Simulation of local ion transport in lamellar block copolymer electrolytes based on electron micrographs

A method is presented to relate local morphology and ionic conductivity in a solid, lamellar block copolymer electrolyte for lithium batteries, by simulating conductivity through transmission electron micrographs. The electrolyte consists of polystyrene-block-poly(ethylene oxide) mixed with lithium bis(trifluoromethanesulfonyl) imide salt (SEO/LiTFSI), where the polystyrene phase is structural phase and the poly(ethylene oxide)/LiTFSI phase is ionically conductive. The electric potential distribution is simulated in binarized micrographs by solving the Laplace equation with constant potential boundary conditions. A morphology factor, f, is reported for each image by calculating the effective conductivity relative to a homogenous conductor. Images from two samples are examined, one annealed with large lamellar grains and one unannealed with small grains. The average value of f is 0.45 ± 0.04 for the annealed sample, and 0.37 ± 0.03 for the unannealed sample, both close to the value predicted by effective medium theory, 1/2. Simulated conductivities are compared to published experimental conductivities. The value of f_Unannealed/f_Annealed is 0.82 for simulations and 6.2 for experiments. Simulation results correspond well to predictions by effective medium theory but do not explain the experimental measurements. Observation of nanoscale morphology over length scales greater than the size of the micrographs (∼1 μm) may be required to explain the experimental results.