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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry