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Contract No. DE-AC36-08GO28308

Computational Modeling of 

Degradation of Substituted 

Benzyltrimethyl Ammonium

Preprint

H. Long and B. S. Pivovar

To be presented at the 226th Meeting of the Electrochemical 

Society

Cancun, Mexico

October 5–10, 2014

Conference Paper

NREL/CP-2C00-62309

September 2014
NOTICE

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16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.
1 

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Computational Modeling of Degradation of Substituted Benzyltrimethyl 

Ammonium

H. Long and B. S. Pivovar 

National Renewable Energy Laboratory, Golden, CO 80401, USA

The degradation of cations on the alkaline exchange membranes is 

the major challenge for alkaline membrane fuel cells. In this paper, 

we investigated the degradation barriers by density functional 

theory for substituted benzyltrimethyl ammonium (BTMA+) 

cations, which is one of the most commonly used cations for 

alkaline exchange membranes. We found that substituted cations 

with electron-releasing substituent groups at meta-position of the 

benzyl ring could result in improved degradation barriers. 

However, after investigating more than thirty substituted BTMA+

cations with ten different substituent groups, the largest 

improvement of degradation barriers is only 1.6 kcal/mol. This 

implies that the lifetime of alkaline membrane fuel cells could 

increase from a few months to a few years by using substituted 

BTMA+ cations, an encouraging but still limited improvement for 

real-world applications. 

Introduction

Alkaline fuel cell (AFC) is one of the oldest types of fuel cells1 and has the advantage of 

enablement of cheaper, non-precious catalysts.2 However, application of this type of fuel 

cell is still limited due to the carbonate salt precipitation formed on the electrodes when 

carbon dioxide from air reacts with alkaline electrolytes.3-4 Researches on AFC have been 

renewed in recent years because of the development of the alkaline membrane fuel cells 

(AMFCs).5-6 In an AMFC, an anion exchange membrane (AEM) is used between the 

electrodes to allow hydroxide (OH-

) to transport across the membrane and prevents 

carbonate from forming precipitation. However, AEM degrades over time due to the 

reactions between OH- and the cations that are attached to the polymer backbone of the 

membrane, which is the major challenge for the AEFCs.6-8

Benzyltrimethyl ammonium (BTMA+) cation is the most commonly used cation in 

AEMs and has been investigated extensively for its application in AMFC.9-16 Our 

experimental measurements had shown that the unsubstituted BTMA+ cation degraded

~10% within 29 days in 5M NaOH at 80°C.10 Two major degradation pathways for 

BTMA+ are benzyl SN2 pathway and methyl SN2 pathway:17-18

C6H5CH2N+(CH3)3 + OH- = C6H5CH2OH+N(CH3)3, [1]

and 

C6H5CH2N+(CH3)3 + OH- = C6H5CH2N(CH3)2 + CH3OH. [2]
2 

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Our density functional theory (DFT) calculations had shown that the transition state 

(TS) barriers (ΔG≠

) for BTMA+ benzyl SN2 pathway and methyl SN2 pathway were 23.3 

kcal/mol and 25.1 kcal/mol respectively at 160°C and 1 atm.19 Thus, the benzyl SN2 

pathway is the dominant degradation pathway for BTMA+. 

In order to further improve the stability of BTMA+, a straightforward method is to 

add substituent groups to the benzyl ring of BTMA+. In this manuscript, we modeled the 

BTMA+ with different substituent groups at different positions and calculated 

degradation barriers using DFT method in order to search for cations with higher 

degradation barriers. To guide the search, we also investigated the relationship between 

ΔG≠ and Hammett substituents constants. We found that substituent –NRR’ (where R and 

R’ are alkyl groups) is the best type of substituents for improvement of the degradation 

barrier. 

Method

The detail method used for DFT calculations are described in our previous report.19 In 

short, we use Gaussian 09 (G09)20 to optimize the reactants and TS structures by 

B3LYP21 method, 6-311++G(2d,p) basis set, and polarizable continuum solvation model 

(PCM). The free energies at 160° C and 1 atm for the reactants and TS were then 

calculated 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.19 During the calculations, no 

symmetry is used. 

Results

Neutral substituents 

 We have computed ΔG≠ values of benzyl SN2 and methyl SN2 for substituted 

BTMA+ cations at different positions on the benzene ring (Figure 1 and Table I). Five 

electron-releasing substituent groups and one electron-withdrawing substituent group, i.e., 

−NO2, were investigated. For each substituent, we tried single substitutions at ortho, meta, 

and para positions (position 2, 3, and 4) and double substitutions at the meta positions 

(position 3 and 5). 

Figure 1. Substituted BTMA+ cations investigated in Section 3.1. X = −OH, −OCH3, 

−CH3, −NH2, −N(CH3)2, and −NO2. 

Table I. ΔG≠ values in kcal/mol of benzyl SN2 and methyl SN2 pathways for the 

unsubstituted and substituted BTMA+ cations at 160°C and 1 atm. The one with a larger 

ΔG≠ than the unsubstituted BTMA+ is shown in red. 
3 

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Substitution Position 2(o) 3(m) 4(p) 3&5

−H (no substitution) 23.3/25.1

−OH 20.2/25.1 23.4/24.7 23.4/25.5 23.8/24.5

−OCH3 24.6/26.1 22.9/25.6 23.8/26.3 23.8/25.0

−CH3 23.2/25.3 23.9/24.9 21.7/23.3 24.6/26.1

−NH2 22.0/25.4 23.1/25.3 23.0/26.3 24.9/25.4

−N(CH3)2 24.1/26.5 24.5/25.1 22.0/27.8 24.9/26.9

−NO2 20.7/24.3 21.6/24.2 21.6/24.4 20.5/22.2

Figure 2. ΔΔG≠ values of (A) benzyl SN2 and (B) methyl SN2 for the substituted BTMA+

cations compared with the unsubstituted BTMA+. 

(A) (B)

Figure 2 illustrates the ΔΔG≠ of the substituted BTMA+ cations compared with the 

unsubstituted BTMA+. For the methyl SN2 reaction (Figure 2A), the ΔΔG≠ are between -

3 ~ +3 kcal/mol. The ΔΔG≠ values for −N(CH3)2 substitutions at all positions are ≥ 0 and 

the ΔΔG≠ values for all −NO2 substitutions are < 0. The ΔΔG≠ for other substituted 

cations are either larger or smaller than 0, depending on the substitution positions. The 

largest ΔΔG≠

 is 2.7 kcal/mol from the para −N(CH3)2 substitution. 

 For the benzyl SN2 reaction (Figure 2B), the ΔΔG≠ are between -3 ~ +2 kcal/mol. The 

largest ΔΔG≠ is 1.6 kcal/mol from the double-meta substituted −NH2 and −N(CH3)2. 

Again, the ΔΔG≠ values for all −NO2 substitutions are less than 0. For all of the 

substitutions, the ΔG≠ values of benzyl SN2 are always smaller than the methyl ones, 

indicating that the methyl SN2 reaction is always not the rate-limiting step for the 

degradation of the substituted BTMA+ cations. All of the benzyl SN2 ΔG≠ values for the 

double-meta substitutions with electron-releasing substituent groups are larger than the 

unsubstituted BTMA+, indicating that this type of substitutions is promising candidate

cations with higher stability.
4 

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ΔG≠ and Hammett substituent constants 

The correlation between ΔG≠ and substituent groups could be described by the 

Hammett equation where ΔG≠ has a linear relationship with the Hammett substituent 

constants σ.

22-23 Values of σ depend on the substituent groups and the substitution 

positions. For the neutral para substitutions, when the reaction TS structure has positive 

or negative charges, σpara+ or σpara- values should be used instead of σpara.

23 Table II

presents the Hammett substituent constants compiled by Hansch et al23 for the 

substituents investigated in the previous section and Figure 3 and 4 illustrate the plots of 

ΔG≠ vs. σ. 

Table II. The Hammett substituent constants from Hansch et al23. 

Substitution Position σmeta σpara σpara+ σpara-

−H (no substitution) 0

−OH 0.12 -0.37 -0.92 -0.37

−OCH3 0.12 -0.27 -0.78 -0.26

−CH3 -0.07 -0.17 -0.31 -0.17

−NH2 -0.16 -0.66 -1.3 -0.15

−N(CH3)2 -0.16 -0.83 -1.7 -0.12

−NO2 0.71 0.78 0.79 1.27

For the meta substitutions, the ΔG≠ vs. σmeta plot (Figure 3A) shows a linear 

relationship. The linear regression analysis results in a slope of -2.6 kcal/mol with the 

coefficient of determination R = 0.87. For the double-meta substitutions, because –OH 

and −OCH3 have the same ΔG≠

 and σmeta values, and –NH2 and −N(CH3)2 have the 

same ΔG≠ and σmeta values, only five data points are shown on Figure 3B. The slope for 

Figure 3B is -4.9 kcal/mol, almost double the values of Figure 3A, indicating that doublemeta substitutions result in a stronger stabilization effect (or destabilization effect for –

NO2) from the substituent groups. The R-value for this fit is 0.97, showing a much better 

linear relationship than the single-meta substitution case.

Figure 3. ΔG≠ as a function of σmeta for (A) single-meta substitutions and (B) doublemeta substitutions. The red trend lines are fitted by linear regression.

A B
5 

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For the para substitutions, the ΔG≠ vs. σpara plot (Figure 4A) shows no linear 

relationship. Since the cations are charged, we also made plots for ΔG≠ vs. σpara+ (Figure 

4B) and ΔG≠ vs. σpara- (Figure 4C). Only Figure 4C shows somewhat linear relationship 

but two data points are still far from the trend line (in blue color). These two points are 

from −CH3 and −N(CH3)2. The TS structure of the benzyl SN2 reaction for the BTMA+

cation is neutral and the cation is positively charged. This case is similar to the reaction 

with a negatively charged TS structure and a neutral reactant, in which the TS structure 

has more negative charge than the reactant, which may be the reason that the σpara- results 

in the best linear relationship. If the two data points far from the trend line are omitted, a 

slope of -1.2 kcal/mol is obtained from the linear regression.

Figure 4. ΔG≠ as a function of (A) σpara, (B) σpara+

, and (C) σpara- for para substitutions. In 

C, only the black data points were used to fit the red trend line. 

A B C

Multiple-charged BTMA+ 

The substituent group itself could have positive charges, resulting in a cation with

multiple positive charges. We calculated the benzyl SN2 ΔΔG≠ of –CH2N+(CH3)3

substituted BTMA+ cations. The ortho, meta, and para substitutions have benzyl SN2 

ΔΔG≠ values of -1.8 kcal/mol, -3.4 kcal/mol and -1.2 kcal/mol respectively, when 

compared to the unsubstituted BTMA+ cation. Obviously, substituted BTMA+

 cations 

with multiple-charge centers will have smaller ΔG≠ values than the unsubstituted BTMA+

due to the strong charge-charge repulsion. Therefore, for cations with high stability, the 

substituent groups should be neutral. 

Double-meta substitutions by –NRR’

Encouraged by the large benzyl SN2 ΔΔG≠ values of −NH2 and −N(CH3)2, we 

further investigated substituent groups in –NRR’ form at meta and double-meta positions. 

We studied four substituent groups with large negative σmeta values and expected them to 

have improved degradation barriers. The four substituent groups are: −N(CH2CH3)2, 

−N(CH2CH2CH3)2, −NH(CH3), and −NH(CH2CH2CH2CH3). Table III presents their 

σmeta values23 and calculation results. Although they all show some improvement when 

compared to the unsubstituted BTMA+, none of them has a benzyl SN2 ΔG≠ larger than 

the one of double-meta −N(CH3)2, which is 24.9 kcal/mol. Figure 5 shows the case that 

the corresponding four data points are added to the plots of Figure 3. Although these 

points still follow the trend lines, in some case, the deviations from the trend lines are 
6 

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more than 0.5 kcal/mol. This suggests that we could use the Hammett substituent 

constants to roughly estimate the benzyl SN2 ΔG≠

, however, the predictions made by this 

method are still not accurate enough to guide us in search for cations with even higher 

degradation barriers. 

Table III. ΔG≠

 values in kcal/mol of benzyl SN2/methyl SN2 for –NRR’ substituted 

BTMA+ cations at 160°C and 1 atm. 

σmeta 3-substitution ΔG≠ 3&5 substitution ΔG≠

−N(CH2CH3)2 -0.23 24.3/27.4 24.6/26.3

−N(CH2CH2CH3)2 -0.26 23.9/25.7 24.4/25.7

−NH(CH3) -0.21 24.0/26.2 24.4/26.1

−NH(CH2CH2CH2CH3) -0.34 24.2/25.7 24.5/25.9 

Figure 5. ΔG≠ as a function of σmeta for (A) single-meta substitutions and (B) doublemeta substitutions. The four blue data points are for –NRR’ substituted BTMA+ reported 

in this section and were not used to fit the red trend line. 

A B

SN1 pathway 

Besides the benzyl and methyl SN2 pathways, BTMA+ may also take the benzyl SN1 

pathway, 

X-C6H4CH2N+(CH3)3 = X-C6H4CH2++N(CH3)3, [3a]

X-C6H4CH2+ + OH- = X-C6H4CH2OH; [3b]

and the methyl SN1 pathway, 

X-C6H4CH2N+(CH3)3 = X-C6H4CH2N(CH3)2 + CH3+, [4a]

CH3+ + OH- = CH3OH [4b]

where X is the substituent group. For the unsubstituted BTMA+

, these degradation 

pathways were not investigated in previous reports because reaction barriers for reactions 

[3a] and [4a] are obviously very high in aqueous solution owing to the formation of the 

highly unstable CH3

+ and C6H5CH2+ cations. However, when there are one or more 
7 

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electron-releasing substituent groups on the benzyl ring, the X-C6H4CH2

+ cation is 

stabilized, which may result in a relatively lower reaction barrier for reaction [3a]. Table 

IV presents the benzyl SN1 ΔG≠ of select cations. For the unsubstituted BTMA+

, benzyl 

SN1 ΔG≠ is 33.2 kcal/mol, much larger than the benzyl SN2 ΔG≠ 23.3 kcal/mol. This is 

consistent with previous conclusion that benzyl SN2 pathway is the dominant degradation 

pathway.17, 19, 24-25 For the double-meta −OCH3 substitution, the benzyl SN1 ΔG≠ is 32.6 

kcal/mol, close to one of the unsubstituted BTMA+

. For the double-meta −N(CH3)2

substitution, the benzyl SN1 ΔG≠ is 27.7 kcal/mol, still larger than its benzyl SN2 ΔG≠

(24.9 kcal/mol), although the gap between SN1 ΔG≠ and SN2 ΔG≠ is much smaller. The 

stabilization effect is much stronger for electron-releasing substituents at ortho and para 

positions. The para −N(CH3)2 has a benzyl SN1 ΔG≠ as small as 11.3 kcal/mol, much 

smaller than its benzyl SN2 ΔG≠

, 22.0 kcal/mol. For the double-ortho −OCH3 substitution, 

it has a relative large benzyl SN2 ΔG≠, 24.1 kcal/mol, but its benzyl SN1 ΔG≠ is only 20.6 

kcal/mol. In both cases, the benzyl SN1 pathway becomes the dominant degradation 

pathway, and thus, the rate-limiting step for the degradation. Therefore, in search for the 

BTMA+ derivative cations with high stability, meta substitutions with electron-releasing 

substituents are preferred, not only because meta substitutions have larger benzyl SN2 

ΔG≠

, but also because ortho and para substitutions may have relatively small benzyl SN1 

ΔG≠. 

Table IV. ΔG≠ values in kcal/mol of benzyl SN1 and SN2 pathways for the unsubstituted 

and select substituted BTMA+

 cations at 160°C and 1 atm. 

−H −OCH3

−N(CH3)

2

−N(CH3)

2

−OCH3

Position N/A 3&5 3&5 4 2&6

Benzyl SN1 

ΔG≠ 33.2 32.6 27.7 11.3 20.6 

Benzyl SN2 

ΔG≠ 23.3 23.8 24.9 22.0 24.1 

Conclusions

According to our calculation results, we could conclude that methyl SN2 pathway is 

not the rate-limiting step of degradation for substituted BTMA+ cations. Double-meta 

substitutions with electron-releasing substituent groups result in improved stability for the 

benzyl SN2 pathway. For cations with electron-releasing substituents, especially for those 

with substituents at ortho and para positions, the barrier of benzyl SN1 pathway could be 

low enough to become the rate-limiting step. In addition, positively charge substituent 

groups will decrease the stability of cations. We also found that although Hammett 

substituent constants could be used to predict the degradation barrier, these predictions 

were not accurate enough to guarantee a high degradation barrier. 

We noted that some of the substituted BTMA+ cations would be very difficult to 

synthesize and/or purify experimentally, for example, the ones with –OH, –NH2, or –

NRR’. The most important finding of this computational work, however, is that 

substituted BTMA+ cations show less than one magnitude of improvement on stability. 

Although we have investigated degradation barriers for more than thirty cations with ten 
8 

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different substituent groups, the cation with the largest improvement found in this 

manuscript, that is, the one with double-meta −N(CH3)2, only has a ΔΔG≠ of 1.6 

kcal/mol at 160°C. At a temperature of 80°C, which is the typical working temperature of 

a fuel cell, our calculation shows that its ΔΔG≠ is 1.5 kcal/mol. According to the 

transition state theory, degradation reaction rate constant k ∝ exp(-ΔΔG≠/RT), where R is 

the gas constant and T is the temperature. A ΔΔG≠ of 1.5 kcal/mol will result in a 

decrease in degradation rate of 8.5 times at 80°C. Our experimental work had shown that 

unsubstituted BTMA+ cation degrades ~10% within 29 days in 5M NaOH at 80°C.10

Thus, it could be predicted that for the double-meta −N(CH3)2 substituted BTMA+, it 

would degrades ~10% within ~8 months. This degradation rate implies that an AEMFC 

with a lifetime of a few years could be built, much better than the AEMFC using the 

unsubstituted BTMA+

, which would only have a lifetime in months, and this might be 

useful for some real-world applications. However, in order to build fuel cell vehicles with 

a comparable lifetime of conventional ones, this is still far from sufficient. Therefore, our 

calculation results suggest that the improvement of the BTMA+ stability by adding 

substituent groups to the benzyl ring is limited. In search for even larger improvement of 

cation stability, other types of cations should be investigated. Our recent calculation 

results indicated that substituted imidazolium cations may have several magnitudes of 

improvement of stability over the BTMA+ cation and thus are more promising than 

BTMA+ derivative cations.26

Acknowledgements 

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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