Positron annihilation lifetime spectroscopy measurements were conducted on a series of epoxy specimens, prepared by systematically varying the network rigidity and crosslink density. The investigations demonstrate that changes in the molecular structure of the constituent monomers change the microscopic parameters of the epoxy networks. An increase of chain rigidity increases the size and the number density of the trapping sites where orthopositronium localizes, which leads to an increase of the hole volume fraction at T-g. It was found that the hole volume fraction at T-g approximates a linear relationship with the packing densities of the epoxies under investigation. The results are interpreted as a decrease of the efficiency of molecular packing with increasing network rigidity. As a result, macroscopic materials properties such as glass transition temperature, density and thermal expansion show considerable variations.