Fractal mesoporosity and proton transport in WO3 xerogels

Abstract

Mesoporous WO₃ xerogels with mixed proton–electron conductance were prepared by a non-hydrolytic sol–gel route based on alcoholysis of WCl₆ solutions. By varying the alkyl-chain length and carbocation stability of the alcohol reagent, oxides with a widely varying mesoporous structure were obtained. These materials were systematically analysed in terms of their surface fractal dimension as derived from nitrogen-adsorption isotherms according to the Frenkel–Halsey–Hill equation. The fractal dimension is shown to be a key parameter in controlling and tailoring the mesoporous properties of these xerogels: specific surface area (56–184 m² g⁻¹), pore volume (0.06–0.35 cm³ g⁻¹) and average pore diameter (3.2–8.6 nm). Resistance of the mesoporous structure to thermal conditions was also found to be correlated with the fractal dimension. Using electrical-impedance spectroscopy, d.c. proton conductivities as high as 4.7 × 10⁻² S cm⁻¹ were measured at 25 °C and 100% relative humidity. Proton-dynamics relaxation times and Cole–Cole exponents, as determined by fitting impedance data to a proper model circuit, are shown to be related to the fractal dimension. Importantly, a sharp transition from a fast- to a slow-transport regime was observed as this parameter increases beyond a critical threshold. It is discussed how the fractal dimension is crucial to understand proton transport as it relates to the porous structure.