  Glycerol acts as a natural cryoprotectant by depressing the temperature of
ice nucleation and slowing down the dynamics of water mixtures. In this work we
characterize dynamics -- diffusion, viscosity, and hydrogen-bond dynamics -- as
well as density anomaly and structure of water mixtures with 1\% to 50\% w/w
glycerol at low temperatures via molecular dynamics simulations using all-atom
and coarse-grained models. Simulations reveal distinct violations of the
Stokes-Einsten relation in the low temperature regime for water and glycerol.
Deviations are positive for water at all concentrations, and positive for
glycerol in very dilute solutions but turning negative in concentrated ones.
The all-atom and coarse-grained models reveal an unexpected crossover in the
dynamics of the 1% and 10 % w/w glycerol at the lowest simulated temperatures.
This crossover manifests in the diffusion coefficients of water and glycerol,
as well as in the viscosity and lifetime of hydrogen-bonds in water. We
interpret that the crossover originates on the opposing dependence with
glycerol concentration of the two factors controlling the solution's slow-down:
the increase in tetrahedrally coordinated water and the dynamics and clustering
of the glycerol molecules. We anticipate that this dynamic crossover will also
occur for solution of water with other polyols.
