of the OweOw (Ow is oxygen atom of water molecule) or OweHw (Hw is hydrogen atom of water molecule) [41,43]. Therefore, in the following section, hydrogen bonds in these membranes are compared using Radial Distribution Function (RDF) analysis. 3.6. Radial distribution function (RDF) It is well known that hydrogen bond network plays an important role in hydronium ions transfer. Therefore, calculating the
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781
RDFs of H2OeH2O and H2OeH3Oþ in PVA, SPEEK and PBI polymer membranes is necessary. In this investigation, RDFs of studied systems were calculated using equation (4). Fig. 5 shows the RDFs of hydronium ions (H3Oþ-H3Oþ) together in PVA, SPEEK and PBI with different water concentrations. As it is seen, there is no sharp peak in this figure which indicates that hydronium ions are not willing to bond with each other. Generally, Fig. 5 shows that the tendency of hydronium ions to each other in membrane with 10 wt % of water is weak and they are dispersed throughout this membrane. The RDF results (Fig. 5) of hydrogen bond between hydronium ions in systems with 20 wt % of water show that the first weak peak at 4.75 Å is related to PVA membrane which illustrates the tendency of hydronium ions to each other in PVA is more than the other membranes. The results from study PBI shows that the least tendency of hydronium ions to hydrogen bonding in this membrane causes hydronium ions to move more easily. Therefore it can be said that hydronium ions can move easily when they are close to water molecules but away from each other. In other words, the percentage of water molecules and also the kind of polymer atoms in the membrane determine the strength of hydrogen bond which is effective in mobility of hydronium ions. As shown in Fig. 5 and , RDF results indicate that the maximum and minimum tendency of hydronium ions to each other occurs in PVA and SPEEK, respectively. Due to less tendency of H3Oþ ions to each other in SPEEK, it can be said that H3Oþ ions prefer to surround polymer chains which can influence the conductivity of ions in studied systems. Fig. 6a, b, and c indicates RDF of H2OeH2O molecules in PVA, SPEEK and PBI membranes, respectively. The first peak comprises two shoulder peaks located at 2.75 and 3.30 Å for each the RDFs
9
which directly relate to hydrogen bonds between water molecules. It is also observed (in Fig. 6) that the tendency of water molecules to each other is reduced with increasing water concentration in these membranes. On the other hand, increasing the tendency of water molecules to polymer chains is because of more water concentration. But there is an exception; the results from Fig. 6b for PVA membrane show that RDF sharp peak is related to 20 wt % of water. It is because of the existence of OH bonds in PVA monomers (as it is seen in Fig. 1) and water molecules mostly connect to PVA polymer chains with 10 wt % of water and their tendency to each other is less. With increasing water concentration in PVA membrane, the excess numbers of water molecules which cannot bond with PVA polymer chains connect to each other. RDFs of HW-HW (HW i.e. hydrogen atom of water molecule) in SPEEK, PVA and PBI membranes with different water concentrations are calculated and they are shown in Fig. 7. The RDF results show that there are two sharp peaks at distance of 2.5 Å and 3.7 Å [24] and the height of the first peak decreases as the water concentration increases, in the other word, the tendency of water molecules together decrease. But, as shown in Fig. 7b, the behavior of water molecules in the PVA membrane at 10 wt % of water is different and the first peak of RDF of HW-HW is lower than the other water concentration. At this water concentration, the hydrogen bods between water molecules and OH groups of PVA chain are more than water molecules. As shown in Fig. 8, the RDFs of HW-OW in SPEEK, PVA and PBI membranes are approximately the same as the RDFs of HW-HW, with the difference that the two sharp peak of RDFs of HW-OW at distance of 1.7 Å and 3.1 Å.
Fig. 10. RDFs of water-hydronium ions in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
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Fig. 9 show the RDFs of OW-OW in SPEEK, PVA and PBI membranes with different water concentrations with the evident sharp peaks located at 2.7 Å [24]. Similarly, the peak height decreases as the hydration level increases in three membranes and all hydration levels, but there is an exception in PVA membrane at 10 wt % water. Fig. 10 indicates RDFs of water-hydronium ions in SPEEK, PBI and PVA membranes with different water concentrations. The RDF results show that there are two sharp peaks at distance of 2.55 Å and 3.25 Å, so; these sharp peaks indicate the formation of hydrogen bonds between hydronium ions and water molecules. It can also be observed (in Fig. 10) that the sharpness of these two peaks strongly decrease with increasing water concentration suggests that the number of water molecules which are surrounded by the hydronium ions decreases. Based on the results of RDF results for PBI in Fig. 10a, the hydrogen bonds between water molecules and hydronium ions in l0 wt. % of water are stronger than the other membranes. Therefore the transport of hydronium ions in PBI must be easier and MSD results (Fig. 2) also confirms this. Fig. 10b indicates the tendency of hydronium ions to bond with water molecules in 20 wt % of water in PBI, PVA and SPEEK membranes which is in this way: PBI > PVA > SPEEK. Since the movement of hydronium ions with water molecules is easier so the MSD of hydronium ions in PBI must be more. As seen, the tendency of hydronium ions to water molecules in PBI and PVA with 30 wt % of water shows the similar result. The comparison of Fig. 10a with Fig. 10d indicates that intensity of RDF peaks in the membrane with 10 wt % of water is almost 4 times of that of the membrane with 40 wt % of water which is due to the number of water molecules. The MSD and RDF results show that mobility of hydronium ions depends on water concentration and molecular structure of polymer chains in these membranes. To determine the exact effect of molecular structure of polymer chains on transportation of hydronium ions in the polymer membrane, the RDF of hydronium ions bond with polymer chain atoms was studied in PVA, SPEEK and PBI. The coordination numbers of hydronium ion and water molecules in SPEEK, PVA and PBI membranes with different water concentrations versus distance is presented in Fig. 11. It can be seen in Fig. 11 that the number of water molecules which are surrounded by the hydronium ions increases with increasing distance. The results indicate that the hydrated structure of hydronium ions with radius of 5 Å contains 4, 4 and 5 water molecules, respectively, in SPEEK, PBI and PVA membranes. Also, according to the results in Fig. 11, the maximum coordination number of hydronium ions (water molecules) in SPEEK, PVA and PBI membranes belongs to the water concentration 20, 10 and 40 wt %, respectively. The RDFs of hydronium ions with carbon and nitrogen atoms of PBI polymer chains with different water concentrations were calculated and shown in Fig. 12. The RDF of N-hydronium ions in Fig. 12a shows two sharp peaks at distance of 2.56 and 4.75 Å that the first peak is for nitrogen atoms with double bond with C and the second peak is related to nitrogen atoms with single bond with C. The first sharp peak at 2.65 Å distance represents the hydrogen bonds between them which become weaker with increasing water in the membrane. The RDF results of hydronium ions-C atoms in Fig. 12b indicate that the first sharp peak is at 3.65 Å, so the distance between hydronium ions and carbon atoms is more than their distance from nitrogen atoms. The results show that the tendency of hydronium ions to bond with nitrogen atoms is more than their tendency to carbon atoms in PBI which is reduced with increasing water concentration. In fact, the access of hydronium ions to polymer chains reduces with increasing water concentration in the membrane because water molecules cover polymer chains. The results clearly show that hydronium ions don’t have any tendency to bond with nitrogen and carbon in PBI with 30 and 40 wt % of water.
Fig. 11. Coordination numbers of hydronium ion and water molecules in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
The RDFs of hydronium ions with oxygen and carbon in PVA polymer chains with different water concentrations are shown in Fig. 13. As it can be seen in Fig. 13a, a sharp peak at 2.55 Å shows bonding between hydronium ions and oxygen atoms in PVA and their high tendency to bond with each other. In fact, oxygen atoms in PVA polymer chains have strong hydrogen bonds with hydronium ions. A peak at 3.65 Å in Fig. 13b shows the tendency of hydronium ions to carbon atoms decrease with increasing water concentration. The comparison between RDF results in Figs. 12 and 13 shows that hydrogen bonds in PVA are stronger than PBI. Fig. 14 is RDF of hydronium ions with atoms of carbon, sulfur and oxygen in SPEEK polymer chain with different water concentrations. The results clearly show that there is low tendency between
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781
11
Fig. 12. RDFs of the hydronium ions with a) N and b) C atoms of polymer chains in PBI membranes with different amounts of water concentration.
Fig. 13. RDFs of the hydronium ions with a) O and b) C atoms of polymer chains in PVA membranes with different amounts of water concentration.
hydronium ions and carbon in SPEEK because the sharp peak is not observed in this RDF graph. However, other results show that hydronium ions tend to be near oxygen and sulfur in SPEEK at 2.75 and 3.95 Å distance which is due to more tendency of hydronium ions to bond with sulfur. Since sulfur atoms in SPEEK chain bond to several oxygen atoms and the tendency between hydronium ions and oxygen atoms is more, then the distance between hydronium ions and sulfur atoms is more than their distance from oxygen atoms. The results also show that increasing water concentration in the membrane does not effect on decreasing of hydronium ions tendency to bond with atoms in SPEEK which is different in comparison with PVA and PBI membranes. In fact, the maximum and minimum tendency of hydronium ions to oxygen and sulfur atoms in SPEEK polymer membrane is in 40 and 30 wt % of water. In addition, the results show that increasing water concentration in SPEEK membrane increases the intensity of peaks in RDFs for H3Oþ-O and H3Oþ-S which indicates more tendencies of hydronium ions to atoms in SPEEK polymer chains. There is an exception for this tendency in 30 wt % of water.
The comparison of simulation results finally declare that in similar conditions, PVA membrane has better proton conductivity in comparison with other membranes and the effect of water concentration on proton conductivity in this membrane is not significant in more than 30 wt % of water. As a conclusion, it can be said that because of a better conductivity, the best membrane for using in PEMFCs is PVA membrane at room temperature. 4. Conclusion The mobility of hydronium ions in PVA, PBA and SPEEK membranes was investigated using molecular dynamics simulation. In the first step, MD results of density and solubility parameter of these membranes confirm that the molecular dynamics simulation is a good and reliable method to investigate the effect that molecular structure of polymer chain and water concentration have on transportation of proton. The results show that PVA membrane has the highest conductivity in comparison with other studied membranes where by
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Compliance with ethical standards The authors confirm that there are no known conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.molliq.2019.111781. References [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] Fig. 14. RDFs of the hydronium ions with a) C, b) O and c) S atoms of polymer chains in SPEEK membranes with different amounts of water concentration.
[34] [35] [36]
increasing water concentration from 10 to 30 wt % of water, the conductivity increases and after that it approximately remains constant. Also, the comparison of MD simulation results for these three membranes using RDF analysis show that the type of atom in polymer chain of membrane plays a significant role in diffusion of hydronium ions. When these atoms have tendency to water molecules with hydrogen bonds, more mobility of hydronium ions is because of increasing the water concentration in the membrane. In other words, water molecules cover polymer chains so tendency and access of hydronium ions to them are reduced, and they easily move. It can be said that hydrogen bonds between water molecules and polymer chains is effective on the movement of hydronium ions in the membrane.
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
An investigation of proton conductivity of PVA, PBI and SPEEK polymer membranes using molecular dynamics simulation Mahmoud Rahmati a, *, Marjan Jangali b, Hossein Rezaei c, d a
Department of Chemical Engineering, Graduate University of Advanced Technology, Kerman, Iran Department of Chemical Engineering, Shahid Bahonar University of Kerman, Iran c Petroleum Engineering and Development Company (PEDEC), National Iranian Oil Company (NIOC), Tehran, Iran d Chemical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 January 2019 Received in revised form 8 September 2019 Accepted 19 September 2019 Available online 8 October 2019
The conductivity and diffusion of hydronium ions at 298 K in PVA (Polyvinyl alcohol), PBI (Polybenzimidazole) and SPEEK (Sulfonated polyether ether ketone) as known membranes of PEMFCs have been investigated using molecular dynamics simulation method throughout this work. The simulation results show that the diffusion of hydronium ions in these polymer membranes depends on the polymer structure and water concentration in the membrane. On the other hand, RDF analysis results also show that the tendency of hydronium ions to polymer atoms strongly depends on the water concentration. So their tendency to polymer chains decreases with increasing the water concentration in PBI and PVA. Based on the results of this investigation, the conductivity of hydronium ions in PVA is more than the two other membranes (¼19.83 ms/cm in 30 wt % of water). © 2019 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics simulation Polymer membrane Proton conductivity PEMFCs
1. Introduction Proton exchange membrane fuel cells (PEMFCs) convert chemical energy into electrical energy which has high efficiency, high energy and low impact on environmental pollution as environmentally friendly energy resource [1e4]. Recently, PEMFCs have attracted much attention due to its simplicity of operation, high efficiency and low cost. Proton exchange membrane (PEM) which conducts the proton flow from anode to cathode plays an important role in PEMFCs [4e6]. Based on previous studies, the polymer chain structure which has an important effect on the proton conduction process in PEM [7e12] can be investigated with experimental and simulation methods [13e19]. Molecular dynamics (MD) simulation as a powerful method can precisely predict the physical and thermodynamic properties of materials. This method can be used to study the mechanism of the processes in atomic and molecular scales. It is also usable for atomic study of proton permeability through the polymer membranes which has been attractive for researchers and there have been many studies in this field. Bahlakeh et al. [19] have used molecular dynamics simulation in order to compare transport
* Corresponding author. E-mail address: [email protected] (M. Rahmati). https://doi.org/10.1016/j.molliq.2019.111781 0167-7322/© 2019 Elsevier B.V. All rights reserved.
properties of hydronium ions in non-sulfonated and fully sulfonated poly ether ketone (SPEEK) membranes. They have observed that the diffusion coefficient and conductivity of hydronium ions enhance with increasing degree of sulfonation and temperature in non-SPEEK and fully SPEEK membranes. Pahari et al. [20] have characterized the structural and dynamical properties of phosphoric acid doped polybenzimidazole (PBI) membrane at various concentrations of phosphoric acid using MD simulation. They have reported the contribution of different atoms in bonding with hydrogen in this membrane. The simulation performed by Zhu et al. [21] shows that the hydrogen bonds have effect on proton mobility in PBI membrane which is dependent on the polymer structure. The mobility of water molecules in blend membranes of polyvinyl alcohol (PVA) and its relation to polymer structure have been studied using MD simulation by Wang et al. [8] and Wei et al. [10]. In this investigation, the proton mobility in PVA, SPEEK and PBI as the most common proton exchange membranes has been investigated using MD simulation. For this purpose, mean square displacement (MSD) and diffusion coefficients of hydronium ions and water molecules were calculated in different conditions. In addition, the effect of hydrogen bonds on mobility of hydronium ions in these membranes was also investigated. Then, a comprehensive analysis of radial distribution function (RDF) was performed to study the behavior of hydronium ions and water
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molecules in polymer chains. And finally, the simulation results were compared with the results of the previous studies.
2. Models and methods 2.1. Molecular structure The structure of monomer, polymer chain and polymer membrane were constructed to perform MD simulation and calculate diffusion coefficient and proton mobility of hydronium ions and water molecules. The molecular structures of PVA, PBI and SPEEK monomers are shown in Fig. 1. PVA, PBI and SPEEK polymer chains with 50, 15 and 15 monomers consist of different types of atoms. The oxygen and sulfur atoms in SPEEK, nitrogen atoms in PBI and oxygen atoms in PVA have an effect on mobility of hydronium ions in these membranes. The degree of sulfonation (DS) of 60% was chosen for SPEEK polymer chains.
2.2. Calculation methods In this investigation, the mobility of hydronium ions and water molecules was estimated using mean square displacement (MSD) which calculates average distance of molecules passing during simulation. The MSD is defined as equation (1) [19,22]:
MSDðtÞ ¼ ðri ðtÞ ri ð0ÞÞ2 ¼
N h i 1 X ðri ðtÞ ri ð0ÞÞ2 N
(1)
i¼1
where N is the total number of particles, ri(t) is the position of particles at time t and ri(0) is their position at the beginning of dynamic calculations. The diffusion coefficient of hydronium ions and water molecules was also calculated using Einstein relation which is defined as following equation [19,22]:
D¼
1 dMSDðtÞ 1 d lim ¼ lim 6 t/∞ dt 6N t/∞ dt
N h X
ðri ðtÞ ri ð0ÞÞ2
i
(2)
Fig. 1. The chemical structure of SPEEK, PBI and PVA monomers (blue, red, yellow, white and gray stand respectively for nitrogen, oxygen, sulfur, hydrogen and carbon) and a schematic of PBI, SPEEK and PVA membranes with 10 wt % of water after the MD simulation under NPT ensemble.
i¼1
The conductivity of hydronium ions ðsÞ in the polymer membrane was estimated using equation (3) [19,23]:
Nz2 e2 D s¼ VkT
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DHvap RT V
nB 4pr 2 Dr
gAB ðrÞ ¼
(5)
NB V
(3)
where N is the number of hydronium ions per cell volume, z is charge number and e is the elementary charge. D, V, k and T are, respectively, the diffusion coefficient of hydronium ions, the total volume of the polymer membrane, Boltzmann constant and Kelvin temperature. The solubility parameter (d) is the square root of the cohesive energy density. The cohesive energy is closely related to the enthalpy of vaporization (DHvap) which is the amount of heat that must be added to a substance in order to change from a liquid to a gas state. The solubility parameter was calculated by the following equation [10]:
d¼
where nB is the number of atoms B around atoms A that are located inside a spherical shell of thickness Dr, NB is the total number of atoms B and V is the total system volume. The coordination number (CN) is defined as the average number of molecules around the molecule of interest, which is good method to characterized local structure. CN can be obtained by integrating the corresponding gA-B(r) with the following equation [24]:
ðr CN ¼
r4pr2 gðrÞdr
(6)
0
(4)
where R is the gas constant, T is Kelvin temperature, and V is the total volume. The radial distribution function (RDF) shows the probability of finding atoms A from atoms B at the distance r (gA-B(r)) which was averaged over the MD trajectories using equation (5) [19,22]:
where dr is the thickness of the spherical shell and r stands for the average number. 2.3. Molecular simulation details The Amorphous Cell module in the Materials Studio software (Version 4.3) [25] was used for generating simulation box
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781
3
Table 1 Simulation boxes details for the PVA, SPEEK and PBI polymer membranes. Water concentration (wt. %) PVA
SPEEK
PBI
H3Oþ H2O Polymer chains Density (g/cm3) H3Oþ H2O Polymer chains Density (g/cm3) H3Oþ H2O Polymer chains Density (g/cm3) 10 20 30 40
30 30 30 30
126 285 486 756
9 9 9 9
1.12 1.09 1.09 1.09
30 30 30 30
289 650 1113 1730
9 9 9 9
1.30 1.29 1.25 1.19
30 30 30 30
261 585 1002 1560
9 9 9 9
0.98 1.12 1.18 1.17
Table 2 Physical properties (densities and solubility parameters) of PVA, SPEEK and PBI polymers at 298 K. Polymer
PVA SPEEK PBI
Density (g/cm3)
Solubility parameter ((J/cm3)1/2)
Simulation
Experimental
Simulation
Experimental
1.26 1.27 1.16
1.24e1.27 [8,10] 1.26e1.32 [40] 1.17e1.33 [21,38,44]
23.01 20.92 19.59
23.54 [8,10] e e
Fig. 2. Mean square displacements of H3Oþ in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
[7,8,26e30]. The initial density of simulation box is 0.3 g/cm3 in which polymer chains, water molecules and hydronium ions have been dispersed randomly [19,22]. The details of simulation box for three polymer membranes are summarized in Table 1. After the construction of simulation box, the minimization was performed using the smart method for 5000 steps with the convergence criterion of 0.001 (kcal mol1/Å) [22]. In the next step, a 500 ps of MD equilibration was run on the simulation box in NPT ensemble to obtain the final equilibrium density at 298 K and 1 bar. Afterward, an MD equilibration run on the membranes were performed by annealing procedure and the temperature cycle method [31].
During annealing process, the membranes were heated from 298 to 498 K with intervals of 20 K and then were cooled with the same intervals. At each step of annealing process, a 100 ps of NPT ensemble was imposed to the system. Afterward, a 200 ps of MD equilibration run on the membranes were performed in NPT ensemble to obtain the final equilibrium density at 298 K and 1 bar [31]. Finally, MD simulation of NVT ensemble under periodic boundary condition at 298 K was used to investigate the mobility of hydronium ions in the membranes. The atomic trajectory which is suitable for the structural and equilibrium thermodynamic properties analysis was recorded every picosecond.
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Fig. 3. Mean square displacements of H2O in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
The pervious molecular simulation studies show that COMPASS1 force field [32] is appropriate for the simulation polymers, water molecules and hydronium ions in PVA [10,11,14,26,27,33e37], SPEEK [19,28], PBI [20,21,38] and PEM [7]. So COMPASS force field was used in all of MD simulations which were done using 4.3 version of Materials Studio software with 1 fs time step till 20 ns run times for all calculation [30,39]. The Berendsen thermostat and barostat were used to control temperature and pressure during the simulations with a decay constant of 0.1 ps [22]. Ewald summation method with the accuracy of 0.001 kcal/mol was used for longrange Coulomb interactions [23,28e30]. The cutoff distance of 1.25 nm was considered for van der Waals (vdW) interaction [28,29]. Furthermore, each proton in the form of hydronium ion (H3Oþ) was assumed to be hydrated with a water molecule during MD simulation.
3. Results and discussion 3.1. Density and solubility parameter Density and solubility parameter of PVA, PBI and SPEEK polymers were calculated using MD simulation and its results were
1 Condensed-phase Optimized Molecular Potential for Atomistic Simulation Studies.
compared to available experimental data. The average density of these polymers was calculated from the equilibrium time. The calculated density for pure PVA, PBI and SPEEK polymers are 1.26, 1.16 and 1.27 g/cm3, respectively. Based on the results that have been displayed in Table 2, the simulation results are in good agreement with the experimental data. The solubility parameter of PVA polymer which was calculated by MD simulation and equation (4) is 23.01 (J/cm3)1/2 which is close to the experimental data 23.54 (J/cm3)1/2 [8,10]. Therefore, it can be said that the COMPASS is an appropriate force field for MD simulation because of its acceptable results. In the following, this force field has been used in order to do all calculations. In this investigation, MD simulation was used to investigate the effect of water concentration on the proton mobility in PVA and PBI membranes. For this purpose, simulation boxes with different water concentration were constructed for PVA, SPEEK and PBI Table 3 The diffusion coefficients of hydronium ions (DH) and water molecules (DW) in the PVA, SPEEK and PBI membranes. Water concentration (wt. %)
DH ( 1010 m2/s)
DW ( 1010 m2/s)
PVA
SPEEK
PBI
PVA
SPEEK
PBI
10 20 30 40
0.31 1.83 4.85 5.63
0.24 1.34 4.10 8.26
0.37 2.40 4.50 6.50
1.84 6.20 7.58 14.96
1.16 4.37 8.69 16.02
3.31 5.48 10.45 14.75
M. Rahmati et al. / Journal of Molecular Liquids 296 (2019) 111781 Table 4 The conductivity of hydronium ions in the PVA, SPEEK and PBI membranes. Water concentration (wt. %)
The conductivity of hydronium ions(ms/cm) PVA Sim.
10 20 30 40
PBI Exp.
1.67 2e25 8.63 [45] 19.83 19.91
Sim.
SPEEK Exp.
0.54 1-8 3.13 [46] 8.82 15.05
Sim.
Table 5 The hydrogen bond energy of PVA, SPEEK and PBI membranes. Water concentration (wt. %)
Number of Hydrogen bonds
Hydrogen bond energy (kcal/mol)
PVA
PBI
SPEEK
PVA
PBI
SPEEK
10 20 30 40 Number of O and N atoms of polymer membrane
269 373 482 676 e
176 352 645 1007 e
264 521 841 1284 e
372.5 587.2 855.6 1229.4 450
291.2 682.8 1268.2 2055.1 540
444.6 954.3 1622.1 2532.6 810
Exp.
0.94 0.9e12 [19,47e49] 5.42 8.57 10.10
membranes (see Table 1) which were equilibrated using NPT ensemble. A schematic of PVA, SPEEK and PBI as equilibrated membranes with 10 wt % of water is shown in Fig. 1. The equilibrium density of these membranes is also listed in Table 1. The results indicate that the density of SPEEK decreases with increasing the concentration of water. The previous studies also show the same results [19,40].
3.2. Mean square displacement (MSD) The mobility of hydronium ions and water molecules in PVA, SPEEK and PBI membranes were calculated using MSD and equation (1). The study results of systems with different water concentrations are shown in Fig. 2. These results indicate that increasing water concentration (wt. %) in polymeric membranes increases MSD of hydronium ions. On the other hand, increasing the number of water molecules in membranes causes these molecules to surround the polymeric chains and leads to decreasing of
Fig. 4. A schematic illustration of the simulation box of PBI, SPEEK, and PVA membranes with 40 wt % of water and the hydrogen bonds in these membranes.
5
attraction between polymers and hydronium ions and also polymers and other water molecules that is due to their hydrogen bonds. Therefore, hydronium ions can easily move around. Based on MSD results in 10 wt % of water (in Fig. 2a), maximum MSD of hydronium ions is in PBI membrane and its minimum is in SPEEK membrane. On the other hand, MSD results of 20 wt % of water (Fig. 2b) indicate that movement of hydronium ions in PBI membrane is more than the two other membranes which is almost twice of hydronium ions movement in SPEEK membrane. In addition, the simulation results (Fig. 2c) show that MSD of hydronium ions in PBI membrane is close to that reported for SPEEK membrane. In other words, attraction and repulsion between polymer chains and hydronium ions in 30 wt % of water in these two membranes are the same. Finally, the maximum MSD of hydronium ions in SPEEK membrane is in 40 wt % of water concentration and its minimum is in 10 wt % of water. Based on the results illustrated in Fig. 3, it can be said that water concentration in SPEEK, PVA and PBI strongly influence MSD of hydronium ions in these membranes. Fig. 3 represents MSD of water molecules in PVA, SPEEK and PBI with different water concentrations. Increasing water concentration in these membranes increases MSD of water molecules based on Fig. 3 results. The presence of more water molecules in these membranes decreases interactions between polymer chains and water molecules in a way that they can easily move. The results from Fig. 3 indicate that maximum and minimum MSD of water molecules are in 10 wt % of water both in PBI and PVA. The number of oxygen atoms in PVA polymer chains is more than the other polymers so the hydrogen bonds between water molecules and the PVA polymer chains are the strongest. The MSDs of water molecules in PVA, PBI, and SPEEK with 30 wt % of water (Fig. 3c) are similar to those with 10 wt % of water. MSD of water molecules for 40 wt % of water concentration in PVA, PBI, and SPEEK are close together (see Fig. 3d) that is due to the presence of more water molecules around polymer chains which decrease interactions of water molecules and polymer chains. So effect of molecular structure of polymer chains on water molecules mobility is not significant. Also, the simulation results, in Figs. 2 and 3, show that the MSD of water molecules is almost 2e9 times as much as the MSD of the hydronium ions that is because of the strong attraction between H3Oþ and the polymer chains. For example, in the SPEEK membrane, the maximum MSD of hydronium ions with different water concentrations (10, 20, 30 and 40 wt %) is 420, 1500, 4800 and 1050 Å2 while it is 2375, 5280, 10720 and 19150 Å2 for water molecules, respectively. It can be concluded that depending on the molecular structure of polymeric chains in PVA, PBI and SPEEK, hydrogen bonds have a significant role in movement and conductivity of hydronium ions in these membranes. There is a direct relation between this role of hydrogen bonds and the number of water molecules (water concentration) in these membranes.
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Fig. 5. RDFs of the hydronium ions (H3Oþ-H3Oþ) together in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
3.3. Diffusion coefficient The diffusion coefficient of hydronium ions (DH) and water molecules (DW) in different polymer membranes which was calculated using Eq. (2) are listed in Table 3. The results from this table show that increasing wt. % of water is effective on increasing DH in all these membranes which is consistent with the previous results obtained by MD simulations [41]. DH in PBI and PVA with 40 wt % of water is almost 20 times of DH with 10 wt % of water in these membranes. However, the ratio of DH for 40 wt % and 10 wt % of water in SPEEK membrane is almost 34. Its reason is the presence of more water molecules around polymer chains which decreases interactions between hydronium ions and polymer atoms and makes the transport of hydronium ions easier. Generally, the maximum amounts of diffusion coefficients of hydronium ions in PBI are for 10 and 20 wt % of water. The maximum amounts of (DH) in PVA and SPEEK are for 30 and 40 wt % of water, respectively. As seen in Table 3, Dw is a function of water concentration in membrane and it depends on hydrogen bonds between water molecules and polymer chains. Also the simulation results show that the maximum DW corresponds to PBI, PVA, PBI and SPEEK membranes with 10, 20, 30 and 40 wt % water concentrations, respectively. It is also clear that the mobility of hydronium ions is related to the mobility of water molecules and the self-diffusion coefficient of them increases as a function of water concentration and finally they will be close to the bulk water. It is important to note that the self-diffusion coefficient of water is 22.9 1010 m2/s at 298 K [42]. 3.4. Proton conductivity The conductivity of hydronium ions in PVA, SPEEK and PBI polymer membranes which listed in Table 4 was calculated using MD simulation and equation (3). The conductivity of hydronium ions by using MD simulation is 1.67e19.91, 0.54e15.05 and
0.94e10.10 ms/cm in the PVA, SPEEK and PBI membranes, respectively, which are dependent on water content and degree of polymerization. A Comparison between simulation results and available experimental data (2e25, 1e8 and 0.9e12 ms/cm for PVA, SPEEK and PBI membranes, respectively) in relation to conductivity of hydronium ions in Table 4 shows that there is an acceptable agreement between them. However, the amount of discrepancy can be due to the operating conditions and membrane purity in the molecular simulation and the experiment is not the same. Therefore, it can be said that molecular dynamics simulation is a useful tool for analyzing proton conductivity in polymer membranes. In addition, simulation results show that proton conductivity depends on water concentration in polymer membrane and it is increased with increasing water concentration. Based on the results from Table 4, the maximum conductivity of hydronium ions occurs in PVA membrane that is due to the presence of highly regulated groups of OH in polymer chains and hydrogen bonding between them which causes easier movement of hydronium ions in this membrane. The hydrogen bonds between water molecules and OH groups in polymer chains are increased with increasing water concentration in PVA membrane which causes less attraction of hydronium ions in polymer chains of this membrane and more conductivity of them. Fig. 4 represents a schematic illustration of simulation boxes for PBI, SPEEK, and PVA with 40 wt % of water. The results from Fig. 4 which are related to hydrogen bonds between hydronium ions and polymer chains in PBI, SPEEK, and PVA confirm that a small number of hydronium ions are located near PVA polymer chains and the proximity of OH groups in these chains has an effect on the transport of hydronium ions in this membrane. It can be said that polymer chains in SPEEK and PBI contain more number of donor or acceptor groups of hydrogen bonding in comparison with PVA polymer chains (Table 5). The hydrogen bonds in these two membranes are stronger too. In addition, their distance is high in polymer chains and hydronium ions cannot
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Fig. 6. RDFs of water-water molecules in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
easily transfer because they are attracted to polymer chains by hydrogen bonds. In conclusion, hydronium ions diffusion in SPEEK and PBI membranes is less than their diffusion in PVA. This behavior can clearly be seen in Fig. 4. Generally, PVA is the best polymer membrane with the highest amount of proton conductivity at room temperature.
3.5. Hydrogen bonds It should be noted that due to the presence of water molecules, oxygen and nitrogen atoms in polymer chains and hydronium ions, a hydrogen bond plays an important role in mobility and conductivity of protons which is electrostatic interaction between two polar groups that occurs when a hydrogen atom (H) covalently
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Fig. 7. RDFs of HW-HW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
bonds to atoms of nitrogen (N), oxygen (O), or fluorine (F). This bond is stronger than van der Waals interaction, but weaker than covalent or ionic bonds. Therefore, it is necessary to study the hydrogen bonds in the polymer membrane. The energy of hydrogen bonds in PVA, SPEEK and PBI membranes with different water concentrations which listed in Table 5 were calculated using Deriding force field during MD simulation. The results from Table 5 show that the maximum numbers of oxygen and nitrogen atoms in polymer chains exist in SPEEK membrane so the energy of hydrogen bond in this membrane is more than the other membranes. The low mobility of hydronium ions and water molecules in this membrane with 10, 20 and 30 wt % of water is due to their strong interactions (hydrogen bonds) with polymer chains. The results show that the number of hydrogen
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Fig. 8. RDFs of HW-OW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
bonds increases by the increasing water concentration in the membrane, and this exhibits that the similar hydration structures with that in bulk water. It was also observed that the energy of hydrogen bond depends on the kind of polymer chains and water concentration in the polymer membrane. Furthermore, the review of Fig. 4 related to the hydrogen bonds in PBI, SPEEK, and PVA confirms that the strength of hydrogen bond between hydronium ions and polymer chains in theses membrane can be shown in this way: SPEEK > PBI > PVA. The hydrogen bonds in PBI, SPEEK, and PVA membranes include hydrogen bonds of (1) (hydronium-hydronium ions, (2) waterwater molecules, (3) water-hydronium ions, (4) hydroniumpolymer atoms, (5) water-polymer atoms and (6) polymerpolymer atoms. Geometric and energetic criteria are two methods
Fig. 9. RDFs of OW-OW in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
widely used to identify hydrogen bonds [41,43]. Herein, we focus on geometric criterion method to study of hydrogen bonds in the polymer membrane. In the geometric criterion method the hydrogen bonds among water molecules are identified when ROwOw 0.40 nm, and ROw-Hw0.23 nm which R is the minimum position of the OweOw (Ow is oxygen atom of water molecule) or OweHw (Hw is hydrogen atom of water molecule) [41,43]. Therefore, in the following section, hydrogen bonds in these membranes are compared using Radial Distribution Function (RDF) analysis. 3.6. Radial distribution function (RDF) It is well known that hydrogen bond network plays an important role in hydronium ions transfer. Therefore, calculating the
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RDFs of H2OeH2O and H2OeH3Oþ in PVA, SPEEK and PBI polymer membranes is necessary. In this investigation, RDFs of studied systems were calculated using equation (4). Fig. 5 shows the RDFs of hydronium ions (H3Oþ-H3Oþ) together in PVA, SPEEK and PBI with different water concentrations. As it is seen, there is no sharp peak in this figure which indicates that hydronium ions are not willing to bond with each other. Generally, Fig. 5 shows that the tendency of hydronium ions to each other in membrane with 10 wt % of water is weak and they are dispersed throughout this membrane. The RDF results (Fig. 5) of hydrogen bond between hydronium ions in systems with 20 wt % of water show that the first weak peak at 4.75 Å is related to PVA membrane which illustrates the tendency of hydronium ions to each other in PVA is more than the other membranes. The results from study PBI shows that the least tendency of hydronium ions to hydrogen bonding in this membrane causes hydronium ions to move more easily. Therefore it can be said that hydronium ions can move easily when they are close to water molecules but away from each other. In other words, the percentage of water molecules and also the kind of polymer atoms in the membrane determine the strength of hydrogen bond which is effective in mobility of hydronium ions. As shown in Fig. 5 and , RDF results indicate that the maximum and minimum tendency of hydronium ions to each other occurs in PVA and SPEEK, respectively. Due to less tendency of H3Oþ ions to each other in SPEEK, it can be said that H3Oþ ions prefer to surround polymer chains which can influence the conductivity of ions in studied systems. Fig. 6a, b, and c indicates RDF of H2OeH2O molecules in PVA, SPEEK and PBI membranes, respectively. The first peak comprises two shoulder peaks located at 2.75 and 3.30 Å for each the RDFs
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which directly relate to hydrogen bonds between water molecules. It is also observed (in Fig. 6) that the tendency of water molecules to each other is reduced with increasing water concentration in these membranes. On the other hand, increasing the tendency of water molecules to polymer chains is because of more water concentration. But there is an exception; the results from Fig. 6b for PVA membrane show that RDF sharp peak is related to 20 wt % of water. It is because of the existence of OH bonds in PVA monomers (as it is seen in Fig. 1) and water molecules mostly connect to PVA polymer chains with 10 wt % of water and their tendency to each other is less. With increasing water concentration in PVA membrane, the excess numbers of water molecules which cannot bond with PVA polymer chains connect to each other. RDFs of HW-HW (HW i.e. hydrogen atom of water molecule) in SPEEK, PVA and PBI membranes with different water concentrations are calculated and they are shown in Fig. 7. The RDF results show that there are two sharp peaks at distance of 2.5 Å and 3.7 Å [24] and the height of the first peak decreases as the water concentration increases, in the other word, the tendency of water molecules together decrease. But, as shown in Fig. 7b, the behavior of water molecules in the PVA membrane at 10 wt % of water is different and the first peak of RDF of HW-HW is lower than the other water concentration. At this water concentration, the hydrogen bods between water molecules and OH groups of PVA chain are more than water molecules. As shown in Fig. 8, the RDFs of HW-OW in SPEEK, PVA and PBI membranes are approximately the same as the RDFs of HW-HW, with the difference that the two sharp peak of RDFs of HW-OW at distance of 1.7 Å and 3.1 Å.
Fig. 10. RDFs of water-hydronium ions in SPEEK, PBI and PVA membranes with different water concentrations of a) 10 wt %, b) 20 wt %, c) 30 wt % and d) 40 wt %.
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Fig. 9 show the RDFs of OW-OW in SPEEK, PVA and PBI membranes with different water concentrations with the evident sharp peaks located at 2.7 Å [24]. Similarly, the peak height decreases as the hydration level increases in three membranes and all hydration levels, but there is an exception in PVA membrane at 10 wt % water. Fig. 10 indicates RDFs of water-hydronium ions in SPEEK, PBI and PVA membranes with different water concentrations. The RDF results show that there are two sharp peaks at distance of 2.55 Å and 3.25 Å, so; these sharp peaks indicate the formation of hydrogen bonds between hydronium ions and water molecules. It can also be observed (in Fig. 10) that the sharpness of these two peaks strongly decrease with increasing water concentration suggests that the number of water molecules which are surrounded by the hydronium ions decreases. Based on the results of RDF results for PBI in Fig. 10a, the hydrogen bonds between water molecules and hydronium ions in l0 wt. % of water are stronger than the other membranes. Therefore the transport of hydronium ions in PBI must be easier and MSD results (Fig. 2) also confirms this. Fig. 10b indicates the tendency of hydronium ions to bond with water molecules in 20 wt % of water in PBI, PVA and SPEEK membranes which is in this way: PBI > PVA > SPEEK. Since the movement of hydronium ions with water molecules is easier so the MSD of hydronium ions in PBI must be more. As seen, the tendency of hydronium ions to water molecules in PBI and PVA with 30 wt % of water shows the similar result. The comparison of Fig. 10a with Fig. 10d indicates that intensity of RDF peaks in the membrane with 10 wt % of water is almost 4 times of that of the membrane with 40 wt % of water which is due to the number of water molecules. The MSD and RDF results show that mobility of hydronium ions depends on water concentration and molecular structure of polymer chains in these membranes. To determine the exact effect of molecular structure of polymer chains on transportation of hydronium ions in the polymer membrane, the RDF of hydronium ions bond with polymer chain atoms was studied in PVA, SPEEK and PBI. The coordination numbers of hydronium ion and water molecules in SPEEK, PVA and PBI membranes with different water concentrations versus distance is presented in Fig. 11. It can be seen in Fig. 11 that the number of water molecules which are surrounded by the hydronium ions increases with increasing distance. The results indicate that the hydrated structure of hydronium ions with radius of 5 Å contains 4, 4 and 5 water molecules, respectively, in SPEEK, PBI and PVA membranes. Also, according to the results in Fig. 11, the maximum coordination number of hydronium ions (water molecules) in SPEEK, PVA and PBI membranes belongs to the water concentration 20, 10 and 40 wt %, respectively. The RDFs of hydronium ions with carbon and nitrogen atoms of PBI polymer chains with different water concentrations were calculated and shown in Fig. 12. The RDF of N-hydronium ions in Fig. 12a shows two sharp peaks at distance of 2.56 and 4.75 Å that the first peak is for nitrogen atoms with double bond with C and the second peak is related to nitrogen atoms with single bond with C. The first sharp peak at 2.65 Å distance represents the hydrogen bonds between them which become weaker with increasing water in the membrane. The RDF results of hydronium ions-C atoms in Fig. 12b indicate that the first sharp peak is at 3.65 Å, so the distance between hydronium ions and carbon atoms is more than their distance from nitrogen atoms. The results show that the tendency of hydronium ions to bond with nitrogen atoms is more than their tendency to carbon atoms in PBI which is reduced with increasing water concentration. In fact, the access of hydronium ions to polymer chains reduces with increasing water concentration in the membrane because water molecules cover polymer chains. The results clearly show that hydronium ions don’t have any tendency to bond with nitrogen and carbon in PBI with 30 and 40 wt % of water.
Fig. 11. Coordination numbers of hydronium ion and water molecules in a) SPEEK, b) PVA and c) PBI membranes with different water concentrations.
The RDFs of hydronium ions with oxygen and carbon in PVA polymer chains with different water concentrations are shown in Fig. 13. As it can be seen in Fig. 13a, a sharp peak at 2.55 Å shows bonding between hydronium ions and oxygen atoms in PVA and their high tendency to bond with each other. In fact, oxygen atoms in PVA polymer chains have strong hydrogen bonds with hydronium ions. A peak at 3.65 Å in Fig. 13b shows the tendency of hydronium ions to carbon atoms decrease with increasing water concentration. The comparison between RDF results in Figs. 12 and 13 shows that hydrogen bonds in PVA are stronger than PBI. Fig. 14 is RDF of hydronium ions with atoms of carbon, sulfur and oxygen in SPEEK polymer chain with different water concentrations. The results clearly show that there is low tendency between
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Fig. 12. RDFs of the hydronium ions with a) N and b) C atoms of polymer chains in PBI membranes with different amounts of water concentration.
Fig. 13. RDFs of the hydronium ions with a) O and b) C atoms of polymer chains in PVA membranes with different amounts of water concentration.
hydronium ions and carbon in SPEEK because the sharp peak is not observed in this RDF graph. However, other results show that hydronium ions tend to be near oxygen and sulfur in SPEEK at 2.75 and 3.95 Å distance which is due to more tendency of hydronium ions to bond with sulfur. Since sulfur atoms in SPEEK chain bond to several oxygen atoms and the tendency between hydronium ions and oxygen atoms is more, then the distance between hydronium ions and sulfur atoms is more than their distance from oxygen atoms. The results also show that increasing water concentration in the membrane does not effect on decreasing of hydronium ions tendency to bond with atoms in SPEEK which is different in comparison with PVA and PBI membranes. In fact, the maximum and minimum tendency of hydronium ions to oxygen and sulfur atoms in SPEEK polymer membrane is in 40 and 30 wt % of water. In addition, the results show that increasing water concentration in SPEEK membrane increases the intensity of peaks in RDFs for H3Oþ-O and H3Oþ-S which indicates more tendencies of hydronium ions to atoms in SPEEK polymer chains. There is an exception for this tendency in 30 wt % of water.
The comparison of simulation results finally declare that in similar conditions, PVA membrane has better proton conductivity in comparison with other membranes and the effect of water concentration on proton conductivity in this membrane is not significant in more than 30 wt % of water. As a conclusion, it can be said that because of a better conductivity, the best membrane for using in PEMFCs is PVA membrane at room temperature. 4. Conclusion The mobility of hydronium ions in PVA, PBA and SPEEK membranes was investigated using molecular dynamics simulation. In the first step, MD results of density and solubility parameter of these membranes confirm that the molecular dynamics simulation is a good and reliable method to investigate the effect that molecular structure of polymer chain and water concentration have on transportation of proton. The results show that PVA membrane has the highest conductivity in comparison with other studied membranes where by
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Compliance with ethical standards The authors confirm that there are no known conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.molliq.2019.111781. References [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] Fig. 14. RDFs of the hydronium ions with a) C, b) O and c) S atoms of polymer chains in SPEEK membranes with different amounts of water concentration.
[34] [35] [36]
increasing water concentration from 10 to 30 wt % of water, the conductivity increases and after that it approximately remains constant. Also, the comparison of MD simulation results for these three membranes using RDF analysis show that the type of atom in polymer chain of membrane plays a significant role in diffusion of hydronium ions. When these atoms have tendency to water molecules with hydrogen bonds, more mobility of hydronium ions is because of increasing the water concentration in the membrane. In other words, water molecules cover polymer chains so tendency and access of hydronium ions to them are reduced, and they easily move. It can be said that hydrogen bonds between water molecules and polymer chains is effective on the movement of hydronium ions in the membrane.
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