  The origin of the dramatic changes in the behavior of liquids as they
approach their vitreous state - increases of many orders of magnitude in
transport properties and dynamic time scales - is a major unsolved problem in
condensed matter. These changes are accompanied by greater dynamic
heterogeneity, which refers to both spatial variation and spatial correlation
of molecular mobilities. The question is whether the changing dynamics is
coupled to this heterogeneity; that is, does the latter cause the former? To
address this we carried out the first nonlinear dielectric experiments at
elevated hydrostatic pressures on two liquids, to measure the third-order
harmonic component of their susceptibilities. We extract from this the number
of dynamically correlated molecules for various state points, and find that the
dynamic correlation volume for non-associated liquids depends primarily on the
relaxation time, sensibly independent of temperature and pressure. We support
this result by molecular dynamic simulations showing that the maximum in the
four-point dynamic susceptibility of density fluctuations varies less than 10%
for molecules that do not form hydrogen bonds. Our findings are consistent with
dynamic heterogeneity serving as the principal control parameter for the
slowing down of molecular motions in supercooled materials.
