Excess thermodynamic properties of glassforming liquids: The rational scaling of heat capacities, and the thermodynamic fragility dilemma resolved

With the overall objective of clarifying some perennial issues with the concept of liquid fragility, and with thermodynamic fragility in particular focus, we review the determination of excess thermodynamic properties of liquids as the temperature rises above T_g. We treat the compressibility first, as it is the one most commonly encountered in theory where it may be derived from the radial distribution function (specifically, from its Fourier transform (the structure factor) at zero wave vector), and is known to be proportional to the mean square density fluctuation. We show that the compressibility of glassforming liquids, and also the difference in compressibility between liquid and glass, always decreases as T_g is approached with the exception of a few water-like (anomalous) liquids. Secondly we examine the heat capacity which is favored in the analysis of glassforming liquid behavior. Contrasting with the compressibility, the excess heat capacity (determined by entropy fluctuations), mostly increases as temperature approaches T_g (with the same exceptions). But here we encounter the problem of the appropriate scaling of the measured molar quantity, which plagues comparisons of ∆ C_p between different substances. We solve this problem by defining C_p as an entropy derivative and scaling by the absolute excess entropy at T_g - which avoids the need for “beads” or other artificial scaling methods. Finally, we revisit the subject of thermodynamic fragility, which has been discussed before using a related scaling strategy.