  We study the freezing kinetics of colloidal polycrystals made of micelles of
Pluronic F108, a thermosensitive copolymer, to which a small amount of silica
nanoparticles of size comparable to that of the micelles are added. We use
rheology and calorimetry to measure Tc, the crystallization temperature, and
find that Tc increases with the heating rate \dot{T} used to crystallize the
sample. To rationalize our results, we first use viscosity measurements to
establish a linear mapping between temperature T and the effective volume
fraction, {\phi}, of the micelles, treated as hard spheres. Next, we reproduce
the experimental \dot{T} dependence of the crystallization temperature with
numerical calculations based on standard models for the nucleation and growth
of hard spheres crystals, classical nucleation theory and the
Johnson-Mehl-Avrami-Kolmogorov theory. The models have been adapted to account
for the peculiarities of our experiments: the presence of nanoparticles that
are expelled in the grain boundaries, and the steady increase of T and hence
{\phi} during the experiment. We moreover show that the polycrystal grain size
obtained from the calculations is in good agreement with light microscopy data.
Finally, we find that the {\phi} dependence of the nucleation rate for the
micellar polycrystal is in remarkable quantitative agreement with that found in
previous experiments on colloidal hard spheres. These results suggests that
deep analogies exist between hard-sphere colloidal crystals and Pluronics
micellar crystals, in spite of the difference in particle softness. More
generally, our results demonstrate that crystallization processes can be
quantitatively probed using standard rheometry.
