In the present paper we establish a temperature dependent constraint model of alkali phosphate glasses considering the structural and topological role of the modifying ion sub-network constituted by alkali ions and their non-bonding oxygen coordination spheres. The model is consistent with available structural data by NMR and molecular dynamics simulations and with dynamic data such glass transition temperature (T_g) and liquid fragility (m). Alkali phosphate glasses are exemplary systems for developing constraint model since the modifying cation network plays an important role besides the primary phosphate network. The proposed topological model predicts the changing trend of the Tg and m with increasing alkali oxide content for alkali phosphate glasses, including an anomalous minimum at around 20 mol. alkali oxide content. We find that the minimum in Tg and m is caused by increased connectivity of the modifying ion sub-network, as the alkali ions must share non-bonding oxygen to satisfy their coordination requirements at higher alkali oxide contents. We argue that the systematically decreasing the Tg values of alkali phosphate glasses from Li_2O to Na_2O to Cs_2O could be caused by a weakening of the modifying ion sub-network and can be accounted for by lower constraint onset temperatures.
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