| 11 |
|
|
| 12 |
|
%\usepackage{PNASTWOF} |
| 13 |
|
\usepackage[version=3]{mhchem} |
| 14 |
< |
%\usepackage[square, comma, sort&compress]{natbib} |
| 14 |
> |
\usepackage[round,numbers,sort&compress]{natbib} |
| 15 |
> |
\usepackage{fixltx2e} |
| 16 |
> |
\bibpunct{(}{)}{,}{n}{,}{,} |
| 17 |
> |
\bibliographystyle{pnas2011} |
| 18 |
|
|
| 19 |
|
%% OPTIONAL MACRO DEFINITIONS |
| 20 |
|
\def\s{\sigma} |
| 30 |
|
|
| 31 |
|
\begin{document} |
| 32 |
|
|
| 33 |
< |
\title{Friction at Water / Ice-I$_\mathrm{h}$ interfaces: Do the |
| 34 |
< |
Different Facets of Ice Have Different Hydrophilicities?} |
| 33 |
> |
\title{Friction at water / ice-I\textsubscript{h} interfaces: Do the |
| 34 |
> |
different facets of ice have different hydrophilicities?} |
| 35 |
|
|
| 36 |
|
\author{Patrick B. Louden\affil{1}{Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, |
| 37 |
|
IN 46556} |
| 48 |
|
\maketitle |
| 49 |
|
|
| 50 |
|
\begin{article} |
| 51 |
< |
\begin{abstract} |
| 52 |
< |
{In this follow up paper of the basal and prismatic facets of the |
| 53 |
< |
Ice-I$_\mathrm{h}$/water interface, we present the |
| 54 |
< |
pyramidal and secondary prismatic |
| 55 |
< |
interfaces for both the quiescent and sheared systems. The structural and |
| 56 |
< |
dynamic interfacial widths for all four crystal facets were found to be in good |
| 57 |
< |
agreement, and were found to be independent of the shear rate over the shear |
| 58 |
< |
rates investigated. |
| 59 |
< |
Decomposition of the molecular orientational time correlation function showed |
| 60 |
< |
different behavior for the short- and longer-time decay components approaching |
| 61 |
< |
normal to the interface. Lastly we show through calculation of the interfacial |
| 62 |
< |
friction coefficient and dynamic water contact angle measurement |
| 63 |
< |
that the basal and pyramidal facets are more |
| 64 |
< |
hydrophilic than the prismatic and secondary prismatic facets.} |
| 51 |
> |
\begin{abstract} |
| 52 |
> |
In this paper we present evidence that some of the crystal facets |
| 53 |
> |
of ice-I$_\mathrm{h}$ posess structural features that can halve |
| 54 |
> |
the effective hydrophilicity of the ice/water interface. The |
| 55 |
> |
spreading dynamics of liquid water droplets on ice facets exhibits |
| 56 |
> |
long-time behavior that differs substantially for the prismatic |
| 57 |
> |
$\{1~0~\bar{1}~0\}$ and secondary prism $\{1~1~\bar{2}~0\}$ facets |
| 58 |
> |
when compared with the basal $\{0001\}$ and pyramidal |
| 59 |
> |
$\{2~0~\bar{2}~1\}$ facets. We also present the results of |
| 60 |
> |
simulations of solid-liquid friction of the same four crystal |
| 61 |
> |
facets being drawn through liquid water. Both simulation |
| 62 |
> |
techniques provide evidence that the two prismatic faces have an |
| 63 |
> |
effective surface area in contact with the liquid water of |
| 64 |
> |
approximately half of the total surface area of the crystal. The |
| 65 |
> |
ice / water interfacial widths for all four crystal facets are |
| 66 |
> |
similar (using both structural and dynamic measures), and were |
| 67 |
> |
found to be independent of the shear rate. Additionally, |
| 68 |
> |
decomposition of orientational time correlation functions show |
| 69 |
> |
position-dependence for the short- and longer-time decay |
| 70 |
> |
components close to the interface. |
| 71 |
|
\end{abstract} |
| 72 |
|
|
| 73 |
|
\keywords{ice | water | interfaces | hydrophobicity} |
| 74 |
|
\abbreviations{QLL, quasi liquid layer; MD, molecular dynamics; RNEMD, |
| 75 |
|
reverse non-equilibrium molecular dynamics} |
| 76 |
|
|
| 77 |
< |
\dropcap{T}he quiescent ice-I$_\mathrm{h}$/water interface has been |
| 78 |
< |
extensively studied using computer simulations over the past 30 |
| 79 |
< |
years. Haymet \emph{et al.} characterized and measured the width of |
| 80 |
< |
these interfaces for the SPC,\cite{Karim90} SPC/E,\cite{Gay02,Bryk02}, |
| 81 |
< |
CF1,\cite{Hayward01,Hayward02} and TIP4P\cite{Karim88} water models in |
| 82 |
< |
neat water and with solvated |
| 83 |
< |
ions.\cite{Bryk04,Smith05,Wilson08,Wilson10} Nada and Furukawa have |
| 84 |
< |
studied the width of basal- and prismatic-water |
| 85 |
< |
interfaces\cite{Nada95} as well as crystal restructuring at |
| 86 |
< |
temperatures approaching the melting point.\cite{Nada00} |
| 77 |
> |
\dropcap{S}urfaces can be characterized as hydrophobic or hydrophilic |
| 78 |
> |
based on the strength of the interactions with water. Hydrophobic |
| 79 |
> |
surfaces do not have strong enough interactions with water to overcome |
| 80 |
> |
the internal attraction between molecules in the liquid phase, and the |
| 81 |
> |
degree of hydrophilicity of a surface can be described by the extent a |
| 82 |
> |
droplet can spread out over the surface. The contact angle formed |
| 83 |
> |
between the solid and the liquid depends on the free energies of the |
| 84 |
> |
three interfaces involved, and is given by Young's |
| 85 |
> |
equation.\cite{Young} |
| 86 |
> |
\begin{equation}\label{young} |
| 87 |
> |
\cos\theta = (\gamma_{sv} - \gamma_{sl})/\gamma_{lv} . |
| 88 |
> |
\end{equation} |
| 89 |
> |
Here $\gamma_{sv}$, $\gamma_{sl}$, and $\gamma_{lv}$ are the free |
| 90 |
> |
energies of the solid/vapor, solid/liquid, and liquid/vapor interfaces |
| 91 |
> |
respectively. Large contact angles, $\theta > 90^{\circ}$, correspond |
| 92 |
> |
to hydrophobic surfaces with low wettability, while small contact |
| 93 |
> |
angles, $\theta < 90^{\circ}$, correspond to hydrophilic surfaces. |
| 94 |
> |
Experimentally, measurements of the contact angle of sessile drops is |
| 95 |
> |
often used to quantify the extent of wetting on surfaces with |
| 96 |
> |
thermally selective wetting |
| 97 |
> |
characteristics.\cite{Tadanaga00,Liu04,Sun04} |
| 98 |
|
|
| 99 |
+ |
Nanometer-scale structural features of a solid surface can influence |
| 100 |
+ |
the hydrophilicity to a surprising degree. Small changes in the |
| 101 |
+ |
heights and widths of nano-pillars can change a surface from |
| 102 |
+ |
superhydrophobic, $\theta \ge 150^{\circ}$, to hydrophilic, $\theta |
| 103 |
+ |
\sim 0^{\circ}$.\cite{CBW} This is often referred to as the |
| 104 |
+ |
Cassie-Baxter to Wenzel transition. Nano-pillared surfaces with |
| 105 |
+ |
electrically tunable Cassie-Baxter and Wenzel states have also been |
| 106 |
+ |
observed.\cite{Herbertson06,Dhindsa06,Verplanck07,Ahuja08,Manukyan11} |
| 107 |
+ |
Luzar and coworkers have modeled these transitions on nano-patterned |
| 108 |
+ |
surfaces\cite{Daub07,Daub10,Daub11,Ritchie12}, and have found the |
| 109 |
+ |
change in contact angle is due to the field-induced perturbation of |
| 110 |
+ |
hydrogen bonding at the liquid/vapor interface.\cite{Daub07} |
| 111 |
+ |
|
| 112 |
+ |
One would expect the interfaces of ice to be highly hydrophilic (and |
| 113 |
+ |
possibly the most hydrophilic of all solid surfaces). In this paper we |
| 114 |
+ |
present evidence that some of the crystal facets of ice-I$_\mathrm{h}$ |
| 115 |
+ |
have structural features that can halve the effective hydrophilicity. |
| 116 |
+ |
Our evidence for this comes from molecular dynamics (MD) simulations |
| 117 |
+ |
of the spreading dynamics of liquid droplets on these facets, as well |
| 118 |
+ |
as reverse non-equilibrium molecular dynamics (RNEMD) simulations of |
| 119 |
+ |
solid-liquid friction. |
| 120 |
+ |
|
| 121 |
+ |
Quiescent ice-I$_\mathrm{h}$/water interfaces have been studied |
| 122 |
+ |
extensively using computer simulations. Haymet \textit{et al.} |
| 123 |
+ |
characterized and measured the width of these interfaces for the |
| 124 |
+ |
SPC~\cite{Karim90}, SPC/E~\cite{Gay02,Bryk02}, |
| 125 |
+ |
CF1~\cite{Hayward01,Hayward02} and TIP4P~\cite{Karim88} models, in |
| 126 |
+ |
both neat water and with solvated |
| 127 |
+ |
ions~\cite{Bryk04,Smith05,Wilson08,Wilson10}. Nada and Furukawa have |
| 128 |
+ |
studied the width of basal/water and prismatic/water |
| 129 |
+ |
interfaces~\cite{Nada95} as well as crystal restructuring at |
| 130 |
+ |
temperatures approaching the melting point~\cite{Nada00}. |
| 131 |
+ |
|
| 132 |
|
The surface of ice exhibits a premelting layer, often called a |
| 133 |
< |
quasi-liquid layer (QLL), at temperatures near the melting point. |
| 134 |
< |
Molecular dynamics simulations of the facets of ice-I$_\mathrm{h}$ |
| 135 |
< |
exposed to vacuum have found QLL widths of approximately 10 \AA\ at 3 |
| 136 |
< |
K below the melting point.\cite{Conde08} Similarly, Limmer and |
| 137 |
< |
Chandler have used the mW water model\cite{Molinero09} and statistical field |
| 138 |
< |
theory to estimate QLL widths at similar temperatures to be about 3 |
| 86 |
< |
nm.\cite{Limmer14} |
| 133 |
> |
quasi-liquid layer (QLL), at temperatures near the melting point. MD |
| 134 |
> |
simulations of the facets of ice-I$_\mathrm{h}$ exposed to vacuum have |
| 135 |
> |
found QLL widths of approximately 10 \AA\ at 3 K below the melting |
| 136 |
> |
point.\cite{Conde08} Similarly, Limmer and Chandler have used the mW |
| 137 |
> |
water model~\cite{Molinero09} and statistical field theory to estimate |
| 138 |
> |
QLL widths at similar temperatures to be about 3 nm.\cite{Limmer14} |
| 139 |
|
|
| 140 |
< |
Recently, Sazaki and Furukawa have developed a technique using |
| 141 |
< |
laser confocal micrscopy combined with differential interference |
| 142 |
< |
contrast microscopy |
| 143 |
< |
that has sufficient spatial and temporal resolution to visulaize and |
| 144 |
< |
quantitatively analyze QLLs on ice crystals at temperatures near |
| 145 |
< |
melting.\cite{Sazaki10} They have found the width of the QLLs |
| 146 |
< |
perpindicular to the surface at -2.2$^{o}$C to be 3-4 \AA\ wide. They |
| 147 |
< |
have also seen the formation of two immiscible QLLs, which displayed |
| 96 |
< |
different dynamics on the crystal surface.\cite{Sazaki12} |
| 140 |
> |
Recently, Sazaki and Furukawa have developed a technique using laser |
| 141 |
> |
confocal microscopy combined with differential interference contrast |
| 142 |
> |
microscopy that has sufficient spatial and temporal resolution to |
| 143 |
> |
visulaize and quantitatively analyze QLLs on ice crystals at |
| 144 |
> |
temperatures near melting.\cite{Sazaki10} They have found the width of |
| 145 |
> |
the QLLs perpindicular to the surface at -2.2$^{o}$C to be 3-4 \AA\ |
| 146 |
> |
wide. They have also seen the formation of two immiscible QLLs, which |
| 147 |
> |
displayed different dynamics on the crystal surface.\cite{Sazaki12} |
| 148 |
|
|
| 149 |
< |
There is significant interest in the properties of ice/ice and |
| 150 |
< |
ice/water interfaces in the geophysics community. Understanding the |
| 151 |
< |
dynamics of solid-solid shearing mediated by a liquid |
| 152 |
< |
layer\cite{Cuffey99, Bell08} will aid in understanding the macroscopic |
| 153 |
< |
motion of large ice masses.\cite{Casassa91, Sukhorukov13, Pritchard12, |
| 154 |
< |
Lishman13} |
| 149 |
> |
There is now significant interest in the \textit{tribological} |
| 150 |
> |
properties of ice/ice and ice/water interfaces in the geophysics |
| 151 |
> |
community. Understanding the dynamics of solid-solid shearing that is |
| 152 |
> |
mediated by a liquid layer\cite{Cuffey99, Bell08} will aid in |
| 153 |
> |
understanding the macroscopic motion of large ice |
| 154 |
> |
masses.\cite{Casassa91, Sukhorukov13, Pritchard12, Lishman13} |
| 155 |
|
|
| 156 |
|
Using molecular dynamics simulations, Samadashvili has recently shown |
| 157 |
|
that when two smooth ice slabs slide past one another, a stable |
| 158 |
< |
liquid-like layer develops between them.\cite{Samadashvili13} We have |
| 159 |
< |
previously used reverse non-equilibrium molecular dynamics (RNEMD) |
| 160 |
< |
simulations of ice-I$_\mathrm{h}$ / water interfaces to shear the |
| 161 |
< |
solid phase relative to the surrounding liquid.\cite{Louden13} The |
| 162 |
< |
computed solid-liquid kinetic friction coefficients displayed a factor |
| 163 |
< |
of two difference between the basal $\{0001\}$ and prismatic |
| 164 |
< |
$\{1~0~\bar{1}~0\}$ facets. The friction was found to be independent |
| 165 |
< |
of shear direction relative to the surface orientation. We attributed |
| 166 |
< |
facet-based difference in liquid-solid friction to the 6.5 \AA\ |
| 167 |
< |
corrugation of the prismatic face which reduces the effective surface |
| 117 |
< |
area of the ice that is in direct contact with liquid water. |
| 118 |
< |
|
| 119 |
< |
Surfaces can be charactarized as hydrophobic or hydrophilic based on |
| 120 |
< |
the strength of the interactions with water. Hydrophobic surfaces do |
| 121 |
< |
not have strong enough interactions with water to overcome the |
| 122 |
< |
internal attraction between molecules in the liquid phase. Water on |
| 123 |
< |
hydrophobic surfaces maintains a nearly-spherical droplet shape. |
| 124 |
< |
Conversely, hydrophilic surfaces have strong solid-liquid interactions |
| 125 |
< |
and exhibit droplets that spread over the surface. |
| 158 |
> |
liquid-like layer develops between them.\cite{Samadashvili13} In a |
| 159 |
> |
previous study, our RNEMD simulations of ice-I$_\mathrm{h}$ shearing |
| 160 |
> |
through liquid water have provided quantitative estimates of the |
| 161 |
> |
solid-liquid kinetic friction coefficients.\cite{Louden13} These |
| 162 |
> |
displayed a factor of two difference between the basal and prismatic |
| 163 |
> |
facets. The friction was found to be independent of shear direction |
| 164 |
> |
relative to the surface orientation. We attributed facet-based |
| 165 |
> |
difference in liquid-solid friction to the 6.5 \AA\ corrugation of the |
| 166 |
> |
prismatic face which reduces the effective surface area of the ice |
| 167 |
> |
that is in direct contact with liquid water. |
| 168 |
|
|
| 169 |
< |
The hydrophobicity or hydrophilicity of a surface can be described by |
| 170 |
< |
the extent a droplet can spread out over the surface. The contact |
| 171 |
< |
angle formed between the solid and the liquid, $\theta$, which relates |
| 172 |
< |
the free energies of the three interfaces involved, is given by |
| 173 |
< |
Young's equation. |
| 174 |
< |
\begin{equation}\label{young} |
| 133 |
< |
\cos\theta = (\gamma_{sv} - \gamma_{sl})/\gamma_{lv} |
| 134 |
< |
\end{equation} |
| 135 |
< |
Here $\gamma_{sv}$, $\gamma_{sl}$, and $\gamma_{lv}$ are the free energies |
| 136 |
< |
of the solid/vapor, solid/liquid, and liquid/vapor interfaces respectively. |
| 137 |
< |
Large contact angles ($\theta$ $\gg$ 90\textsuperscript{o}) correspond to low |
| 138 |
< |
wettability and hydrophobic surfaces, while small contact angles |
| 139 |
< |
($\theta$ $\ll$ 90\textsuperscript{o}) correspond to high wettability and |
| 140 |
< |
hydrophilic surfaces. Experimentally, measurements of the contact angle |
| 141 |
< |
of sessile drops has been used to quantify the extent of wetting on surfaces |
| 142 |
< |
with thermally selective wetting charactaristics\cite{Tadanaga00,Liu04,Sun04}, |
| 143 |
< |
as well as nano-pillared surfaces with electrically tunable Cassie-Baxter and |
| 144 |
< |
Wenzel states\cite{Herbertson06,Dhindsa06,Verplanck07,Ahuja08,Manukyan11}. |
| 145 |
< |
Luzar and coworkers have done significant work modeling these transitions on |
| 146 |
< |
nano-patterned surfaces\cite{Daub07,Daub10,Daub11,Ritchie12}, and have found |
| 147 |
< |
the change in contact angle to be due to the external field perturbing the |
| 148 |
< |
hydrogen bonding of the liquid/vapor interface\cite{Daub07}. |
| 169 |
> |
In the sections that follow, we outline the methodology used to |
| 170 |
> |
simulate droplet-spreading dynamics using standard MD and tribological |
| 171 |
> |
properties using RNEMD simulations. These simulation methods give |
| 172 |
> |
complementary results that point to the prismatic and secondary prism |
| 173 |
> |
facets having roughly half of their surface area in direct contact |
| 174 |
> |
with the liquid. |
| 175 |
|
|
| 150 |
– |
In this paper we present the same analysis for the pyramidal and secondary |
| 151 |
– |
prismatic facets, and show that the differential interfacial friction |
| 152 |
– |
coefficients for the four facets of ice-I$_\mathrm{h}$ are determined by their |
| 153 |
– |
relative hydrophilicity by means of dynamics water contact angle simulations. |
| 154 |
– |
|
| 176 |
|
\section{Methodology} |
| 177 |
+ |
\subsection{Construction of the Ice / Water Interfaces} |
| 178 |
+ |
To construct the four interfacial ice/water systems, a proton-ordered, |
| 179 |
+ |
zero-dipole crystal of ice-I$_\mathrm{h}$ with exposed strips of |
| 180 |
+ |
H-atoms and lone pairs was constructed using Structure 6 of Hirsch and |
| 181 |
+ |
Ojam\"{a}e's set of orthorhombic representations for |
| 182 |
+ |
ice-I$_{h}$.\cite{Hirsch04} This crystal structure was cleaved along |
| 183 |
+ |
the four different facets being studied. The exposed face was |
| 184 |
+ |
reoriented normal to the $z$-axis of the simulation cell, and the |
| 185 |
+ |
structures were and extended to form large exposed facets in |
| 186 |
+ |
rectangular box geometries. Liquid water boxes were created with |
| 187 |
+ |
identical dimensions (in $x$ and $y$) as the ice, and a $z$ dimension |
| 188 |
+ |
of three times that of the ice block, and a density corresponding to |
| 189 |
+ |
$\sim$ 1 g / cm$^3$. Each of the ice slabs and water boxes were |
| 190 |
+ |
independently equilibrated, and the resulting systems were merged by |
| 191 |
+ |
carving out any liquid water molecules within 3 \AA\ of any atoms in |
| 192 |
+ |
the ice slabs. Each of the combined ice/water systems were then |
| 193 |
+ |
equilibrated at 225K, which is the liquid-ice coexistence temperature |
| 194 |
+ |
for SPC/E water.\cite{} Ref. \citealp{Louden13} contains a more |
| 195 |
+ |
detailed explanation of the construction of ice/water interfaces. The |
| 196 |
+ |
resulting dimensions, number of ice, and liquid water molecules |
| 197 |
+ |
contained in each of these systems can be seen in Table |
| 198 |
+ |
\ref{tab:method}. |
| 199 |
|
|
| 200 |
< |
\subsection{Water Model} |
| 201 |
< |
Understanding ice/water interfaces inherently begins with the isolated |
| 202 |
< |
systems. There has been extensive work parameterizing models for liquid water, |
| 203 |
< |
such as the SPC\cite{Berendsen81}, SPC/E\cite{Berendsen87}, |
| 204 |
< |
TIP4P\cite{Jorgensen85}, TIP4P/2005\cite{Abascal05}, |
| 162 |
< |
($\dots$), and more recently, models for simulating |
| 163 |
< |
the solid phases of water, such as the TIP4P/Ice\cite{Abascal05b} model. The |
| 164 |
< |
melting point of various crystal structures of ice have been calculated for |
| 165 |
< |
many of these models |
| 166 |
< |
(SPC\cite{Karim90,Abascal07}, SPC/E\cite{Baez95,Arbuckle02,Gay02,Bryk02,Bryk04b,Sanz04b,Fernandez06,Abascal07,Vrbka07}, TIP4P\cite{Karim88,Gao00,Sanz04,Sanz04b,Koyama04,Wang05,Fernandez06,Abascal07}, TIP5P\cite{Sanz04,Koyama04,Wang05,Fernandez06,Abascal07}), |
| 167 |
< |
and the partial or complete phase diagram for the model has been determined |
| 168 |
< |
(SPC/E\cite{Baez95,Bryk04b,Sanz04b}, TIP4P\cite{Sanz04,Sanz04b,Koyama04}, TIP5P\cite{Sanz04,Koyama04}). |
| 200 |
> |
We used SPC/E Why? Extensively characterized over a wide range of |
| 201 |
> |
liquid conditions. Well-studied phase diagram. Reasonably accurate |
| 202 |
> |
crystalline free energies. Mostly avoids spurious crystalline |
| 203 |
> |
morphologies like ice-i and ice-B. Most importantly, the use of SPC/E |
| 204 |
> |
has been well characterized in previous ice/water interfacial studies. |
| 205 |
|
|
| 170 |
– |
Haymet et al. have studied the quiescent Ice-I$_\mathrm{h}$/water interface |
| 171 |
– |
using the rigid SPC, SPC/E, TIP4P, and the flexible CF1 water models, and has seen good |
| 172 |
– |
agreement for structural and dynamic measurements of the interfacial |
| 173 |
– |
width. Given the expansive size of our systems of interest, and the |
| 174 |
– |
apparent independence of water model on interfacial width, we have chosen to use the rigid SPC/E |
| 175 |
– |
water model in this study. |
| 206 |
|
|
| 207 |
< |
\subsection{Pyramidal and secondary prismatic ice/water interface construction} |
| 208 |
< |
To construct the pyramidal and secondary prismatic ice/water systems, |
| 209 |
< |
first a proton-ordered zero dipole crystal of ice-I$_\mathrm{h}$ with exposed strips |
| 210 |
< |
of H-atoms and lone pairs was constructed from Structure 6 of Hirsch |
| 211 |
< |
and Ojam\"{a}e's recent paper\cite{Hirsch04}. The crystal was then cut |
| 212 |
< |
along the plane of the desired facet, and reoriented so that the |
| 213 |
< |
$z$-axis was perpdicular to the exposed face. Two orthoganol cuts were |
| 214 |
< |
then made to the crystal such that perfect periodic replication could |
| 215 |
< |
be perfromed in the $x$ and $y$ dimensions. The slab was then |
| 216 |
< |
replicated along the $x$ and $y$ axes until the desired crystal size |
| 217 |
< |
was obtained. Liquid water boxes were created having identical |
| 218 |
< |
dimensions (in $x$ and$y$) as the ice blocks, and a $z$ dimension of |
| 219 |
< |
three times that of the ice block. Each of the ice slabs and water |
| 220 |
< |
boxes were independently equilibrated to 50K, and the resulting |
| 221 |
< |
systems were merged by carving out any liquid water molecules within 3 |
| 222 |
< |
\AA\ of any atoms in the ice slabs. Each of the combined ice/water |
| 223 |
< |
systems were then equilibrated to 225K, which was found to be a stable |
| 224 |
< |
temperature for each of the interfaces over a 5 ns simulation. |
| 225 |
< |
For a more detailed explanation of |
| 226 |
< |
the ice/water systems construction, please refer to a previous |
| 227 |
< |
paper\cite{Louden13}. The resulting dimensions, number of ice, and liquid water molecules |
| 228 |
< |
contained in each of these systems can be seen in Table \ref{tab:method}. |
| 229 |
< |
\subsection{Shearing simulations} |
| 207 |
> |
|
| 208 |
> |
There has been extensive work parameterizing good models for liquid |
| 209 |
> |
water over a wide range of conditions. The melting points of various |
| 210 |
> |
crystal structures of ice have been calculated for many of these |
| 211 |
> |
models (SPC\cite{Karim90,Abascal07}, |
| 212 |
> |
SPC/E\cite{Baez95,Arbuckle02,Gay02,Bryk02,Bryk04b,Sanz04b,Fernandez06,Abascal07,Vrbka07}, |
| 213 |
> |
TIP4P\cite{Karim88,Gao00,Sanz04,Sanz04b,Koyama04,Wang05,Fernandez06,Abascal07}, |
| 214 |
> |
TIP5P\cite{Sanz04,Koyama04,Wang05,Fernandez06,Abascal07}), and the |
| 215 |
> |
partial or complete phase diagram for the model has been determined |
| 216 |
> |
(SPC/E\cite{Baez95,Bryk04b,Sanz04b}, |
| 217 |
> |
TIP4P\cite{Sanz04,Sanz04b,Koyama04}, TIP5P\cite{Sanz04,Koyama04}). |
| 218 |
> |
|
| 219 |
> |
|
| 220 |
> |
such as the SPC\cite{Berendsen81}, SPC/E\cite{Berendsen87}, |
| 221 |
> |
TIP4P\cite{Jorgensen85}, TIP4P/2005\cite{Abascal05}, ($\dots$), and |
| 222 |
> |
more recently, models for simulating the solid phases of water, such |
| 223 |
> |
as the TIP4P/Ice\cite{Abascal05b} model. |
| 224 |
> |
|
| 225 |
> |
Haymet et al. have studied the quiescent Ice-I$_\mathrm{h}$/water |
| 226 |
> |
interface using the rigid SPC, SPC/E, TIP4P, and the flexible CF1 |
| 227 |
> |
water models, and has seen good agreement for structural and dynamic |
| 228 |
> |
measurements of the interfacial width. Given the expansive size of our |
| 229 |
> |
systems of interest, and the apparent independence of water model on |
| 230 |
> |
interfacial width, we have chosen to use the rigid SPC/E water model |
| 231 |
> |
in this study. |
| 232 |
> |
|
| 233 |
> |
\subsection{Shearing simulations (interfaces in bulk water)} |
| 234 |
|
% Should we mention number of runs, sim times, etc. ? |
| 235 |
< |
To perform the shearing simulations, the velocity shearing and scaling |
| 235 |
> |
To perform the shearing simulations, the velocity shearing and scaling |
| 236 |
|
varient of reverse nonequilibrium molecular dynamics (VSS-RNEMD) was |
| 237 |
|
conducted. This method performs a series of simultaneous velocity |
| 238 |
|
exchanges between two regions of the simulation cell, to |
| 252 |
|
secondary prismatic simulations were performed under the NVE ensamble. |
| 253 |
|
|
| 254 |
|
\subsection{Droplet simulations} |
| 255 |
< |
To construct ice surfaces to perform water contact angle calculations |
| 256 |
< |
on, ice crystals were created as described earlier (see Pyramidal and |
| 257 |
< |
secondary prismatic ice/water interface construction). The crystals |
| 258 |
< |
were then cut from the negative $z$ dimension, ensuring the remaining |
| 259 |
< |
ice crystal was thicker in $z$ than the potential cutoff. The crystals |
| 260 |
< |
were then replicated in $x$ and $y$ until a sufficiently large surface |
| 261 |
< |
had been created. The sizes and number of molecules in each of the surfaces is given in Table |
| 262 |
< |
\ref{tab:ice_sheets}. Molecular restraints were applied to the center of mass |
| 263 |
< |
of the rigid bodies to prevent surface melting, however the molecules were |
| 264 |
< |
allowed to reorient themselves freely. The water doplet contained 2048 |
| 265 |
< |
SPC/E molecules, which has been found to produce |
| 266 |
< |
agreement for the Young contact angle extrapolated to an infinite drop |
| 267 |
< |
size\cite{Daub10}. The surfaces and droplet were independently |
| 268 |
< |
equilibrated to 225 K, at which time the droplet was placed 3-5 \AA\ |
| 269 |
< |
above the positive $z$ dimension of the surface at 5 unique |
| 270 |
< |
locations. Each simulation was 5 ns in length and conducted in the NVE ensemble. |
| 271 |
< |
|
| 255 |
> |
Ice interfaces with a thickness of $\sim 30 \AA$ were created as |
| 256 |
> |
described above, but were not solvated in a liquid box. The crystals |
| 257 |
> |
were then replicated along the $x$ and $y$ axes (parallel to the |
| 258 |
> |
surface) until a large surface had been created. The sizes and |
| 259 |
> |
numbers of molecules in each of the surfaces is given in Table |
| 260 |
> |
\ref{tab:ice_sheets}. Weak translational restraining potentials with |
| 261 |
> |
spring constants of XXXX were applied to the center of mass of each |
| 262 |
> |
molecule in order to prevent surface melting, although the molecules |
| 263 |
> |
were allowed to reorient freely. A water doplet containing 2048 SPC/E |
| 264 |
> |
molecules was created separately. Droplets of this size can produce |
| 265 |
> |
agreement with the Young contact angle extrapolated to an infinite |
| 266 |
> |
drop size\cite{Daub10}. The surfaces and droplet were independently |
| 267 |
> |
equilibrated to 225 K, at which time the droplet was placed 3-5 \AA\ |
| 268 |
> |
above the surface. Five statistically independent simulations were |
| 269 |
> |
carried out for each facet, and the droplet was placed at unique $x$ |
| 270 |
> |
and $y$ locations for each of these simulations. Each simulation was |
| 271 |
> |
5 ns in length and conducted in the microcanonical (NVE) ensemble. |
| 272 |
|
|
| 273 |
|
\section{Results and discussion} |
| 274 |
|
\subsection{Interfacial width} |
| 597 |
|
provided by the Center for Research Computing (CRC) at the |
| 598 |
|
University of Notre Dame. |
| 599 |
|
\end{acknowledgments} |
| 566 |
– |
|
| 567 |
– |
\newpage |
| 600 |
|
|
| 569 |
– |
\bibliographystyle{pnas2011} |
| 601 |
|
\bibliography{iceWater} |
| 602 |
|
% ***************************************** |
| 603 |
|
% There is significant interest in the properties of ice/ice and ice/water |
