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\begin{document} |
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\title{Simulations of solid-liquid friction at Secondary Prism and Pyramidal ice-I$_\mathrm{h}$ / water interfaces} |
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\author{Patrick B. Louden and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: |
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gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\date{\today} |
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\maketitle |
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\begin{doublespace} |
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\begin{abstract} |
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Abstract abstract abstract... |
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\end{abstract} |
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\newpage |
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\section{Introduction} |
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Explain a little bit about ice Ih, point group stuff. |
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|
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Mention previous work done / on going work by other people. Haymet and Rick |
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seem to be investigating how the interfaces is perturbed by the presence of |
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ions. This is the conlcusion of a recent publication of the basal and |
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prismatic facets of ice Ih, now presenting the pyramidal and secondary |
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prism facets under shear. |
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|
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\section{Methodology} |
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|
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\begin{figure} |
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\includegraphics[width=\linewidth]{SP_comic_strip} |
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\caption{\label{fig:spComic} The secondary prism interface with a shear |
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rate of 3.5 ms\textsuperscript{-1}. Lower panel: the local tetrahedral order |
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parameter, $q(z)$, (black circles) and the hyperbolic tangent fit (red line). |
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Middle panel: the imposed thermal gradient required to maintain a fixed |
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interfacial temperature. Upper panel: the transverse velocity gradient that |
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develops in response to an imposed momentum flux. The vertical dotted lines |
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indicate the locations of the midpoints of the two interfaces.} |
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\end{figure} |
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|
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\begin{figure} |
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\includegraphics[width=\linewidth]{Pyr_comic_strip} |
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\caption{\label{fig:pyrComic} The pyramidal interface with a shear rate of 3.8 \ |
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ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:spComic}.} |
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\end{figure} |
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|
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\subsection{Pyramidal and secondary prism system construction} |
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|
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The construction of the pyramidal and secondary prism systems follows that of |
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the basal and prismatic systems presented elsewhere\cite{Louden13}, however |
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the ice crystals and water boxes were equilibrated and combined at 50K and |
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then equilibrated to 225K. The resulting pyramidal system was |
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$37.47 \times 29.50 \times 93.02$ \AA\ with 1216 |
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SPC/E molecules in the ice slab, and 2203 in the liquid phase. The secondary |
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prism system generated was $71.87 \times 31.66 \times 161.55$ \AA\ with 3840 |
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SPC/E molecules in the ice slab and 8176 molecules in the liquid phase. |
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|
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\subsection{Computational details} |
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% Do we need to justify the sims at 225K? |
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% No crystal growth or shrinkage over 2 successive 1 ns NVT simulations for |
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% either the pyramidal or sec. prism ice/water systems. |
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|
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The computational details performed here were equivalent to those reported |
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in the previous publication\cite{Louden13}. The only changes made to the |
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previously reported procedure were the following. VSS-RNEMD moves were |
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attempted every 2 fs instead of every 50 fs. Due to the more frequent |
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perturbation of the system, a smaller imposed kinetic energy and momentum |
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flux was able to be used to obtain the thermal and velocity gradients |
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of interest. The resulting perturbations to the system were gentler |
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over the less frequent previously used VSS-RNEMD attempt interval. |
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|
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All pyramidal simulations were performed under the NVT ensamble except those |
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during which statistics were accumulated for the orientational correlation |
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function, which were performed under the NVE ensamble. All secondary prism |
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simulations were performed under the NVE ensamble. |
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|
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\section{Results and discussion} |
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|
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\subsection{Structural interfacial width} |
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From fitting the tetrahedrality profiles for each of the 0.5 nanosecond |
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simulations (panel c of \ref{spComic} and \ref{pyrComic}) |
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by Eq. 6\cite{Louden13},we find the interfacial width for the pyramidal and |
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secondary prism to be $3.2 \pm 0.2$ and $3.2 \pm 0.2$ \AA\ , respectively, |
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with no applied momentum flux. Over the range of shear rates investigated, |
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$0.6 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 5.6 \pm 0.4 \mathrm{ms}^{-1}$ for |
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the pyramidal system and $0.9 \pm 0.3 \mathrm{ms}^{-1} \rightarrow 5.4 \pm 0.1 |
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\mathrm{ms}^{-1}$ for the secondary prism, we found no significant change in |
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the interfacial width. This follows our previous findings of the basal and |
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prismatic systems, in which the interfacial width was invarient of the |
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shear rate of the ice. The interfacial width of the quiescent basal and |
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prismatic systems was found to be $3.2 \pm 0.4$ \AA\ and $3.6 \pm 0.2$ \AA\ |
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respectively. Over the range of shear rates investigated, $0.6 \pm 0.3 |
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\mathrm{ms}^{-1} \rightarrow 5.3 \pm 0.5 \mathrm{ms}^{-1}$ for the basal |
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system and $0.9 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 4.5 \pm 0.1 |
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\mathrm{ms}^{-1}$ for the prismatic, we found no significant change in the |
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interfacial width. |
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|
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\subsection{Orientational dynamics} |
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|
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|
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The coefficient of friction for the pyramidal and secondary prism interfaces were found to be independent of shear direction (x or y). |
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|
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\begin{figure} |
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\includegraphics[width=\linewidth]{Pyr-orient} |
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\caption{\label{fig:PyrOrient} The three decay constants of the |
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orientational time correlation function, $C_2(t)$, for water as a function |
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of distance from the center of the ice slab. The vertical dashed line |
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indicates the edge of the pyramidal ice slab determined by the local order |
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tetrahedral parameter. The control (black circles) and sheared (red squares) |
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experiments were fit by a shifted exponential decay (Eq. 9\cite{Louden13}) |
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shown by the black and red lines respectively. The upper two panels show that |
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translational and hydrogen bond making and breaking events slow down |
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through the interface while approaching the ice slab. The bottom most panel |
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shows the librational motion of the water molecules speeding up approaching |
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the ice block due to the confined region of space allowed for the molecules |
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to move in.} |
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\end{figure} |
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|
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\begin{figure} |
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\includegraphics[width=\linewidth]{SP-orient-less} |
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\caption{\label{fig:SPorient} Decay constants for $C_2(t)$ at the secondary |
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prism face. Panel descriptions match those in \ref{fig:PyrOrient}.} |
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\end{figure} |
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\section{Conclusion} |
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Conclude conclude conclude... |
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\section{Acknowledgements} |
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Support for this progect was provided by the National Science Foundation under grant CHE-0848243. Computational time was provided by the Center for Research Computing (CRC) at the University of Notre Dame. |
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\newpage |
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\bibliography{iceWater} |
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\end{document} |