Fragility and compressibility at the glass transition

Isothermal compressibilities and Brillouin sound velocities from the literature allow us to separate the compressibility at the glass transition into a high-frequency vibrational and a low-frequency relaxational part. Their ratio shows the linear fragility relation discovered by x-ray Brillouin scattering, though the data bend away from the line at higher fragilities. Using the concept of constrained degrees of freedom, one can show that the vibrational part follows the fragility-independent Lindemann criterion; the fragility dependence seems to stem from the relaxational part. The physical meaning of this finding is discussed.