Hydroxide Ion Diffusion in Anion-Exchange Membranes at Low

Article Cite This: Chem. Mater. XXXX, XXX, XXX−XXX

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Hydroxide Ion Diffusion in Anion-Exchange Membranes at Low Hydration: Insights from Ab Initio Molecular Dynamics Tamar Zelovich,† Leslie Vogt-Maranto,† Michael A. Hickner,‡ Stephen J. Paddison,§ Chulsung Bae,∥ Dario R. Dekel,⊥ and Mark E. Tuckerman*,†,#,¶

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†

Department of Chemistry and #Courant Institute of Mathematical Sciences, New York University (NYU), New York, New York 10003, United States ‡ Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Chemical & Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States ∥ Department of Chemistry and Chemical Biology, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ⊥ The Wolfson Department of Chemical Engineering, and the Nancy & Stephan Grand Technion Energy Program (GTEP), TechnionIsrael Institute of Technology, Haifa 3200003, Israel ¶ NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Rd. North, Shanghai 200062, China S Supporting Information *

ABSTRACT: Operation of anion-exchange membrane (AEM) fuel cells (AEMFCs) results in gradients in the cell that can lead to low-hydration conditions within the cell. It is therefore important to investigate hydroxide ion diffusion in AEMs with low water-to-cation ratios (λ ≤ 4, λ≡nH2O/ncation). In this work, ab initio molecular dynamics simulations are presented to explore hydroxide ion solvation complexes and diffusion mechanisms in model AEMs at low hydration. By changing the cation spacing within the AEM and the degree of hydration, six different idealized AEM models are created in which the water distribution is not uniform. It is shown that distinct water distributions impart unique OH− diffusion mechanisms that fall into three regimes. The observed mechanisms, nondiffusive, vehicular, and a mixture of structural and vehicular diffusion, depend on the presence or absence of a second solvation shell of the hydroxide ion and on the local water structure. The results suggest that the water distribution is a better descriptor than the value of λ for classifying AEMs under low-hydration conditions. These results enable us to posit idealized mechanisms for the three diffusion regimes and to define requirements for promoting OH− conductivity in high-performance AEMFC devices operating under lowhydration conditions.

1. INTRODUCTION Anion-exchange membrane (AEM) fuel cells (AEMFCs) have great potential as cost-effective energy conversion devices due to an alkaline environment that does not require expensive platinum catalysts.1−14 The ability of AEMFCs to operate with a variety of fuels at low temperatures results in a low-cost, clean-energy technology. However, hydroxide ion conductivity and cation stability of AEMs remain key hurdles to realizing the full potential of AEMFCs.2,5,10,15−19 The critical role of water in promoting efficient hydroxide ion diffusion within AEMs has been studied extensively.17−22 For this purpose, it is common to classify AEM environments and operation according to the number of water molecules per cation (denoted as the hydration number λ). Systems with high and intermediate hydration levels (λ > 8) are often studied, yet the AEM behavior under low-hydration conditions (λ < 5) has not been closely examined. Characterizing the key components of hydroxide ion diffusion mechanisms under these low-hydration conditions is critical, as the prevailing © XXXX American Chemical Society

assumption is that certain regions in the AEMFCs will ultimately operate at low-hydration levels (regardless of the λ value set at the beginning of operation) because of water consumption at the cathode as a result of the oxygen reduction reaction.9,10,15,17−19 Interestingly, recent studies exploring the chemical stability of AEMs show that cation degradation significantly increases under low-hydration conditions because of a deficiency of water molecules solvating the hydroxide anions in the system.17−19,23,24 This degradation was recently shown to be caused mainly at the AEM cathode interface, where hydration levels are the lowest.25 A molecular level understanding of OH − transport under low-hydration conditions will play an important role in determining the key design principles for new stable polymer electrolyte materials with high hydroxide ion conductivity. Received: May 9, 2019 Revised: June 28, 2019 Published: June 28, 2019 A

DOI: 10.1021/acs.chemmater.9b01824 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials

Figure 1. Typical cell (shown without water molecules) demonstrating the effective distance between the two graphane sheets along the z-axis (Δz) on the left and the cation spacing along the x- and y-axes on the right (Δx and Δy). The blue and orange areas in the right figure indicate the BRs and the center of the cell regions, respectively. White, turquoise, and blue spheres represent H, C, and N atoms, respectively. The GB atoms (C and H atoms) were removed from the right figure to better show the cation structures. The light blue rectangle in the right panel shows the extent of the simulation cell.

Table 1. System Parameters for the Three GB Structures Presented in This Study, Arranged in the Order of Ascending Effective Water Density cation spacing (Å)

cell geometry (Å)

diffusion class

system

λ

effective water density (g/cm3)

Δx

Δy

x-axis

y-axis

z-axis

I II III

b2 a4 b4

2 4 4

0.224 0.267 0.373

10 10 10

6.6 8.7 6.6

10 10 10

13 17.4 13

7.3 7.3 7.3

depending on the water distribution and the hydroxide ion solvation structure, we identify three diffusion regimes: nondiffusive, predominantly vehicular diffusion, or a mixture of structural and vehicular diffusion. As the hydroxide ion diffusion mechanism is strongly affected by the water distribution, we find that the water distribution serves as a better classifier than the hydration level for low-hydration environments. On the basis of the results presented here, we define the key features we believe are required for achieving high hydroxide ion diffusion in AEMFC devices under lowhydration conditions.

We have previously studied hydroxide ion diffusion mechanisms in AEM-like environments21 by employing nanoconfined structures26−49 to mimic different polymer architectures. This work showed that water molecules under such confinement exhibit intriguing and unusual structures that depend on system size and water density. The hydroxide ion diffusion mechanism, which is a well-studied fundamental phenomenon in bulk basic aqueous solution,50−60 was shown to be strongly dependent on the water structure. Specifically, it was suggested21,61 that for relatively low-hydration levels (i.e., λ = 4), the hydroxide ion could exhibit unusual solvation patterns, and the diffusion process may be driven by a predominantly vehicular diffusion mechanism rather than by structural diffusion, which occurs in bulk solution. Because this otherwise intriguing suggestion is based on a relatively crude model, we are led to conclude that a further, more rigorous study of AEMs under low-hydration conditions (λ < 5) is warranted. For this purpose, we employed fully atomistic ab initio molecular dynamics (AIMD)62 simulations to investigate the molecular behavior, solvation patterns, and diffusion mechanism of hydroxide ions in AEMs under low-λ levels. On the basis of a previous coarse-grained study,20 we designed six idealized low-hydration AEM environments. In order to mimic the polymer backbone, our theoretical model employs a graphane bilayer (GB) system, with two trimethyl alkyl ammonium (TMA) cations tethered inside by short carbon chains,17,61,63−65 two hydroxide ions, and a varying number of water molecules. By changing the cation spacing and hydration level, six architecturally distinct cells showing significantly different water distributions are studied. Using AIMD simulations, we determined the OH− diffusion mechanism in each of these distinct environments. In these AEM models, the few water molecules present are distributed nonuniformly within the simulation cell, resulting in an unequal partitioning of water molecules between the hydroxide ions. As a result, each hydroxide oxygen can have different solvation patterns, some of which lack a second solvation shell. Furthermore,

2. DESCRIPTION OF THE SYSTEMS In this study, we explored six different GB systems, representing six different AEM structures. Of these six AEM systems, we ultimately chose three representatives that best captured the mechanisms of the three diffusion regimes described above (a detailed description of the six systems can be found in the Supporting Information). Each of the systems contains two identical graphane layers aligned in the xy-plane, two TMA cations, two hydroxide ions (whose oxygen atoms are referred to as O*1 and O*2 ), and a variable number of water molecules. The two cations are attached to fixed points in the GB but are otherwise free to move in the aqueous solution. As presented in Figure 1, the two attachment points define the polymer electrolyte cation spacing in the x and y directions. As a result, the simulation cell is partitioned into an open region in the center of the cell and constricted regions between the cations, which we refer to as bottleneck regions (BRs). On the basis of ref 20, the tunable parameters for the six systems (summarized in Table 1 and the Supporting Information) are (i) the hydration level, λ, chosen to be 2, 3, or 4; (ii) the distance between the two carbon sheets, Δz, fixed at 7.3 Å for all systems (see the Supporting Information for rationale); and (iii) the polymer electrolyte cation spacing in the x and y directions, as measured between two nitrogen atoms (Δx and Δy), in which Δx is fixed at 10 Å for all systems and Δy is chosen to be 6.6 Å or 8.7 Å. After obtaining the desired B


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Chemistry of Materials starting structures, AIMD simulations62 were run using the CPMD code.66,67 Each system was equilibrated at the desired temperature using a massive Nosé−Hoover chain thermostat,68 followed by 15−20 ps of canonical (NVT) dynamics, also using a Nosé−Hoover chain thermostat, and finally ∼80 ps of microcanonical (NVE) dynamics. To account for dispersion forces, we employed the dispersion-corrected atomic core pseudopotentials (DCACP) scheme within the Kohn−Sham formulation of density functional theory and the B-LYP exchange−correlation functional.69,70 The performance B-LYP + DCACP has previously been shown to give satisfactory results for water−acene interactions71 and for liquid water.72 All simulations were carried out at room temperature (300 K) and constant volume. A detailed description of the computational method can be found in the Supporting Information and in our previous work.21 As the primary motivation of this work is to gain insight into how changing various design parameters affects hydroxide diffusion in the model systems employed, we believe that the simulation protocol is sufficiently accurate to provide the information we seek. For each system, the effective water density is estimated by ρ=

mH20[g] (Vcell − VTMA )[Å3]

Figure 2. Snapshots of hydroxide ion solvation structures obtained from AIMD trajectories that demonstrate the water distribution, the void regions, and the distinct hydroxide ion solvation shells of the three systems, as presented from a z-perspective. Specifically, system b2 exhibits a nonuniform water distribution with H7O4− (threefold) and a H3O2− (singly coordinated) structures for O*1 and O*2 , respectively. A second solvation shell is absent for both ions, suggesting something resembling a “microsolvated” environment for both ions. System a4 exhibits a nonuniform water distribution with clusters of three and five water molecules in the vicinity of O*1 and O2*, respectively, in which only O1* is missing a second solvation shell. System b4 exhibits a momentarily uniform water distribution in the shape of a wire. Red, white, turquoise, and blue spheres represent O, H, C, and N atoms, respectively. Yellow and green spheres show the position of O1* and O2*, respectively. The GB atoms (C and H atoms) were removed to better show the water molecules, hydroxide ions, and cation structures. For better view of the systems, we repeat atoms in periodic images beyond the simulation cell boundaries.

, in which the effective volume in the

denominator is obtained by subtracting the volume of the cations, VTMA (estimated by the size of the cation in its initial configuration), from the volume between the two graphane sheets, Vcell. As a result of varying the system parameters (Δy and λ), the six systems were constructed with different effective water densities. For clarity, we refer to the three representative systems as b2, a4, and b4, in which the notation “a” and “b” represent the two Δy values, 8.7 and 6.6, respectively, and the numbers represent the hydration level (system b4 was previously referred to as system GB4 in ref 21). The system parameters are presented in Table 1, arranged in ascending order of the calculated effective water densities, and classified according to the diffusion regimes I, II, and III presented in Section 4. The effective densities presented in Table 1 should be regarded only as very rough estimates to be compared with those of ref 21. Greater detail of the water distribution is gleaned from the radial distribution functions (RDFs) to be described in the Results section.

the simulation cell (see Figure 2). Unlike in bulk solution, in which the water oxygen has, on average, a fourfold-tetrahedral coordination pattern, the clustering results in a first solvation shell of either zero or one for the water oxygens, while a momentarily uniform water distribution results in a water oxygen first solvation shell coordination number equal to 221 (see OO RDFs in the Supporting Information and Figure 2 for clarification). The specific patterns formed in these clusters influence whether OH− diffusion is predominantly vehicular or remains nondiffusive (see Section 4). 3.2. OH− Solvation Structure. As indicated above, the water molecules form spatially separated clusters in the vicinity of each hydroxide. Depending on the value of λ, the number of water molecules in each cluster varies from one to five. As a result, the two hydroxide oxygens may not share the same solvation pattern or have the same coordination number (CN). Therefore, we find it useful to refer to the two hydroxide ions as two different species. For this purpose, we plot the O*O RDF and CNs for O1*, and O2* separately, as shown in Figure 3 (see the inset for O*O CN values of the first and second solvation shells). The first solvation shell of the hydroxide oxygen, in all three systems, is located at 2.7 Å, as reported for bulk solution,50−60 and contains one to three water oxygens, depending on the value of λ (as opposed to four water oxygens as observed in bulk solution58). The second solvation shell of the hydroxide oxygen (located at ∼4 Å in bulk solution50−60) varies from zero to two water oxygens. Specifically, the results reveal that the two hydroxide ions of system b2 and O1* of system a4 are missing a second solvation shell, while O*2 of system a4 and the two hydroxide ions of system b4 possess a second solvation shell, at ∼4 Å, containing one or two water molecules. It is well known that the hydroxide ion transport mechanism is strongly affected by the solvation structure of OH−.50−58 In bulk solution, the hydroxide ions typically share a similar environment, which results in a similar diffusion behavior.

3. RESULTS 3.1. Water Structure. The water density calculation described above assumes that the water molecules are uniformly distributed throughout the system and are equally shared between the hydroxide ions, as they would be in bulk solution.50−60 However, inspection of the configurations from the AIMD trajectories reveals that the water distribution in the cell is actually not uniform. At such low-hydration levels, all water in the system can be regarded as interfacial, that is, in contact with some part of the “membrane”, and inhomogeneous throughout the system. For the two systems with the lowest water density (i.e., systems b2 and a4), the nonuniform water distribution persists throughout the simulation. However, for system b4, which has the highest water density among the three systems, the water distribution alternates between a nonuniform distribution and a momentarily uniform distribution, in the shape of a water wire73−80 (see Figure 2). A nonuniform water distribution refers to the formation of spatially separated (by roughly 4 Å) water clusters in the vicinity of each hydroxide. As a result, void areas are formed in C


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contribute negligibly to the overall diffusion). In order to distinguish between different hydroxide ion diffusion mechanisms, we label proton transfer (PT) events (excluding events in which the PTs forth and back before transferring to a third oxygen, known as “rattling” events) with gray lines, where each line represents a change in the identity of the hydroxide oxygen. A smooth change in the hydroxide ion oxygen coordinates is indicative of vehicular diffusion,21 while a sharp jump in the coordinates of one of the OH− oxygens, caused by a PT event, is associated with structural diffusion,53−58 often referred to as “Grotthuss diffusion”. It is important to note, however, that an idealized Grotthuss process generally refers to a series of proton hops that merely change the role of covalent and hydrogen bonds (HBs), with little consideration of the fluctuations in the local H-bond arrangement. Here, however, as will be described below, the nonuniformity of the water distribution leads to a structural diffusion mechanism driven by significantly more complex factors not captured in such an idealized “Grotthuss” picture. A comparison of the diffusion constants of the three systems shows that the average hydroxide ion diffusion increases with the water density. Specifically, system b2 is seen to have the lowest hydroxide diffusion constants along all axes. This agrees with the evolution of the coordinates of the two hydroxide ions (Figure 4), in which both ions are nondiffusive and show no PT events (any relatively large change in the coordinates (∼30−35 ps for O1* in Figure 4 for system b2) corresponds to motion in the center of the cell, as the two hydroxides are trapped in this region). In system a4, hydroxide ion diffusion occurs only along the x-axis, with a diffusion constant of 0.343 Å2/ps along this direction, which is roughly three-fourths of the bulk hydroxide diffusion constant. According to Figure 4, only O*2 undergoes vehicular diffusion along the x-axis, while O*1 is nondiffusive. On the basis of a dearth of PT events involving hydroxide ions along the trajectory, we can claim that diffusion of O2* is predominantly vehicular. System b4 possesses the highest hydroxide ion diffusion constant, with a value of 0.428 Å2/ps along the y-axis, which is roughly equal to the bulk hydroxide diffusion constant. Here, both structural and vehicular diffusion mechanisms are clearly seen for both hydroxide ions. Moreover, system b4 is the only system that shows synchronous diffusion for the two hydroxide ions. The conditions that enable the diffusion of the two hydroxide ions will be discussed later in the text. It should be noted that we find a strong correlation between water and hydroxide ion diffusion constants, which will be addressed in separate discussions below.

Figure 3. O*O RDFs of O*, O1*, and O2* (black, red, and green, respectively) for systems b2, a4, and b4. The colored dotted lines represent the integrated CNs and the dotted gray line represents the estimated location of the hydroxide oxygen’s second solvation shell. The numbers in the inset represent the CNs, rounded to the nearest integer, of the first (CN1) and second (CN2) solvation shells of O*1 and O2*.

However, in these low-hydration systems, the heterogeneity of the environments of each hydroxide suggests that over the time scales probed in the present simulations, each OH− might undergo different diffusion processes, which are discussed in Section 4. Of course, over sufficiently long times, mobile hydroxides (nondiffusive hydroxide ions remain an exception) are expected to diffuse in all possible ways, yet the different diffusion mechanisms, nevertheless, remain distinct. 3.3. Dynamical Results. The systems examined in this work have geometries that influence the mobility of the water molecules and hydroxide ions differently in each of the three spatial directions.21 Therefore, in order to shed additional light on the anisotropy of the hydroxide ion transport in this environment, we calculate diffusion constants along each of the axes separately (see Table 2). These components can be interpreted as the diagonal elements of the diffusion tensor, an important quantity in the calculation of ionic conductivities. To understand the reasons underlying the differences in diffusion constants and to present a complete analysis of the mechanism of hydroxide ion transport, we plot the coordinates of the OH− oxygens in each system as a function of time along the x- and y-axes separately in Figure 4 (the hydroxide ion coordinates along the z-axis are not presented as they

4. DISCUSSION OF OH− DIFFUSION REGIMES Further insight into the unusual OH− diffusion mechanisms can be gleaned by turning to the solvation patterns (Figure 3). We find that hydroxide ions diffuse only when they acquire a

Table 2. Diffusion Constants Obtained from the Slope of the Mean Square Displacement in Units of 10−8 m2/s (i.e., Å2/ps). DOH−

DH2O

system

D

DX

DY

b2 a4 b4 bulk solutiona

0.021 0.135 0.170 0.450a

0.018 0.343 0.069

0.047 0.040 0.428

DZ

D

DX

DY

DZ

0.023 0.032

0.030 0.252 0.060 0.17b

0.021 0.522 0.049

0.064 0.201 0.126

0.005 0.034 0.023

a

Results taken from (a) ref 57 and (b) ref 81 using the B-LYP functional. D


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Figure 4. Hydroxide ion oxygen coordinates as a function of time (black and red curves for x and y coordinates, respectively) for O1* and O2* during the simulations for systems b2, a4, and b4. Gray lines indicate PT events (excluding rattling) that result in a change of the hydroxide ion identity.

On the basis of this analysis, we find the following characteristic features of nondiffusive hydroxide ions: (i) absence of a second solvation shell; (ii) a well-defined first solvation shell consisting of no more than three water molecules with no or very infrequent exchanges of water molecules between the first solvation shells of the hydroxide ions; and (iii) long-time persistence of this nonuniform water distribution resulting in a lack of diffusion of water throughout the system. The nondiffusivity of the hydroxide ions results either from a strong cation-hydroxide ion interaction, as occurs when the CN is less than three, or as a result of hindered diffusion of the hdyroxide ions through the BR, as seen when the CN is equal to 3 (see Section 4.2 for a detailed explanation of hydroxide ion diffusion through the BR). 4.2. OH− Transport Mechanisms. In order for diffusion to occur, the system setup should result in a water distribution in which the hydroxide ions possess both a first and a second solvation shell. This is achieved by a cluster of at least four water molecules in the vicinity of an OH− ion. According to the structural population probabilities, the dominant complex of these hydroxide ions is the 3A + 0D structure (see the Supporting Information for exact values). This is consistent with the results presented in ref 21, in which the threefold structure was found to be the dominant complex in lowhydration conditions (as opposed to the fourfold structure observed in bulk solution58). Moreover, the threefold structure was found to be energetically stable in studies characterizing the shell structure of OH−(H2O)n in gas-phase clusters.82,83 As the hydroxide is most likely to be found within 4.7 Å of a cation (see the Supporting Information for NO* RDFs), it appears that the cation plays the role of a fourth neighbor that stabilizes the configuration;21 this may be considered as a modified version of the “dynamical hyper-coordination” concept observed in bulk water.21,53−55,57 The stabilization of an OH− by a threefold structure in the vicinity of a cation and the presence of a nonuniform water distribution are the main factors that determine the type of observed hydroxide ion diffusion mechanism. As will be explained in detail below, vehicular diffusion occurs as long as a nonuniform water distribution persists, mainly because of void regions present in the simulation cell, and structural diffusion occurs once the water molecules form a uniform wire structure in which each water oxygen is twofold coordinated.73−80 4.2.1. Regime IIVehicular Diffusion (System a4). Vehicular diffusion is the dominant diffusion mechanism under low-hydration conditions. The preference for vehicular

second solvation shell of at least one water oxygen (see Figure 3). The role of the second solvation shell is important for providing sufficient hydration of the OH− to shift the competition between its electrostatic attraction to the cation and its hydrophobic repulsion from the cation, resulting in vehicular diffusion. It is also critical for forming coordination patterns that support structural diffusion. Therefore, the absence of a second solvation shell seems to suppress OH− diffusion in system b2 and O*1 of system a4. Similarly, the presence of a second solvation shell appears to promote vehicular diffusion in the case of O2* in system a4, and the combination of structural and vehicular diffusion observed in system b4. Although the existence or absence of the OH− oxygen second solvation shell determines whether the ion diffuses or not, the complete hydroxide ion solvation structure, including both first and second solvation shells, and the water distribution determine the diffusion mechanism. On the basis of the results presented here, we propose three diffusion regimes for AEMs under low-hydration levels: (i) nondiffusive, seen for hydroxide ions with no second solvation shell (system b2 and O*1 of system a4), (ii) predominantly vehicular diffusion, seen for hydroxide ions with a second solvation shell and a nonuniform water distribution (O*2 of system a4), and (iii) mixed diffusion, including both structural and vehicular components, seen for hydroxide ions with a second solvation shell and a water distribution that alternates between nonuniform and a (uniform) water wire structure (system b4). Next, we present detailed idealized mechanistic pictures for the three diffusion regimes, supported by population probabilities for different hydroxide ion solvation complexes (see the Supporting Information for exact numbers), the O*O RDF and CN (see Figure 3), and the AIMD trajectories. 4.1. Regime INondiffusive (System b2). In order to understand the very low diffusivity of hydroxide ions in this system, we inspected the sequence of configurations in the trajectory. In doing so, we found that all of the water molecules in the system are located in the first solvation shells of the hydroxide ions. The solvation patterns thus formed are either a threefold H7O4− (3A + 0D) structure or an H3O2− (1A + 0D) structure, and they are maintained throughout the trajectory with only rare exchanges of water molecules between the two solvation shells (see Figure 2). The stability of the solvation patterns is indicated by the similarity of the H2O and OH− diffusion constants in Table 2. E


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Figure 5. Representative configurations showing the vehicular diffusion for system a4 from a z-perspective, in the center of the cell (a−d) and in the BR (e−h), including five water molecules from the first and second solvation shells. Red, white, turquoise, and blue spheres represent O, H, C, and N atoms, respectively. A green sphere represents the hydroxide ion. (a) A hydroxide ion is in a stable threefold structure near a cation, with two water molecules in the second solvation shell. (b) The hydroxide ion is in a fourfold planar structure in the center of the cell with one water molecule in the second solvation shell. (c) The hydroxide ion and the five water molecules move toward the nearby cation. (d) The hydroxide ion is in a stable threefold structure near a cation. Two water molecules are located at neighboring BRs. (e) The hydroxide ion forms a stable OH−(H2O)4 complex in which three water molecules are part of a threefold tetrahedral structure and one water molecules is in the second solvation shell. A water molecule is located below the hydroxide ion in the BR. (f) The hydroxide ion and five water molecules are diffusing through the BR. (g) The hydroxide ion crosses the BR and is located near a cation in a stable threefold structure. (h) The hydroxide ion’s threefold structure changes back into a fourfold planar structure as it diffuses toward the center of the cell.

Figure 6. Representative configurations showing the hydroxide ion structural diffusion mechanism proposed for system b4 from a z-perspective, for a momentarily uniform water distribution in the shape of a wire, with important water molecules from the first and second solvation shells. Red, white, turquoise, and blue spheres represent O, H, C, and N atoms, respectively. Yellow spheres represent the instantaneous hydroxide oxygen. (a) Water molecules form a wire shape with the hydroxide ion in its stable threefold structure near a cation. A similar threefold structure is seen for a water oxygen in the vicinity of the nearby cation. (b) A HB is formed between the OH− oxygen and a first solvation water molecule. (c) A PT event occurs, and a second HB is formed between the nascent OH− oxygen and a first solvation water molecule. The nascent hydroxide is in a twofold structure while the coordinating water oxygen is presolvated with three oxygens and is located in the vicinity of a cation. (d) A PT event occurs. The hydroxide ion reaches a stable tetrahedral threefold structure near a cation.

over structural diffusion is caused by void regions present in the system due to an insufficient number of water molecules around the hydroxide ions to facilitate PT events. Inspection of configurations from the trajectory shows that OH− ion diffusion depends on the location of the hydroxide ions relative to the cations in the cell. Therefore, we divide the system into two regions (see Figure 1): (i) the center of the cell and (ii) the region between a pair of cations, which is characterized as a BR. In Figure 5, we use O2* of system a4 to describe the solvation patterns that enable vehicular hydroxide ion diffusion under these hydration conditions and propose an idealized diffusion mechanism in each region. For this description, we show the hydroxide ion along with five significant water molecules from the first and second solvation shells. Initially, the hydroxide ion is located near a cation, in a stable threefold coordinated structure, which was found to be the stable or “resting” structure under low-hydration conditions, with two water molecules in the second solvation shell.21 Once the majority of water molecules are in the center of the cell, the hydroxide ions drift toward them via vehicular diffusion, forming a fourfold planar structure with one water molecule in the second solvation shell (see Figure 5a,b). The hydroxide ion continues to move via vehicular diffusion with its five water molecules toward the nearby cation, until the hydroxide ion structure returns to its stable threefold structure in the vicinity of the next cation (see Figure 5c,d).

When located at the center of the cell, the hydroxide ion diffuses relatively freely, but when it is located between a pair of cations, we find that its diffusion is restricted considerably, as the diffusion path in this region is rather narrow. Therefore, we identify the areas between each pair of cations as BRs (see Figure 1). To initiate hydroxide ion diffusion into the BR, a water molecule must be located near the bottleneck entrance. Moreover, in order to draw the hydroxide ion through the BR, a water molecule is also required to be located on the other side of the BR. Greater mobility of the water increases the probability of achieving these two conditions. Once the hydroxide ion is located in the BR, the hydroxide ion forms a threefold tetrahedral structure as part of a well-ordered stable OH−(H2O)4 complex.21 We find that the existence of a water molecule above/below the hydroxide ion, as part of the tetrahedral structure, is essential in establishing OH− diffusion through a BR (see Figure 5e,f). Once the majority of the first solvation shell water oxygens pass into the next open region, the hydroxide ion is drawn toward the other side of the BR. When the hydroxide ion returns to its stable threefold structure near a cation, the mechanistic cycle is complete (see Figure 5g,h). As vehicular diffusion requires simultaneous diffusion of the hydroxide ion along with its five water molecules from the first and second solvation shells, we find, as expected, that the F


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Chemistry of Materials diffusion constants of the hydroxide ions and the water molecules are similar. 4.2.2. Regime IIIMixed Structural and Vehicular Diffusion (System b4). The water distribution in systems b2 and a4 was found to be persistently nonuniform. However, increasing the water density by changing the cell geometry/ cation spacing or the hydration level leads to fluctuations in the water distribution causing the clusters to approach each other within a separation of 4 Å. Specifically, in system b4, which has the highest water density among the three systems, the water structure alternates between a nonuniform distribution and a wire structure,73−80 in which the water oxygens are each twofold (1A + 1D) coordinated. For a nonuniform water distribution, vehicular diffusion occurs according to the mechanism illustrated in Figure 5. However, the formation of a water wire structure permits structural diffusion (i.e., proton hopping). A proposed mechanism for this structural diffusion is shown in Figure 6. Two events initiate the PT. First, the eight water molecules in the simulation box must rearrange to form a wire, while at the same time, the hydroxide ion is in a stable threefold configuration near one of the cations. In this configuration, the OH− ion and water molecules have coordination patterns containing three and two water molecules, respectively, with the hydroxide ion accepting three HBs, and each H2O accepting one HB and donating one HB. Second, the H2O at the end of the water wire must be near a cation and achieve, via ordinary fluctuations, a threefold pattern in which it accepts two HBs; in this configuration, its solvation structure resembles the coordination pattern of the OH−. When those two processes happen, a series of proton hops is seen to occur in succession along the wire, with each of the doubly coordinated water molecules transferring a proton to its neighbor until a nascent hydroxide ion is formed at the threefold coordinated water site (see Figure 6). The number of intermediate hops is predetermined by the length of the wire at the moment the endpoint water becomes “presolvated” like a hydroxide ion. This phenomenon can be regarded as a new realization of the presolvation concept, first introduced for bulk structural diffusion,53,54 that is particular to low-hydration environments.21 The structural diffusion mechanism proposed here does not require the water to diffuse in order to achieve high hydroxide ion diffusion. This contrasts with vehicular diffusion, which requires mobility of the water molecules. Indeed, the water molecules in system b4 are found to exhibit low diffusivities compared to those in system a4, in which the vehicular diffusion was found to be dominant.

Figure 7. Average diffusion coefficient of hydroxide ions as a function of water density (parameters are presented in Table 1 and Supporting Information). Inset: Hydroxide ion diffusion coefficient versus the hydration level.

the effective water density and value of λ for six different systems. Although the hydroxide ion diffusion constant increases with increasing water density, this trend is not directly correlated with the hydration level. Moreover, we find that all six idealized AEM systems studied using AIMD fall within the three diffusion regimes identified in this work. While we cannot use these water density values to determine a precise threshold for high hydroxide ion diffusion, we find that the water distribution and the hydroxide solvation structures serve as parameters that determine the OH− diffusion mechanisms and the requirements for high hydroxide ion conductivity. Nondiffusive hydroxide ions (i.e., regime I) have a cluster of three or fewer water molecules, possess only a well-defined first solvation shell, no second shell, and a water distribution with well-separated clusters and void regions between them. Vehicular diffusion (i.e., regime II) of the hydroxide ions occurs when the water distribution is nonuniform but is such that the hydroxide ions possess both a first and a second solvation shell, comprising a cluster of at least four water molecules. Combined vehicular and structural diffusion (i.e., regime III) occurs when there is sufficient water for fluctuations in the water distribution to create transient uniform structures in the form of water wires. As the uniqueness of AEMs at low-hydration levels lies in the unusual water distribution, we surmise that a system should be considered within the low-hydration regime only as long as the water is distributed nonuniformly within the AEM. Furthermore, we believe that for systems under low-hydration conditions, it is the nature of this non-uniform water distribution and the corresponding effective density that characterize the system, as opposed to the hydration level customarily used at higher hydration conditions. Compared to bulk solution and hydrated AEMs,21 the hydroxide ion diffusion constants calculated for systems a4 and b4 (i.e., regimes II and III) yield rather high values, indicating the potential for low-hydration AEMs to exhibit high OH− conductivity. As one of the aims of this and our recent work20,21 on simulations of AEM environments is to determine a set of design rules for new AEMs with high hydroxide ion diffusion, the results presented in this work allow us to suggest

5. PRELIMINARY DESIGN RULES AND CONCLUSIONS In the present work, we simulated six different idealized AEM environments under low-hydration conditions (λ = 2, 3, and 4). We found that a common feature among the three systems is the nonuniform water distribution associated with the dearth of water molecules in each idealized simulation cell, resulting in void areas within these cells. These unusual water distributions result in the absence of a second solvation shell for a hydroxide ion or in dissimilar solvation structures for each of the hydroxide ions in each system. We find these unusual water distributions to be the key factor affecting the hydroxide ion diffusion mechanism under low-hydration conditions. In order to support this claim, in Figure 7, we summarize the dependence of the average hydroxide ion diffusion constant on G


Article

Chemistry of Materials conditions likely to achieve high OH− conductivity under lowhydration conditions. (i) The existence of a water molecule in the second solvation shell of the hydroxide oxygen is crucial in achieving high diffusivities. This feature enables either vehicular diffusion, in the case of a nonuniform water distribution, or structural diffusion, in the case of a momentarily uniform water distribution, such as a wire structure. To acquire a second solvation shell, the effective water density should be in the intermediate to high regime (as illustrated in Figure 7). For this purpose, small-diameter pores, a high density of polymer cations, or cations with long hydrophobic tails should be considered as possible routes to achieving relatively highly effective water densities under low-hydration conditions. (ii) For confined systems exhibiting a lamellar structure (mimicked in this work by the use of GBs), we find that the OH− diffusion mechanism correlates with the hydroxide ion location in the cell: hydroxide ions can diffuse freely when located in the center of the cell while diffusion of hydroxide ions located between pairs of cations (the BR) depends sensitively on the cation spacing. This design parameter can restrict OH− diffusion, as structures that promote hydroxide ion motion in the narrow channels cannot be easily achieved. In order to accelerate hydroxide ion diffusion in the BR, we suggest the following: • Water molecule mobility is crucial for the hydroxide ion diffusion in these confined regions, as their presence on both sides of the BR is essential for the hydroxide ion diffusion through these regions. Hence, we predict that increasing the temperature (beyond room temperature) and/ or applying an external electric field should facilitate higher water mobility. • To preclude formation of BRs, additional polymers whose mesoscale morphology is characterized by cylindrical pores of intermediate width rather than lamellae should be sought. (iii) A challenge for AEMs is the ability to promote high diffusion of multiple hydroxide ions simultaneously. In this work, system b4 illustrates how this issue might be addressed. In particular, by restricting the diffusion of hydroxide ions to occur along a single spatial direction, directed transport could be achieved. Looking more closely at the hydroxide oxygen coordinates for system b4 (Figure 4), one can also see a hint of synchronous diffusion for the two hydroxide ions. Hence, designing membranes with a single path direction for increasing hydroxide ion conductivity should be considered. In summary, this work is the first to explore idealized AEM models under low-hydration conditions. Using AIMD simulations, we have been able to provide atomistic insight and a preliminary fundamental understanding of the unique hydroxide ion solvation patterns and diffusion mechanisms in this hitherto unstudied regime. We recognize that nuclear quantum effects, not treated in this study, could affect certain quantitative aspects of the diffusion process,52 and future work employing ab initio path integral methods84 in selected systems will investigate this approach. However, even in the absence of such effects, we believe the results presented in this

study enable us to suggest design protocols for achieving high hydroxide ion conductivity in high-performance AEMFC devices under low-hydration conditions.

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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.chemmater.9b01824. Detailed explanation of the steps required to construct the six systems including the computational method and a summary of the systems parameters; O*O, and NO* RDFs and CNs; summary of hydroxide solvation complexes; diffusion constants for O and O*; and full description of the hydroxide diffusion mechanism for a wider BR (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 (212) 9988471. ORCID

Leslie Vogt-Maranto: 0000-0002-7006-4582 Chulsung Bae: 0000-0002-9026-3319 Dario R. Dekel: 0000-0002-8610-0808 Mark E. Tuckerman: 0000-0003-2194-9955 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation, grant # CHE-1534374. Computational resources were provided by the Computational Center for Nanotechnology Innovation at Rensselaer Polytechnic Institute in Troy, New York.

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REFERENCES

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