ReaxFF Reactive Molecular Dynamics Simulation of Functionalized

Article pubs.acs.org/JPCC

ReaxFF Reactive Molecular Dynamics Simulation of Functionalized Poly(phenylene oxide) Anion Exchange Membrane Weiwei Zhang and Adri C. T. van Duin* Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: Three functionalized poly(phenylene oxide) (PPO) anion exchange membranes (AEMs), PPO−trimethylamine (PPO−TMA), PPO−dimethylbutylamine (PPO−DMBA), and PPO−dimethyloctylamine (PPO−DMOA), at two hydration levels (λ = 8.3 and 20.8) have been studied by ReaxFF reactive molecular dynamics simulations. Our simulations reveal that with increasing hydration the microstructures of membrane swell and water molecules are more likely to form a channel, which improves the diffusion of hydroxide ion (OH−). Our study of OH− diffusion demonstrates that PPO−TMA hydrated membrane provides the biggest diffusion constant at the high hydration level. However, from comparison of the structural and dynamical properties of the three membranes at the same water content, it is found that when one methyl group of quaternary ammonium center is replaced by a long alkyl chain group, the hydrophobic effects block the OH− approaching nitrogen, resulting in a lower rate of degradation and an improved alkaline stability of PPO−DMOA hydrated membrane. On the basis of these simulation results, we expect that a high performance AEM fuel cell should balance the conductivity with stability of the membrane. ether).15 Theory works in this field are included in the study of the structure of quaternary ammonium polysulfone hydroxide (QAPS-OH) and the hydroxide ion (OH−) diffusion in dry and wet conditions by Merinov et al.16 Also, Han et al. compared the nanophase-segregated structural and transport properties of polysulfone-based anion and proton exchange membranes by classical MD simulations.17 In this paper, we focused on three hydrated functionalized poly(phenylene oxide) (PPO) AEMs, namely, PPO−trimethylamine (PPO− TMA), PPO−dimethylbutylamine (PPO−DMBA), and PPO− dimethyloctylamine (PPO−DMOA). The chemical structure units of the three membranes are presented in Figure 1. The PPO chain was selected due to its low cost and good relative stability in alkaline environment. Furthermore, similar functionalized PPO AEMs have also been synthesized recently.18,19 It is generally known that conductivity is one of the most important factors to evaluate the efficiency of a fuel cell, in which the role of AEM is to transport OH− from the cathode to anode at a high rate.12 To improve the conductivity of the fuel cells, many experimental studies focus on fixing cation chemistries and modifications of the membrane network.20,21 Additionally, it is found that conductivity is also influenced by the water content because the diffusion of the charge carriers (hydroxide or hydronium ions) strongly depend on the formation of the water channel in hydrated membranes. The

1. INTRODUCTION Polymer electrolyte membranes fuel cells, which convert chemical energy to electrical energy with high efficiency and minimal pollution, have attracted widespread attention in recent years.1−3 Various kinds of proton exchange membrane (PEM) fuel cells have been studied by experiments and molecular dynamics simulations (MD).4−8 However, the PEM fuel cell requiring expensive platinum as catalysts remains intractable for the commercialization of the fuel cell technology. To reduce the dependence on the noble metal catalysts, anion exchange membranes (AEM) fuel cells are expected to be of lower cost, in which cheaper metal catalysts are used as their electrodes, such as nickel.9,10 On the other hand, compared to the liquid alkaline fuel cells using high-concentration potassium hydroxide as an electrolyte, the most significant advantage of the AEM fuel cell is that they can prevent carbonate precipitation and reduce corrosion.11 Since the overall efficiency of a fuel cell is influenced by many factors including its solubility, conductivity, stability, etc.,12 theoretical investigation based on molecular simulations is thus an efficient way to understand of membrane chemistry, and it is helpful in the design of high-performance AEM fuel cells. To design an AEM fuel cell, a covalently bonded cation, such as quaternary ammonium, is usually attached to a goodperformance engineering polymer, featured by hard wearing, high temperature resistance, and high mechanical strength. Based on this principle, many AEMs have been successfully synthesized by experimentalists, such as poly(arylene ether sulfone),13 poly(ether ether ketone),14 and poly(arylene © 2015 American Chemical Society

Received: July 27, 2015 Revised: November 12, 2015 Published: November 13, 2015 27727

DOI: 10.1021/acs.jpcc.5b07271 J. Phys. Chem. C 2015, 119, 27727−27736

Article

The Journal of Physical Chemistry C

Reactive force-field (ReaxFF), a bond-order-based empirical reactive force field, provides a suitable alternative to deal with the proton transport as well as chemical reactions.27 It has been successfully applied for modeling complex chemical transformations involving high-energy materials, silion/silicon oxides, and polymer decompositions in the gas and solid phase and at the interface.28−31 Moreover, ReaxFF is also able to describe the dissociation of water and structural migration of OH− and H3 O+, and it succeeds in reproducing the experimental results for both water self-diffusion and H3O+ diffusion in aqueous solution.32,33 Consequently, ReaxFF is a promising method to investigate complex chemical reactions in relatively larger scale molecular systems. Based on this reason, ReaxFF reactive MD simulations were carried out to study the transport property of the AEMs in the present work. Besides studying the structural and transport properties of the AEMs at room temperature, we have also noted that the AEM exhibits poor chemical stability in alkaline environments at a high temperature in comparison with PEMs. Accordingly, we believe that the stability of an AEM fuel cell should also take into account and the poor stability could be a fatal issue to limit the performance and lifetime of the AEM fuel cell in applications. Previous studies found that the degradation of quaternary ammonium membranes usually involves many kinds of reactions related to the quaternary ammonium center group (R4N+), such as Hoffman elimination, chemical rearrangements induced through ylide intermediate formation, direct nucleophilic substitution, and so on.34−37 In addition, the degradation of backbone of membranes is another important issue because the backbone structure impacts the mechanical toughness of the membranes.38−40 However, it rarely attracts attention compared to conductivity.41 What is more, to our knowledge, the degradation of AEMs in nanoscale has not been investigated by MD simulations. The remaining sections of this paper are organized as follows: In section 2, we describe the details of the simulation including the calculation of the diffusion constant and the method to track the hydroxide ions in the systems. Section 3 presents the results and discussion. Conclusions are then given in section 4.

Figure 1. Chemical structure units of (a) PPO−TMA-OH, (b) PPO− DMBA-OH, and (c) PPO−DMOA-OH.

experimental work in Nafion showed that the proton transport followed different mechanisms with the various levels of hydration.6 In this paper, the hydration level, denoted by λ, is the ratio of the numbers of water molecules and quaternary ammonium groups. Jang et al. employed classical MD simulations to study three dendrimer-grafted polymer membranes, and it was found that the structure and dynamic of the water molecules and transport of protons were strongly affected by the hydration level of the membrane.22 In this work, we investigated the conductivity of AEMs in terms of two aspects: the effect of (1) water content and (2) the length of alkyl chain of the functionalized group on the structural and transport properties of the hydrated AEMs. Because OH− diffusion involves both so-called Grotthuss hopping (also named structural diffusion) and vehicular diffusion mechanisms in the hydrated AEM,12 different level computational methods are usually adopted to study these mechanisms.23 In principle, ab initio MD simulation is able to provide accurate and detailed descriptions of the proton transfer in fuel cells. However, it is still restricted to small models (∼102 atoms) and impractical to simulate the systems at nanoscale level (both time and system size). On the other hand, empirical force-field methods based on classical mechanics are much faster and are usually employed to handle the big systems (≫104 atoms). Unfortunately, traditional classical methods only describe the vehicular diffusion of OH− but cannot take the Grotthuss hopping mechanism into account because the latter refers to the forming and breaking oxygen−hydrogen bonds between hydroxide ion and water molecules. That is the main reason why the diffusion constant of OH− predicted by classical MD simulation is usually much smaller than that of the water self-diffusion.16,17 Therefore, a method to bridge the gap between quantum chemistry and traditional force field method is required. One option is the multistate empirical valence bond (MS-EVB) method developed by Voth and co-workers.24−26 This model combines the states to represent the chemical bonding topologies. It was successfully applied for the investigation of proton transport in bulk water and polymer electrolyte membranes. However, this method currently cannot yet handle complicated systems, where both proton transfer and complex chemical reactions involved. Recently, Devanathan et al. used the quantum hopping (Q-HOP) MD method, which combines classical MD simulations with stochastic hopping algorithm to describe the proton shutting process, to compute the diffusion constant of proton transport in the hydrated Nafion.23

2. SIMULATION DETAILS The hydrated AEMs consisting of three chains and 24 OH− ions were built with 200 and 500 water molecules, in which the hydration levels corresponded to λ = 8.3 and λ = 20.8, respectively. In more detail, the degree polymerization of each chain is 8, and both ends of the chain were terminated with hydrogens. The total atom numbers of three chains, including 24 R4N+ groups, are 771, 987, and 1275 for PPO−TMA, PPO−DMBA, and PPO−DMOA, respectively. The details of the hydrated AEMs are summarized in Table 1. The initial Table 1. Composition of Hydrated Membranes and Simulation Conditions AEM no. of water no. of R4N+ total atoms no. hydration level (λ) density at 300 K (g/cm3) 27728

PPO-TMA 200 8/ chain 1419 8.3 1.26

500 8/ chain 2319 20.8 1.11

PPO−DMBA 200 8/ chain 1635 8.3 1.25

500 8/ chain 2535 20.8 1.12

PPO−DMOA 200 8/ chain 1923 8.3 1.24

500 8/ chain 2823 20.8 1.14


Article


Figure 2. Snapshot of projection of H2O and OH− in (a, d) PPO−TMA, (b, e) PPO−DMBA, and (c, f) PPO−DMOA membranes at the low (upper) and high (lower) hydration levels. Water molecules and hydroxide ions are shown with tubes, and the membranes are visualized as a surface. Oxygen is shown in red, nitrogen in blue, hydrogen in gray, and carbon in cyan.

amorphous structure was first constructed using Monte Carlo techniques at a lower density, and then the system was minimized and compressed it to the density with 1.00 g/cm3 during our MD simulations at 300 K. After that, we relaxed the systems by the following annealing procedure, which have succeeded in study of various polymer membranes:16,22 (1) Gradually expanded the initial volume by 50% over 25 ps while the temperature was increased from 300 to 600 K. (2) NVT simulation was performed over 100 ps at 600 K for the larger cell. (3) Gradually compressed the system back to 1.00 g/cm3 while cooling the temperature down to the 300 K. Such operation was repeated four times, which guarantees that the system attains its equilibrium. The 24 OH− anions were replaced by 24 water molecules during the anneal procedure to avoid polymer damage during the anneal stage. Finishing the annealing procedure simulation, 24 water molecules were replaced with 24 hydroxide ions randomly, and the system was minimized again. Then, 100 ps NPT simulation was preformed to equilibrate the system and obtain the final density. The equilibrated densities of three hydrated membranes at 300 K are summarized in Table 1. Following above simulations, 350 ps NVT simulation was continued, and the last 120 ps result was used for the statistical analyses of the structural properties and calculations of the diffusion constant of water and OH−. In our simulations, the time step was set to 0.25 fs and Berendsen thermostat with a coupling time constant of 100 fs was used to control the temperature of the entire system. All of the present ReaxFF MD calculations were performed by ADF-2012 computational chemistry package.42 To investigate the structural properties of the AEMs, we calculated the radial distribution function (RDF) and its corresponding coordination number (CN) within a given radius shell43

g (r ) = CN =

∫0

r′

n(r ) ρ 4πr 2Δr ρ 4πr 2g (r ) dr

(1)

where g(r) and CN are RDF and coordination number, respectively. n(r) is the number of atoms within a distance r of a central atom, and ρ strands for the bulk number density. The RDF and CN were obtained by averaging over the trajectory. The diffusion constants of OH− water were determined based on the mean-square displacement (MSD)44 MSD(m) = ⟨|r(t ) − r |2 ⟩ =

1 n

n

∑ |r(m + i) − r(i)|2 i=1

(2)

where r represents the position of the particle in the unfolded trajectory, t is the time, m is denoted the maximum number of points allowed for the MSD calculation, n is the number of data points used for averaging, m + n stands for the total number of frames, and i is the step counter. With the result of MSD, the diffusion constants were then obtained using the Einstein relation

D=

1 ⟨|r(t ) − r |2 ⟩ 6Nt

(3)

where N is the atom number of the hydroxide ions or water molecules. In order to obtain the structural and transport properties referring to hydroxide ions, the index of oxygen (O*) of the hydroxide ion should be monitored and distinguished from water molecules because the index of O* may change as a result of the proton transfer from water molecule to hydroxide ion. 27729


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The Journal of Physical Chemistry C We evaluated the sequence of proton transport events referring to the previous studies.33,45 The same index number of O* between two adjacent frames from MD trajectory indicates the vehicular diffusion without any proton transfer. While the index changes between the adjacent frames, it indicates that the Grotthuss hopping or proton transfer occurs. In the present work, to guarantee the linear response of MSD to time, we averaged over 30 trajectories to determine the diffusion constant of the OH−.

3. RESULTS AND DISCUSSION 3.1. Microstructures of Membrane. The microstructure of membrane can be characterized as a hydrophobic polymer backbone penetrated by a network of interlinked hydrophilic channels,16 and the hydrophilic channels allow water molecules to access the void of membrane to form water channel, which helps the hydroxide ions to transport from the cathode to anode. Therefore, the formation of the water channel is important to understand the work mechanism of the AEM fuel cell. The microstructures of PPO membranes at low and high hydration levels are shown in Figure 2. At the low hydration level, as shown in Figure 2a, the water channels are well formed in PPO−TMA membrane due to the small scale of R4N+ group. As large-scale alkyl chain instead of methyl in R4N+ group, the water channel is broken, especially in PPO−DMOA membrane, which is illustrated in Figure 2c. At the high water content, the three-dimensional water channel expands further as shown in Figure 2d−f. This observation is consistent with the study of Nafion PEM.23 One expects that the diffusion constants of hydroxide ions and water molecules should decrease as increasing the size of R4N+ group; meanwhile, they would increase with more water uptake. More details about OH− diffusion will be discussed in the following section. For a better understanding of the structure of hydrated membranes, we further analyze the RDF and CN as follows. Distribution of R4N+ Group. Since the water molecules gather around the hydrophilic R4N+ groups, analysis of the distribution of R4N+ group as a function of water content and substituent is helpful to understand the microstructures of membranes. Figure 3 shows the simulated RDF and CN of nitrogen−nitrogen (N−N). It is clearly observed that the RDF has two main peaks. The position of first peak corresponds to the N−N distance between two chains, and the second peak is the adjacent N−N distance in the same chain. As water content increases, the first peak shifts outward, which means the distance between interchain R4N + increases when the membrane absorbs more water molecules. There is evidence that the distance of N−N with a CN of ∼1 is about 6.5 and 8.0 Å at low and high hydration levels, respectively. Another feature is that the intensity of first peak becomes weak with increasing membrane hydration, revealing that the PPO chains move away from each other leading to weak correlation as a consequence of the swelling of the membrane. This result is also observed in the previous simulations of PEMs.4,17 It is also found that the second peak becomes much sharper at the high hydration level; the reason might be the flexible chain favors stretching conformation on the condition with more water content. As a result, the distance of N−N is mainly located at the characteristic length (∼9.0 Å) of two repeat units. In addition, the correlation of interchain N−N is weakened once methyl is replaced by a butyl or an octyl group. Solvation of R4N+ Group. To investigate how the R4N+ group is solvated by water, the RDF of nitrogen and oxygen

Figure 3. Radial distribution functions g(r) of nitrogen−nitrogen and their CNs in the hydrated PPO−TMA, PPO−DMBA, and PPO− DMOA membranes at (a) low and (b) high levels of hydration. The RDF is shown by a solid line and the CN by a dashed line.

(water), as well as its CN, were collected in Figure 4. Unlike the RDF of N−N, the correlation between R4N+ and water is insensitive to hydration level while the CNs of the first solvation shell are about 11 and 15 at low and high levels of hydration, respectively. Compared to the CN of sulfur−oxygen (water) (∼4.0) in hydrated Niflon PEM membrane,4 such many water molecules are involved in the first salvation shell owe to the bulkiness of the R4N+ group. It is worthwhile to note that the CN of nitrogen and oxygen (water) is much bigger than the value of hydration level for the membranes with λ = 8.3. It indicates that the hydrophilic quaternary ammonium group is buried deeply inside the water phase. Therefore, the hydroxide ions would easily diffuse between adjacent R4N+ groups through the overlapped water molecules even at a lower hydration level. The similar finding has been also predicted by means of classical MD simulations for PSU-A by Han et al.17 They found the nitrogen−oxygen (water) CNs of the first solvation shell was 11.5 at the λ = 8.1 hydration level, which is very close to our results from ReaxFF simulations at low hydration level with λ = 8.3. For the structural properties of nitrogen and oxygen (water) at the same hydration level, the RDFs of the three hydrated membranes are almost the same. This observation indicates the length of alkyl chain has slight impact on the correlation of nitrogen and water molecules. R4N+ Group−Hydroxide Ion Correlation. In order to analyze the correlation of R4N+ groups with hydroxide ions, the RDF of nitrogen−oxygen (hydroxide) was calculated, and 27730


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Figure 4. Radial distribution functions g(r) of nitrogen−oxygen (water) and their CNs in the hydrated PPO−TMA, PPO−DMBA, and PPO−DMOA membranes at (a) low and (b) high levels of hydration. The RDF is shown by the solid line and the CN by the dashed line.

Figure 5. Radial distribution functions g(r) of nitrogen−oxygen (hydroxide) and their CNs in the hydrated PPO−TMA, PPO− DMBA, and PPO−DMOA membranes at (a) low and (b) high levels of hydration. The RDF is shown by the solid line and the CN by dashed line.

the result is shown in Figure 5. Compared to the RDF of nitrogen and oxygen (water), the nitrogen−oxygen (hydroxide) correlation becomes weaker, which means the hydroxide ion may be much easier to dissociate from the membrane in aqueous solution. Furthermore, from the comparison of the RDF for the two levels of hydration, it is found the intensity of first peak decreases from about 1.5 to 1.3 Å, which indicates the correlation of nitrogen−oxygen (hydroxide) is weakened further with more water content. On the other hand, the distance between nitrogen and the nearest hydroxide ion moves from about 5.5 Å at low hydration level to 6.5 Å at high hydration level. It reveals that the hydration ions can spread out more broadly from the R4N+ group center into the water channel with the increasing hydration of membrane. From Figure 5, it also illustrates that for PPO−TMA, PPO−DMBA, and PPO−DMOA membranes, nitrogen−oxygen (hydroxide) distances with CN = 1 are ∼5.3, ∼5.4, and ∼5.6 Å at the low hydration level and ∼6.3, ∼6.4, and ∼6.5 Å at the high hydration level, respectively. This result indicates the steric effects arising from the large scale substituent reduce the probability of hydroxide ion approaching the quaternary ammonium center. Actually, such difference would influence the alkaline stability of the membranes, which will be addressed in the section Degradation of Membranes. Solvation of Hydroxide Ion. From above discussion, it has shown that the correlation of R4N+ group and OH− is quite weak, which means the hydroxide ion may be well solvated by

water. Therefore, we further investigated the interaction of hydroxide ion and water molecules. The RDF and CN of oxygen (hydroxide)−oxygen (water) are presented in Figure 6. Compared to the correlation of nitrogen and hydroxide ion, the RDFs of O (hydroxide)−O (water) demonstrate much stronger correlation at both hydration levels. It indicates the hydroxide ion prefers to be surrounded by water molecules to form the OH−(H2O)n cluster. Moreover, the CNs of the first solvation shell are roughly the same at low and high hydration levels (∼4.2 and ∼4.4 at low and high levels, respectively), which demonstrates the number of water molecules binding to the hydroxide ion approximates a constant with increasing water content. It is also found that the substituent does not influence the first solvation shell of hydroxide ion. However, for the second solvation shell of hydroxide ion at low hydration level as shown in Figure 6a, the CNs differ significantly at a long distance due to the steric effects of the long alkyl chain groups, which deform the water channel and perturb the outer solvation shell structures of hydroxide ion. Structure of Water. As mentioned above, the characteristics of the water phase are very important for the transport of hydroxide ions in the membranes. It has been proved that the diffusion constants of hydroxide ions and water molecules in bulk water are much larger than that in hydrated membranes due to the good development of hydrogen-bonding network.22,46 Therefore, we expect the water molecules are featured by a bulk-water phase to aid hydroxide ions transport 27731


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Figure 6. Radial distribution functions g(r) of oxygen (hydroxide)− oxygen (water) and their CNs in hydrated PPO−TMA, PPO−DMBA, and PPO−DMOA membranes at (a) low and (b) high levels of hydration. The RDF is shown by the solid line and the CN by the dashed line.

Figure 7. Radial distribution functions g(r) of oxygen (water)−oxygen (water) and their CNs in the hydrated PPO−TMA, PPO−DMBA, and PPO−DMOA membranes at (a) low and (b) high levels of hydration. The RDF is shown by the solid line and the CN by the dashed line.

Table 2. Diffusion Constants (Å2/ps) of OH− and H2O in Hydrated Membranes at 300 K

in hydrated membranes. In order to characterize the structure of water phase in hydrated membranes, we calculated the RDF and CN of oxygen (water)−oxygen (water) and show them in Figure 7. For straightforward comparison, the RDF of oxygen− oxygen in bulk water is also incorporated referring to ref 32. Clearly, the water phase in the hydrated membranes resembles the well-organized bulk water in structure with growing water content. In addition, the CNs of the first solvation shell are 3.5 and 4.2 at low and high levels of hydration, respectively. The latter is nearly close to that in bulk water (CN = 4.5). On the basis of analyses of RDF and CN, one expects the diffusion of hydroxide ions and water molecules should be fast in the membrane at the high level of hydration. It is also noted that the substituent has small impact on the first solvation shell of water, especially at a high level of hydration. This feature is similar to the RDF and CN of oxygen (hydroxide)−oxygen (water) as shown in Figure 6. 3.2. Transport Properties. Since the OH− diffusion and water self-diffusion are the most critical factors of an AEM fuel cell, the diffusion constants of them were calculated and collected in Table 2. It is clear that the diffusion constants of OH− are much bigger than the self-diffusion constants of water molecules at two levels of hydration. Such consistency between simulation and experiment indicates that both vehicular diffusion and Grotthuss hopping mechanisms are well described with our present ReaxFF MD simulations. Considering the

λ = 8.3

a

λ = 20.8

hydration level membrane

Dwater

DOH−

ka

Dwater

DOH−

ka

PPO−TMA PPO−DMBA PPO−DMOA

0.048 0.046 0.039

0.289 0.213 0.155

6.0 4.6 4.0

0.154 0.145 0.132

0.576 0.473 0.428

3.7 3.3 3.2

Ratio of DOH− and Dwater.

dramatic underestimation of diffusion constant of OH− by classical simulation, we expect that the Grotthuss hopping mechanism has a significant contribution to the overall diffusion constant of hydroxide ions. Comparing the diffusion constants between two hydration levels, we find both Dwater and DOH− increase with growing water content. Such results agree with the above analysis on the water phase structure, which suggests the diffusions of hydroxide ions and water molecules can be enlarged when the water molecules form a wellorganized hydrogen-bonding network. However, the diffusion constant of water molecules at the high hydration level is smaller than that in the bulk water, which is 0.23 Å2/ps in our previous ReaxFF simulations.32 It indicates the water phase still has a relatively less developed hydrogen-bonding network in hydrated membranes. Another interesting result is that the ratio 27732


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The Journal of Physical Chemistry C of DOH− and Dwater at low level of hydration is much bigger than that at a high hydration level. One expects the hydroxide ion is more active in the dry condition, and it thus enhances the possibility of Grotthuss hopping of proton. When the long alkyl chain groups take the place of the methyl group, both DOH− and Dwater, as well as their ratio, decrease with increasing length of the alkyl chains. This is because the water channel is broken by the chain with high hydrophobicity, as clearly shown in Figure 2. For instance, comparing Figure 2c to Figure 2a, it is found the water channel is decomposed to small quantities of clusters, and the water molecules are localized on the voids of the membrane separately, leading to a slow diffusion of the hydroxide ions and water molecules. From above discussion, it is evident that the PPO−TMA membrane at high hydration level may potentially be a good AEM candidate due to the highest diffusion constants of OH− and H2O. However, an AEM fuel cell should provide high ionic conductivity as well as good chemical or thermal stability. For this reason, we also studied the degradation of membranes in this work, as shown in the next section. 3.3. Degradation of Membranes. Degradation of the AEM has been studied in recent experimental work. However, only few discussions have been addressed this issue in theoretical simulations. One reason is that the chemical reactions of AEM cannot be described by classical, nonreactive simulations. Furthermore, although ab initio approaches can overcome the limitation of the classical simulations, their application is currently restricted to the studies of degradation of membrane with very small modeling systems.47,48 ReaxFF is able to handle large simulations and describe the reactions of the system at the same time, so it allows direct observation of membrane degradation. In experiment, it has been demonstrated that the steric effects of the large-scale substituent embracing the quaternary ammonium center stabilize the membranes in alkaline environment.18 For further understanding of the effects, the degradation of membranes with the various lengths of alkyl chain was investigated with ReaxFF reactive MD simulations. Using a monoexponential model, the residual number of hydroxide ions as a function of time was fitted to estimate the lifetime of hydroxide ions and the fitting equation is expressed by ⎧ N0 , t ≤ t1 ⎪ N=⎨ ⎪ −(t − t1)/ t 2 , t > t1 ⎩ N0e

Figure 8. Time dependence of residual number of hydroxide ions in hydrated PPO−TMA, PPO−DMBA, and PPO−DMOA. The simulated results are presented by solid lines and fittings by black lines with symbols.

between R4N+ and OH− is reduced. It is interesting to note that the time-dependent residual number of OH− exhibits a small oscillatory feature. This phenomenon may be elucidated from analysis of the time dependence of products in the procedure of membrane degradation. It is demonstrated that the reverse of the ylide reactions (OH− abstracts one proton from alkyl group of R4N+) was involved in our ReaxFF MD simulations. This result is consistent with that reported in previous experimental and theoretical studies.34,36 For the details of degradation, it is noted that there are two pathways (methyl and benzyl) for PPO−TMA and three pathways (methyl, benzyl, and butyl or octyl) for PPO−DMBA and PPO−DMOA amenable to attack by OH−, and the barriers of reactions at these pathways are comparable.34,48 To understand the possibility of the degradation at different pathways, the yields of products related to these reactions were compared and the results show that comparing with benzyl reaction, the degradation favors methyl pathway attack for PPO−TMA due to the high quality and less steric hindrance. While one of methyl groups was replaced by butyl or octyl group, the yields decrease in the order of methyl < butyl (octyl) < benzyl reactions. It is also interesting to find that the possibility of abstracting hydrogen from butyl or octyl group is very close to that from methyl group even though the big size of butyl and octyl groups introduces steric hindrance. It is explained that the reaction barrier of Hoffman elimination pathway involving butyl or octyl group is much lower than that of the SN2 pathway of the methyl group. A similar result was also be reported by DFT calculations.34 Besides, it should be mentioned that further chemical rearrangements were also observed in our MD simulationsthis will be discussed in future publications. Furthermore, we also noted the above cation degradation was slower than the backbone degradation for the benzyltrimethylammonium-functionalized polyaromatic alkaline membranes.40 However, we did not observe backbone degradation in ReaxFF MD simulations. One reason might be that the OH− first attacks the hydrophilic reaction sites at the present time scale and alkaline condition. This can be confirmed by the analyses of MD products, which show that the yield of methyl reaction is much higher than benzyl reaction in PPO−TMA membrane. Another reason is the introducing of −CH3 group on the ortho-position of aryl−ether reduces the rate of backbone degradation compared with the membrane in

(4)

where N0 is the initial number of hydroxide ions, which equals 24 in this work. t is the time in picoseconds. t1 stands for the initial decay time, and t2 represents the exponential time constant. Based on this equation, the lifetime is simply estimated by the sum of t1 and t2. The similar formula has been used to characterize the rate of degradation of the polymer melts.49 Figure 8 illustrates the residual numbers of hydroxide ions as a function of simulation time in the three membranes at high hydration level at 500 K. After 400 ps simulations, the averaged residual numbers of OH− are 1.1, 2.7, and 3.3 in PPO−TMA, PPO−DMBA, and PPO−DMOA membranes, respectively. It indicates the rate of degradation of PPO−TMA is the fastest while the PPO−DMOA is the slowest. We expect the stability of PPO−DMOA is caused by the long alkyl chain substituent, which blocks the hydroxide ion approaching to the quaternary ammonium center. As a result, the rate of the chemical reaction 27733


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The Journal of Physical Chemistry C Scheme 1. Three Reactions for the Modeling Compounda

a

Reactions 1 and 2 correspond to methyl and benzyl pathway degradations, respectively. Reaction 3 is the backbone degradation.

4. CONCLUSIONS We performed ReaxFF reactive molecular dynamics (MD) simulations to investigate three functionalized poly(phenylene oxide) (PPO) anion exchange membranes (AEMs), PPO− trimethylamine (PPO−TMA), PPO−dimethylbutylamine (PPO−DMBA), and PPO−dimethyloctylamine (PPO− DMOA). In order to study the effect of substituent and hydration level on the structural and transport properties of the AEMs, we compared the radial distribution function (RDF), coordination number (CN), and diffusion constants for the three membranes. From analysis of the RDF and CN of nitrogen and nitrogen (N−N), it was found the distance between the functionalized quaternary ammonium groups was increased with more water content. From the correlation function of N−O(OH−), N−O(H2O), O(OH−)−O(H2O), and O(H2O)−O(H2O) pairs, we found that a well-developed water phase was formed at the high level of hydration to aid the OH− transport. When the methyl was replaced by long alkyl chain groups, the hydrogen-bonding network of water molecules might be broken by the hydrophobic alkyl groups. From the results of diffusion constant, we found that the diffusion of both hydroxide ions and water molecules can be successfully predicted by ReaxFF reactive MD simulations; in particular, the contributions of both vehicle diffusion and Grottuss hopping mechanisms were taken into account for the diffusion of OH−. Additionally, the diffusion constants of hydroxide ions and water molecules in the PPO−TMA membrane was the fastest, which was consistent with our analyses of the structure properties. However, investigations on the degradation of the membranes demonstrate that the PPO− DMOA membrane with large-scale substituent group exhibits good chemical stability due to the steric effects of big size alkyl group. This study provides a guideline for experimental scientists to reduce the degradation of the membrane in pursuit of conductivity of the fuel cell and design good performance AEM fuel cells.

ref 40. To further understand this, we compared the energy barriers of three possible degradation reactions with three explicit water molecules at ReaxFF level as shown in Scheme 1. We find the ReaxFF barrier of methyl reaction (30.86 kcal/ mol) is comparable to that with explicit water model at the DFT level, which is 25.00 kcal/mol.34 Furthermore, although the barrier of benzyl reaction (22.03 kcal/mol) is much lower than the methyl reaction, the MD simulations show the methyl pathway degradation is favored. It indicates the degradation indeed first occurs in the hydrophilic phase. Besides, the ReaxFF barrier of backbone reaction for the present modeling compound is 37.04 kcal/mol. While the ortho-position −CH3 groups are replaced by hydrogens, the barrier reduces to 28.80 kcal/mol. It illustrates the introducing of −CH3 really helps to reduce the backbone degradation rate. For the H-substituent, it is noted the ReaxFF barrier is still significantly higher than the DFT barrier, which is 20.53 kcal/mol for the similar compound.40 Such difference arises from the introducing of explicit water molecules in this work. Considering the two factors, the backbone degradation is much slower than the cation degradation and the backbone degradation cannot be straightforwardly sampled with ReaxFF MD simulation for the current hydrated membranes at the present alkaline condition and time scale. To understand the rate of degradation better, we fitted the residual number of OH− as a function of time, and the result is also shown in Figure 8. Based on the fitted functions, it is easy to evaluate the mean lifetimes of OH− and they are 166, 192, and 219 ps in PPO−TMA, PPO−DMBA, and PPO−DMOA hydrated membranes, respectively. This order of stability of the three membranes is consistent with our analysis of the RDF of N−O (hydroxide) as mentioned in section 3.1. From above discussions, it demonstrates that the chemical stability increases in the order of PPO−TMA < PPO−DMBA < PPO−DMOA membranes. This result is consistent with experimental observations.18,19 However, as shown in the last section, the diffusion constant increases in the order of PPO−DMOA < PPO−DMBA < PPO−TMA. Therefore, we have to compromise between conductivity and stability to design high performance AEM fuel cells. In other words, the degradation of the membrane should also be considered in the pursuit of improved transport properties.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07271. ReaxFF reactive force field parameters (PDF) 27734


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.C.T.v.D.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from the U.S. Army Research Laboratory through the Collaborative Research Alliance (CRA) for Multi Scale Multidisciplinary Modeling of Electronic Materials (MSME).

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ReaxFF Reactive Molecular Dynamics Simulation of Functionalized

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