Ultrasonic cryoporometry: determining pore-size distributions from acoustic measurements

The standard experimental approaches for determining pore size distribution (PSD) are gas adsorption (e.g., nitrogen porosimetry) and mercury intrusion porosimetry. While widely used, these methods have limitations: gas adsorption experiments often require high-temperature heating and are less sensitive in macropores, whereas mercury intrusion is destructive and involves hazardous materials. Therefore, there is always a demand for alternative methods for characterization of porous materials. Thermodynamics of fluids confined in nanopores depend on the pore size. In particular, both the capillary condensation pressure and the freezing/melting point are shifted relative to their bulk values due to confinement. Capillary condensation is the basis of gas adsorption porosimetry, while the melting/freezing temperature shift can also be used for PSD determination through the Gibbs—Thomson equation, which links the transition temperature to the pore radius. This is the main idea of thermoporometric methods such as differential scanning calorimetry (DSC) based thermoporometry, and nuclear magnetic resonance (NMR) cryoporometry. Both techniques, however, typically require complex and costly instrumentation. Ultrasonic measurements provide an alternative route to probe phase transitions in porous materials. In ultrasonic pulse-transmission technique, speed of an ultrasonic wave depends on the density and elastic moduli of the composite system. When a fluid confined within nanopores freezes, the shear modulus of the composite increases, and the difference between the liquid-like and solid-like states reflects the contribution of the confined phase to the overall modulus. In this work, we analyze literature ultrasonic data for fluids (heptane, nonane, argon) confined in nanoporous media using a phenomenological model by Denoyel and Pellenq for phase transitions under confinement. We demonstrate that the temperature-dependent ultrasonic response provides information on the fraction of solidified fluid and, consequently, used to extract the pore size distribution. Our results suggest that ultrasonic data on porous materials can be used for determining PSD, providing an alternative to the methods based on NMR or DSC.