Evaluating the\nPressure Dependence of the Longitudinal\nModulus of an Adsorbate in Nanopores Using Ultrasound: A Novel Procedure\nTaking the Effect of Emptying Pore Ends into Account

The determination of the elastic properties of nanoconfined\nsubstances\nfrom measured effective quantities is a challenging task. In this\narticle, we explore the possibilities to determine an adsorbate’s\nelastic modulus and its pressure dependence using ultrasound. As a\nmodel system, we study the isothermal adsorption and desorption of\nliquid argon in nanoporous glass with an average pore diameter of <i>d</i><sub><i>P</i></sub> = 25.6 nm. The longitudinal\nmodulus of an adsorbate, β<sub><i>ads</i></sub>, is\nusually determined by means of an effective medium equation using\nthe average modulus of the filled porous system, βav=cl2ρ, with <i>c</i><sub><i>l</i></sub> being the measured velocity of longitudinal ultrasonic pulses\npropagating through the sample and ρ the average density. However,\nin the so-called plateau region of a sorption isotherm, curved liquid–vapor\nmenisci and empty pore ends are present at the outer surface of the\nsample, i.e., the filling of the pores and the density vary within\nthe sample. With the analysis of our ultrasonic measurements, we show\nthat the determination of the pressure dependence of an adsorbate’s\nmodulus requires the careful consideration of the accurate geometrical\narrangement of the adsorbate in the volume, where the ultrasonic pulses\npropagate. Thereby, we have developed a method for the correct determination\nof the pressure dependence of an adsorbate’s modulus that can\nbe applied to other porous systems. Thus, our findings will have an\nimmediate impact on the interpretation and analysis of ultrasonic\nstudies on elastic properties of nanoconfined materials.