  The conventional wisdom is that liquids are completely disordered and lack
non-trivial structure beyond nearest-neighbor distances. Recent observations
have upended this view and demonstrated that the microstructure in liquids is
surprisingly rich and plays a critical role in numerous physical, biological,
and industrial processes. However, approaches to uncover this structure are
either system-specific or yield results that are not physically intuitive.
Here, through single-particle resolved three-dimensional confocal microscope
imaging and the use of a recently introduced four-point correlation function,
we show that bidisperse colloidal liquids have a highly non-trivial structure
comprising alternating layers with icosahedral and dodecahedral order, which
extends well-beyond nearest-neighbor distances and grows with supercooling. By
quantifying the dynamics of the system on the particle level, we establish that
it is this intermediate-range order, and not the short-range order, which has a
one-to-one correlation with dynamical heterogeneities, a property directly
related to the relaxation dynamics of glassy liquids. Our experimental findings
provide a direct and much sought-after link between the structure and dynamics
of liquids and pave the way for probing the consequences of this
intermediate-range order in other liquid state processes.
