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Grotthuss vs Vehicular Transport of Hydroxide in Anion-Exchange Membranes: Insight From Combined Reactive and Nonreactive Molecular Simulations Dengpan Dong, Weiwei Zhang, Adri C.T. van Duin, and Dmitry Bedrov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00004 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 2, 2018
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Grotthuss vs Vehicular Transport of Hydroxide in Anion-Exchange Membranes: Insight from Combined Reactive and Nonreactive Molecular Simulations. Dengpan Dong1, Weiwei Zhang2, Adri C.T. van Duin2, Dmitry Bedrov1 1
Department of Materials Science & Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112, United States 2
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States
Abstract A combined reactive and non-reactive polarizable molecular dynamics simulations were used to probe the transport mechanisms of hydroxide in hydrated anion-exchange membranes (AEMs) comprised of poly(p-phenylene oxide)-functionalized with the quaternary ammonium cationic groups. The direct mapping of membrane morphologies between two models allowed to investigate the contributions of vehicular and Grotthuss mechanisms into hydroxide motion and correlate these mechanisms with the details of local structure. In AEMs with non-blocky polymer structure, where anion transport occurs through narrow (sub-nanometer size) percolating water channels, simulations indicate the importance of the Grotthuss mechanism. In non-reactive simulations, in order to diffuse through bottlenecks in the water channels, the hydroxide anion has to lose part of its hydration structure, therefore creating large kinetic barrier for such events. However, when the Grotthuss mechanism is involved, the hydroxide transport through these bottlenecks can easily occur without loss of anion hydration structure and with a much lower barrier.
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In recent years, significant research interest has been focused on the design of anionexchange membranes (AEM) for fuel cell applications.1,2,3 Compared to fuel cells with protonexchange membranes, the cost of AEM-based cells can be reduced significantly, since no precious metal catalysts, such as platinum, are required for the electrodes. Continuous enhancement in the performance of AEMs, including electrical conductivity, mechanical properties and chemical stability has been demonstrated in recent studies. 4,5,6,7,8 Despite substantial advances in experimental and theoretical exploration of AEMs, the transport mechanism of hydroxide and AEM structure-transport efficiency relationships are barely investigated. Understanding of the mechanism(s) by which OH- diffuses through water channels in AEMs helps to uncover the key correlations between the charge transport efficiency and polymer structure, therefore providing guidance for systematic investigation and design of novel AEMs. A recent study based on multi-state empirical valance bond (MS-EVB) proposed that the contribution of the Grotthuss mechanism to the total diffusivity of OH- is about 20% and the charge transport primarily relies on OH- vehicular motion through continuous overlapping regions of the first hydration shells of cationic groups.3 This mechanism might indeed be operational in AEMs with highly functionalized polymers (in ref.[3] the considered polymers had every repeat unit functionalized with benzyltrimethylammonium cationic group) that represent a bulk phase of the highly hydrated hydrophilic domains in a block copolymer morphology. However, many of the recently developed AEMs are comprised of non-blocky polymers with a relatively low degree of functionalization ranging between 20-60%. It has been demonstrated that these randomly functionalized copolymers are very promising candidates for AEMs with enhanced transport characteristics and low degree of swelling. 9,10 For example, membranes comprised of poly(pphenylene oxide) (PPO) polymer chains functionalized with quaternary ammonium groups
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showed no phase segregation based on the analysis of structure factors from small angle X-ray scattering and transmission electronic microscopy.7,11 These membranes have the advantage of being robust for the synthesis and maintaining enhanced chemical stability at 373 K, the target temperature for AEM operation.8 They also showed a low degree of swelling and yet good conductivity indicating the formation of a network of sub-nanometer wide water channels capable to transport charge. In such confined environments one can expect the Grotthuss-type motion of OH- to be significantly enhanced, sometime becoming even faster than that in bulk water.12,13,14,15
Figure 1. Structure of PPO-polymers with different quaternary ammonium cation functional group investigated in this study.
In this letter, atomistic molecular dynamics (MD) simulations were used to gain molecular scale insight into the charge transport in PPO-based AEMs. A joint MD simulation study employing reactive ReaxFF 16,17 and non-reactive Atomistic Polarizable Potential for Liquids, Electrolytes, and Polymers (APPLE&P) force fields18 has been conducted for two representative PPO-based AEMs (M1 and M2) with the polymer structure as illustrated in Figure 1. The systems were comprised of 16 chains with n=5 which corresponds to the degree of functionalization of 50%. Both membranes have the degree of hydration λ = 𝑁𝐻2𝑂 ⁄𝑁𝑐𝑎𝑡𝑖𝑜𝑛 = 10.
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Simulations using the APPLE&P force field were used to generate long-time MD trajectories to equilibrate the AEM morphologies and to investigate details of the vehicular motion of hydroxide through membrane. Previous studies have demonstrated that simulations with the APPLE&P can accurately reproduced the dynamics of different species in alkylammonium aqueous solutions. 19 Subsequently, morphologies equilibrated using the APPLE&P force field were mapped to the ReaxFF representation, which allows empirical representation of chemical reactions and has been used to investigate the chemical stability of functionalized PPO-based polymers. 20 More importantly, ReaxFF simulations can model the Grotthuss type motion by reproducing the Eigen-Zundel-Eigen hopping process.16, 21 Further details on force field, simulation and mapping protocols can be found in the Supplementary Information (SI). Figure 2A illustrates the morphology of AEM membrane equilibrated using the APPLE&P force field. The snapshot indicates water channels defined by isosurfaces where the density of water is equal 50% of bulk water density. The cross-sectional dimensions of water channels can be estimated by sampling the distribution of sizes of the largest test spheres that can fit inside the water channel at various locations. The details of these calculations can be found in the SI while Figure 2B shows the resulting distribution for the M1 membrane indicating that majority of the channels have sub-nanometer cross-sectional dimensions. Moreover, based on the anion-water radial distribution functions (shown in Figure S4 in SI) the regions in water channels with crosssectional diameter less than 4.5Å can be defined as “bottlenecks” that are too narrow for hydroxide anion to diffuse with its complete hydration structure. (The 4.5 Å corresponds to twice the closest approach distance in the Owater - Ohydroxide radial distribution function). Figure 2C illustrates the distribution of such bottlenecks in the M1 membrane.
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Figure 2. A) A snapshot of hydrated M1 membrane with water channels illustrated by isosurfaces corresponding to 50% of bulk water density. B) The distribution of water channel width. C) Blue spheres illustrate the locations of the “bottlenecks” inside water channels (see text and SI for definition and discussion) D) Illustration of correspondence of membrane morphologies obtained from the APPLE&P simulation and mapped to ReaxFF. The red chain shows a polymer backbone for the selected chain in the APPLE&P simulation, while the green chain shows the same chain after mapping and relaxation in ReaxFF simulation.
This equilibrated morphology was subsequently mapped to ReaxFF representation. The hydrophobic regions (non-hydrated regions) of the formed membranes should be glassy at room temperature and hence, while some local rearrangement of chain segments is possible after models are switched, the overall distribution of water channels should remain the same. To confirm this, we have calculated the displacement of polymer backbone atoms between original coordinates
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given by the APPLE&P model and those obtained after relaxation simulation using ReaxFF. The averaged displacements of polymer backbone atoms were 3.4 Å and 2.9 Å for M1 and M2, respectively. A direct comparison of a selected polymer chain backbone in the M1 membrane obtained from simulations using the two models is shown in Figure 2D, indicating small local shifting in location of polymer segments while the overall chain conformation is preserved. Similarly, Figure 2B confirms that both models predict the same distribution of water channel sizes.
Table 1. Diffusion coefficients of OH- and H2O in investigated AEMs at 298K. Values in parenthesis are from ReaxFF simulations with the Grotthuss mechanism turned off. M1
M2
ReaxFF
APPLE&P
ReaxFF
APPLE&P
𝑫𝑶𝑯− (Å2/ps)
0.236(0.031)
0.0020
0.162
0.00079
𝑫𝑯𝟐𝑶 (Å2/ps)
0.040(0.068)
0.0083
0.033
0.00420
𝑫𝑯𝟐𝑶 /𝑫𝑶𝑯−
0.17(2.2)
4.1
0.20
5.3
The diffusion coefficients of OH- and H2O calculated from MSDs are shown in Table 1. As expected the mobility of both components is orders of magnitude lower than in bulk water (see SI information for MSDs and diffusion coefficients in dilute aqueous solution). Both models predict that diffusion coefficients in M1 are faster than in M2. However, in non-reactive simulations the diffusion is two orders of magnitude slower than what predicted by ReaxFF and the ratio of water and hydroxide diffusions are very different. In APPLE&P simulations, the 𝑫𝑶𝑯− is lower than 𝑫𝑯𝟐𝑶 by factor of 4-5, while in ReaxFF simulations there is an opposite trend with the diffusivity of H2O being only around 20% of OH-, indicating remarkably enhanced dynamics of OH- when introducing Grotthuss mechanism. Note that when the Grotthuss mechanism is turned
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off in ReaxFF simulations (numbers in parenthesis) the ratio of diffusion coefficients becomes consistent with the predictions from non-reactive simulations. The observed differences in the ratios of diffusion coefficient clearly indicate that the Grotthuss hopping must be the defining mechanism of hydroxide transport in investigated membranes. Following the method to decompose total MSD into vehicular and Grotthuss contributions 3 the significance of the latter in M1 and M2 is further confirmed from the analysis of ReaxFF simulations. The individual contributions and cross-correlations to each mechanism and their ratios are shown in Figures S2-S3. Contrary to what was observed in bulk water (shown in Figure S1), where the Grotthuss-vehicular correlation was positive (i.e., contributing to overall MSD), in the investigated membranes this correlation is negative, which is consistent with Chen et al. observations.3 The observation of such reverse trend reveals the role of confined environments of considered water channels and the underlying OH- transport mechanism. The contribution from the vehicular MSD to the total hydroxide diffusivity is less than 3%, making the Grotthuss to be the dominant mechanism in the transport of hydroxide in these water channels. This is consistent both with experimental and simulation studies that showed that proton hopping is dramatically enhanced in confined environments, leading to an order of magnitude increase in the hopping rate inside sub-nanometer wide channels.14,22,23,24 In addition to MSDs we also characterized the residence time of hydroxide in the first hydration shell of cationic nitrogen. The method to calculate the residence time is given in SI. The auto-correlation function (ACF) of OH- within the first hydration shell (defined as 6.1 Å from the N+ atom) and the corresponding fits with the Kohlrausch-Williams-Watts (KWW) function are shown in Figure 3. In fully-reactive ReaxFF simulations, the N+-O- residence time in M1 membrane is around 19.0 ps. When the reactivity is turned off, the decay in the N+-O- ACF shifts to longer times, approaching the ACF given by simulations with non-reactive APPLE&P model.
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The residence time calculated from non-reactive ReaxFF simulation is 350.7 ps, while for the APPLE&P model is 4.1 ns. In the non-reactive simulations, the N+-O- correlation is significantly enhanced due to strong Coulombic interaction between ions allowing the OH- to be trapped in the cationic hydration shell. However, in ReaxFF simulation, the migration of hydroxide from cationic hydration shell to the outer region can be easily fulfilled through one proton hop event. Therefore, in addition to switching the underlying transport mechanism of OH -, the introduction of the Grotthuss mechanism also redefines the cation-anion correlation in AEM.
Figure 3. Residence time auto-correlation functions of N+-O- in M1 (solid lines) and the corresponding KWW fits (dashed lines).
To further understand the role of the Grotthuss mechanism on hydroxide transport, we examined the changes in hydroxide environment as it moves along water channels. From simulations with non-reactive APPLE&P model, we found that the transport of OH- through bottlenecks in water channels requires a partial destruction of the anion immediate hydration shell, which is the rate determining step defining the hydroxide overall mobility. Therefore, a comparison between ReaxFF and APPLE&P models for the OH- transporting through the same bottlenecks should provide the most straightforward evidence for the role of the Grotthuss mechanism in
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facilitating diffusion through AEMs. The transition of hydroxide through the same region in the hydrated AEM and tracked from simulations using APPLE&P and ReaxFF models is illustrated in Figure 4. The timescale required for OH- to diffuse through the same region with a bottleneck is several orders of magnitude longer in simulations with APPLE&P than with ReaxFF force field. In this particular example, the simulation time needed for transition through the bottleneck was 40.0 ps in ReaxFF, compared to 7.0 ns in APPLE&P simulation. In ReaxFF, the diffusion through the bottleneck relies primarily on proton hopping. As a result, the originally coordinating waters remain in the original location after OH- hopped into the next water-rich domain. During this transition through the bottleneck the total number of hydrating waters does not change, i.e. it fluctuates around four water molecules as can be seen from Figure 4 where the number of OHcoordinating waters is monitored together with the anion displacement. In non-reactive APPLE&P simulation, however, the diffusion through the same bottleneck requires a loss of one or two coordinating waters (see Figure 4) to complete the transition. Additionally, part of the original coordination structure is moving with the hydroxide through the bottleneck. More examples of OH- transition events showing the same trend are illustrated in Figure S6 in SI.
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Figure 4. Diffusion of OH- through pocket of water channel. The green sphere corresponds to the O in OH-, with red spheres indicating the coordinated water oxygen at the beginning. The corresponding in displacement from original coordinate is shown in bottom-right panel. Top three panels show snapshots from ReaxFF simulations, with the middle three panels illustrating snapshots from APPLE&P simulations. The tracking of displacement from original point and coordination number of water within first hydration shell is shown in the bottom panels.
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In summary, for investigated non-blocky AEMs, in which the sub-nanometer wide channels of the water-network are responsible for the charge transport, the hydroxide mobility is strongly tempered by the presence of narrow bottlenecks. To transport through these bottlenecks using only the vehicular mechanism requires for hydroxide anion to partially dehydrate which is thermodynamically unfavorable and therefore leading to larger activation energy for such process. On the other hand, Grotthuss hopping provides an efficient mechanism for hydroxide to transition from one side of the bottleneck to another without any loss of its hydration structure and hence with a very small activation barrier. The balance between the size distribution of water-rich domains and bottlenecks connecting them is the key factor that should define the relative importance of the vehicular and Grotthuss mechanisms for OH- transport in such membranes.
ASSOCIATED CONTENT Supporting Information. Supporting Information is available free of charge on the ACS Publications website as pdf file providing simulation/analysis details and additional data (force field description, simulation protocols, analysis of water channel size distributions, mean squared displacements, illustration of mechanisms of hydroxide transfer through water channel bottlenecks). AUTHOR INFORMATION Corresponding Author. E-mail:
[email protected] NOTES The authors declare no competing financial interests. ACKNOWLEDGEMENT Authors gratefully acknowledge the support from the project sponsored by the Army Research Laboratory under Cooperative Agreement Number W911NF-12-2-0023. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of ARL or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. We also would like to acknowledge the Center of High Performance Computing at the University of Utah for generous allocation of computing resources and technical support.
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