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Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water

Marco G. Mazza1, Nicolas Giovambattista2, H. Eugene Stanley1, and Francis W. Starr3

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
  • 2Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
  • 3Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA

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Phys. Rev. E 76, 031203 – Published 26 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031203

Abstract

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, Dt=kBT∕6πηR and Dr=kBT∕8πηR3, where Dt and Dr are the translational and rotational diffusivity, respectively, T is the temperature, η the viscosity, kB the Boltzmann constant, and R the “molecular” radius. Our results are based on molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE and SED relations break down at low temperature. To explore the relationship between these breakdowns and dynamical heterogeneities (DHs), we also calculate the SE and SED relations for subsets of the 7% “fastest” and 7% “slowest” molecules. We find that the SE and SED relations break down in both subsets, and that the breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in contrast with a view where only the most mobile molecules are the origin of the breakdown of the SE and SED relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED relations in both subsets of molecules are replaced with “fractional” SE and SED relations, Dt∼(τ∕T)−ξt and Dr∼(τ∕T)−ξr, where ξt≈0.84(<1) and ξr≈0.75(<1). We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both the fastest and slowest subsets of molecules. Further, we find that, the decoupling increases upon cooling, but that the probability of a molecule being classified as both translationally and rotationally fastest also increases. To study the effect of time scale for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both the decoupling and SE and SED breakdowns originate at a time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DHs are more relevant. Our work also demonstrates that selecting DHs on the basis of translational or rotational motion more strongly biases the calculation of diffusion constants than other dynamical properties such as relaxation times.

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Phys. Rev. E 76, 031203– Published 26 September, 2007
  • Received 30 May 2007

© 2007 American Physical Society

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