Spurious violation of the Stokes\u2013Einstein\u2013Debye relation in supercooled water

Takeshi Kawasaki,Kang Kim

doi:10.1038/s41598-019-44517-4

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.

Highlights

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
The substantial decoupling displayed between the two diffusion constants indicates that the translational and rotational dynamics are decoupling, which is comparable with the previously reported results on ST249, SPC/E52, and TIP4P/200557 models
We report the numerical results of molecular dynamics (MD) simulations of the relationship between the translational and rotational dynamics in TIP4P/2005 supercooled liquid water

Summary

Introduction

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. Characterization of the translational and rotational motions of molecules in liquid states is of great significance[1,2,3] For this purpose, various transport properties, such as shear viscosity, translational diffusion constant, and rotational relaxation time have been measured both experimentally, and through molecular dynamics (MD) simulations. The Stokes–Einstein (SE) relation is one of the important characteristics of the translational diffusion constant, Dt, in many liquid state systems, Dt = kBT /(6πηR), where kB, T, η represent the Boltzmann constant, the temperature, and the shear viscosity, respectively This SE relation is derived originally from the theories of hydrodynamics and Brownian motion, where a rigid spherical particle with a radius R is assumed to be perfectly suspended in a Stokes flow of a constant shear viscosity η under the stick boundary condition[12]. R is conventionally regarded as the effective hydrodynamic radius of the molecule when applying the SE relation to molecular liquids[13]

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