Liquid inclusions in soft materials: Capillary effect, mechanical stiffening and enhanced electromechanical response

Abstract

Recent experiments and modeling appear to suggest that “small” liquid inclusions may significantly stiffen soft solids. Surface energy or capillary effects are considered responsible for this rather non-intuitive phenomenology. In this work, we develop a theoretical framework and construct a simple homogenization model that unambiguously explains this phenomenon. Our theoretical construct of capillary effects is specifically intended for soft matter and differs in the manner in which the classical Gurtin–Murdoch surface elasticity theory has been widely interpreted and used in the literature. We use the developed theory to elucidate several subtle aspects pertaining to the capillary phenomenon that may not be often appreciated; specifically in regards to the developments across different scientific communities. One such key aspect is the often missed connection between the concept of surface tension as understood in the fluids and materials science community and superficial elasticity of solid surfaces. While the purely mechanical effects underpinning liquid inclusions in soft solids are of significant interest in of themselves, we hypothesize that the interplay of capillary effect, electrostatics, soft solids and ionic liquid inclusions may offer prospects for designing soft materials that display an unusually large size-dependent electromechanical coupling. To emphasize this, we extend the capillary framework for soft solids to electrostatics and find that electrostrictive properties may be significantly altered. Due to a rather interesting confluence of two contradictory effects, the electrostrictive deformation is only marginally altered by capillarity. However, the soft solid’s maximum energy conversion capability may be enhanced by 75% or higher.