trunk/iceWater2/Supplemental_Information.tex

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%% For PNAS Only:
%\url{www.pnas.org/cgi/doi/10.1073/pnas.0709640104}
\copyrightyear{2014}
\issuedate{Issue Date}
\volume{Volume}
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\begin{document}

\title{Supporting Information for: \\
The different facets of ice have different hydrophilicities: Friction at water /
  ice-I\textsubscript{h} interfaces}

\author{Patrick B. Louden\affil{1}{Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame,
IN 46556}
\and
J. Daniel Gezelter\affil{1}{}}

\contributor{Submitted to Proceedings of the National Academy of Sciences
of the United States of America}

\maketitle

\begin{article}

\section{Overview}
The supporting information contains further details about the model
construction, analysis methods, and supplies figures that support the
data presented in the main text.

\section{Construction of the Ice / Water interfaces}
Ice I$_\mathrm{h}$ crystallizes in the hexagonal space group
P$6_3/mmc$, and common ice crystals form hexagonal plates with the
basal face $\{0~0~0~1\}$ forming the top and bottom of each plate, and
the prismatic facet $\{1~0~\bar{1}~0\}$ forming the sides.  In extreme
temperatures or low water saturation conditions, ice crystals can
easily form as hollow columns, needles and dendrites.  These are
structures that expose other crystalline facets of the ice to the
surroundings.  Among the more common facets are the secondary prism,
$\{1~1~\bar{2}~0\}$, and pyramidal, $\{2~0~\bar{2}~1\}$, faces.  

We found it most useful to work with proton-ordered, zero-dipole
crystals that expose strips of dangling H-atoms and lone
pairs.\cite{Buch:2008fk} Our structures were created starting from
Structure 6 of Hirsch and Ojam\"{a}e's set of orthorhombic
representations for ice-I$_{h}$~\cite{Hirsch04}.  This crystal
structure was cleaved along the four different facets.  The exposed
face was reoriented normal to the $z$-axis of the simulation cell, and
the structures were and extended to form large exposed facets in
rectangular box geometries.  Liquid water boxes were created with
identical dimensions (in $x$ and $y$) as the ice, with a $z$ dimension
of three times that of the ice block, and a density corresponding to 1
g / cm$^3$.  Each of the ice slabs and water boxes were independently
equilibrated at a pressure of 1 atm, and the resulting systems were
merged by carving out any liquid water molecules within 3 \AA\ of any
atoms in the ice slabs.  Each of the combined ice/water systems were
then equilibrated at 225K, which is the liquid-ice coexistence
temperature for SPC/E water~\cite{Bryk02}. Reference
\citealp{Louden13} contains a more detailed explanation of the
construction of similar ice/water interfaces. The resulting dimensions
as well as the number of ice and liquid water molecules contained in
each of these systems are shown in Table S1.

\section{A second method for computing contact angles}
In addition to the spherical cap method outlined in the main text, a
second method for obtaining the contact angle was described by
Ruijter, Blake, and Coninck~\cite{Ruijter99}.  This method uses a
cylindrical averaging of the droplet's density profile.  A threshold
density of 0.5 g cm\textsuperscript{-3} is used to estimate the
location of the edge of the droplet.  The $r$ and $z$-dependence of
the droplet's edge is then fit to a circle, and the contact angle is
computed from the intersection of the fit circle with the $z$-axis
location of the solid surface.  Again, for each stored configuration,
the density profile in a set of annular shells was computed. Due to
large density fluctuations close to the ice, all shells located within
2 \AA\ of the ice surface were left out of the circular fits.  The
height of the solid surface ($z_\mathrm{suface}$) along with the best
fitting origin ($z_\mathrm{droplet}$) and radius
($r_\mathrm{droplet}$) of the droplet can then be used to compute the
contact angle,
\begin{equation}
\theta =  90 + \frac{180}{\pi} \sin^{-1}\left(\frac{z_\mathrm{droplet} -
  z_\mathrm{surface}}{r_\mathrm{droplet}} \right).
\end{equation}

\section{Determining interfacial widths using structural information}
To determine the structural widths of the interfaces under shear, each
of the systems was divided into 100 bins along the $z$-dimension, and
the local tetrahedral order parameter (Eq. 5 in Reference
\citealp{Louden13}) was time-averaged in each bin for the duration of
the shearing simulation.  The spatial dependence of this order
parameter, $q(z)$, is the tetrahedrality profile of the interface.
The lower panels in figures S2-S5 in the SI show tetrahedrality
profiles (in circles) for each of the four interfaces.  The $q(z)$
function has a range of $(0,1)$, where a value of unity indicates a
perfectly tetrahedral environment.  The $q(z)$ for the bulk liquid was
found to be $\approx~0.77$, while values of $\approx~0.92$ were more
common in the ice. The tetrahedrality profiles were fit using a
hyperbolic tangent function (see Eq. 6 in Reference
\citealp{Louden13}) designed to smoothly fit the bulk to ice
transition while accounting for the weak thermal gradient. In panels
$b$ and $c$ of the same figures, the resulting thermal and velocity
gradients from an imposed kinetic energy and momentum fluxes can be
seen. The vertical dotted lines traversing these figures indicate the
midpoints of the interfaces as determined by the tetrahedrality
profiles.

\section{Determining interfacial widths using dynamic information}
To determine the dynamic widths of the interfaces under shear, each of
the systems was divided into bins along the $z$-dimension ($\approx$ 3
\AA\ wide) and $C_2(z,t)$ was computed using only those molecules that
were in the bin at the initial time. The time-dependence was fit to a
triexponential decay, with three time constants: $\tau_{short}$,
measuring the librational motion of the water molecules,
$\tau_{middle}$, measuring the timescale for breaking and making of
hydrogen bonds, and $\tau_{long}$, corresponding to the translational
motion of the water molecules.  An additional constant was introduced
in the fits to describe molecules in the crystal which do not
experience long-time orientational decay.

In Figures S6-S9 in the supporting information, the $z$-coordinate
profiles for the three decay constants, $\tau_{short}$,
$\tau_{middle}$, and $\tau_{long}$ for the different interfaces are
shown.  (Figures S6 \& S7 are new results, and Figures S8 \& S9 are
updated plots from Ref \citealp{Louden13}.)  In the liquid regions of
all four interfaces, we observe $\tau_{middle}$ and $\tau_{long}$ to
have approximately consistent values of $3-6$ ps and $30-40$ ps,
respectively.  Both of these times increase in value approaching the
interface.  Approaching the interface, we also observe that
$\tau_{short}$ decreases from its liquid-state value of $72-76$ fs.
The approximate values for the decay constants and the trends
approaching the interface match those reported previously for the
basal and prismatic interfaces.

We have estimated the dynamic interfacial width $d_\mathrm{dyn}$ by
fitting the profiles of all the three orientational time constants
with an exponential decay to the bulk-liquid behavior,
\begin{equation}\label{tauFit}
  \tau(z)\approx\tau_{liquid}+(\tau_{wall}-\tau_{liquid})e^{-(z-z_{wall})/d_\mathrm{dyn}}
\end{equation}
where $\tau_{liquid}$ and $\tau_{wall}$ are the liquid and projected
wall values of the decay constants, $z_{wall}$ is the location of the
interface, as measured by the structural order parameter.  These
values are shown in table \ref{tab:kappa}. Because the bins must be
quite wide to obtain reasonable profiles of $C_2(z,t)$, the error
estimates for the dynamic widths of the interface are significantly
larger than for the structural widths.  However, all four interfaces
exhibit dynamic widths that are significantly below 1~nm, and are in
reasonable agreement with the structural width above.

\end{article}

\begin{table}[h]
\centering
\caption{Sizes of the droplet and shearing simulations.  Cell
  dimensions are measured in \AA. \label{tab:method}}
\begin{tabular}{r|cccc|ccccc} 
\toprule
 \multirow{2}{*}{Interface} & \multicolumn{4}{c|}{Droplet} & \multicolumn{5}{c}{Shearing} \\
  & $N_\mathrm{ice}$ & $N_\mathrm{droplet}$ & $L_x$ & $L_y$ & $N_\mathrm{ice}$ & $N_\mathrm{liquid}$ & $L_x$ & $L_y$ & $L_z$  \\ 
\midrule
Basal  $\{0001\}$                    & 12960 & 2048 & 134.70 & 140.04 & 900 & 1846  & 23.87 & 35.83 & 98.64  \\
Pyramidal  $\{2~0~\bar{2}~1\}$       & 11136 & 2048 & 143.75 & 121.41 & 1216 & 2203 & 37.47 & 29.50 & 93.02  \\
Prismatic  $\{1~0~\bar{1}~0\}$       &  9900 & 2048 & 110.04 & 115.00 & 3000 & 5464 & 35.95 & 35.65 & 205.77 \\
Secondary Prism  $\{1~1~\bar{2}~0\}$ & 11520 & 2048 & 146.72 & 124.48 & 3840 & 8176 & 71.87 & 31.66 & 161.55 \\
\bottomrule
\end{tabular}
\end{table}

%S1: contact angle
\begin{figure}
\includegraphics[width=\linewidth]{ContactAngle}
\caption{\label{fig:ContactAngle} The dynamic contact angle of a
  droplet after approaching each of the four ice facets.  The decay to
  an equilibrium contact angle displays similar dynamics.  Although
  all the surfaces are hydrophilic, the long-time behavior stabilizes
  to significantly flatter droplets for the basal and pyramidal
  facets.  This suggests a difference in hydrophilicity for these
  facets compared with the two prismatic facets.}
\end{figure}


%S2-S5 are the z-rnemd profiles
\begin{figure}
\includegraphics[width=\linewidth]{Pyr_comic_strip}
\caption{\label{fig:pyrComic} Properties of the pyramidal interface
  being sheared through water at 3.8 ms\textsuperscript{-1}. Lower
  panel: the local tetrahedral order parameter, $q(z)$, (circles) and
  the hyperbolic tangent fit (turquoise line).  Middle panel: the
  imposed thermal gradient required to maintain a fixed interfacial
  temperature of 225 K. Upper panel: the transverse velocity gradient
  that develops in response to an imposed momentum flux. The vertical
  dotted lines indicate the locations of the midpoints of the two
  interfaces.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{SP_comic_strip}
\caption{\label{fig:spComic} The secondary prism interface with a shear 
rate of 3.5 \
ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{B_comic_strip}
\caption{\label{fig:bComic} The basal interface with a shear 
rate of 1.3 \
ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{prismatic_comic_strip}
\caption{\label{fig:pComic} The prismatic interface with a shear 
rate of 2 \
ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
\end{figure}

%Figures S6-S9 are the z-orientation times
\begin{figure}
\includegraphics[width=\linewidth]{Pyr-orient}
\caption{\label{fig:PyrOrient} The three decay constants of the
  orientational time correlation function, $C_2(z,t)$, for water as a
  function of distance from the center of the ice slab. The vertical
  dashed line indicates the edge of the pyramidal ice slab determined
  by the local order tetrahedral parameter. The control (circles) and
  sheared (squares) simulations were fit using shifted-exponential
  decay (see Eq. 9 in Ref. \citealp{Louden13}).}
\end{figure}  

\begin{figure}
\includegraphics[width=\linewidth]{SP-orient}
\caption{\label{fig:SPorient} Decay constants for $C_2(z,t)$ at the secondary 
prism face. Panel descriptions match those in \ref{fig:PyrOrient}.}
\end{figure}


\begin{figure}
\includegraphics[width=\linewidth]{B-orient}
\caption{\label{fig:Borient} Decay constants for $C_2(z,t)$ at the basal face. Panel descriptions match those in \ref{fig:PyrOrient}.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{prismatic-orient}
\caption{\label{fig:Porient} Decay constants for $C_2(z,t)$ at the 
prismatic face. Panel descriptions match those in \ref{fig:PyrOrient}.}
\end{figure}

\bibliography{iceWater}

\end{document}
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1	plouden	4259	%load any "/usepackage" here...
2			\documentclass{pnastwo}
3
4			%% ADDITIONAL OPTIONAL STYLE FILES Font specification
5
6			%\usepackage{PNASTWOF}
7			\usepackage[version=3]{mhchem}
8			\usepackage[round,numbers,sort&compress]{natbib}
9			\usepackage{fixltx2e}
10			\usepackage{booktabs}
11			\usepackage{multirow}
12	gezelter	4261	\usepackage{tablefootnote}
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14	plouden	4259	\bibpunct{(}{)}{,}{n}{,}{,}
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21
22			%% OPTIONAL MACRO DEFINITIONS
23			\def\s{\sigma}
24			%%%%%%%%%%%%
25			%% For PNAS Only:
26			%\url{www.pnas.org/cgi/doi/10.1073/pnas.0709640104}
27			\copyrightyear{2014}
28			\issuedate{Issue Date}
29			\volume{Volume}
30			\issuenumber{Issue Number}
31			%\setcounter{page}{2687} %Set page number here if desired
32			%%%%%%%%%%%%
33
34	plouden	4259	\begin{document}
35
36	gezelter	4261	\title{Supporting Information for: \\
37			The different facets of ice have different hydrophilicities: Friction at water /
38			ice-I\textsubscript{h} interfaces}
39
40			\author{Patrick B. Louden\affil{1}{Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame,
41			IN 46556}
42			\and
43			J. Daniel Gezelter\affil{1}{}}
44
45			\contributor{Submitted to Proceedings of the National Academy of Sciences
46			of the United States of America}
47
48			\maketitle
49
50			\begin{article}
51
52			\section{Overview}
53			The supporting information contains further details about the model
54			construction, analysis methods, and supplies figures that support the
55			data presented in the main text.
56
57			\section{Construction of the Ice / Water interfaces}
58			Ice I$_\mathrm{h}$ crystallizes in the hexagonal space group
59			P$6_3/mmc$, and common ice crystals form hexagonal plates with the
60			basal face $\{0~0~0~1\}$ forming the top and bottom of each plate, and
61			the prismatic facet $\{1~0~\bar{1}~0\}$ forming the sides. In extreme
62			temperatures or low water saturation conditions, ice crystals can
63			easily form as hollow columns, needles and dendrites. These are
64			structures that expose other crystalline facets of the ice to the
65			surroundings. Among the more common facets are the secondary prism,
66			$\{1~1~\bar{2}~0\}$, and pyramidal, $\{2~0~\bar{2}~1\}$, faces.
67
68			We found it most useful to work with proton-ordered, zero-dipole
69			crystals that expose strips of dangling H-atoms and lone
70			pairs.\cite{Buch:2008fk} Our structures were created starting from
71			Structure 6 of Hirsch and Ojam\"{a}e's set of orthorhombic
72			representations for ice-I$_{h}$~\cite{Hirsch04}. This crystal
73			structure was cleaved along the four different facets. The exposed
74			face was reoriented normal to the $z$-axis of the simulation cell, and
75			the structures were and extended to form large exposed facets in
76			rectangular box geometries. Liquid water boxes were created with
77			identical dimensions (in $x$ and $y$) as the ice, with a $z$ dimension
78			of three times that of the ice block, and a density corresponding to 1
79			g / cm$^3$. Each of the ice slabs and water boxes were independently
80			equilibrated at a pressure of 1 atm, and the resulting systems were
81			merged by carving out any liquid water molecules within 3 \AA\ of any
82			atoms in the ice slabs. Each of the combined ice/water systems were
83			then equilibrated at 225K, which is the liquid-ice coexistence
84			temperature for SPC/E water~\cite{Bryk02}. Reference
85			\citealp{Louden13} contains a more detailed explanation of the
86			construction of similar ice/water interfaces. The resulting dimensions
87			as well as the number of ice and liquid water molecules contained in
88			each of these systems are shown in Table S1.
89
90			\section{A second method for computing contact angles}
91			In addition to the spherical cap method outlined in the main text, a
92			second method for obtaining the contact angle was described by
93			Ruijter, Blake, and Coninck~\cite{Ruijter99}. This method uses a
94			cylindrical averaging of the droplet's density profile. A threshold
95			density of 0.5 g cm\textsuperscript{-3} is used to estimate the
96			location of the edge of the droplet. The $r$ and $z$-dependence of
97			the droplet's edge is then fit to a circle, and the contact angle is
98			computed from the intersection of the fit circle with the $z$-axis
99			location of the solid surface. Again, for each stored configuration,
100			the density profile in a set of annular shells was computed. Due to
101			large density fluctuations close to the ice, all shells located within
102			2 \AA\ of the ice surface were left out of the circular fits. The
103			height of the solid surface ($z_\mathrm{suface}$) along with the best
104			fitting origin ($z_\mathrm{droplet}$) and radius
105			($r_\mathrm{droplet}$) of the droplet can then be used to compute the
106			contact angle,
107			\begin{equation}
108			\theta = 90 + \frac{180}{\pi} \sin^{-1}\left(\frac{z_\mathrm{droplet} -
109			z_\mathrm{surface}}{r_\mathrm{droplet}} \right).
110			\end{equation}
111
112			\section{Determining interfacial widths using structural information}
113			To determine the structural widths of the interfaces under shear, each
114			of the systems was divided into 100 bins along the $z$-dimension, and
115			the local tetrahedral order parameter (Eq. 5 in Reference
116			\citealp{Louden13}) was time-averaged in each bin for the duration of
117			the shearing simulation. The spatial dependence of this order
118			parameter, $q(z)$, is the tetrahedrality profile of the interface.
119			The lower panels in figures S2-S5 in the SI show tetrahedrality
120			profiles (in circles) for each of the four interfaces. The $q(z)$
121			function has a range of $(0,1)$, where a value of unity indicates a
122			perfectly tetrahedral environment. The $q(z)$ for the bulk liquid was
123			found to be $\approx~0.77$, while values of $\approx~0.92$ were more
124			common in the ice. The tetrahedrality profiles were fit using a
125			hyperbolic tangent function (see Eq. 6 in Reference
126			\citealp{Louden13}) designed to smoothly fit the bulk to ice
127			transition while accounting for the weak thermal gradient. In panels
128			$b$ and $c$ of the same figures, the resulting thermal and velocity
129			gradients from an imposed kinetic energy and momentum fluxes can be
130			seen. The vertical dotted lines traversing these figures indicate the
131			midpoints of the interfaces as determined by the tetrahedrality
132			profiles.
133
134			\section{Determining interfacial widths using dynamic information}
135			To determine the dynamic widths of the interfaces under shear, each of
136			the systems was divided into bins along the $z$-dimension ($\approx$ 3
137			\AA\ wide) and $C_2(z,t)$ was computed using only those molecules that
138			were in the bin at the initial time. The time-dependence was fit to a
139			triexponential decay, with three time constants: $\tau_{short}$,
140			measuring the librational motion of the water molecules,
141			$\tau_{middle}$, measuring the timescale for breaking and making of
142			hydrogen bonds, and $\tau_{long}$, corresponding to the translational
143			motion of the water molecules. An additional constant was introduced
144			in the fits to describe molecules in the crystal which do not
145			experience long-time orientational decay.
146
147			In Figures S6-S9 in the supporting information, the $z$-coordinate
148			profiles for the three decay constants, $\tau_{short}$,
149			$\tau_{middle}$, and $\tau_{long}$ for the different interfaces are
150			shown. (Figures S6 \& S7 are new results, and Figures S8 \& S9 are
151			updated plots from Ref \citealp{Louden13}.) In the liquid regions of
152			all four interfaces, we observe $\tau_{middle}$ and $\tau_{long}$ to
153			have approximately consistent values of $3-6$ ps and $30-40$ ps,
154			respectively. Both of these times increase in value approaching the
155			interface. Approaching the interface, we also observe that
156			$\tau_{short}$ decreases from its liquid-state value of $72-76$ fs.
157			The approximate values for the decay constants and the trends
158			approaching the interface match those reported previously for the
159			basal and prismatic interfaces.
160
161			We have estimated the dynamic interfacial width $d_\mathrm{dyn}$ by
162			fitting the profiles of all the three orientational time constants
163			with an exponential decay to the bulk-liquid behavior,
164			\begin{equation}\label{tauFit}
165			\tau(z)\approx\tau_{liquid}+(\tau_{wall}-\tau_{liquid})e^{-(z-z_{wall})/d_\mathrm{dyn}}
166			\end{equation}
167			where $\tau_{liquid}$ and $\tau_{wall}$ are the liquid and projected
168			wall values of the decay constants, $z_{wall}$ is the location of the
169			interface, as measured by the structural order parameter. These
170			values are shown in table \ref{tab:kappa}. Because the bins must be
171			quite wide to obtain reasonable profiles of $C_2(z,t)$, the error
172			estimates for the dynamic widths of the interface are significantly
173			larger than for the structural widths. However, all four interfaces
174			exhibit dynamic widths that are significantly below 1~nm, and are in
175			reasonable agreement with the structural width above.
176
177			\end{article}
178
179			\begin{table}[h]
180			\centering
181			\caption{Sizes of the droplet and shearing simulations. Cell
182			dimensions are measured in \AA. \label{tab:method}}
183			\begin{tabular}{r\|cccc\|ccccc}
184			\toprule
185			\multirow{2}{*}{Interface} & \multicolumn{4}{c\|}{Droplet} & \multicolumn{5}{c}{Shearing} \\
186			& $N_\mathrm{ice}$ & $N_\mathrm{droplet}$ & $L_x$ & $L_y$ & $N_\mathrm{ice}$ & $N_\mathrm{liquid}$ & $L_x$ & $L_y$ & $L_z$ \\
187			\midrule
188			Basal $\{0001\}$ & 12960 & 2048 & 134.70 & 140.04 & 900 & 1846 & 23.87 & 35.83 & 98.64 \\
189			Pyramidal $\{2~0~\bar{2}~1\}$ & 11136 & 2048 & 143.75 & 121.41 & 1216 & 2203 & 37.47 & 29.50 & 93.02 \\
190			Prismatic $\{1~0~\bar{1}~0\}$ & 9900 & 2048 & 110.04 & 115.00 & 3000 & 5464 & 35.95 & 35.65 & 205.77 \\
191			Secondary Prism $\{1~1~\bar{2}~0\}$ & 11520 & 2048 & 146.72 & 124.48 & 3840 & 8176 & 71.87 & 31.66 & 161.55 \\
192			\bottomrule
193			\end{tabular}
194			\end{table}
195
196			%S1: contact angle
197	plouden	4259	\begin{figure}
198	gezelter	4261	\includegraphics[width=\linewidth]{ContactAngle}
199			\caption{\label{fig:ContactAngle} The dynamic contact angle of a
200			droplet after approaching each of the four ice facets. The decay to
201			an equilibrium contact angle displays similar dynamics. Although
202			all the surfaces are hydrophilic, the long-time behavior stabilizes
203			to significantly flatter droplets for the basal and pyramidal
204			facets. This suggests a difference in hydrophilicity for these
205			facets compared with the two prismatic facets.}
206			\end{figure}
207
208
209			%S2-S5 are the z-rnemd profiles
210			\begin{figure}
211	plouden	4259	\includegraphics[width=\linewidth]{Pyr_comic_strip}
212			\caption{\label{fig:pyrComic} Properties of the pyramidal interface
213			being sheared through water at 3.8 ms\textsuperscript{-1}. Lower
214			panel: the local tetrahedral order parameter, $q(z)$, (circles) and
215			the hyperbolic tangent fit (turquoise line). Middle panel: the
216			imposed thermal gradient required to maintain a fixed interfacial
217			temperature of 225 K. Upper panel: the transverse velocity gradient
218			that develops in response to an imposed momentum flux. The vertical
219			dotted lines indicate the locations of the midpoints of the two
220			interfaces.}
221			\end{figure}
222
223			\begin{figure}
224			\includegraphics[width=\linewidth]{SP_comic_strip}
225			\caption{\label{fig:spComic} The secondary prism interface with a shear
226			rate of 3.5 \
227			ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
228			\end{figure}
229
230			\begin{figure}
231	gezelter	4261	\includegraphics[width=\linewidth]{B_comic_strip}
232			\caption{\label{fig:bComic} The basal interface with a shear
233	plouden	4259	rate of 1.3 \
234			ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
235			\end{figure}
236
237			\begin{figure}
238	gezelter	4261	\includegraphics[width=\linewidth]{prismatic_comic_strip}
239			\caption{\label{fig:pComic} The prismatic interface with a shear
240	plouden	4259	rate of 2 \
241			ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:pyrComic}.}
242			\end{figure}
243
244	gezelter	4261	%Figures S6-S9 are the z-orientation times
245	plouden	4259	\begin{figure}
246			\includegraphics[width=\linewidth]{Pyr-orient}
247			\caption{\label{fig:PyrOrient} The three decay constants of the
248			orientational time correlation function, $C_2(z,t)$, for water as a
249			function of distance from the center of the ice slab. The vertical
250			dashed line indicates the edge of the pyramidal ice slab determined
251			by the local order tetrahedral parameter. The control (circles) and
252			sheared (squares) simulations were fit using shifted-exponential
253			decay (see Eq. 9 in Ref. \citealp{Louden13}).}
254			\end{figure}
255
256			\begin{figure}
257			\includegraphics[width=\linewidth]{SP-orient}
258			\caption{\label{fig:SPorient} Decay constants for $C_2(z,t)$ at the secondary
259			prism face. Panel descriptions match those in \ref{fig:PyrOrient}.}
260			\end{figure}
261
262
263			\begin{figure}
264	gezelter	4261	\includegraphics[width=\linewidth]{B-orient}
265			\caption{\label{fig:Borient} Decay constants for $C_2(z,t)$ at the basal face. Panel descriptions match those in \ref{fig:PyrOrient}.}
266	plouden	4259	\end{figure}
267
268			\begin{figure}
269	gezelter	4261	\includegraphics[width=\linewidth]{prismatic-orient}
270			\caption{\label{fig:Porient} Decay constants for $C_2(z,t)$ at the
271	plouden	4259	prismatic face. Panel descriptions match those in \ref{fig:PyrOrient}.}
272			\end{figure}
273
274	gezelter	4261	\bibliography{iceWater}
275
276			\end{document}