  Porous mesophases, where well-defined particle-depleted 'void' spaces are
present within a particle-rich background fluid, can be self-assembled from
colloidal particles interacting via isotropic pair interactions with competing
attractions and repulsions. While such structures could be of wide interest for
technological applications (e.g., filtration, catalysis, absorption, etc.),
relatively few studies have investigated the interactions that lead to these
morphologies and how they compare to those that produce other
micro-phase-separated structures, such as clusters. In this work, we use
inverse methods of statistical mechanics to design model isotropic pair
potentials that form porous mesophases. We characterize the resulting porous
structures, correlating features of the pair potential with the targeted pore
size and the particle packing fraction. The former is primarily encoded by the
amplitude and range of the repulsive barrier of the designed pair potential and
the latter by the attractive well depth. We observe a trade-off with respect to
the packing fraction of the targeted morphology: greater values support more
spherical and monodisperse pores that themselves organize into periodic
structures, while lower values yield more mobile pores that do not assemble
into ordered structures but remain stable over a larger range of packing
fraction. We conclude by commenting on the limitations of targeting a specific
pore diameter within the present inverse design approach as well as by
describing future directions to overcome these limitations.
