trunk/iceWater2/iceWater2.tex

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\begin{document}

\title{Simulations of solid-liquid friction at Secondary Prism and Pyramidal ice-I$_\mathrm{h}$ / water interfaces}

\author{Patrick B. Louden and J. Daniel
Gezelter\footnote{Corresponding author. \ Electronic mail:
  gezelter@nd.edu} \\
Department of Chemistry and Biochemistry,\\
University of Notre Dame\\
Notre Dame, Indiana 46556}

\date{\today}
\maketitle
\begin{doublespace}

\begin{abstract}
Abstract abstract abstract...
\end{abstract}

\newpage

\section{Introduction}
Explain a little bit about ice Ih, point group stuff. 

Mention previous work done / on going work by other people. Haymet and Rick
seem to be investigating how the interfaces is perturbed by the presence of 
ions. This is the conlcusion of a recent publication of the basal and 
prismatic facets of ice Ih, now presenting the pyramidal and secondary 
prism facets under shear.

\section{Methodology}

\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}. Lower panel: the local tetrahedral order
parameter, $q(z)$, (black circles) and the hyperbolic tangent fit (red line).
Middle panel: the imposed thermal gradient required to maintain a fixed
interfacial temperature. 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]{Pyr_comic_strip}
\caption{\label{fig:pyrComic} The pyramidal interface with a shear rate of 3.8 \
ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:spComic}.}
\end{figure}

\subsection{Pyramidal and secondary prism system construction}

The construction of the pyramidal and secondary prism systems follows that of 
the basal and prismatic systems presented elsewhere\cite{Louden13}, however
the ice crystals and water boxes were equilibrated and combined at 50K and
then equilibrated to 225K. The resulting pyramidal system was 
$37.47 \times 29.50 \times 93.02$ \AA\ with 1216
SPC/E molecules in the ice slab, and 2203 in the liquid phase. The secondary 
prism system generated was $71.87 \times 31.66 \times 161.55$ \AA\ with 3840 
SPC/E molecules in the ice slab and 8176 molecules in the liquid phase.

\subsection{Computational details}
% Do we need to justify the sims at 225K? 
% No crystal growth or shrinkage over 2 successive 1 ns NVT simulations for
%    either the pyramidal or sec. prism ice/water systems.

The computational details performed here were equivalent to those reported
in the previous publication\cite{Louden13}. The only changes made to the 
previously reported procedure were the following. VSS-RNEMD moves were 
attempted every 2 fs instead of every 50 fs. Due to the more frequent
perturbation of the system, a smaller imposed kinetic energy and momentum
flux was able to be used to obtain the thermal and velocity gradients
of interest. The resulting perturbations to the system were gentler 
over the less frequent previously used VSS-RNEMD attempt interval.

All pyramidal simulations were performed under the NVT ensamble except those
during which statistics were accumulated for the orientational correlation
function, which were performed under the NVE ensamble. All secondary prism 
simulations were performed under the NVE ensamble. 

\section{Results and discussion}

\subsection{Structural interfacial width}
From fitting the tetrahedrality profiles for each of the 0.5 nanosecond 
simulations (panel c of \ref{spComic} and \ref{pyrComic}) 
by Eq. 6\cite{Louden13},we find the interfacial width for the pyramidal and 
secondary prism to be $3.2 \pm 0.2$ and $3.2 \pm 0.2$ \AA\ , respectively, 
with no applied momentum flux. Over the range of shear rates investigated, 
$0.6 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 5.6 \pm 0.4 \mathrm{ms}^{-1}$ for 
the pyramidal system and $0.9 \pm 0.3 \mathrm{ms}^{-1} \rightarrow 5.4 \pm 0.1
\mathrm{ms}^{-1}$ for the secondary prism, we found no significant change in
the interfacial width. This follows our previous findings of the basal and
prismatic systems, in which the interfacial width was invarient of the
shear rate of the ice. The interfacial width of the quiescent basal and 
prismatic systems was found to be $3.2 \pm 0.4$ \AA\ and $3.6 \pm 0.2$ \AA\ 
respectively. Over the range of shear rates investigated, $0.6 \pm 0.3 
\mathrm{ms}^{-1} \rightarrow 5.3 \pm 0.5 \mathrm{ms}^{-1}$ for the basal 
system and $0.9 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 4.5 \pm 0.1 
\mathrm{ms}^{-1}$ for the prismatic, we found no significant change in the 
interfacial width.
 
\subsection{Orientational dynamics}


The coefficient of friction for the pyramidal and secondary prism interfaces were found to be independent of shear direction (x or y). 

\begin{figure}
\includegraphics[width=\linewidth]{Pyr-orient}
\caption{\label{fig:PyrOrient} The three decay constants of the 
orientational time correlation function, $C_2(t)$, 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 (black circles) and sheared (red squares) 
experiments were fit by a shifted exponential decay (Eq. 9\cite{Louden13})
shown by the black and red lines respectively. The upper two panels show that 
translational and hydrogen bond making and breaking events slow down 
through the interface while approaching the ice slab. The bottom most panel
shows the librational motion of the water molecules speeding up approaching
the ice block due to the confined region of space allowed for the molecules
 to move in.}
\end{figure}  

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


\section{Conclusion}
Conclude conclude conclude...

\section{Acknowledgements}
Support for this progect was provided by the National Science Foundation under grant CHE-0848243. Computational time was provided by the Center for Research Computing (CRC) at the University of Notre Dame.


\newpage
\bibliography{iceWater}

\end{doublespace}

\end{document}
Revision:	4192
Committed:	Wed Jun 25 16:52:33 2014 UTC (11 years, 1 month ago) by plouden
Content type:	application/x-tex
File size:	8449 byte(s)
Log Message:	adding the images, .tex, and .bib files
#	User	Rev	Content
1	plouden	4192	\documentclass[11pt]{article}
2			\usepackage{amsmath}
3			\usepackage{amssymb}
4			\usepackage{setspace}
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6			\usepackage{caption}
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13			%\usepackage{bibentry}
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15			%\usepackage[ref]{overcite}
16			\usepackage[square, comma, sort&compress]{natbib}
17			\usepackage{url}
18			\pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
19			\evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
20			9.0in \textwidth 6.5in \brokenpenalty=10000
21
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32			% \documentclass[journal = jpccck, manuscript = article]{achemso}
33			% \setkeys{acs}{usetitle = true}
34			% \usepackage{achemso}
35			% \usepackage{natbib}
36			% \usepackage{multirow}
37			% \usepackage{wrapfig}
38			% \usepackage{fixltx2e}
39
40			\usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions
41			\usepackage{url}
42
43
44			\begin{document}
45
46			\title{Simulations of solid-liquid friction at Secondary Prism and Pyramidal ice-I$_\mathrm{h}$ / water interfaces}
47
48			\author{Patrick B. Louden and J. Daniel
49			Gezelter\footnote{Corresponding author. \ Electronic mail:
50			gezelter@nd.edu} \\
51			Department of Chemistry and Biochemistry,\\
52			University of Notre Dame\\
53			Notre Dame, Indiana 46556}
54
55			\date{\today}
56			\maketitle
57			\begin{doublespace}
58
59			\begin{abstract}
60			Abstract abstract abstract...
61			\end{abstract}
62
63			\newpage
64
65			\section{Introduction}
66			Explain a little bit about ice Ih, point group stuff.
67
68			Mention previous work done / on going work by other people. Haymet and Rick
69			seem to be investigating how the interfaces is perturbed by the presence of
70			ions. This is the conlcusion of a recent publication of the basal and
71			prismatic facets of ice Ih, now presenting the pyramidal and secondary
72			prism facets under shear.
73
74			\section{Methodology}
75
76			\begin{figure}
77			\includegraphics[width=\linewidth]{SP_comic_strip}
78			\caption{\label{fig:spComic} The secondary prism interface with a shear
79			rate of 3.5 ms\textsuperscript{-1}. Lower panel: the local tetrahedral order
80			parameter, $q(z)$, (black circles) and the hyperbolic tangent fit (red line).
81			Middle panel: the imposed thermal gradient required to maintain a fixed
82			interfacial temperature. Upper panel: the transverse velocity gradient that
83			develops in response to an imposed momentum flux. The vertical dotted lines
84			indicate the locations of the midpoints of the two interfaces.}
85			\end{figure}
86
87			\begin{figure}
88			\includegraphics[width=\linewidth]{Pyr_comic_strip}
89			\caption{\label{fig:pyrComic} The pyramidal interface with a shear rate of 3.8 \
90			ms\textsuperscript{-1}. Panel descriptions match those in figure \ref{fig:spComic}.}
91			\end{figure}
92
93			\subsection{Pyramidal and secondary prism system construction}
94
95			The construction of the pyramidal and secondary prism systems follows that of
96			the basal and prismatic systems presented elsewhere\cite{Louden13}, however
97			the ice crystals and water boxes were equilibrated and combined at 50K and
98			then equilibrated to 225K. The resulting pyramidal system was
99			$37.47 \times 29.50 \times 93.02$ \AA\ with 1216
100			SPC/E molecules in the ice slab, and 2203 in the liquid phase. The secondary
101			prism system generated was $71.87 \times 31.66 \times 161.55$ \AA\ with 3840
102			SPC/E molecules in the ice slab and 8176 molecules in the liquid phase.
103
104			\subsection{Computational details}
105			% Do we need to justify the sims at 225K?
106			% No crystal growth or shrinkage over 2 successive 1 ns NVT simulations for
107			% either the pyramidal or sec. prism ice/water systems.
108
109			The computational details performed here were equivalent to those reported
110			in the previous publication\cite{Louden13}. The only changes made to the
111			previously reported procedure were the following. VSS-RNEMD moves were
112			attempted every 2 fs instead of every 50 fs. Due to the more frequent
113			perturbation of the system, a smaller imposed kinetic energy and momentum
114			flux was able to be used to obtain the thermal and velocity gradients
115			of interest. The resulting perturbations to the system were gentler
116			over the less frequent previously used VSS-RNEMD attempt interval.
117
118			All pyramidal simulations were performed under the NVT ensamble except those
119			during which statistics were accumulated for the orientational correlation
120			function, which were performed under the NVE ensamble. All secondary prism
121			simulations were performed under the NVE ensamble.
122
123			\section{Results and discussion}
124
125			\subsection{Structural interfacial width}
126			From fitting the tetrahedrality profiles for each of the 0.5 nanosecond
127			simulations (panel c of \ref{spComic} and \ref{pyrComic})
128			by Eq. 6\cite{Louden13},we find the interfacial width for the pyramidal and
129			secondary prism to be $3.2 \pm 0.2$ and $3.2 \pm 0.2$ \AA\ , respectively,
130			with no applied momentum flux. Over the range of shear rates investigated,
131			$0.6 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 5.6 \pm 0.4 \mathrm{ms}^{-1}$ for
132			the pyramidal system and $0.9 \pm 0.3 \mathrm{ms}^{-1} \rightarrow 5.4 \pm 0.1
133			\mathrm{ms}^{-1}$ for the secondary prism, we found no significant change in
134			the interfacial width. This follows our previous findings of the basal and
135			prismatic systems, in which the interfacial width was invarient of the
136			shear rate of the ice. The interfacial width of the quiescent basal and
137			prismatic systems was found to be $3.2 \pm 0.4$ \AA\ and $3.6 \pm 0.2$ \AA\
138			respectively. Over the range of shear rates investigated, $0.6 \pm 0.3
139			\mathrm{ms}^{-1} \rightarrow 5.3 \pm 0.5 \mathrm{ms}^{-1}$ for the basal
140			system and $0.9 \pm 0.2 \mathrm{ms}^{-1} \rightarrow 4.5 \pm 0.1
141			\mathrm{ms}^{-1}$ for the prismatic, we found no significant change in the
142			interfacial width.
143
144			\subsection{Orientational dynamics}
145
146
147			The coefficient of friction for the pyramidal and secondary prism interfaces were found to be independent of shear direction (x or y).
148
149			\begin{figure}
150			\includegraphics[width=\linewidth]{Pyr-orient}
151			\caption{\label{fig:PyrOrient} The three decay constants of the
152			orientational time correlation function, $C_2(t)$, for water as a function
153			of distance from the center of the ice slab. The vertical dashed line
154			indicates the edge of the pyramidal ice slab determined by the local order
155			tetrahedral parameter. The control (black circles) and sheared (red squares)
156			experiments were fit by a shifted exponential decay (Eq. 9\cite{Louden13})
157			shown by the black and red lines respectively. The upper two panels show that
158			translational and hydrogen bond making and breaking events slow down
159			through the interface while approaching the ice slab. The bottom most panel
160			shows the librational motion of the water molecules speeding up approaching
161			the ice block due to the confined region of space allowed for the molecules
162			to move in.}
163			\end{figure}
164
165			\begin{figure}
166			\includegraphics[width=\linewidth]{SP-orient-less}
167			\caption{\label{fig:SPorient} Decay constants for $C_2(t)$ at the secondary
168			prism face. Panel descriptions match those in \ref{fig:PyrOrient}.}
169			\end{figure}
170
171
172
173			\section{Conclusion}
174			Conclude conclude conclude...
175
176			\section{Acknowledgements}
177			Support for this progect was provided by the National Science Foundation under grant CHE-0848243. Computational time was provided by the Center for Research Computing (CRC) at the University of Notre Dame.
178
179
180			\newpage
181			\bibliography{iceWater}
182
183			\end{doublespace}
184
185			\end{document}