Generalized excluded volume and the diffusivity and viscosity of supercooled liquids and glasses over the entire fragility spectrum

Transport properties of glass-formers near glass transition reflect the varying degrees of the sensitivity of the solid-like dynamics and structures with respect to temperature, depending on their fragility. Notably, however, most glasses resume Arrehenius transport behavior upon onset of vitrification. To address this phenomenon a theory of the self-diffusion coefficient and viscosity is developed on the basis of a model constructed for the generalized excluded volume of glass-formers described by the generic van der Waals equation of state. The molecular clustering behavior of a glass-former is exploited in terms of an order parameter that measures the concentration of glassy, clustered molecules, which is then related to the excluded volume. The formulas arrived therefrom are shown to excellently account for the self-diffusion coefficient and viscosity of various glass-formers over the entire fragility spectrum studied experimentally: e.g., _GeO2${\mathrm{GeO}}_2$, silica, ethanol, glycerol, diopside, propylene carbonate, o$o$-terphenyl, tris-napthylbenzene, toluene, and so on. The excluded volume effect thus investigated is shown to essentially characterize the fragility of the glass-formers. The resulting theory not only predicts for fragile glass-formers to resume Arrehenius transport behavior upon the onset of the glass transition, but also explains a crossover between strong and fragile glass-formers in their diffusivity and viscosity profiles as vitrification sets in.