  A microscopic theory for cation diffusion in polymer electrolytes is
presented. Based on a thorough analysis of molecular dynamics simulations on
PEO with LiBF$_4$ the mechanisms of cation dynamics are characterised. 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_{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_{Li} can be predicted and compared
with experimental data. This dependence can be fully understood without
referring to entanglement effects.
