Ultrasound measures surface stress in nanopores

By Lucy Smith on January 11, 2017

Ultrasound is a versatile technique to study the elastic behaviour of materials. In a recent Letter in Journal of Physics: Condensed Matter Klaus Schappert and Rolf Pelster have shown that changes of the longitudinal modulus during sorption of a substance in a nanoporous matrix reveal the adsorption-induced changes of surface stress. Below the authors of the study explain more about their research.

Surface and interfacial energies are key parameters for many adsorption phenomena, e.g. for the sorption-induced deformation of porous materials. Adsorbates in nanoporous solids exert a normal pressure on the pore walls, which leads to a deformation of the porous matrix. This effect is due to a change of the material’s surface stress, i.e. it is linked to the free energy per unit area necessary to
deform the pore walls.

For non-porous solids changes of surface stress are easily determined from the bending of a film or cantilever. For porous materials such a method is inappropriate and this raises the question of how a change of surface stress in consequence of adsorption can be measured experimentally. Now, we have developed an indirect method using ultrasonic waves, which supplies values that correspond to
theoretical predictions.

For our model system of argon in nanoporous glass a reduction of the vapour pressure p below the saturation vapour pressure p₀ results in a decrease of the adsorbed argon’s longitudinal modulus (cp. Fig. 1). The continuous decrease of β_Ar,ads can be explained by the simultaneous decrease of the deforming normal pressure Δp_s acting on the pore surface. One term contributing to Δp_s is the negative Laplace pressure due to the curved liquid-vapour interfaces at the pore ends (cp. Fig. 1). Lowering the vapour pressure leads to an increase of the curvature and thus to a decrease of the normal pressure Δp_s. But also the adsorbate is exposed to this pressure. Therefore, the longitudinal modulus of the adsorbate differs always slightly from the modulus of the bulk substance, in particular at the saturation vapour pressure p₀, where Δp_s takes its maximum value.

Fig. 1: Longitudinal modulus of adsorbed liquid argon,βAr,ads, at 86 K and 80 K as a function of the reduced pressure p/p0 (for full pores). A reduction of the vapour pressure p increases the curvature of the menisci at the pore ends (cp. schematic sketch).

Fig. 1: Longitudinal modulus of adsorbed liquid argon,β_Ar,ads, at 86 K and
80 K as a function of the reduced pressure p/p₀ (for full pores). A reduction of the vapour pressure p increases the curvature of the menisci at the pore ends (cp. schematic sketch).

Now we have discovered that the measured change of elasticity reveals the normal pressure at saturation, Δp_s(p=p₀)=Δp_s^sat. As we show in Fig. 2 there is a linear relation between the longitudinal modulus of the adsorbate β_Ar,ads and the deforming normal pressure Δp_s. When the normal pressure vanishes, i.e. Δp_s=0, we can expect the elastic behaviour of bulk argon. Consequently, a linear extrapolation of the longitudinal modulus of the adsorbed argon to the value for the longitudinal modulus of bulk argon yields the normal pressure at saturation, Δp_s^sat. This also gives access to the change of surface stress, (Δf)_sat, since Δp_s^sat= -(Δf)_sat/r holds, where r ≈ 4 nm denotes the pore radius.

Fig. 2: Dependence of the longitudinal modulus of adsorbed liquid argon, β_Ar,ads, on the pressure Δp_s – Δp_s^satat 86 K and 80 K. The points of intersection of the linear extrapolation with the horizontal lines (showing the bulk values of the longitudinal modulus at the respective temperatures) reveal the normal pressure at saturation, Δp_s^sat ≈ 15 MPa.

Thus, for nanoporous materials our experimental method offers the possibility to study adsorption-induced changes of surface stress from changes in the adsorbate’s elasticity. The application of our method on other porous systems, in particular on those that are considered as storage materials (e.g. for methane or CO₂) or for other technical applications, will help to gain a better understanding of the behaviour of such systems.

About the authors
Klaus Schappert is postdoctoral researcher in the Physics Department at the Universität des Saarlandes in Saarbrücken, Germany. He studies effects of adsorption in nanoporous materials and his current research focuses on influences of nanoconfinement on the elastic behaviour of adsorbed substances, on their phase behaviour, and on sorption-induced deformation.

Rolf Pelster is Professor for Experimental Physics and Didactics of Physics at the Universität des Saarlandes in Saarbrücken, Germany. His group specialises in the study of heterogeneous materials applying different techniques including dielectric spectroscopy, infrared spectroscopy, and ultrasonic measurements. More information can be found at http://www.uni-saarland.de/lehrstuhl/pelster.html.