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Recently, it became possible to experimentally generate and characterize avery thin silica system on a substrate which can be basically described as a 2Drandom network. The key structural properties, in particular related to thering statistics, could be numerically reproduced by performing moleculardynamics simulations with an appropriately chosen 2D force field. Using amaximum entropy formulation it is shown that the probability distribution ofthe individual rings and triplets can be related to the ring and tripletenergies, respectively, obtained from the simulations. Using additionalLagrange parameters, the correct average properties of random networks areguaranteed. In agreement with previous work, based on distributions ofcomplementary rings and triplets, respectively, one finds a Boltzmann-typerelation albeit with an effective temperature which largely deviates from thebath temperature. Furthermore, it is shown that the ring and triplet energiescan be estimated based on the properties of their average inner angles. Thiscalculation supports, on a quantitative level, the previously suggested anglemismatch theory. It suggests that correlations among adjacent rings originatefrom the net mismatch in the inner ring angles in a triplet of rings. By takinginto account an average effect from the surrounding rings of a triplet, an evenbetter estimate of the correlations can be provided. That approach is alsoapplied to estimate of the Aboav-Wearie parameter.

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