Hydroxide Degradation Pathways for Imidazolium Cations: A DFT Study

Article pubs.acs.org/JPCC

Hydroxide Degradation Pathways for Imidazolium Cations: A DFT Study Hai Long and Bryan Pivovar* National Renewable Energy Laboratory, MS ESIF302, 15013 Denver West Parkway, Golden, Colorado 80401, United States ABSTRACT: Imidazolium cations are promising candidates as covalently tetherable cations for application in anion exchange membranes. They have generated specific interest in alkaline membrane fuel cell applications where ammonium-based cations have been the most commonly applied but have been found to be susceptible to hydroxide attack. In the search for high stability cations, a detailed understanding of the degradation pathways and reaction barriers is required. In this work, we investigate imidazolium and benzimidazolium cations in the presence of hydroxide using density functional theory calculations for their potential in alkaline membrane fuel cells. The dominant degradation pathway for these cations is predicted to be the nucleophilic addition−elimination pathway at the C-2 atom position on the imidazolium ring. Steric interferences, introduced by substitutions at the C-2, C-4, and C-5 atom positions, were investigated and found to have a significant, positive impact on calculated degradation energy barriers. Benzimidazolium cations, with their larger conjugated systems, are predicted to degrade much faster than their imidazolium counterparts. The reported results provide important insight into designing stable cations for anion exchange membranes. Some of the molecules studied have significantly increased degradation energy barriers suggesting that they could possess significantly improved (several orders of magnitude) durability compared to traditional cations and potentially enable new applications. SN2 reaction at 160 °C and 1 atm calculated by the density functional theory (DFT).10 In order to search for cations with even higher stability under alkaline conditions, imidazolium and benzimidazolium (Table 1) have been suggested to be promising candidates.13−20 The nitrogen atoms in (benz-)imidazolium derivatives are in the sp2 hybridization and, thus, may take different degradation pathways and demonstrate greatly altered degradation rates when compared with substituted ammonium cations. Experimental evidence has indicated that (benz-)imidazolium may degrade by the nucleophilic addition−elimination pathway.13,14 In this pathway, the OH− first attacks at the C-2 position, and then one of the C−N bonds is broken and the ring is opened. However, the details of this degradation mechanism and associated energy barriers have not been presented in detail. Additionally, specific substitutions can be made at the imidazolium ring, and how such substitutions impact TSs and degradation barriers also requires further study. To address these issues, we extended our computational research to study (benz-)imidazolium cations and used DFT calculations to investigate the TS barriers of the degradation pathways for these cations. We present our findings for imidazolium and benzimidazolium cations with select substitutions and compare the relative, calculated stabilities of these cations to BTMA+.

1. INTRODUCTION The alkaline membrane fuel cell (AMFC) is the alkaline counterpart of the more commonly reported proton exchange membrane fuel cell (PEMFC).1 The major difference is that, in AMFC, the ionic species transported through the membrane are hydroxide ions (OH−) instead of protons (H+). The primary driver toward AMFCs is the enablement of cheaper, nonprecious catalysis, as materials stability is greatly improved under basic conditions for catalytically active materials.2 In order to allow OH− to transport across the membrane in AMFCs, cations, most commonly substituted ammoniums, are attached to the polymer backbones.3−6 However, OH− can react irreversibly with these cations causing the conductivity of the anion exchange membrane (AEM) to degrade over time. The stability of AEMs in the presence of OH− remains a major challenge for the AMFCs. In our previous studies, we have investigated the stability of substituted ammonium cations under attack of OH− by both experimental and computational methods.7−12 In these ammonium cation studies, nitrogen atoms are in the sp3 hybridization. Three degradation pathways, ylide, Hofmann elimination, and SN2, have been identified and investigated for substituted ammonium cations.7,10 The Hofmann elimination pathway has typically been found to be the most vulnerable pathway for degradation of alkyl trimethylammonium (TMA+) cations.10 For ammonium ions that lack β-hydrogen atoms and are therefore immune to Hofmann elimination, the SN2 pathway is the major degradation pathway. For reference to the other numbers reported here, benzyltrimethylammonium (BTMA+), the most commonly employed cation in AEMs, has a transition state (TS) barrier of 23.3 kcal/mol for the benzyl © 2014 American Chemical Society

Received: October 19, 2013 Revised: April 16, 2014 Published: April 18, 2014 9880

dx.doi.org/10.1021/jp501362y | J. Phys. Chem. C 2014, 118, 9880−9888

The Journal of Physical Chemistry C

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2. METHOD The detailed method used for DFT calculations is described in our previous report.10 In short, we use Gaussian 09 (G09)21 to optimize the reactants and TS structures by B3LYP22 method, 6-311++G(2d,p) basis set, and polarizable continuum solvation model (PCM). The free energies at 80 °C and 1 atm for the reactants and TS were calculated by M0623 and SMD24 solvation model using the same basis set based on the optimized structure. The reaction free energy barrier ΔG⧧ was then obtained by comparing the total free energies of the ground states of reactants (cation + OH−) with the free energy of the TS state.10 During the calculations, no symmetry is used. The cations investigated are presented in Table 1, and the calculation results are summarized in Table 2.

Table 1. Cations Investigated in This Work

3. RESULTS 3.1. Degradation Pathways for 1,3-Dimethyl Imidazolium. We first present results investigating the simplest imidazolium cation, 1,3-dimethyl Imidazolium (DMIm+), as a basis for the mechanisms probed for degradation and as a comparison to other calculated energy barriers. We identified four potential degradation pathways for DMIm+ (eqs 1−4). OH− can attack the N-1/N-3 methyl group (eq 1) by SN2 mechanism; C-4/C-5/C-2 (eq 2) by the nucleophilic addition− elimination mechanism; N-1/N-3 methyl hydrogen atoms (eq 3) by the ylide pathway; and H-4/H-5/H-2 (eq 4) by the ylidene pathway. SN2 pathway at C-1N/C-3N:

nucleophilic addition−elimination at C-2:

ylide pathway at H-1N/H-3N:

ylidene pathway at H-2:

Among these four pathways, the nucleophilic addition− elimination pathway is found to be the main degradation pathway for DMIm+.13 In this section, we will focus on this pathway, and the possibility for cations to degrade by other pathways will be discussed in detail in section 4.3. The reference zero energy state for energies reported in this section is DMIm+ + OH−. In the nucleophilic addition−elimination pathway, OH− attacks the sp2 carbon atoms of the five-membered ring. There are two ways of attacking, either at the C-2 or C-4 position (the C-5 position is symmetric with the C-4 position for this cation). Because C-2 is between two positively charged nitrogen atoms (Mulliken charge, +0.11), the charge of C-2 (Mulliken

charge, −0.14) is more positive than C-4’s (Mulliken charge, −0.25). This makes attacking the C-2 atom much easier than C-4. For C-4 attack, the TS structure is presented in Figure 1A. The distance between O−C is as close as 1.71 Å. ΔG⧧ for this TS is 32.8 kcal/mol. For C-2 attack, the TS structure is shown 9881



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Table 2. Calculated ΔG⧧ Values (kcal/mol) for Cations at 80° C and 1 atma nucleophilic addition−elimination at C-2 cations

TS1

Imidazolium Derivatives DMIm+ 16.4 TMIm+ 17.1 BDMIm+ 19.8 PDMIm+ 21.9 MPDMIm+ 22.4 DMPDMIm+ 35.9 PMIm+ 20.1 DMPTMIm+ 30.9 DMOPTMIm+ 34.7 Benzimidazolium Derivatives DMBIm+ 9.2 PDMBIm+ 14.7 MPDMBIm+ 16.5 DMPDMBIm+ 26.5 a

at C-4/C-5

at C-1N/C-3N

IS1

IS2

trans-TS2

cis-TS2

TS1

S N2

4.7 7.5 9.5 10.8 14.2 26.4 11.9 25.7 −

2.3 − − − − − − − −

19.2 21.3 23.4 22.6 25.7 39.7 27.5 43.7 41.9

20.5 21.4 24.6 20.4 22.5 35.4 28.5 39.2 36.0

32.8 32.9 35.3 31.1 32.2 38.0 41.2 41.6 −

37.7 36.7 39.4 37.0 38.2 42.2 41.3 40.1 −

−1.9 0.1 5.1 13.2

− − − −

7.9 10.9 14.7 25.5

11.3 14.0 17.7 25.1

− − − −

37.0 37.3 37.1 37.4

Symbol “−” means that we did not calculate this number. Values in bold show the rate-limiting step barriers for the degradation.

Figure 2. (A) Illustration of direct ring-opening mechanism and (B) its TS structure for DMIm+.

DFT calculation predicted that this proton would react with OH− spontaneously without any TS barrier. After the hydroxyl proton is abstracted, another intermediate state (named as IS2, Figure 3A) is obtained. Its ΔG is 2.3 kcal/mol and is 2.4 kcal/ mol more stable than IS1. It is possible that if we added explicit water molecules, a TS barrier could be found. However, since the proton transfer process is energetically favorable, the barrier

Figure 1. Structures for (A) C-4 attack TS, (B) C-2 attack TS, and (C) IS1 formed after C-2 attack for DMIm+. Unit of distance in this work is in angstroms (Å). Color scheme: oxygen in red; carbon in cyan; hydrogen in white; and nitrogen in blue. Images were created using VMD.25

in Figure 1B. The distance between O−C is 2.06 Å, 0.35 Å larger than the case of C-4 attack. The ΔG⧧ for this reaction is 16.4 kcal/mol. Since ΔG⧧ of C-2 attack is much lower than that of C-4 attack, we focus on this pathway, as it will be highly favored, a finding supported by experimental studies.13 After OH− attacks the C-2 atom, an intermediate state (named as IS1, Figure 1C) is formed with a ΔG of 4.7 kcal/mol. The next step of degradation will open the ring as shown in eq 2b. We first investigated a direct mechanism in which one of the C−N bonds is broken and the hydroxyl proton is transferred to the nitrogen atom in a single step (Figure 2A). The TS identified by DFT calculation is shown in Figure 2B. ΔG⧧ for this reaction is 41.6 kcal/mol, which is an exceptionally high barrier. We also investigated a multistep reaction. Because the degradation reactions occur in a high pH environment, we investigated abstraction of the hydroxyl proton of IS1. Figure 3. Structures of (A) IS2, (B) trans-TS2, and cis-TS2 for DMIm+. 9882



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For methyl substitution at C-2, or 1,2,3-trimethyl imidazolium (TMIm+), the attack of OH− at the C-2 position is slightly hindered and ΔG⧧ of TS1 is increased by 0.7 kcal/mol compared to DMIm+. For the trans-TS2 (Figure 5A), ΔG⧧ is

is expected to be low. Thus, we think that this proton transfer barrier is not the rate-limiting step of the overall reaction and identifying a specific TS would not be of use in our degradation analysis. Because IS2 has a charge of −1 and the ring-opening product is neutral, another reactant is needed to balance charge. Because an abundance of water is available, it was investigated as the most likely candidate. An alternative ring-opening pathway involving IS2 and water results in the breaking of a C−N bond to form one amine and one OH− (eq 5b).

Thus, in eq 5a and eq 5b, OH− functions as a catalyst in the overall reaction. There are two possible TS structures for reaction 5b. The TS structure presented in Figure 3B, referred to as trans-TS2, has the two methyl groups on different sides of the five-membered ring plane. An alternative TS structure is cisTS2 (Figure 3C), in which both methyl groups are on the same side of the five-membered ring plane. The barrier for the transTS2 structure is only 19.2 kcal/mol, much lower than the ΔG⧧ calculated for the single step, direct ring-opening reaction. The barrier for the cis-TS2 structure is 20.5 kcal/mol. The ΔG⧧ of trans-TS2 is slightly smaller due to less steric interference between methyl groups and a hydrogen bond formed between water and the O atom. Since trans-TS2 has a smaller free energy than cis-TS2, trans-TS2 is the main TS structure for reaction 5b. In summary, the overall nucleophilic addition−elimination reaction catalyzed by OH− for DMIm+ is shown in eq 2a, eq 5a, and eq 5b. The free-energy diagram is shown in Figure 4. The highest barrier for the entire process is 19.2 kcal/mol, for the trans-TS2, and this step is predicted to be the rate-limiting step for the degradation.

Figure 5. Structures of (A) trans-TS2 and (B) cis-TS2 for TMIm+.

21.3 kcal/mol or an increase of 2.1 kcal/mol. For the cis-TS2 (Figure 5B), ΔG⧧ is 21.4 kcal/mol or an increase of 0.9 kcal/ mol. The barrier of trans-TS2 increased more because of the steric interference introduced between the C-2 methyl and a neighboring N-methyl group, which has a closest calculated distance of 2.49 Å. TS2 remains the rate-limiting step, but the barriers of the cis-TS2 and trans-TS2 are nearly identical. For some larger substitution groups at the C-2 position, cis-TS2 could become more stable than the trans-TS2 owing to the steric interferences between the C-2 substitution group and the neighboring N-methyl group in the trans-TS2 configuration. For benzyl substitution (2-benyl-1,3-dimethyl imidazolium or BDMIm+) at the C-2 position, TS1’s barrier increases 2.7 kcal/ mol compared to TMIm+, and trans-TS2 shows a 2.1 kcal/mol increase. TS2 is still the rate-limiting step. ΔG⧧ of the cis-TS2 is 1.2 kcal/mol higher than that of the trans-TS2. Compared with benzyl substitution, the benzene ring in the phenyl substitution (2-phenyl-1,3-dimethyl imidazolium or PDMIm+) is closer to the C-2 atom. Thus, the enhancement of the TS1 barrier for the phenyl substitution is larger due to increased steric hindrance. The ΔG⧧ for TS1 (Figure 6A) is calculated to be 21.9 kcal/mol, or 4.8 kcal/mol larger than that of TMIm+ TS1. Also because the benzene ring is closer to the C-2 atom, ΔG⧧ of trans-TS2 (Figure 6B) is 22.6 kcal/mol, a 1.3 kcal/mol increase compared to that of TMIm+. In this case, however, the cis-TS2 (Figure 6C) has a ΔG⧧ of 20.4 kcal/mol, 2.2 kcal/mol less than the ΔG⧧ of trans-TS2. This makes cisTS2 the dominant TS for the ring-opening step (eq 5b). 3.3. Substitutions at the Phenyl Group of PDMIm+. To make the C-2 substitution even bulkier to result in further enhancement of reaction barriers, Holdcroft et al. proposed to make substitutions at C-2′ and C-6′ of the phenyl ring.14 Parts A−C of Figure 7 show the dihedral angles of N1−N3−C2′− C6′ in PDMIm+, 2-(2′-methyl)-phenyl-1,3-dimethyl imidazolium (MPDMIm+), and 2-(2′,6′-dimethyl)-phenyl-1,3-dimethyl imidazolium (DMPDMIm+) in their ground states, respectively. If the phenyl ring and the imidazole ring are in the same plane (dihedral angle = 0°), they can form a much larger conjugated system, resulting in a lower energy. However, due to steric interference between H-2′/H-6′ and N-1/N-3 methyl groups, PDMIm+ can only attain a calculated dihedral angle of 56°. In both MPDMIm+ and DMPDMIm+, the steric interferences between C-2′/C-6′ methyls and N-1/N-3 methyls are more significant, and thus, the calculated dihedral angle is even larger (82°). In this configuration, the C-2′/C-6′ methyls are located

Figure 4. Free-energy diagram for the nucleophilic addition− elimination pathway for DMIm+. Unit: kcal/mol.

3.2. C-2 Substitutions of DMIm+. In the attempt to probe for cations of DMIm+ derivatives with higher degradation barriers, a logical approach is to first investigate substitutions at the C-2 position as this has been identified as the most vulnerable to hydroxide attack.13 Substitution at the C-2 position will make the TS1 barrier higher. However, this may also influence the barrier of TS2, the rate-limiting step for the unsubstituted DMIm+. We present here how substitution at the C-2 position impacts the calculated barriers of both TS1 and TS2. We considered three substitution groups: methyl, benzyl, and phenyl. The reference zero energy point for all of the following cations is the total free energy of cation + OH−. 9883



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Figure 8. Structure of cis-TS2 for MPDMIm+.

Figure 6. Structures of (A) TS1, (B) trans-TS2, and (C) cis-TS2 for PDMIm+.

Figure 9. Structure of cis-TS2 for DMPDMIm+.

singly methyl-substituted MPDMIm+ and doubly methylsubstituted DMPDMIm+ is particularly dramatic. Whereas the singly methyl-substituted MPDMIm+ offers rather modest increases in energy barriers, the doubly methyl-substituted DMPDMIm+ significantly inhibits OH− attack vulnerability. Through steric interference created by the C-2 substitutions, we have found that the reaction barrier can be increased significantly. Steric interference can manifest itself in different ways. The most direct way is through the direct inhibition of OH− attack, by physically blocking the preferred trajectory. Indirect steric interference occurs when conformational states of the reaction process are inhibited due to rotational freedom within the cation, such as interactions between the C-2 substitution groups and the neighboring N-methyls in transTS2 structures. 3.4. Methyl Substitutions at C-4 and C-5 of DMIm+. We also investigated methyl substitutions at C-4/C-5 positions, which may also have a positive effect on stability through bonding or steric effects. Another advantage of these substitutions is that H atoms at the C-4/C-5 positions are susceptible to hydrogen abstraction and ylidene formation.26 By substituting them into methyls, potentially important degradation reactions involving ylidene (similar to eq 4) are avoided. First, we investigated 1,2,3,4,5-pentamethyl imidazolium (PMIm+). The TS1 ΔG⧧ of this cation is 20.1 kcal/mol, 3.0 kcal/mol larger than that of TMIm+. The trans-TS2 (Figure 10) is the dominant TS2 structure for the ring-opening step, and its ΔG⧧ is 27.5 kcal/mol, or 6.2 kcal/mol larger than that of TMIm+. These data suggest that C-4/C-5 substitutions have a positive impact on degradation barrier. We also investigated methyl substitutions at the C-4/C-5 positions of DMPDMIm+. This cation, 2-(2′,6′-dimethyl)phenyl-1,3,4,5-tetramethyl imidazolium (DMPTMIm+), shows

Figure 7. Structures of (A) PDMIm+, (B) MPDMIm+, and (C) DMPDMIm+. The dihedral angle N1−N3−C2′−C6′ is shown as a red dotted line.

directly above/below the C-2 atom and serve as a barrier inhibiting OH− attack. For the singly methyl-substituted MPDMIm+, the barrier of TS1 is 22.4 kcal/mol, only 0.5 kcal/mol larger than that of PDMIm+. This is because the OH− can attack the C-2 atom from the side without methyl on it. Its cis-TS2 (Figure 8) ΔG⧧ is 2.1 kcal/mol larger than that of PDMIm+ due to the steric interference between the C-2′ methyl and N-methyl. Its transTS2 ΔG⧧ is 3.1 kcal/mol larger than that of PDMIm+. For the doubly methyl-substituted DMPDMIm+, both TS1 and TS2 barriers increase significantly over PDMIm+. ΔG⧧ of TS1 is 35.9 kcal/mol, an enhancement of 14.0 kcal/mol as the C-2 atom is shielded from OH− attack on both sides. ΔG⧧ of trans-TS2 is 39.7 kcal/mol and ΔG⧧ of cis-TS2 (Figure 9) is 35.4 kcal/mol, a 15.0 kcal/mol enhancement. This is due to the steric interference between C-2′/C-6′ methyls and N-1/N-3 methyls. TS1 is the rate-limiting step for the overall nucleophilic addition−elimination reaction, and this degradation barrier is 16.7 kcal/mol larger than the DMIm+’s, a major increase in calculated durability. The contrast between the 9884



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of magnitude improvements in hydroxide stability compared to other cations employed to date. In order to explore the influence of increased electron donating substituents at the phenyl ring, we also investigated methoxy substitutions at C-2′ and C-6′. This cation, 2-(2′,6′dimethoxy)phenyl-1,3,4,5-tetramethyl imidazolium (DMOPTMIm+), has a TS1 ΔG⧧ of 34.7 kcal/mol, or 3.8 kcal/mol more than that of DMPTMIm+. The larger TS1 barrier may result from the stronger charge−charge repulsion between the oxygen atoms of the methoxy group and OH−. Their Mulliken charges are −0.53 and −1.28, respectively. The barrier for the ratelimiting step, that is, the cis-TS2 barrier, however, is only 36.0 kcal/mol, or 3.2 kcal/mol smaller than that of DMPTMIm+ resulting in a predicted degradation energy barrier where the increased electron donating effects of the methoxy groups are outweighed by steric factors. 3.5. Benzimidazolium and Its Derivatives. The use of benzimidazolium in some ways is an extension of the C-4/C-5 substitution study, although it also imparts greater conjugation with the imidazolium ring. Experimental measurements have shown that benzimidazolium has limited stability.19 We have modeled benzimidazolium and its derivatives as a comparison data set. For 1,3-dimethyl benzimidazolium (DMBIm+), ΔG⧧ of TS1 is only 9.2 kcal/mol, 7.2 kcal/mol smaller than that of DMIm+. This suggests an exceptionally poor stability and is attributed to the more positively charged C-2 atom in DMBIm+. In DMBIm+, Mulliken charges on N-1/N-3 are +0.17, and the charge on C-2 is +0.13. But in DMIm+, they are +0.20 and −0.13, respectively. The larger conjugated system in DMBIm+ distributes the positive charge more evenly. This results in more positive charge on C-2 and makes OH− attack more favorable. The IS1 is also more stable, with a ΔG of −1.9 kcal/mol. The TS2 structures of DMBIm+ are also more stable than their DMIm+ counterparts. ΔG⧧ of trans-TS2 (Figure 12) is 7.9

Figure 10. Structure of trans-TS2 for PMIm+.

further improvements in calculated degradation barrier. Its TS1 (Figure 11A) ΔG⧧ is 30.9 kcal/mol, or 5.0 kcal/mol less than

Figure 11. Structures of (A) TS1 and (B) cis-TS2 for DMPTMIm+.

that of DMPDMIm+. The explanation is that due to the stronger steric interference inside DMPTMIm+, the energy of the ground state has a larger enhancement than the trans-TS2 structure of DMPDMIm+. This results in a smaller TS barrier (shown schematically in Scheme 1). A similar result had been Scheme 1. Relationship between Ground State and Transition State Energiesa

Figure 12. Structure of trans-TS2 for DMBIm+.

kcal/mol and of cis-TS2 is 11.3 kcal/mol, while they are 19.2 and 20.5 kcal/mol, respectively, in DMIm+. The TS2 structures of DMBIm+ are again stabilized by the larger conjugated system on the benzene ring, where the lone pairs of N-1 and N-3 can participate in the conjugated system. Because of the stronger conjugation in TS2 of DMBIm+, the dihedral angle of C8−C9− N3−C3N in trans-TS2 is 148° (Figure 13A), closer to a planar shape, while the dihedral angle of C5−C4−N3−C3N in DMIm+ is 135° (Figure 13B). This results in the N3-methyl being further from the C-2 atom in DMBIm+ than DMIm+ and a more stable trans-TS2 structure. ΔG⧧ of trans-TS2 is 3.4 kcal/ mol smaller than that of cis-TS2 in DMBIm+, a larger difference than in DMIm+ where it is 1.3 kcal/mol. For DMBIm+ with C-2 substitutions, we can still observe the effect of the greater conjugation. For both TS1 and TS2, ΔG⧧ are smaller than those of the DMIm+ counterparts. In addition,

a

Diagram shows that when the ground state structure has a larger energy enhancement than the TS structure, a smaller ΔG⧧ can be observed.

observed in our pervious work when comparing the degradation barriers of isobutylTMA+ and n-butylTMA+.10 The cis-TS2 (Figure 11B) has a barrier of 39.2 kcal/mol due to steric interference between substituent groups. This is the highest rate-limiting degradation energy barrier that we have calculated and suggests this cation could exhibit several orders 9885



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Because of this, the data presented in this work is based on the M06/SMD method. From our earlier work in the area, we tend to focus on these results as a qualitative tool of most relevance for comparing relative degradation barriers. For ammonium cations, we have found that for barriers of SN2 and Hofmann elimination pathways, data obtained by B3LYP/PCM were 6−7 kcal/mol smaller than the experimental data and data by M06/SMD were 2−4 kcal/mol larger than the experimental data.10 However, M06/SMD results were less consistent with the experimental data, which prompted us to use B3LYP/PCM instead. However, in this study of imidazolium reactions, M06/ SMD is better than B3LYP/PCM in both aspects. Clearly, this implies that the current solvation model is far from optimal and deviation from experimental data might be dramatically different in different compounds or different reactions. It also highlights the need for verification with experimental data when evaluating the results of different DFT calculations. These calculations may best be viewed in terms of guides to specific cation strategies on a relative basis, of highest value when large differences in calculated barriers are obtained (such as that for the substituted imidazoliums reported here). We have tried to optimize structures using M06/SMD directly but found that some TS structures were not converging during the geometry optimization process. We also tried, by adding explicit water molecules, an approach that we found resulted in improved agreement between modeling results and experimental findings.7 However, this approach was more difficult/complex to apply to larger cation systems such as those studied here and again geometry optimization had the convergence issue. Therefore, these methods have not been used in this work. 4.2. Benzimidazolium vs Imidazolium vs BenzylTMA+. It is clear that benzimidazolium derivatives are less stable than their imidazolium counterparts (Tables 2 and 3). In large part, this has been attributed to benzimidazolium having a larger conjugated system than imidazolium. During the first step of the nucleophilic addition−elimination reaction, OH− attacks the C-2 atom. In benzimidazolium, a larger conjugated system makes the positive charge more evenly distributed around the cations. This makes the C-2 atom more positive and easier to be attacked by OH−. During the second step of the nucleophilic addition−elimination reaction, the five-membered ring is opened. The remaining benzene ring in the degraded benzimidazolium can stabilize the TS structures by conjugation and thus makes the second step also easier. Those two factors make the imidazolium a better candidate than the benzimidazolium. BTMA+ is a cation that has been widely used in AEM applications. Varcoe et al. summarized the experimental data of

Figure 13. (A) Dihedral angle of C8−C9−N3−C3N in trans-TS2 of DMBIm+ and (B) dihedral angle of C5−C4−N3−C3N in trans-TS2 of DMIm+.

trans-TS2 is more stable than the cis-TS2 in the phenyl substitution, and (2′-methyl)phenyl substitution, while cis-TS2 is more stable in their DMIm+ counterparts. Only in the (2′,6′methyl)phenyl substitution case, larger steric interference between C-2′/C-6′ methyls and N-methyl make cis-TS2 (ΔG⧧ = 25.1 kcal/mol) (Figure 14) slightly more stable than trans-TS2 (ΔG⧧ = 25.5 kcal/mol). For all benzimidazolium cations investigated in this work, TS1 is always the rate-limiting step for degradation.

Figure 14. Structure of cis-TS2 for DMPDMBIm+.

4. DISCUSSION 4.1. Comparisons with Experimental Data. Table 3 presents ΔG⧧ obtained from experimental data compared to our theoretical results from the B3LYP/PCM solvation model as well as the M06/SMD solvation model with the same basis set 6-311++G(2d,p) based on the same optimized structures. The H-2 ylidene reaction is eq 4 for DMIm+ and a similar reaction for DMBIm+. ΔG⧧ values from the B3LYP/PCM solvation model are 8−20 kcal/mol smaller than the experimental data, while the values from the M06/SMD solvation model are 6−10 kcal/mol smaller. Both methods result in poor underestimation of TS barriers on an absolute energy barrier basis, but data from M06/SMD is better and more consistent with the experimental data on a relative basis.

Table 3. Comparison of Computational Results and Experimental Measurementsa ΔG⧧ (kcal/mol) DMIm+

DMBIm+ PDMBIm+

type of reacn

T (°C)

exptl

degradation13,b degradation13,b H-2 ylidene27 H-2 ylidene27 degradation14

25 80 25 25 25

24.0 ± 0.5 27.6 ± 0.5 12.2 10.3 19.3

a

calcd by B3LYP/PCM 9.0 10.6 −7.5 −9.7 10.9

(−15.0) (−17.0) (−19.7) (−20.0) (−8.4)

The values in parentheses are the differences between the experimental and computational data. methacryloyloxy)ethyl]-3-butyl imidazolium. 9886

calcd by M06/SMD 15.4 19.2 2.7 1.0 12.7

b

(−8.6) (−8.4) (−9.5) (−9.3) (−6.6)

Experimental data are for 1-[(2-



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stability measurement for AEM with BTMA+ and DMIm+,17 and found BTMA+ to be the more stable cation in the presence of hydroxide. The experimental ΔG⧧ for DMIm+ at 80 °C from Table 3 is 27.6 ± 0.5 kcal/mol. The experimental ΔG⧧ for benzylTMA+ at 160 °C is 30.0 kcal/mol.10 Since many degradation experiments were performed at 60−80 °C, we will estimate the ΔG⧧ at 80 °C for BTMA+. The M06/SMD model shows a decrease in ΔG⧧ of 2.3 kcal/mol when temperature drops from 160 to 80 °C. The B3LYP/PCM model (the “better” model for benzylTMA+) shows a decrease of 2.0 kcal/mol. These result in ΔG⧧ of 28.0 or 27.7 kcal/mol for benzylTMA+. In both cases, this indicates a slightly higher (0.1−0.4 kcal/mol) degradation barrier than DMIm+. However, this result remains inconclusive after consideration of the error bar for the DMIm+ barrier (±0.5 kcal/mol). It should also be noted that a slight change of ΔG⧧ could result in a measurable change of cation stability. For example, an increase of ΔG⧧ by 0.5 kcal/mol will result in a decrease in the degradation rate of 50% at 80 °C. However, our computational findings (Table 2) have found that some substituted DMIm+ cations, such as DMPTMIm+, have much larger calculated degradation barriers than the DMIm+ cation (39.2 vs 19.2 kcal/mol). These increases in predicted stability are so large (20 kcal/mol equivalent to a ∼1012 decrease in degradation rate) that it gives increased confidence that these materials will exhibit greatly improved stability in OH− solution. 4.3. Other Potential Degradation Pathways. Experimental measurement13,14 and our results indicated that the nucleophilic addition−elimination pathway at C-2 is the major degradation pathway. As we stated above, OH− attack at the C4/C-5 position through nucleophilic addition−elimination mechanism is also possible. However, the calculated TS1 barriers for this attack have always been larger than those for the C-2 position (Table 2). The OH− can also attack N-1/N-3 methyls by SN2 mechanism (Figure 15, Table 2). Again, these SN2 barriers have been calculated to be larger than addition−elimination at the C-2 position for all of the cations studied.

(and C-4/C-5 in DMIm+) substitutions, which will also result in higher degradation barriers. A number of the cations investigated show extremely promising results for their stability in the presence of OH− and merit further investigation for their inclusion in anion exchange membranes.

5. CONCLUSION In this work, we used DFT calculations to estimate degradation barriers of imidazolium and benzimidazolium cations. The dominant degradation pathway is the nucleophilic addition− elimination pathway at the C-2 atom of the cations. Steric interference can be introduced by making substitutions of bulky groups. Our results showed that C-2 substitutions could not only make the OH− attack more difficult but also make the ring-opening step more difficult. Both are owing to the creation of steric interferences in the TS structures. C-4/C-5 substitutions of DMIm+ were also able to enhance the TS barriers, implying that structural modifications further away from the reaction site might also have significant influence on the degradation reaction. Although we did not explore this further in this work, it is possible that by making C-4/C-5 substitution groups even bulkier, the stability of cations can be improved even more. However, for practical applications in membranes where issues such as hydrophobicity and packing need to be considered, this may actually be detrimental. We also found that DMBIm+ are less stable than their DMIm+ analogues. Some of the DMIm+ derivatives reported in this work have very high stability and have not yet been investigated experimentally or applied to anion exchange membranes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 303-275-3809. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering, under Contract No. DE-AC36-08-GO28308. This research used capabilities of the National Renewable Energy Laboratory Computational Science Center, which is supported by the Office of Energy Efficiency and Renewable Energy of the U.S. Department of Energy.

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REFERENCES

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Figure 15. TS structure of SN2 attack for DMIm+.

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Hydroxide Degradation Pathways for Imidazolium Cations: A DFT Study

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