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Porous mesophases, where well-defined particle-depleted 'void' spaces arepresent within a particle-rich background fluid, can be self-assembled fromcolloidal particles interacting via isotropic pair interactions with competingattractions and repulsions. While such structures could be of wide interest fortechnological applications (e.g., filtration, catalysis, absorption, etc.),relatively few studies have investigated the interactions that lead to thesemorphologies and how they compare to those that produce othermicro-phase-separated structures, such as clusters. In this work, we useinverse methods of statistical mechanics to design model isotropic pairpotentials that form porous mesophases. We characterize the resulting porousstructures, correlating features of the pair potential with the targeted poresize and the particle packing fraction. The former is primarily encoded by theamplitude and range of the repulsive barrier of the designed pair potential andthe latter by the attractive well depth. We observe a trade-off with respect tothe packing fraction of the targeted morphology: greater values support morespherical and monodisperse pores that themselves organize into periodicstructures, while lower values yield more mobile pores that do not assembleinto ordered structures but remain stable over a larger range of packingfraction. We conclude by commenting on the limitations of targeting a specificpore diameter within the present inverse design approach as well as bydescribing future directions to overcome these limitations.

Interactions and design rules for assembly of porous colloidal mesophases