Evaluating the Pressure Dependence of the Longitudinal Modulus of an Adsorbate in Nanopores Using Ultrasound: A Novel Procedure Taking the Effect of Emptying Pore Ends into Account

Abstract

The determination of the elastic properties of nanoconfined substances from measured effective quantities is a challenging task. In this article, we explore the possibilities to determine an adsorbate's elastic modulus and its pressure dependence using ultrasound. As a model system, we study the isothermal adsorption and desorption of liquid argon in nanoporous glass with an average pore diameter of d P = 25.6 nm. The longitudinal modulus of an adsorbate, β ads , is usually determined by means of an effective medium equation using the average modulus of the filled porous system, c, with c l being the measured velocity of longitudinal ultrasonic pulses propagating through the sample and ρ the average density. However, in the so-called plateau region of a sorption isotherm, curved liquid−vapor menisci and empty pore ends are present at the outer surface of the sample, i.e., the filling of the pores and the density vary within the sample. With the analysis of our ultrasonic measurements, we show that the determination of the pressure dependence of an adsorbate's modulus requires the careful consideration of the accurate geometrical arrangement of the adsorbate in the volume, where the ultrasonic pulses propagate. Thereby, we have developed a method for the correct determination of the pressure dependence of an adsorbate's modulus that can be applied to other porous systems. Thus, our findings will have an immediate impact on the interpretation and analysis of ultrasonic studies on elastic properties of nanoconfined materials.