Empirical Relationship between Relative Electrical Conductivity and Relative Density of the Al-Foam Fabricated through Pressure Assisted Sintering/Dissolution Process

Graph Theory Design of 3D Printed Conductive Lattice Electrodes

“…Figure 2c also provides a direct comparison between these engineered, periodic 3D lattices’ conductivity and the conductivity of a random open cell metallic foam measured experimentally. [ 24–26 ] At low relative densities, our engineered periodic solid lattices exceed the conductivity of random foams [ 24–26 ] by up to 5×. Because the periodic structure of our lattices is more uniform, current can be conducted isotropically even at low relative densities.…”

“…c) Graph‐theory based calculations of electronic conductivity of engineered 3D solid lattices, normalized by the conductivity of the bulk material, vs. relative density for octet, cubic, diamond, BCC, and kelvin lattices compared with experimentally measured conductivity of a random open cell metal foam. [ 24–26 ]…”

“…The conductivity is observed to approximately scale with the square root of the relative density of the lattice (a power law fit indicates an exponent ≈0.57) because only the surface conducts current. More complex structures such [24][25][26] as the BCC and octet lattices generally provide the highest conductivity for coated lattices, with the overall trend showing elevated conductivity for lattices with higher surface area per volume that provide more parallel pathways for conduction, as shown in Figure 2b. This scaling exhibits an interesting contrast to solid lattices formed from a structural conducting material (Figure 2c), which favor unit cells with fewer internal cross-bracing elements that do not directly aid conduction.…”

“…b) Graph-theory based calculations of electronic conductivity of engineered 3D coated lattices, normalized by the conductivity of the coating material, vs. relative density for octet, cubic, diamond, BCC, and kelvin lattice structures. c) Graph-theory based calculations of electronic conductivity of engineered 3D solid lattices, normalized by the conductivity of the bulk material, vs. relative density for octet, cubic, diamond, BCC, and kelvin lattices compared with experimentally measured conductivity of a random open cell metal foam [24][25][26].…”