Hydroxide Degradation Pathways for Substituted Trimethylammonium

Mar 28, 2012 - Chempath , S.; Einsla , B. R.; Pratt , L. R.; Macomber , C. S.; Boncella , J. M.; Rau , J. A.; Pivovar , B. S. J. Phys. Chem. C 2008, 1...
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Hydroxide Degradation Pathways for Substituted Trimethylammonium Cations: A DFT Study Hai Long, Kwiseon Kim, and Bryan S. Pivovar* National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401 ABSTRACT: Substituted trimethylammonium cations serve as small molecule analogues for tetherable cations in anion exchange membranes. In turn, these membranes serve as the basis for alkaline membrane fuel cells by allowing facile conduction of hydroxide. As these cations are susceptible to hydroxide attack, they degrade over time and greatly limit the lifetime of the fuel cell. In this research, we performed density functional theory calculations to investigate the degradation pathways of substituted trimethylammonium cations to probe the relative durability of cation tethering strategies in alkyl and aromatic tethers. Our results show that significant changes in calculated energy barriers occur when substitution groups change. Specifically, we have found that, when available, the Hofmann elimination pathway is the most vulnerable pathway for degradation; however, this barrier is also found to depend on the carbon chain length and number of hydrogens susceptible to Hofmann elimination. SN2 barriers were also investigated for both methyl groups and substitution groups. The reported findings give important insight into potential tethering strategies for trimethylammonium cations in anion exchange membranes.

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INTRODUCTION Alkaline fuel cells (AFCs) are one of the oldest types of fuel cells.1 AFCs use high-concentration potassium hydroxide (KOH) as an electrolyte2,3 and have an advantage over other acidic fuel cells in that they can effectively employ nonprecious metal catalysts.4,5 However, the high concentration of KOH electrolyte is corrosive, and carbon dioxide (CO2) in the air gradually forms carbonate that can precipitate, preventing diffusion and thus decreasing the efficiency over time.6 In recent years, alkaline membrane fuel cells (AMFCs) have been explored by replacing KOH with anion exchange membranes (AEMs).7 The replacement of the free electrolyte KOH with a membrane still allows for nonprecious catalysis but prevents carbonate precipitation and reduces corrosion and liquid electrolyte handling concerns.8 In AEMs, substituted ammonium cations are usually tethered to a polymer backbone9−12 and result in a membrane that has high anion (hydroxide, a.k.a. OH−) conductivity. Typical ammonium cations have stability concerns and will degrade at moderate temperatures (60−100 °C) in the presence of OH−. This degradation limits the performance and lifetime of AMFCs and is therefore of current interest. The ammonium cation most commonly employed in AEMs is benzyltrimethylammonium (benzylTMA+), where the tether to the polymer backbone is made to the aromatic ring of the benzyl group. However, a number of other potential tethering strategies are available and are the focus of this work where multiple substituted trimethylammonium cations are investigated using DFT models for susceptibility to reaction with hydroxide through ylide formation, SN2 attack, and Hofmann © 2012 American Chemical Society

elimination (when applicable). The choice of trimethyl substitution is predicated on its lack of susceptibility to Hofmann elimination and concerns about cation size and hydrophobicity that would make attempts to use other larger groups (ie. neopentyl, benzyl) potentially more problematic when applied to multiple ammonium sites. In our previous modeling studies, we investigated hydroxidebased reaction pathways in tetramethylammonium (TMA+), ethyltrimethylammonium (ethylTMA+), and benzylTMA+ using density functional theory (DFT) calculations.13−15 All cations can form ylides, where OH− reacts with hydrogen (αH) on carbon α (α-C) to the ammonium nitrogen. OH− can also attack the α-C atom, and then, the cation degrades by taking the SN2 pathways. For cations such as ethylTMA+ or other longer alkyl chain substituents, like many of those investigated here, the OH− can also attack hydrogen (β-H) on carbon β to the ammonium nitrogen, resulting in the Hofmann elimination pathway. The ylide reaction has the lowest transition state (TS) barrier; however, this reaction is reversible and does not typically result in a cation degradation event.13,14 For ethylTMA+, the calculated TS barrier of Hofmann elimination is much lower than the typical SN2 TS barrier, which means that Hofmann elimination is the major degradation pathway for ethylTMA+.13 Because Hofmann elimination has typically been found to be the most vulnerable pathway for degradation, to improve cation Received: February 14, 2012 Revised: March 27, 2012 Published: March 28, 2012 9419

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calculations on the 10 cations presented in Table 1. The

stability, a straightforward approach is to make cations with less or no β-Hs. For example, β-H can be substituted by methyl groups, which impact degradation rates through both electronic and steric factors, as well as decreasing the number of β-H sites susceptible to Hofmann elimination. In the limit of no β-Hs, the SN2 pathway becomes the most vulnerable remaining degradation pathway. The barrier of SN2 attack also depends on substitution. In this work, our systematic probing of substitution to trimethylammonium yields insight into the relative importance and rates of TS barriers relevant to the tethering and degradation of model cations for AEMs. There are a few experimental works that have studied cations relevant to the computational studies presented here. It has been shown that n-alkyltrimethylammonium (n-alkylTMA+) becomes more stable when the alkyl chain is longer,16−18 and in some cases, it is even more stable than cations without βH.15,16,19 These results imply that the TS barrier of Hofmann elimination depends on the chain length of the alkyl group. Additionally, our recent work specifically investigated the role of systematic substitution of methyl groups on the β carbon for ethylTMA+20 and also showed a dependence on the degree of branching of the alkyl chain. The work here provides a basis for an increased understanding of the degradation pathways of substituted trimethylammonium. We used the DFT method to investigate the TS barriers for eight alkylTMA+ and two aromaticTMA+ cations. We specifically included trans versus gauche attack for methyl SN2 pathways and anti versus syn elimination for Hofmann elimination pathways. We also calculated TS barriers for SN2 attack on nonmethyl groups. The work presented here moves beyond our earlier studies and those of other groups by focusing specifically on the role of the substitution groups on TS barriers. It overlaps our recent experimental degradation studies conducted under dry conditions on ethyl, n-propyl, isobutyl, and neo-pentyl trimethylammonium cations and shows similar qualitative trends.20 The results give fundamental insight into the degradation process of ammonium cations in the presence of OH− and have strong implications for AMFC researches.

calculation results are summarized in Table 2. Table 1. Cations Investigated in This Paper

4 5

N(CH2CH2CH2CH3) (CH3)3+ N[(CH2)4CH3](CH3)3+

6

N[(CH2)5CH3](CH3)3+

7

N[CH(CH3)2](CH3)3+

8

N[C(CH3)3](CH3)3+

9

N(C6H5)(CH3)3+ N(CH2C6H5)(CH3)3+

tetramethylammonium (TMA+) ethyltrimethylammonium (ethylTMA+) n-propyltrimethylammonium (npropylTMA+) n-butyltrimethylammonium (nbutylTMA+) n-pentyltrimethylammonium (npentylTMA+) n-hexyltrimethylammonium (nhexylTMA+) iso-butyltrimethylammonium (isobutylTMA+) neo-pentyltrimethylammonium (neopentylTMA+) phenyltrimethylammonium (phenylTMA+) benzyltrimethylammonium (benzylTMA+)

Table 2. Calculated ΔG≠ Values for Cationsa ylide

unit: kcal/mol TMA+ ethylTMA+ n-propylTMA+ n-butylTMA+ n-pentylTMA+ n-hexylTMA+ iso-butylTMA+ neopentylTMA+ phenylTMA+ benzylTMA+

■

Hofmann elimination

S N2

@ methyl

@ transmethyl

@ gauchemethyl

@ nonmethyl

anti

syn

16.8 18.2 18.4 − − − − −

26.7 24.7 25.9 25.3 25.6 25.6 25.7 25.0

26.7 25.1 26.3 − − − − −

NA 27.0 29.7 31.1 30.4 29.7 28.3 34.5

NA 17.5 22.9 23.9 24.1 23.7 21.7 NA

NA 21.4 26.3 − − − 24.8 NA

18.4 16.9

22.6 25.1

24.3 26.5

NA 23.3

NA NA

NA NA

“NA” means that this reaction is not possible. “−” means that we did not calculate this number.

a

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RESULTS AND DISCUSSION 1. Degradation of n-AlkylTMA+. TMA+ is the simplest ammonium cation. It can react with hydroxide by two different pathways: ylide and SN2. The reaction of the ylide pathway is N(CH3)4 + + OH− = (N+ − CH 2−)(CH3)3 + H 2O

(3)

The TS structure for the ylide pathway is shown in Figure 1a. The ΔG≠ calculated from Gaussian is only 0.8 kcal/mol for the reverse reaction and 16.8 kcal/mol for the forward reaction. Thus, the forward reaction is uphill and highly reversible. The free energy change (ΔG) for the forward reaction is 16.0 kcal/ mol, which means under equilibrium conditions at 160 °C, the ratio of ylide to TMA+ is ∼10−8. Considering that there are 12 H atoms that can react with OH− to form ylide, the overall ΔG≠ is further reduced by RT ln(12). Therefore, the overall forward ΔG≠ is 14.7 kcal/mol. The other cations investigated in this paper give similar ylide ΔG≠ and ΔG. While the ylide pathway occurs and can serve as an intermediate for rearrangement products (Stevens or Sommelet-Hauser),13 in our experimental studies to date, these rearrangement products

(1) ≠

the reaction free energy barrier ΔG can be computed by ΔG≠ = G([A···OH]≠ ) − G(A+) − G(OH−)

N(CH3)4+ N(CH2CH3)(CH3)3+ N(CH2CH2CH3)(CH3)3+

10

METHOD We use Gaussian 09 (G09)21 to optimize and calculate energies for the reactant and TS structures. The optimization of TS structures uses the Berny algorithm. During the calculations, we use the DFT B3LYP22 method, 6-311++G(2d,p) basis set, and polarizable continuum solvation model (PCM) implemented in G09. During the calculation, no symmetry is used. We then compute the force constants based on the optimized structure, resulting in the vibrational frequencies and thermodynamic free energies (G). For the reaction in which OH− attacks cation A+ and forms TS: A+ + OH− → [A···OH]≠

1 2 3

(2)

Although the working temperature of AMFC is generally less than 100 °C, cation degradation measurements are usually done at higher temperature to speed up the degradation rate so that experiments can be finished within a reasonable time frame. To compare our results with experimental data, we used a temperature of 160 °C in calculations. We performed 9420

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Figure 1. (a) TS structures for TMA+ ylide pathway and (b) SN2 pathway. In this figure and all other TS structure figures, the unit of distance is in Angstroms (Å). Color scheme: oxygen in red, carbon in cyan, hydrogen in white, and nitrogen in blue. Images were created using VMD.23

represent a small percent of reaction; therefore, in the following sections, we will not further discuss this pathway. The reaction for the SN2 pathway is N(CH3)4 + + OH− = N(CH3)3 + CH3OH

(4)

Figure 2. (a) Optimized structure for ethylTMA+ and (b) TS structures for trans-methyl and (c) gauche-methyl SN2 reactions.

≠

The ΔG for the forward reaction is 26.7 kcal/mol, and for the reverse direction, it is as high as 56.2 kcal/mol. The reverse reaction goes uphill, and its ΔG≠ is so high that we can presume that the reaction is effectively irreversible. Considering that there are four methyl groups in TMA+, the overall SN2 forward reaction barrier is 26.7 − RT ln(4) = 25.5 kcal/mol. While TMA+ is the simplest ammonium cation analogue to cations used in AEMs, it lacks a covalent linking point, and, in practice, cations need a tether to attach to a polymer backbone. The presence of the tether is required but may bring about additional degradation pathways. We will first study the ethyl as a surrogate tether for TMA+. We have chosen to investigate ethyl SN2, methyl SN2, and Hofmann elimination (βelimination) for ethylTMA+ and other related polymers because they are the most likely degradation pathways. The reaction for the ethyl SN2 is

van der Waals radius for the H atom is 1.2 Å.24 Therefore, the two H atoms are in close contact. However, both ΔG≠ are lower than the ΔG≠ of the ethyl SN2 attack. This means that the methyl group is more vulnerable to SN2 attack than the ethyl group. Although the ethyl group can rotate around the C−N bond and trans-methyl can change into gauche-methyl and vice versa, there are always one trans-methyl and two gauche-methyls in the cation. Therefore, if we assume that the probability of OH− attack on all methyls is the same, and because the reaction rate constant is proportional to exp(−ΔG≠/RT), the overall methyl SN2 ΔG≠ can be computed approximately by: ΔG≠ (overall) = −RT ln[exp( −24.7/RT )

N(CH 2CH3)(CH3)3+ + OH− = N(CH3)3 + CH 2CH3OH

+ 2 × exp(− 25.1/RT )]

(5)

= 24.0 kcal/mol

Its ΔG≠ is 27.0 kcal/mol, slightly higher than the TMA+ methyl SN2 ΔG≠. The reaction for the methyl SN2 is

The overall methyl SN2 ΔG is slightly smaller than the transmethyl SN2 ΔG≠. The β-elimination reaction for EthylTMA+ is

N(CH 2CH3)(CH3)3+ + OH− = N(CH 2CH3)(CH3)2 + CH3OH

(7)

≠

N(CH 2CH3)(CH3)3+ + OH−

(6)

The optimized structure of ethylTMA+ has Cs symmetry (Figure 2a). Thus, there are two types of methyl on ethylTMA+. We call the methyl that lies on the plane of reflection “trans-methyl” and the other two “gauche-methyl”. The SN2 attack on the trans-methyl results in ΔG≠ of 24.7 kcal/ mol. The ΔG≠ for the SN2 attack on the gauche-methyl is 25.1 kcal/mol. This barrier is slightly higher than that of transmethyl due to the steric interference between the H atoms of methyl and the β-H of the ethyl (Figure 2b,c). The distance between them is only 2.27 Å. In the classic point of view, the

= N(CH3)3 + C2H4 + H 2O

(8)

This reaction can also take two different pathways. One is called antielimination, where the leaving groups [β-H and N(CH3)3] are on the opposite side of the CH2CH2 group (Figure 3a). The other is called syn-elimination, where the leaving groups are on the same side (Figure 3b). The ΔG≠ for antielimination is usually lower than that of syn-elimination due to weaker steric interference and favorable molecular orbital arrangement. Our calculation results are consistent with these 9421

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Figure 4. TS structures of (a) syn-elimination and (b) anti-elimination reactions for n-propylTMA+.

Figure 3. TS structures of (a) syn-elimination and (b) anti-elimination reactions for ethylTMA+.

theories. ΔG≠ is 21.4 kcal/mol for syn-elimination and 17.5 kcal/mol for anti-elimination. Thus, anti-elimination is preferred. The anti-elimination ΔG≠ is also much less than the SN2 barriers for both methyl and ethyl. It can be concluded that the much favored anti-elimination pathway is the major pathway for the ethylTMA+ degradation in agreement with experimental results previously reported.16−18,20 Similar to ethylTMA+, n-propylTMA+ can follow the same pathways: propyl SN2, methyl SN2, and β-elimination. ΔG≠ for the propyl SN2 is 29.7 kcal/mol, 2.7 kcal/mol higher than ethylTMA+ ethyl SN2 ΔG≠. ΔG≠ is 25.9 kcal/mol for the transmethyl SN2 and 26.3 kcal/mol for the gauche-methyl. The overall methyl SN2 ΔG≠ is 25.2 kcal/mol. We see a similar trend for n-propylTMA+ and ethylTMA+, where trans-methyl SN2 ΔG≠ is ∼0.4 kcal/mol smaller than that of gauche-methyl and the overall methyl SN2 ΔG≠ is ∼0.7 kcal/mol smaller than that of trans-methyl. However, n-propylTMA+ methyl SN2 barriers are ∼1.2 kcal/mol higher than the counterparts of ethylTMA+. ΔG≠ is 26.3 kcal/mol for the n-propylTMA+ syn-elimination pathway and 22.9 kcal/mol for the anti-elimination. As compared to ethylTMA+ ΔG≠ values, these are enhanced by 4.7 and 5.4 kcal/mol, respectively. The Mulliken charges of β-H atoms in ethylTMA+ and n-propylTMA+ are +0.170 and +0.131, respectively. This suggests that the β-H in n-PTMA+ is less positive and more difficult to be attacked by OH−, which results in a higher barrier. To understand why anti-elimination increases ΔG≠ more than syn-elimination does, we examine the TS structures (Figure 4). A steric interference is identified in the antielimination TS structure, where one of the γ-H atoms of propyl is within 2.17 Å from one of H atoms on methyls. Clearly, this steric hindrance contributes to the enhancement of ΔG≠ in anti-elimination. For the n-butylTMA+, ΔG≠ for the butyl SN2 is 31.1 kcal/ mol, slightly higher than n-propylTMA+ propyl SN2 barrier ΔG≠ by 0.4 kcal/mol. ΔG≠ for the trans-methyl SN2 is 25.3 kcal/mol. ΔG≠ for the anti-elimination pathway is 23.9 kcal/ mol, 1.0 kcal/mol higher than ΔG≠ of n-propylTMA+. This may be partly due to less positive Mulliken charge on the β-H atoms (+0.126 for n-butylTMA+, 0.005 less than β-H atom charge of n-propylTMA+). In addition, the distance between the H atom of OH− and one of the δ-H atoms of butyl is 2.44 Å (Figure 5a). This may also contribute to the enhancement of the barrier.

Figure 5. TS structure of antielimination reaction for n-butylTMA+.

The anti-elimination TS structure of n-butylTMA+ shows that when the carbon chain is even longer, the chain can grow in the direction shown by the arrow on Figure 5a and move away from the reaction site. Thus, no additional steric interference will occur between the n-alkyl and the N(CH3)3 group, as well as OH−. In addition, as the carbon chain becomes longer, the Mulliken charge on the β-H atoms will also become stable. Therefore, the anti-elimination ΔG≠ will change little. Indeed, the calculation result of n-hexylTMA+ confirms our hypothesis. Its TS structure (Figure 5b) is highly similar to the n-butylTMA+ TS structure, and no additional steric inference is created. The anti-elimination ΔG≠ is 23.7 kcal/mol, only 0.2 kcal/mol smaller than the n-butylTMA+ ΔG≠. As a summary, Figure 6 presents ΔG≠ values for SN2 at nalkyl, SN2 at trans-methyl, and the anti-elimination as a function of n-alkyl carbon chain length n. The n-alkyl SN2 ΔG≠ increases from n = 1 to 4 and then drops gradually. For all of the cations, this barrier is always no smaller than other pathway barriers. The trans-methyl SN2 ΔG≠ first drops from n = 1 to 2 and then fluctuates around ∼25.5 kcal/mol. If we consider the overall methyl SN2 ΔG≠, the barrier will be further reduced by ∼0.7 kcal/mol, so that the barrier will be around ∼25 kcal/mol. The anti-elimination ΔG≠ increases from n = 2 to 4 and then fluctuates around 24 kcal/mol. For n = 2−6, this pathway is always the most vulnerable pathway for the cation degradation. To obtain more stable cations, we need to improve the barrier of this pathway. These results, in relation to other theory and experimental results, will be discussed in greater detail. 2. Degradation of AlkylTMA+ as a Function of Number of β-Hs. Because Hofmann elimination is the most vulnerable pathway for n-alkylTMA+ degradation, we can make the cations more stable by increasing this pathway's barrier or by completely eliminating this pathway. Iso-butylTMA+ 9422

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wants to take a staggered configuration with the N atom to minimize the steric interference between them. Therefore, the dihedral angle formed by H, N, and the two C atoms between them is ∼20° to avoid forming an eclipse configuration. However, this creates another steric interference between this H atom and one of the H atoms of the N(CH3)3 group. The distance between them is only 2.10 Å. This H atom also forms another steric interference with the H atoms on the other side, and the distance between them is 2.33 Å. Thus, the ground state G of iso-butylTMA+ is higher than that of n-butylTMA+. Because the G of the ground state iso-butylTMA+ is 4.3 kcal/ mol higher, and the G of TS is only 2.1 kcal/mol higher than nbutylTMA+'s counterparts, ΔG≠ is effectively 2.2 kcal/mol lower. This case study shows the importance of considering the steric effects in both the TS and the ground state structures when trying to understand the activation barriers and design more stable cations. Completely removing all β-H and replacing with methyl groups, as in neo-pentylTMA+, will result in no Hofmann elimination pathways. For neo-pentylTMA+, the SN2 ΔG≠ for neo-pentyl is as high as 34.5 kcal/mol, the highest such barrier reported in this paper. The bulky neo-pentyl group has many steric interferences with the bulky N(CH3)3 group, and it takes an awkward TS (Figure 8). In normal SN2 TS, the angle

Figure 6. ΔG≠ as a function of n-alkyl carbon chain length.

represents the next step in replacing a β-H with a methyl group. One might expect that it would have even higher antielimination ΔG≠ than n-alkylTMA+ because its TS may have two steric interferences between the iso-butyl γ-H atoms and N(CH3)3 group. However, calculation results show that ΔG≠ for the iso-butyl anti-elimination pathway is only 21.7 kcal/mol, 2.2 kcal/mol smaller than the ΔG≠ for n-butylTMA+. Because iso-butylTMA+ and n-butylTMA+ are isomers, we can compare their free energies (G) directly. For their anti-elimination TSs, G of iso-butylTMA+ is 2.1 kcal/mol higher than G of nbutylTMA+. The TS structure of iso-butylTMA+ is shown in Figure 7a. Two steric interferences are created between the iso-

Figure 8. TS structure of SN2 attack at neo-pentyl for neopentylTMA+.

between the O−C−N atoms is close to 180°. In the neo-pentyl SN2 TS, however, due to the steric interferences, this angle is close to 150°. Its SN2 ΔG≠ for trans-methyl is 25.0 kcal/mol, slightly higher than the typical antielimination ΔG≠ (∼24 kcal/ mol) in n-alkylTMA+ for n = 4−6. According to our calculation results, this cation may have the highest degradation barrier and is therefore the most stable cation among those investigated in this research. 3. Degradation of Aromatic-TMA+. We investigated the degradation pathways for two aromatic-TMA+ cations. In the first one, phenylTMA+, there is no α-H atom on the substitution group, and in the second one, benzylTMA+, there is no β-H atom. Thus, both are insusceptible to the Hofmann elimination pathway. For phenylTMA+, the trans-methyl SN2 ΔG≠ is 22.6 kcal/ mol, and that of the gauche-methyl is 24.3 kcal/mol. Because the gap between the two ΔG≠ is relatively large, the overall methyl SN2 ΔG≠ is 22.4 kcal/mol, very close to that of the trans-methyl. This ΔG≠ is also smaller than the typical nalkylTMA+ methyl SN2 barriers (∼25.5 kcal/mol) and antielimination barriers (∼24 kcal/mol).

Figure 7. (a) Anti-elimination TS structure and (b) ground state structure for iso-butylTMA+.

butyl γ-H atoms and the N(CH3)3 group. They are 2.23 and 2.24 Å, respectively. These interferences result in higher G, which is consistent with our predictions. The syn-elimination ΔG≠ for iso-butylTMA+ is 24.8 kcal/mol, 3.1 kcal/mol higher than the antielimination ΔG≠. The ΔG≠ values of trans-methyl and iso-butyl SN2 pathways are 25.7 and 28.3 kcal/mol, respectively. Therefore, the anti-(Hofmann) elimination pathway is still the most vulnerable degradation pathway for isobutylTMA+. For the ground states, G of iso-butylTMA+ is 4.3 kcal/mol higher than the G of n-butylTMA+. Figure 7b shows the ground state structure of iso-butylTMA+. This cation takes a very awkward structure. Because of the bulky N(CH3)3 group and the bulky iso-butyl group, the β-H has to point downward to minimize the steric interference. However, this H atom also 9423

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For benzylTMA+, the trans-methyl SN2 ΔG≠ is 25.1 kcal/ mol, and that of the gauche-methyl is 26.5 kcal/mol. The overall methyl SN2 ΔG≠ is 24.8 kcal/mol, which is close to the typical n-alkylTMA+ methyl SN2 barriers. The SN2 ΔG≠ for benzyl is only 23.3 kcal/mol, which is smaller than the methyl SN2 barriers. This number is also smaller than the typical nalkylTMA+ anti-elimination barriers. Thus, both phenylTMA+ and benzylTMA+ are predicted to be slightly less stable than nalkylTMA+ when the alkyl's carbon chain length is larger than 3. 4. Comparison of ΔG≠ with Other Theory and Experiment Results. In our earlier work, the ΔG≠ for ethylTMA+ and benzylTMA+ was calculated using the same basis set, method, and initial structures.13 Our current ΔG≠ values are around 4−5 kcal/mol larger than in this paper. The main reason is that our results are reported at 160 °C while our earlier results were at 25 °C. For example, for reaction 5, our ΔG≠ is 27.0 kcal/mol at 160 °C and 24.0 kcal/mol at 25 °C, while our earlier work has a ΔG≠ for the same reaction of 23.2 kcal/mol at 25 °C. The small difference (0.8 kcal/mol) between the 25 °C values can be attributed to using Gaussian 09, where a new version of PCM solvation model is implemented, for our current results, while our earlier study used Gaussian 03 and old version of PCM.25 There are several experimental reports that have investigated the thermal stability of ammonium cations. Tomoi et al. studied the thermal stability of anion exchange resins and found that the stability of resins with different cations follows N[(CH2)6OC6H5](CH3)3+ > N[(CH2) 4OC6H5](CH3) 3+ > benzylTMA+ > N[(CH2)3OC6H5](CH3)3+.16 Komkova et al. studied stability of AEMs containing −N+(CH3)2−(CH2)n− N+(CH3)2− cations and concluded that stability follows n = 6 > n = 4 > n = 3 > n = 2.17 Sata et al. also measured the stability of AEMs and found that the anion exchange capacity has the least loss in the following order benzylTMA+, N(CH2C6H5)(C4H9)3+, N(CH2C6H5)(C3H7)3+, and then N(CH2C6H5)(C2H5)3+.18 A common trend for these studies is that ethyl groups tend to be the weakest ammonium groups, and chemical stability to hydroxide attack increases as chain length increases. These experimental observations are generally consistent with our results: The Hofmann elimination barrier increases when the alkyl chain number n increases from 2 to 4. Our numbers also indicate that benzylTMA+ is more stable than npropylTMA+ but less stable than n-butylTMA+ since their lowest degradation barriers are 23.3, 22.9, and 23.9 kcal/mol, respectively (Table 2). These barriers are qualitatively consistent with the results reported by Tomoi et al. Our calculations also predict a degradation barrier for n-hexylTMA+ that is slightly (0.2 kcal/mol) less than n-butylTMA+. While experimentally observed degradation rates of both Tomoi and Komkova et al. show cations with hexyl substitution are more stable than ones with butyl substitution, it should be noted that Tomoi et al.'s cation has a benzyl ether at the end of the alkyl and Komkova et al.'s has a second ammonium. These chemical groups have not been included in our calculations to reduce computational cost. Still, the qualitative agreement between experimental studies and our computational effort is good and lends insight into the rates and mechanisms of hydroxide attack on trimethylammonium cations. Our experimental efforts, published elsewhere, have paralleled our computational studies and have used evolved gas analysis (EGA), mass spectrometry (MS), and nuclear magnetic resonance (NMR) to investigate the degradation process of different cations.15,26 EGA, in particular, has been performed to

study the decomposition of of [ethylTMA][OH], [npropylTMA][OH], [iso-butylTMA][OH], and [neopentylTMA][OH].20 Samples including deuterated water were included in these studies to probe the relative importance of ylide formation and isotopic scrambling. The results from these studies are summarized in Table 3. Deuterium scrambling Table 3. Degradation Pathways Identified from EGA Measurement and their ΔG≠ Computed in This Research kcal/mol

cation

ylide

Hofmann elimination

SN2

antielimination ΔG≠

ethylTMA+ npropylTMA+ isobutylTMA+ neopentylTMA+

yes yes

yes yes

no no

17.5 22.9

24.7 25.9

yes

yes

yes

21.7

25.7

yes

N/A

yes

N/A

25.0

trans-methyl SN2 ΔG≠

is observed for all degraded cations, indicating that ylide formation has a low relative energy barrier. For ethylTMA+, Hofmann elimination is the main degradation pathway, and SN2 attack is not observed. This is consistent with our model calculations where the anti-elimination ΔG≠ was calculated to be 7.2 kal/mol smaller than the trans-methyl SN2 ΔG≠. Our model results comparing Hofmann elimination,17.5 kcal/mol, and ylide formation, 18.2 kcal/mol, for ethylTMA+ predict that Hofmann attack is favored even over ylide formation for ethylTMA+. While Table 3 shows that ylide formation is observed for ethylTMA+ degradation, it is not observed at short times but only over longer times. Further comparisons between these experimental results and our model results are presented in Edson et al.20 In general, we again find good qualitative agreement with our calculated energy barriers, particularly considering that our calculations have been performed under well solvated “wet” condition, whereas the experimental results have been obtained under dry conditions. Finally, there exist experimental measurements of half-time of cations, which makes it possible for us to calculate the TS barriers and compare experimentally obtained TS barriers with our computational results. Einsla et al. measured remaining concentrations of cation benzylTMA+ and N[(CH2)6OC6H5](CH3)3+ over time at 160 °C, 2 M NaOH, and 0.1 M cation concentration by NMR.19 Because OH− concentration is much larger than cation concentration in this study, the reaction can be approximately treated as first-order. The half-times (τ) fitted from these data are 32.1 min for benzylTMA+ and 71.8 min for N[(CH2)6OC6H5](CH3)3+. In addition, Bauer et al. also measured τ = 29.1 min for benzylTMA+ at 160 °C, 2 M KOH, and 0.01 M cation concentration,27 which is consistent with Einsla's τ value. Because the rate constant k can be computed by: k=

ln 2 τγ[OH−]

(9)

where γ is the activity coefficient, which are 0.860 for 2 M KOH and 0.714 for 2 M NaOH, we can then use the TS theory to compute the ΔG≠ from k: 9424

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⎛ ΔG≠ ⎞ kT RT k=κ exp ⎜− ⎟ h p0 ⎝ RT ⎠

dramatically when the carbon chain of n-alkylTMA+ is extended from 2 to 4 and becomes stable from 4 to 6, where the Hofmann elimination barrier is around 1.5 kcal/mol lower than the methyl SN2 barrier. According to eq 9, this means that the reaction rate of the Hofmann elimination is ∼6 times faster than the methyl SN2 reaction rate at 160 °C. To design more stable cations, we need to either increase the Hofmann elimination barrier or use cations without α-H atoms or β-H atoms. For the former case, we can use steric effects to increase the reaction barrier. However, steric effects may play an important role in both the ground state and the TS, and we must consider those effects to ensure that steric effects generate more enhancement in TS energy than in ground state energy. For the latter case, although we can prevent the Hofmann elimination reaction from happening, substituting α-H atoms or β-H atoms with functional groups may influence the chemistry of other pathways. Other pathways' barriers should be scrutinized to make sure that they are not brought down. In this paper, we use the PCM solvation model in the DFT calculations. The solvent is implicit water, and the dielectric constant is 78.5. In the fuel cells, cations may experience a lower and inhomogeneous dielectric environment. We tried to apply a smaller dielectric constant in our calculations, which results in smaller degradation barriers (data not shown) and thus faster degradation rates. This is consistent with results by Chempath et al.14 However, by reducing the dielectric constant, barriers of different degradation pathways decrease by nearly the same amount, so the most vulnerable pathway was unchanged. We attribute this effect to the PCM solvation model, which is effectively a mean-field theory, reducing dielectric constant evenly throughout the space. To simulate an inhomogeneous environment, explicit solvation, which we have found to improve agreement with experiment, is suggested, although this also comes with increased computational cost and difficulty for optimization to converge for complicated cations.13

(10)

where κ is the transmission coefficient, and for simple reactions such as SN2 or Hofmann elimination, we assume κ is equal to 1. The RT/p0 term appears in this equation to calculate the ΔG≠ at 1 atm standard state,28 where p0 = 1 atm. The ΔG≠ obtained from G09 calculation are also at 1 atm standard state so that we can compare the numbers. The ΔG≠ at 160 °C calculated from experimental data for benzylTMA+ is 29.9 kcal/mol from Einsla and 30.0 from Bauer and that of N[(CH2)6OC6H5](CH3)3+ is 30.6 kcal/mol. Our theoretical results show that for benzylTMA+, the most vulnerable pathway is the SN2 attack at benzyl, and its ΔG≠ = 23.3 kcal/mol, 6.6−6.7 kcal/mol smaller than the experimental measurement. For N[(CH2)6OC6H5](CH3)3+, its structure is close to n-hexylTMA+, and for n-hexylTMA+, theoretical calculations indicate that the most vulnerable pathway is the antielimination pathway, and its ΔG≠ = 23.7 kcal/mol, 6.9 kcal/mol smaller than the experimental measurement. Our theoretical results are ∼7 kcal/mol smaller than the experimental measurement by Einsla et al. but reasonably consistent. In general, the calculated barriers tend to deviate from experimentally measured barriers, but we have shown strong evidence that relative values of experimental values show good qualitative agreement with our models. We also investigated the impact of the DFT method and solvation model employed within our computational studies. Selected results employing M0629 and SMD30 as an alternate DFT method and solvation model, respectively, are presented in Table 4 for benzylTMA and hexylTMA. The ΔG≠ obtained Table 4. ΔG≠ Values Calculated from Different Solvation Models and DFT Methods unit: kcal/mol benzylTMA+ benzyl SN2 n-hexylTMA+ βelimination

experimental measurement

B3LYP/ PCM

B3LYP/ SMD

M06/ PCM

M06/ SMD

29.9a/30.0b

23.3

33.5

21.9

33.6

23.7

36.8

20.8

32.8

30.6

c

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

■

a

From Einsla et al. bFrom Bauer el al. cFrom Einsla et al. for N[(CH2)6OC6H5](CH3)3+.

ACKNOWLEDGMENTS Discussions with Dr. Philip Jeffrey Hay are greatly acknowledged. 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-AC36-08GO28308 with the National Renewable Energy Laboratory. 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 under Contract No. DE-AC36-08GO28308.

from M06 was smaller than ΔG≠ from B3LYP with the same solvation model. Additionally, M06 yields a larger ΔG≠ for benzylTMA+, which contradicts the experimental data. For SMD solvation calculations, ΔG≠ was found to be 10−13 kcal/ mol higher as compared to PCM calculations. The B3LYP/ SMD combination overestimates ΔG≠ by ∼3 kcal/mol for benzylTMA+ and ∼6 kcal/mol for n-hexylTMA+, showing less consistency than B3LYP/PCM results. On the basis of our findings, we currently use the B3LYP/PCM method as our standard method, although we continue to explore the connection between different DFT method and solvation model results to experimental data.

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REFERENCES

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CONCLUDING REMARKS We used DFT calculations to investigate the cation degradation pathways. Our calculation results indicate that among the possible degradation pathways, the Hofmann elimination is the most vulnerable pathway for n-alkylTMA+ cations. Because of steric interference, the Hofmann elimination barrier increases 9425

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Article

NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on April 23, 2012, without an author affiliation present. The corrected version was reposted on May 3, 2012.

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