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The effective hydrodynamic radius in the Stokes-Einstein relation is not a constant


 Variants based on the assumption of effective hydrodynamic radius is constant are usually adopted to test the Stokes-Einstein relation. The rationality of the assumption is examined by performing molecular dynamics simulations with the truncated Lennard-Jones-like (TLJ) model, Kob-Andersen model and ortho-terphenyl (OTP) model. The results indicate the assumption is generally not established except for special case. The effective hydrodynamic radius is observed to increase with decreasing temperature for TLJ model but is decreased for Kob-Andersen and OTP model; and which is almost a constant for TLJ particle with enough rigidity. The variant of Stokes-Einstein relation D ~ T/η is invalid for the three models except for the TLJ particle with enough rigidity. We propose similar inconsistency may be also existed in other liquids and the assumption should be critically evaluated when adopted to test the Stokes-Einstein relation.