Relating local structures, energies, and occurrence probabilities in a two-dimensional silica network

Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring statistics, could be numerically reproduced by performing molecular dynamics simulations with an appropriately chosen 2D force field. Using a maximum entropy formulation it is shown that the probability distribution of the individual rings and triplets can be related to the ring and triplet energies, respectively, obtained from the simulations. Using additional Lagrange parameters, the correct average properties of random networks are guaranteed. In agreement with previous work, based on distributions of complementary rings and triplets, respectively, one finds a Boltzmann-type relation albeit with an effective temperature which largely deviates from the bath temperature. Furthermore, it is shown that the ring and triplet energies can be estimated based on the properties of their average inner angles. This calculation supports, on a quantitative level, the previously suggested angle mismatch theory. It suggests that correlations among adjacent rings originate from the net mismatch in the inner ring angles in a triplet of rings. By taking into account an average effect from the surrounding rings of a triplet, an even better estimate of the correlations can be provided. That approach is also applied to estimate the Aboav-Wearie parameter.