  Correlated anion and cation motion can significantly reduce the overall ion
conductivity in electrolytes versus the ideal conductivity calculated based on
the diffusion constants alone. Using coarse-grained molecular dynamics
simulations, we calculate conductivity and the degree of uncorrelated ion
motion in salt-doped homopolymers and block copolymers as a function of
concentration and interaction strengths. Calculating conductivity from ion
mobility under an applied electric field increases accuracy versus the typical
use of fluctuation dissipation relationships in equilibrium simulations. In
typical electrolytes, correlation in cation-anion motion is often expected to
be reduced at low ion concentrations. However, for these polymer electrolytes
with strong ion-polymer and ion-ion interactions, we find correlations are
increased at lower concentrations when other variables are held constant. We
show this phenomenon is related to the slower ion cluster relaxation rate at
low concentrations rather than the static spatial state of ion aggregation or
the fraction of free ions.
