A multi-scale mathematical model, which accounts for mass transport on the crystal and agglomerate length-scales, is used to investigate the electrochemical performance of lithium-magnetite electrochemical cells. Experimental discharge and voltage recovery data are compared to three sets of simulations, which incorporate crystal-only, agglomerate-only, or multi-scale transport effects. Mass transport diffusion coefficients are determined by fitting the simulated voltage recovery times to experimental data. In addition, a further extension of the multi-scale model is proposed which accounts for the impact of agglomerate size distributions on electrochemical performance. The results of the study indicate that, depending on the crystal size, the low utilization of the active material is caused by transport limitations on the agglomerate and/or crystal length-scales. For electrodes composed of small crystals (6 and 8 nm diameters), it is concluded that the transport limitations in the agglomerate are primarily responsible for the long voltage recovery times and low utilization of the active mass. In the electrodes composed of large crystals (32 nm diameter), the slow voltage recovery is attributed to transport limitations on both the agglomerate and crystal length-scales. Large increases in the use of distributed and intermittent energy sources (i.e., wind and solar) have increased the need for cost effective, reliable, and efficient energy storage technologies.1 To address these needs, significant research efforts have focused on the development of next generation materials for secondary batteries, which can provide inexpensive and long lasting energy storage solutions.2-4 In particular, considerable work has focused on the advancement of magnetite (Fe 3 O 4 ) as an electrode in lithium-ion batteries due to its high theoretical capacity (926 mAh g −1 ), low cost and safety (non-toxic). 5-14Despite these advantages, one of the major challenges limiting the advancement of magnetite electrodes is a considerable difference between the maximum, theoretical capacity and the observed, experimental capacity of the active material. This difference increases the anticipated cost of magnetite batteries because it requires the electrodes to be overdesigned with excess amounts of active material. The difference between the theoretical and experimental capacity is related to the close-packed inverse spinel structure of Fe 3 O 4 , which restricts the transport of lithium in the material. To address this issue, several authors have synthesized Fe 3 O 4 nano-crystallites in attempts to minimize the path length for ion transport.9-14 The smaller path length increases the utilization of the active material by making it possible for ions to penetrate to the center of the crystals, especially at high rates of discharge. Electrodes fabricated with nano-crystalline magnetite have shown significant improvement in capacity; however, the theoretical capacity has still proven difficult to obtain.11 Further improvements in capacity may requir...

The mass transport processes occurring within magnetite electrodes during discharge and voltage recovery are investigated using a combined experimental and modeling approach. Voltage recovery data are analyzed through a comparison of the mass transport time-constants associated with different length-scales within the electrode. The long voltage recovery times can be hypothesized to result from the relaxation of concentration profiles on the mesoscale, which consists of the agglomerate and crystallite length-scales. The hypothesis was tested through the development of a multi-scale mathematical model, which showed good agreement with experimental data.

The whole versus the sum of its parts; contributions of nanoscale iron-containing materials to the bulk electrochemistry of composite electrodes.