Voltage-Relaxation GITT and Reverse Monte Carlo to Determine Lithium Diffusion and Distribution in TiO 2 and Highly-Ordered Nanoporous Hard Carbons

Amorphous hard carbons (AHCs) and metal oxides such as TiO 2  are of interest in applications for energy storage including pseudo/super-capacitors and lithium-ion batteries. We present measurements of lithium diffusion and distribution in anatase TiO 2  and several ordered AHCs prepared by soft/hard-templating techniques, some with capacities > 800 mAh/g. The investigated AHCs have surface areas between 60–937 m 2 /g and pore volumes between 0.04–1.01 cc/g. Li-diffusion was measured using two complimentary techniques (1) Galvanostatic Intermittent Titration Technique (GITT), and (2) a stretched exponential to investigate the voltage-relaxation (VR) GITT curve. VR-GITT provides two parameters related to (i) the geometry through which the diffusion is occurring, and (ii) a time scale yielding the diffusion constant with knowledge of an appropriate length scale. Both methods find diffusion constants in very good agreement with each other. Most importantly, the VR-GITT fitting parameters serve as a distinctive characterization tool and are able to distinguish between AHCs with different pore geometries and synthesis techniques. Further analysis of the VR curves was performed by numerical integration of the diffusion equation and reverse Monte Carlo simulated annealing to investigate the Li density profile in both TiO 2  and the carbons, and suggest that lithium may plate nanopores of AHCs.