Static and dynamic length scales in supercooled liquids: insights from molecular dynamics simulations of water and tri-propylene oxide.

We perform molecular dynamics simulations to study static and dynamic length scales in molecular supercooled liquids, in particular, water. For a determination of these scales, we use equilibrium configurations and pin appropriate subsets of molecules so as to obtain random matrices, cylindrical pores, and slit confinements. Static length scales ξ(s) are determined by analyzing overlap correlation functions for various fractions of pinned molecules or distances to the confining walls. For water in all confinements and for propylene oxide trimers in random geometry, a linear increase of ξ(s) with inverse temperature is found. Dynamic length scales ξ(d) are determined by analogous analysis of fraction-dependent or position-resolved correlation times of structural relaxation. While ξ(d) continuously grows upon cooling in the cylindrical and slit confinements, we find no evidence for a temperature dependence in random matrices, implying that molecular dynamics in parsed volumes is qualitatively different from that in bulk liquids. Finally, we study possible connections between the growth of the static and dynamic length scales and the slowdown of the structural relaxation of the supercooled bulk liquids. For water, we observe a linear relation between ln τ(α) and ξ(s)²/T in the whole accessible range down to the critical temperature of mode-coupling theory, T(c). In the weakly supercooled regime, the same relation holds also for ξ(d), as obtained from cylindrical and slit confinements, but deviations from this behavior are observed near T(c). The results are discussed in connection with random first-order theory and experimental studies of liquid dynamics in nanoscopic confinements and binary mixtures.