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A thermodynamic connection to the fragility of glass-forming liquids


Although liquids normally crystallize on cooling, there are members of all liquid types (including molecular, ionic and metallic) that supercool and then solidify at their glass transition temperature, Tg. This continuous solidification process exhibits great diversity within each class of liquid—both in the steepness of the viscosity–temperature profile, and in the rate at which the excess entropy of the liquid over the crystalline phase changes as Tg is approached. However, the source of the diversity is unknown. The viscosity and associated relaxation time behaviour have been classified between ‘strong’ and ‘fragile’ extremes, using Tg as a scaling parameter1, but attempts to correlate such kinetic properties with the thermodynamic behaviour have been controversial2,3. Here we show that the kinetic fragility can be correlated with a scaled quantity representing excess entropy, using data over the entire fragility range and embracing liquids of all classes. The excess entropy used in our correlation contains both configurational and vibration-related contributions. In order to reconcile our correlation with existing theory and simulations, we propose that variations in the fragility of liquids originate in differences between their vibrational heat capacities, harmonic and anharmonic, which we interpret in terms of an energy landscape. The differences evidently relate to behaviour of low-energy modes near and below the boson peak.

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Figure 2: Plots of scaled excess entropy versus Tg-scaled inverse temperature.
Figure 1: Tg-scaled Arrhenius plot for liquids of every class for which thermodynamic data are also available.
Figure 3: Correlation of the thermodynamic and kinetic F1/2 fragilities from Figs 1 and 2.
Figure 4: Graphical explanation of how high liquid fragility originates in the change of energy landscape ‘basin shape’ (hence of the vibrational density of states) during thermal excitation to high potential energies.


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We thank S. Sastry, R. Speedy and F. Sciortino for comments and criticisms. This work was supported by the NSF, Division of Materials Research, Solid State Chemistry program.

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Correspondence to C. A. Angell.

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Martinez, LM., Angell, C. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663–667 (2001).

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