Hydrogen fuel cells are a clean alternative to traditional lithium-based power sources because their waste products are only water and heat. The development of solid-state proton exchange membranes (PEMs), a key component of hydrogen fuel cells, is an active area of research, due to their higher heat and pressure resistance over their liquid counterparts. Hydrogen-bonded organic frameworks (HOFs) – solid, microporous, organic materials that are held together by hydrogen bonds – have shown high proton conductivities, but they are typically less stable under ambient conditions. Recently, two HOFs, namely GTUB5 [1] and UPC-5a [2], were developed that are chemically stable and thermally stable up to 250°C and 125°C, respectively. These systems contain porphyrin-phosphonate linkers, with the main chemical difference being that UPC-5a contains a nickel atom in its porphyrin core while GTUB5 does not. Under high relative humidity (r.h.), the activation energies of GTUB5 and UPC-5a are 0.14 eV (at 90% r.h) and 0.20 eV (at 95% r.h.), respectively, suggesting that both GTUB5 and UPC-5a conduct protons via a Grotthus mechanism. However, the proton conductivity of UPC-5a is 4 orders of magnitude higher than that of GTUB5 (viz., \(3.42 S m^{-1}\) vs. \(4.20 x 10^{-4} S m^{-1}\)). Although the structures possess similarities, it is expected that fundamental differences at the atomic level lead to this large difference in proton conductivities.

To gain insight into the proton conduction mechanisms of both HOFs, Born-Oppenheimer molecular dynamics (BOMD) simulations are performed. Systems with 8 and 10 water molecules (corresponding to high relative humidities) in the pores are considered, each at three different temperatures. For each system, the diffusion coefficient of the excess proton in each pore (1 pore in GTUB5 vs. 3 pores in UPC-5a) is calculated and substituted into the Nernst-Einstein equation to estimate the proton conductivity (σ). Using the proton conductivities at the three different temperatures for a given relative humidity, we estimate the activation energy of the proton transfer from the slope of the linear Arrhenius plot of \(log(σ [S*cm^{-1}])\) vs. \(1000/T[K^{-1}]\). The results for the two HOFs are compared and contrasted to build a picture of the proton conduction mechanisms and, in turn, elucidate the structural/dynamical factors that contribute to the large difference in proton conductivities.

[1] Tholen, P.; Peeples, C. A.; Schaper, R.; Bayraktar, C.; Erkal, T. S.; Ayhan, M. M.; Çoşut, B.; Beckmann, J.; Yazaydin, A. O.; Wark, M.; Hanna, G.; Zorlu, Y.; Yücesan, G. Semiconductive microporous hydrogen-bonded organophosphonic acid frameworks. Nat. Commun. 2020, 11 (1), 1–7.

[2] Wang, Y.; Yin, J.; Liu, D.; Gao, C.; Kang, Z.; Wang, R.; Sun, D.; Jiang, J. Guest-tuned proton conductivity of a porphyrinylphosphonate-based hydrogen-bonded organic framework. J. Mater. Chem. A 2021, 9 (5), 2683–2688.