Abstract
The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the {boldsymbol{ell }}-th degree Legendre polynomials {{boldsymbol{tau }}}_{{boldsymbol{ell }}}, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, {{boldsymbol{tau }}}_{{boldsymbol{ell }}}kBT/η and Dt{{boldsymbol{tau }}}_{{boldsymbol{ell }}}, where Dt is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values are decoupled with η/T, but are coupled with the translational diffusion constant Dt. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.
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