Influence of the Laplace pressure on the elasticity of argon in nanopores

Abstract

At the beginning of an isothermal desorption process with the adsorbate argon, the nanopores of the porous glass sample remain virtually completely filled over a certain pressure range. A reduction of the external pressure p below the bulk vapour pressure of argon, p0, results, however, in the formation of concave menisci at the pore ends. The related decrease of the radius of curvature causes an increase of the negative Laplace pressure. This occurance is known to provoke a contraction of porous samples. Here we show that the Laplace pressure also influences the elastic properties of the filled porous sample. A decrease of the radius of curvature at the pore ends becomes noticeable in a decrease of the effective longitudinal modulus. The analysis of our ultrasonic measurements reveals that this decrease of the effective longitudinal modulus originates in a reduction of the longitudinal modulus of the adsorbate.

Relation between pore size and the compressibility of a confined fluid

“…4 based on GC-TMMC simulations (lines) for 2.5 nm, 3 nm, 4 nm and 5 nm pores [44]. Our calculations show that the dependence of K T on log( p/p 0 ) is nearly linear, which is in agreement with the previous DFT calculations [8] and experimental observations [5, 7]. …”

“…Such experiments for argon and hexane in the pores of Vycor glass show that the fluid compressibility is affected by the Laplace pressure in the pores [4–7]. This effect has been recently confirmed by calculations based on macroscopic thermodynamics and classical density functional theory (DFT) [8].…”

Modulus–pressure equation for confined fluids

“…First we derived the elastic modulus from the average density of confined argon, predicted by classical density functional theory (cDFT) [29]. Our calculations reproduced the experimentally observed linear relation between the modulus and the solvation pressure (also referred to as the adsorption stress), and the slope in this relation was close to the slope reported in ultrasonic experiments [18]. Those calculations, however, required use of macroscopic Gibbs-Duhem equation, whose validity is not obvious for a confined system.…”

“…Experiments showed that in contrast with the constant shear modulus, the longitudinal modulus of the saturated sample M c is several percent higher than the longitudinal modulus of the dry material M 0 [18]. Moreover, for the argon-filled pores the change of the longitudinal modulus of the sample Δ M = M c – M 0 is a function of equilibrium gas pressure p .…”

Adsorption-induced deformation of nanoporous materials—A review

“…This change was not only shown by Monte Carlo simulations 132 but also measured in ultrasonic experiments. 133,134 In particular, it was shown that the change in the elastic modulus of the adsorbed fluid is linearly related to the adsorption stress in the pores. 135,136 E. Surface stress approach…”