  We numerically investigate the dynamic heterogeneity and its length scale
found in the coarse-grained ionic liquid model systems. In our ionic liquid
model systems, cations are modeled as dimers with positive charge, while anions
are modeled as monomers with negative charge, respectively. To study the effect
of the charge distributions on the cations, two ionic liquid models with
different charge distributions are used and the model with neutral charge is
also considered as a counterpart. To reveal the heterogeneous dynamics in the
model systems, we examine spatial distributions of displacement and time
distributions of exchange and persistence times. All the models show
significant increase of the dynamic heterogeneity as the temperature is
lowered. The dynamic heterogeneity is quantified via the well-known four-point
susceptibility which measures the fluctuation of a time correlation function.
The dynamic correlation length is calculated by fitting the dynamic structure
factor, S4(k,t), with Ornstein-Zernike form at the time scale at which the
dynamic heterogeneity reaches the maximum value. Obtained time and length
scales exhibit a power law relation at the low temperatures, similar to various
supercooled liquid models. Especially, the charged model systems show unusual
crossover behaviors which are not observed in the uncharged model system. We
ascribe the crossover behavior to the enhanced cage effect caused by charges on
the particles.
