Relation between the Widom line and the breakdown of the Stokes–Einstein relation in supercooled water

^†Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215;
^§Department of Physics, Yeshiva University, 500 West 185th Street, New York, NY 10033;
^¶Department of Physics, Wesleyan University, Middletown, CT 06459; and
^‖Department of Physics, St. Francis Xavier University, Antigonish, NS, Canada B2G 2W5

Contributed by H. E. Stanley, March 24, 2007 (received for review October 29, 2006)

Abstract

Supercooled water exhibits a breakdown of the Stokes–Einstein relation between the diffusion constant D and the alpha relaxation time τ_α. For water simulated with two different potentials, TIP5P and ST2, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line T _W(P). Specifically, we find that our results for Dτ_α/T collapse onto a single “master curve” if temperature is replaced by T − T _W(P). We further find that the size of the mobile molecule clusters (dynamical heterogeneities) increases sharply near T _W(P). Moreover, our calculations of mobile particle cluster size <n(t*)>_w for different pressures, where t* is the time for which the mobile particle cluster size is largest, also collapse onto a single master curve if T is replaced by T − T _W(P). The crossover to a more locally structured low density liquid (LDL) as T → T _W(P) appears to be well correlated both with the breakdown of the Stokes–Einstein relation and with the growth of dynamic heterogeneities. Our results are consistent with the possibility that the breakdown of the SE relation in supercooled water at low pressures is associated with the hypothesized liquid–liquid phase transition.

Footnotes

^‡To whom correspondence may be addressed. E-mail: pradeep{at}physics.bu.edu or hes{at}bu.edu
Author contributions: P.K., S.V.B., S.R.B., P.H.P., F.W.S., and H.E.S. designed research; P.K., S.V.B., S.R.B., P.H.P., F.W.S., and H.E.S. performed research; P.K., S.V.B., S.R.B., P.H.P., F.W.S., and H.E.S. contributed new reagents/analytic tools; P.K., S.V.B., S.R.B., P.H.P., F.W.S., and H.E.S. analyzed data; and P.K., S.V.B., P.H.P., F.W.S., and H.E.S. wrote the paper.
The authors declare no conflict of interest.
Abbreviations:

LL,

liquid–liquid;

SE,

Stokes–Einstein.