In this work, the structure of glassy polymers is represented as a random distribution of lattice sites. We refer to each particular realization of this structure as a matrix. While conceptually simple, this approach captures several essential features of a glassy polymer, such as the rigidity of the structure and its amorphous, disordered nature. The key property of this structure is the volume fraction of solid lattice sites, ϕ s . The fraction ϕ s is varied between 0 (empty) and 0.40. At the highest value of ϕ s , the volume fraction of the remaining empty space (0.60) corresponds approximately to the percolation threshold for square lattice systems. All the properties of interest are averaged over three independent realizations of the polymer matrix with a particular value of ϕ s .