  Using computer simulations, we validate a simple free energy model that can
be analytically solved to predict the equilibrium size of self-limiting
clusters of particles in the fluid state governed by a combination of
short-range attractive and long-range repulsive pair potentials. The model is a
semi-empirical adaptation and extension of the canonical free energy-based
result due to Groenewold and Kegel [J. Phys. Chem. B, 105 (2001)], where we use
new computer simulation data to systematically improve the cluster-size
scalings with respect to the strengths of the competing interactions driving
aggregation. We find that one can adapt a classical nucleation like theory for
small energetically-frustrated aggregates provided one appropriately accounts
for a size-dependent, microscopic energy penalty of interface formation, which
requires new scaling arguments. This framework is verified in part by
considering the extensive scaling of intracluster bonding, where we uncover a
superlinear scaling regime distinct from (and located between) the known
regimes for small and large aggregates. We validate our model based on
comparisons against approximately 100 different simulated systems comprising
compact spherical aggregates with characteristic (terminal) sizes between six
and sixty monomers, which correspond to wide ranges in
experimentally-controllable parameters.
