**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 *p _{0}* results in a decrease of the adsorbed argon’s longitudinal modulus (cp. Fig. 1). The continuous decrease of

*β*can be explained by the simultaneous decrease of the deforming normal pressure

_{Ar,ads}*Δp*acting on the pore surface. One term contributing to

_{s}*Δp*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

_{s}*Δp*. 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

_{s}*p*, where

_{0}*Δp*takes its maximum value.

_{s}Now we have discovered that the measured change of elasticity reveals the normal pressure at saturation, *Δp _{s}(p=p_{0})=Δp_{s}^{sat}*. As we show in Fig. 2 there is a linear relation between the longitudinal modulus of the adsorbate

*β*and the deforming normal pressure

_{Ar,ads}*Δp*. When the normal pressure vanishes, i.e.

_{s}*Δp*=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,

_{s}*Δp*. This also gives access to the change of surface stress, (Δ

_{s}^{sat}*f*)

_{sat}, since

*Δp*= -(Δ

_{s}^{sat}*f*)

_{sat}/

*r*holds, where r ≈ 4 nm denotes the pore radius.

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 CO_{2}) 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.

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Images taken from Klaus Schappert and Rolf Pelster, J. Phys.: Condens. Matter 29, 06LT01 (2017),

© IOP Publishing. (Figure 1 was modified by the authors for this blog.)

Categories: Journal of Physics: Condensed Matter, JPhys+