| 94 |
|
|
| 95 |
|
The construction of the pyramidal and secondary prism systems follows that of |
| 96 |
|
the basal and prismatic systems presented elsewhere\cite{Louden13}, however |
| 97 |
< |
the ice crystals and water boxes were equilibrated and combined at 50K and |
| 98 |
< |
then equilibrated to 225K. The resulting pyramidal system was |
| 97 |
> |
the ice crystals and water boxes were equilibrated and combined at 50K |
| 98 |
> |
instead of 225K. The ice / water systems generated were then equilibrated |
| 99 |
> |
to 225K. The resulting pyramidal system was |
| 100 |
|
$37.47 \times 29.50 \times 93.02$ \AA\ with 1216 |
| 101 |
|
SPC/E molecules in the ice slab, and 2203 in the liquid phase. The secondary |
| 102 |
|
prism system generated was $71.87 \times 31.66 \times 161.55$ \AA\ with 3840 |
| 110 |
|
The computational details performed here were equivalent to those reported |
| 111 |
|
in the previous publication\cite{Louden13}. The only changes made to the |
| 112 |
|
previously reported procedure were the following. VSS-RNEMD moves were |
| 113 |
< |
attempted every 2 fs instead of every 50 fs. Due to the more frequent |
| 114 |
< |
perturbation of the system, a smaller imposed kinetic energy and momentum |
| 114 |
< |
flux was able to be used to obtain the thermal and velocity gradients |
| 115 |
< |
of interest. The resulting perturbations to the system were gentler |
| 116 |
< |
over the less frequent previously used VSS-RNEMD attempt interval. |
| 113 |
> |
attempted every 2 fs instead of every 50 fs. This was done to minimize |
| 114 |
> |
the magnitude of each individual VSS-RNEMD perturbation to the system. |
| 115 |
|
|
| 116 |
|
All pyramidal simulations were performed under the NVT ensamble except those |
| 117 |
|
during which statistics were accumulated for the orientational correlation |
| 119 |
|
simulations were performed under the NVE ensamble. |
| 120 |
|
|
| 121 |
|
\section{Results and discussion} |
| 122 |
+ |
\subsection{Interfacial width} |
| 123 |
+ |
In the literature there is good agreement that between the solid ice and |
| 124 |
+ |
the bulk water, there exists a region of 'slush-like' water molecules. |
| 125 |
+ |
In this region, the water molecules are structured differently and |
| 126 |
+ |
behave differently than those of the solid ice or the bulk water. |
| 127 |
+ |
The characteristics of this region have been defined by both structural |
| 128 |
+ |
and dynamic properties; and width has been measured by the change of these |
| 129 |
+ |
properties from their bulk liquid values to those of the solid ice. |
| 130 |
+ |
Examples of these properties include the density, the diffusion constant, and |
| 131 |
+ |
the translational order profile. \cite{Bryk02,Karim90,Gay02,Hayword01,Hayword02,Karim88} |
| 132 |
|
|
| 133 |
< |
\subsection{Structural interfacial width} |
| 133 |
> |
Since the VSS-RNEMD moves perturb the velocities of the water molecules in |
| 134 |
> |
the systems, parameters that depend on the translational motion may give |
| 135 |
> |
faulty results. A stuructural parameter will be less effected by the |
| 136 |
> |
VSS-RNEMD perturbations to the system. Due to this we have used the |
| 137 |
> |
local order tetrahedral parameter, which was originally described by |
| 138 |
> |
Kumar\cite{Kumar09} and Errington\cite{Errington01} and explained in our |
| 139 |
> |
previous publication\cite{Louden13} in relation to an ice/water system. |
| 140 |
> |
|
| 141 |
> |
Each of the systems were divided into 100 artificial bins along the |
| 142 |
> |
$z$-dimension, and the local tetrahedral order parameter, $q(z)$, was |
| 143 |
> |
time-averaged for each of the bins, resulting in a tetrahedrality profile of |
| 144 |
> |
the system. These profiles are shown across the $z$-dimension of the systems |
| 145 |
> |
in panel $a$ of Figures \ref{fig:spComic} |
| 146 |
> |
and \ref{fig:pyrComic} (black circles). The $q(z)$ function has a range of |
| 147 |
> |
(0,1), where a larger value indicates a more tetrahedral environment. |
| 148 |
> |
The $q(z)$ for the bulk liquid was found to be $\approx $0.77, while values of |
| 149 |
> |
$\approx $0.92 were more common for the ice. The tetrahedrality profiles were |
| 150 |
> |
fit using a hyperbolic tangent\cite{Louden13} designed to smoothly fit the |
| 151 |
> |
bulk to ice |
| 152 |
> |
transition, while accounting for the thermal influence on the profile by the |
| 153 |
> |
kinetic energy exchanges of the VSS-RNEMD moves. In panels $b$ and $c$, the |
| 154 |
> |
imposed thermal and velocity gradients can be seen. The verticle dotted |
| 155 |
> |
lines traversing all three panels indicate the midpoints of the interface |
| 156 |
> |
as determined by the hyperbolic tangent fit of the tetrahedrality profiles. |
| 157 |
> |
|
| 158 |
|
From fitting the tetrahedrality profiles for each of the 0.5 nanosecond |
| 159 |
< |
simulations (panel c of \ref{spComic} and \ref{pyrComic}) |
| 159 |
> |
simulations (panel c of Figures \ref{fig:spComic} and \ref{fig:pyrComic}) |
| 160 |
|
by Eq. 6\cite{Louden13},we find the interfacial width for the pyramidal and |
| 161 |
|
secondary prism to be $3.2 \pm 0.2$ and $3.2 \pm 0.2$ \AA\ , respectively, |
| 162 |
|
with no applied momentum flux. Over the range of shear rates investigated, |
| 170 |
|
respectively. Over the range of shear rates investigated, $0.6 \pm 0.3 |
| 171 |
|
\mathrm{ms}^{-1} \rightarrow 5.3 \pm 0.5 \mathrm{ms}^{-1}$ for the basal |
| 172 |
|
system and $0.9 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 4.5 \pm 0.1 |
| 173 |
< |
\mathrm{ms}^{-1}$ for the prismatic, we found no significant change in the |
| 174 |
< |
interfacial width. |
| 175 |
< |
|
| 173 |
> |
\mathrm{ms}^{-1}$ for the prismatic. |
| 174 |
> |
|
| 175 |
> |
These results indicate that the surface structure of the exposed ice crystal |
| 176 |
> |
has little to no effect on how far into the bulk the ice-like structural |
| 177 |
> |
ordering is. Also, it appears that the interface is not structurally effected |
| 178 |
> |
by shearing the ice through water. |
| 179 |
> |
|
| 180 |
> |
|
| 181 |
|
\subsection{Orientational dynamics} |
| 182 |
+ |
To investigate the dynamics of the water molecules across the interface, the |
| 183 |
+ |
systems were divided into $n$ bins, each $\approx$ 3 \AA\ wide in $z$, and |
| 184 |
+ |
the orientational time |
| 185 |
+ |
correlation function was computed for each of the $n$ bins. This was done by |
| 186 |
+ |
averaging the second order Legendre polynomial of the bisecting HOH vector |
| 187 |
+ |
dotted with itself at an initial time and some time later, over all molecules |
| 188 |
+ |
in the bin. |
| 189 |
|
|
| 190 |
|
|
| 147 |
– |
The coefficient of friction for the pyramidal and secondary prism interfaces were found to be independent of shear direction (x or y). |
| 191 |
|
|
| 192 |
+ |
\subsection{Coefficient of friction of the interfaces} |
| 193 |
+ |
|
| 194 |
+ |
|
| 195 |
+ |
\begin{table}[h] |
| 196 |
+ |
\centering |
| 197 |
+ |
\caption{Solid-liquid friction coefficients (measured in amu~fs\textsuperscript\ |
| 198 |
+ |
{-1}) } |
| 199 |
+ |
\label{tab:lambda} |
| 200 |
+ |
\begin{tabular}{|ccc|} \hline |
| 201 |
+ |
& \multicolumn{2}{c|}{Drag direction} \\ |
| 202 |
+ |
Interface & $x$ & $y$ \\ \hline |
| 203 |
+ |
basal\textsuperscript{a} & $0.08 \pm 0.02$ & $0.09 \pm 0.03$ \\ |
| 204 |
+ |
prismatic\textsuperscript{a} & $0.037 \pm 0.008$ & $0.04 \pm 0.01$ \\ |
| 205 |
+ |
pyramidal & $0.13 \pm 0.03$ & $0.14 \pm 0.03$ \\ |
| 206 |
+ |
secondary prism & $0.13 \pm 0.02$ & $0.12 \pm 0.03$ \\ \hline |
| 207 |
+ |
\end{tabular} |
| 208 |
+ |
\caption{\textsuperscript{a}Reference \cite{Louden13}} |
| 209 |
+ |
\end{table} |
| 210 |
+ |
|
| 211 |
+ |
|
| 212 |
|
\begin{figure} |
| 213 |
|
\includegraphics[width=\linewidth]{Pyr-orient} |
| 214 |
|
\caption{\label{fig:PyrOrient} The three decay constants of the |
