Spurious violation of the Stokes-Einstein-Debye relation in supercooled water

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 $\ell$-th degree Legendre polynomials ${\tau }_{\ell }$, and viscosity divided by temperature, $\eta /T$. Experiments on supercooled liquids are frequently performed to measure the SED relations, ${\tau }_{\ell }{k}_{\mathrm{B}}T/\eta$ and $D_{\mathrm{t}}{\tau }_{\ell }$, where $D_{\mathrm{t}}$ 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 ${\tau }_{\ell }$ values exhibit a temperature dependence similar to that of $\eta /T$, whereas the lowest-order ${\tau }_{\ell }$ values are decoupled with $\eta /T$, but are coupled with the translational diffusion constant. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

8 pages with 5 figures for main text, 2 pages with 3 figures for supplementary materials, to appear in Scientific Reports

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