Efficient proton transport is paramount in numerous biological and technological applications, including fuel cells, batteries, and biological systems. Two primary mechanisms govern proton transport: the vehicular mechanism, where a proton moves attached to a molecule, and the structural diffusion mechanism, where protons transfer between molecules within a hydrogen bond network. The latter is significantly more efficient as it doesn't require the movement of entire molecules. The Grotthuss mechanism, a specific type of structural diffusion proposed over two centuries ago, posits a collective, chain-like proton transfer along hydrogen-bonded networks. This mechanism, if realized, would lead to exceptionally fast charge transport. However, despite extensive research, direct experimental observation of the Grotthuss mechanism in bulk liquids remains elusive. Many studies incorrectly attribute low energy barriers in ionic conductivity to a Grotthuss mechanism, failing to distinguish it from the vehicular mechanism which can also exhibit low activation energy. This ambiguity necessitates direct experimental verification. Phosphoric acid (PA) provides an ideal system for studying bulk proton transport due to its exceptionally high intrinsic proton conductivity. NMR studies show much faster proton than phosphorus diffusion, indicative of proton transfer dominance. The high conductivity persists even below the glass transition temperature, suggesting proton mobility unaffected by frozen molecular motion. Further supporting this hypothesis is the observed substantial isotope effect upon hydrogen/deuterium substitution and computational findings indicating correlated proton transfer along short chains of PA molecules. Despite these suggestive findings, direct experimental evidence of structural diffusion as the primary driver of high PA conductivity was still missing. Previous neutron scattering investigations detected proton displacements considerably larger than expected for proton transfer, hindering direct observation. This study aims to fill this knowledge gap by employing a multi-faceted approach.

Previous studies have explored proton transport mechanisms using various techniques. Theoretical works, such as molecular dynamics simulations, have suggested the existence of correlated proton transfer in systems like water and phosphoric acid, providing computational evidence for the Grotthuss mechanism. Experimental investigations have focused on measuring conductivity and diffusion coefficients using techniques such as nuclear magnetic resonance (NMR) and impedance spectroscopy. While these studies have provided indirect evidence for the Grotthuss mechanism, direct visualization of proton transfer events has remained elusive, primarily due to the limitations in spatial and temporal resolution of the experimental methods used. Neutron scattering, often used to probe atomic-scale dynamics, has previously been hampered by the inability to resolve the short proton jumps characteristic of the Grotthuss mechanism. The challenge has been to disentangle the Grotthuss mechanism from other transport mechanisms, such as vehicular transport, which may also exhibit fast conductivity.

This research employed a comprehensive, multi-technique approach to study proton transport in pure phosphoric acid (PA) and an 85% aqueous PA solution (PA85). The methodology integrated: 1. **Broadband Dielectric Spectroscopy (BDS):** This technique covered a broad frequency range (0.1 Hz to 30 GHz) to characterize the conductivity spectra, identifying the transition from frequency-dependent AC conductivity (protons trapped in cages) to frequency-independent DC conductivity (diffusive regime). The conductivity relaxation time, τ₀, was derived from the AC-DC crossover frequency, providing insights into the timescale of proton mobility. 2. **Depolarized Light Scattering (LS):** Used to determine the structural relaxation time, τLS, which characterizes the overall molecular rearrangement. The comparison of τLS and τ₀ enabled the assessment of whether proton transport was significantly faster than the structural relaxation of the matrix. 3. **Quasielastic Neutron Scattering (QENS):** QENS, focusing on incoherent scattering from hydrogen atoms, directly probed proton dynamics on atomic time and length scales. The Q-dependent broadening of the QENS spectra revealed the characteristic relaxation time (τQENS) and jump length (λ) for proton transfer. A Cole-Davidson distribution function was used to fit the susceptibility spectra obtained from QENS. The energy transfer window used in this study was extended compared to previous QENS studies of PA to capture the faster proton transfer events. 4. **Ab initio Molecular Dynamics (AIMD) simulations:** AIMD simulations were performed to understand the molecular-level details of proton transport. The simulations enabled the calculation of the self-intermediate scattering function (ISF) of protons, providing information about proton dynamics comparable to QENS but over a much wider Q range. The trajectories from the simulations were analyzed to identify proton jumps and their characteristics. The simulations were conducted for both pure PA and PA85, using the CPMD code with appropriate pseudopotentials and exchange-correlation functional. The radial distribution function (RDF) was also calculated to determine the spatial distribution of protons and oxygen atoms.

The combined analysis of BDS, LS, QENS, and AIMD data revealed several key findings: 1. **Short Proton Jumps:** Proton jumps were surprisingly short (0.5-0.7 Å), substantially smaller than typical ion jump lengths in ionic liquids and consistent with the equilibrium distance of proton transfer between PA molecules determined by previous simulations. This short jump length is a hallmark of the Grotthuss mechanism. 2. **Correlation Effects:** Proton jumps were found to be correlated. However, these correlations did not enhance conductivity as typically expected for a Grotthuss mechanism; instead, they led to a *reduction* in conductivity. The inverse Haven ratio (H⁻¹) was less than 1, indicating a negative contribution from distinct ion correlations. 3. **Dominant Structural Diffusion:** The conductivity relaxation time (τ₀) from BDS and the characteristic relaxation time from QENS (τQENS) were in excellent agreement, and both were significantly faster than the structural relaxation time (τLS) from LS. This confirms the dominance of structural diffusion (proton transfer) over vehicular transport in both pure PA and PA85. 4. **Mechanism of Proton Transfer:** AIMD simulations revealed a detailed molecular mechanism involving short proton hops between oxygen atoms, often between the same pair. Longer jumps, associated with OH bond rotation and hydrogen bond reorganization, were much less frequent. The AIMD analysis validated the short jump length and stretched exponential dynamics observed in QENS. 5. **Suppression of Conductivity:** The negative distinct proton-proton correlations, determined from the AIMD simulations, led to a decrease in conductivity (H⁻¹ < 1), contrasting with the anticipated enhancement in the Grotthuss mechanism. This finding indicates that the expected enhancement of conductivity is not achievable in bulk liquids due to the presence of always negative ionic correlations. 6. **Role of Water:** The similarity in the observed proton transport behavior between pure PA and PA85 indicates that proton transfer is the dominant mechanism in PA85 as well. However, the water molecules enhance proton diffusion compared to pure PA by reducing the viscosity of the system.

The results directly demonstrate that proton transport in both pure and aqueous phosphoric acid is dominated by short-range proton jumps between oxygen atoms involved in hydrogen bonding. The observation of correlated jumps, but with a decrease in conductivity, challenges the classical notion of the Grotthuss mechanism as necessarily implying conductivity enhancement. The negative correlation between proton displacements likely arises from momentum conservation effects, similar to those observed in ionic liquids. The remarkably short jump lengths observed support a picture of concerted proton transfer events rather than a simple, uncorrelated hopping between molecules. The shorter jump lengths in PA85 than in neat PA suggest that water may act as a facilitator, enhancing the ease of proton transfer. The study's results significantly impact our understanding of proton conductivity in bulk liquids. The findings suggest that the conventional interpretation of the Grotthuss mechanism, expecting conductivity enhancement from correlated proton transfer, may not hold true in many systems. This necessitates a reassessment of models for proton transport in bulk liquids.

This work presents the first experimental observation of short proton jumps between molecules in bulk phosphoric acid, demonstrating the dominance of structural diffusion in proton transport. While correlated proton jumps were observed, these correlations surprisingly suppressed conductivity, contradicting the traditional Grotthuss mechanism expectation. The findings highlight the limitations of relying solely on low energy barriers as indicators of the Grotthuss mechanism. Further research could explore the role of specific molecular structures and interactions in influencing the correlation effects and examine other highly proton-conducting systems to determine the generality of this observation. The study’s insights can potentially lead to better design strategies for electrochemical devices and facilitate improved understanding of proton transport in biological systems.

The study primarily focused on phosphoric acid and its aqueous solution. The extent to which these findings generalize to other proton-conducting systems requires further investigation. While the AIMD simulations provided valuable insights into molecular mechanisms, the simulations were performed at elevated temperatures to enhance proton dynamics, potentially affecting some aspects of the observed behavior. The accuracy of the estimated jump lengths depends somewhat on the theoretical models used to fit the experimental data.