Molecular Origins of the Barriers to Proton Transport in Acidic Aqueous Solutions

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Fast Structural Dynamics in Concentrated HCl Solutions: From Proton Hopping to the Bulk Viscosity

Concentrated acid solutions, particularly HCl, have been studied extensively to examine the proton hopping and infrared spectral signatures of hydronium ions. Much less attention has been given to the structural dynamics of concentrated HCl solutions. Here, we apply optical heterodyne detected-optical Kerr effect (OHD-OKE) measurements to examine HCl concentration-dependent dynamics from moderate (0.8 m) to very high (15.5 m) concentrations and compare the results to the dynamics of NaCl solutions, as Na+ is similar in size to the hydronium cation. Both HCl and NaCl OHD-OKE signals decay as triexponentials at all concentrations, in contrast to pure water, which decays as a biexponential. Two remarkable features of the HCl dynamics are the following: (1) the bulk viscosity is linearly related to the slowest decay constant, t3, and (2) the concentration-dependent proton hopping times, determined by ab initio MD simulations and 2D IR chemical exchange experiments, both obtained from the literature, fall on the same line as the slowest structural dynamics relaxation time, t3, within experimental error. The structural dynamics of hydronium/chloride/water clusters, with relaxation times t3, are responsible for the concentration dependence of microscopic property of proton hopping and the macroscopic bulk viscosity. The slowest time constant (t3), which does not have a counterpart in pure water, is 3 ps at 0.8 m and increases by a factor of ∼2 by 15.5 m. The two fastest HCl decay constants, t1 and t2, are similar to those of pure water and increase mildly with the concentration.

Relative Insignificance of Polyamide Layer Selectivity for Seawater Electrolysis Applications

Low-cost polyamide thin-film composite (TFC) membranes are being explored as alternatives to cation exchange membranes for seawater electrolysis. An optimal membrane should have a low electrical resistance to minimize applied potentials needed for water electrolysis and be able to block chloride ions present in a seawater catholyte from reaching the anode. The largest energy loss associated with a TFC membrane was the Nernstian overpotential of 0.74 V (equivalent to 37 Ω cm2 at 20 mA cm-2), derived from the pH difference between the anolyte and catholyte and not the membrane ohmic overpotential. Based on analysis using electrochemical impedance spectroscopy, the pristine TFC membrane contributed only 5.00 Ω cm2 to the ohmic resistance. Removing the polyester support layer reduced the resistance by 79% to only 1.04 Ω cm2, without altering the salt ion transport between the electrolytes. Enlarging the pore size (∼5 times) in the polyamide active layer minimally impacted counterion transport across the membrane during electrolysis, but it increased the total concentration of chloride transported by 60%. Overall, this study suggests that TFC membranes with thinner but mechanically strong supporting layers and size-selective active layers should reduce energy consumption and the potential for chlorine generation for seawater electrolyzers.

Unraveling the phase diagram-ion transport relationship in aqueous electrolyte solutions and correlating conductivity with concentration and temperature by semi-empirical modeling

The relationship between structure and ion transport in liquid electrolyte solutions is not well understood over the whole concentration and temperature ranges. In this work, we have studied the ionic conductivity (κ) as a function of molar fraction (x) and Temperature (T) for aqueous solutions of salts with nitrate anion and different cations (proton, lithium, calcium, and ammonium) along with their liquid-solid phase diagrams. The connection between the known features in the phase diagrams and the ionic conductivity isotherms is established with an insight on the conductivity mechanism. Also, known isothermal (κ vs.. x) and iso-compositional (κ vs.. T) equations along with a proposed two variables semi-empirical model (κ = f (x, T)) were fitted to the collected data to validate their accuracy. The role of activation energy and free volume in controlling ionic conductivity is discussed. This work brings us closer to the development of a phenomenological model to describe the structure and transport in liquid electrolyte solutions.

Highly Altered State of Proton Transport in Acid Pools in Charged Reverse Micelles

Transport mechanisms of solvated protons of 1 M HCl acid pools, confined within reverse micelles (RMs) containing the negatively charged surfactant sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT) or the positively charged cetyltrimethylammonium bromide (CTABr), are analyzed with reactive force field simulations to interpret dynamical signatures from TeraHertz absorption and dielectric relaxation spectroscopy. We find that the forward proton hopping events for NaAOT are further suppressed compared to a nonionic RM, while the Grotthuss mechanism ceases altogether for CTABr. We attribute the sluggish proton dynamics for both charged RMs as due to headgroup and counterion charges that expel hydronium and chloride ions from the interface and into the bulk interior, thereby increasing the pH of the acid pools relative to the nonionic RM. For charged NaAOT and CTABr RMs, the localization of hydronium near a counterion or conjugate base reduces the Eigen and Zundel configurations that enable forward hopping. Thus, localized oscillatory hopping dominates, an effect that is most extreme for CTABr in which the proton residence time increases dramatically such that even oscillatory hopping is slow.

Ab initio molecular dynamics study of proton transport in imidazolium-based ionic liquids with added imidazole

Development of efficient anhydrous proton-conducting materials would expand the operational temperature ranges of hydrogen fuels cells (HFCs) and eliminate their dependence on maintaining sufficient hydration levels to function efficiently. Protic ionic liquids (PILs), which have high ionic densities and low vapor pressures, have emerged as a potential material for proton conducting layers in HFCs. In this work, we investigate proton transport via the Grotthuss mechanism in 1-ethylimidazolium bis-(trifluoromethanesulfonyl)imide ([C₂HIm][TFSI]) protic ionic liquids with added imidazole (Im⁰) using ab initio molecular dynamics. In particular, we vary the composition of the systems studied from pure [C₂HIm][TFSI] to those where the mole fraction of Im⁰ is 0.67. Given the large difference in pK_a between C₂HIm⁺ and HTFSI, TFSI^- does not accept acidic protons from C₂HIm⁺; conversely, imidazolium (HIm⁺) and C₂HIm⁺ have very similar pK_a values, and thus Im⁰ can readily accept protons. We find that the unprotonated nitrogen on Im⁰ dominates solvation of the labile protons on C₂HIm⁺ and other Im⁰ species, resulting in formation of robust imidazole wires. Given the amphoteric nature of Im⁰, i.e. its ability to accept and donate protons, these wires provide conduits along which protons can rapidly traverse via the Grotthuss mechanism, thereby greatly increasing the proton coefficient of self-diffusion. We find that the average length of the wires increases with added Im⁰, and thus as the mole fraction of Im⁰ increases so too does the proton diffusion constant. Lastly, we analyze our trajectories to determine the energy and time scales associated with proton transfer.

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

The theoretical basis for linking spectral signatures of hydrated excess protons with microscopic proton-transfer mechanisms has so far relied on normal-mode analysis. We introduce trajectory-decomposition techniques to analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric-acid solutions beyond the normal-mode scenario. We show that the actual proton transfer between two water molecules involves for relatively large water-water separations crossing of a free-energy barrier and thus is not a normal mode, rather it is characterized by two non-vibrational time scales: Firstly, the broadly distributed waiting time for transfer to occur with a mean value of 200-300 fs, which leads to a broad and weak shoulder in the absorption spectrum around 100 cm-1, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm-1 and agrees in location and width with previous experimental mid-infrared spectra.

Revealing the Anticorrelation Behavior Mechanism between the Grotthuss and Vehicular Diffusions for Proton Transport in Concentrated Acid Solutions

In this study, we performed reactive molecular dynamics simulations to characterize proton solvation and transport in concentrated hydrochloric acid solutions. The correlation contribution to the total proton mean square displacement is found to be negative for all acid concentrations, indicating the anticorrelation between the Grotthuss and vehicular diffusions. For the vehicular diffusion, the hydronium ions tend to move freely toward the lone pair side independent of acid concentrations, whereas for the Grotthuss diffusion, the proton hopping direction is limited to one of the hydrogen-bonded water molecules on the opposite side of the lone pair region, which are specifically oriented with respect to the neighboring hydronium ion at higher acid concentrations. This result is justified by our findings of the higher fraction of proton rattling with the single hopping event and longer hydrogen bond lifetimes at higher acid concentrations. However, the angular distribution for both the vehicular and Grotthuss diffusions is found to be rather broad and comparable for all acid concentrations, and thus, the anticorrelation shows a minimal dependence on the acid concentration. Our results reveal that the anticorrelation behavior between the vehicle and Grotthuss diffusions is attributed to the amphiphilic nature of hydronium ions and thus is independent of the acid concentrations in solutions.

Resolving the Structural Debate for the Hydrated Excess Proton in Water

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H₉O₄⁺) and that of the Zundel cation (H₅O₂⁺). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

Coupled Local-Mode Approach for the Calculation of Vibrational Spectra: Application to Protonated Water Clusters

Spectroscopic studies of protonated water clusters (PWCs) have yielded enormous insights into the fundamental nature of the hydrated proton. Here, we introduce a new coupled local-mode (CLM) approach to calculate PWC OH stretch vibrational spectra. The CLM method combines a sampling of representative configurations from density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations with DFT calculations of local-mode vibrational frequencies and couplings. Calculations of inhomogeneous OH stretch vibrational spectra for H⁺(H₂O)₄ and H⁺(H₂O)₂₁ agree well with experiment and higher-level calculations, and decompositions of the calculated spectra in terms of the coupled modes aids in the interpretation of the spectra. This observation is consistent with the idea that capturing anharmonicity and coupling is as important to accuracy as the underlying level of electronic structure theory. The CLM calculations can easily discern the configuration that dominates the experimental measurement for H⁺(H₂O)₅, which can adopt several low-energy conformations.

Pseudo Jahn-Teller Origin of the Proton-transfer Energy Barrier in the Hydrogen-bonded [FHF]-System

The results of ab initio calculations of the adiabatic potential energy surfaces for the proton-bound [FHF]- system at different F-F distances have been rationalized in the framework of the vibronic theory. It is shown that the instability of the symmetric D∞h structure at increased F∙∙∙F distances and the proton displacement to one of the fluorine atoms is due to the pseudo Jahn–Teller mixing of the ground 1Σg electronic state with the lowest excited state of 1Σu symmetry through the asymmetric σu vibrational mode.

The hopping mechanism of the hydrated excess proton and its contribution to proton diffusion in water

In this work, a series of analyses are performed on ab initio molecular dynamics simulations of a hydrated excess proton in water to quantify the relative occurrence of concerted hopping events and "rattling" events and thus to further elucidate the hopping mechanism of proton transport in water. Contrary to results reported in certain earlier papers, the new analysis finds that concerted hopping events do occur in all simulations but that the majority of events are the product of proton rattling, where the excess proton will rattle between two or more waters. The results are consistent with the proposed "special-pair dance" model of the hydrated excess proton wherein the acceptor water molecule for the proton transfer will quickly change (resonate between three equivalent special pairs) until a decisive proton hop occurs. To remove the misleading effect of simple rattling, a filter was applied to the trajectory such that hopping events that were followed by back hops to the original water are not counted. A steep reduction in the number of multiple hopping events is found when the filter is applied, suggesting that many multiple hopping events that occur in the unfiltered trajectory are largely the product of rattling, contrary to prior suggestions. Comparing the continuous correlation function of the filtered and unfiltered trajectories, we find agreement with experimental values for the proton hopping time and Eigen-Zundel interconversion time, respectively.