The speed of sound in a medium provides information on its compressibility, and can therefore be used to investigate the properties of the fluid within a porous material. Ultrasonic experiments carried out during an adsorption measurement show that below saturation, the fluid compressibility is affected by Laplace pressure in the pores [1,2]. This effect has been recently confirmed by calculations based on macroscopic thermodynamics and classical density functional theory . Additionally, these calculations predicted that compressibility of the fluid confined in the pore linearly decreases with the decrease of the pore size. Such a simple relation can provide a basis for calculation of pore sizes based on measurements of compressibility of the confined fluid. However, these results are based on macroscopic theories and therefore may not apply to pores below several nanometers in size.
Here we perform grand-canonical Monte Carlo (GCMC) simulations to calculate the compressibility of Lennard-Jones argon in silica pores from the fluctuations of number of particles. We confirm the linear relation from  for the pore sizes above 2.5 nm, but for smaller pores conventional GCMC simulations are inefficient, and fail to give a normal distribution for the number of particles. We therefore use transition-matrix Monte Carlo simulations  to calculate compressibility of the fluid in micropores. Our results provide a theoretical framework for determination of pore sizes from ultrasonic experiments on fluid saturated samples.
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2. Schappert, K. & Pelster, R. Influence of the Laplace pressure on the elasticity of argon in nanopores EPL, 2014, 105, 56001
3. Gor, G. Y. Adsorption Stress Changes the Elasticity of Liquid Argon Confined in a Nanopore Langmuir, 2014, 30, 13564-13569
4. Siderius, D. W. & Shen, V. K. Use of the grand canonical transition-matrix monte carlo method to model gas adsorption in porous materials J. Phys. Chem. C, 2013, 117, 5861-5872