The electrical. (ionic) conductivity of polymer electrolytes for lithi
um-polymer cells increases greatly with increasing temperature (in con
trast to the thermal conductivity). This paper examines, by both a Lin
ear perturbation analysis and by numerical calculation, an instability
that could arise from this temperature dependence. The instability is
one where a local perturbation to a higher temperature results in hig
her electrical conductivity and therefore the passage of more current
in this region with an attendant increase in heat generation. If this
excess heat generation cannot be conduced into adjacent cooler regions
, instability (growth of the perturbation) results. The numerical calc
ulations were carried out for constant potential drop across the elect
rolyte, for constant mean current density, and for constant mean power
discharge schedules. The calculations suggest that this instability i
s unlikely for small batteries (of the order of 0.1 m in the direction
s parallel to the electrodes) but may occur for larger batteries such
as those intended for use in an electric vehicle. However, the growth
rates of the perturbations do not appear to be high. Changes in cell m
aterials /thickness have little effect on the instability. The Linear
perturbation analysis is in approximate agreement with the numerical c
alculations.