Distinct roles of fast, slow, and unobservable relaxation regimes controlling proton transport barriers in lanthanide metal–organic coordination polymers featuring hexameric water clusters

Abstract

Understanding proton conduction at the microscopic level requires going beyond static crystallographic descriptions to capture the dynamic behavior of hydrogen-bonded networks. However, most existing techniques probe only limited or discrete frequency windows, preventing a continuous view of the molecular motions governing proton transport in solids. Herein, three praseodymium-based coordination polymers featuring distinct hexameric water clusters—{[Pr(pda)(H₂O)₄Ce(pda)₂(H₂pda)]·7H₂O}_n (Pr-Ce-H₂pda-H₂O, H₂pda = 2,6-pyridinedicarboxylic acid), {[Pr(pda)(Hpda)(H₂O)₂]·4H₂O}_n (Pr-Hpda-H₂O) and {[Pr₂(pda)₃(H₂O)₃]·H₂O}_n (Pr-pda-H₂O)—are employed as model systems to elucidate the relationship between hydrogen-bonded network dynamics and proton transport. By combining proton conductivity measurements with broadband dielectric spectroscopy, we establish a direct correlation between collective dielectric relaxation of water clusters and proton-transfer activation barriers within the same temperature range. The results reveal that proton conduction is governed by a critical kinetic balance between hydrogen-bond network rearrangement capability and pathway continuity. Moderately slow relaxation of hydrogen-bonded networks facilitates O–H bond reformation and hydrogen-bond reorientation, thereby lowering the activation energy for proton transfer, whereas excessively fast relaxation disrupts network continuity and hinders proton hopping, leading to increased activation barriers. In contrast, the absence of observable relaxation reflects a largely static hydrogen-bonded network, which lacks the dynamic adaptability required for optimized proton transport and thus exhibits intermediate activation energies. Furthermore, the necessity of segmented fitting for the proton-conduction activation energy in Pr-Hpda-H₂O directly motivates a re-examination of the applicability of the Grotthuss mechanism in solid-state systems. These findings demonstrate that proton conduction in the solid state arises not solely from static structural pathways, but from an optimal interplay between hydrogen-bond network topology and dynamic reorganization. This work provides a dynamic framework for understanding proton-conduction mechanisms and offers new guidance for the rational design of advanced proton-conducting materials.