| 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 |
| 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 |
| 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 |
| 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 |
| 75 |
> |
the structures were 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 |
| 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{Further details on the shearing (RNEMD) simulations} |
| 91 |
+ |
All simulations were performed using OpenMD~\cite{OOPSE,openmd}, with a |
| 92 |
+ |
time step of 2 fs and periodic boundary conditions in all three |
| 93 |
+ |
dimensions. Electrostatics were handled using the damped-shifted |
| 94 |
+ |
force real-space electrostatic kernel~\cite{Ewald}. The systems were |
| 95 |
+ |
divided into 100 bins along the $z$-axis for the VSS-RNEMD moves, |
| 96 |
+ |
which were attempted every 2~fs. |
| 97 |
+ |
|
| 98 |
+ |
The interfaces were equilibrated for a total of 10 ns at equilibrium |
| 99 |
+ |
conditions before being exposed to either a shear or thermal gradient. |
| 100 |
+ |
This consisted of 5 ns under a constant temperature (NVT) integrator |
| 101 |
+ |
set to 225~K followed by 5 ns under a microcanonical (NVE) integrator. |
| 102 |
+ |
Weak thermal gradients were allowed to develop using the VSS-RNEMD |
| 103 |
+ |
(NVE) integrator using a small thermal flux ($-2.0\times 10^{-6}$ |
| 104 |
+ |
kcal/mol/\AA$^2$/fs) for a duration of 5 ns to allow the gradient to |
| 105 |
+ |
stabilize. The resulting temperature gradient was $\approx$ 10K over |
| 106 |
+ |
the entire box length, which was sufficient to keep the temperature at |
| 107 |
+ |
the interface within $\pm 1$ K of the 225~K target. |
| 108 |
+ |
|
| 109 |
+ |
Velocity gradients were then imposed using the VSS-RNEMD (NVE) |
| 110 |
+ |
integrator with a range of momentum fluxes. These gradients were |
| 111 |
+ |
allowed to stabilize for 1~ns before data collection started. Once |
| 112 |
+ |
established, four successive 0.5~ns runs were performed for each shear |
| 113 |
+ |
rate. During these simulations, configurations of the system were |
| 114 |
+ |
stored every 1~ps, and statistics on the structure and dynamics in |
| 115 |
+ |
each bin were accumulated throughout the simulations. Although there |
| 116 |
+ |
was some small variation in the measured interfacial width between |
| 117 |
+ |
succcessive runs, no indication of bulk melting or crystallization was |
| 118 |
+ |
observed. That is, no large scale changes in the positions of the top |
| 119 |
+ |
and bottom interfaces occurred during the simulations. |
| 120 |
+ |
|
| 121 |
|
\section{A second method for computing contact angles} |
| 122 |
|
In addition to the spherical cap method outlined in the main text, a |
| 123 |
|
second method for obtaining the contact angle was described by |
| 140 |
|
z_\mathrm{surface}}{r_\mathrm{droplet}} \right). |
| 141 |
|
\end{equation} |
| 142 |
|
|
| 143 |
< |
\section{Determining interfacial widths using structural information} |
| 143 |
> |
\section{Interfacial widths using structural information} |
| 144 |
|
To determine the structural widths of the interfaces under shear, each |
| 145 |
|
of the systems was divided into 100 bins along the $z$-dimension, and |
| 146 |
|
the local tetrahedral order parameter (Eq. 5 in Reference |
| 162 |
|
midpoints of the interfaces as determined by the tetrahedrality |
| 163 |
|
profiles. |
| 164 |
|
|
| 165 |
< |
\section{Determining interfacial widths using dynamic information} |
| 165 |
> |
\section{Interfacial widths using dynamic information} |
| 166 |
|
To determine the dynamic widths of the interfaces under shear, each of |
| 167 |
|
the systems was divided into bins along the $z$-dimension ($\approx$ 3 |
| 168 |
|
\AA\ wide) and $C_2(z,t)$ was computed using only those molecules that |
| 169 |
< |
were in the bin at the initial time. The time-dependence was fit to a |
| 170 |
< |
triexponential decay, with three time constants: $\tau_{short}$, |
| 171 |
< |
measuring the librational motion of the water molecules, |
| 172 |
< |
$\tau_{middle}$, measuring the timescale for breaking and making of |
| 173 |
< |
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. |
| 169 |
> |
were in the bin at the initial time. To compute these correlation |
| 170 |
> |
functions, each of the 0.5 ns simulations was followed by a shorter |
| 171 |
> |
200 ps microcanonical (NVE) simulation in which the positions and |
| 172 |
> |
orientations of every molecule in the system were recorded every 0.1 |
| 173 |
> |
ps. |
| 174 |
|
|
| 175 |
< |
In Figures S6-S9 in the supporting information, the $z$-coordinate |
| 176 |
< |
profiles for the three decay constants, $\tau_{short}$, |
| 177 |
< |
$\tau_{middle}$, and $\tau_{long}$ for the different interfaces are |
| 178 |
< |
shown. (Figures S6 \& S7 are new results, and Figures S8 \& S9 are |
| 179 |
< |
updated plots from Ref \citealp{Louden13}.) In the liquid regions of |
| 180 |
< |
all four interfaces, we observe $\tau_{middle}$ and $\tau_{long}$ to |
| 181 |
< |
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. |
| 175 |
> |
The time-dependence was fit to a triexponential decay, with three time |
| 176 |
> |
constants: $\tau_{short}$, measuring the librational motion of the |
| 177 |
> |
water molecules, $\tau_{middle}$, measuring the timescale for breaking |
| 178 |
> |
and making of hydrogen bonds, and $\tau_{long}$, corresponding to the |
| 179 |
> |
translational motion of the water molecules. An additional constant |
| 180 |
> |
was introduced in the fits to describe molecules in the crystal which |
| 181 |
> |
do not experience long-time orientational decay. |
| 182 |
|
|
| 183 |
+ |
In Figures S6-S9, the $z$-coordinate profiles for the three decay |
| 184 |
+ |
constants, $\tau_{short}$, $\tau_{middle}$, and $\tau_{long}$ for the |
| 185 |
+ |
different interfaces are shown. (Figures S6 \& S7 are new results, |
| 186 |
+ |
and Figures S8 \& S9 are updated plots from Ref \citealp{Louden13}.) |
| 187 |
+ |
In the liquid regions of all four interfaces, we observe |
| 188 |
+ |
$\tau_{middle}$ and $\tau_{long}$ to have approximately consistent |
| 189 |
+ |
values of $3-6$ ps and $30-40$ ps, respectively. Both of these times |
| 190 |
+ |
increase in value approaching the interface. Approaching the |
| 191 |
+ |
interface, we also observe that $\tau_{short}$ decreases from its |
| 192 |
+ |
liquid-state value of $72-76$ fs. The approximate values for the |
| 193 |
+ |
decay constants and the trends approaching the interface match those |
| 194 |
+ |
reported previously for the basal and prismatic interfaces. |
| 195 |
+ |
|
| 196 |
|
We have estimated the dynamic interfacial width $d_\mathrm{dyn}$ by |
| 197 |
|
fitting the profiles of all the three orientational time constants |
| 198 |
|
with an exponential decay to the bulk-liquid behavior, |
| 202 |
|
where $\tau_{liquid}$ and $\tau_{wall}$ are the liquid and projected |
| 203 |
|
wall values of the decay constants, $z_{wall}$ is the location of the |
| 204 |
|
interface, as measured by the structural order parameter. These |
| 205 |
< |
values are shown in table \ref{tab:kappa}. Because the bins must be |
| 205 |
> |
values are shown in table 1 in the main text. Because the bins must be |
| 206 |
|
quite wide to obtain reasonable profiles of $C_2(z,t)$, the error |
| 207 |
|
estimates for the dynamic widths of the interface are significantly |
| 208 |
|
larger than for the structural widths. However, all four interfaces |
| 209 |
|
exhibit dynamic widths that are significantly below 1~nm, and are in |
| 210 |
|
reasonable agreement with the structural width above. |
| 211 |
|
|
| 212 |
+ |
\bibliography{iceWater} |
| 213 |
|
\end{article} |
| 214 |
|
|
| 215 |
|
\begin{table}[h] |
| 307 |
|
prismatic face. Panel descriptions match those in \ref{fig:PyrOrient}.} |
| 308 |
|
\end{figure} |
| 309 |
|
|
| 274 |
– |
\bibliography{iceWater} |
| 310 |
|
|
| 311 |
|
\end{document} |
