From Grotthuss Transfer to Conductivity: Machine Learning Molecular Dynamics of Aqueous KOH

Abstract

Accurate conductivity predictions of KOH(aq) are crucial for electrolysis applications. OH^- is transferred in water by the Grotthuss transfer mechanism, thereby increasing its mobility compared to that of other ions. Classical and ab initio molecular dynamics struggle to capture this enhanced mobility due to limitations in computational costs or in capturing chemical reactions. Most studies to date have provided only qualitative descriptions of the structure during Grotthuss transfer, without quantitative results for the transfer rate and the resulting transport properties. Here, machine learning molecular dynamics is used to investigate 50,000 transfer events. Analysis confirmed earlier works that Grotthuss transfer requires a reduction in accepted and a slight increase in donated hydrogen bonds to the hydroxide, indicating that hydrogen-bond rearrangements are rate-limiting. The computed self-diffusion coefficients and electrical conductivities are consistent with experiments for a wide temperature range, outperforming classical interatomic force fields and earlier AIMD simulations.

1

Schematic description of Grotthuss transfer, where the OH^– takes a hydrogen of a H₂O molecule. Before the transfer event, oxygen 1 (O1) and the center hydrogen (H) are part of the H₂O molecule. After the reaction, O1 becomes part of the OH^– molecule, and H is now chemically bonded to O2. As this reaction is an identity switch, no change in concentration occurs.

2

(a) Parity between forces predicted by DFT versus the MLFF. (b) and (c) Radial distribution function of K⁺ and the oxygen of the OH^– (O*) with the oxygen of water molecules (Ow), respectively. The continuous blue lines indicate the g(r) of MLMD, the blue circles indicate AIMD, and the dashed blue lines indicate classical MD. The radius depending on the hydration number is the red line, where the diamond indicates the hydration number at the minimum of g(r).

3

(a) Time correlation functions C(Δt) from which the OH^– lifetimes τ are computed using the stable state picture. , The orange curve shows simulation results at 15 °C, and the dashed blue line is fitted to A exp­(−Δtτ₁ ^–1) + (1 – A) exp­(−Δtτ₂ ^–1). The gray lines below the orange curve indicate the other temperatures (25–65 °C), and the light-brown lines above the orange curve are simulation results with heavy water at 15 °C, with m _H = 2, 3 u. (b) Bar chart of the average number of hydrogen bonds in the reactive configuration (50 fs before and after Grotthuss transfer) and the nonreactive hydration mode. The total average hydrogen-bond number (n _HB) is indicated, as well. We separated the results in donated (red bars) and accepted (green bars) hydrogen bonds. (c) and (d) Typical GaTewAY − graphs of the hydrogen-bonding network in the nonreactive and reactive hydration modes, respectively. The color indicates the molecule type: K⁺ is blue, OH^– is yellow, and H₂O is red. The red arrows between the molecules indicate the direction of the hydrogen bonds (from donor to acceptor). The blue dashed lines indicate the ionic interactions between K⁺ and the water.

4

(a) and (b) Self-diffusion coefficients of K⁺ and OH^–, respectively. (c) Electrical conductivities of the KOH­(aq) mixture. In all subfigures, the closed blue circles are the MLMD results of light water, the open blue circles are the MLMD results of heavy water (m _H = 2 u), and the orange squares are the classical MD data points. The green diamond (b) is the AIMD result by Muñoz-Santiburcio. The red diamond and curve (c) represent experimental results of electrical conductivities and an experimental fit curve, respectively.