Topological constraints and the Makishima–Mackenzie model

• The effect of connectivity on elastic properties of networks was computed.
• All elastic constants were found to drop to zero as connectivity dropped to 2.4.
• The failure of the Makishima–Mackenzie model in this regime was noted.
• A similar model explicity including connectivity was proposed.

Computations of the elastic properties of networks with bond stretch and bond angle bend forces are carried out in order to study their behavior as a function of average coordination number. It is found that the elastic constants essentially vanish as the average coordination number drops to 2.4. It is argued this phenomenon is responsible for the failure of the Makishima–Mackenzie model to predict accurately the elastic properties of borate glass, originating with B2O3 itself which also has an average coordination number of 2.4. Finally, a new model is proposed, similar to the Makishima–Mackenzie model but including explicitly the dependence on network connectivity.