| 438 |
|
molecules. The rate at which the function decays provides information |
| 439 |
|
about hindered motions and the timescales for relaxation. In |
| 440 |
|
eq. \eqref{C(t)1}, $P_{2}$ is the second-order Legendre polynomial, |
| 441 |
< |
the vector $\mathbf{u}$ is usually taken as HOH bisector, although |
| 442 |
< |
slightly different behavior is observed when $\mathbf{u}$ is the |
| 441 |
> |
the vector $\mathbf{u}$ is often taken as HOH bisector, although |
| 442 |
> |
slightly different behavior can be observed when $\mathbf{u}$ is the |
| 443 |
|
vector along one of the OH bonds. The angle brackets denote an |
| 444 |
|
ensemble average over all water molecules in a given spatial region. |
| 445 |
|
|
| 447 |
|
have computed $C_{2}(z,t)$ for molecules that are present within a |
| 448 |
|
particular slab along the $z$- axis at the initial time. The change |
| 449 |
|
in the decay behavior as a function of the $z$ coordinate is another |
| 450 |
< |
measure of the change of how the environment changes as we traverse |
| 451 |
< |
the ice/water interface. To compute these correlation functions, each |
| 452 |
< |
of the 0.5 ns simulations was followed by a shorter 200 ps simulation |
| 453 |
< |
where the positions of every molecule in the system were recorded |
| 454 |
< |
every 0.1 ps. The systems were then divided into 30 bins and $C_2(t)$ |
| 455 |
< |
was evaluated for each bin. |
| 450 |
> |
measure of the change of how the local environment changes across the |
| 451 |
> |
ice/water interface. To compute these correlation functions, each of |
| 452 |
> |
the 0.5 ns simulations was followed by a shorter 200 ps microcanonical |
| 453 |
> |
(NVE) simulation in which the positions and orientations of every |
| 454 |
> |
molecule in the system were recorded every 0.1 ps. The systems were |
| 455 |
> |
then divided into 30 bins and $C_2(t)$ was evaluated for each bin. |
| 456 |
|
|
| 457 |
< |
In simulations at biological interfaces, it has been shown that |
| 458 |
< |
$C_2(t)$ for water can be fit by a triexponential decay\cite{Furse08}, |
| 459 |
< |
where the three components of the decay correspond to a fast (<200 fs) |
| 460 |
< |
reorientational piece driven by the restoring forces of existing |
| 461 |
< |
hydrogen bonds, a middle (on the order of several ps) piece describing |
| 462 |
< |
the large angle jumps that occur during the breaking and formation of |
| 463 |
< |
new hydrogen bonds,\cite{Laage08,Laage11} and a slow (on the order of |
| 464 |
< |
tens of ps) contribution describing the translational motion of the |
| 465 |
< |
molecules. We have similarly fit our correlation functions |
| 457 |
> |
In simulations of water at biological interfaces, Furse {\em et al.} |
| 458 |
> |
fit $C_2(t)$ functions for water with triexponential |
| 459 |
> |
functions,\cite{Furse08} where the three components of the decay |
| 460 |
> |
correspond to a fast (<200 fs) reorientational piece driven by the |
| 461 |
> |
restoring forces of existing hydrogen bonds, a middle (on the order of |
| 462 |
> |
several ps) piece describing the large angle jumps that occur during |
| 463 |
> |
the breaking and formation of new hydrogen bonds,and a slow (on the |
| 464 |
> |
order of tens of ps) contribution describing the translational motion |
| 465 |
> |
of the molecules. The model for orientational decay presented |
| 466 |
> |
recently by Laage and Hynes {\em et al.}\cite{Laage08,Laage11} also |
| 467 |
> |
includes three similar decay constants, although two of the time |
| 468 |
> |
constants are linked, and the resulting decay curve has two parameters |
| 469 |
> |
governing the dynamics of decay. |
| 470 |
> |
|
| 471 |
> |
In our ice/water interfaces, we are at substantially lower |
| 472 |
> |
temperatures, and the water molecules are further perturbed by the |
| 473 |
> |
presence of the ice phase nearby. We have obtained the most |
| 474 |
> |
reasonable fits using triexponential functions with three distinct |
| 475 |
> |
time domains, as well as a constant piece that accounts for the water |
| 476 |
> |
stuck in the ice phase that does not experience any long-time |
| 477 |
> |
orientational decay, |
| 478 |
|
\begin{equation} |
| 479 |
|
C_{2}(t) \approx a e^{-t/\tau_\mathrm{short}} + b e^{-t/\tau_\mathrm{middle}} + c |
| 480 |
|
e^{-t/\tau_\mathrm{long}} + (1-a-b-c) |
| 481 |
|
\end{equation} |
| 482 |
< |
An average value and standard deviation for each $\tau$ was obtained |
| 483 |
< |
for each bin from the four runs. To improve statistics, the data is |
| 484 |
< |
shown as a function of distance from the center of the ice slab in |
| 485 |
< |
figures \ref{fig:basal_Tau_comic_strip} and |
| 486 |
< |
\ref{fig:prismatic_Tau_comic_strip}. |
| 482 |
> |
Average values for the three decay constants (and error estimates) |
| 483 |
> |
were obtained for each bin. In figures \ref{fig:basal_Tau_comic_strip} |
| 484 |
> |
and \ref{fig:prismatic_Tau_comic_strip}, the three orientational decay |
| 485 |
> |
times are shown as a function of distance from the center of the ice |
| 486 |
> |
slab. |
| 487 |
|
|
| 488 |
|
\begin{figure} |
| 489 |
|
\includegraphics[width=\linewidth]{basal_Tau_comic_strip.pdf} |
