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 DELT A H_m.The combination of the above correlation with the 2/3 rale 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 relect 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.
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