Elastocapillarity in nanopores: sorption strain from the actions of surface tension and surface stress

Adsorption-induced deformation of porous materials is the generation of strains in a solid due to its interaction with adsorbing fluids. The theoretical description of adsorption-induced deformation often relies on the so-called solvation pressure, the normal component of a pressure tensor in the liquid adsorbed in the pore. Recent measurements of adsorption-induced strains in two dimensions require a description that allows for the deformation to be anisotropic. Here, we present such a description. We refrain from using the solvation pressure concept and instead base the discussion on a phenomenological description of coupled mechanics and adsorption that has well-established links to continuum mechanics. We find that our approach captures all relevant features of anisotropic sorption strain; the approach thus provides a useful alternative to the solvation pressure concept. We derive analytical expressions for the stress-strain relations in a model porous material with an array of parallel channel-like pores of high aspect ratio (length/width). These relations include separate terms from the liquid pressure, from the surface stress at the liquid-solid interface, and from a spreading tension at the solid-liquid-vapor triple line. Surface stress and liquid pressure contribute to the strains along and normal to the pore axis in a qualitatively different manner. The underlying discussion of capillary forces sheds light on the variation of the surface stress during adsorption and capillary condensation.