A microscopic theory for cation diffusion in polymer electrolytes is presented. Based on a thorough analysis of molecular dynamics simulations on poly(ethylene) oxide with ${\mathrm{LiBF}}_4$, the mechanisms of cation dynamics are characterized. Cation jumps between polymer chains can be identified as renewal processes. This allows us to obtain an explicit expression for the lithium ion diffusion constant $D_{\mathrm{Li}}$ by invoking polymer-specific properties such as the Rouse dynamics. This extends previous phenomenological and numerical approaches. In particular, the chain length dependence of $D_{\mathrm{Li}}$ can be predicted and compared with experimental data. This dependence can be fully understood without referring to entanglement effects.

• Received 8 February 2007

DOI:https://doi.org/10.1103/PhysRevLett.98.227802