Soft wetting and the Shuttleworth effect, at the crossroads between thermodynamics and mechanics

Extremely compliant elastic materials, such as thin membranes or soft gels, can be deformed when wetted by a liquid drop. It is commonly assumed that the solid capillarity in “soft wetting” can be treated in the same manner as liquid surface tension. However, the physical chemistry of a solid interface is itself affected by any distortion with respect to the elastic reference state. This gives rise to phenomena that have no counterpart in liquids: the mechanical surface stress is different from the excess free energy in surface. Here we point out some striking consequences of this “Shuttleworth effect” in the context of wetting on deformable substrates, such as the appearance of elastic singularities and unconventional capillary forces. We provide a synthesis between different viewpoints on soft wetting (microscopic and macroscopic, mechanics and thermodynamics), and point out key open issues in the field. perspective Copyright c © EPLA, 2016 The canonical example of elasto-capillarity consists of a liquid drop in contact with a highly deformable elastic material [1]. The forces of surface tension of the liquid can induce wrinkles on a thin membrane [2–4], bundling of slender rods [5–7], capillary origami [8–11], and the slowing-down of droplets moving over soft gels [12–16]. These phenomena play a role in a broad variety of applications, with many examples in the natural world and in technology. The equilibrium shapes of the drop and the elastic solid, and, therefore, also the contact angles, emerge from a balance between capillarity and elasticity [1,4,17–35]. Elastic interfaces exhibit an intriguing feature that is not present for liquid interfaces: the excess mechanical tension inside the interfacial region, referred to as the surface stress Υ, is in general different from the surface free energy γ. This was pointed out already by Shuttleworth [36] and studied in detail in crystals [37], with consequences in phenomena such as elastic instabilities [37], surface segregation [38], surface adsorption [39,40], surface reconstruction [41,42], nanostructuration [43] or Fig. 1: (Colour online) Perspectives on the Shuttleworth effect. Thermodynamics involves free-energy minimisation, while the language of mechanics is expressed in terms of force balance. Macroscopically, these respectively involve the free energy per unit area γ, and the interfacial force per unit length Υ. Microscopic equivalents, describing the molecular scale are given by density functional theory (DFT) and molecular dynamics (MD). Reprinted with permission from Cao Z. and Dobrynin A. V., Macromolecules, 48 (2015) 443. Copyright (2015) American Chemical Society.