Search for a Grotthuss mechanism through the observation of proton transfer

The study investigates how protons are transported in bulk liquids, focusing on whether a Grotthuss-like, chain-mediated structural diffusion mechanism operates and enhances conductivity. Proton transport is generally described by two mechanisms: vehicular transport, in which protons move with molecular entities, and structural diffusion, in which protons are transferred along hydrogen-bond networks between molecules. The latter is believed to be more efficient and potentially collective (the Grotthuss mechanism), but despite over two centuries since its proposal, direct experimental evidence in bulk systems has been lacking. Phosphoric acid (PA) is an ideal system due to its high intrinsic proton conductivity and prior observations indicating proton diffusion much faster than phosphorus diffusion, strong isotope effects, and significant conductivity below the glass transition temperature. The research aims to observe and characterize proton transfer events directly in neat PA and in 85 wt% aqueous PA (PA85), determine the proton jump length and timescales, and assess whether correlations among proton jumps enhance or suppress conductivity as would be expected from a Grotthuss mechanism.

Prior work has largely inferred Grotthuss-like behavior indirectly, often from low activation barriers in conductivity, which are not a sufficient fingerprint as vehicular mechanisms can also exhibit low barriers. NMR studies in PA showed proton self-diffusion exceeding phosphorus diffusion, supporting structural diffusion; conductivity persists below Tg, and strong H/D isotope effects further support proton transfer mechanisms. Computational studies suggested correlated transfer along short molecular chains (~2–4 molecules). However, earlier neutron scattering experiments detected motions with larger displacements than expected for proton transfer and missed fast processes due to limited energy windows. More recent NMR suggested structural diffusion dominates in pure PA, while H3O+ diffusion contributes significantly in PA85. This body of literature set the stage for a direct, multimodal experimental observation of proton transfer and its characteristics in bulk PA systems.

- Materials: High-purity phosphoric acid (PA, ≥99.99%) and commercial 85 wt% aqueous PA (PA85) were used as received. Samples were handled in a dry argon glovebox and sealed for measurements; pure PA was studied in the supercooled liquid below its crystallization temperature. - Broadband Dielectric Spectroscopy (BDS): Complex conductivity and permittivity were measured across 0.1 Hz to 30 GHz using three instruments: Novocontrol Alpha-A (0.1–10^6 Hz), Agilent E4991A RF Impedance Analyzer (10^6–3×10^9 Hz), and Agilent E8364C PNA with 85070E Dielectric Probe (5×10^8–3×10^10 Hz). Temperature control via Novocontrol Quattro and Julabo Presto W80 with stabilization (±0.2 K). Conductivity spectra were analyzed with the Random Barrier Model to extract DC conductivity and conductivity relaxation time τ0 (from the DC–AC crossover frequency). - Light Scattering (LS): Depolarized light scattering using a Tandem Fabry-Perot (TFP-1) interferometer (mirror spacings 0.4, 3, 15 mm) with a 532 nm laser in backscattering geometry and a T64000 Raman spectrometer. Samples were measured in HV and HH polarizations; optical Raman modes were used for normalization. Structural relaxation times τLS were obtained from the peak frequency fmax via τLS=1/(2πfmax). - Quasielastic Neutron Scattering (QENS): Measurements performed on the BASIS spectrometer (SNS, ORNL) in extended energy-transfer mode (−200 to +200 μeV), incident wavelength centered at 6.15 Å, energy resolution ~3.7 μeV (FWHM). Flat-plate gold-coated Al cells (0.25 mm thickness) minimized multiple scattering; samples sealed with indium. Data reduced with Mantid and analyzed with DAVE. Spectra were fit with a Cole–Davidson function to obtain Emax(Q) and the elastic fraction; Emax(Q) was modeled by the Singwi–Sjolander jump-diffusion model to extract DQENS, τQENS, and jump length. - Ab initio molecular dynamics (AIMD): CPMD code with BLYP functional and dispersion-corrected atom-centered pseudopotentials (DCACP). Pure PA: 54 PA molecules in a cubic box (L=16.696 Å, ρ=1.885 g cm−3). PA85: 38 PA + 38 H2O molecules (L=16.317 Å, ρ=1.685 g cm−3). Plane-wave cutoff 80 Ry; hydrogen atoms assigned deuterium mass; fictitious electron mass 500 au; time step 4 au. Systems pre-equilibrated classically (10 ns), then 15–20 ps with AIMD (NVT) using Nose–Hoover chains; production runs ~60 ps in NVE at elevated temperatures to enhance proton dynamics. Analysis included self-intermediate scattering function ISF(Q,t), proton transfer population correlation functions, and proton displacement vector correlations to compute self and distinct diffusivities via Einstein relations.

- Direct observation of proton transfer in bulk PA and PA85: Proton motion exhibits very short jump lengths of approximately 0.5–0.7 Å. - From BDS + NMR: Rearrangement length at the DC–AC crossover estimated via λp=√(6DNMR τ0) yields λp=0.7±0.2 Å (PA) and 0.5±0.2 Å (PA85). These are 5–6 times smaller than typical ionic jump lengths in ionic liquids (~2.5–3.5 Å). - QENS: Emax(Q) increases linearly with Q^2 at low Q and saturates at higher Q, consistent with jump diffusion. Fits yield jump lengths ⟨λ⟩=0.7±0.2 Å (PA) and 0.6±0.2 Å (PA85) and diffusion coefficients consistent with NMR. Characteristic relaxation times τQENS match conductivity relaxation times τ0 from BDS and are much faster than structural relaxation τLS. The characteristic energy scale of the proton transfer process is ~130 μeV. - AIMD: ISF(Q,t) shows a fast vibrational process (few fs), an intermediate local rattling process (~0.1–0.3 ps), and a slow diffusive process with stretched exponential decay (β≈0.7±0.2). Fits reproduce QENS Emax(Q) and yield λ≈0.7±0.2 Å (PA) and λc≈0.5±0.1 Å (PA85). Proton trajectories show predominantly short hops (~0.5 Å) between the same pair of oxygen atoms with rare larger jumps (~2 Å) associated with OH reorientation and hydrogen bond network reorganization. - Correlations and conductivity: Inverse Haven ratio H−1=σDC/σNE is less than 1 across the full temperature range for both PA and PA85, indicating that correlations suppress conductivity rather than enhance it. At 400 K in PA, AIMD gives Dself≈3.59×10^−6 cm^2 s^−1 and Ddistinct≈−1.53×10^−6 cm^2 s^−1, yielding H−1≈0.58. Distinct proton–proton correlations are negative (anticorrelated), consistent with reduced conductivity relative to the Nernst–Einstein expectation. - Consistency across methods: τQENS≈τ0 (BDS) and both are much shorter than τLS; jump lengths from BDS+NMR, QENS, and AIMD are in excellent agreement.

The results directly address the long-standing question of whether Grotthuss-like structural diffusion operates in bulk liquids and whether it enhances proton conductivity. By combining BDS, QENS, LS, and AIMD, the study demonstrates that proton transport in neat PA and PA85 is dominated by short proton hops between hydrogen-bonded oxygen atoms with characteristic lengths ~0.5–0.7 Å. These hops correspond to structural diffusion events and constitute the first experimental observation of proton jumps between molecules in a bulk liquid system. However, the observed proton–proton correlations are anticorrelated, as evidenced by H−1<1 and negative distinct diffusivity, leading to a suppression of conductivity relative to the uncorrelated Nernst–Einstein limit. This contradicts the common expectation that a Grotthuss chain-like mechanism should enhance conductivity via cooperative, chain-directed transport. Instead, in bulk liquids, correlated motion and momentum conservation effects produce backflow that reduces net charge transport, similar to observations in ionic liquids. AIMD reveals a mechanistic picture where sub-ps sequences of proton hop events occur along hydrogen bonds, interspersed with multi-ps quiescent periods while the hydrogen bond network reorganizes; occasional large-angle OH reorientation breaks and reforms hydrogen bonds, enabling escape from local cages. The similarity of behavior in PA and PA85 indicates that adding water lowers viscosity and boosts conductivity but still via short proton transfers rather than vehicular H3O+ diffusion.

This study provides the first direct experimental evidence that proton transport in bulk phosphoric acid and its 85 wt% aqueous solution proceeds via short proton jumps (~0.5–0.7 Å) between hydrogen-bonded oxygen atoms, confirming structural diffusion as the dominant mechanism. Multimodal agreement between BDS, QENS, and AIMD establishes the jump length and timescales and shows that proton hopping dynamics govern the measured conductivity. Crucially, proton–proton correlations are anticorrelated (H−1<1), which suppresses conductivity, indicating that the anticipated Grotthuss-like enhancement via chain-like cooperative motion does not materialize in bulk liquids. These insights refine the mechanistic understanding of proton transport in strong proton conductors and suggest that to realize Grotthuss-like enhancement, one may need to consider confined systems or engineered environments that mitigate anticorrelations and momentum backflow. Potential future directions include: probing confinement or one-dimensional channels to promote directional proton chains; exploring chemical modifications that tune hydrogen-bond network dynamics and OH reorientation rates; extending QENS to broader energy/momentum windows and temperatures; and longer, larger-scale AIMD or path-integral simulations to capture quantum nuclear effects and rare-event pathways.

- BDS identifies the conductivity relaxation time but does not directly measure proton jump lengths; length estimates rely on combining with NMR diffusivities and model assumptions (e.g., temperature-independent rearrangement length). - QENS-derived jump lengths depend on the chosen jump-diffusion model and fitting (Cole–Davidson lineshape, Singwi–Sjolander model), though consistency with NMR and AIMD mitigates this. - AIMD simulations are limited in time and length scales (~60 ps, tens of molecules) and employed elevated temperatures, deuterium masses for hydrogens, and specific DFT functionals/pseudopotentials; while these choices enhance sampling, they may influence detailed dynamics. - Earlier neutron studies’ limited energy windows underscore sensitivity to instrumental range; although the present work used extended windows, ultra-fast or rare events beyond the measured window could still be underrepresented. - Generalization to other proton-conducting liquids or solids requires caution; conclusions about the impossibility of Grotthuss-like enhancement pertain to bulk liquids where ionic correlations reduce conductivity.