Fragility and thermodynamics in nonpolymeric glass-forming liquids

Abstract

For nonpolymeric supercooled liquids, the empirical correlation m=56TgΔCp(Tg)∕ΔHm provides a reliable means of correlating dynamic and thermodynamic variables. The dynamics are characterized by the fragility or steepness index m and the glass transition temperature Tg, while thermodynamics enter in terms of the heat capacity step ΔCp at Tg and the melting enthalpy ΔHm. The combination of the above correlation with the 2∕3 rule for the Tg∕Tm ratio yields an expression, m=40ΔCp(Tg)∕ΔSm, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via ΔCp(Tg)∕ΔSm also reveals that the slopes in Kauzmann’s original ΔS(T)∕ΔSm versus T∕Tm plot reflect the fragility concept [Chem. Rev. 43, 219 (1948)], so long as Tm∕Tg=1.5. For the many liquids whose excess heat capacity is a hyperbolic function of temperature, we deduce that the fragility cannot exceed m=170, unless the Tg∕Tm=2∕3 rule breaks down.