A double inclusion model for liquid metal polymer composites

Liquid metal elastomer composites have gained significant attention in advanced technologies including wearable electronics, soft robotics, and human-computer interactions. This is due to the combination of metallic conductivity and fluidic properties of liquid metal (LM) inclusions in addition to their facile fabrication process. With the emergence of gallium-based liquid metal nanocomposites and advances in synthesis and integration of LM nanoparticles in a variety of polymer matrices, there is a pressing need for a materials design tool to accelerate the development of these multifunctional composites. Here, we introduce a double inclusion (DI) model capable of predicting the properties of polymer composites with core-shell liquid metal droplets. The sizedependent elasticity of LM inclusions is modeled by considering the solid gallium oxide interphase between the liquid metal core and the solid polymer matrix. As the size of inclusions reduces from tens of microns to tens of nanometers, the role of the oxide interface (shell) becomes more dominant. The results of the DI model show excellent agreement with finite element analysis and experimental results for a wide range of droplet sizes and volume fractions. This model provides a design framework for the synthesis of LM composites with tailored multifunctional properties.