Requirements to Determine the Average Pore Size of Nanoporous Media Using Ultrasound

Liquids in nanoporous media are exposed to an adsorption-induced pressure, a consequence of the interaction with the pore surface. The smaller the pore diameter, d _P, the higher the pressure at saturation and thus the bulk modulus of the confined liquid. Therefore, it has been proposed to use ultrasonic measurements on saturated nanoporous media for the determination of the average pore size. Here, we discuss the requirements for such an analysis. Although predictions for the size-dependent pore pressure and the liquid's modulus, K ^iso(d _P), are based on isothermal simulations, an experimentalist studying the propagation of ultrasonic waves determines adiabatic moduli, K ^ad(d _P). We show that the quantity relating adiabatic and isothermal moduli, the heat capacity ratio γ = c _p/c _v = K ^ad/K ^iso, exhibits a strong pressure dependence for many bulk liquids. In nanopores, this translates into a size-dependent γ(d _P), provided the confinement does not alter the heat capacity ratio. Disregarding this effect in the analysis of ultrasonic data would yield an underestimate of the isothermal modulus and thus an overestimate of the average pore size. For a correct analysis, an experimentalist thus needs to know the size dependence of three quantities: the isothermal modulus, adsorption-induced pressure, and heat capacity ratio.