Fragility and thermodynamics in nonpolymeric glass-forming liquids

For nonpolymeric supercooled liquids, the empirical correlation m = 56T _gΔC _p(T _g)/ΔH _m 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 T _g, while thermodynamics enter in terms of the heat capacity step ΔC _p at T _g and the melting enthalpy ΔH _m. The combination of the above correlation with the 2/3 rule for the T _g/T _m ratio yields an expression, m = 40ΔC _p(T _g)/ΔS _m, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via ΔC _p(T _g)/ΔS _m also reveals that the slopes in Kauzmann's original ΔS(T)/ΔS _m versus T/T _m plot reflect the fragility concept [Chem. Rev. 43, 219 (1948)], so long as T _m/T _g= 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 T _g/T _m = 2/3 rule breaks down.