  Inverse methods of statistical mechanics are becoming productive tools in the
design of materials with specific microstructures or properties. While initial
studies have focused on solid-state design targets (e.g, assembly of colloidal
superlattices), one can alternatively design fluid states with desired
morphologies. This work addresses the latter and demonstrates how a simple
iterative Boltzmann inversion strategy can be used to determine the isotropic
pair potential that reproduces the radial distribution function of a fluid of
amorphous clusters with prescribed size. The inverse designed pair potential of
this "ideal" cluster fluid, with its broad attractive well and narrow repulsive
barrier at larger separations, is qualitatively different from the so-called
SALR form most commonly associated with equilibrium cluster formation in
colloids, which features short-range attractive (SA) and long-range repulsive
(LR) contributions. These differences reflect alternative mechanisms for
promoting cluster formation with an isotropic pair potential, and they in turn
produce structured fluids with qualitatively different static and dynamic
properties. Specifically, equilibrium simulations show that the amorphous
clusters resulting from the inverse designed potentials display more uniformity
in size and shape, and they also show greater spatial and temporal resolution
than those resulting from SALR interactions.
