Deriving fundamental measure theory from the virial series: consistency with the zero-dimensional limit

Fundamental measure theory (FMT) for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes. The modern versions of FMT are usually derived from the zero-dimensional limit, a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle. In Phys. Rev. E 85, 041150 (2012), a derivation from an approximated and resummed virial expansion was presented, whose result was not fully consistent with the FMT from the zero-dimensional limit. Here we improve on this derivation and obtain exactly the same FMT functional as was obtained earlier from the zero-dimensional limit. As a result, further improvements of FMT based on the virial expansion can now be formulated, some of which we suggest in the outlook.