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Using computer simulations, we validate a simple free energy model that canbe analytically solved to predict the equilibrium size of self-limitingclusters of particles in the fluid state governed by a combination ofshort-range attractive and long-range repulsive pair potentials. The model is asemi-empirical adaptation and extension of the canonical free energy-basedresult due to Groenewold and Kegel [J. Phys. Chem. B, 105 (2001)], where we usenew computer simulation data to systematically improve the cluster-sizescalings with respect to the strengths of the competing interactions drivingaggregation. We find that one can adapt a classical nucleation like theory forsmall energetically-frustrated aggregates provided one appropriately accountsfor a size-dependent, microscopic energy penalty of interface formation, whichrequires new scaling arguments. This framework is verified in part byconsidering the extensive scaling of intracluster bonding, where we uncover asuperlinear scaling regime distinct from (and located between) the knownregimes for small and large aggregates. We validate our model based oncomparisons against approximately 100 different simulated systems comprisingcompact spherical aggregates with characteristic (terminal) sizes between sixand sixty monomers, which correspond to wide ranges inexperimentally-controllable parameters.

Fluids with competing interactions: II. Validating a free energy model for equilibrium cluster size