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\chapter{\label{chap:ice}PHASE BEHAVIOR OF WATER IN COMPUTER \\ SIMULATIONS} |
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\chapter[PHASE BEHAVIOR OF WATER IN COMPUTER \\ SIMULATIONS]{\label{chap:ice}PHASE BEHAVIOR OF WATER IN COMPUTER SIMULATIONS} |
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As mentioned in the previous chapter, water has proven to be a |
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challenging substance to depict in simulations, and a variety of |
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considered energetic stabilization and neglected entropic |
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contributions to the overall free energy. To address this issue, we |
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have calculated the absolute free energy of this crystal using |
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thermodynamic integration and compared to the free energies of ice |
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thermodynamic integration and compared it to the free energies of ice |
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I$_\textrm{c}$ and ice I$_\textrm{h}$ (the common low-density ice |
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polymorphs) and ice B (a higher density, but very stable crystal |
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structure observed by B\'{a}ez and Clancy in free energy studies of |
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SPC/E & -12.99(3) & -13.00(3) & -13.03(3) & - & -12.99(3) \\ |
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SSD/RF & -11.83(3) & -11.66(4) & -12.32(3) & -12.39(3) & - \\ |
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TRED & -12.61(3) & -12.43(3) & -12.89(3) & -13.12(3) & - \\ |
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\bottomrule |
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\end{tabular} |
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\label{tab:dampedFreeEnergy} |
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\end{table} |
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Ice-$i$ was still observed to be a stable polymorph for all of the |
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studied water models. |
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So what is the preferred solid polymorph for simulated water? As |
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indicated above, the answer appears to be dependent both on the |
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conditions and the model used. In the case of short cutoffs without a |
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long-range interaction correction, Ice-$i$ and Ice-$i^\prime$ have |
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the lowest free energy of the studied polymorphs with all the models. |
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Ideally, crystallization of each model under constant pressure |
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conditions, as was done with SSD/E, would aid in the identification of |
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their respective preferred structures. This work, however, helps |
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illustrate how studies involving one specific model can lead to |
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insight about important behavior of others. |
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So what is the preferred solid polymorph for simulated water? The |
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answer appears to be dependent both on the conditions and the model |
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used. In the case of short cutoffs without a long-range interaction |
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correction, Ice-$i$ and Ice-$i^\prime$ have the lowest free energy of |
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the studied polymorphs with all the models. Ideally, crystallization |
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of each model under constant pressure conditions, as was done with |
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SSD/E, would aid in identifying their respective preferred structures. |
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This work, however, helps illustrate how studies involving one |
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specific model can lead to insight about important behavior of others. |
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We also note that none of the water models used in this study are |
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polarizable or flexible models. It is entirely possible that the |
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computational cost increase that comes with including polarizability |
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is an issue. |
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Finally, due to the stability of Ice-$i$ in the investigated |
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simulation conditions, a question arises as to possible experimental |
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observation of this polymorph. The rather extensive past and current |
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experimental investigation of water in the low pressure regime makes |
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us hesitant to ascribe any relevance to this work outside of the |
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simulation community. It is for this reason that we chose a name for |
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this polymorph which involves an imaginary quantity. That said, there |
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are certain experimental conditions that would provide the most ideal |
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situation for possible observation. These include the negative |
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pressure or stretched solid regime, small clusters in vacuum |
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deposition environments, and in clathrate structures involving small |
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non-polar molecules. For the purpose of comparison with experimental |
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results, we have calculated the oxygen-oxygen pair correlation |
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function, $g_\textrm{OO}(r)$, and the structure factor, $S(\vec{q})$ |
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for the two Ice-$i$ variants (along with example ice I$_\textrm{h}$ |
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and I$_\textrm{c}$ plots) at 77~K, and they are shown in figures |
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\ref{fig:gofr} and \ref{fig:sofq}. It is interesting to note that the |
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structure factors for Ice-$i^\prime$ and ice I$_\textrm{c}$ are quite |
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similar. The primary differences are small peaks at 1.125, 2.29, and |
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2.53~\AA$^{-1}$, so particular attention to these regions would be |
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needed to distinguish Ice-$i^\prime$ from ice I$_\textrm{c}$. |
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Finally, the stability of Ice-$i$ in these simulations raises the |
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possibility of experimental observation. The extensive body of |
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research on water in the low pressure regime makes us hesitant to |
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ascribe any relevance to this work outside the simulation community. |
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It is for this reason that we chose a name for this polymorph |
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involving an imaginary quantity. That said, there are certain |
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conditions that would be ideal for experimental observation of |
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Ice-$i$. These include the negative pressure or stretched solid |
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regime, clusters deposited in vacuum environments, and clathrate |
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structures involving small non-polar molecules. For the purpose of |
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comparison with future experimental results, we calculated the |
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oxygen-oxygen pair correlation function, $g_\textrm{OO}(r)$, and the |
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structure factor, $S(\vec{q})$ for the two Ice-$i$ variants (along |
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with ice I$_\textrm{h}$ and I$_\textrm{c}$) at 77~K (figures |
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\ref{fig:gofr} and \ref{fig:sofq}). It is interesting to note that |
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the structure factors for Ice-$i^\prime$ and ice I$_\textrm{c}$ are |
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quite similar. The primary differences are small peaks at 1.125, |
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2.29, and 2.53~\AA$^{-1}$, so particular attention to these regions |
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would be needed to distinguish Ice-$i^\prime$ from ice I$_\textrm{c}$. |
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\begin{figure} |
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\includegraphics[width=\linewidth]{./figures/iceGofr.pdf} |
