Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently a new approach to the determination of dynamic correlation lengths, ξ, for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [L. Hong, V.N. Novikov, and A.P. Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, Tg, the assumption is that the structure of the liquid is frozen at Tg, so that the ξ characterize dynamic heterogeneity in the supercooled liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above Tg have a different, and unrealistic, temperature dependence.

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