Fragility and thermodynamics in nonpolymeric glass-forming liquids

For nonpolymeric supercooled liquids, the empirical correlation m=56T(g)Delta C-p(T-g)/Delta H-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 Delta C-p at T-g and the melting enthalpy Delta H-m. The combination of the above correlation with the 2/3 rule for the T-g/T-m ratio yields an expression, m=40 Delta C-p(T-g)/Delta S-m, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via Delta C-p(T-g)/Delta S-m also reveals that the slopes in Kauzmann's original Delta S(T)/Delta S-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. (c) 2006 American Institute of Physics.