Translation-rotation paradox for diffusion in fragile glass-forming liquids

Abstract

Translational and rotational diffusion rates in low-molecular-weight liquids tend to conform well to the predictions of the classic Stokes-Einstein-Debye model if temperature T is not too low. Specifically, the diffusion constants ${\mathit{D}}_{\mathrm{trans}}$ and ${\mathit{D}}_{\mathrm{rot}}$ are proportional to T/η(T), where η is the shear viscosity. However, fragile glass formers seem to present a paradox: near the glass transition temperature ${\mathit{T}}_{\mathit{g}}$ this proportionality continues for ${\mathit{D}}_{\mathrm{rot}}$, but ${\mathit{D}}_{\mathrm{trans}}$ can be enhanced by ${10}^2$. A ‘‘fluidized domain’’ model is proposed to explain these observations. Owing to a suitable combination of domain parameters (mean size, lifetime, concentration, internal viscosity), the observed diffusion rate discrepancy can indeed be rationalized. Rough estimates for these domain parameters are provided for two fragile glass formers (orthoterphenyl and 1,3,5-tri-α-naphthyl benzene) at their respective ${\mathit{T}}_{\mathit{g}}$’s.