Models of rotational relaxation above the glass transition

Abstract

Below a temperature TB, the rotational relaxation of small molecules in supercooled liquids appears to bifurcate into slow α and faster β relaxations. The characteristic time for the former diverges in Vogel–Fulcher fashion at the glass transition Tg and that of the latter follows Arrhenius behavior from above TB to below Tg. We have examined models for α- and β-rotational relaxation. Above TB, it appears that only β relaxation occurs and that τ1/τ2≊3, where τl is the relaxation time for the lth order spherical harmonic, while below TB it seems that for α relaxation this ratio is closer to unity and for β relaxation it is unknown. The value of three for the ratio is characteristic of rotational diffusion, the smaller ratio of large angular jumps and of restricted diffusion. We have ascribed β relaxation to rapid angular diffusion within a long-lived torsional potential well and the α relaxation to random restructuring of the torsional potential itself. Thus, the appearance of the α relaxation signals the emergence of a longer length scale, which is consistent with the observation that the τ corresponding to the α relaxation appears to diverge at the glass transition.