Design criteria for nanostructured Li-ion batteries

Extensive experimental research has indicated that active/inactive nanocomposites are promising electrode materials for rechargeable Li-ion batteries. Nanocomposite anode materials allow for capacities between 900 and 4000 mAh g^-1 whereas graphitic anodes, which are currently being used by industry, allow for a much lower capacity of 372 mAh g^-1. By treating the active sites (which may be comprised of Si, Sn, Al, or Bi) as nanospheres embedded in an inert matrix, linear elastic fracture mechanics are employed in order to develop design criteria for these alternative battery systems, with respect to fracture that results from the large volume expansions that the active sites undergo upon Li-insertion. In particular, the present study: (i) predicts that smaller active site volume fractions are more stable; (ii) Griffith's criterion is used to estimate the crack radius at which cracking will stop; (iii) based on the ultimate tensile strength of the inactive matrix the critical crack length at which the electrode will fracture is calculated; (iv) a theoretical estimation is made for the size of the active sites that will not allow cracks to develop and hence fracture of the electrode will be prevented. Based on the above analysis, Si active sites allow for a greater anode lifetime and therefore are preferred over Sn, furthermore the formulation can be applied to determine the most appropriate matrix materials.