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Unique among traditional fillers, the metallically conductive liquid metal galinstan has emerged as an inherently deformable alternative for polymer composites. Galinstan exhibits high electrical conductivity with liquid-like flow, which sets it apart from the solid metals and ceramics typically used to impart electrical behavior to polymers. Upon exposure to atmospheric oxygen, galinstan forms a solid oxide shell that adds mechanical complexity when blended with polymers to create liquid metal polymer composites (LMPCs). This study investigates the mechanical behavior of LMPCs under tension, compression, and torsion as a function of LM droplet size and loading. Experimental analysis and computational modeling reveal distinct behaviors in LMPCs depending on the applied force and droplet characteristics that do not follow the classic composite models like Eshelby theory or more recent, updated versions thereof. Despite the large modulus difference between the LM and oxide shell, focusing exclusively on individual droplet mechanics overlooks the importance of surface energy dynamics within the system. By incorporating interfacial energy into a novel model, the origins of the LMPC mechanical response under deformation were illustrated. Our findings contribute to a broader understanding of composite materials with implications for soft robotics, where material response to various deformations is crucial for functionality. 

Polymeric materials that couple deformation and electrostatics have the potential for use in soft sensors and actuators with potential applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. In contrast to the mechanics of polymers that has been studied using statistical mechanics approaches for decades, the coupled response under deformation and electrical field has largely been modeled only phenomenologically at the continuum scale. In this work, we examine the physics of the coupled deformation and electrical response of an electrically-responsive polymer chain using statistical mechanics. We begin with a simple anisotropic model for the electrostatic dipole response to electric field of a single monomer, and use a separation of energy scales between the electrostatic field energy and the induced dipole field energy to reduce the nonlocal and infinite-dimensional statistical averaging to a simpler local finite-dimensional averaging. In this simplified setting, we derive the equations of the most likely monomer orientation density using the maximum term approximation, and a chain free energy is derived using this approximation. These equations are investigated numerically and the results provide insight into the physics of electro-mechanically coupled elastomer chains. Closed-form approximations are also developed in the limit of small electrical energy with respect to thermal energy; in the limit of small mechanical tension force acting on the chain; and using asymptotic matching for general chain conditions.