Relation between Rotational and Translational Dynamic Heterogeneities in Water

We use molecular dynamics simulations to probe the rotational dynamics of the extended simple point charge model of water for a range of temperatures down to 200 K, 6 K above the mode coupling temperature. We find that rotational dynamics is spatially heterogeneous; i.e., there are clusters of molecules that rotate significantly more than the average for a given time interval, and we study the size and the temporal behavior of these clusters. We find that the position of a rotational heterogeneity is strongly correlated with the position of a translational heterogeneity, and that the fraction of molecules belonging to both kinds of heterogeneities increases with decreasing temperature. We further find that although the two types of heterogeneities are not identical, they are related to the same physical picture.

Figure 1

(a) RMSD for rotations of the polarization vector, $\widehat{p}$, in a range of temperatures from 200 to 350 K. (b) Rotational diffusivity, $D_R$, as a function of $T^{-1}$ for all three principal vectors, $\widehat{p}$, $\widehat{q}$, and $\widehat{r}$. The inset shows a schematic defining these vectors ($\widehat{p}$ is parallel to the dipolar moment of the molecule, $\widehat{r}$ is parallel the hydrogen-hydrogen direction, and $\widehat{q}$ is perpendicular to both $\widehat{p}$ and $\widehat{r}$).

Figure 2

(a) Non-Gaussian parameter ${\alpha }_2(t)$ for the range of temperatures indicated. (b) Self-part of the van Hove distribution function, $G_s(\phi ,t)$, for $\mathrm{T}=200\mathrm{K}$ and $t^{*}(200\mathrm{K})\approx 1.05\mathrm{ps}$, compared with the Gaussian approximation, $G_0(\phi ,t)$, obtained using $⟨{\phi }^2(t^{*})⟩$ also at $\mathrm{T}=200\mathrm{K}$.

Figure 3

Weight average cluster size for $\mathrm{T}=200–350\mathrm{K}$ for molecules belonging to the 7% most rotationally mobile molecules. The values are normalized to the random cluster contribution.

Figure 4

(a) Weight average cluster size as a function of temperature for TH and RH. Both quantities are calculated at the corresponding $t_{\max }$. Note that the TH are larger than the RH. (b) The time $t_{\max }$ at which the maximum of the weight average cluster size occurs.

Figure 5

(a) A snapshot of a typical cluster at $\mathrm{T}=200\mathrm{K}$. The red molecules belong to TH, blue to RH, and the green molecules belong to both clusters. (b) Fraction of molecules in both a TH and RH for the three principal vectors; the strongest correlations are for vectors $\widehat{q}$ and $\widehat{r}$. (c) RDF between the sets of translationally mobile and rotationally mobile molecules for $\mathrm{T}=200\mathrm{K}$. The inset shows the corresponding ratios of these functions to $g_{\mathrm{bulk}}(r)$. For clarity $g_{\mathrm{T}-\mathrm{T}}$ is shifted by 5 and $g_{\mathrm{R}-\mathrm{R}}$ by 10 on the vertical axis; the ratio involving $g_{\mathrm{T}-\mathrm{T}}$ is shifted by 3 and the ratio involving $g_{\mathrm{R}-\mathrm{R}}$ by 6 in the inset.