The fundamental Debye-Stokes-Einstein (DSE) relation between rotational relaxation times and shear viscosity attracts longstanding research interest as one of the most important characteristics of many glass-forming liquids. Here, we provide strong evidence, missing so far, for the relevance of anisotropy for DSE-related behavior. Dielectric spectroscopy and shear viscosity measurements were employed to get insight into the decoupling between reorientation relaxation times and viscosity for anisotropic glass-formers with dipole moments oriented parallel or perpendicular to the long molecular axis.
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