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%Geologists are concerned with the flow of water over ice |
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%Antifreeze protein in fish--Haymet's group has cited this before |
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With the recent development of velocity shearing and scaling reverse non-equilibrium molecular dynamics (VSS-RNEMD), it is now possible to calculate transport properties from heterogeneous systems. |
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\section{Methodology} |
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\subsection{System Construction} |
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To construct the basal and prismatic systems, first the ice lattices were created. Hirsch and Ojam\"{a}e recently determined possible proton-ordered structures of ice Ih for an orthorhombic unit cell containing eight water molecules. \cite{Hirsch04} The crystallographic coordinates for structure 6 (P$2_{1}2_{1}2_{1}$) were used to construct an orthorhombic unit cell which was then replicated in all three dimensions yielding a proton-ordered block of ice Ih. To expose the desired face, the ice block was then cut along the ($0001$) plane or the ($10\overline{1}0$) plane for the basal and prismatic faces respectively. The ice block was also cut perpendicular to the initial cuts, and oriented so that the desired face is exposed to the $z$-axis. The ice block was then replicated in the $x$ and $y$ dimensions, and lastly liquid phase water molecules were added to the system. Haymet \emph{et al.} have done extensive work on studying and characterizing the ice/water interface. They have found for the SPC/E water model (used here), the ice/water interface is most stable at 225$\pm$5K. Therefore, the average temperature of each simulation was 225K. Molecular translation and orientation resrtaints were imposed in the early stages of equilibration to prevent melting of the ice block. These restraints were removed during NVT equilibration, long before data collection. |
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To construct the basal and prismatic systems, first the ice lattices were created. Hirsch and Ojam\"{a}e recently determined possible proton-ordered structures of ice Ih for an orthorhombic unit cell containing eight water molecules. \cite{Hirsch04} The crystallographic coordinates for structure 6 (P$2_{1}2_{1}2_{1}$) were used to construct an orthorhombic unit cell which was then replicated in all three dimensions yielding a proton-ordered block of ice Ih. To expose the desired face, the ice block was then cut along the ($0001$) plane or the ($10\overline{1}0$) plane for the basal and prismatic faces respectively. The ice block was also cut perpendicular to the initial cuts, and oriented so that the desired face is exposed to the $z$-axis. The ice block was then replicated in the $x$ and $y$ dimensions, and lastly liquid phase water molecules were added to the system. Haymet \emph{et al.} have done extensive work on studying and characterizing the ice/water interface. They have found for the SPC/E water model\cite{Berendsen87} (used here), the ice/water interface is most stable at 225$\pm$5K. Therefore, the average temperature of each simulation was 225K. Molecular translation and orientation resrtaints were imposed in the early stages of equilibration to prevent melting of the ice block. These restraints were removed during NVT equilibration, long before data collection. |
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\subsection{Computational Details} |
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All simulations were performed using OpenMD with a time step of 2 fs, and periodic boundary conditions in all three dimensions. The systems were divided into 100 artificial bins along the $z$-axis for the VSS-RNEMD moves, which were attempted every 50 fs. The gradients were allowed to develop for 1 ns before data collection was began. Once established, snapshots of the system were taken every 1 ps, and the average velocities and densities of each bin were accumulated every attempted VSS-RNEMD move. |
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\section{Results and discussion} |
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%Images to include: 3-long comic strip style of <Vx>, T, q_z as a function of z for the basal and prismatic faces. q_z by z with fit for basal and prismatic. interface width as a function of deltaVx (shear rate) with basal and prismatic on the same plot, error bars in the x and y. <Vx> by flux with basal and prismatic on same graph, back out slope from xmgr and error in slope to get lambda, friction coefficient of interface. |
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\subsection{Interfacial Width} |
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For the basal and prismatic systems, the ice blocks were sheared through the water at varying rates while an imposed thermal gradient kept the interface at the stable temperature range as described by Byrk and Haymet. The interfacial width as described by the fit of the tetrahedrally profile shows no dependence on shear rate as seen in Figure \ref{fig:FIGURENAME}. |
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