  In the present work, we employ broadband dielectric spectroscopy to study the
molecular dynamics of the prototypical glass former glycerol confined in two
microporous zeolitic imidazolate frameworks (ZIF-8 and ZIF-11) with
well-defined pore diameters of 1.16 and 1.46 nm, respectively. The spectra
reveal information on the modified alpha relaxation of the confined supercooled
liquid, whose temperature dependence exhibits clear deviations from the typical
super-Arrhenius temperature dependence of the bulk material, depending on
temperature and pore size. This allows assigning well-defined cooperativity
length scales of molecular motion to certain temperatures above the glass
transition. We relate these and previous results on glycerol confined in other
host systems to the temperature-dependent length scale deduced from nonlinear
dielectric measurements. The combined experimental data can be consistently
described by a critical divergence of this correlation length as expected
within theoretical approaches assuming that the glass transition is due to an
underlying phase transition.
