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| 179 |
|
\subsection{Construction of the Ice / Water Interfaces} |
| 180 |
|
To construct the four interfacial ice/water systems, a proton-ordered, |
| 181 |
|
zero-dipole crystal of ice-I$_\mathrm{h}$ with exposed strips of |
| 182 |
< |
H-atoms and lone pairs was constructed using Structure 6 of Hirsch and |
| 183 |
< |
Ojam\"{a}e's set of orthorhombic representations for |
| 184 |
< |
ice-I$_{h}$.\cite{Hirsch04} This crystal structure was cleaved along |
| 185 |
< |
the four different facets being studied. The exposed face was |
| 186 |
< |
reoriented normal to the $z$-axis of the simulation cell, and the |
| 187 |
< |
structures were and extended to form large exposed facets in |
| 188 |
< |
rectangular box geometries. Liquid water boxes were created with |
| 189 |
< |
identical dimensions (in $x$ and $y$) as the ice, and a $z$ dimension |
| 190 |
< |
of three times that of the ice block, and a density corresponding to |
| 191 |
< |
$\sim$ 1 g / cm$^3$. Each of the ice slabs and water boxes were |
| 192 |
< |
independently equilibrated, and the resulting systems were merged by |
| 193 |
< |
carving out any liquid water molecules within 3 \AA\ of any atoms in |
| 194 |
< |
the ice slabs. Each of the combined ice/water systems were then |
| 195 |
< |
equilibrated at 225K, which is the liquid-ice coexistence temperature |
| 196 |
< |
for SPC/E water.\cite{Bryk02} Ref. \citealp{Louden13} contains a more |
| 197 |
< |
detailed explanation of the construction of ice/water interfaces. The |
| 198 |
< |
resulting dimensions, number of ice, and liquid water molecules |
| 199 |
< |
contained in each of these systems can be seen in Table |
| 182 |
> |
H-atoms was created using Structure 6 of Hirsch and Ojam\"{a}e's set |
| 183 |
> |
of orthorhombic representations for ice-I$_{h}$~\cite{Hirsch04}. This |
| 184 |
> |
crystal structure was cleaved along the four different facets. The |
| 185 |
> |
exposed face was reoriented normal to the $z$-axis of the simulation |
| 186 |
> |
cell, and the structures were and extended to form large exposed |
| 187 |
> |
facets in rectangular box geometries. Liquid water boxes were created |
| 188 |
> |
with identical dimensions (in $x$ and $y$) as the ice, with a $z$ |
| 189 |
> |
dimension of three times that of the ice block, and a density |
| 190 |
> |
corresponding to 1 g / cm$^3$. Each of the ice slabs and water boxes |
| 191 |
> |
were independently equilibrated at a pressure of 1 atm, and the |
| 192 |
> |
resulting systems were merged by carving out any liquid water |
| 193 |
> |
molecules within 3 \AA\ of any atoms in the ice slabs. Each of the |
| 194 |
> |
combined ice/water systems were then equilibrated at 225K, which is |
| 195 |
> |
the liquid-ice coexistence temperature for SPC/E |
| 196 |
> |
water~\cite{Bryk02}. Ref. \citealp{Louden13} contains a more detailed |
| 197 |
> |
explanation of the construction of similar ice/water interfaces. The |
| 198 |
> |
resulting dimensions as well as the number of ice and liquid water |
| 199 |
> |
molecules contained in each of these systems are shown in Table |
| 200 |
|
\ref{tab:method}. |
| 201 |
|
|
| 202 |
< |
Mostly avoids spurious crystalline morphologies like ice-i and ice-B. |
| 201 |
< |
|
| 202 |
< |
The SPC/E water model\cite{Berendsen87} has been extensively |
| 202 |
> |
The SPC/E water model~\cite{Berendsen87} has been extensively |
| 203 |
|
characterized over a wide range of liquid |
| 204 |
< |
conditions,\cite{Arbuckle02, Kuang12} and its phase diagram has been well studied.\cite{Baez95,Bryk04b,Sanz04b} |
| 205 |
< |
The free energies \cite{Baez95} and melting points |
| 206 |
< |
\cite{Baez95,Arbuckle02,Gay02,Bryk02,Bryk04b,Sanz04b,Fernandez06,Abascal07,Vrbka07} |
| 207 |
< |
of various crystal structures have also been calculated. |
| 208 |
< |
Haymet et al. have studied the quiescent Ice-I$_\mathrm{h}$/water |
| 209 |
< |
interface using the SPC/E water model, and has seen good agreement for |
| 210 |
< |
structural and dynamic measurements of the interfacial width when compared with more |
| 211 |
< |
expensive water models. For these reasons, the SPC/E water |
| 212 |
< |
model was used in this study. |
| 213 |
< |
|
| 214 |
< |
\subsection{Shearing simulations (interfaces in bulk water)} |
| 215 |
< |
% Should we mention number of runs, sim times, etc. ? |
| 216 |
< |
To perform the shearing simulations, the velocity shearing and scaling |
| 217 |
< |
varient of reverse nonequilibrium molecular dynamics (VSS-RNEMD) was |
| 218 |
< |
conducted. This method performs a series of simultaneous velocity |
| 219 |
< |
exchanges between two regions of the simulation cell, to |
| 220 |
< |
simultaneously create a velocity and temperature gradient. The thermal |
| 221 |
< |
gradient is necessary when performing shearing simulations as to |
| 222 |
< |
prevent frictional heating from the shear from melting the |
| 223 |
< |
interface. For more details on the VSS-RNEMD method please refer to a |
| 224 |
< |
pervious paper\cite{Louden13}. |
| 225 |
< |
|
| 226 |
< |
The computational details performed here were equivalent to those reported |
| 227 |
< |
in a previous publication\cite{Louden13}, with the following changes. |
| 228 |
< |
VSS-RNEMD moves were attempted every 2 fs instead of every 50 fs. This was done to minimize |
| 229 |
< |
the magnitude of each individual VSS-RNEMD perturbation to the system. |
| 230 |
< |
All pyramidal simulations were performed under the canonical (NVT) ensamble |
| 231 |
< |
except those during which configurations were accumulated for the orientational correlation |
| 232 |
< |
function, which were performed under the microcanonical (NVE) ensamble. All |
| 233 |
< |
secondary prismatic simulations were performed under the NVE ensamble. |
| 204 |
> |
conditions,\cite{Arbuckle02,Kuang12} and its phase diagram has been |
| 205 |
> |
well studied.\cite{Baez95,Bryk04b,Sanz04b,Fennell:2005fk} With longer |
| 206 |
> |
cutoff radii and careful treatment of electrostatics, SPC/E mostly |
| 207 |
> |
avoids metastable crystalline morphologies like |
| 208 |
> |
ice-\textit{i}~\cite{Fennell:2005fk} and ice-B~\cite{Baez95}. The |
| 209 |
> |
free energies and melting points |
| 210 |
> |
\cite{Baez95,Arbuckle02,Gay02,Bryk02,Bryk04b,Sanz04b,Fennell:2005fk,Fernandez06,Abascal07,Vrbka07} |
| 211 |
> |
of various other crystalline polymorphs have also been calculated. |
| 212 |
> |
Haymet \textit{et al.} have studied quiescent Ice-I$_\mathrm{h}$/water |
| 213 |
> |
interfaces using the SPC/E water model, and have seen structural and |
| 214 |
> |
dynamic measurements of the interfacial width that agree well with |
| 215 |
> |
more expensive water models, although the coexistence temperature for |
| 216 |
> |
SPC/E is still well below the experimental melting point of real |
| 217 |
> |
water~\cite{Bryk02}. Given the extensive data and speed of this model, |
| 218 |
> |
it is a reasonable choice even though the temperatures required are |
| 219 |
> |
somewhat lower than real ice / water interfaces. |
| 220 |
|
|
| 221 |
< |
\subsection{Droplet simulations} |
| 222 |
< |
Ice interfaces with a thickness of $\sim 20 \AA$ were created as |
| 221 |
> |
\subsection{Droplet Simulations} |
| 222 |
> |
Ice interfaces with a thickness of $\sim$~20~\AA\ were created as |
| 223 |
|
described above, but were not solvated in a liquid box. The crystals |
| 224 |
|
were then replicated along the $x$ and $y$ axes (parallel to the |
| 225 |
< |
surface) until a large surface had been created. The sizes and |
| 226 |
< |
numbers of molecules in each of the surfaces is given in Table |
| 227 |
< |
\ref{tab:ice_sheets}. Weak translational restraining potentials with |
| 228 |
< |
spring constants of 1.5 to 4.0 UNITS were applied to the center of mass of each |
| 229 |
< |
molecule in order to prevent surface melting, although the molecules |
| 230 |
< |
were allowed to reorient freely. A water doplet containing 2048 SPC/E |
| 231 |
< |
molecules was created separately. Droplets of this size can produce |
| 232 |
< |
agreement with the Young contact angle extrapolated to an infinite |
| 233 |
< |
drop size\cite{Daub10}. The surfaces and droplet were independently |
| 234 |
< |
equilibrated to 225 K, at which time the droplet was placed 3-5 \AA\ |
| 235 |
< |
above the surface. Five statistically independent simulations were |
| 236 |
< |
carried out for each facet, and the droplet was placed at unique $x$ |
| 237 |
< |
and $y$ locations for each of these simulations. Each simulation was |
| 238 |
< |
5 ns in length and conducted in the microcanonical (NVE) ensemble. |
| 225 |
> |
surface) until a large surface ($>$ 126 nm\textsuperscript{2}) had |
| 226 |
> |
been created. The sizes and numbers of molecules in each of the |
| 227 |
> |
surfaces is given in Table \ref{tab:method}. Weak translational |
| 228 |
> |
restraining potentials with spring constants of 1.5-4.0~$\mathrm{kcal\ |
| 229 |
> |
mol}^{-1}\mathrm{~\AA}^{-2}$ were applied to the centers of mass of |
| 230 |
> |
each molecule in order to prevent surface melting, although the |
| 231 |
> |
molecules were allowed to reorient freely. A water doplet containing |
| 232 |
> |
2048 SPC/E molecules was created separately. Droplets of this size can |
| 233 |
> |
produce agreement with the Young contact angle extrapolated to an |
| 234 |
> |
infinite drop size~\cite{Daub10}. The surfaces and droplet were |
| 235 |
> |
independently equilibrated to 225 K, at which time the droplet was |
| 236 |
> |
placed 3-5~\AA\ above the surface. Five statistically independent |
| 237 |
> |
simulations were carried out for each facet, and the droplet was |
| 238 |
> |
placed at unique $x$ and $y$ locations for each of these simulations. |
| 239 |
> |
Each simulation was 5~ns in length and was conducted in the |
| 240 |
> |
microcanonical (NVE) ensemble. Representative configurations for the |
| 241 |
> |
droplet on the prismatic facet are shown in figure \ref{fig:Droplet}. |
| 242 |
|
|
| 243 |
< |
\section{Results and discussion} |
| 244 |
< |
\subsection{Dynamic water contact angle} |
| 243 |
> |
|
| 244 |
> |
\subsection{Shearing Simulations (Interfaces in Bulk Water)} |
| 245 |
> |
|
| 246 |
> |
To perform the shearing simulations, the velocity shearing and scaling |
| 247 |
> |
variant of reverse non-equilibrium molecular dynamics (VSS-RNEMD) was |
| 248 |
> |
employed \cite{Kuang12}. This method performs a series of simultaneous |
| 249 |
> |
non-equilibrium exchanges of linear momentum and kinetic energy |
| 250 |
> |
between two physically-separated regions of the simulation cell. The |
| 251 |
> |
system responds to this unphysical flux with velocity and temperature |
| 252 |
> |
gradients. When VSS-RNEMD is applied to bulk liquids, transport |
| 253 |
> |
properties like the thermal conductivity and the shear viscosity are |
| 254 |
> |
easily extracted assuming a linear response between the flux and the |
| 255 |
> |
gradient. At the interfaces between dissimilar materials, the same |
| 256 |
> |
method can be used to extract \textit{interfacial} transport |
| 257 |
> |
properties (e.g. the interfacial thermal conductance and the |
| 258 |
> |
hydrodynamic slip length). |
| 259 |
> |
|
| 260 |
> |
The kinetic energy flux (producing a thermal gradient) is necessary |
| 261 |
> |
when performing shearing simulations at the ice-water interface in |
| 262 |
> |
order to prevent the frictional heating due to the shear from melting |
| 263 |
> |
the interface. Reference \citealp{Louden13} provides more details on |
| 264 |
> |
the VSS-RNEMD method as applied to ice-water interfaces. A |
| 265 |
> |
representative configuration of the solvated prismatic facet being |
| 266 |
> |
sheared through liquid water is shown in figure \ref{fig:Shearing}. |
| 267 |
> |
|
| 268 |
> |
In the results discussed below, the exchanges between the two regions |
| 269 |
> |
were carried out every 2 fs (e.g. every time step). This was done to |
| 270 |
> |
minimize the magnitude of each individual momentum exchange. Because |
| 271 |
> |
individual VSS-RNEMD exchanges conserve both total energy and linear |
| 272 |
> |
momentum, the method can be ``bolted-on'' to simulations in any |
| 273 |
> |
ensemble. The simulations of the pyramidal interface were performed |
| 274 |
> |
under the canonical (NVT) ensemble. When time correlation functions |
| 275 |
> |
were computed (see section \ref{sec:orient}), these simulations were |
| 276 |
> |
done in the microcanonical (NVE) ensemble. All simulations of the |
| 277 |
> |
other interfaces were done in the microcanonical ensemble. |
| 278 |
> |
|
| 279 |
> |
\section{Results} |
| 280 |
> |
\subsection{Ice - Water Contact Angles} |
| 281 |
|
|
| 282 |
|
To determine the extent of wetting for each of the four crystal |
| 283 |
< |
facets, water contact angle simuations were performed. Contact angles |
| 284 |
< |
were obtained from these simulations by two methods. In the first |
| 285 |
< |
method, the contact angle was obtained from the $z$-center of mass |
| 286 |
< |
($z_{c.m.}$) of the water droplet as described by Hautman and Klein\cite{Hautman91} |
| 287 |
< |
and utilized by Hirvi and Pakkanen in their investigation of water |
| 288 |
< |
droplets on polyethylene and poly(vinyl chloride) |
| 289 |
< |
surface\cite{Hirvi06}. At each snapshot of the simulation, the contact |
| 290 |
< |
angle, $\theta$, was found by |
| 283 |
> |
facets, contact angles for liquid droplets on the ice surfaces were |
| 284 |
> |
computed using two methods. In the first method, the droplet is |
| 285 |
> |
assumed to form a spherical cap, and the contact angle is estimated |
| 286 |
> |
from the $z$-axis location of the droplet's center of mass |
| 287 |
> |
($z_\mathrm{cm}$). This procedure was first described by Hautman and |
| 288 |
> |
Klein~\cite{Hautman91}, and was utilized by Hirvi and Pakkanen in |
| 289 |
> |
their investigation of water droplets on polyethylene and poly(vinyl |
| 290 |
> |
chloride) surfaces~\cite{Hirvi06}. For each stored configuration, the |
| 291 |
> |
contact angle, $\theta$, was found by inverting the expression for the |
| 292 |
> |
location of the droplet center of mass, |
| 293 |
|
\begin{equation}\label{contact_1} |
| 294 |
< |
\langle z_{c.m.}\rangle = 2^{-4/3}R_{0}\bigg(\frac{1-cos\theta}{2+cos\theta}\bigg)^{1/3}\frac{3+cos\theta}{2+cos\theta} , |
| 294 |
> |
\langle z_\mathrm{cm}\rangle = 2^{-4/3}R_{0}\bigg(\frac{1-cos\theta}{2+cos\theta}\bigg)^{1/3}\frac{3+cos\theta}{2+cos\theta} , |
| 295 |
|
\end{equation} |
| 296 |
< |
where $R_{0}$ is the radius of the free water droplet. In the second |
| 270 |
< |
method, the contact angle was obtained from fitting the droplet's |
| 271 |
< |
$z$-profile after radial averaging to a |
| 272 |
< |
circle as described by Ruijter, Blake, and |
| 273 |
< |
Coninck\cite{Ruijter99}. At each snapshot of the simulation the water droplet was |
| 274 |
< |
broken into bins, and the location of bin containing half-bulk density was |
| 275 |
< |
stored. Due to fluctuations close to the ice, all bins located within |
| 276 |
< |
2.0 \AA\ of the ice were discarded. The remaining stored bins were |
| 277 |
< |
then fit by a circle, whose tangential intersection with the ice plane could |
| 278 |
< |
be used to calculate the water |
| 279 |
< |
contact angle. These results proved noisey and unreliable when |
| 280 |
< |
compared with the first method, for these purposes we omit the data |
| 281 |
< |
from the second method. |
| 296 |
> |
where $R_{0}$ is the radius of the free water droplet. |
| 297 |
|
|
| 298 |
< |
The resulting water contact angle profiles generated by the first method |
| 299 |
< |
had an initial value of 180$^{o}$, and decayed over time. Each of |
| 300 |
< |
these profiles were fit to a biexponential decay, with a short time |
| 301 |
< |
piece to account for the water droplet initially adhering to the |
| 302 |
< |
surface, a long time piece describing the spreading of the droplet |
| 303 |
< |
over the surface, and an added constant to capture the infinite |
| 304 |
< |
decay of the contact angle. We have found that the rate of the water |
| 305 |
< |
droplet spreading across all four crystal facets to be $\approx$ 0.7 |
| 306 |
< |
ns$^{-1}$. However, the basal and pyramidal facets |
| 307 |
< |
had an infinite decay value for $\theta$ of $\approx$ 35$^{o}$, while |
| 308 |
< |
prismatic and secondary prismatic had values for $\theta$ near |
| 309 |
< |
43$^{o}$ as seen in Table \ref{tab:kappa}. These results indicate that the |
| 310 |
< |
basal and pyramidal facets are more hydrophilic than the prismatic and |
| 311 |
< |
secondary prismatic, and surprisingly, that the differential hydrophilicities of |
| 312 |
< |
the crystal facets is not reflected in the spreading rate of the droplet. |
| 298 |
> |
The second method for obtaining the contact angle was described by |
| 299 |
> |
Ruijter, Blake, and Coninck~\cite{Ruijter99}. This method uses a |
| 300 |
> |
cylindrical averaging of the droplet's density profile. A threshold |
| 301 |
> |
density of 0.5 g cm\textsuperscript{-3} is used to estimate the |
| 302 |
> |
location of the edge of the droplet. The $r$ and $z$-dependence of |
| 303 |
> |
the droplet's edge is then fit to a circle, and the contact angle is |
| 304 |
> |
computed from the intersection of the fit circle with the $z$-axis |
| 305 |
> |
location of the solid surface. Again, for each stored configuration, |
| 306 |
> |
the density profile in a set of annular shells was computed. Due to |
| 307 |
> |
large density fluctuations close to the ice, all shells located within |
| 308 |
> |
2 \AA\ of the ice surface were left out of the circular fits. The |
| 309 |
> |
height of the solid surface ($z_\mathrm{suface}$) along with the best |
| 310 |
> |
fitting central height ($z_\mathrm{center}$) and radius |
| 311 |
> |
($r_\mathrm{droplet}$) of the droplet can then be used to compute the |
| 312 |
> |
contact angle, |
| 313 |
> |
\begin{equation} |
| 314 |
> |
\theta = 90 + \frac{180}{\pi} \sin^{-1}\left(\frac{z_\mathrm{center} - |
| 315 |
> |
z_\mathrm{surface}}{r_\mathrm{droplet}} \right). |
| 316 |
> |
\end{equation} |
| 317 |
> |
Both methods provided similar estimates of the dynamic contact angle, |
| 318 |
> |
although the first method is significantly less prone to noise, and |
| 319 |
> |
is the method used to report contact angles below. |
| 320 |
> |
|
| 321 |
> |
Because the initial droplet was placed above the surface, the initial |
| 322 |
> |
value of 180$^{\circ}$ decayed over time. See fig. XXXX. Each of |
| 323 |
> |
these profiles were fit to a biexponential decay, with a short-time |
| 324 |
> |
contribution that describes the initial contact with the surface, a |
| 325 |
> |
long time contribution that describes the spread of the droplet over |
| 326 |
> |
the surface, and a constant to capture the infinite-time estimate of |
| 327 |
> |
the equilibrium contact angle, |
| 328 |
> |
\begin{equation} |
| 329 |
> |
\theta(t) = \theta_\infty + (180-\theta_\infty) \left[ a e^{-k_\mathrm{contact} t} + |
| 330 |
> |
(1-a) e^{-k_\mathrm{spread} t} \right] |
| 331 |
> |
\end{equation} |
| 332 |
> |
|
| 333 |
> |
We have found that the rate of the water droplet spreading across all |
| 334 |
> |
four crystal facets to be $k_\mathrm{spread} \approx$ 0.7 |
| 335 |
> |
ns$^{-1}$. However, the basal and pyramidal facets had estimated |
| 336 |
> |
equilibrium contact angles of $\theta_\infty \approx$ 35$^{o}$, while |
| 337 |
> |
prismatic and secondary prismatic had values for $\theta_\infty$ near |
| 338 |
> |
43$^{o}$ as seen in Table \ref{tab:kappa}. |
| 339 |
> |
|
| 340 |
> |
These results indicate that the basal and pyramidal facets are |
| 341 |
> |
somewhat more hydrophilic than the prismatic and secondary prism |
| 342 |
> |
facets, and surprisingly, that the differential hydrophilicities of |
| 343 |
> |
the crystal facets is not reflected in the spreading rate of the |
| 344 |
> |
droplet. |
| 345 |
> |
|
| 346 |
|
% This is in good agreement with our calculations of friction |
| 347 |
|
% coefficients, in which the basal |
| 348 |
|
% and pyramidal had a higher coefficient of kinetic friction than the |
| 482 |
|
by the movement of water over the ice. |
| 483 |
|
|
| 484 |
|
|
| 485 |
< |
\subsection{Orientational dynamics} |
| 485 |
> |
\subsection{Orientational dynamics \label{sec:orient}} |
| 486 |
|
%Should we include the math here? |
| 487 |
|
The orientational time correlation function, |
| 488 |
|
\begin{equation}\label{C(t)1} |
| 769 |
|
|
| 770 |
|
|
| 771 |
|
\end{article} |
| 772 |
+ |
|
| 773 |
+ |
\begin{figure} |
| 774 |
+ |
\includegraphics[width=\linewidth]{Droplet} |
| 775 |
+ |
\caption{\label{fig:Droplet} Computational model of a droplet of |
| 776 |
+ |
liquid water spreading over the prismatic $\{1~0~\bar{1}~0\}$ facet |
| 777 |
+ |
of ice, before (left) and 5 ns after (right) being introduced to the |
| 778 |
+ |
surface. The contact angle ($\theta$) shrinks as the simulation |
| 779 |
+ |
proceeds, and the long-time behavior of this angle is used to |
| 780 |
+ |
estimate the hydrophilicity of the facet.} |
| 781 |
+ |
\end{figure} |
| 782 |
|
|
| 783 |
|
\begin{figure} |
| 784 |
+ |
\includegraphics[width=\linewidth]{ } |
| 785 |
+ |
\caption{\label{fig:Shearing} Computational model of a slab of ice |
| 786 |
+ |
being sheared through liquid water (above and below). In this |
| 787 |
+ |
figure, the ice is presenting the prismatic $\{1~0~\bar{1}~0\}$ |
| 788 |
+ |
facet towards the liquid phase.} |
| 789 |
+ |
\end{figure} |
| 790 |
+ |
|
| 791 |
+ |
|
| 792 |
+ |
\begin{figure} |
| 793 |
|
\includegraphics[width=\linewidth]{Pyr_comic_strip} |
| 794 |
|
\caption{\label{fig:pyrComic} The pyramidal interface with a shear |
| 795 |
|
rate of 3.8 ms\textsuperscript{-1}. Lower panel: the local tetrahedral order |
| 832 |
|
|
| 833 |
|
\begin{table}[h] |
| 834 |
|
\centering |
| 835 |
< |
\caption{Droplet and Shearing simulation parameters} |
| 836 |
< |
\label{tab:method} |
| 837 |
< |
\begin{tabular}{|cccc|ccc|} \hline |
| 838 |
< |
& \multicolumn{3}{c}{Droplet} & \multicolumn{3}{c|}{Shearing}\\ |
| 839 |
< |
Interface & $N_{ice}$ & $N_{droplet}$ & Lx, Ly (\AA) & |
| 840 |
< |
$N_{ice}$ & $N_{liquid}$ & Lx, Ly, Lz (\AA) \\ \hline |
| 841 |
< |
Basal & 12960& 2048 & (134.70, 140.04) & 900 & 1846 & (23.87, 35.83, 98.64)\\ |
| 842 |
< |
Prismatic & 9900& 2048 & (110.04, 115.00) & 3000 & 5464 & |
| 843 |
< |
(35.95, 35.65, 205.77)\\ |
| 844 |
< |
Pyramidal & 11136 & 2048& (143.75, 121.41) & 1216 & 2203 & |
| 845 |
< |
(143.75, 121.41)\\ |
| 846 |
< |
Secondary Prismatic & 11520 & 2048 & (146.72, 124.48) & 3840 & |
| 780 |
< |
8176 & (71.87, 31.66, 161.55)\\ |
| 781 |
< |
\hline |
| 835 |
> |
\caption{Sizes of the droplet and shearing simulations. Cell |
| 836 |
> |
dimensions are measured in \AA. \label{tab:method}} |
| 837 |
> |
\begin{tabular}{r|cccc|ccccc} |
| 838 |
> |
\toprule |
| 839 |
> |
\multirow{2}{*}{Interface} & \multicolumn{4}{c|}{Droplet} & \multicolumn{5}{c}{Shearing} \\ |
| 840 |
> |
& $N_\mathrm{ice}$ & $N_\mathrm{droplet}$ & $L_x$ & $L_y$ & $N_\mathrm{ice}$ & $N_\mathrm{liquid}$ & $L_x$ & $L_y$ & $L_z$ \\ |
| 841 |
> |
\midrule |
| 842 |
> |
Basal $\{0001\}$ & 12960 & 2048 & 134.70 & 140.04 & 900 & 1846 & 23.87 & 35.83 & 98.64 \\ |
| 843 |
> |
Pyramidal $\{2~0~\bar{2}~1\}$ & 11136 & 2048 & 143.75 & 121.41 & 1216 & 2203 & 37.47 & 29.50 & 93.02 \\ |
| 844 |
> |
Prismatic $\{1~0~\bar{1}~0\}$ & 9900 & 2048 & 110.04 & 115.00 & 3000 & 5464 & 35.95 & 35.65 & 205.77 \\ |
| 845 |
> |
Secondary Prism $\{1~1~\bar{2}~0\}$ & 11520 & 2048 & 146.72 & 124.48 & 3840 & 8176 & 71.87 & 31.66 & 161.55 \\ |
| 846 |
> |
\bottomrule |
| 847 |
|
\end{tabular} |
| 848 |
|
\end{table} |
| 849 |
|
|
| 850 |
|
|
| 851 |
|
\begin{table}[h] |
| 852 |
|
\centering |
| 853 |
< |
\caption{Phyiscal properties of the basal, prismatic, pyramidal, and secondary prismatic facets of Ice-I$_\mathrm{h}$} |
| 854 |
< |
\label{tab:kappa} |
| 855 |
< |
\begin{tabular}{|ccc|cccc|} \hline |
| 856 |
< |
& \multicolumn{2}{c}{Droplet} & \multicolumn{4}{c|}{Shearing}\\ |
| 857 |
< |
Interface & $\theta^{\circ}_{\infty}$ & $K_{spread} (ns^{-1})$ & |
| 858 |
< |
$\kappa_{x}$ & $\kappa_{y}$ & d$_{q_{z}}$ (\AA) & d$_{\tau}$ (\AA) \\ \hline |
| 859 |
< |
Basal & $34.1 \pm 0.9$ &$0.60 \pm 0.07$ & $5.9 \pm 0.3$&$6.5 \pm 0.8$ |
| 860 |
< |
& $3.2 \pm 0.4$ & $2.9$ \\ |
| 861 |
< |
Pyramidal & $35 \pm 3$ & $0.7 \pm 0.1$ & $5.8 \pm 0.4$ & $6.1 \pm |
| 862 |
< |
0.5$ & $3.2 \pm 0.2$ & $2.7$ \\ |
| 863 |
< |
Prismatic & $45 \pm 3$ & $0.75 \pm 0.09$ & $3.0 \pm 0.2$ & $3.0 \pm |
| 864 |
< |
0.1$ & $3.6 \pm 0.2$ & $3.5$ \\ |
| 865 |
< |
Secondary Prismatic & $42 \pm 2$ & $0.69 \pm 0.03$ & $3.5 \pm 0.1$ & |
| 866 |
< |
$3.3 \pm 0.2$ & $3.2 \pm 0.2$ & $3$ \\ \hline |
| 853 |
> |
\caption{Structural and dynamic properties of the interfaces of Ice-I$_\mathrm{h}$ |
| 854 |
> |
with water. Liquid-solid friction coefficients ($\kappa_x$ and $\kappa_y$) are expressed in 10\textsuperscript{-4} amu |
| 855 |
> |
\AA\textsuperscript{-2} fs\textsuperscript{-1}. \label{tab:kappa}} |
| 856 |
> |
\begin{tabular}{r|cc|cccc} |
| 857 |
> |
\toprule |
| 858 |
> |
\multirow{2}{*}{Interface} & \multicolumn{2}{c|}{Droplet} & \multicolumn{4}{c}{Shearing}\\ |
| 859 |
> |
& $\theta_{\infty}$ ($^\circ$) & $k_\mathrm{spread}$ (ns\textsuperscript{-1}) & |
| 860 |
> |
$\kappa_{x}$ & $\kappa_{y}$ & $d_{q_{z}}$ (\AA) & $d_{\tau}$ (\AA) \\ |
| 861 |
> |
\midrule |
| 862 |
> |
Basal $\{0001\}$ & $34.1 \pm 0.9$ &$0.60 \pm 0.07$ & $5.9 \pm 0.3$ & $6.5 \pm 0.8$ & $3.2 \pm 0.4$ & $2.9$ \\ |
| 863 |
> |
Pyramidal $\{2~0~\bar{2}~1\}$ & $35 \pm 3$ & $0.7 \pm 0.1$ & $5.8 \pm 0.4$ & $6.1 \pm 0.5$ & $3.2 \pm 0.2$ & $2.7$ \\ |
| 864 |
> |
Prismatic $\{1~0~\bar{1}~0\}$ & $45 \pm 3$ & $0.75 \pm 0.09$ & $3.0 \pm 0.2$ & $3.0 \pm 0.1$ & $3.6 \pm 0.2$ & $3.5$ \\ |
| 865 |
> |
Secondary Prism $\{1~1~\bar{2}~0\}$ & $42 \pm 2$ & $0.69 \pm 0.03$ & $3.5 \pm 0.1$ & $3.3 \pm 0.2$ & $3.2 \pm 0.2$ & $3$ \\ |
| 866 |
> |
\bottomrule |
| 867 |
|
\end{tabular} |
| 868 |
|
\end{table} |
| 869 |
|
|
