Graph Theory Design of 3D Printed Conductive Lattice Electrodes

3D printing has the promising capability to fabricate engineered lattice structures with broadly tunable surface area and optimal geometries for maximizing structural and functional properties. This study characterizes the electrical conductivity of 3D lattices of varying size, structure, and porosity to guide additively manufactured electrode design in energy storage devices. Graph theory-based calculations and experiments comparing the conductivity of multiple strut lattice structures and illustrating the scaling laws governing architectures with either coated or solid conductive struts are presented. The lightweight lattices explored here show higher conductivity than random foams that lack a periodic mesostructure. It is experimentally demonstrated that the 3D lattice type influences the specific capacity when employed in supercapacitors, outperforming 2D supercapacitor counterparts, and other 3D printed electrodes while allowing for optimization of the design for different energy storage applications. Additionally, it is shown that tuning the physical structure of the lattices allows for precise control over the electrical response to mechanical loading, as confirmed through experimental measurements. The lattice structure programs the electrodes' mechanical stiffness, with higher relative density samples showing higher Young's modulus. These results can serve to guide the design of 3D printed electrodes in a variety of electrochemical and electromechanical device applications.